pax_global_header00006660000000000000000000000064126412540110014506gustar00rootroot0000000000000052 comment=8b73c223b43cad07de459233b4c7c7ca8b39e643 arb-2.8.1/000077500000000000000000000000001264125401100122625ustar00rootroot00000000000000arb-2.8.1/Makefile.in000066400000000000000000000244041264125401100143330ustar00rootroot00000000000000ifdef $(DLPATH) $(DLPATH):=$($(DLPATH)):$(DLPATH_ADD) else $(DLPATH):=$(DLPATH_ADD) endif LIBDIR=lib QUIET_CC = @echo ' ' CC ' ' $@; QUIET_CXX = @echo ' ' CXX ' ' $@; QUIET_AR = @echo ' ' AR ' ' $@; AT=@ BUILD_DIRS = fmpr arf mag arb arb_mat arb_poly arb_calc acb acb_mat acb_poly \ acb_calc acb_hypgeom acb_modular fmprb bernoulli hypgeom fmpz_extras partitions \ $(EXTRA_BUILD_DIRS) TEMPLATE_DIRS = export SOURCES = LIB_SOURCES = $(wildcard $(patsubst %, %/*.c, $(BUILD_DIRS))) $(patsubst %, %/*.c, $(TEMPLATE_DIRS)) HEADERS = $(patsubst %, %.h, $(BUILD_DIRS)) OBJS = $(patsubst %.c, build/%.o, $(SOURCES)) LIB_OBJS = $(patsubst %, build/%/*.o, $(BUILD_DIRS)) LOBJS = $(patsubst %.c, build/%.lo, $(SOURCES)) LIB_LOBJS = $(patsubst %, build/%/*.lo, $(BUILD_DIRS)) MOD_LOBJS = $(patsubst %, build/%.lo, $(BUILD_DIRS)) EXMP_SOURCES = $(wildcard examples/*.c) EXMPS = $(patsubst %.c, %, $(EXMP_SOURCES)) TEST_SOURCES = $(wildcard test/*.c) TESTS = $(patsubst %.c, build/%$(EXEEXT), $(TEST_SOURCES)) PROF_SOURCES = $(wildcard profile/*.c) PROFS = $(patsubst %.c, %$(EXEEXT), $(PROF_SOURCES)) TUNE_SOURCES = $(wildcard tune/*.c) TUNE = $(patsubst %.c, %$(EXEEXT), $(TUNE_SOURCES)) EXT_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/*.c))) EXT_TEST_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/test/t-*.c))) EXT_TUNE_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/tune/*.c))) EXT_PROF_SOURCES = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), $(wildcard $(ext)/$(dir)/profile/p-*.c))) EXT_OBJS = $(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), build/$(dir).lo)) EXT_HEADERS = $(foreach ext, $(EXTENSIONS), $(wildcard $(ext)/*.h)) all: library quiet: library verbose: $(MAKE) AT= QUIET_CC= QUIET_CXX= QUIET_AR= clean: $(AT)$(foreach dir, $(BUILD_DIRS), BUILD_DIR=../build/$(dir); 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BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) profile || exit $$?;)) else $(AT)$(foreach dir, $(MOD), mkdir -p build/$(dir)/profile; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) profile || exit $$?;) endif tune: library $(TUNE_SOURCES) $(EXT_TUNE_SOURCES) mkdir -p build/tune $(AT)$(foreach prog, $(TUNE), $(CC) $(CFLAGS) $(INCS) $(prog).c -o build/$(prog) $(LIBS) || exit $$?;) $(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/tune; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) tune || exit $$?;) $(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/tune; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) tune || exit $$?;)) examples: library $(EXMP_SOURCES) mkdir -p build/examples $(AT)$(foreach prog, $(EXMPS), $(CC) $(CFLAGS) $(INCS) $(prog).c -o build/$(prog) $(LIBS) || exit $$?;) $(ARB_LIB): $(LOBJS) $(LIB_SOURCES) $(EXT_SOURCES) $(HEADERS) $(EXT_HEADERS) | build build/interfaces $(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir); 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then \ $(MAKE) shared; \ fi $(AT)if [ "$(ARB_STATIC)" -eq "1" ]; then \ $(MAKE) static; \ fi shared: $(ARB_LIB) static: libarb.a tests: library $(TESTS) $(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) tests || exit $$?;) $(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) tests || exit $$?;)) mkdir -p build/interfaces/test $(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \ $(MAKE) build/interfaces/test/t-NTL-interface; \ fi check: library ifndef MOD $(AT)$(MAKE) $(TESTS) $(AT)$(foreach prog, $(TESTS), $(prog) || exit $$?;) $(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) check || exit $$?;)) $(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) check || exit $$?;) mkdir -p build/interfaces/test $(AT)if [ "$(WANT_NTL)" -eq "1" ]; then \ $(MAKE) build/interfaces/test/t-NTL-interface; \ build/interfaces/test/t-NTL-interface; \ fi else $(AT)$(foreach dir, $(MOD), test ! -d $(dir) || mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; test ! -d $(dir) || $(MAKE) -f ../Makefile.subdirs -C $(dir) check || exit $$?;) $(AT)$(foreach ext, $(EXTENSIONS), $(AT)$(foreach dir, $(MOD), MOD_DIR=$(dir); export MOD_DIR; test ! -d $(ext)/$(dir) || mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; test ! -d $(ext)/$(dir) || $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) check || exit $$?;)) endif valgrind: library ifndef MOD $(AT)$(foreach dir, $(BUILD_DIRS), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) valgrind || exit $$?;) $(AT)$(foreach ext, $(EXTENSIONS), $(foreach dir, $(patsubst $(ext)/%.h, %, $(wildcard $(ext)/*.h)), mkdir -p build/$(dir)/test; BUILD_DIR=$(CURDIR)/build/$(dir); export BUILD_DIR; MOD_DIR=$(dir); export MOD_DIR; $(MAKE) -f $(CURDIR)/Makefile.subdirs -C $(ext)/$(dir) valgrind || exit $$?;)) else $(AT)$(foreach dir, $(MOD), mkdir -p build/$(dir)/test; BUILD_DIR=../build/$(dir); export BUILD_DIR; $(MAKE) -f ../Makefile.subdirs -C $(dir) valgrind || exit $$?;) endif install: library mkdir -p $(DESTDIR)$(PREFIX)/$(LIBDIR) mkdir -p $(DESTDIR)$(PREFIX)/include $(AT)if [ "$(ARB_SHARED)" -eq "1" ]; then \ cp $(ARB_LIB) "$(DESTDIR)$(PREFIX)/$(LIBDIR)"; \ cp -a $(shell ls $(ARB_LIBNAME)*) "$(DESTDIR)$(PREFIX)/$(LIBDIR)"; \ fi $(AT)if [ "$(ARB_STATIC)" -eq "1" ]; then \ cp libarb.a $(DESTDIR)$(PREFIX)/lib; \ fi cp $(HEADERS) $(DESTDIR)$(PREFIX)/include $(AT)if [ ! -z $(EXT_HEADERS) ]; then \ cp $(EXT_HEADERS) $(DESTDIR)$(PREFIX)/include; \ fi build: mkdir -p build build/%.lo: %.c $(HEADERS) | build $(QUIET_CC) $(CC) $(PIC_FLAG) $(CFLAGS) $(INCS) -c $< -o $@; build/%.o: %.c $(HEADERS) | build $(QUIET_CC) $(CC) $(CFLAGS) $(INCS) -c $< -o $@; build/test/%$(EXEEXT): test/%.c $(HEADERS) | build/test $(QUIET_CC) $(CC) $(CFLAGS) $(INCS) $< -o $@ $(LIBS) build/test: mkdir -p build/test build/interfaces: mkdir -p build/interfaces print-%: @echo '$*=$($*)' .PHONY: profile library shared static clean examples tune check tests distclean dist install all valgrind arb-2.8.1/Makefile.subdirs000066400000000000000000000046771264125401100154120ustar00rootroot00000000000000QUIET_CC = @echo ' ' CC ' ' $@; AT=@ SOURCES = $(wildcard *.c) HEADERS = $(wildcard ../*.h) TEST_HEADERS = $(wildcard *.h) OBJS = $(patsubst %.c, $(BUILD_DIR)/$(MOD_DIR)_%.o, $(SOURCES)) LOBJS = $(patsubst %.c, $(BUILD_DIR)/%.lo, $(SOURCES)) MOD_LOBJ = $(BUILD_DIR)/../$(MOD_DIR).lo TEST_SOURCES = $(wildcard test/*.c) TESTXX_SOURCES = $(wildcard test/*.cpp) PROF_SOURCES = $(wildcard profile/*.c) TUNE_SOURCES = $(wildcard tune/*.c) TESTS = $(patsubst %.c, $(BUILD_DIR)/%$(EXEEXT), $(TEST_SOURCES)) \ $(patsubst %.cpp, $(BUILD_DIR)/%$(EXEEXT), $(TESTXX_SOURCES)) TESTS_RUN = $(patsubst %, %_RUN, $(TESTS)) VALGRIND_RUN = $(patsubst %, %_VALGRIND_RUN, $(TESTS)) PROFS = $(patsubst %.c, $(BUILD_DIR)/%$(EXEEXT), $(PROF_SOURCES)) TUNE = $(patsubst %.c, %$(EXEEXT), $(TUNE_SOURCES)) all: shared static shared: $(MOD_LOBJ) static: $(OBJS) profile: $(PROFS) -include $(patsubst %, %.d, $(PROFS)) $(BUILD_DIR)/profile/%$(EXEEXT): profile/%.c $(BUILD_DIR)/../profiler.o $(QUIET_CC) $(CC) $(ABI_FLAG) -O2 -std=c99 -g $(INCS) $< $(BUILD_DIR)/../profiler.o -o $@ $(LIBS) -MMD -MP -MF $@.d -MT "$@" -MT "$@.d" tune: $(TUNE_SOURCES) $(HEADERS) $(AT)$(foreach prog, $(TUNE), $(CC) $(CFLAGS) $(INCS) $(prog).c -o $(BUILD_DIR)/$(prog) $(LIBS) || exit $$?;) -include $(OBJS:.o=.d) $(BUILD_DIR)/$(MOD_DIR)_%.o: %.c $(QUIET_CC) $(CC) $(CFLAGS) $(INCS) -c $< -o $@ -MMD -MP -MF "$(BUILD_DIR)/$(MOD_DIR)_$*.d" -MT "$(BUILD_DIR)/$(MOD_DIR)_$*.d" -MT "$@" $(MOD_LOBJ): $(LOBJS) $(QUIET_CC) $(CC) $(ABI_FLAG) -Wl,-r $^ -o $@ -nostdlib -include $(LOBJS:.lo=.d) $(BUILD_DIR)/%.lo: %.c $(QUIET_CC) $(CC) $(PIC_FLAG) $(CFLAGS) $(INCS) -c $< -o $@ -MMD -MP -MF "$(BUILD_DIR)/$*.d" -MT "$(BUILD_DIR)/$*.d" -MT "$@" clean: rm -rf $(BUILD_DIR) $(MOD_LOBJ) tests: $(TESTS) check: tests $(TESTS_RUN) valgrind: tests $(VALGRIND_RUN) -include $(patsubst %, %.d, $(TESTS)) ifeq ($(ARB_SHARED), 0) $(BUILD_DIR)/test/%$(EXEEXT): $(BUILD_DIR)/../../libarb.a endif $(BUILD_DIR)/test/%$(EXEEXT): test/%.c $(QUIET_CC) $(CC) $(CFLAGS) $(INCS) $< -o $@ $(LIBS) -MMD -MP -MF $@.d -MT "$@" -MT "$@.d" $(BUILD_DIR)/test/%$(EXEEXT): test/%.cpp $(BUILD_DIR)/../../test_helpers.o $(QUIET_CC) $(CXX) $(CFLAGS) $(INCS) $< -o $@ $(LIBS) -MMD -MP -MF $@.d -MT "$@" -MT "$@.d" %_RUN: % @$< %_VALGRIND_RUN: % valgrind --track-origins=yes --leak-check=full --show-reachable=yes --log-file="$*.valgrind" $< .PHONY: profile tune clean check tests all shared static valgrind %_RUN %_VALGRIND_RUN arb-2.8.1/README.md000066400000000000000000000130161264125401100135420ustar00rootroot00000000000000# Arb Arb is a C library for arbitrary-precision interval arithmetic. It has full support for both real and complex numbers. The library is thread-safe, portable, and extensively tested. ![arb logo](http://fredrikj.net/blog/2015/01/arb-2-5-0-released/arbtext.png) Documentation: http://fredrikj.net/arb/ Development updates: http://fredrikj.net/blog/ Author: Fredrik Johansson Bug reports, feature requests and other comments are welcome in private communication, on the GitHub issue tracker, or on the FLINT mailing list . ## Code example The following program evaluates `sin(pi + exp(-10000))`. Since the input to the sine function matches a root to within 4343 digits, at least 4343-digit (14427-bit) precision is needed to get an accurate result. The program repeats the evaluation at 64-bit, 128-bit, ... precision, stopping only when the result is accurate to at least 53 bits. #include "arb.h" int main() { slong prec; arb_t x, y; arb_init(x); arb_init(y); for (prec = 64; ; prec *= 2) { arb_const_pi(x, prec); arb_set_si(y, -10000); arb_exp(y, y, prec); arb_add(x, x, y, prec); arb_sin(y, x, prec); arb_printn(y, 15, 0); printf("\n"); if (arb_rel_accuracy_bits(y) >= 53) break; } arb_clear(x); arb_clear(y); flint_cleanup(); } The output is: [+/- 6.01e-19] [+/- 2.55e-38] [+/- 8.01e-77] [+/- 8.64e-154] [+/- 5.37e-308] [+/- 3.63e-616] [+/- 1.07e-1232] [+/- 9.27e-2466] [-1.13548386531474e-4343 +/- 3.91e-4358] Each line shows a rigorous enclosure of the exact value of the expression. The program demonstrates how the user can rely on Arb's automatic error bound tracking to get an output that is guaranteed to be accurate -- no error analysis needs to be done by the user. For several other example programs, see: http://fredrikj.net/arb/examples.html ## General features Besides basic arithmetic, Arb allows working with univariate polynomials, truncated power series, and matrices over both real and complex numbers. Basic linear algebra is supported, including matrix multiplication, determinant, inverse, nonsingular solving and matrix exponential. Support for polynomial and power series is quite extensive, including methods for composition, reversion, product trees, multipoint evaluation and interpolation, complex root isolation, and transcendental functions of power series. Arb has partial support for automatic differentiation (AD), and includes rudimentary functionality for rigorous calculus based on AD (including real root isolation and complex integration). ## Special functions Arb can compute a wide range of transcendental and special functions, including the gamma function, polygamma functions, Riemann zeta and Hurwitz zeta function, polylogarithm, error function, Gauss hypergeometric function 2F1, confluent hypergeometric functions, Bessel functions, Airy functions, Legendre functions and other orthogonal polynomials, exponential and trigonometric integrals, incomplete gamma function, Jacobi theta functions, modular functions, Weierstrass elliptic function, complete elliptic integrals, arithmetic-geometric mean, Bernoulli numbers, partition function, Barnes G-function. ## Speed Arb uses a midpoint-radius (ball) representation of real numbers. At high precision, this allows doing interval arithmetic without significant overhead compared to plain floating-point arithmetic. Various low-level optimizations have also been implemented to reduce overhead at precisions of just a few machine words. Most operations on polynomials and power series use asymptotically fast FFT multiplication. For basic arithmetic, Arb should generally be around as fast as MPFR (http://mpfr.org), though it can be a bit slower at low precision, and around twice as fast as MPFI (https://perso.ens-lyon.fr/nathalie.revol/software.html). Transcendental functions in Arb are quite well optimized and should generally be faster than any other arbitrary-precision software currently available. The following table compares the time in seconds to evaluate the Gauss hypergeometric function `2F1(1/2, 1/4, 1, z)` at the complex number `z = 5^(1/2) + 7^(1/2)i`, to a given number of decimal digits (Arb 2.8-git and mpmath 0.19 on an 1.90 GHz Intel i5-4300U, Mathematica 9.0 on a 3.07 GHz Intel Xeon X5675). | Digits | Mathematica | mpmath | Arb | | -------:|:------------|:-----------|:----------| | 10 | 0.00066 | 0.00090 | 0.00011 | | 100 | 0.0039 | 0.0017 | 0.00075 | | 1000 | 0.23 | 1.5 | 0.019 | | 10000 | 42.6 | 98 | 1.2 | ## Dependencies, installation, and interfaces Arb depends on FLINT (http://flintlib.org/), either GMP (http://gmplib.org) or MPIR (http://mpir.org), and MPFR (http://mpfr.org). See http://fredrikj.net/arb/setup.html for instructions on building and installing Arb directly from the source code. Arb might also be available (or coming soon) as a package for your Linux distribution. SageMath will include Arb as a standard package in an upcoming version, including a high-level Python interface to Arb as part of the SageMath standard library. Nemo is a computer algebra package for the Julia programming language which includes a high-level Julia interface to Arb. The Nemo installation script will create a local installation of Arb along with other dependencies. arb-2.8.1/acb.h000066400000000000000000000657571264125401100132040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef ACB_H #define ACB_H #ifdef ACB_INLINES_C #define ACB_INLINE #else #define ACB_INLINE static __inline__ #endif #include "arf.h" #include "arb.h" #ifdef __cplusplus extern "C" { #endif typedef struct { arb_struct real; arb_struct imag; } acb_struct; typedef acb_struct acb_t[1]; typedef acb_struct * acb_ptr; typedef const acb_struct * acb_srcptr; #define acb_realref(x) (&(x)->real) #define acb_imagref(x) (&(x)->imag) ACB_INLINE void acb_init(acb_t x) { arb_init(acb_realref(x)); arb_init(acb_imagref(x)); } ACB_INLINE void acb_clear(acb_t x) { arb_clear(acb_realref(x)); arb_clear(acb_imagref(x)); } ACB_INLINE acb_ptr _acb_vec_init(slong n) { slong i; acb_ptr v = (acb_ptr) flint_malloc(sizeof(acb_struct) * n); for (i = 0; i < n; i++) acb_init(v + i); return v; } ACB_INLINE void _acb_vec_clear(acb_ptr v, slong n) { slong i; for (i = 0; i < n; i++) acb_clear(v + i); flint_free(v); } ACB_INLINE arb_ptr acb_real_ptr(acb_t z) { return acb_realref(z); } ACB_INLINE arb_ptr acb_imag_ptr(acb_t z) { return acb_imagref(z); } ACB_INLINE void acb_get_real(arb_t re, const acb_t z) { arb_set(re, acb_realref(z)); } ACB_INLINE void acb_get_imag(arb_t im, const acb_t z) { arb_set(im, acb_imagref(z)); } ACB_INLINE int acb_is_zero(const acb_t z) { return arb_is_zero(acb_realref(z)) && arb_is_zero(acb_imagref(z)); } ACB_INLINE int acb_is_one(const acb_t z) { return arb_is_one(acb_realref(z)) && arb_is_zero(acb_imagref(z)); } ACB_INLINE int acb_is_exact(const acb_t z) { return arb_is_exact(acb_realref(z)) && arb_is_exact(acb_imagref(z)); } ACB_INLINE int acb_is_int(const acb_t z) { return arb_is_zero(acb_imagref(z)) && arb_is_int(acb_realref(z)); } ACB_INLINE void acb_zero(acb_t z) { arb_zero(acb_realref(z)); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_one(acb_t z) { arb_one(acb_realref(z)); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_onei(acb_t z) { arb_zero(acb_realref(z)); arb_one(acb_imagref(z)); } ACB_INLINE void acb_set(acb_t z, const acb_t x) { arb_set(acb_realref(z), acb_realref(x)); arb_set(acb_imagref(z), acb_imagref(x)); } ACB_INLINE void acb_set_round(acb_t z, const acb_t x, slong prec) { arb_set_round(acb_realref(z), acb_realref(x), prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_neg_round(acb_t z, const acb_t x, slong prec) { arb_neg_round(acb_realref(z), acb_realref(x), prec); arb_neg_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_swap(acb_t z, acb_t x) { arb_swap(acb_realref(z), acb_realref(x)); arb_swap(acb_imagref(z), acb_imagref(x)); } ACB_INLINE int acb_equal(const acb_t x, const acb_t y) { return arb_equal(acb_realref(x), acb_realref(y)) && arb_equal(acb_imagref(x), acb_imagref(y)); } ACB_INLINE int acb_eq(const acb_t x, const acb_t y) { return arb_eq(acb_realref(x), acb_realref(y)) && arb_eq(acb_imagref(x), acb_imagref(y)); } ACB_INLINE int acb_ne(const acb_t x, const acb_t y) { return arb_ne(acb_realref(x), acb_realref(y)) || arb_ne(acb_imagref(x), acb_imagref(y)); } ACB_INLINE int acb_overlaps(const acb_t x, const acb_t y) { return arb_overlaps(acb_realref(x), acb_realref(y)) && arb_overlaps(acb_imagref(x), acb_imagref(y)); } ACB_INLINE int acb_contains_zero(const acb_t x) { return arb_contains_zero(acb_realref(x)) && arb_contains_zero(acb_imagref(x)); } ACB_INLINE int acb_contains_fmpq(const acb_t x, const fmpq_t y) { return arb_contains_fmpq(acb_realref(x), y) && arb_contains_zero(acb_imagref(x)); } ACB_INLINE int acb_contains_fmpz(const acb_t x, const fmpz_t y) { return arb_contains_fmpz(acb_realref(x), y) && arb_contains_zero(acb_imagref(x)); } ACB_INLINE int acb_contains(const acb_t x, const acb_t y) { return arb_contains(acb_realref(x), acb_realref(y)) && arb_contains(acb_imagref(x), acb_imagref(y)); } ACB_INLINE void acb_set_ui(acb_t z, ulong c) { arb_set_ui(acb_realref(z), c); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_set_d(acb_t z, double c) { arb_set_d(acb_realref(z), c); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_set_si(acb_t z, slong c) { arb_set_si(acb_realref(z), c); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_set_si_si(acb_t z, slong x, slong y) { arb_set_si(acb_realref(z), x); arb_set_si(acb_imagref(z), y); } ACB_INLINE void acb_set_d_d(acb_t z, double x, double y) { arb_set_d(acb_realref(z), x); arb_set_d(acb_imagref(z), y); } ACB_INLINE void acb_set_fmpz(acb_t z, const fmpz_t c) { arb_set_fmpz(acb_realref(z), c); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_set_fmpz_fmpz(acb_t z, const fmpz_t x, const fmpz_t y) { arb_set_fmpz(acb_realref(z), x); arb_set_fmpz(acb_imagref(z), y); } ACB_INLINE void acb_set_round_fmpz(acb_t z, const fmpz_t y, slong prec) { arb_set_round_fmpz(acb_realref(z), y, prec); arb_zero(acb_imagref(z)); } int acb_contains_int(const acb_t x); int acb_get_unique_fmpz(fmpz_t z, const acb_t x); ACB_INLINE void acb_set_fmpq(acb_t z, const fmpq_t c, slong prec) { arb_set_fmpq(acb_realref(z), c, prec); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_set_arb(acb_t z, const arb_t c) { arb_set(acb_realref(z), c); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_set_arb_arb(acb_t z, const arb_t x, const arb_t y) { arb_set(acb_realref(z), x); arb_set(acb_imagref(z), y); } ACB_INLINE void acb_set_round_arb(acb_t z, const arb_t x, slong prec) { arb_set_round(acb_realref(z), x, prec); arb_zero(acb_imagref(z)); } ACB_INLINE void acb_trim(acb_t z, const acb_t x) { arb_trim(acb_realref(z), acb_realref(x)); arb_trim(acb_imagref(z), acb_imagref(x)); } ACB_INLINE void acb_add_error_arf(acb_t x, const arf_t err) { arb_add_error_arf(acb_realref(x), err); arb_add_error_arf(acb_imagref(x), err); } ACB_INLINE void acb_add_error_mag(acb_t x, const mag_t err) { arb_add_error_mag(acb_realref(x), err); arb_add_error_mag(acb_imagref(x), err); } void acb_get_mag(mag_t z, const acb_t x); void acb_get_mag_lower(mag_t z, const acb_t x); ACB_INLINE void acb_get_abs_ubound_arf(arf_t u, const acb_t z, slong prec) { if (arb_is_zero(acb_imagref(z))) { arb_get_abs_ubound_arf(u, acb_realref(z), prec); } else if (arb_is_zero(acb_realref(z))) { arb_get_abs_ubound_arf(u, acb_imagref(z), prec); } else { arf_t v; arf_init(v); arb_get_abs_ubound_arf(u, acb_realref(z), prec); arb_get_abs_ubound_arf(v, acb_imagref(z), prec); arf_mul(u, u, u, prec, ARF_RND_UP); arf_mul(v, v, v, prec, ARF_RND_UP); arf_add(u, u, v, prec, ARF_RND_UP); arf_sqrt(u, u, prec, ARF_RND_UP); arf_clear(v); } } ACB_INLINE void acb_get_abs_lbound_arf(arf_t u, const acb_t z, slong prec) { if (arb_is_zero(acb_imagref(z))) { arb_get_abs_lbound_arf(u, acb_realref(z), prec); } else if (arb_is_zero(acb_realref(z))) { arb_get_abs_lbound_arf(u, acb_imagref(z), prec); } else { arf_t v; arf_init(v); arb_get_abs_lbound_arf(u, acb_realref(z), prec); arb_get_abs_lbound_arf(v, acb_imagref(z), prec); arf_mul(u, u, u, prec, ARF_RND_DOWN); arf_mul(v, v, v, prec, ARF_RND_DOWN); arf_add(u, u, v, prec, ARF_RND_DOWN); arf_sqrt(u, u, prec, ARF_RND_DOWN); arf_clear(v); } } ACB_INLINE void acb_get_rad_ubound_arf(arf_t u, const acb_t z, slong prec) { /* fixme: this bound is very sloppy */ if (mag_cmp(arb_radref(acb_realref(z)), arb_radref(acb_imagref(z))) >= 0) arf_set_mag(u, arb_radref(acb_realref(z))); else arf_set_mag(u, arb_radref(acb_imagref(z))); arf_mul_2exp_si(u, u, 1); } void acb_arg(arb_t r, const acb_t z, slong prec); ACB_INLINE void acb_add(acb_t z, const acb_t x, const acb_t y, slong prec) { arb_add(acb_realref(z), acb_realref(x), acb_realref(y), prec); arb_add(acb_imagref(z), acb_imagref(x), acb_imagref(y), prec); } ACB_INLINE void acb_sub(acb_t z, const acb_t x, const acb_t y, slong prec) { arb_sub(acb_realref(z), acb_realref(x), acb_realref(y), prec); arb_sub(acb_imagref(z), acb_imagref(x), acb_imagref(y), prec); } ACB_INLINE void acb_add_si(acb_t z, const acb_t x, ulong c, slong prec) { arb_add_si(acb_realref(z), acb_realref(x), c, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_add_ui(acb_t z, const acb_t x, ulong c, slong prec) { arb_add_ui(acb_realref(z), acb_realref(x), c, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_sub_si(acb_t z, const acb_t x, ulong c, slong prec) { arb_sub_si(acb_realref(z), acb_realref(x), c, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_sub_ui(acb_t z, const acb_t x, ulong c, slong prec) { arb_sub_ui(acb_realref(z), acb_realref(x), c, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_add_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) { arb_add_fmpz(acb_realref(z), acb_realref(x), y, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_add_arb(acb_t z, const acb_t x, const arb_t y, slong prec) { arb_add(acb_realref(z), acb_realref(x), y, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_sub_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) { arb_sub_fmpz(acb_realref(z), acb_realref(x), y, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_sub_arb(acb_t z, const acb_t x, const arb_t y, slong prec) { arb_sub(acb_realref(z), acb_realref(x), y, prec); arb_set_round(acb_imagref(z), acb_imagref(x), prec); } ACB_INLINE void acb_neg(acb_t z, const acb_t x) { arb_neg(acb_realref(z), acb_realref(x)); arb_neg(acb_imagref(z), acb_imagref(x)); } ACB_INLINE void acb_conj(acb_t z, const acb_t x) { arb_set(acb_realref(z), acb_realref(x)); arb_neg(acb_imagref(z), acb_imagref(x)); } ACB_INLINE void acb_abs(arb_t u, const acb_t z, slong prec) { arb_hypot(u, acb_realref(z), acb_imagref(z), prec); } ACB_INLINE void acb_mul_ui(acb_t z, const acb_t x, ulong y, slong prec) { arb_mul_ui(acb_realref(z), acb_realref(x), y, prec); arb_mul_ui(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_mul_si(acb_t z, const acb_t x, slong y, slong prec) { arb_mul_si(acb_realref(z), acb_realref(x), y, prec); arb_mul_si(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_mul_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) { arb_mul_fmpz(acb_realref(z), acb_realref(x), y, prec); arb_mul_fmpz(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_mul_arb(acb_t z, const acb_t x, const arb_t y, slong prec) { arb_mul(acb_realref(z), acb_realref(x), y, prec); arb_mul(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_mul_onei(acb_t z, const acb_t x) { if (z == x) { arb_swap(acb_realref(z), acb_imagref(z)); arb_neg(acb_realref(z), acb_realref(z)); } else { arb_neg(acb_realref(z), acb_imagref(x)); arb_set(acb_imagref(z), acb_realref(x)); } } ACB_INLINE void acb_div_onei(acb_t z, const acb_t x) { if (z == x) { arb_swap(acb_realref(z), acb_imagref(z)); arb_neg(acb_imagref(z), acb_imagref(z)); } else { arb_set(acb_realref(z), acb_imagref(x)); arb_neg(acb_imagref(z), acb_realref(x)); } } void acb_mul(acb_t z, const acb_t x, const acb_t y, slong prec); void acb_mul_naive(acb_t z, const acb_t x, const acb_t y, slong prec); ACB_INLINE void acb_mul_2exp_si(acb_t z, const acb_t x, slong e) { arb_mul_2exp_si(acb_realref(z), acb_realref(x), e); arb_mul_2exp_si(acb_imagref(z), acb_imagref(x), e); } ACB_INLINE void acb_mul_2exp_fmpz(acb_t z, const acb_t x, const fmpz_t c) { arb_mul_2exp_fmpz(acb_realref(z), acb_realref(x), c); arb_mul_2exp_fmpz(acb_imagref(z), acb_imagref(x), c); } void acb_addmul(acb_t z, const acb_t x, const acb_t y, slong prec); void acb_submul(acb_t z, const acb_t x, const acb_t y, slong prec); ACB_INLINE void acb_addmul_ui(acb_t z, const acb_t x, ulong y, slong prec) { arb_addmul_ui(acb_realref(z), acb_realref(x), y, prec); arb_addmul_ui(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_addmul_si(acb_t z, const acb_t x, slong y, slong prec) { arb_addmul_si(acb_realref(z), acb_realref(x), y, prec); arb_addmul_si(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_submul_ui(acb_t z, const acb_t x, ulong y, slong prec) { arb_submul_ui(acb_realref(z), acb_realref(x), y, prec); arb_submul_ui(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_submul_si(acb_t z, const acb_t x, slong y, slong prec) { arb_submul_si(acb_realref(z), acb_realref(x), y, prec); arb_submul_si(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_addmul_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) { arb_addmul_fmpz(acb_realref(z), acb_realref(x), y, prec); arb_addmul_fmpz(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_submul_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) { arb_submul_fmpz(acb_realref(z), acb_realref(x), y, prec); arb_submul_fmpz(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_addmul_arb(acb_t z, const acb_t x, const arb_t y, slong prec) { arb_addmul(acb_realref(z), acb_realref(x), y, prec); arb_addmul(acb_imagref(z), acb_imagref(x), y, prec); } ACB_INLINE void acb_submul_arb(acb_t z, const acb_t x, const arb_t y, slong prec) { arb_submul(acb_realref(z), acb_realref(x), y, prec); arb_submul(acb_imagref(z), acb_imagref(x), y, prec); } void acb_inv(acb_t z, const acb_t x, slong prec); void acb_div(acb_t z, const acb_t x, const acb_t y, slong prec); ACB_INLINE void acb_div_ui(acb_t z, const acb_t x, ulong c, slong prec) { arb_div_ui(acb_realref(z), acb_realref(x), c, prec); arb_div_ui(acb_imagref(z), acb_imagref(x), c, prec); } ACB_INLINE void acb_div_si(acb_t z, const acb_t x, slong c, slong prec) { arb_div_si(acb_realref(z), acb_realref(x), c, prec); arb_div_si(acb_imagref(z), acb_imagref(x), c, prec); } ACB_INLINE void acb_div_arb(acb_t z, const acb_t x, const arb_t c, slong prec) { arb_div(acb_realref(z), acb_realref(x), c, prec); arb_div(acb_imagref(z), acb_imagref(x), c, prec); } ACB_INLINE void acb_div_fmpz(acb_t z, const acb_t x, const fmpz_t c, slong prec) { arb_div_fmpz(acb_realref(z), acb_realref(x), c, prec); arb_div_fmpz(acb_imagref(z), acb_imagref(x), c, prec); } void acb_cube(acb_t y, const acb_t x, slong prec); void acb_pow_fmpz(acb_t y, const acb_t b, const fmpz_t e, slong prec); void acb_pow_ui(acb_t y, const acb_t b, ulong e, slong prec); void acb_pow_si(acb_t y, const acb_t b, slong e, slong prec); ACB_INLINE void acb_const_pi(acb_t x, slong prec) { arb_const_pi(acb_realref(x), prec); arb_zero(acb_imagref(x)); } void acb_log(acb_t r, const acb_t z, slong prec); void acb_log1p(acb_t r, const acb_t z, slong prec); void acb_exp(acb_t r, const acb_t z, slong prec); void acb_exp_pi_i(acb_t r, const acb_t z, slong prec); void acb_exp_invexp(acb_t r, acb_t s, const acb_t z, slong prec); void acb_sin(acb_t r, const acb_t z, slong prec); void acb_cos(acb_t r, const acb_t z, slong prec); void acb_sin_cos(acb_t s, acb_t c, const acb_t z, slong prec); void acb_tan(acb_t r, const acb_t z, slong prec); void acb_cot(acb_t r, const acb_t z, slong prec); void acb_asin(acb_t r, const acb_t z, slong prec); void acb_acos(acb_t r, const acb_t z, slong prec); void acb_atan(acb_t r, const acb_t z, slong prec); void acb_asinh(acb_t r, const acb_t z, slong prec); void acb_acosh(acb_t r, const acb_t z, slong prec); void acb_atanh(acb_t r, const acb_t z, slong prec); ACB_INLINE void acb_sinh(acb_t y, const acb_t x, slong prec) { acb_mul_onei(y, x); acb_sin(y, y, prec); acb_div_onei(y, y); } ACB_INLINE void acb_cosh(acb_t y, const acb_t x, slong prec) { acb_mul_onei(y, x); acb_cos(y, y, prec); } ACB_INLINE void acb_sinh_cosh(acb_t y, acb_t z, const acb_t x, slong prec) { acb_mul_onei(y, x); acb_sin_cos(y, z, y, prec); acb_div_onei(y, y); } ACB_INLINE void acb_tanh(acb_t y, const acb_t x, slong prec) { acb_mul_onei(y, x); acb_tan(y, y, prec); acb_div_onei(y, y); } ACB_INLINE void acb_coth(acb_t y, const acb_t x, slong prec) { acb_mul_onei(y, x); acb_cot(y, y, prec); acb_mul_onei(y, y); } void acb_sin_pi(acb_t r, const acb_t z, slong prec); void acb_cos_pi(acb_t r, const acb_t z, slong prec); void acb_sin_cos_pi(acb_t s, acb_t c, const acb_t z, slong prec); void acb_tan_pi(acb_t r, const acb_t z, slong prec); void acb_cot_pi(acb_t r, const acb_t z, slong prec); void acb_pow_arb(acb_t z, const acb_t x, const arb_t y, slong prec); void acb_pow(acb_t r, const acb_t x, const acb_t y, slong prec); void acb_sqrt(acb_t y, const acb_t x, slong prec); void acb_rsqrt(acb_t y, const acb_t x, slong prec); void acb_root_ui(acb_t y, const acb_t x, ulong k, slong prec); void acb_quadratic_roots_fmpz(acb_t r1, acb_t r2, const fmpz_t a, const fmpz_t b, const fmpz_t c, slong prec); void acb_chebyshev_t_ui(acb_t a, ulong n, const acb_t x, slong prec); void acb_chebyshev_t2_ui(acb_t a, acb_t b, ulong n, const acb_t x, slong prec); void acb_chebyshev_u_ui(acb_t a, ulong n, const acb_t x, slong prec); void acb_chebyshev_u2_ui(acb_t a, acb_t b, ulong n, const acb_t x, slong prec); void acb_rising_ui_bs(acb_t y, const acb_t x, ulong n, slong prec); void acb_rising_ui_rs(acb_t y, const acb_t x, ulong n, ulong m, slong prec); void acb_rising_ui_rec(acb_t y, const acb_t x, ulong n, slong prec); void acb_rising_ui(acb_t z, const acb_t x, ulong n, slong prec); void acb_rising(acb_t z, const acb_t x, const acb_t n, slong prec); void acb_rising2_ui_bs(acb_t u, acb_t v, const acb_t x, ulong n, slong prec); void acb_rising2_ui_rs(acb_t u, acb_t v, const acb_t x, ulong n, ulong m, slong prec); void acb_rising2_ui(acb_t u, acb_t v, const acb_t x, ulong n, slong prec); void acb_rising_ui_get_mag(mag_t bound, const acb_t s, ulong n); void acb_gamma(acb_t y, const acb_t x, slong prec); void acb_rgamma(acb_t y, const acb_t x, slong prec); void acb_lgamma(acb_t y, const acb_t x, slong prec); void acb_log_sin_pi(acb_t res, const acb_t z, slong prec); void acb_digamma(acb_t y, const acb_t x, slong prec); void acb_zeta(acb_t z, const acb_t s, slong prec); void acb_hurwitz_zeta(acb_t z, const acb_t s, const acb_t a, slong prec); void acb_polygamma(acb_t res, const acb_t s, const acb_t z, slong prec); void acb_log_barnes_g(acb_t res, const acb_t z, slong prec); void acb_barnes_g(acb_t res, const acb_t z, slong prec); void acb_polylog(acb_t w, const acb_t s, const acb_t z, slong prec); void acb_polylog_si(acb_t w, slong s, const acb_t z, slong prec); void acb_agm1(acb_t m, const acb_t z, slong prec); void acb_agm1_cpx(acb_ptr m, const acb_t z, slong len, slong prec); /* TBD void acb_invroot_newton(acb_t r, const acb_t a, ulong m, const acb_t r0, slong startprec, slong prec); void acb_root_exp(acb_t r, const acb_t a, slong m, slong index, slong prec); void acb_root_newton(acb_t r, const acb_t a, slong m, slong index, slong prec); void acb_root(acb_t r, const acb_t a, slong m, slong index, slong prec); */ ACB_INLINE int acb_is_finite(const acb_t x) { return arb_is_finite(acb_realref(x)) && arb_is_finite(acb_imagref(x)); } ACB_INLINE void acb_indeterminate(acb_t x) { arb_indeterminate(acb_realref(x)); arb_indeterminate(acb_imagref(x)); } ACB_INLINE acb_ptr _acb_vec_entry_ptr(acb_ptr vec, slong i) { return vec + i; } ACB_INLINE void _acb_vec_zero(acb_ptr A, slong n) { slong i; for (i = 0; i < n; i++) acb_zero(A + i); } ACB_INLINE int _acb_vec_is_zero(acb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) if (!acb_is_zero(vec + i)) return 0; return 1; } ACB_INLINE void _acb_vec_set(acb_ptr res, acb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) acb_set(res + i, vec + i); } ACB_INLINE void _acb_vec_set_round(acb_ptr res, acb_srcptr vec, slong len, slong prec) { slong i; for (i = 0; i < len; i++) acb_set_round(res + i, vec + i, prec); } ACB_INLINE void _acb_vec_neg(acb_ptr res, acb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) acb_neg(res + i, vec + i); } ACB_INLINE void _acb_vec_add(acb_ptr res, acb_srcptr vec1, acb_srcptr vec2, slong len, slong prec) { slong i; for (i = 0; i < len; i++) acb_add(res + i, vec1 + i, vec2 + i, prec); } ACB_INLINE void _acb_vec_sub(acb_ptr res, acb_srcptr vec1, acb_srcptr vec2, slong len, slong prec) { slong i; for (i = 0; i < len; i++) acb_sub(res + i, vec1 + i, vec2 + i, prec); } ACB_INLINE void _acb_vec_scalar_submul(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) { slong i; for (i = 0; i < len; i++) acb_submul(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_addmul(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) { slong i; for (i = 0; i < len; i++) acb_addmul(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_mul(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) { slong i; for (i = 0; i < len; i++) acb_mul(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_mul_ui(acb_ptr res, acb_srcptr vec, slong len, ulong c, slong prec) { slong i; for (i = 0; i < len; i++) acb_mul_ui(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_mul_2exp_si(acb_ptr res, acb_srcptr vec, slong len, slong c) { slong i; for (i = 0; i < len; i++) acb_mul_2exp_si(res + i, vec + i, c); } ACB_INLINE void _acb_vec_scalar_mul_onei(acb_ptr res, acb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) acb_mul_onei(res + i, vec + i); } ACB_INLINE void _acb_vec_scalar_div_ui(acb_ptr res, acb_srcptr vec, slong len, ulong c, slong prec) { slong i; for (i = 0; i < len; i++) acb_div_ui(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_div(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) { slong i; for (i = 0; i < len; i++) acb_div(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_mul_arb(acb_ptr res, acb_srcptr vec, slong len, const arb_t c, slong prec) { slong i; for (i = 0; i < len; i++) acb_mul_arb(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_div_arb(acb_ptr res, acb_srcptr vec, slong len, const arb_t c, slong prec) { slong i; for (i = 0; i < len; i++) { arb_div(acb_realref(res + i), acb_realref(vec + i), c, prec); arb_div(acb_imagref(res + i), acb_imagref(vec + i), c, prec); } } ACB_INLINE void _acb_vec_scalar_mul_fmpz(acb_ptr res, acb_srcptr vec, slong len, const fmpz_t c, slong prec) { slong i; for (i = 0; i < len; i++) acb_mul_fmpz(res + i, vec + i, c, prec); } ACB_INLINE void _acb_vec_scalar_div_fmpz(acb_ptr res, acb_srcptr vec, slong len, const fmpz_t c, slong prec) { slong i; for (i = 0; i < len; i++) acb_div_fmpz(res + i, vec + i, c, prec); } ACB_INLINE void acb_print(const acb_t x) { flint_printf("("); arb_print(acb_realref(x)); flint_printf(", "); arb_print(acb_imagref(x)); flint_printf(")"); } void acb_printd(const acb_t z, slong digits); void acb_randtest(acb_t z, flint_rand_t state, slong prec, slong mag_bits); void acb_randtest_special(acb_t z, flint_rand_t state, slong prec, slong mag_bits); void acb_randtest_precise(acb_t z, flint_rand_t state, slong prec, slong mag_bits); void acb_randtest_param(acb_t z, flint_rand_t state, slong prec, slong mag_bits); slong acb_rel_error_bits(const acb_t x); ACB_INLINE slong acb_rel_accuracy_bits(const acb_t x) { return -acb_rel_error_bits(x); } ACB_INLINE slong acb_bits(const acb_t x) { slong b1, b2; b1 = arb_bits(acb_realref(x)); b2 = arb_bits(acb_imagref(x)); return FLINT_MAX(b1, b2); } ACB_INLINE int acb_is_real(const acb_t x) { return arb_is_zero(acb_imagref(x)); } ACB_INLINE int _acb_vec_is_real(acb_srcptr v, slong len) { slong i; for (i = 0; i < len; i++) { if (!acb_is_real(v + i)) return 0; } return 1; } ACB_INLINE slong _acb_vec_bits(acb_srcptr vec, slong len) { return _arb_vec_bits((arb_srcptr) vec, 2 * len); } ACB_INLINE void _acb_vec_set_powers(acb_ptr xs, const acb_t x, slong len, slong prec) { slong i; for (i = 0; i < len; i++) { if (i == 0) acb_one(xs + i); else if (i == 1) acb_set_round(xs + i, x, prec); else if (i % 2 == 0) acb_mul(xs + i, xs + i / 2, xs + i / 2, prec); else acb_mul(xs + i, xs + i - 1, x, prec); } } ACB_INLINE void _acb_vec_add_error_arf_vec(acb_ptr res, arf_srcptr err, slong len) { slong i; for (i = 0; i < len; i++) acb_add_error_arf(res + i, err + i); } ACB_INLINE void _acb_vec_add_error_mag_vec(acb_ptr res, mag_srcptr err, slong len) { slong i; for (i = 0; i < len; i++) { mag_add(arb_radref(acb_realref(res + i)), arb_radref(acb_realref(res + i)), err + i); mag_add(arb_radref(acb_imagref(res + i)), arb_radref(acb_imagref(res + i)), err + i); } } ACB_INLINE void _acb_vec_indeterminate(acb_ptr vec, slong len) { _arb_vec_indeterminate((arb_ptr) vec, 2 * len); } ACB_INLINE void _acb_vec_trim(acb_ptr res, acb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) acb_trim(res + i, vec + i); } ACB_INLINE int _acb_vec_get_unique_fmpz_vec(fmpz * res, acb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) if (!acb_get_unique_fmpz(res + i, vec + i)) return 0; return 1; } /* sort complex numbers in a nice-to-display order */ void _acb_vec_sort_pretty(acb_ptr vec, slong len); #ifdef __cplusplus } #endif #endif arb-2.8.1/acb/000077500000000000000000000000001264125401100130075ustar00rootroot00000000000000arb-2.8.1/acb/acos.c000066400000000000000000000026341264125401100141050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_acos(acb_t res, const acb_t z, slong prec) { if (acb_is_one(z)) { acb_zero(res); } else { acb_t t; acb_init(t); acb_asin(res, z, prec); acb_const_pi(t, prec); acb_mul_2exp_si(t, t, -1); acb_sub(res, t, res, prec); acb_clear(t); } } arb-2.8.1/acb/acosh.c000066400000000000000000000030501264125401100142460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_acosh(acb_t res, const acb_t z, slong prec) { if (acb_is_one(z)) { acb_zero(res); } else { acb_t t, u; acb_init(t); acb_init(u); acb_add_ui(t, z, 1, prec); acb_sub_ui(u, z, 1, prec); acb_sqrt(t, t, prec); acb_sqrt(u, u, prec); acb_mul(t, t, u, prec); acb_add(t, t, z, prec); acb_log(res, t, prec); acb_clear(t); acb_clear(u); } } arb-2.8.1/acb/addmul.c000066400000000000000000000032721264125401100144250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_addmul(acb_t z, const acb_t x, const acb_t y, slong prec) { if (arb_is_zero(acb_imagref(y))) { arb_addmul(acb_imagref(z), acb_imagref(x), acb_realref(y), prec); arb_addmul(acb_realref(z), acb_realref(x), acb_realref(y), prec); } else if (arb_is_zero(acb_imagref(x))) { arb_addmul(acb_imagref(z), acb_imagref(y), acb_realref(x), prec); arb_addmul(acb_realref(z), acb_realref(y), acb_realref(x), prec); } else { acb_t t; acb_init(t); acb_mul(t, x, y, prec); acb_add(z, z, t, prec); acb_clear(t); } } arb-2.8.1/acb/agm1.c000066400000000000000000000274751264125401100140170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" #include "acb_poly.h" /* Checks that |arg(z)| <= 3 pi / 4 */ static int acb_check_arg(const acb_t z) { mag_t re, im; int res; if (!arb_contains_negative(acb_realref(z))) return 1; mag_init(re); mag_init(im); arb_get_mag(re, acb_realref(z)); arb_get_mag_lower(im, acb_imagref(z)); res = mag_cmp(re, im) < 0; mag_clear(re); mag_clear(im); return res; } static void sqrtmul(acb_t c, const acb_t a, const acb_t b, slong prec) { if (arb_is_positive(acb_realref(a)) && arb_is_positive(acb_realref(b))) { acb_mul(c, a, b, prec); acb_sqrt(c, c, prec); } else if (arb_is_nonnegative(acb_imagref(a)) && arb_is_nonnegative(acb_imagref(b))) { acb_mul(c, a, b, prec); acb_neg(c, c); acb_sqrt(c, c, prec); acb_mul_onei(c, c); } else if (arb_is_nonpositive(acb_imagref(a)) && arb_is_nonpositive(acb_imagref(b))) { acb_mul(c, a, b, prec); acb_neg(c, c); acb_sqrt(c, c, prec); acb_mul_onei(c, c); acb_neg(c, c); } else { acb_t d; acb_init(d); acb_sqrt(c, a, prec); acb_sqrt(d, b, prec); acb_mul(c, c, d, prec); acb_clear(d); } } void acb_agm1_basecase(acb_t res, const acb_t z, slong prec) { acb_t a, b, t, u; mag_t err; int isreal; if (acb_is_zero(z)) { acb_zero(res); return; } if (acb_is_one(z)) { acb_one(res); return; } if (!acb_check_arg(z)) { mag_t one; mag_init(one); mag_init(err); mag_one(one); acb_get_mag(err, z); mag_max(err, err, one); acb_zero(res); acb_add_error_mag(res, err); mag_clear(err); mag_clear(one); return; } isreal = acb_is_real(z) && arb_is_nonnegative(acb_realref(z)); acb_init(a); acb_init(b); acb_init(t); acb_init(u); mag_init(err); acb_one(a); acb_set_round(b, z, prec); while (!acb_overlaps(a, b)) { acb_add(t, a, b, prec); acb_mul_2exp_si(t, t, -1); sqrtmul(u, a, b, prec); acb_swap(t, a); acb_swap(u, b); } /* Dupont's thesis, p. 87: |M(z) - a_n| <= |a_n - b_n| */ acb_sub(t, a, b, prec); acb_get_mag(err, t); if (isreal) arb_add_error_mag(acb_realref(a), err); else acb_add_error_mag(a, err); acb_set(res, a); acb_clear(a); acb_clear(b); acb_clear(t); acb_clear(u); mag_clear(err); } /* Computes (M(z), M'(z)) using a finite difference. Assumes z exact, |arg(z)| <= 3 pi / 4. */ void acb_agm1_deriv_diff(acb_t Mz, acb_t Mzp, const acb_t z, slong prec) { mag_t err, t; fmpz_t rexp, hexp; slong wp; int isreal; if (!acb_is_exact(z) || !acb_is_finite(z) || acb_is_zero(z) || !acb_check_arg(z)) { acb_indeterminate(Mz); acb_indeterminate(Mzp); return; } isreal = acb_is_real(z) && arb_is_nonnegative(acb_realref(z)); /* |M^(k)(z) / k!| <= C * D^k where C = max(1, |z| + r), D = 1/r, and 0 < r < |z| M(z+h) - M(z) |------------- - M'(z)| <= C D^2 h / (1 - D h) h h D < 1. */ fmpz_init(hexp); fmpz_init(rexp); mag_init(err); mag_init(t); /* choose r = 2^rexp such that r < |z| */ acb_get_mag_lower(t, z); fmpz_sub_ui(rexp, MAG_EXPREF(t), 2); /* Choose h = 2^hexp with hexp = rexp - (prec + 5). D = 2^-rexp C D^2 h / (1 - D h) <= C * 2^(-5-prec-rexp+1) */ /* err = C = max(1, |z| + r) */ acb_get_mag(err, z); mag_one(t); mag_mul_2exp_fmpz(t, t, rexp); mag_add(err, err, t); mag_one(t); mag_max(err, err, t); /* multiply by 2^(-5-prec-rexp+1) (use hexp as temp) */ fmpz_set_si(hexp, 1 - 5 - prec); fmpz_sub(hexp, hexp, rexp); mag_mul_2exp_fmpz(err, err, hexp); /* choose h = 2^hexp */ fmpz_sub_ui(hexp, rexp, prec + 5); /* compute finite difference */ wp = 2 * prec + 10; acb_agm1_basecase(Mz, z, wp); acb_one(Mzp); acb_mul_2exp_fmpz(Mzp, Mzp, hexp); acb_add(Mzp, Mzp, z, wp); acb_agm1_basecase(Mzp, Mzp, wp); acb_sub(Mzp, Mzp, Mz, prec); fmpz_neg(hexp, hexp); acb_mul_2exp_fmpz(Mzp, Mzp, hexp); if (isreal) arb_add_error_mag(acb_realref(Mzp), err); else acb_add_error_mag(Mzp, err); acb_set_round(Mz, Mz, prec); fmpz_clear(hexp); fmpz_clear(rexp); mag_clear(err); mag_clear(t); } /* For input z + eps First derivative bound: max(1, |z|+|eps|+r) / r Second derivative bound: 2 max(1, |z|+|eps|+r) / r^2 This is assuming that the circle at z with radius |eps| + r does not cross the negative half axis, which we check. */ void acb_agm1_deriv_right(acb_t Mz, acb_t Mzp, const acb_t z, slong prec) { if (acb_is_exact(z)) { acb_agm1_deriv_diff(Mz, Mzp, z, prec); } else { if (!acb_is_finite(z) || !acb_check_arg(z)) { acb_indeterminate(Mz); acb_indeterminate(Mzp); } else { acb_t t; mag_t r, eps, err, one; int isreal; acb_init(t); mag_init(r); mag_init(err); mag_init(one); mag_init(eps); isreal = acb_is_real(z) && arb_is_nonnegative(acb_realref(z)); mag_hypot(eps, arb_radref(acb_realref(z)), arb_radref(acb_imagref(z))); /* choose r avoiding overlap with negative half axis */ if (arf_sgn(arb_midref(acb_realref(z))) < 0) arb_get_mag_lower(r, acb_imagref(z)); else acb_get_mag_lower(r, z); mag_mul_2exp_si(r, r, -1); if (mag_is_zero(r)) { acb_indeterminate(Mz); acb_indeterminate(Mzp); } else { acb_set(t, z); mag_zero(arb_radref(acb_realref(t))); mag_zero(arb_radref(acb_imagref(t))); acb_get_mag(err, z); mag_add(err, err, r); mag_add(err, err, eps); mag_one(one); mag_max(err, err, one); mag_mul(err, err, eps); acb_agm1_deriv_diff(Mz, Mzp, t, prec); mag_div(err, err, r); if (isreal) arb_add_error_mag(acb_realref(Mz), err); else acb_add_error_mag(Mz, err); mag_div(err, err, r); mag_mul_2exp_si(err, err, 1); if (isreal) arb_add_error_mag(acb_realref(Mzp), err); else acb_add_error_mag(Mzp, err); } acb_clear(t); mag_clear(r); mag_clear(err); mag_clear(one); mag_clear(eps); } } } void acb_agm1(acb_t m, const acb_t z, slong prec) { if (arf_sgn(arb_midref(acb_realref(z))) >= 0) { acb_agm1_basecase(m, z, prec); } else { /* use M(z) = (z+1)/2 * M(2 sqrt(z) / (z+1)) */ acb_t t; acb_init(t); acb_add_ui(t, z, 1, prec); acb_sqrt(m, z, prec); acb_div(m, m, t, prec); acb_mul_2exp_si(m, m, 1); acb_agm1_basecase(m, m, prec); acb_mul(m, m, t, prec); acb_mul_2exp_si(m, m, -1); acb_clear(t); } } void acb_agm1_deriv(acb_t Mz, acb_t Mzp, const acb_t z, slong prec) { /* u = 2 sqrt(z) / (1+z) Mz = (1+z) M(u) / 2 Mzp = [M(u) - (z-1) M'(u) / ((1+z) sqrt(z))] / 2 */ if (arf_sgn(arb_midref(acb_realref(z))) >= 0) { acb_agm1_deriv_right(Mz, Mzp, z, prec); } else { acb_t t, u, zp1, zm1; acb_init(t); acb_init(u); acb_init(zp1); acb_init(zm1); acb_sqrt(t, z, prec); acb_add_ui(zp1, z, 1, prec); acb_sub_ui(zm1, z, 1, prec); acb_div(u, t, zp1, prec); acb_mul_2exp_si(u, u, 1); acb_agm1_deriv_right(Mz, Mzp, u, prec); acb_mul(Mzp, Mzp, zm1, prec); acb_mul(t, t, zp1, prec); acb_div(Mzp, Mzp, t, prec); acb_sub(Mzp, Mz, Mzp, prec); acb_mul_2exp_si(Mzp, Mzp, -1); acb_mul(Mz, Mz, zp1, prec); acb_mul_2exp_si(Mz, Mz, -1); acb_clear(t); acb_clear(u); acb_clear(zp1); acb_clear(zm1); } } void acb_agm1_cpx(acb_ptr m, const acb_t z, slong len, slong prec) { if (len < 1) return; if (len == 1) { acb_agm1(m, z, prec); return; } if (len == 2) { acb_agm1_deriv(m, m + 1, z, prec); return; } if (len >= 3) { acb_t t, u, v; acb_ptr w; slong k, n; acb_init(t); acb_init(u); acb_init(v); w = _acb_vec_init(len); acb_agm1_deriv(w, w + 1, z, prec); /* invert series */ acb_inv(w, w, prec); acb_mul(t, w, w, prec); acb_mul(w + 1, w + 1, t, prec); acb_neg(w + 1, w + 1); if (acb_is_one(z)) { for (k = 2; k < len; k++) { n = k - 2; acb_mul_ui(w + k, w + n + 0, (n+1)*(n+1), prec); acb_addmul_ui(w + k, w + n + 1, 7+3*n*(3+n), prec); acb_div_ui(w + k, w + k, 2*(n+2)*(n+2), prec); acb_neg(w + k, w + k); } } else { /* t = 3z^2 - 1 */ /* u = -1 / (z^3 - z) */ acb_mul(t, z, z, prec); acb_mul(u, t, z, prec); acb_mul_ui(t, t, 3, prec); acb_sub_ui(t, t, 1, prec); acb_sub(u, u, z, prec); acb_inv(u, u, prec); acb_neg(u, u); /* use differential equation for second derivative */ acb_mul(w + 2, z, w + 0, prec); acb_addmul(w + 2, t, w + 1, prec); acb_mul(w + 2, w + 2, u, prec); acb_mul_2exp_si(w + 2, w + 2, -1); /* recurrence */ for (k = 3; k < len; k++) { n = k - 3; acb_mul_ui(w + k, w + n + 0, (n+1)*(n+1), prec); acb_mul(v, w + n + 1, z, prec); acb_addmul_ui(w + k, v, 7+3*n*(3+n), prec); acb_mul(v, w + n + 2, t, prec); acb_addmul_ui(w + k, v, (n+2)*(n+2), prec); acb_mul(w + k, w + k, u, prec); acb_div_ui(w + k, w + k, (n+2)*(n+3), prec); } } /* invert series */ _acb_poly_inv_series(m, w, len, len, prec); acb_clear(t); acb_clear(u); acb_clear(v); _acb_vec_clear(w, len); } } arb-2.8.1/acb/arg.c000066400000000000000000000023001264125401100137170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_arg(arb_t r, const acb_t z, slong prec) { arb_atan2(r, acb_imagref(z), acb_realref(z), prec); } arb-2.8.1/acb/asin.c000066400000000000000000000035241264125401100141110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_asin(acb_t res, const acb_t z, slong prec) { if (arb_is_zero(acb_realref(z))) { arb_asinh(acb_imagref(res), acb_imagref(z), prec); arb_zero(acb_realref(res)); } else { acb_t t; acb_init(t); acb_mul(t, z, z, prec); acb_sub_ui(t, t, 1, prec); acb_neg(t, t); acb_sqrt(t, t, prec); if (acb_is_real(z) && acb_is_real(t)) { arb_atan2(acb_realref(res), acb_realref(z), acb_realref(t), prec); arb_zero(acb_imagref(res)); } else { acb_mul_onei(res, z); acb_add(res, res, t, prec); acb_log(res, res, prec); acb_div_onei(res, res); } acb_clear(t); } } arb-2.8.1/acb/asinh.c000066400000000000000000000023401264125401100142540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_asinh(acb_t res, const acb_t z, slong prec) { acb_mul_onei(res, z); acb_asin(res, res, prec); acb_div_onei(res, res); } arb-2.8.1/acb/atan.c000066400000000000000000000046401264125401100141020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" /* branch cuts are on (+/-i)*[1,inf] */ int acb_atan_on_branch_cut(const acb_t z) { arb_t unit; int result; if (!acb_is_finite(z)) return 1; if (arb_is_nonzero(acb_realref(z))) return 0; if (arb_contains_si(acb_imagref(z), 1) || arb_contains_si(acb_imagref(z), -1)) return 1; arb_init(unit); mag_one(arb_radref(unit)); result = !arb_contains(unit, acb_imagref(z)); arb_clear(unit); return result; } void acb_atan(acb_t r, const acb_t z, slong prec) { if (arb_is_zero(acb_imagref(z))) { arb_atan(acb_realref(r), acb_realref(z), prec); arb_zero(acb_imagref(r)); } else if (!acb_is_finite(z)) { acb_indeterminate(r); } else { acb_t t, u; acb_init(t); acb_init(u); if (acb_atan_on_branch_cut(z)) { acb_mul_onei(u, z); acb_neg(t, u); acb_log1p(t, t, prec); acb_log1p(u, u, prec); acb_sub(t, t, u, prec); } else { acb_onei(t); acb_sub(t, t, z, prec); acb_div(t, z, t, prec); acb_mul_2exp_si(t, t, 1); acb_log1p(t, t, prec); } acb_mul_onei(t, t); acb_mul_2exp_si(r, t, -1); acb_clear(t); acb_clear(u); } } arb-2.8.1/acb/atanh.c000066400000000000000000000023401264125401100142450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_atanh(acb_t res, const acb_t z, slong prec) { acb_mul_onei(res, z); acb_atan(res, res, prec); acb_div_onei(res, res); } arb-2.8.1/acb/barnes_g.c000066400000000000000000000067701264125401100147450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" #include "acb_poly.h" void _arb_const_zeta_minus_one_eval(arb_t y, slong prec) { acb_struct z[2]; acb_t s, a; acb_init(z + 0); acb_init(z + 1); acb_init(s); acb_init(a); acb_set_si(s, -1); acb_one(a); _acb_poly_zeta_cpx_series(z, s, a, 0, 2, prec + 20); arb_set(y, acb_realref(z + 1)); acb_clear(z + 0); acb_clear(z + 1); acb_clear(s); acb_clear(a); } ARB_DEF_CACHED_CONSTANT(_arb_const_zeta_minus_one, _arb_const_zeta_minus_one_eval) /* LogG(z) = (z-1) LogGamma(z) - zeta'(-1,z) + zeta'(-1) LogG'(z) = (1/2)(-2z + 1 + log(2pi)) + (z-1) digamma(z) */ void _acb_log_barnes_g_zeta(acb_t res, const acb_t z, slong prec) { acb_struct t[3]; acb_init(t + 0); acb_init(t + 1); acb_init(t + 2); acb_set_si(t + 2, -1); _acb_poly_zeta_cpx_series(t, t + 2, z, 0, 2, prec); _arb_const_zeta_minus_one(acb_realref(t), prec); arb_zero(acb_imagref(t)); acb_sub(t, t, t + 1, prec); acb_lgamma(t + 1, z, prec); acb_sub_ui(t + 2, z, 1, prec); acb_addmul(t, t + 1, t + 2, prec); acb_set(res, t); acb_clear(t + 0); acb_clear(t + 1); acb_clear(t + 2); } void _acb_barnes_g_ui_rec(acb_t res, ulong n, slong prec) { acb_t t; ulong k; acb_init(t); acb_one(res); acb_one(t); for (k = 3; k < n; k++) { acb_mul_ui(t, t, k - 1, prec); acb_mul(res, res, t, prec); } acb_clear(t); } void acb_log_barnes_g(acb_t res, const acb_t z, slong prec) { if (acb_is_int(z)) { if (arb_is_nonpositive(acb_realref(z))) { acb_indeterminate(res); return; } if (arf_cmpabs_ui(arb_midref(acb_realref(z)), prec) < 0) { _acb_barnes_g_ui_rec(res, arf_get_si(arb_midref(acb_realref(z)), ARF_RND_DOWN), prec); acb_log(res, res, prec); return; } } _acb_log_barnes_g_zeta(res, z, prec); } void acb_barnes_g(acb_t res, const acb_t z, slong prec) { if (acb_is_int(z)) { if (arb_is_nonpositive(acb_realref(z))) { acb_zero(res); return; } if (arf_cmpabs_ui(arb_midref(acb_realref(z)), prec) < 0) { _acb_barnes_g_ui_rec(res, arf_get_si(arb_midref(acb_realref(z)), ARF_RND_DOWN), prec); return; } } _acb_log_barnes_g_zeta(res, z, prec); acb_exp(res, res, prec); } arb-2.8.1/acb/chebyshev_t2_ui.c000066400000000000000000000036241264125401100162420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_chebyshev_t2_ui(acb_t a, acb_t b, ulong n, const acb_t x, slong prec) { int i; acb_set_round(a, x, prec); acb_one(b); if (n <= 1) { if (n == 0) acb_swap(a, b); return; } for (i = FLINT_BIT_COUNT(n - 1) - 1; i >= 0; i--) { if (((n - 1) >> i) & 1) { acb_mul(b, b, a, prec); acb_mul_2exp_si(b, b, 1); acb_sub(b, b, x, prec); acb_mul(a, a, a, prec); acb_mul_2exp_si(a, a, 1); acb_sub_ui(a, a, 1, prec); } else { acb_mul(a, a, b, prec); acb_mul_2exp_si(a, a, 1); acb_sub(a, a, x, prec); acb_mul(b, b, b, prec); acb_mul_2exp_si(b, b, 1); acb_sub_ui(b, b, 1, prec); } } } arb-2.8.1/acb/chebyshev_t_ui.c000066400000000000000000000037431264125401100161620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_chebyshev_t_ui(acb_t y, ulong n, const acb_t x, slong prec) { int i, r; if (n <= 1) { if (n == 0) acb_one(y); else acb_set_round(y, x, prec); return; } count_trailing_zeros(r, n); if ((n >> r) == 1) { acb_mul(y, x, x, prec); acb_mul_2exp_si(y, y, 1); acb_sub_ui(y, y, 1, prec); r -= 1; } else { /* we only need one value, so break out final iteration */ acb_t t, u; acb_init(t); acb_init(u); acb_chebyshev_t2_ui(t, u, (n >> (r + 1)) + 1, x, prec); acb_mul(t, t, u, prec); acb_mul_2exp_si(t, t, 1); acb_sub(y, t, x, prec); acb_clear(t); acb_clear(u); } for (i = 0; i < r; i++) { acb_mul(y, y, y, prec); acb_mul_2exp_si(y, y, 1); acb_sub_ui(y, y, 1, prec); } } arb-2.8.1/acb/chebyshev_u2_ui.c000066400000000000000000000037421264125401100162440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_chebyshev_u2_ui(acb_t a, acb_t b, ulong n, const acb_t x, slong prec) { int i; acb_t t, u; if (n == 0) { acb_one(a); acb_zero(b); return; } acb_set_round(a, x, prec); acb_mul_2exp_si(a, a, 1); acb_one(b); if (n == 1) return; acb_init(t); acb_init(u); for (i = FLINT_BIT_COUNT(n) - 2; i >= 0; i--) { acb_add(t, a, b, prec); acb_sub(u, a, b, prec); if ((n >> i) & 1) { acb_submul(b, x, a, prec); acb_mul(a, a, b, prec); acb_neg(a, a); acb_mul_2exp_si(a, a, 1); acb_mul(b, t, u, prec); } else { acb_submul(a, x, b, prec); acb_mul(b, a, b, prec); acb_mul_2exp_si(b, b, 1); acb_mul(a, t, u, prec); } } acb_clear(t); acb_clear(u); } arb-2.8.1/acb/chebyshev_u_ui.c000066400000000000000000000034211264125401100161540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_chebyshev_u_ui(acb_t y, ulong n, const acb_t x, slong prec) { acb_t a, b; if (n <= 1) { if (n == 0) { acb_one(y); } else { acb_set_round(y, x, prec); acb_mul_2exp_si(y, y, 1); } return; } acb_init(a); acb_init(b); acb_chebyshev_u2_ui(a, b, n / 2, x, prec); if (n % 2 == 0) { acb_add(y, a, b, prec); acb_sub(b, a, b, prec); acb_mul(y, y, b, prec); } else { acb_submul(b, a, x, prec); acb_mul(y, a, b, prec); acb_mul_2exp_si(y, y, 1); acb_neg(y, y); } acb_clear(a); acb_clear(b); } arb-2.8.1/acb/contains_int.c000066400000000000000000000023471264125401100156510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" int acb_contains_int(const acb_t x) { if (!arb_contains_zero(acb_imagref(x))) return 0; return arb_contains_int(acb_realref(x)); } arb-2.8.1/acb/cos.c000066400000000000000000000030661264125401100137440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_cos(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) arb_t sa, ca, sb, cb; arb_init(sa); arb_init(ca); arb_init(sb); arb_init(cb); arb_sin_cos(sa, ca, a, prec); arb_sinh_cosh(sb, cb, b, prec); arb_mul(acb_realref(r), ca, cb, prec); arb_mul(acb_imagref(r), sa, sb, prec); arb_neg(acb_imagref(r), acb_imagref(r)); arb_clear(sa); arb_clear(ca); arb_clear(sb); arb_clear(cb); } arb-2.8.1/acb/cos_pi.c000066400000000000000000000032121264125401100144250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_cos_pi(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) arb_t sa, ca, sb, cb; arb_init(sa); arb_init(ca); arb_init(sb); arb_init(cb); arb_sin_cos_pi(sa, ca, a, prec); arb_const_pi(cb, prec); arb_mul(cb, cb, b, prec); arb_sinh_cosh(sb, cb, cb, prec); arb_mul(acb_realref(r), ca, cb, prec); arb_mul(acb_imagref(r), sa, sb, prec); arb_neg(acb_imagref(r), acb_imagref(r)); arb_clear(sa); arb_clear(ca); arb_clear(sb); arb_clear(cb); #undef a #undef b } arb-2.8.1/acb/cot.c000066400000000000000000000047311264125401100137450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_cot(acb_t r, const acb_t z, slong prec) { if (arb_is_zero(acb_imagref(z))) { arb_cot(acb_realref(r), acb_realref(z), prec); arb_zero(acb_imagref(r)); } else if (arb_is_zero(acb_realref(z))) { arb_coth(acb_imagref(r), acb_imagref(z), prec); arb_neg(acb_imagref(r), acb_imagref(r)); arb_zero(acb_realref(r)); } else { acb_t t; acb_init(t); if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0) { acb_sin_cos(r, t, z, prec + 4); acb_div(r, t, r, prec); } else { acb_mul_2exp_si(t, z, 1); if (arf_sgn(arb_midref(acb_imagref(z))) > 0) { acb_mul_onei(t, t); acb_exp(t, t, prec + 4); acb_sub_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_mul_onei(r, r); } else { acb_div_onei(t, t); acb_exp(t, t, prec + 4); acb_sub_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_div_onei(r, r); } } acb_clear(t); } } arb-2.8.1/acb/cot_pi.c000066400000000000000000000051061264125401100144320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_cot_pi(acb_t r, const acb_t z, slong prec) { if (arb_is_zero(acb_imagref(z))) { arb_cot_pi(acb_realref(r), acb_realref(z), prec); arb_zero(acb_imagref(r)); } else if (arb_is_zero(acb_realref(z))) { arb_t t; arb_init(t); arb_const_pi(t, prec + 4); arb_mul(t, acb_imagref(z), t, prec + 4); arb_coth(acb_imagref(r), t, prec); arb_neg(acb_imagref(r), acb_imagref(r)); arb_zero(acb_realref(r)); arb_clear(t); } else { acb_t t; acb_init(t); if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0) { acb_sin_cos_pi(r, t, z, prec + 4); acb_div(r, t, r, prec); } else { acb_mul_2exp_si(t, z, 1); if (arf_sgn(arb_midref(acb_imagref(z))) > 0) { acb_exp_pi_i(t, t, prec + 4); acb_sub_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_mul_onei(r, r); } else { acb_neg(t, t); acb_exp_pi_i(t, t, prec + 4); acb_sub_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_div_onei(r, r); } } acb_clear(t); } } arb-2.8.1/acb/cube.c000066400000000000000000000037631264125401100141020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_cube(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) if (arb_is_zero(b)) { arb_pow_ui(acb_realref(r), a, 3, prec); arb_zero(acb_imagref(r)); } else if (arb_is_zero(a)) { arb_pow_ui(acb_imagref(r), b, 3, prec); arb_neg(acb_imagref(r), acb_imagref(r)); arb_zero(acb_realref(r)); } else { arb_t t, u, v; arb_init(t); arb_init(u); arb_init(v); arb_mul(t, a, a, prec); arb_mul(u, b, b, prec); arb_set(v, t); /* t = a^2 - 3b^2 */ arb_submul_ui(t, u, 3, prec); /* u = -(b^2 - 3a^2) */ arb_submul_ui(u, v, 3, prec); arb_neg(u, u); arb_mul(acb_realref(r), t, a, prec); arb_mul(acb_imagref(r), u, b, prec); arb_clear(t); arb_clear(u); arb_clear(v); } #undef a #undef b } arb-2.8.1/acb/digamma.c000066400000000000000000000046751264125401100145660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const acb_t x, int use_reflect, int digamma, slong prec); void acb_gamma_stirling_eval(acb_t s, const acb_t z, slong nterms, int digamma, slong prec); void acb_digamma(acb_t y, const acb_t x, slong prec) { int reflect; slong r, n, wp; acb_t t, u, v; if (acb_is_real(x)) { arb_digamma(acb_realref(y), acb_realref(x), prec); arb_zero(acb_imagref(y)); return; } wp = prec + FLINT_BIT_COUNT(prec); acb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 1, wp); acb_init(t); acb_init(u); acb_init(v); /* psi(x) = psi((1-x)+r) - h(1-x,r) - pi*cot(pi*x) */ if (reflect) { acb_sub_ui(t, x, 1, wp); acb_neg(t, t); acb_cot_pi(v, x, wp); arb_const_pi(acb_realref(u), wp); acb_mul_arb(v, v, acb_realref(u), wp); acb_rising2_ui(y, u, t, r, wp); acb_div(u, u, y, wp); acb_add(v, v, u, wp); acb_add_ui(t, t, r, wp); acb_gamma_stirling_eval(u, t, n, 1, wp); acb_sub(y, u, v, wp); } else { acb_add_ui(t, x, r, wp); acb_gamma_stirling_eval(u, t, n, 1, wp); acb_rising2_ui(y, t, x, r, wp); acb_div(t, t, y, wp); acb_sub(y, u, t, prec); } acb_clear(t); acb_clear(u); acb_clear(v); } arb-2.8.1/acb/div.c000066400000000000000000000072161264125401100137430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_div(acb_t z, const acb_t x, const acb_t y, slong prec) { #define a acb_realref(x) #define b acb_imagref(x) #define c acb_realref(y) #define d acb_imagref(y) if (arb_is_zero(d)) { if (arb_is_zero(b)) { arb_div(acb_realref(z), a, c, prec); arb_zero(acb_imagref(z)); } else if (arb_is_zero(a)) { arb_div(acb_imagref(z), b, c, prec); arb_zero(acb_realref(z)); } else if (z != y) { arb_div(acb_realref(z), a, c, prec); arb_div(acb_imagref(z), b, c, prec); } else { arb_t t; arb_init(t); arb_set(t, c); arb_div(acb_realref(z), a, t, prec); arb_div(acb_imagref(z), b, t, prec); arb_clear(t); } } else if (arb_is_zero(c)) { if (arb_is_zero(b)) { arb_div(acb_imagref(z), a, d, prec); arb_neg(acb_imagref(z), acb_imagref(z)); arb_zero(acb_realref(z)); } else if (arb_is_zero(a)) { arb_div(acb_realref(z), b, d, prec); arb_zero(acb_imagref(z)); } else if (z != y) { arb_div(acb_realref(z), a, d, prec); arb_div(acb_imagref(z), b, d, prec); arb_swap(acb_realref(z), acb_imagref(z)); arb_neg(acb_imagref(z), acb_imagref(z)); } else { arb_t t; arb_init(t); arb_set(t, d); arb_div(acb_realref(z), a, t, prec); arb_div(acb_imagref(z), b, t, prec); arb_swap(acb_realref(z), acb_imagref(z)); arb_neg(acb_imagref(z), acb_imagref(z)); arb_clear(t); } } else { if (prec > 256 && acb_bits(y) <= prec / 2) { arb_t t, u, v; arb_init(t); arb_init(u); arb_init(v); arb_mul(t, c, c, prec); arb_addmul(t, d, d, prec); arb_mul(u, a, c, prec); arb_addmul(u, b, d, prec); arb_mul(v, b, c, prec); arb_submul(v, a, d, prec); arb_div(acb_realref(z), u, t, prec); arb_div(acb_imagref(z), v, t, prec); arb_clear(t); arb_clear(u); arb_clear(v); } else { acb_t t; acb_init(t); acb_inv(t, y, prec); acb_mul(z, x, t, prec); acb_clear(t); } } #undef a #undef b #undef c #undef d } arb-2.8.1/acb/exp.c000066400000000000000000000033571264125401100137570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_exp(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) if (arb_is_zero(b)) { arb_exp(acb_realref(r), a, prec); arb_zero(acb_imagref(r)); } else if (arb_is_zero(a)) { arb_sin_cos(acb_imagref(r), acb_realref(r), b, prec); } else { arb_t t, u, v; arb_init(t); arb_init(u); arb_init(v); arb_exp(t, a, prec); arb_sin_cos(u, v, b, prec); arb_mul(acb_realref(r), t, v, prec); arb_mul(acb_imagref(r), t, u, prec); arb_clear(t); arb_clear(u); arb_clear(v); } #undef a #undef b } arb-2.8.1/acb/exp_invexp.c000066400000000000000000000040241264125401100153400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_exp_invexp(acb_t r, acb_t s, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) if (arb_is_zero(b)) { arb_exp_invexp(acb_realref(r), acb_realref(s), a, prec); arb_zero(acb_imagref(r)); arb_zero(acb_imagref(s)); } else if (arb_is_zero(a)) { arb_sin_cos(acb_imagref(r), acb_realref(r), b, prec); acb_conj(s, r); } else { arb_t t, u, v, w; arb_init(t); arb_init(u); arb_init(v); arb_init(w); arb_exp_invexp(t, u, a, prec); arb_sin_cos(v, w, b, prec); arb_mul(acb_realref(r), t, w, prec); arb_mul(acb_imagref(r), t, v, prec); arb_mul(acb_realref(s), u, w, prec); arb_mul(acb_imagref(s), u, v, prec); arb_neg(acb_imagref(s), acb_imagref(s)); arb_clear(t); arb_clear(u); arb_clear(v); arb_clear(w); } #undef a #undef b } arb-2.8.1/acb/exp_pi_i.c000066400000000000000000000037651264125401100147620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_exp_pi_i(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) if (arb_is_zero(b)) { arb_sin_cos_pi(acb_imagref(r), acb_realref(r), a, prec); } else if (arb_is_zero(a)) { arb_const_pi(acb_realref(r), prec); arb_mul(acb_realref(r), acb_realref(r), b, prec); arb_neg(acb_realref(r), acb_realref(r)); arb_exp(acb_realref(r), acb_realref(r), prec); arb_zero(acb_imagref(r)); } else { arb_t t, u, v; arb_init(t); arb_init(u); arb_init(v); arb_const_pi(t, prec); arb_mul(t, t, b, prec); arb_neg(t, t); arb_exp(t, t, prec); arb_sin_cos_pi(u, v, a, prec); arb_mul(acb_realref(r), t, v, prec); arb_mul(acb_imagref(r), t, u, prec); arb_clear(t); arb_clear(u); arb_clear(v); } #undef a #undef b } arb-2.8.1/acb/gamma.c000066400000000000000000000176651264125401100142540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" #include "acb.h" void acb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const acb_t z, int use_reflect, int digamma, slong prec); void acb_gamma_stirling_bound(mag_ptr err, const acb_t z, slong k0, slong knum, slong n); void arb_gamma_stirling_coeff(arb_t b, ulong k, int digamma, slong prec); void acb_gamma_stirling_eval(acb_t s, const acb_t z, slong nterms, int digamma, slong prec) { acb_t t, logz, zinv, zinv2; arb_t b; mag_t err; slong k, term_prec; double z_mag, term_mag; acb_init(t); acb_init(logz); acb_init(zinv); acb_init(zinv2); arb_init(b); acb_log(logz, z, prec); acb_inv(zinv, z, prec); nterms = FLINT_MAX(nterms, 1); acb_zero(s); if (nterms > 1) { acb_mul(zinv2, zinv, zinv, prec); z_mag = arf_get_d(arb_midref(acb_realref(logz)), ARF_RND_UP) * 1.44269504088896; for (k = nterms - 1; k >= 1; k--) { term_mag = bernoulli_bound_2exp_si(2 * k); term_mag -= (2 * k - 1) * z_mag; term_prec = prec + term_mag; term_prec = FLINT_MIN(term_prec, prec); term_prec = FLINT_MAX(term_prec, 10); arb_gamma_stirling_coeff(b, k, digamma, term_prec); if (prec > 2000) { acb_set_round(t, zinv2, term_prec); acb_mul(s, s, t, term_prec); } else acb_mul(s, s, zinv2, term_prec); arb_add(acb_realref(s), acb_realref(s), b, term_prec); } if (digamma) acb_mul(s, s, zinv2, prec); else acb_mul(s, s, zinv, prec); } /* remainder bound */ mag_init(err); acb_gamma_stirling_bound(err, z, digamma ? 1 : 0, 1, nterms); mag_add(arb_radref(acb_realref(s)), arb_radref(acb_realref(s)), err); mag_add(arb_radref(acb_imagref(s)), arb_radref(acb_imagref(s)), err); mag_clear(err); if (digamma) { acb_neg(s, s); acb_mul_2exp_si(zinv, zinv, -1); acb_sub(s, s, zinv, prec); acb_add(s, s, logz, prec); } else { /* (z-0.5)*log(z) - z + log(2*pi)/2 */ arb_one(b); arb_mul_2exp_si(b, b, -1); arb_set(acb_imagref(t), acb_imagref(z)); arb_sub(acb_realref(t), acb_realref(z), b, prec); acb_mul(t, logz, t, prec); acb_add(s, s, t, prec); acb_sub(s, s, z, prec); arb_const_log_sqrt2pi(b, prec); arb_add(acb_realref(s), acb_realref(s), b, prec); } acb_clear(t); acb_clear(logz); acb_clear(zinv); acb_clear(zinv2); arb_clear(b); } static void _acb_gamma(acb_t y, const acb_t x, slong prec, int inverse) { int reflect; slong r, n, wp; acb_t t, u, v; wp = prec + FLINT_BIT_COUNT(prec); acb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 0, wp); acb_init(t); acb_init(u); acb_init(v); if (reflect) { /* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */ acb_sub_ui(t, x, 1, wp); acb_neg(t, t); acb_rising_ui_rec(u, t, r, wp); arb_const_pi(acb_realref(v), wp); acb_mul_arb(u, u, acb_realref(v), wp); acb_add_ui(t, t, r, wp); acb_gamma_stirling_eval(v, t, n, 0, wp); acb_exp(v, v, wp); acb_sin_pi(t, x, wp); acb_mul(v, v, t, wp); } else { /* gamma(x) = gamma(x+r) / rf(x,r) */ acb_add_ui(t, x, r, wp); acb_gamma_stirling_eval(u, t, n, 0, wp); acb_exp(u, u, prec); acb_rising_ui_rec(v, x, r, wp); } if (inverse) acb_div(y, v, u, prec); else acb_div(y, u, v, prec); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_gamma(acb_t y, const acb_t x, slong prec) { if (acb_is_real(x)) { arb_gamma(acb_realref(y), acb_realref(x), prec); arb_zero(acb_imagref(y)); return; } _acb_gamma(y, x, prec, 0); } void acb_rgamma(acb_t y, const acb_t x, slong prec) { if (acb_is_real(x)) { arb_rgamma(acb_realref(y), acb_realref(x), prec); arb_zero(acb_imagref(y)); return; } _acb_gamma(y, x, prec, 1); } /* corrects branch cut of sum_{k=0}^{r-1} log(z+k), given the logarithm of the product */ void _acb_log_rising_correct_branch(acb_t t, const acb_t t_wrong, const acb_t z, ulong r, slong prec) { acb_t f; arb_t pi, u, v; fmpz_t pi_mult; slong i, argprec; acb_init(f); arb_init(u); arb_init(pi); arb_init(v); fmpz_init(pi_mult); argprec = FLINT_MIN(prec, 40); arb_zero(u); for (i = 0; i < r; i++) { acb_add_ui(f, z, i, argprec); acb_arg(v, f, argprec); arb_add(u, u, v, argprec); } if (argprec == prec) { arb_set(acb_imagref(t), u); } else { arb_sub(v, u, acb_imagref(t), argprec); arb_const_pi(pi, argprec); arb_div(v, v, pi, argprec); if (arb_get_unique_fmpz(pi_mult, v)) { arb_const_pi(v, prec); arb_mul_fmpz(v, v, pi_mult, prec); arb_add(acb_imagref(t), acb_imagref(t), v, prec); } else { arb_zero(u); for (i = 0; i < r; i++) { acb_add_ui(f, z, i, prec); acb_arg(v, f, prec); arb_add(u, u, v, prec); } arb_set(acb_imagref(t), u); } } acb_clear(f); arb_clear(u); arb_clear(v); arb_clear(pi); fmpz_clear(pi_mult); } void acb_lgamma(acb_t y, const acb_t x, slong prec) { int reflect; slong r, n, wp; acb_t t, u, v; if (acb_is_real(x) && arb_is_positive(acb_realref(x))) { arb_lgamma(acb_realref(y), acb_realref(x), prec); arb_zero(acb_imagref(y)); return; } wp = prec + FLINT_BIT_COUNT(prec); acb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 0, wp); acb_init(t); acb_init(u); acb_init(v); if (reflect) { /* log gamma(x) = log rf(1-x, r) - log gamma(1-x+r) - log sin(pi x) + log(pi) */ acb_sub_ui(u, x, 1, wp); acb_neg(u, u); acb_rising_ui_rec(t, u, r, prec); acb_log(t, t, wp); _acb_log_rising_correct_branch(t, t, u, r, wp); acb_add_ui(u, u, r, wp); acb_gamma_stirling_eval(v, u, n, 0, wp); acb_sub(t, t, v, wp); acb_log_sin_pi(u, x, wp); acb_sub(t, t, u, wp); acb_const_pi(u, wp); acb_log(u, u, wp); acb_add(y, t, u, wp); } else { /* log gamma(x) = log gamma(x+r) - log rf(x,r) */ acb_add_ui(t, x, r, wp); acb_gamma_stirling_eval(u, t, n, 0, wp); acb_rising_ui_rec(t, x, r, prec); acb_log(t, t, wp); _acb_log_rising_correct_branch(t, t, x, r, wp); acb_sub(y, u, t, prec); } acb_clear(t); acb_clear(u); acb_clear(v); } arb-2.8.1/acb/get_mag.c000066400000000000000000000030521264125401100145560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_get_mag(mag_t u, const acb_t z) { if (arb_is_zero(acb_imagref(z))) { arb_get_mag(u, acb_realref(z)); } else if (arb_is_zero(acb_realref(z))) { arb_get_mag(u, acb_imagref(z)); } else { mag_t v; mag_init(v); arb_get_mag(u, acb_realref(z)); arb_get_mag(v, acb_imagref(z)); mag_mul(u, u, u); mag_addmul(u, v, v); mag_sqrt(u, u); mag_clear(v); } } arb-2.8.1/acb/get_mag_lower.c000066400000000000000000000023771264125401100157770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_get_mag_lower(mag_t z, const acb_t x) { arf_t t; arf_init(t); acb_get_abs_lbound_arf(t, x, MAG_BITS); arf_get_mag_lower(z, t); arf_clear(t); } arb-2.8.1/acb/get_unique_fmpz.c000066400000000000000000000023721264125401100163600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int acb_get_unique_fmpz(fmpz_t z, const acb_t x) { if (!arb_contains_zero(acb_imagref(x))) return 0; return arb_get_unique_fmpz(z, acb_realref(x)); } arb-2.8.1/acb/inlines.c000066400000000000000000000021501264125401100146120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define ACB_INLINES_C #include "acb.h" arb-2.8.1/acb/inv.c000066400000000000000000000033111264125401100137450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_inv(acb_t z, const acb_t x, slong prec) { #define a acb_realref(x) #define b acb_imagref(x) #define c acb_realref(z) #define d acb_imagref(z) if (arb_is_zero(b)) { arb_inv(c, a, prec); arb_zero(d); } else if (arb_is_zero(a)) { arb_inv(d, b, prec); arb_neg(d, d); arb_zero(c); } else { arb_t t; arb_init(t); arb_mul(t, a, a, prec); arb_addmul(t, b, b, prec); arb_div(c, a, t, prec); arb_div(d, b, t, prec); arb_neg(d, d); arb_clear(t); } #undef a #undef b #undef c #undef d } arb-2.8.1/acb/log.c000066400000000000000000000072571264125401100137470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" static int close_to_one(const acb_t z) { mp_limb_t top; if (arf_abs_bound_lt_2exp_si(arb_midref(acb_imagref(z))) > -3) return 0; if (ARF_EXP(arb_midref(acb_realref(z))) == 0) { ARF_GET_TOP_LIMB(top, arb_midref(acb_realref(z))); return (top >> (FLINT_BITS - 4)) == 15; } else if (ARF_EXP(arb_midref(acb_realref(z))) == 1) { ARF_GET_TOP_LIMB(top, arb_midref(acb_realref(z))); return (top >> (FLINT_BITS - 4)) == 8; } return 0; } void acb_log(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) if (arb_is_zero(b)) { if (arb_is_positive(a)) { arb_log(acb_realref(r), a, prec); arb_zero(acb_imagref(r)); } else if (arb_is_negative(a)) { arb_neg(acb_realref(r), a); arb_log(acb_realref(r), acb_realref(r), prec); arb_const_pi(acb_imagref(r), prec); } else { acb_indeterminate(r); } } else if (arb_is_zero(a)) { if (arb_is_positive(b)) { arb_log(acb_realref(r), b, prec); arb_const_pi(acb_imagref(r), prec); arb_mul_2exp_si(acb_imagref(r), acb_imagref(r), -1); } else if (arb_is_negative(b)) { arb_neg(acb_realref(r), b); arb_log(acb_realref(r), acb_realref(r), prec); arb_const_pi(acb_imagref(r), prec); arb_mul_2exp_si(acb_imagref(r), acb_imagref(r), -1); arb_neg(acb_imagref(r), acb_imagref(r)); } else { acb_indeterminate(r); } } else { arb_t t, u; arb_init(t); arb_init(u); if (close_to_one(z)) { arb_sub_ui(u, a, 1, prec + 8); arb_mul(t, u, u, prec + 8); arb_addmul(t, b, b, prec + 8); arb_mul_2exp_si(u, u, 1); arb_add(t, t, u, prec + 8); arb_log1p(t, t, prec); arb_mul_2exp_si(t, t, -1); } else { arb_mul(t, a, a, prec + 8); arb_addmul(t, b, b, prec + 8); if (arb_contains_zero(t) || arf_sgn(arb_midref(t)) < 0) arb_zero_pm_inf(t); else arb_log(t, t, prec); arb_mul_2exp_si(t, t, -1); } acb_arg(u, z, prec); arb_swap(acb_realref(r), t); arb_swap(acb_imagref(r), u); arb_clear(t); arb_clear(u); } if (!acb_is_finite(r)) acb_indeterminate(r); #undef a #undef b } arb-2.8.1/acb/log1p.c000066400000000000000000000044231264125401100142000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" static void acb_log1p_tiny(acb_t r, const acb_t z, slong prec) { mag_t b, c; acb_t t; int real; mag_init(b); mag_init(c); acb_init(t); real = acb_is_real(z); /* if |z| < 1, then |log(1+z) - [z - z^2/2]| <= |z|^3/(1-|z|) */ acb_get_mag(b, z); mag_one(c); mag_sub_lower(c, c, b); mag_pow_ui(b, b, 3); mag_div(b, b, c); acb_mul(t, z, z, prec); acb_mul_2exp_si(t, t, -1); acb_sub(r, z, t, prec); if (real && mag_is_finite(b)) arb_add_error_mag(acb_realref(r), b); else acb_add_error_mag(r, b); mag_clear(b); mag_clear(c); acb_clear(t); } void acb_log1p(acb_t r, const acb_t z, slong prec) { slong magz, magx, magy; if (acb_is_zero(z)) { acb_zero(r); return; } magx = arf_abs_bound_lt_2exp_si(arb_midref(acb_realref(z))); magy = arf_abs_bound_lt_2exp_si(arb_midref(acb_imagref(z))); magz = FLINT_MAX(magx, magy); if (magz < -prec) { acb_log1p_tiny(r, z, prec); } else { if (magz < 0) acb_add_ui(r, z, 1, prec + (-magz) + 4); else acb_add_ui(r, z, 1, prec + 4); acb_log(r, r, prec); } } arb-2.8.1/acb/log_sin_pi.c000066400000000000000000000074611264125401100153050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" static void acb_log_sin_pi_half(acb_t res, const acb_t z, slong prec, int upper) { acb_t t, u, zmid; arf_t n; arb_t pi; acb_init(t); acb_init(u); acb_init(zmid); arf_init(n); arb_init(pi); arf_set(arb_midref(acb_realref(zmid)), arb_midref(acb_realref(z))); arf_set(arb_midref(acb_imagref(zmid)), arb_midref(acb_imagref(z))); arf_floor(n, arb_midref(acb_realref(zmid))); arb_sub_arf(acb_realref(zmid), acb_realref(zmid), n, prec); arb_const_pi(pi, prec); if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(zmid)), 2) < 1) { acb_sin_pi(t, zmid, prec); acb_log(t, t, prec); } else /* i*pi*(z-0.5) + log((1-exp(-2i*pi*z))/2) */ { acb_mul_2exp_si(t, zmid, 1); acb_neg(t, t); if (upper) acb_conj(t, t); acb_exp_pi_i(t, t, prec); acb_sub_ui(t, t, 1, prec); acb_neg(t, t); acb_mul_2exp_si(t, t, -1); acb_log(t, t, prec); acb_one(u); acb_mul_2exp_si(u, u, -1); acb_sub(u, zmid, u, prec); if (upper) acb_conj(u, u); acb_mul_onei(u, u); acb_addmul_arb(t, u, pi, prec); if (upper) acb_conj(t, t); } if (upper) arb_submul_arf(acb_imagref(t), pi, n, prec); else arb_addmul_arf(acb_imagref(t), pi, n, prec); /* propagated error bound from the derivative pi cot(pi z) */ if (!acb_is_exact(z)) { mag_t zm, um; mag_init(zm); mag_init(um); acb_cot_pi(u, z, prec); acb_mul_arb(u, u, pi, prec); mag_hypot(zm, arb_radref(acb_realref(z)), arb_radref(acb_imagref(z))); acb_get_mag(um, u); mag_mul(um, um, zm); acb_add_error_mag(t, um); mag_clear(zm); mag_clear(um); } acb_set(res, t); acb_clear(t); acb_clear(u); acb_clear(zmid); arf_clear(n); arb_clear(pi); } void acb_log_sin_pi(acb_t res, const acb_t z, slong prec) { if (!acb_is_finite(z)) { acb_indeterminate(res); return; } if (arb_is_positive(acb_imagref(z)) || (arb_is_zero(acb_imagref(z)) && arb_is_negative(acb_realref(z)))) { acb_log_sin_pi_half(res, z, prec, 1); } else if (arb_is_negative(acb_imagref(z)) || (arb_is_zero(acb_imagref(z)) && arb_is_positive(acb_realref(z)))) { acb_log_sin_pi_half(res, z, prec, 0); } else { acb_t t; acb_init(t); acb_log_sin_pi_half(t, z, prec, 1); acb_log_sin_pi_half(res, z, prec, 0); arb_union(acb_realref(res), acb_realref(res), acb_realref(t), prec); arb_union(acb_imagref(res), acb_imagref(res), acb_imagref(t), prec); acb_clear(t); } } arb-2.8.1/acb/mul.c000066400000000000000000000151311264125401100137510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" #define a acb_realref(x) #define b acb_imagref(x) #define c acb_realref(y) #define d acb_imagref(y) #define e acb_realref(z) #define f acb_imagref(z) #define ar arb_radref(a) #define br arb_radref(b) #define cr arb_radref(c) #define dr arb_radref(d) static void _acb_sqr_fast(acb_t z, const acb_t x, slong prec) { int inexact; mag_t am, bm, er, fr; mag_fast_init_set_arf(am, arb_midref(a)); mag_fast_init_set_arf(bm, arb_midref(b)); mag_init(er); mag_init(fr); mag_fast_addmul(er, am, ar); mag_fast_addmul(er, bm, br); mag_fast_mul_2exp_si(er, er, 1); mag_fast_addmul(er, ar, ar); mag_fast_addmul(er, br, br); mag_fast_addmul(fr, bm, ar); mag_fast_addmul(fr, am, br); mag_fast_addmul(fr, ar, br); mag_fast_mul_2exp_si(fr, fr, 1); inexact = arf_complex_sqr(arb_midref(e), arb_midref(f), arb_midref(a), arb_midref(b), prec, ARB_RND); if (inexact & 1) arf_mag_add_ulp(arb_radref(e), er, arb_midref(e), prec); else mag_set(arb_radref(e), er); if (inexact & 2) arf_mag_add_ulp(arb_radref(f), fr, arb_midref(f), prec); else mag_set(arb_radref(f), fr); } static void _acb_sqr_slow(acb_t z, const acb_t x, slong prec) { int inexact; mag_t am, bm, er, fr; mag_init_set_arf(am, arb_midref(a)); mag_init_set_arf(bm, arb_midref(b)); mag_init(er); mag_init(fr); mag_addmul(er, am, ar); mag_addmul(er, bm, br); mag_mul_2exp_si(er, er, 1); mag_addmul(er, ar, ar); mag_addmul(er, br, br); mag_addmul(fr, bm, ar); mag_addmul(fr, am, br); mag_addmul(fr, ar, br); mag_mul_2exp_si(fr, fr, 1); inexact = arf_complex_sqr(arb_midref(e), arb_midref(f), arb_midref(a), arb_midref(b), prec, ARB_RND); if (inexact & 1) arf_mag_add_ulp(arb_radref(e), er, arb_midref(e), prec); else mag_swap(arb_radref(e), er); if (inexact & 2) arf_mag_add_ulp(arb_radref(f), fr, arb_midref(f), prec); else mag_swap(arb_radref(f), fr); mag_clear(am); mag_clear(bm); mag_clear(er); mag_clear(fr); } static void _acb_mul_fast(acb_t z, const acb_t x, const acb_t y, slong prec) { int inexact; mag_t am, bm, cm, dm, er, fr; mag_fast_init_set_arf(am, arb_midref(a)); mag_fast_init_set_arf(bm, arb_midref(b)); mag_fast_init_set_arf(cm, arb_midref(c)); mag_fast_init_set_arf(dm, arb_midref(d)); mag_init(er); mag_init(fr); mag_fast_addmul(er, am, cr); mag_fast_addmul(er, bm, dr); mag_fast_addmul(er, cm, ar); mag_fast_addmul(er, dm, br); mag_fast_addmul(er, ar, cr); mag_fast_addmul(er, br, dr); mag_fast_addmul(fr, am, dr); mag_fast_addmul(fr, bm, cr); mag_fast_addmul(fr, cm, br); mag_fast_addmul(fr, dm, ar); mag_fast_addmul(fr, br, cr); mag_fast_addmul(fr, ar, dr); inexact = arf_complex_mul(arb_midref(e), arb_midref(f), arb_midref(a), arb_midref(b), arb_midref(c), arb_midref(d), prec, ARB_RND); if (inexact & 1) arf_mag_add_ulp(arb_radref(e), er, arb_midref(e), prec); else mag_set(arb_radref(e), er); if (inexact & 2) arf_mag_add_ulp(arb_radref(f), fr, arb_midref(f), prec); else mag_set(arb_radref(f), fr); } static void _acb_mul_slow(acb_t z, const acb_t x, const acb_t y, slong prec) { int inexact; mag_t am, bm, cm, dm, er, fr; mag_init_set_arf(am, arb_midref(a)); mag_init_set_arf(bm, arb_midref(b)); mag_init_set_arf(cm, arb_midref(c)); mag_init_set_arf(dm, arb_midref(d)); mag_init(er); mag_init(fr); mag_addmul(er, am, cr); mag_addmul(er, bm, dr); mag_addmul(er, cm, ar); mag_addmul(er, dm, br); mag_addmul(er, ar, cr); mag_addmul(er, br, dr); mag_addmul(fr, am, dr); mag_addmul(fr, bm, cr); mag_addmul(fr, cm, br); mag_addmul(fr, dm, ar); mag_addmul(fr, br, cr); mag_addmul(fr, ar, dr); inexact = arf_complex_mul(arb_midref(e), arb_midref(f), arb_midref(a), arb_midref(b), arb_midref(c), arb_midref(d), prec, ARB_RND); if (inexact & 1) arf_mag_add_ulp(arb_radref(e), er, arb_midref(e), prec); else mag_swap(arb_radref(e), er); if (inexact & 2) arf_mag_add_ulp(arb_radref(f), fr, arb_midref(f), prec); else mag_swap(arb_radref(f), fr); mag_clear(am); mag_clear(bm); mag_clear(cm); mag_clear(dm); mag_clear(er); mag_clear(fr); } void acb_mul(acb_t z, const acb_t x, const acb_t y, slong prec) { if (arb_is_zero(b)) { arb_mul(f, d, a, prec); arb_mul(e, c, a, prec); } else if (arb_is_zero(d)) { arb_mul(f, b, c, prec); arb_mul(e, a, c, prec); } else if (arb_is_zero(a)) { arb_mul(e, c, b, prec); arb_mul(f, d, b, prec); acb_mul_onei(z, z); } else if (arb_is_zero(c)) { arb_mul(e, a, d, prec); arb_mul(f, b, d, prec); acb_mul_onei(z, z); } /* squaring = a^2-b^2, 2ab */ else if (x == y) { if (ARB_IS_LAGOM(a) && ARB_IS_LAGOM(b)) _acb_sqr_fast(z, x, prec); else _acb_sqr_slow(z, x, prec); } else { if (ARB_IS_LAGOM(a) && ARB_IS_LAGOM(b) && ARB_IS_LAGOM(c) && ARB_IS_LAGOM(d)) _acb_mul_fast(z, x, y, prec); else _acb_mul_slow(z, x, y, prec); } } #undef a #undef b #undef c #undef d #undef e #undef f #undef ar #undef br #undef cr #undef dr arb-2.8.1/acb/mul_naive.c000066400000000000000000000070611264125401100151360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_mul_naive(acb_t z, const acb_t x, const acb_t y, slong prec) { #define a acb_realref(x) #define b acb_imagref(x) #define c acb_realref(y) #define d acb_imagref(y) #define e acb_realref(z) #define f acb_imagref(z) if (arb_is_zero(b)) { arb_mul(f, d, a, prec); arb_mul(e, c, a, prec); } else if (arb_is_zero(d)) { arb_mul(f, b, c, prec); arb_mul(e, a, c, prec); } else if (arb_is_zero(a)) { arb_mul(e, c, b, prec); arb_mul(f, d, b, prec); acb_mul_onei(z, z); } else if (arb_is_zero(c)) { arb_mul(e, a, d, prec); arb_mul(f, b, d, prec); acb_mul_onei(z, z); } /* squaring = a^2-b^2, 2ab */ else if (x == y) { /* aliasing */ if (z == x) { arb_t t; arb_init(t); arb_mul(t, a, b, prec); arb_mul_2exp_si(t, t, 1); arb_mul(e, a, a, prec); arb_mul(f, b, b, prec); arb_sub(e, e, f, prec); arb_swap(f, t); arb_clear(t); } else { arb_mul(e, a, a, prec); arb_mul(f, b, b, prec); arb_sub(e, e, f, prec); arb_mul(f, a, b, prec); arb_mul_2exp_si(f, f, 1); } } else { /* aliasing */ if (z == x) { arb_t t, u; arb_init(t); arb_init(u); arb_mul(t, a, c, prec); arb_mul(u, a, d, prec); arb_mul(e, b, d, prec); arb_sub(e, t, e, prec); arb_mul(f, b, c, prec); arb_add(f, u, f, prec); arb_clear(t); arb_clear(u); } else if (z == y) { arb_t t, u; arb_init(t); arb_init(u); arb_mul(t, a, c, prec); arb_mul(u, b, c, prec); arb_mul(e, b, d, prec); arb_sub(e, t, e, prec); arb_mul(f, a, d, prec); arb_add(f, u, f, prec); arb_clear(t); arb_clear(u); } else { arb_t t; arb_init(t); arb_mul(e, a, c, prec); arb_mul(t, b, d, prec); arb_sub(e, e, t, prec); arb_mul(f, a, d, prec); arb_mul(t, b, c, prec); arb_add(f, f, t, prec); arb_clear(t); } } #undef a #undef b #undef c #undef d #undef e #undef f } arb-2.8.1/acb/polygamma.c000066400000000000000000000045121264125401100151430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" #include "acb_poly.h" void acb_polygamma(acb_t res, const acb_t s, const acb_t z, slong prec) { if (acb_is_zero(s)) { acb_digamma(res, z, prec); } else if (acb_is_int(s) && arb_is_positive(acb_realref(s))) { acb_t t, u; acb_init(t); acb_init(u); acb_add_ui(t, s, 1, prec); acb_gamma(u, t, prec); acb_hurwitz_zeta(t, t, z, prec); if (arf_is_int_2exp_si(arb_midref(acb_realref(s)), 1)) acb_neg(t, t); acb_mul(res, t, u, prec); acb_clear(t); acb_clear(u); } else { acb_t t, u; acb_struct v[2]; acb_init(t); acb_init(u); acb_init(v); acb_init(v + 1); /* u = psi(-s) + gamma */ acb_neg(t, s); acb_digamma(u, t, prec); arb_const_euler(acb_realref(v), prec); arb_add(acb_realref(u), acb_realref(u), acb_realref(v), prec); acb_add_ui(t, s, 1, prec); _acb_poly_zeta_cpx_series(v, t, z, 0, 2, prec); acb_addmul(v + 1, v, u, prec); acb_neg(t, s); acb_rgamma(u, t, prec); acb_mul(res, v + 1, u, prec); acb_clear(v); acb_clear(v + 1); acb_clear(t); acb_clear(u); } } arb-2.8.1/acb/polylog.c000066400000000000000000000027151264125401100146450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" #include "acb_poly.h" void acb_polylog(acb_t w, const acb_t s, const acb_t z, slong prec) { acb_t t; acb_init(t); _acb_poly_polylog_cpx(t, s, z, 1, prec); acb_swap(w, t); acb_clear(t); } void acb_polylog_si(acb_t w, slong s, const acb_t z, slong prec) { acb_t t; acb_init(t); acb_set_si(t, s); acb_polylog(w, t, z, prec); acb_clear(t); } arb-2.8.1/acb/pow.c000066400000000000000000000120261264125401100137610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_pow_fmpz_binexp(acb_t y, const acb_t b, const fmpz_t e, slong prec) { slong i, wp, bits; if (-WORD(2) <= *e && *e <= WORD(4)) { if (*e == WORD(0)) { acb_one(y); } else if (*e == WORD(1)) { acb_set_round(y, b, prec); } else if (*e == -WORD(1)) { acb_inv(y, b, prec); } else if (*e == WORD(2)) { acb_mul(y, b, b, prec); } else if (*e == WORD(3)) { acb_cube(y, b, prec); } else if (*e == WORD(4)) { acb_mul(y, b, b, prec); acb_mul(y, y, y, prec); } else { acb_inv(y, b, prec); acb_mul(y, y, y, prec); } return; } if (fmpz_sgn(e) < 0) { fmpz_t f; fmpz_init(f); fmpz_neg(f, e); acb_pow_fmpz_binexp(y, b, f, prec + 2); acb_inv(y, y, prec); fmpz_clear(f); return; } if (!COEFF_IS_MPZ(*e) && ((*e) % 3 == 0)) { fmpz e3 = (*e) / 3; acb_pow_fmpz_binexp(y, b, &e3, prec); acb_cube(y, y, prec); return; } if (y == b) { acb_t t; acb_init(t); acb_set(t, b); acb_pow_fmpz_binexp(y, t, e, prec); acb_clear(t); return; } acb_set(y, b); bits = fmpz_bits(e); wp = ARF_PREC_ADD(prec, bits); for (i = bits - 2; i >= 0; i--) { acb_mul(y, y, y, wp); if (fmpz_tstbit(e, i)) acb_mul(y, y, b, wp); } } void acb_pow_fmpz(acb_t y, const acb_t b, const fmpz_t e, slong prec) { acb_pow_fmpz_binexp(y, b, e, prec); } void acb_pow_ui(acb_t y, const acb_t b, ulong e, slong prec) { fmpz_t f; fmpz_init_set_ui(f, e); acb_pow_fmpz(y, b, f, prec); fmpz_clear(f); } void acb_pow_si(acb_t y, const acb_t b, slong e, slong prec) { fmpz_t f; fmpz_init(f); fmpz_set_si(f, e); acb_pow_fmpz(y, b, f, prec); fmpz_clear(f); } void _acb_pow_exp(acb_t z, const acb_t x, const acb_t y, slong prec) { acb_t t; acb_init(t); acb_log(t, x, prec); acb_mul(t, t, y, prec); acb_exp(z, t, prec); acb_clear(t); } void _acb_pow_arb_exp(acb_t z, const acb_t x, const arb_t y, slong prec) { acb_t t; acb_init(t); acb_log(t, x, prec); acb_mul_arb(t, t, y, prec); acb_exp(z, t, prec); acb_clear(t); } #define BINEXP_LIMIT 64 void acb_pow_arb(acb_t z, const acb_t x, const arb_t y, slong prec) { const arf_struct * ymid = arb_midref(y); const mag_struct * yrad = arb_radref(y); if (arb_is_zero(y)) { acb_one(z); return; } if (acb_is_zero(x)) { if (arb_is_positive(y)) acb_zero(z); else acb_indeterminate(z); return; } if (mag_is_zero(yrad)) { /* small half-integer or integer */ if (arf_cmpabs_2exp_si(ymid, BINEXP_LIMIT) < 0 && arf_is_int_2exp_si(ymid, -1)) { fmpz_t e; fmpz_init(e); if (arf_is_int(ymid)) { arf_get_fmpz_fixed_si(e, ymid, 0); acb_pow_fmpz_binexp(z, x, e, prec); } else { arf_get_fmpz_fixed_si(e, ymid, -1); acb_sqrt(z, x, prec + fmpz_bits(e)); acb_pow_fmpz_binexp(z, z, e, prec); } fmpz_clear(e); return; } } _acb_pow_arb_exp(z, x, y, prec); } void acb_pow(acb_t z, const acb_t x, const acb_t y, slong prec) { if (arb_is_zero(acb_imagref(y))) { acb_pow_arb(z, x, acb_realref(y), prec); } else { if (acb_is_zero(x)) { if (arb_is_positive(acb_realref(y))) acb_zero(z); else acb_indeterminate(z); return; } _acb_pow_exp(z, x, y, prec); } } arb-2.8.1/acb/printd.c000066400000000000000000000033341264125401100144560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_printd(const acb_t z, slong digits) { flint_printf("("); arf_printd(arb_midref(acb_realref(z)), digits); if (arf_sgn(arb_midref(acb_imagref(z))) < 0) { arf_t t; arf_init_neg_shallow(t, arb_midref(acb_imagref(z))); flint_printf(" - "); arf_printd(t, digits); } else { flint_printf(" + "); arf_printd(arb_midref(acb_imagref(z)), digits); } flint_printf("j)"); flint_printf(" +/- "); flint_printf("("); mag_printd(arb_radref(acb_realref(z)), 3); flint_printf(", "); mag_printd(arb_radref(acb_imagref(z)), 3); flint_printf("j)"); } arb-2.8.1/acb/quadratic_roots_fmpz.c000066400000000000000000000035621264125401100174200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_quadratic_roots_fmpz(acb_t r1, acb_t r2, const fmpz_t a, const fmpz_t b, const fmpz_t c, slong prec) { fmpz_t d; fmpz_init(d); /* d = b^2 - 4ac */ fmpz_mul(d, a, c); fmpz_mul_2exp(d, d, 2); fmpz_submul(d, b, b); fmpz_neg(d, d); /* +/- sqrt(d) */ acb_zero(r1); if (fmpz_sgn(d) >= 0) { arb_sqrt_fmpz(acb_realref(r1), d, prec + fmpz_bits(d) + 4); } else { fmpz_neg(d, d); arb_sqrt_fmpz(acb_imagref(r1), d, prec + fmpz_bits(d) + 4); } acb_neg(r2, r1); /* -b */ acb_sub_fmpz(r1, r1, b, prec + 4); acb_sub_fmpz(r2, r2, b, prec + 4); /* divide by 2a */ fmpz_mul_2exp(d, a, 1); acb_div_fmpz(r1, r1, d, prec); acb_div_fmpz(r2, r2, d, prec); fmpz_clear(d); return; } arb-2.8.1/acb/randtest.c000066400000000000000000000041631264125401100150030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_randtest(acb_t z, flint_rand_t state, slong prec, slong mag_bits) { arb_randtest(acb_realref(z), state, prec, mag_bits); arb_randtest(acb_imagref(z), state, prec, mag_bits); } void acb_randtest_special(acb_t z, flint_rand_t state, slong prec, slong mag_bits) { arb_randtest_special(acb_realref(z), state, prec, mag_bits); arb_randtest_special(acb_imagref(z), state, prec, mag_bits); } void acb_randtest_precise(acb_t z, flint_rand_t state, slong prec, slong mag_bits) { arb_randtest_precise(acb_realref(z), state, prec, mag_bits); arb_randtest_precise(acb_imagref(z), state, prec, mag_bits); } void acb_randtest_param(acb_t x, flint_rand_t state, slong prec, slong size) { if (n_randint(state, 8) == 0) { fmpz_t t; fmpz_init(t); fmpz_randtest(t, state, 1 + n_randint(state, prec)); arb_set_fmpz(acb_realref(x), t); arb_zero(acb_imagref(x)); acb_mul_2exp_si(x, x, -1); fmpz_clear(t); } else { acb_randtest(x, state, prec, size); } } arb-2.8.1/acb/rel_error_bits.c000066400000000000000000000044261264125401100161750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" slong acb_rel_error_bits(const acb_t x) { int am, ar, bm, br; slong result; const fmpz * radmag; const fmpz * midmag; fmpz_t t; am = !arf_is_zero(arb_midref(acb_realref(x))); ar = !mag_is_zero(arb_radref(acb_realref(x))); bm = !arf_is_zero(arb_midref(acb_imagref(x))); br = !mag_is_zero(arb_radref(acb_imagref(x))); /* no radius -- exact */ if (!ar && !br) return -ARF_PREC_EXACT; /* no midpoint -- infinite relative error */ if (!am && !bm) return ARF_PREC_EXACT; if (!acb_is_finite(x)) return ARF_PREC_EXACT; #define ame ARF_EXPREF(arb_midref(acb_realref(x))) #define are MAG_EXPREF(arb_radref(acb_realref(x))) #define bme ARF_EXPREF(arb_midref(acb_imagref(x))) #define bre MAG_EXPREF(arb_radref(acb_imagref(x))) if (am && bm) midmag = fmpz_cmp(ame, bme) >= 0 ? ame : bme; else if (am) midmag = ame; else midmag = bme; if (ar && br) radmag = fmpz_cmp(are, bre) >= 0 ? are : bre; else if (ar) radmag = are; else radmag = bre; fmpz_init(t); fmpz_add_ui(t, radmag, 1); result = _fmpz_sub_small(t, midmag); fmpz_clear(t); return result; } arb-2.8.1/acb/rising2_ui.c000066400000000000000000000024761264125401100152360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_rising2_ui(acb_t u, acb_t v, const acb_t x, ulong n, slong prec) { if (prec < 256 || n < 8 || acb_bits(x) < prec / 8) acb_rising2_ui_bs(u, v, x, n, prec); else acb_rising2_ui_rs(u, v, x, n, 0, prec); } arb-2.8.1/acb/rising2_ui_bs.c000066400000000000000000000045301264125401100157130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" static void bsplit(acb_t p, acb_t q, const acb_t x, ulong a, ulong b, slong prec) { if (b - a < 8) { ulong k; acb_t t; acb_one(p); acb_add_ui(q, x, a, prec); acb_init(t); for (k = a + 1; k < b; k++) { acb_add_ui(t, x, k, prec); acb_mul(p, p, t, prec); acb_add(p, p, q, prec); acb_mul(q, q, t, prec); } acb_clear(t); } else { acb_t r, s; ulong m; acb_init(r); acb_init(s); m = a + (b - a) / 2; bsplit(p, q, x, a, m, prec); bsplit(r, s, x, m, b, prec); acb_mul(p, p, s, prec); acb_mul(r, r, q, prec); acb_add(p, p, r, prec); acb_mul(q, q, s, prec); acb_clear(r); acb_clear(s); } } void acb_rising2_ui_bs(acb_t u, acb_t v, const acb_t x, ulong n, slong prec) { if (n == 0) { acb_zero(v); acb_one(u); } else if (n == 1) { acb_set(u, x); acb_one(v); } else { acb_t t; slong wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); acb_init(t); /* support aliasing */ acb_set(t, x); bsplit(v, u, t, 0, n, wp); acb_clear(t); } } arb-2.8.1/acb/rising2_ui_rs.c000066400000000000000000000061351264125401100157360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void _gamma_rf_bsplit(fmpz * A, ulong a, ulong b); void acb_rising2_ui_rs(acb_t u, acb_t v, const acb_t x, ulong n, ulong m, slong prec) { if (n == 0) { acb_zero(v); acb_one(u); } else if (n == 1) { acb_set(u, x); acb_one(v); } else { slong wp; ulong i, j, a, b; acb_ptr xs; acb_t S, T, U, V; fmpz *A, *B; wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); if (m == 0) { ulong m1, m2; m1 = 0.6 * pow(wp, 0.4); m2 = n_sqrt(n); m = FLINT_MIN(m1, m2); } m = FLINT_MAX(m, 1); xs = _acb_vec_init(m + 1); A = _fmpz_vec_init(2 * m + 1); B = A + (m + 1); acb_init(S); acb_init(T); acb_init(U); acb_init(V); _acb_vec_set_powers(xs, x, m + 1, wp); for (i = 0; i < n; i += m) { a = i; b = FLINT_MIN(n, a + m); if (a == 0 || b != a + m) { _gamma_rf_bsplit(A, a, b); } else { fmpz tt = m; _fmpz_poly_taylor_shift(A, &tt, m + 1); } _fmpz_poly_derivative(B, A, b - a + 1); acb_set_fmpz(S, A); for (j = 1; j <= b - a; j++) acb_addmul_fmpz(S, xs + j, A + j, wp); acb_set_fmpz(T, B); for (j = 1; j < b - a; j++) acb_addmul_fmpz(T, xs + j, B + j, wp); if (i == 0) { acb_set(U, S); acb_set(V, T); } else { acb_mul(V, V, S, wp); acb_addmul(V, U, T, wp); acb_mul(U, U, S, wp); } } acb_set(u, U); acb_set(v, V); _acb_vec_clear(xs, m + 1); _fmpz_vec_clear(A, 2 * m + 1); acb_clear(S); acb_clear(T); acb_clear(U); acb_clear(V); } } arb-2.8.1/acb/rising_ui.c000066400000000000000000000037411264125401100151500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_rising_ui(acb_t y, const acb_t x, ulong n, slong prec) { if (n < FLINT_MAX(prec, 100)) { acb_rising_ui_rec(y, x, n, prec); } else { acb_t t; acb_init(t); acb_add_ui(t, x, n, prec); acb_gamma(t, t, prec); acb_rgamma(y, x, prec); acb_mul(y, y, t, prec); acb_clear(t); } } void acb_rising(acb_t y, const acb_t x, const acb_t n, slong prec) { if (acb_is_int(n) && arf_sgn(arb_midref(acb_realref(n))) >= 0 && arf_cmpabs_ui(arb_midref(acb_realref(n)), FLINT_MAX(prec, 100)) < 0) { acb_rising_ui_rec(y, x, arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN), prec); } else { acb_t t; acb_init(t); acb_add(t, x, n, prec); acb_gamma(t, t, prec); acb_rgamma(y, x, prec); acb_mul(y, y, t, prec); acb_clear(t); } } arb-2.8.1/acb/rising_ui_bs.c000066400000000000000000000044021264125401100156270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" /* assumes y and x are not aliased */ static void bsplit(acb_t y, const acb_t x, ulong a, ulong b, slong prec) { if (b - a == 1) { acb_set_round(y, x, prec); } else if (b - a <= 10) { slong i; acb_t t; acb_init(t); acb_add_ui(t, x, a, prec); acb_add_ui(y, x, a + 1, prec); acb_mul(y, y, t, prec); for (i = a + 2; i < b; i++) { acb_add_ui(t, x, i, prec); acb_mul(y, y, t, prec); } acb_clear(t); } else { acb_t t, u; ulong m = a + (b - a) / 2; acb_init(t); acb_init(u); bsplit(t, x, a, m, prec); bsplit(u, x, m, b, prec); acb_mul(y, t, u, prec); acb_clear(t); acb_clear(u); } } void acb_rising_ui_bs(acb_t y, const acb_t x, ulong n, slong prec) { if (n == 0) { acb_one(y); } else if (n == 1) { acb_set_round(y, x, prec); } else { acb_t t; slong wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); acb_init(t); bsplit(t, x, 0, n, wp); acb_set_round(y, t, prec); acb_clear(t); } } arb-2.8.1/acb/rising_ui_get_mag.c000066400000000000000000000056771264125401100166450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void mag_add_ui_2exp_si(mag_t, const mag_t, ulong, slong); static void acb_rising_get_mag2_right(mag_t bound, const arb_t a, const arb_t b, ulong n) { mag_t t, u; ulong k; mag_init(t); mag_init(u); arb_get_mag(t, a); arb_get_mag(u, b); mag_mul(bound, t, t); mag_addmul(bound, u, u); mag_set(u, bound); mag_mul_2exp_si(t, t, 1); for (k = 1; k < n; k++) { mag_add_ui_2exp_si(u, u, 2 * k - 1, 0); mag_add(u, u, t); mag_mul(bound, bound, u); } mag_clear(t); mag_clear(u); } void acb_rising_ui_get_mag(mag_t bound, const acb_t s, ulong n) { if (n == 0) { mag_one(bound); return; } if (n == 1) { acb_get_mag(bound, s); return; } if (!acb_is_finite(s)) { mag_inf(bound); return; } if (arf_sgn(arb_midref(acb_realref(s))) >= 0) { acb_rising_get_mag2_right(bound, acb_realref(s), acb_imagref(s), n); } else { arb_t a; slong k; mag_t bound2, t, u; arb_init(a); mag_init(bound2); mag_init(t); mag_init(u); arb_get_mag(u, acb_imagref(s)); mag_mul(u, u, u); mag_one(bound); for (k = 0; k < n; k++) { arb_add_ui(a, acb_realref(s), k, MAG_BITS); if (arf_sgn(arb_midref(a)) >= 0) { acb_rising_get_mag2_right(bound2, a, acb_imagref(s), n - k); mag_mul(bound, bound, bound2); break; } else { arb_get_mag(t, a); mag_mul(t, t, t); mag_add(t, t, u); mag_mul(bound, bound, t); } } arb_clear(a); mag_clear(bound2); mag_clear(t); mag_clear(u); } mag_sqrt(bound, bound); } arb-2.8.1/acb/rising_ui_rec.c000066400000000000000000000024601264125401100157760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_rising_ui_rec(acb_t y, const acb_t x, ulong n, slong prec) { if (prec < 256 || n < 8 || acb_bits(x) < prec / 8) acb_rising_ui_bs(y, x, n, prec); else acb_rising_ui_rs(y, x, n, 0, prec); } arb-2.8.1/acb/rising_ui_rs.c000066400000000000000000000060571264125401100156570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void rising_difference_polynomial(fmpz * s, fmpz * c, ulong m); void acb_rising_ui_rs(acb_t y, const acb_t x, ulong n, ulong m, slong prec) { acb_ptr xs; acb_t t, u, v; ulong i, k, rem; fmpz_t c, h; fmpz *s, *d; slong wp; if (n == 0) { acb_one(y); return; } if (n == 1) { acb_set_round(y, x, prec); return; } wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); acb_init(t); acb_init(u); acb_init(v); fmpz_init(c); fmpz_init(h); if (m == 0) { ulong m1, m2; m1 = 0.2 * pow(2.0 * wp, 0.4); m2 = n_sqrt(n); m = FLINT_MIN(m1, m2); } m = FLINT_MIN(m, n); m = FLINT_MAX(m, 1); xs = _acb_vec_init(m + 1); d = _fmpz_vec_init(m * m); s = _fmpz_vec_init(m + 1); _acb_vec_set_powers(xs, x, m + 1, wp); rising_difference_polynomial(s, d, m); /* tail */ rem = m; while (rem + m <= n) rem += m; acb_one(y); for (k = rem; k < n; k++) { acb_add_ui(t, xs + 1, k, wp); acb_mul(y, y, t, wp); } /* initial rising factorial */ acb_zero(t); for (i = 1; i <= m; i++) acb_addmul_fmpz(t, xs + i, s + i, wp); acb_mul(y, y, t, wp); /* the leading coefficient is always the same */ acb_mul_fmpz(xs + m - 1, xs + m - 1, d + m - 1 + 0, wp); for (k = 0; k + 2 * m <= n; k += m) { for (i = 0; i < m - 1; i++) { fmpz_set_ui(h, k); _fmpz_poly_evaluate_horner_fmpz(c, d + i * m, m - i, h); if (i == 0) acb_add_fmpz(t, t, c, wp); else acb_addmul_fmpz(t, xs + i, c, wp); } acb_add(t, t, xs + m - 1, wp); acb_mul(y, y, t, wp); } acb_set_round(y, y, prec); acb_clear(t); acb_clear(u); acb_clear(v); _acb_vec_clear(xs, m + 1); _fmpz_vec_clear(d, m * m); _fmpz_vec_clear(s, m + 1); fmpz_clear(c); fmpz_clear(h); } arb-2.8.1/acb/root_ui.c000066400000000000000000000033651264125401100146420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_root_ui(acb_t res, const acb_t z, ulong n, slong prec) { if (n == 0) { acb_indeterminate(res); } else if (n == 1) { acb_set_round(res, z, prec); } else if (n == 2) { acb_sqrt(res, z, prec); } else if (n == 4) { acb_sqrt(res, z, prec + 4); acb_sqrt(res, res, prec); } else if (acb_is_real(z) && arb_is_nonnegative(acb_realref(z))) { arb_root(acb_realref(res), acb_realref(z), n, prec); arb_zero(acb_imagref(res)); } else { acb_log(res, z, prec + 4); acb_div_ui(res, res, n, prec + 4); acb_exp(res, res, prec); } } arb-2.8.1/acb/rsqrt.c000066400000000000000000000054261264125401100143350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_rsqrt(acb_t y, const acb_t x, slong prec) { arb_t r, t, u, v; slong wp; #define a acb_realref(x) #define b acb_imagref(x) #define c acb_realref(y) #define d acb_imagref(y) if (arb_is_zero(b)) { if (arb_is_nonnegative(a)) { arb_rsqrt(c, a, prec); arb_zero(d); return; } else if (arb_is_nonpositive(a)) { arb_neg(d, a); arb_rsqrt(d, d, prec); arb_neg(d, d); arb_zero(c); return; } } if (arb_is_zero(a)) { if (arb_is_nonnegative(b)) { arb_mul_2exp_si(c, b, 1); arb_rsqrt(c, c, prec); arb_neg(d, c); return; } else if (arb_is_nonpositive(b)) { arb_mul_2exp_si(c, b, 1); arb_neg(c, c); arb_rsqrt(c, c, prec); arb_set(d, c); return; } } /* based on the identity sqrt(z) = sqrt(r) (z+r) / |z+r|: */ /* 1/sqrt(a+bi) = (1/v)((a+r) - b*i), r = |a+bi|, v = sqrt(r*(b^2+(a+r)^2)) */ wp = prec + 6; arb_init(r); arb_init(t); arb_init(u); arb_init(v); /* u = b^2, r = |a+bi| */ arb_mul(t, a, a, wp); arb_mul(u, b, b, wp); arb_add(r, t, u, wp); arb_sqrtpos(r, r, wp); /* t = a+r, v = r*(b^2+(a+r)^2) */ arb_add(t, r, a, wp); arb_mul(v, t, t, wp); arb_add(v, v, u, wp); arb_mul(v, v, r, wp); /* v = 1/sqrt(v) */ arb_rsqrt(v, v, wp); arb_mul(c, t, v, prec); arb_mul(d, b, v, prec); arb_neg(d, d); arb_clear(r); arb_clear(t); arb_clear(u); arb_clear(v); #undef a #undef b #undef c #undef d } arb-2.8.1/acb/sin.c000066400000000000000000000030111264125401100137370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_sin(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) arb_t sa, ca, sb, cb; arb_init(sa); arb_init(ca); arb_init(sb); arb_init(cb); arb_sin_cos(sa, ca, a, prec); arb_sinh_cosh(sb, cb, b, prec); arb_mul(acb_realref(r), sa, cb, prec); arb_mul(acb_imagref(r), sb, ca, prec); arb_clear(sa); arb_clear(ca); arb_clear(sb); arb_clear(cb); } arb-2.8.1/acb/sin_cos.c000066400000000000000000000032321264125401100146100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_sin_cos(acb_t s, acb_t c, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) arb_t sa, ca, sb, cb; arb_init(sa); arb_init(ca); arb_init(sb); arb_init(cb); arb_sin_cos(sa, ca, a, prec); arb_sinh_cosh(sb, cb, b, prec); arb_mul(acb_realref(s), sa, cb, prec); arb_mul(acb_imagref(s), sb, ca, prec); arb_mul(acb_realref(c), ca, cb, prec); arb_mul(acb_imagref(c), sa, sb, prec); arb_neg(acb_imagref(c), acb_imagref(c)); arb_clear(sa); arb_clear(ca); arb_clear(sb); arb_clear(cb); } arb-2.8.1/acb/sin_cos_pi.c000066400000000000000000000033341264125401100153030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_sin_cos_pi(acb_t s, acb_t c, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) arb_t sa, ca, sb, cb; arb_init(sa); arb_init(ca); arb_init(sb); arb_init(cb); arb_const_pi(sb, prec); arb_mul(sb, sb, b, prec); arb_sin_cos_pi(sa, ca, a, prec); arb_sinh_cosh(sb, cb, sb, prec); arb_mul(acb_realref(s), sa, cb, prec); arb_mul(acb_imagref(s), sb, ca, prec); arb_mul(acb_realref(c), ca, cb, prec); arb_mul(acb_imagref(c), sa, sb, prec); arb_neg(acb_imagref(c), acb_imagref(c)); arb_clear(sa); arb_clear(ca); arb_clear(sb); arb_clear(cb); } arb-2.8.1/acb/sin_pi.c000066400000000000000000000031351264125401100144360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_sin_pi(acb_t r, const acb_t z, slong prec) { #define a acb_realref(z) #define b acb_imagref(z) arb_t sa, ca, sb, cb; arb_init(sa); arb_init(ca); arb_init(sb); arb_init(cb); arb_sin_cos_pi(sa, ca, a, prec); arb_const_pi(cb, prec); arb_mul(cb, cb, b, prec); arb_sinh_cosh(sb, cb, cb, prec); arb_mul(acb_realref(r), sa, cb, prec); arb_mul(acb_imagref(r), sb, ca, prec); arb_clear(sa); arb_clear(ca); arb_clear(sb); arb_clear(cb); #undef a #undef b } arb-2.8.1/acb/sqrt.c000066400000000000000000000061751264125401100141550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_sqrt(acb_t y, const acb_t x, slong prec) { arb_t r, t, u; slong wp; #define a acb_realref(x) #define b acb_imagref(x) #define c acb_realref(y) #define d acb_imagref(y) if (arb_is_zero(b)) { if (arb_is_nonnegative(a)) { arb_sqrt(c, a, prec); arb_zero(d); return; } else if (arb_is_nonpositive(a)) { arb_neg(d, a); arb_sqrt(d, d, prec); arb_zero(c); return; } } if (arb_is_zero(a)) { if (arb_is_nonnegative(b)) { arb_mul_2exp_si(c, b, -1); arb_sqrt(c, c, prec); arb_set(d, c); return; } else if (arb_is_nonpositive(b)) { arb_mul_2exp_si(c, b, -1); arb_neg(c, c); arb_sqrt(c, c, prec); arb_neg(d, c); return; } } wp = prec + 4; arb_init(r); arb_init(t); arb_init(u); acb_abs(r, x, wp); arb_add(t, r, a, wp); if (arb_rel_accuracy_bits(t) > 8) { /* sqrt(a+bi) = sqrt((r+a)/2) + b/sqrt(2*(r+a))*i, r = |a+bi| */ arb_mul_2exp_si(u, t, 1); arb_sqrt(u, u, wp); arb_div(d, b, u, prec); arb_set_round(c, u, prec); arb_mul_2exp_si(c, c, -1); } else { /* sqrt(a+bi) = sqrt((r+a)/2) + (b/|b|)*sqrt((r-a)/2)*i (sign) */ arb_mul_2exp_si(t, t, -1); arb_sub(u, r, a, wp); arb_mul_2exp_si(u, u, -1); arb_sqrtpos(c, t, prec); if (arb_is_nonnegative(b)) { arb_sqrtpos(d, u, prec); } else if (arb_is_nonpositive(b)) { arb_sqrtpos(d, u, prec); arb_neg(d, d); } else { arb_sqrtpos(t, u, wp); arb_neg(u, t); arb_union(d, t, u, prec); } } arb_clear(r); arb_clear(t); arb_clear(u); #undef a #undef b #undef c #undef d } arb-2.8.1/acb/submul.c000066400000000000000000000032721264125401100144660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_submul(acb_t z, const acb_t x, const acb_t y, slong prec) { if (arb_is_zero(acb_imagref(y))) { arb_submul(acb_imagref(z), acb_imagref(x), acb_realref(y), prec); arb_submul(acb_realref(z), acb_realref(x), acb_realref(y), prec); } else if (arb_is_zero(acb_imagref(x))) { arb_submul(acb_imagref(z), acb_imagref(y), acb_realref(x), prec); arb_submul(acb_realref(z), acb_realref(y), acb_realref(x), prec); } else { acb_t t; acb_init(t); acb_mul(t, x, y, prec); acb_sub(z, z, t, prec); acb_clear(t); } } arb-2.8.1/acb/tan.c000066400000000000000000000046501264125401100137420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_tan(acb_t r, const acb_t z, slong prec) { if (arb_is_zero(acb_imagref(z))) { arb_tan(acb_realref(r), acb_realref(z), prec); arb_zero(acb_imagref(r)); } else if (arb_is_zero(acb_realref(z))) { arb_tanh(acb_imagref(r), acb_imagref(z), prec); arb_zero(acb_realref(r)); } else { acb_t t; acb_init(t); if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0) { acb_sin_cos(r, t, z, prec + 4); acb_div(r, r, t, prec); } else { acb_mul_2exp_si(t, z, 1); if (arf_sgn(arb_midref(acb_imagref(z))) > 0) { acb_mul_onei(t, t); acb_exp(t, t, prec + 4); acb_add_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_div_onei(r, r); } else { acb_div_onei(t, t); acb_exp(t, t, prec + 4); acb_add_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_mul_onei(r, r); } } acb_clear(t); } } arb-2.8.1/acb/tan_pi.c000066400000000000000000000050251264125401100144270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" void acb_tan_pi(acb_t r, const acb_t z, slong prec) { if (arb_is_zero(acb_imagref(z))) { arb_tan_pi(acb_realref(r), acb_realref(z), prec); arb_zero(acb_imagref(r)); } else if (arb_is_zero(acb_realref(z))) { arb_t t; arb_init(t); arb_const_pi(t, prec + 4); arb_mul(t, acb_imagref(z), t, prec + 4); arb_tanh(acb_imagref(r), t, prec); arb_zero(acb_realref(r)); arb_clear(t); } else { acb_t t; acb_init(t); if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0) { acb_sin_cos_pi(r, t, z, prec + 4); acb_div(r, r, t, prec); } else { acb_mul_2exp_si(t, z, 1); if (arf_sgn(arb_midref(acb_imagref(z))) > 0) { acb_exp_pi_i(t, t, prec + 4); acb_add_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_div_onei(r, r); } else { acb_neg(t, t); acb_exp_pi_i(t, t, prec + 4); acb_add_ui(r, t, 1, prec + 4); acb_div(r, t, r, prec + 4); acb_mul_2exp_si(r, r, 1); acb_sub_ui(r, r, 1, prec); acb_mul_onei(r, r); } } acb_clear(t); } } arb-2.8.1/acb/test/000077500000000000000000000000001264125401100137665ustar00rootroot00000000000000arb-2.8.1/acb/test/t-acos.c000066400000000000000000000057351264125401100153320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("acos...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_acos(a, x, prec1); acb_acos(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check cos(acos(x)) = x */ acb_cos(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_acos(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-acosh.c000066400000000000000000000057441264125401100155020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("acosh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_acosh(a, x, prec1); acb_acosh(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check cosh(acosh(x)) = x */ acb_cosh(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_acosh(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-agm1.c000066400000000000000000000166661264125401100152370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" #define EPS 1e-13 #define NUM_DERIVS 4 #define NUM_TESTS 11 const double agm_testdata[NUM_TESTS][10] = { {1.0, 0.0, 1.0, 0.0, 0.5, 0.0, -0.0625, 0.0, 0.03125, 0.0}, {0.25, 0.0, 0.56075714507190064253, 0.0, 0.76633907325304843764, 0.0, -0.58010113691169132987, 0.0, 1.2991960360521313649, 0.0}, {1.0, 1.0, 1.0491605287327802205, 0.47815574608816122933, 0.44643105633549979073, -0.08043578677710866283, -0.015455284495904882924, 0.031976374729700173479, -0.005073437378084728324, -0.010673958729796444985}, {0.0, 1.0, 0.59907011736779610372, 0.59907011736779610372, 0.43640657965245804105, -0.16266353771533806267, 0.031271486774469549792, 0.031271486774469549792, -0.0084910439043492636266, 0.022780442870120286166}, {-1.0, 1.0, 0.18841106798868002055, 0.77800407878895828015, 0.39320630832295102335, -0.19287323123455182026, 0.016808115488846724979, 0.020163502567351546742, -0.011189063384352573532, -0.0045629824424054816356}, {-0.25, 0.0, 0.24392673474953340413, 0.27799893427725564501, 0.079794586546549867566, -0.32574453868033984617, -0.27530931370867131683, -0.60287933825809104112, -0.54714813521966247214, -0.97291617788393560861}, {-2.0, 0.0, -0.42296620840880168736, 0.66126618346180476447, 0.29655367830470777795, -0.27314834694816402295, 0.018331225229748304014, -0.043277191398267359935, 0.0094104572902577354423, -0.021071819981331905571}, {-0.99999994039535522461, 0.0, 0.0069953999943208591971, 0.08334545077423930704, 12454.444757282471906, 73670.447089584396744, -87884330303.90316493, -553342797575.05204396, 909784741818095264.43, 5883796037072491540.4}, {-1.0000000596046447754, 0.0, -0.0069954003670321135601, 0.083345455480285282001, 12454.451634795395449, -73670.529975671147878, 87884324285.574775284, -553342761339.97964199, 909784713383817144.98, -5883795855289758433.3}, {-1.0, 5.9604644775390625e-8, 2.3677293150757997928e-9, 0.083932595219022127005, 75242.17179390509748, -0.041726661532440829443, -18488.306894081923308, 563725525035.34898339, -5988414396610684162.5, -92537341636.835656296}, {-1.0, -5.9604644775390625e-8, 2.3677293150757997928e-9, -0.083932595219022127005, 75242.17179390509748, 0.041726661532440829443, -18488.306894081923308, -563725525035.34898339, -5988414396610684162.5, 92537341636.835656296}, }; int main() { slong iter; flint_rand_t state; flint_printf("agm1...."); fflush(stdout); flint_randinit(state); /* check particular values against table */ { acb_t z, t; acb_ptr w1; slong i, j, prec, cnj; acb_init(z); acb_init(t); w1 = _acb_vec_init(NUM_DERIVS); for (prec = 32; prec <= 512; prec *= 4) { for (i = 0; i < NUM_TESTS; i++) { for (cnj = 0; cnj < 2; cnj++) { if (cnj == 1 && agm_testdata[i][0] < 0 && agm_testdata[i][1] == 0) continue; acb_zero(z); arf_set_d(arb_midref(acb_realref(z)), agm_testdata[i][0]); arf_set_d(arb_midref(acb_imagref(z)), cnj ? -agm_testdata[i][1] : agm_testdata[i][1]); acb_agm1_cpx(w1, z, NUM_DERIVS, prec); for (j = 0; j < NUM_DERIVS; j++) { arf_set_d(arb_midref(acb_realref(t)), agm_testdata[i][2+2*j]); mag_set_d(arb_radref(acb_realref(t)), fabs(agm_testdata[i][2+2*j]) * EPS); arf_set_d(arb_midref(acb_imagref(t)), cnj ? -agm_testdata[i][2+2*j+1] : agm_testdata[i][2+2*j+1]); mag_set_d(arb_radref(acb_imagref(t)), fabs(agm_testdata[i][2+2*j+1]) * EPS); if (!acb_overlaps(w1 + j, t)) { flint_printf("FAIL\n\n"); flint_printf("j = %wd\n\n", j); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1 + j, 15); flint_printf("\n\n"); abort(); } } } } } _acb_vec_clear(w1, NUM_DERIVS); acb_clear(z); acb_clear(t); } /* self-consistency test */ for (iter = 0; iter < 1000; iter++) { acb_ptr m1, m2; acb_t z1, z2, t; slong i, len1, len2, prec1, prec2; len1 = n_randint(state, 10); len2 = n_randint(state, 10); prec1 = 2 + n_randint(state, 2000); prec2 = 2 + n_randint(state, 2000); m1 = _acb_vec_init(len1); m2 = _acb_vec_init(len2); acb_init(z1); acb_init(z2); acb_init(t); acb_randtest(z1, state, prec1, 1 + n_randint(state, 100)); if (n_randint(state, 2)) { acb_set(z2, z1); } else { acb_randtest(t, state, prec2, 1 + n_randint(state, 100)); acb_add(z2, z1, t, prec2); acb_sub(z2, z2, t, prec2); } acb_agm1_cpx(m1, z1, len1, prec1); acb_agm1_cpx(m2, z2, len2, prec2); for (i = 0; i < FLINT_MIN(len1, len2); i++) { if (!acb_overlaps(m1 + i, m2 + i)) { flint_printf("FAIL (overlap)\n\n"); flint_printf("iter = %wd, i = %wd, len1 = %wd, len2 = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, i, len1, len2, prec1, prec2); flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 30); flint_printf("\n\n"); flint_printf("m1 = "); acb_printd(m1, 30); flint_printf("\n\n"); flint_printf("m2 = "); acb_printd(m2, 30); flint_printf("\n\n"); abort(); } } _acb_vec_clear(m1, len1); _acb_vec_clear(m2, len2); acb_clear(z1); acb_clear(z2); acb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-asin.c000066400000000000000000000057361264125401100153400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("asin...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_asin(a, x, prec1); acb_asin(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check sin(asin(x)) = x */ acb_sin(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_asin(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-asinh.c000066400000000000000000000057441264125401100155070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("asinh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_asinh(a, x, prec1); acb_asinh(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check sinh(asinh(x)) = x */ acb_sinh(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_asinh(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-atan.c000066400000000000000000000057361264125401100153310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("atan...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_atan(a, x, prec1); acb_atan(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check tan(atan(x)) = x */ acb_tan(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_atan(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-atanh.c000066400000000000000000000057441264125401100155000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("atanh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_atanh(a, x, prec1); acb_atanh(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check tanh(atanh(x)) = x */ acb_tanh(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_atanh(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-barnes_g.c000066400000000000000000000067461264125401100161700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("barnes_g...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 200); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); acb_init(d); arb_randtest_precise(acb_realref(a), state, 1 + n_randint(state, 300), 1 + n_randint(state, 8)); arb_randtest_precise(acb_imagref(a), state, 1 + n_randint(state, 300), 1 + n_randint(state, 8)); acb_log_barnes_g(b, a, prec1); if (n_randint(state, 4) == 0) { acb_randtest(c, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_add(a, a, c, prec1); acb_sub(a, a, c, prec1); } acb_log_barnes_g(c, a, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_barnes_g(d, a, prec1); acb_exp(c, b, prec1); if (!acb_overlaps(c, d)) { flint_printf("FAIL: overlap 2\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } /* check lG(z+1) = lG(z) + lgamma(z) */ acb_lgamma(c, a, prec1); acb_add(b, b, c, prec1); acb_add_ui(c, a, 1, prec1); acb_log_barnes_g(c, c, prec1); if (!acb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-chebyshev_t_ui.c000066400000000000000000000076461264125401100174100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("chebyshev_t_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, b, c, d; ulong n; slong prec; n = n_randtest(state); prec = 2 + n_randint(state, 300); acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(a, state, 1 + n_randint(state, 300), 5); acb_randtest(c, state, 1 + n_randint(state, 300), 5); acb_cos(b, a, prec); acb_chebyshev_t_ui(c, n, b, prec); acb_mul_ui(d, a, n, prec); acb_cos(d, d, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: c = T_n(cos(a)) = d = cos(n*a)\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("d = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_chebyshev_t_ui(b, n, b, prec); if (!acb_equal(b, c)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_randtest(a, state, 1 + n_randint(state, 300), 5); acb_randtest(b, state, 1 + n_randint(state, 300), 5); acb_randtest(c, state, 1 + n_randint(state, 300), 5); acb_chebyshev_t2_ui(b, c, n, a, prec); acb_chebyshev_t_ui(d, n, a, prec); if (!acb_overlaps(b, d)) { flint_printf("FAIL: T_n\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } if (n == 0) acb_set(d, a); else acb_chebyshev_t_ui(d, n - 1, a, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: T_{n-1}\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-chebyshev_u_ui.c000066400000000000000000000105461264125401100174020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("chebyshev_u_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, b, c, d, e; ulong n; slong prec; n = n_randtest(state); prec = 2 + n_randint(state, 300); acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(e); acb_randtest_precise(a, state, 1 + n_randint(state, 300), 5); acb_randtest_precise(c, state, 1 + n_randint(state, 300), 5); acb_sin_cos(d, b, a, prec); acb_chebyshev_u_ui(c, n, b, prec); acb_mul(d, c, d, prec); if (n == LIMB_ONES) acb_mul_2exp_si(e, a, FLINT_BITS); else acb_mul_ui(e, a, n + 1, prec); acb_sin(e, e, prec); if (!acb_overlaps(d, e)) { flint_printf("FAIL: sin(a)*U_n(cos(a)) = sin((n+1)a)\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_printd(d, 15); flint_printf("\n\n"); flint_printf("e = "); acb_printd(e, 15); flint_printf("\n\n"); abort(); } acb_chebyshev_u_ui(b, n, b, prec); if (!acb_equal(b, c)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_printd(c, 15); flint_printf("\n\n"); abort(); } acb_randtest(a, state, 1 + n_randint(state, 300), 5); acb_randtest(b, state, 1 + n_randint(state, 300), 5); acb_randtest(c, state, 1 + n_randint(state, 300), 5); acb_chebyshev_u2_ui(b, c, n, a, prec); acb_chebyshev_u_ui(d, n, a, prec); if (!acb_overlaps(b, d)) { flint_printf("FAIL: U_n\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } if (n == 0) acb_zero(d); else acb_chebyshev_u_ui(d, n - 1, a, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: U_{n-1}\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-cos_pi.c000066400000000000000000000060751264125401100156570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("cos_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, y, a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_randtest(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_cos_pi(a, x, prec1); acb_cos_pi(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* compare with cos */ arb_const_pi(acb_realref(c), prec1); acb_mul_arb(y, x, acb_realref(c), prec1); acb_cos(c, y, prec1); if (!acb_overlaps(a, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_cos_pi(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-cot.c000066400000000000000000000065071264125401100151700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("cot...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, y, a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest(y, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_cot(a, x, prec1); acb_cot(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* check cot(x+y) = (cot(x) cot(y) - 1) / (cot(x) + cot(y)) */ acb_add(b, x, y, prec1); acb_cot(b, b, prec1); acb_cot(c, y, prec1); acb_add(d, a, c, prec1); acb_mul(c, a, c, prec1); acb_sub_ui(c, c, 1, prec1); acb_div(d, c, d, prec1); if (!acb_overlaps(b, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_cot(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-cot_pi.c000066400000000000000000000060761264125401100156610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("cot_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, y, a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_randtest(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_cot_pi(a, x, prec1); acb_cot_pi(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* compare with cot */ arb_const_pi(acb_realref(c), prec1); acb_mul_arb(y, x, acb_realref(c), prec1); acb_cot(c, y, prec1); if (!acb_overlaps(a, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_cot_pi(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-coth.c000066400000000000000000000065161264125401100153400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("coth...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, y, a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 200); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(x, state, 1 + n_randint(state, 200), 2 + n_randint(state, 100)); acb_randtest(y, state, 1 + n_randint(state, 200), 2 + n_randint(state, 100)); acb_coth(a, x, prec1); acb_coth(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* check coth(x+y) = (1 + coth(x) coth(y)) / (coth(x) + coth(y)) */ acb_add(b, x, y, prec1); acb_coth(b, b, prec1); acb_coth(c, y, prec1); acb_add(d, a, c, prec1); acb_mul(c, a, c, prec1); acb_add_ui(c, c, 1, prec1); acb_div(d, c, d, prec1); if (!acb_overlaps(b, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_coth(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-digamma.c000066400000000000000000000061161264125401100157760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("digamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { acb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); arb_randtest_precise(acb_realref(a), state, 1 + n_randint(state, 1000), 3); arb_randtest_precise(acb_imagref(a), state, 1 + n_randint(state, 1000), 3); acb_digamma(b, a, prec1); acb_digamma(c, a, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_set(c, a); acb_digamma(c, c, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } /* check digamma(z+1) = digamma(z) + 1/z */ acb_inv(c, a, prec1); acb_add(b, b, c, prec1); acb_add_ui(c, a, 1, prec1); acb_digamma(c, c, prec1); if (!acb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-div.c000066400000000000000000000144171264125401100151640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("div...."); fflush(stdout); flint_randinit(state); /* test aliasing of c and a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_div(c, a, b, prec); acb_div(a, a, b, prec); if (!acb_equal(a, c)) { flint_printf("FAIL: aliasing c, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test aliasing of c and b */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_div(c, a, b, prec); acb_div(b, a, b, prec); if (!acb_equal(b, c)) { flint_printf("FAIL: aliasing c, b\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test aliasing a, a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c, d; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_set(b, a); acb_div(c, a, a, prec); acb_div(d, a, b, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: aliasing a, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } /* test aliasing a, a, a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_set(b, a); acb_div(c, a, b, prec); acb_div(a, a, a, prec); if (!acb_overlaps(a, c)) { flint_printf("FAIL: aliasing a, a, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test (a+b)/c = a/c + b/c */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c, d, e, f; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(e); acb_init(f); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); acb_add(d, a, b, 2 + n_randint(state, 200)); acb_div(e, d, c, 2 + n_randint(state, 200)); acb_div(d, a, c, 2 + n_randint(state, 200)); acb_div(f, b, c, 2 + n_randint(state, 200)); acb_add(f, d, f, 2 + n_randint(state, 200)); if (!acb_overlaps(e, f)) { flint_printf("FAIL: (a+b)/c = a/c + b/c\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("e = "); acb_print(e); flint_printf("\n\n"); flint_printf("f = "); acb_print(f); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(e); acb_clear(f); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-exp.c000066400000000000000000000046701264125401100151760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("exp...."); fflush(stdout); flint_randinit(state); /* check exp(a+b) = exp(a)*exp(b) */ for (iter = 0; iter < 10000; iter++) { acb_t a, b, c, d, e; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(e); acb_randtest(a, state, 1 + n_randint(state, 200), 3); acb_randtest(b, state, 1 + n_randint(state, 200), 3); acb_randtest(c, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); acb_add(c, a, b, prec); acb_exp(c, c, prec); acb_exp(d, a, prec); acb_exp(e, b, prec); acb_mul(d, d, e, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-exp_invexp.c000066400000000000000000000043161264125401100165640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_invexp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t a, b, c, d, e; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(e); acb_randtest(a, state, 1 + n_randint(state, 200), 3); acb_randtest(b, state, 1 + n_randint(state, 200), 3); acb_randtest(c, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); acb_exp_invexp(b, c, a, prec); acb_mul(b, b, c, prec); acb_one(c); if (!acb_contains(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-exp_pi_i.c000066400000000000000000000056101264125401100161710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_pi_i...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t a, b, c, d; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(a, state, 1 + n_randint(state, 200), 3); acb_randtest(b, state, 1 + n_randint(state, 200), 3); acb_randtest(c, state, 1 + n_randint(state, 200), 3); acb_randtest(d, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); acb_exp_pi_i(b, a, prec); acb_const_pi(c, prec); acb_mul(c, c, a, prec); acb_mul_onei(c, c); acb_exp(d, c, prec); if (!acb_overlaps(d, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n"); flint_printf("d = "); acb_printd(d, 30); flint_printf("\n\n"); abort(); } acb_set(c, a); acb_exp_pi_i(c, c, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-gamma.c000066400000000000000000000052331264125401100154600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { acb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); arb_randtest_precise(acb_realref(a), state, 1 + n_randint(state, 1000), 3); arb_randtest_precise(acb_imagref(a), state, 1 + n_randint(state, 1000), 3); acb_gamma(b, a, prec1); acb_gamma(c, a, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } /* check gamma(z+1) = z gamma(z) */ acb_mul(b, b, a, prec1); acb_add_ui(c, a, 1, prec1); acb_gamma(c, c, prec1); if (!acb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-lgamma.c000066400000000000000000000057251264125401100156420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("lgamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 500); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); arb_randtest_precise(acb_realref(a), state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); arb_randtest_precise(acb_imagref(a), state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_lgamma(b, a, prec1); if (n_randint(state, 4) == 0) { acb_randtest(c, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_add(a, a, c, prec1); acb_sub(a, a, c, prec1); } acb_lgamma(c, a, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } /* check lgamma(z+1) = lgamma(z) + log(z) */ acb_log(c, a, prec1); acb_add(b, b, c, prec1); acb_add_ui(c, a, 1, prec1); acb_lgamma(c, c, prec1); if (!acb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-log.c000066400000000000000000000057311264125401100151620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("log...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_log(a, x, prec1); acb_log(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check exp(log(x)) = x */ acb_exp(b, b, prec1); if (!acb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_log(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-log1p.c000066400000000000000000000061351264125401100154220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("log1p...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_init(x); acb_init(a); acb_init(b); acb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_log1p(a, x, prec1); acb_log1p(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check log1p(x) = log(1+x) */ acb_add_ui(b, x, 1, prec2); acb_log(b, b, prec2); if (!acb_overlaps(a, b)) { flint_printf("FAIL: log1p vs log\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n\n"); abort(); } acb_log1p(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-log_sin_pi.c000066400000000000000000000056151264125401100165240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("log_sin_pi...."); fflush(stdout); flint_randinit(state); /* check functional equation S(s+1) = S(s) + log(-s) - log(s) */ for (iter = 0; iter < 10000; iter++) { acb_t s, s1, r, r1, t; slong prec; acb_init(s); acb_init(s1); acb_init(r); acb_init(r1); acb_init(t); prec = 2 + n_randint(state, 500); acb_randtest(s, state, 1 + n_randint(state, 500), 1 + n_randint(state, 10)); acb_randtest(r, state, 1 + n_randint(state, 500), 1 + n_randint(state, 10)); acb_randtest(r1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 10)); acb_log_sin_pi(r, s, prec); acb_add_ui(s1, s, 1, prec); if (n_randint(state, 4) == 0) { acb_randtest(t, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_add(s1, s1, t, prec); acb_sub(s1, s1, t, prec); } acb_log_sin_pi(r1, s1, prec); acb_log(t, s, prec); acb_sub(r, r, t, prec); acb_neg(t, s); acb_log(t, t, prec); acb_add(r, r, t, prec); if (!acb_overlaps(r, r1)) { flint_printf("FAIL: overlap\n\n"); flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n"); flint_printf("s1 = "); acb_printd(s1, 30); flint_printf("\n\n"); flint_printf("r = "); acb_printd(r, 30); flint_printf("\n\n"); flint_printf("r1 = "); acb_printd(r1, 30); flint_printf("\n\n"); abort(); } acb_clear(s); acb_clear(s1); acb_clear(r); acb_clear(r1); acb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-mul.c000066400000000000000000000231211264125401100151670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); /* test aliasing of c and a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_mul(c, a, b, prec); acb_mul(a, a, b, prec); if (!acb_equal(a, c)) { flint_printf("FAIL: aliasing c, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test aliasing of c and b */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_mul(c, a, b, prec); acb_mul(b, a, b, prec); if (!acb_equal(b, c)) { flint_printf("FAIL: aliasing b, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test aliasing a, a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c, d; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_set(b, a); acb_mul(c, a, a, prec); acb_mul(d, a, b, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: aliasing a, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } /* test aliasing a, a, a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_set(b, a); acb_mul(c, a, b, prec); acb_mul(a, a, a, prec); if (!acb_overlaps(a, c)) { flint_printf("FAIL: aliasing a, a, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test a*(b+c) = a*b + a*c */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c, d, e, f; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(e); acb_init(f); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); acb_add(d, b, c, 2 + n_randint(state, 200)); acb_mul(e, a, d, 2 + n_randint(state, 200)); acb_mul(d, a, b, 2 + n_randint(state, 200)); acb_mul(f, a, c, 2 + n_randint(state, 200)); acb_add(f, d, f, 2 + n_randint(state, 200)); if (!acb_overlaps(e, f)) { flint_printf("FAIL: a*(b+c) = a*b + a*c\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("e = "); acb_print(e); flint_printf("\n\n"); flint_printf("f = "); acb_print(f); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(e); acb_clear(f); } /* compare with mul_naive */ /* main test */ for (iter = 0; iter < 10000; iter++) { acb_t x, y, z, v; slong prec; acb_init(x); acb_init(y); acb_init(z); acb_init(v); for (iter2 = 0; iter2 < 100; iter2++) { acb_randtest_special(x, state, n_randint(state,2) ? 2000 : 200, 200); acb_randtest_special(y, state, n_randint(state,2) ? 2000 : 200, 200); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 5)) { case 0: acb_mul(z, x, y, prec); acb_mul_naive(v, x, y, prec); if (!acb_overlaps(z, v)) { flint_printf("FAIL!\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); flint_printf("v = "); acb_print(v); flint_printf("\n\n"); abort(); } break; case 1: acb_set(y, x); acb_mul(z, x, y, prec); acb_mul(v, x, x, prec); if (!acb_overlaps(z, v)) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); flint_printf("v = "); acb_print(v); flint_printf("\n\n"); abort(); } break; case 2: acb_mul(v, x, x, prec); acb_mul(x, x, x, prec); if (!acb_equal(v, x)) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); flint_printf("v = "); acb_print(v); flint_printf("\n\n"); abort(); } break; case 3: acb_mul(v, x, y, prec); acb_mul(x, x, y, prec); if (!acb_equal(v, x)) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("v = "); acb_print(v); flint_printf("\n\n"); abort(); } break; default: acb_mul(v, x, y, prec); acb_mul(x, y, x, prec); if (!acb_overlaps(v, x)) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("v = "); acb_print(v); flint_printf("\n\n"); abort(); } break; } } acb_clear(x); acb_clear(y); acb_clear(z); acb_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-mul_naive.c000066400000000000000000000145271264125401100163630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_naive...."); fflush(stdout); flint_randinit(state); /* test aliasing of c and a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_mul_naive(c, a, b, prec); acb_mul_naive(a, a, b, prec); if (!acb_equal(a, c)) { flint_printf("FAIL: aliasing c, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test aliasing of c and b */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_mul_naive(c, a, b, prec); acb_mul_naive(b, a, b, prec); if (!acb_equal(b, c)) { flint_printf("FAIL: aliasing b, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test aliasing a, a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c, d; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_set(b, a); acb_mul_naive(c, a, a, prec); acb_mul_naive(d, a, b, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: aliasing a, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } /* test aliasing a, a, a */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); acb_set(b, a); acb_mul_naive(c, a, b, prec); acb_mul_naive(a, a, a, prec); if (!acb_overlaps(a, c)) { flint_printf("FAIL: aliasing a, a, a\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } /* test a*(b+c) = a*b + a*c */ for (iter = 0; iter < 100000; iter++) { acb_t a, b, c, d, e, f; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(e); acb_init(f); acb_randtest(a, state, 1 + n_randint(state, 200), 10); acb_randtest(b, state, 1 + n_randint(state, 200), 10); acb_randtest(c, state, 1 + n_randint(state, 200), 10); acb_add(d, b, c, 2 + n_randint(state, 200)); acb_mul_naive(e, a, d, 2 + n_randint(state, 200)); acb_mul_naive(d, a, b, 2 + n_randint(state, 200)); acb_mul_naive(f, a, c, 2 + n_randint(state, 200)); acb_add(f, d, f, 2 + n_randint(state, 200)); if (!acb_overlaps(e, f)) { flint_printf("FAIL: a*(b+c) = a*b + a*c\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("e = "); acb_print(e); flint_printf("\n\n"); flint_printf("f = "); acb_print(f); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(e); acb_clear(f); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-polygamma.c000066400000000000000000000067531264125401100163740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" static const char *testdata[5] = { "-0.2487544770337842625472529935761139760973697136685351169998556396906930329999105060928584336658420889 +/- 1e-90", "-0.9189385332046727417803297364056176398613974736377834128171515404827656959272603976947432986359541976 +/- 1e-90", "-0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495 +/- 1e-90", "1.644934066848226436472415166646025189218949901206798437735558229370007470403200873833628900619758705 +/- 1e-90", "-2.404113806319188570799476323022899981529972584680997763584543110683676411572626180372911747218670516 +/- 1e-90", }; int main() { slong iter; flint_rand_t state; flint_printf("polygamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, s, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 500); prec2 = prec1 + 30; acb_init(a); acb_init(s); acb_init(b); acb_init(c); if (iter < 200) { slong i = n_randint(state, 5); acb_set_si(s, -2 + i); acb_one(a); acb_randtest(c, state, 1 + n_randint(state, 500), 3); acb_add(s, s, c, prec2); acb_sub(s, s, c, prec2); acb_polygamma(b, s, a, prec1); acb_zero(c); arb_set_str(acb_realref(c), testdata[i], prec2); } else { acb_randtest(a, state, 1 + n_randint(state, 500), 3); acb_randtest(s, state, 1 + n_randint(state, 500), 3); acb_polygamma(b, s, a, prec1); acb_randtest(c, state, 1 + n_randint(state, 500), 3); acb_add(s, s, c, prec2); acb_sub(s, s, c, prec2); acb_polygamma(c, s, a, prec2); } if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("s = "); acb_print(s); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(s); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-pow.c000066400000000000000000000103601264125401100152000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("pow...."); fflush(stdout); flint_randinit(state); /* check large arguments */ for (iter = 0; iter < 20000; iter++) { acb_t a, b, c, d, e, f; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(e); acb_init(f); acb_randtest(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200)); if (n_randint(state, 4) == 0) arb_zero(acb_imagref(a)); acb_randtest(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200)); if (n_randint(state, 4) == 0) arb_zero(acb_imagref(b)); acb_pow(c, a, b, prec1); acb_pow(d, a, b, prec2); if (!acb_overlaps(c, d)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_randtest(c, state, 1 + n_randint(state, 1000), 200); /* check a^(b+c) = a^b*a^c */ acb_add(e, b, c, prec1); acb_pow(d, a, e, prec1); acb_pow(e, a, b, prec1); acb_pow(f, a, c, prec1); acb_mul(e, e, f, prec1); if (!acb_overlaps(d, e)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); flint_printf("e = "); acb_print(e); flint_printf("\n\n"); abort(); } acb_pow(c, a, b, prec1); acb_set(d, a); acb_pow(d, d, b, prec2); if (!acb_overlaps(c, d)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_set(d, b); acb_pow(d, a, d, prec2); if (!acb_overlaps(c, d)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(e); acb_clear(f); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-pow_fmpz.c000066400000000000000000000063601264125401100162410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { acb_t a, b, c, d; fmpz_t e1, e2, e3; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); acb_init(d); fmpz_init(e1); fmpz_init(e2); fmpz_init(e3); acb_randtest(a, state, 1 + n_randint(state, 1000), 200); acb_randtest(b, state, 1 + n_randint(state, 1000), 200); fmpz_randtest(e1, state, 200); fmpz_randtest(e2, state, 200); acb_pow_fmpz(b, a, e1, prec1); acb_pow_fmpz(c, a, e1, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("e1 = "); fmpz_print(e1); flint_printf("\n\n"); abort(); } /* check a^(e1+e2) = a^e1*a^e2 */ acb_pow_fmpz(c, a, e2, prec1); acb_mul(d, b, c, prec1); fmpz_add(e3, e1, e2); acb_pow_fmpz(c, a, e3, prec1); if (!acb_overlaps(c, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); flint_printf("e1 = "); fmpz_print(e1); flint_printf("\n\n"); flint_printf("e2 = "); fmpz_print(e2); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); fmpz_clear(e1); fmpz_clear(e2); fmpz_clear(e3); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-quadratic_roots_fmpz.c000066400000000000000000000062701264125401100206370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("quadratic_roots_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t r1, r2, x, y; fmpz_t a, b, c; slong prec; fmpz_init(a); fmpz_init(b); fmpz_init(c); acb_init(r1); acb_init(r2); acb_init(x); acb_init(y); prec = 2 + n_randint(state, 1000); fmpz_randtest_not_zero(a, state, 1 + n_randint(state, 1000)); fmpz_randtest(b, state, 1 + n_randint(state, 1000)); fmpz_randtest(c, state, 1 + n_randint(state, 1000)); acb_randtest(r1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(r2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_quadratic_roots_fmpz(r1, r2, a, b, c, prec); acb_mul(x, r1, r1, prec); acb_mul_fmpz(x, x, a, prec); acb_addmul_fmpz(x, r1, b, prec); acb_add_fmpz(x, x, c, prec); acb_mul(y, r2, r2, prec); acb_mul_fmpz(y, y, a, prec); acb_addmul_fmpz(y, r2, b, prec); acb_add_fmpz(y, y, c, prec); if (!acb_contains_zero(x) || !acb_contains_zero(y) || acb_rel_accuracy_bits(r1) < prec - 4 || acb_rel_accuracy_bits(r2) < prec - 4) { flint_printf("FAIL: containment / accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("a = "); fmpz_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("c = "); fmpz_print(c); flint_printf("\n\n"); flint_printf("r1 = "); acb_printd(r1, 30); flint_printf("\n\n"); flint_printf("r2 = "); acb_printd(r2, 30); flint_printf("\n\n"); abort(); } fmpz_clear(a); fmpz_clear(b); fmpz_clear(c); acb_clear(r1); acb_clear(r2); acb_clear(x); acb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rel_accuracy_bits.c000066400000000000000000000071511264125401100200540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rel_accuracy_bits...."); fflush(stdout); flint_randinit(state); /* test aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t x; acb_t z; slong a1, a2; arb_init(x); acb_init(z); arb_randtest_special(x, state, 1 + n_randint(state, 200), 1 + n_randint(state, 200)); acb_set_arb(z, x); a1 = arb_rel_accuracy_bits(x); a2 = acb_rel_accuracy_bits(z); if (a1 != a2) { flint_printf("FAIL: acb != arb\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); flint_printf("a1 = %wd, a2 = %wd\n\n", a1, a2); abort(); } acb_randtest_special(z, state, 1 + n_randint(state, 200), 1 + n_randint(state, 200)); a1 = acb_rel_accuracy_bits(z); if (n_randint(state, 2)) arf_swap(arb_midref(acb_realref(z)), arb_midref(acb_imagref(z))); if (n_randint(state, 2)) mag_swap(arb_radref(acb_realref(z)), arb_radref(acb_imagref(z))); a2 = acb_rel_accuracy_bits(z); if (a1 != a2) { flint_printf("FAIL: swapping\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); flint_printf("a1 = %wd, a2 = %wd\n\n", a1, a2); abort(); } acb_randtest_special(z, state, 1 + n_randint(state, 200), 1 + n_randint(state, 200)); if (arf_cmpabs(arb_midref(acb_realref(z)), arb_midref(acb_imagref(z))) >= 0) arf_set(arb_midref(x), arb_midref(acb_realref(z))); else arf_set(arb_midref(x), arb_midref(acb_imagref(z))); if (mag_cmp(arb_radref(acb_realref(z)), arb_radref(acb_imagref(z))) >= 0) mag_set(arb_radref(x), arb_radref(acb_realref(z))); else mag_set(arb_radref(x), arb_radref(acb_imagref(z))); a1 = acb_rel_accuracy_bits(z); a2 = arb_rel_accuracy_bits(x); if (a1 != a2) { flint_printf("FAIL: acb != arb (2)\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); flint_printf("a1 = %wd, a2 = %wd\n\n", a1, a2); abort(); } arb_clear(x); acb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rgamma.c000066400000000000000000000052351264125401100156440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rgamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { acb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); arb_randtest_precise(acb_realref(a), state, 1 + n_randint(state, 1000), 3); arb_randtest_precise(acb_imagref(a), state, 1 + n_randint(state, 1000), 3); acb_rgamma(b, a, prec1); acb_rgamma(c, a, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } /* check 1/gamma(z+1) = 1/gamma(z)/z */ acb_div(b, b, a, prec1); acb_add_ui(c, a, 1, prec1); acb_rgamma(c, c, prec1); if (!acb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising2_ui.c000066400000000000000000000076031264125401100164530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising2_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, u, v, u2, v2; fmpz *f; acb_ptr g; ulong n; slong i, prec; acb_init(a); acb_init(u); acb_init(v); acb_init(u2); acb_init(v2); acb_randtest(a, state, 1 + n_randint(state, 4000), 10); acb_randtest(u, state, 1 + n_randint(state, 4000), 10); acb_randtest(v, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 120); f = _fmpz_vec_init(n + 1); g = _acb_vec_init(n + 1); prec = 2 + n_randint(state, 4000); acb_rising2_ui(u, v, a, n, prec); arith_stirling_number_1u_vec(f, n, n + 1); for (i = 0; i <= n; i++) acb_set_fmpz(g + i, f + i); _acb_poly_evaluate(u2, g, n + 1, a, prec); _acb_poly_derivative(g, g, n + 1, prec); _acb_poly_evaluate(v2, g, n, a, prec); if (!acb_overlaps(u, u2) || !acb_overlaps(v, v2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n"); flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n"); abort(); } acb_set(u2, a); acb_rising2_ui(u2, v, u2, n, prec); if (!acb_equal(u2, u)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_set(v2, a); acb_rising2_ui(u, v2, v2, n, prec); if (!acb_equal(v2, v)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_clear(a); acb_clear(u); acb_clear(v); acb_clear(u2); acb_clear(v2); _fmpz_vec_clear(f, n + 1); _acb_vec_clear(g, n + 1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising2_ui_bs.c000066400000000000000000000076171264125401100171440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising2_ui_bs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, u, v, u2, v2; fmpz *f; acb_ptr g; ulong n; slong i, prec; acb_init(a); acb_init(u); acb_init(v); acb_init(u2); acb_init(v2); acb_randtest(a, state, 1 + n_randint(state, 4000), 10); acb_randtest(u, state, 1 + n_randint(state, 4000), 10); acb_randtest(v, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 120); f = _fmpz_vec_init(n + 1); g = _acb_vec_init(n + 1); prec = 2 + n_randint(state, 4000); acb_rising2_ui_bs(u, v, a, n, prec); arith_stirling_number_1u_vec(f, n, n + 1); for (i = 0; i <= n; i++) acb_set_fmpz(g + i, f + i); _acb_poly_evaluate(u2, g, n + 1, a, prec); _acb_poly_derivative(g, g, n + 1, prec); _acb_poly_evaluate(v2, g, n, a, prec); if (!acb_overlaps(u, u2) || !acb_overlaps(v, v2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n"); flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n"); abort(); } acb_set(u2, a); acb_rising2_ui_bs(u2, v, u2, n, prec); if (!acb_equal(u2, u)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_set(v2, a); acb_rising2_ui_bs(u, v2, v2, n, prec); if (!acb_equal(v2, v)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_clear(a); acb_clear(u); acb_clear(v); acb_clear(u2); acb_clear(v2); _fmpz_vec_clear(f, n + 1); _acb_vec_clear(g, n + 1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising2_ui_rs.c000066400000000000000000000076301264125401100171570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising2_ui_rs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, u, v, u2, v2; fmpz *f; acb_ptr g; ulong n; slong i, prec; acb_init(a); acb_init(u); acb_init(v); acb_init(u2); acb_init(v2); acb_randtest(a, state, 1 + n_randint(state, 4000), 10); acb_randtest(u, state, 1 + n_randint(state, 4000), 10); acb_randtest(v, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 120); f = _fmpz_vec_init(n + 1); g = _acb_vec_init(n + 1); prec = 2 + n_randint(state, 4000); acb_rising2_ui_rs(u, v, a, n, 0, prec); arith_stirling_number_1u_vec(f, n, n + 1); for (i = 0; i <= n; i++) acb_set_fmpz(g + i, f + i); _acb_poly_evaluate(u2, g, n + 1, a, prec); _acb_poly_derivative(g, g, n + 1, prec); _acb_poly_evaluate(v2, g, n, a, prec); if (!acb_overlaps(u, u2) || !acb_overlaps(v, v2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n"); flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n"); abort(); } acb_set(u2, a); acb_rising2_ui_rs(u2, v, u2, n, 0, prec); if (!acb_equal(u2, u)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); acb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); acb_printd(u2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_set(v2, a); acb_rising2_ui_rs(u, v2, v2, n, 0, prec); if (!acb_equal(v2, v)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("v = "); acb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); acb_printd(v2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_clear(a); acb_clear(u); acb_clear(v); acb_clear(u2); acb_clear(v2); _fmpz_vec_clear(f, n + 1); _acb_vec_clear(g, n + 1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising_ui.c000066400000000000000000000065001264125401100163640ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui...."); fflush(stdout); flint_randinit(state); /* check functional equation */ for (iter = 0; iter < 1000; iter++) { acb_t x, xn, y, z; ulong n, m; acb_init(x); acb_init(xn); acb_init(y); acb_init(z); acb_randtest(x, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 80); m = n_randint(state, 40); acb_add_ui(xn, x, n, 1 + n_randint(state, 4000)); acb_rising_ui(y, x, n, 2 + n_randint(state, 4000)); acb_rising_ui(z, xn, m, 2 + n_randint(state, 4000)); acb_mul(y, y, z, 2 + n_randint(state, 4000)); acb_rising_ui(z, x, n + m, 2 + n_randint(state, 4000)); if (!acb_overlaps(y, z)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("m = %wu\n", m); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("xn = "); acb_print(xn); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(xn); acb_clear(y); acb_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 1000; iter++) { acb_t x, y; ulong n; slong prec; acb_init(x); acb_init(y); acb_randtest(x, state, 1 + n_randint(state, 200), 10); acb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); prec = 2 + n_randint(state, 4000); acb_rising_ui(y, x, n, prec); acb_rising_ui(x, x, n, prec); if (!acb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_clear(x); acb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising_ui_bs.c000066400000000000000000000065221264125401100170540ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_bs...."); fflush(stdout); flint_randinit(state); /* check functional equation */ for (iter = 0; iter < 1000; iter++) { acb_t x, xn, y, z; ulong n, m; acb_init(x); acb_init(xn); acb_init(y); acb_init(z); acb_randtest(x, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 40); m = n_randint(state, 40); acb_add_ui(xn, x, n, 1 + n_randint(state, 4000)); acb_rising_ui_bs(y, x, n, 2 + n_randint(state, 4000)); acb_rising_ui_bs(z, xn, m, 2 + n_randint(state, 4000)); acb_mul(y, y, z, 2 + n_randint(state, 4000)); acb_rising_ui_bs(z, x, n + m, 2 + n_randint(state, 4000)); if (!acb_overlaps(y, z)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("m = %wu\n", m); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("xn = "); acb_print(xn); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(xn); acb_clear(y); acb_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 1000; iter++) { acb_t x, y; ulong n; slong prec; acb_init(x); acb_init(y); acb_randtest(x, state, 1 + n_randint(state, 200), 10); acb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); prec = 2 + n_randint(state, 4000); acb_rising_ui_bs(y, x, n, prec); acb_rising_ui_bs(x, x, n, prec); if (!acb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_clear(x); acb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising_ui_get_mag.c000066400000000000000000000044011264125401100200450ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_get_mag...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, y, z; mag_t b; ulong n; acb_init(x); acb_init(y); acb_init(z); mag_init(b); acb_randtest(x, state, 1 + n_randint(state, 400), 1 + n_randint(state, 100)); n = n_randint(state, 80); acb_rising_ui(y, x, n, 2 + n_randint(state, 400)); acb_rising_ui_get_mag(b, x, n); acb_zero(z); acb_add_error_mag(z, b); if (!acb_overlaps(y, z)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); acb_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(z); mag_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising_ui_rec.c000066400000000000000000000065301264125401100172200ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_rec...."); fflush(stdout); flint_randinit(state); /* check functional equation */ for (iter = 0; iter < 1000; iter++) { acb_t x, xn, y, z; ulong n, m; acb_init(x); acb_init(xn); acb_init(y); acb_init(z); acb_randtest(x, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 80); m = n_randint(state, 40); acb_add_ui(xn, x, n, 1 + n_randint(state, 4000)); acb_rising_ui_rec(y, x, n, 2 + n_randint(state, 4000)); acb_rising_ui_rec(z, xn, m, 2 + n_randint(state, 4000)); acb_mul(y, y, z, 2 + n_randint(state, 4000)); acb_rising_ui_rec(z, x, n + m, 2 + n_randint(state, 4000)); if (!acb_overlaps(y, z)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("m = %wu\n", m); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("xn = "); acb_print(xn); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(xn); acb_clear(y); acb_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 1000; iter++) { acb_t x, y; ulong n; slong prec; acb_init(x); acb_init(y); acb_randtest(x, state, 1 + n_randint(state, 200), 10); acb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); prec = 2 + n_randint(state, 4000); acb_rising_ui_rec(y, x, n, prec); acb_rising_ui_rec(x, x, n, prec); if (!acb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_clear(x); acb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rising_ui_rs.c000066400000000000000000000070651264125401100170770ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_rs...."); fflush(stdout); flint_randinit(state); /* check functional equation */ for (iter = 0; iter < 1000; iter++) { acb_t x, xn, y, z; ulong n, m, step1, step2, step3; acb_init(x); acb_init(xn); acb_init(y); acb_init(z); acb_randtest(x, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 80); m = n_randint(state, 40); acb_add_ui(xn, x, n, 1 + n_randint(state, 4000)); step1 = n_randint(state, 20); step2 = n_randint(state, 20); step3 = n_randint(state, 20); acb_rising_ui_rs(y, x, n, step1, 2 + n_randint(state, 4000)); acb_rising_ui_rs(z, xn, m, step2, 2 + n_randint(state, 4000)); acb_mul(y, y, z, 2 + n_randint(state, 4000)); acb_rising_ui_rs(z, x, n + m, step3, 2 + n_randint(state, 4000)); if (!acb_overlaps(y, z)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("m = %wu\n", m); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("xn = "); acb_print(xn); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(xn); acb_clear(y); acb_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 1000; iter++) { acb_t x, y; ulong n; slong prec; ulong step; acb_init(x); acb_init(y); acb_randtest(x, state, 1 + n_randint(state, 200), 10); acb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); step = n_randint(state, 20); prec = 2 + n_randint(state, 4000); acb_rising_ui_rs(y, x, n, step, prec); acb_rising_ui_rs(x, x, n, step, prec); if (!acb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } acb_clear(x); acb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-root_ui.c000066400000000000000000000046311264125401100160570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("root_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, b, c; ulong k; slong prec; prec = 2 + n_randint(state, 1000); k = n_randtest_not_zero(state); acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_root_ui(b, a, k, prec); acb_pow_ui(c, b, k, prec); if (!acb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("k = %wu\n", k); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_root_ui(a, a, k, prec); if (!acb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-rsqrt.c000066400000000000000000000047061264125401100155550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("rsqrt...."); fflush(stdout); flint_randinit(state); /* check (a^(-1/2))^(-2) = a */ for (iter = 0; iter < 10000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 2000), 10); acb_randtest(b, state, 1 + n_randint(state, 2000), 10); prec = 2 + n_randint(state, 2000); acb_rsqrt(b, a, prec); acb_inv(c, b, prec); acb_mul(c, c, c, prec); if (!acb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_rsqrt(a, a, prec); if (!acb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-sin_cos.c000066400000000000000000000101341264125401100160270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos...."); fflush(stdout); flint_randinit(state); /* check sin(a+b) = cos(b)*sin(a) + cos(a)*sin(b) */ for (iter = 0; iter < 10000; iter++) { acb_t a, b, c, d, cosa, sina, cosb, sinb; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(cosa); acb_init(sina); acb_init(cosb); acb_init(sinb); acb_randtest(a, state, 1 + n_randint(state, 200), 3); acb_randtest(b, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); acb_add(c, a, b, prec); acb_sin(c, c, prec); acb_sin_cos(sina, cosa, a, prec); acb_sin_cos(sinb, cosb, b, prec); acb_mul(cosb, cosb, sina, prec); acb_mul(cosa, cosa, sinb, prec); acb_add(d, cosa, cosb, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: sin(a+b) = cos(b)*sin(a) + cos(a)*sin(b)\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(cosa); acb_clear(sina); acb_clear(cosb); acb_clear(sinb); } /* check cos(a+b) = cos(b)*cos(a) - sin(a)*sin(b) */ for (iter = 0; iter < 10000; iter++) { acb_t a, b, c, d, cosa, sina, cosb, sinb; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(cosa); acb_init(sina); acb_init(cosb); acb_init(sinb); acb_randtest(a, state, 1 + n_randint(state, 200), 3); acb_randtest(b, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); acb_add(c, a, b, prec); acb_cos(c, c, prec); acb_sin_cos(sina, cosa, a, prec); acb_sin_cos(sinb, cosb, b, prec); acb_mul(cosa, cosa, cosb, prec); acb_mul(sina, sina, sinb, prec); acb_sub(d, cosa, sina, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: cos(a+b) = cos(b)*cos(a) - sin(a)*sin(b)\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(cosa); acb_clear(sina); acb_clear(cosb); acb_clear(sinb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-sin_pi.c000066400000000000000000000060751264125401100156640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, y, a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_randtest(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_sin_pi(a, x, prec1); acb_sin_pi(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* compare with cos */ arb_const_pi(acb_realref(c), prec1); acb_mul_arb(y, x, acb_realref(c), prec1); acb_sin(c, y, prec1); if (!acb_overlaps(a, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_sin_pi(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-sinh_cosh.c000066400000000000000000000101741264125401100163530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("sinh_cosh...."); fflush(stdout); flint_randinit(state); /* check sinh(a+b) = cosh(b)*sinh(a) + cosh(a)*sinh(b) */ for (iter = 0; iter < 10000; iter++) { acb_t a, b, c, d, cosa, sina, cosb, sinb; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(cosa); acb_init(sina); acb_init(cosb); acb_init(sinb); acb_randtest(a, state, 1 + n_randint(state, 200), 3); acb_randtest(b, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); acb_add(c, a, b, prec); acb_sinh(c, c, prec); acb_sinh_cosh(sina, cosa, a, prec); acb_sinh_cosh(sinb, cosb, b, prec); acb_mul(cosb, cosb, sina, prec); acb_mul(cosa, cosa, sinb, prec); acb_add(d, cosa, cosb, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: sinh(a+b) = cosh(b)*sinh(a) + cosh(a)*sinh(b)\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(cosa); acb_clear(sina); acb_clear(cosb); acb_clear(sinb); } /* check cosh(a+b) = cosh(b)*cosh(a) + sinh(a)*sinh(b) */ for (iter = 0; iter < 10000; iter++) { acb_t a, b, c, d, cosa, sina, cosb, sinb; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_init(cosa); acb_init(sina); acb_init(cosb); acb_init(sinb); acb_randtest(a, state, 1 + n_randint(state, 200), 3); acb_randtest(b, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); acb_add(c, a, b, prec); acb_cosh(c, c, prec); acb_sinh_cosh(sina, cosa, a, prec); acb_sinh_cosh(sinb, cosb, b, prec); acb_mul(cosa, cosa, cosb, prec); acb_mul(sina, sina, sinb, prec); acb_add(d, cosa, sina, prec); if (!acb_overlaps(c, d)) { flint_printf("FAIL: cosh(a+b) = cosh(b)*cosh(a) + sinh(a)*sinh(b)\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); acb_clear(cosa); acb_clear(sina); acb_clear(cosb); acb_clear(sinb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-sqrt.c000066400000000000000000000046421264125401100153720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt...."); fflush(stdout); flint_randinit(state); /* check (a^(1/2))^2 = a */ for (iter = 0; iter < 10000; iter++) { acb_t a, b, c; slong prec; acb_init(a); acb_init(b); acb_init(c); acb_randtest(a, state, 1 + n_randint(state, 2000), 10); acb_randtest(b, state, 1 + n_randint(state, 2000), 10); prec = 2 + n_randint(state, 2000); acb_sqrt(b, a, prec); acb_mul(c, b, b, prec); if (!acb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_sqrt(a, a, prec); if (!acb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-tan.c000066400000000000000000000065361264125401100151670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("tan...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, y, a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_randtest(y, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_tan(a, x, prec1); acb_tan(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* check tan(x+y) = (tan(x) + tan(y)) / (1 - tan(x) tan(y)) */ acb_add(b, x, y, prec1); acb_tan(b, b, prec1); acb_tan(c, y, prec1); acb_add(d, a, c, prec1); acb_mul(c, a, c, prec1); acb_sub_ui(c, c, 1, prec1); acb_neg(c, c); acb_div(d, d, c, prec1); if (!acb_overlaps(b, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_tan(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-tan_pi.c000066400000000000000000000060761264125401100156560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("tan_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t x, y, a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_randtest(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); acb_tan_pi(a, x, prec1); acb_tan_pi(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* compare with tan */ arb_const_pi(acb_realref(c), prec1); acb_mul_arb(y, x, acb_realref(c), prec1); acb_tan(c, y, prec1); if (!acb_overlaps(a, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_tan_pi(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-tanh.c000066400000000000000000000065161264125401100153350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("tanh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t x, y, a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 200); prec2 = prec1 + 30; acb_init(x); acb_init(y); acb_init(a); acb_init(b); acb_init(c); acb_init(d); acb_randtest(x, state, 1 + n_randint(state, 200), 2 + n_randint(state, 100)); acb_randtest(y, state, 1 + n_randint(state, 200), 2 + n_randint(state, 100)); acb_tanh(a, x, prec1); acb_tanh(b, x, prec2); /* check consistency */ if (!acb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); abort(); } /* check tanh(x+y) = (tanh(x) + tanh(y)) / (1 + tanh(x) tanh(y)) */ acb_add(b, x, y, prec1); acb_tanh(b, b, prec1); acb_tanh(c, y, prec1); acb_add(d, a, c, prec1); acb_mul(c, a, c, prec1); acb_add_ui(c, c, 1, prec1); acb_div(d, d, c, prec1); if (!acb_overlaps(b, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); flint_printf("y = "); acb_print(y); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("d = "); acb_print(d); flint_printf("\n\n"); abort(); } acb_tanh(x, x, prec1); if (!acb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("x = "); acb_print(x); flint_printf("\n\n"); abort(); } acb_clear(x); acb_clear(y); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/test/t-zeta.c000066400000000000000000000042521264125401100153410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { acb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 500); prec2 = prec1 + 30; acb_init(a); acb_init(b); acb_init(c); arb_randtest_precise(acb_realref(a), state, 1 + n_randint(state, 500), 5); arb_randtest_precise(acb_imagref(a), state, 1 + n_randint(state, 500), 3); acb_zeta(b, a, prec1); acb_zeta(c, a, prec2); if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb/vec_sort_pretty.c000066400000000000000000000034761264125401100164200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" #ifndef __compar_fn_t typedef int (*__compar_fn_t) (__const void *, __const void *); #endif int acb_cmp_pretty(const acb_t a, const acb_t b) { arb_t t, u, v; int res; arb_init(t); arb_init(u); arb_init(v); arb_abs(u, acb_imagref(a)); arb_abs(v, acb_imagref(b)); arb_sub(t, u, v, MAG_BITS); res = 0; if (arb_contains_zero(t)) { arb_sub(t, acb_realref(a), acb_realref(b), MAG_BITS); res = arb_is_positive(t) ? 1 : -1; } else { res = arb_is_positive(t) ? 1 : -1; } arb_clear(t); arb_clear(u); arb_clear(v); return res; } void _acb_vec_sort_pretty(acb_ptr vec, slong len) { qsort(vec, len, sizeof(acb_struct), (__compar_fn_t) acb_cmp_pretty); } arb-2.8.1/acb/zeta.c000066400000000000000000000056711264125401100141270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb.h" #include "acb_poly.h" void acb_zeta_si(acb_t z, slong s, slong prec) { if (s >= 0) { arb_zeta_ui(acb_realref(z), s, prec); } else { arb_bernoulli_ui(acb_realref(z), 1-s, prec); arb_div_ui(acb_realref(z), acb_realref(z), 1-s, prec); arb_neg(acb_realref(z), acb_realref(z)); } arb_zero(acb_imagref(z)); return; } void acb_hurwitz_zeta(acb_t z, const acb_t s, const acb_t a, slong prec) { if (acb_is_one(a) && acb_is_int(s) && arf_cmpabs_2exp_si(arb_midref(acb_realref(s)), FLINT_BITS - 1) < 0) { acb_zeta_si(z, arf_get_si(arb_midref(acb_realref(s)), ARF_RND_DOWN), prec); return; } _acb_poly_zeta_cpx_series(z, s, a, 0, 1, prec); } void acb_zeta(acb_t z, const acb_t s, slong prec) { acb_t a; acb_init(a); acb_one(a); if (acb_is_int(s) && arf_cmpabs_2exp_si(arb_midref(acb_realref(s)), FLINT_BITS - 1) < 0) { acb_zeta_si(z, arf_get_si(arb_midref(acb_realref(s)), ARF_RND_DOWN), prec); return; } if (arf_sgn(arb_midref(acb_realref(s))) < 0) { acb_t t, u, v; slong wp = prec + 6; acb_init(t); acb_init(u); acb_init(v); acb_sub_ui(t, s, 1, wp); /* 2 * (2pi)^(s-1) */ arb_const_pi(acb_realref(u), wp); acb_mul_2exp_si(u, u, 1); acb_pow(u, u, t, wp); acb_mul_2exp_si(u, u, 1); /* sin(pi*s/2) */ acb_mul_2exp_si(v, s, -1); acb_sin_pi(v, v, wp); acb_mul(u, u, v, wp); /* gamma(1-s) zeta(1-s) */ acb_neg(t, t); acb_gamma(v, t, wp); acb_mul(u, u, v, wp); acb_hurwitz_zeta(v, t, a, wp); acb_mul(z, u, v, prec); acb_clear(t); acb_clear(u); acb_clear(v); } else { acb_hurwitz_zeta(z, s, a, prec); } acb_clear(a); } arb-2.8.1/acb_calc.h000066400000000000000000000033751264125401100141520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #ifndef ACB_CALC_H #define ACB_CALC_H #include "acb.h" #include "acb_poly.h" #include "acb_mat.h" #include "arb_calc.h" #ifdef __cplusplus extern "C" { #endif typedef int (*acb_calc_func_t)(acb_ptr out, const acb_t inp, void * param, slong order, slong prec); /* Bounds */ void acb_calc_cauchy_bound(arb_t bound, acb_calc_func_t func, void * param, const acb_t x, const arb_t radius, slong maxdepth, slong prec); /* Integration */ int acb_calc_integrate_taylor(acb_t res, acb_calc_func_t func, void * param, const acb_t a, const acb_t b, const arf_t inner_radius, const arf_t outer_radius, slong accuracy_goal, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/acb_calc/000077500000000000000000000000001264125401100137715ustar00rootroot00000000000000arb-2.8.1/acb_calc/cauchy_bound.c000066400000000000000000000062431264125401100166050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_calc.h" void acb_calc_cauchy_bound(arb_t bound, acb_calc_func_t func, void * param, const acb_t x, const arb_t radius, slong maxdepth, slong prec) { slong i, n, depth, wp; arb_t pi, theta, v, s1, c1, s2, c2, st, ct; acb_t t, u; arb_t b; arb_init(pi); arb_init(theta); arb_init(v); arb_init(s1); arb_init(c1); arb_init(s2); arb_init(c2); arb_init(st); arb_init(ct); acb_init(t); acb_init(u); arb_init(b); wp = prec + 20; arb_const_pi(pi, wp); arb_zero_pm_inf(b); for (depth = 0, n = 16; depth < maxdepth; n *= 2, depth++) { arb_zero(b); /* theta = 2 pi / n */ arb_div_ui(theta, pi, n, wp); arb_mul_2exp_si(theta, theta, 1); /* sine and cosine of i*theta and (i+1)*theta */ arb_zero(s1); arb_one(c1); arb_sin_cos(st, ct, theta, wp); arb_set(s2, st); arb_set(c2, ct); for (i = 0; i < n; i++) { /* sine and cosine of 2 pi ([i,i+1]/n) */ /* since we use power of two subdivision points, the sine and cosine are monotone on each subinterval */ arb_union(acb_realref(t), c1, c2, wp); arb_union(acb_imagref(t), s1, s2, wp); acb_mul_arb(t, t, radius, wp); acb_add(t, t, x, prec); /* next angle */ arb_mul(v, c2, ct, wp); arb_mul(c1, s2, st, wp); arb_sub(c1, v, c1, wp); arb_mul(v, c2, st, wp); arb_mul(s1, s2, ct, wp); arb_add(s1, v, s1, wp); arb_swap(c1, c2); arb_swap(s1, s2); func(u, t, param, 1, prec); acb_abs(v, u, prec); arb_add(b, b, v, prec); } arb_div_ui(b, b, n, prec); if (arb_is_positive(b)) break; } arb_set(bound, b); arb_clear(pi); arb_clear(theta); arb_clear(v); acb_clear(t); acb_clear(u); arb_clear(b); arb_clear(s1); arb_clear(c1); arb_clear(s2); arb_clear(c2); arb_clear(st); arb_clear(ct); } arb-2.8.1/acb_calc/integrate_taylor.c000066400000000000000000000162241264125401100175160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_calc.h" #include "math.h" int acb_calc_integrate_taylor(acb_t res, acb_calc_func_t func, void * param, const acb_t a, const acb_t b, const arf_t inner_radius, const arf_t outer_radius, slong accuracy_goal, slong prec) { slong num_steps, step, N, bp; int result; acb_t delta, m, x, y1, y2, sum; acb_ptr taylor_poly; arf_t err; acb_init(delta); acb_init(m); acb_init(x); acb_init(y1); acb_init(y2); acb_init(sum); arf_init(err); acb_sub(delta, b, a, prec); /* precision used for bounds calculations */ bp = MAG_BITS; /* compute the number of steps */ { arf_t t; arf_init(t); acb_get_abs_ubound_arf(t, delta, bp); arf_div(t, t, inner_radius, bp, ARF_RND_UP); arf_mul_2exp_si(t, t, -1); num_steps = (slong) (arf_get_d(t, ARF_RND_UP) + 1.0); /* make sure it's not something absurd */ num_steps = FLINT_MIN(num_steps, 10 * prec); num_steps = FLINT_MAX(num_steps, 1); arf_clear(t); } result = ARB_CALC_SUCCESS; acb_zero(sum); for (step = 0; step < num_steps; step++) { /* midpoint of subinterval */ acb_mul_ui(m, delta, 2 * step + 1, prec); acb_div_ui(m, m, 2 * num_steps, prec); acb_add(m, m, a, prec); if (arb_calc_verbose) { flint_printf("integration point %wd/%wd: ", 2 * step + 1, 2 * num_steps); acb_printd(m, 15); flint_printf("\n"); } /* evaluate at +/- x */ /* TODO: exactify m, and include error in x? */ acb_div_ui(x, delta, 2 * num_steps, prec); /* compute bounds and number of terms to use */ { arb_t cbound, xbound, rbound; arf_t C, D, R, X, T; double DD, TT, NN; arb_init(cbound); arb_init(xbound); arb_init(rbound); arf_init(C); arf_init(D); arf_init(R); arf_init(X); arf_init(T); /* R is the outer radius */ arf_set(R, outer_radius); /* X = upper bound for |x| */ acb_get_abs_ubound_arf(X, x, bp); arb_set_arf(xbound, X); /* Compute C(m,R). Important subtlety: due to rounding when computing m, we will in general be farther than R away from the integration path. But since acb_calc_cauchy_bound actually integrates over the area traced by a complex interval, it will catch any extra singularities (giving an infinite bound). */ arb_set_arf(rbound, outer_radius); acb_calc_cauchy_bound(cbound, func, param, m, rbound, 8, bp); arf_set_mag(C, arb_radref(cbound)); arf_add(C, arb_midref(cbound), C, bp, ARF_RND_UP); /* Sanity check: we need C < inf and R > X */ if (arf_is_finite(C) && arf_cmp(R, X) > 0) { /* Compute upper bound for D = C * R * X / (R - X) */ arf_mul(D, C, R, bp, ARF_RND_UP); arf_mul(D, D, X, bp, ARF_RND_UP); arf_sub(T, R, X, bp, ARF_RND_DOWN); arf_div(D, D, T, bp, ARF_RND_UP); /* Compute upper bound for T = (X / R) */ arf_div(T, X, R, bp, ARF_RND_UP); /* Choose N */ /* TODO: use arf arithmetic to avoid overflow */ /* TODO: use relative accuracy (look at |f(m)|?) */ DD = arf_get_d(D, ARF_RND_UP); TT = arf_get_d(T, ARF_RND_UP); NN = -(accuracy_goal * 0.69314718055994530942 + log(DD)) / log(TT); N = NN + 0.5; N = FLINT_MIN(N, 100 * prec); N = FLINT_MAX(N, 1); /* Tail bound: D / (N + 1) * T^N */ { mag_t TT; mag_init(TT); arf_get_mag(TT, T); mag_pow_ui(TT, TT, N); arf_set_mag(T, TT); mag_clear(TT); } arf_mul(D, D, T, bp, ARF_RND_UP); arf_div_ui(err, D, N + 1, bp, ARF_RND_UP); } else { N = 1; arf_pos_inf(err); result = ARB_CALC_NO_CONVERGENCE; } if (arb_calc_verbose) { flint_printf("N = %wd; bound: ", N); arf_printd(err, 15); flint_printf("\n"); flint_printf("R: "); arf_printd(R, 15); flint_printf("\n"); flint_printf("C: "); arf_printd(C, 15); flint_printf("\n"); flint_printf("X: "); arf_printd(X, 15); flint_printf("\n"); } arb_clear(cbound); arb_clear(xbound); arb_clear(rbound); arf_clear(C); arf_clear(D); arf_clear(R); arf_clear(X); arf_clear(T); } /* evaluate Taylor polynomial */ taylor_poly = _acb_vec_init(N + 1); func(taylor_poly, m, param, N, prec); _acb_poly_integral(taylor_poly, taylor_poly, N + 1, prec); _acb_poly_evaluate(y2, taylor_poly, N + 1, x, prec); acb_neg(x, x); _acb_poly_evaluate(y1, taylor_poly, N + 1, x, prec); acb_neg(x, x); /* add truncation error */ arb_add_error_arf(acb_realref(y1), err); arb_add_error_arf(acb_imagref(y1), err); arb_add_error_arf(acb_realref(y2), err); arb_add_error_arf(acb_imagref(y2), err); acb_add(sum, sum, y2, prec); acb_sub(sum, sum, y1, prec); if (arb_calc_verbose) { flint_printf("values: "); acb_printd(y1, 15); flint_printf(" "); acb_printd(y2, 15); flint_printf("\n"); } _acb_vec_clear(taylor_poly, N + 1); if (result == ARB_CALC_NO_CONVERGENCE) break; } acb_set(res, sum); acb_clear(delta); acb_clear(m); acb_clear(x); acb_clear(y1); acb_clear(y2); acb_clear(sum); arf_clear(err); return result; } arb-2.8.1/acb_calc/test/000077500000000000000000000000001264125401100147505ustar00rootroot00000000000000arb-2.8.1/acb_calc/test/t-cauchy_bound.c000066400000000000000000000054561264125401100200320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_calc.h" /* sin(x) */ int sin_x(acb_ptr out, const acb_t inp, void * params, slong order, slong prec) { int xlen = FLINT_MIN(2, order); acb_set(out, inp); if (xlen > 1) acb_one(out + 1); _acb_poly_sin_series(out, out, xlen, order, prec); return 0; } static const double answers[10] = { 1.04570093561423094, 2.0358667496686487, 4.82706400405656566, 11.2347033850581819, 27.1331828778516522, 67.210305990439042, 168.564351176369878, 427.496180295369909, 1093.56959348921777, 2815.70144392142227 }; int main() { slong iter; flint_rand_t state; flint_printf("cauchy_bound...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { arb_t b, radius, ans; acb_t x; slong r, prec, maxdepth; arb_init(b); arb_init(radius); arb_init(ans); acb_init(x); acb_set_ui(x, 5); r = 1 + n_randint(state, 10); arb_set_ui(radius, r); prec = 2 + n_randint(state, 100); maxdepth = n_randint(state, 10); acb_calc_cauchy_bound(b, sin_x, NULL, x, radius, maxdepth, prec); arf_set_d(arb_midref(ans), answers[r-1]); mag_set_d(arb_radref(ans), 1e-8); if (!arb_overlaps(b, ans)) { flint_printf("FAIL\n"); flint_printf("r = %wd, prec = %wd, maxdepth = %wd\n\n", r, prec, maxdepth); arb_printd(b, 15); flint_printf("\n\n"); arb_printd(ans, 15); flint_printf("\n\n"); abort(); } arb_clear(b); arb_clear(radius); arb_clear(ans); acb_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_calc/test/t-integrate_taylor.c000066400000000000000000000063031264125401100207330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_calc.h" /* sin(x) */ int sin_x(acb_ptr out, const acb_t inp, void * params, slong order, slong prec) { int xlen = FLINT_MIN(2, order); acb_set(out, inp); if (xlen > 1) acb_one(out + 1); _acb_poly_sin_series(out, out, xlen, order, prec); return 0; } int main() { slong iter; flint_rand_t state; flint_printf("integrate_taylor...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 150; iter++) { acb_t ans, res, a, b; arf_t inr, outr; double t; slong goal, prec; acb_init(ans); acb_init(res); acb_init(a); acb_init(b); arf_init(inr); arf_init(outr); goal = 2 + n_randint(state, 300); prec = 2 + n_randint(state, 300); acb_randtest(a, state, 1 + n_randint(state, 200), 2); acb_randtest(b, state, 1 + n_randint(state, 200), 2); acb_cos(ans, a, prec); acb_cos(res, b, prec); acb_sub(ans, ans, res, prec); t = (1 + n_randint(state, 20)) / 10.0; arf_set_d(inr, t); arf_set_d(outr, t + (1 + n_randint(state, 20)) / 5.0); acb_calc_integrate_taylor(res, sin_x, NULL, a, b, inr, outr, goal, prec); if (!acb_overlaps(res, ans)) { flint_printf("FAIL! (iter = %wd)\n", iter); flint_printf("prec = %wd, goal = %wd\n", prec, goal); flint_printf("inr = "); arf_printd(inr, 15); flint_printf("\n"); flint_printf("outr = "); arf_printd(outr, 15); flint_printf("\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n"); flint_printf("b = "); acb_printd(b, 15); flint_printf("\n"); flint_printf("res = "); acb_printd(res, 15); flint_printf("\n\n"); flint_printf("ans = "); acb_printd(ans, 15); flint_printf("\n\n"); abort(); } acb_clear(ans); acb_clear(res); acb_clear(a); acb_clear(b); arf_clear(inr); arf_clear(outr); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom.h000066400000000000000000000224351264125401100147160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #ifndef ACB_HYPGEOM_H #define ACB_HYPGEOM_H #include "acb.h" #include "acb_poly.h" #ifdef __cplusplus extern "C" { #endif void acb_hypgeom_pfq_bound_factor(mag_t C, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, ulong n); slong acb_hypgeom_pfq_choose_n(acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong prec); void acb_hypgeom_pfq_sum_forward(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec); void acb_hypgeom_pfq_sum_rs(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec); void acb_hypgeom_pfq_sum_bs(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec); void acb_hypgeom_pfq_sum_fme(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec); void acb_hypgeom_pfq_sum(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec); void acb_hypgeom_pfq_sum_bs_invz(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec); void acb_hypgeom_pfq_sum_invz(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, const acb_t zinv, slong n, slong prec); void acb_hypgeom_pfq_direct(acb_t res, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec); slong acb_hypgeom_pfq_series_choose_n(const acb_poly_struct * a, slong p, const acb_poly_struct * b, slong q, const acb_poly_t z, slong len, slong prec); void acb_hypgeom_pfq_series_direct(acb_poly_t res, const acb_poly_struct * a, slong p, const acb_poly_struct * b, slong q, const acb_poly_t z, int regularized, slong n, slong len, slong prec); void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong n, slong prec); void acb_hypgeom_u_1f1_series(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t z, slong len, slong prec); void acb_hypgeom_u_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec); void acb_hypgeom_u(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec); int acb_hypgeom_u_use_asymp(const acb_t z, slong prec); void acb_hypgeom_m_asymp(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec); void acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec); void acb_hypgeom_m(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec); void acb_hypgeom_erf_1f1a(acb_t res, const acb_t z, slong prec); void acb_hypgeom_erf_1f1b(acb_t res, const acb_t z, slong prec); void acb_hypgeom_erf_asymp(acb_t res, const acb_t z, slong prec, slong prec2); void acb_hypgeom_erf(acb_t res, const acb_t z, slong prec); void acb_hypgeom_bessel_j_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_j_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_j(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_i_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_i_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_i(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_k_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_k_0f1_series(acb_poly_t res, const acb_poly_t n, const acb_poly_t z, slong len, slong prec); void acb_hypgeom_bessel_k_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_k(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_y(acb_t res, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_bessel_jy(acb_t res1, acb_t res2, const acb_t nu, const acb_t z, slong prec); void acb_hypgeom_0f1_asymp(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec); void acb_hypgeom_0f1_direct(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec); void acb_hypgeom_0f1(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec); void acb_hypgeom_airy_bound(mag_t ai, mag_t aip, mag_t bi, mag_t bip, const acb_t z); void acb_hypgeom_airy_asymp(acb_t ai, acb_t aip, acb_t bi, acb_t bip, const acb_t z, slong n, slong prec); void acb_hypgeom_airy_direct(acb_t ai, acb_t aip, acb_t bi, acb_t bip, const acb_t z, slong n, slong prec); void acb_hypgeom_airy(acb_t ai, acb_t aip, acb_t bi, acb_t bip, const acb_t z, slong prec); void acb_hypgeom_gamma_upper_asymp(acb_t res, const acb_t s, const acb_t z, int modified, slong prec); void acb_hypgeom_gamma_upper_1f1a(acb_t res, const acb_t s, const acb_t z, int modified, slong prec); void acb_hypgeom_gamma_upper_1f1b(acb_t res, const acb_t s, const acb_t z, int modified, slong prec); void acb_hypgeom_gamma_upper_singular(acb_t res, slong s, const acb_t z, int modified, slong prec); void acb_hypgeom_gamma_upper(acb_t res, const acb_t s, const acb_t z, int modified, slong prec); void acb_hypgeom_expint(acb_t res, const acb_t s, const acb_t z, slong prec); void acb_hypgeom_erfc(acb_t res, const acb_t z, slong prec); void acb_hypgeom_erfi(acb_t res, const acb_t z, slong prec); void acb_hypgeom_ei_asymp(acb_t res, const acb_t z, slong prec); void acb_hypgeom_ei_2f2(acb_t res, const acb_t z, slong prec); void acb_hypgeom_ei(acb_t res, const acb_t z, slong prec); void acb_hypgeom_si_asymp(acb_t res, const acb_t z, slong prec); void acb_hypgeom_si_1f2(acb_t res, const acb_t z, slong prec); void acb_hypgeom_si(acb_t res, const acb_t z, slong prec); void acb_hypgeom_ci_asymp(acb_t res, const acb_t z, slong prec); void acb_hypgeom_ci_2f3(acb_t res, const acb_t z, slong prec); void acb_hypgeom_ci(acb_t res, const acb_t z, slong prec); void acb_hypgeom_shi(acb_t res, const acb_t z, slong prec); void acb_hypgeom_chi_asymp(acb_t res, const acb_t z, slong prec); void acb_hypgeom_chi_2f3(acb_t res, const acb_t z, slong prec); void acb_hypgeom_chi(acb_t res, const acb_t z, slong prec); void acb_hypgeom_li(acb_t res, const acb_t z, int offset, slong prec); void acb_hypgeom_2f1_continuation(acb_t res0, acb_t res1, const acb_t a, const acb_t b, const acb_t c, const acb_t z0, const acb_t z1, const acb_t f0, const acb_t f1, slong prec); void acb_hypgeom_2f1_series_direct(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t c, const acb_poly_t z, int regularized, slong len, slong prec); void acb_hypgeom_2f1_direct(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec); void acb_hypgeom_2f1_transform(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, int which, slong prec); void acb_hypgeom_2f1_transform_limit(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, int which, slong prec); void acb_hypgeom_2f1_corner(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec); int acb_hypgeom_2f1_choose(const acb_t z); void acb_hypgeom_2f1(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec); void acb_hypgeom_legendre_p_uiui_rec(acb_t res, ulong n, ulong m, const acb_t z, slong prec); void acb_hypgeom_legendre_p(acb_t res, const acb_t n, const acb_t m, const acb_t z, int type, slong prec); void acb_hypgeom_legendre_q(acb_t res, const acb_t n, const acb_t m, const acb_t z, int type, slong prec); void acb_hypgeom_jacobi_p(acb_t res, const acb_t n, const acb_t a, const acb_t b, const acb_t z, slong prec); void acb_hypgeom_gegenbauer_c(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec); void acb_hypgeom_laguerre_l(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec); void acb_hypgeom_hermite_h(acb_t res, const acb_t n, const acb_t z, slong prec); void acb_hypgeom_chebyshev_t(acb_t res, const acb_t n, const acb_t z, slong prec); void acb_hypgeom_chebyshev_u(acb_t res, const acb_t n, const acb_t z, slong prec); void acb_hypgeom_spherical_y(acb_t res, slong n, slong m, const acb_t theta, const acb_t phi, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/acb_hypgeom/000077500000000000000000000000001264125401100145375ustar00rootroot00000000000000arb-2.8.1/acb_hypgeom/0f1.c000066400000000000000000000100471264125401100152730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_0f1_asymp(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec) { acb_t t, u, v; int neg; acb_init(t); acb_init(u); acb_init(v); /* both expansions are correct, but we want the one that works better on the real line */ neg = arf_sgn(arb_midref(acb_realref(z))) < 0; if (neg) acb_neg(t, z); else acb_set(t, z); acb_sqrt(t, t, prec); acb_mul_2exp_si(v, t, 1); acb_sub_ui(u, a, 1, prec); if (neg) acb_hypgeom_bessel_j_asymp(v, u, v, prec); else acb_hypgeom_bessel_i_asymp(v, u, v, prec); acb_neg(u, u); acb_pow(t, t, u, prec); acb_mul(v, v, t, prec); if (!regularized) { acb_gamma(t, a, prec); acb_mul(v, v, t, prec); } acb_set(res, v); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_hypgeom_0f1_direct(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec) { if (regularized) { if (acb_is_int(a) && arf_sgn(arb_midref(acb_realref(a))) <= 0) { acb_t t, u; acb_init(t); acb_init(u); acb_sub_ui(t, a, 2, prec); acb_neg(t, t); acb_sub_ui(u, a, 1, prec); acb_neg(u, u); acb_pow(u, z, u, prec); /* this cannot recurse infinitely, because t will either be an exact positive integer, or inexact */ acb_hypgeom_0f1_direct(res, t, z, regularized, prec); acb_mul(res, res, u, prec); acb_clear(t); acb_clear(u); } else /* todo: could skip when a=1 or a=2 */ { acb_t t; acb_init(t); acb_rgamma(t, a, prec); acb_hypgeom_0f1_direct(res, a, z, 0, prec); acb_mul(res, res, t, prec); acb_clear(t); } } else { acb_struct bb[2]; bb[0] = *a; acb_init(bb + 1); acb_one(bb + 1); acb_hypgeom_pfq_direct(res, NULL, 0, bb, 2, z, -1, prec); acb_clear(bb + 1); } } int acb_hypgeom_0f1_use_asymp(const acb_t z, slong prec) { double x, y, c; if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 0) < 0 && arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0)) { return 0; } if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 0) > 128 || arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) > 128)) { return 1; } x = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN); y = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN); c = prec * 0.69314718055994530942; c = c * c; c = c * c; return x * x + y * y > c; } void acb_hypgeom_0f1(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec) { if (acb_hypgeom_0f1_use_asymp(z, prec)) acb_hypgeom_0f1_asymp(res, a, z, regularized, prec); else acb_hypgeom_0f1_direct(res, a, z, regularized, prec); } arb-2.8.1/acb_hypgeom/2f1.c000066400000000000000000000116341264125401100153000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" static void _acb_hypgeom_2f1r_reduced(acb_t res, const acb_t b, const acb_t c, const acb_t z, slong prec) { acb_t t, u; acb_init(t); acb_init(u); acb_sub_ui(t, z, 1, prec); acb_neg(t, t); acb_neg(u, b); acb_pow(t, t, u, prec); acb_rgamma(u, c, prec); acb_mul(t, t, u, prec); acb_set(res, t); acb_clear(t); acb_clear(u); return; } void acb_hypgeom_2f1(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec) { int algorithm; if (!acb_is_finite(a) || !acb_is_finite(b) || !acb_is_finite(c) || !acb_is_finite(z)) { acb_indeterminate(res); return; } if (acb_is_zero(z)) { if (regularized) acb_rgamma(res, c, prec); else acb_one(res); return; } if (regularized && acb_is_int(c) && arb_is_nonpositive(acb_realref(c))) { if ((acb_is_int(a) && arb_is_nonpositive(acb_realref(a)) && arf_cmp(arb_midref(acb_realref(a)), arb_midref(acb_realref(c))) >= 0) || (acb_is_int(b) && arb_is_nonpositive(acb_realref(b)) && arf_cmp(arb_midref(acb_realref(b)), arb_midref(acb_realref(c))) >= 0)) { acb_zero(res); return; } } if (regularized && acb_eq(a, c)) { _acb_hypgeom_2f1r_reduced(res, b, c, z, prec); return; } if (regularized && acb_eq(b, c)) { _acb_hypgeom_2f1r_reduced(res, a, c, z, prec); return; } /* polynomial */ if (acb_is_int(a) && arf_sgn(arb_midref(acb_realref(a))) <= 0 && arf_cmpabs_ui(arb_midref(acb_realref(a)), prec) < 0) { acb_hypgeom_2f1_direct(res, a, b, c, z, regularized, prec); return; } /* polynomial */ if (acb_is_int(b) && arf_sgn(arb_midref(acb_realref(b))) <= 0 && arf_cmpabs_ui(arb_midref(acb_realref(b)), prec) < 0) { acb_hypgeom_2f1_direct(res, a, b, c, z, regularized, prec); return; } /* Try to reduce to a polynomial case using the Pfaff transformation */ if (acb_is_exact(c)) { acb_t t; acb_init(t); acb_sub(t, c, b, prec); if (acb_is_int(t) && arb_is_nonpositive(acb_realref(t))) { acb_hypgeom_2f1_transform(res, a, b, c, z, regularized, 1, prec); acb_clear(t); return; } acb_sub(t, c, a, prec); if (acb_is_int(t) && arb_is_nonpositive(acb_realref(t))) { acb_hypgeom_2f1_transform(res, b, a, c, z, regularized, 1, prec); acb_clear(t); return; } acb_clear(t); } /* special value at z = 1 */ if (acb_is_one(z)) { acb_t t, u, v; acb_init(t); acb_init(u); acb_init(v); acb_sub(t, c, a, prec); acb_sub(u, c, b, prec); acb_sub(v, t, b, prec); if (arb_is_positive(acb_realref(v))) { acb_rgamma(t, t, prec); acb_rgamma(u, u, prec); acb_mul(t, t, u, prec); acb_gamma(v, v, prec); acb_mul(t, t, v, prec); if (!regularized) { acb_gamma(v, c, prec); acb_mul(t, t, v, prec); } acb_set(res, t); } else { acb_indeterminate(res); } acb_clear(t); acb_clear(u); acb_clear(v); return; } algorithm = acb_hypgeom_2f1_choose(z); if (algorithm == 0) { acb_hypgeom_2f1_direct(res, a, b, c, z, regularized, prec); } else if (algorithm >= 1 && algorithm <= 5) { acb_hypgeom_2f1_transform(res, a, b, c, z, regularized, algorithm, prec); } else { acb_hypgeom_2f1_corner(res, a, b, c, z, regularized, prec); } } arb-2.8.1/acb_hypgeom/2f1_choose.c000066400000000000000000000042671264125401100166440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" #define ALWAYS1 (0.25 * 0.25) #define ALWAYS2 (0.75 * 0.75) #define LIMIT (0.75 * 0.75) int acb_hypgeom_2f1_choose(const acb_t z) { double x, y; double mag[7]; int i, pick; x = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN); y = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN); x = FLINT_MAX(FLINT_MIN(x, 1e10), -1e10); y = FLINT_MAX(FLINT_MIN(y, 1e10), -1e10); mag[0] = x*x + y*y; /* |z|^2 */ mag[4] = (1.0-x)*(1.0-x) + y*y; /* |1-z|^2 */ if (mag[0] <= ALWAYS1) return 0; mag[1] = mag[0] / FLINT_MAX(mag[4], 1e-10); /* |z/(z-1)|^2 */ if (mag[1] <= ALWAYS1) return 1; if (mag[0] <= ALWAYS2 || mag[1] <= ALWAYS2) return mag[0] <= mag[1] ? 0 : 1; mag[2] = 1.0 / mag[0]; /* |1/z|^2 */ mag[3] = 1.0 / FLINT_MAX(mag[4], 1e-10); /* 1/|1-z|^2 */ mag[5] = mag[4] / mag[0]; /* |1-1/z|^2 = |(1-z)/z|^2 */ pick = 0; for (i = 1; i < 6; i++) { if (mag[i] < mag[pick]) pick = i; } if (mag[pick] <= LIMIT) return pick; return 6; } arb-2.8.1/acb_hypgeom/2f1_continuation.c000066400000000000000000000153261264125401100200740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* Differential equation for F(a,b,c,y+z): (y+z)(y-1+z) F''(z) + ((y+z)(a+b+1) - c) F'(z) + a b F(z) = 0 Coefficients in the Taylor series are bounded by A * binomial(N+k, k) * nu^k using the Cauchy-Kovalevskaya majorant method. See J. van der Hoeven, "Fast evaluation of holonomic functions near and in regular singularities" */ static void bound(mag_t A, mag_t nu, mag_t N, const acb_t a, const acb_t b, const acb_t c, const acb_t y, const acb_t f0, const acb_t f1) { mag_t M0, M1, t, u; acb_t d; acb_init(d); mag_init(M0); mag_init(M1); mag_init(t); mag_init(u); /* nu = max(1/|y-1|, 1/|y|) = 1/min(|y-1|, |y|) */ acb_get_mag_lower(t, y); acb_sub_ui(d, y, 1, MAG_BITS); acb_get_mag_lower(u, d); mag_min(t, t, u); mag_one(u); mag_div(nu, u, t); /* M0 = 2 nu |ab| */ acb_get_mag(t, a); acb_get_mag(u, b); mag_mul(M0, t, u); mag_mul(M0, M0, nu); mag_mul_2exp_si(M0, M0, 1); /* M1 = 2 nu |(a+b+1)y-c| + 2|a+b+1| */ acb_add(d, a, b, MAG_BITS); acb_add_ui(d, d, 1, MAG_BITS); acb_get_mag(t, d); acb_mul(d, d, y, MAG_BITS); acb_sub(d, d, c, MAG_BITS); acb_get_mag(u, d); mag_mul(u, u, nu); mag_add(M1, t, u); mag_mul_2exp_si(M1, M1, 1); /* N = max(sqrt(2 M0), 2 M1) / nu */ mag_mul_2exp_si(M0, M0, 1); mag_sqrt(M0, M0); mag_mul_2exp_si(M1, M1, 1); mag_max(N, M0, M1); mag_div(N, N, nu); /* A = max(|f0|, |f1| / (nu (N+1)) */ acb_get_mag(t, f0); acb_get_mag(u, f1); mag_div(u, u, nu); mag_div(u, u, N); /* upper bound for dividing by N+1 */ mag_max(A, t, u); acb_clear(d); mag_clear(M0); mag_clear(M1); mag_clear(t); mag_clear(u); } static void mag_add_ui(mag_t y, const mag_t x, ulong k) { mag_t t; mag_init(t); /* no need to free */ mag_set_ui(t, k); mag_add(y, x, t); } /* F(x) = c0 + c1 x + c2 x^2 + c3 x^3 + [...] F'(x) = c1 + 2 c2 x + 3 c3 x^2 + 4 c4 x^3 + [...] */ static void evaluate_sum(acb_t res, acb_t res1, const acb_t a, const acb_t b, const acb_t c, const acb_t y, const acb_t x, const acb_t f0, const acb_t f1, slong num, slong prec) { acb_t s, s2, w, d, e, xpow, ck, cknext; slong k; acb_init(s); acb_init(s2); acb_init(w); acb_init(d); acb_init(e); acb_init(xpow); acb_init(ck); acb_init(cknext); /* d = (y-1)*y */ acb_sub_ui(d, y, 1, prec); acb_mul(d, d, y, prec); acb_one(xpow); for (k = 0; k < num; k++) { if (k == 0) { acb_set(ck, f0); acb_set(cknext, f1); } else { acb_add_ui(w, b, k-1, prec); acb_mul(w, w, ck, prec); acb_add_ui(e, a, k-1, prec); acb_mul(w, w, e, prec); acb_add(e, a, b, prec); acb_add_ui(e, e, 2*(k+1)-3, prec); acb_mul(e, e, y, prec); acb_sub(e, e, c, prec); acb_sub_ui(e, e, k-1, prec); acb_mul_ui(e, e, k, prec); acb_addmul(w, e, cknext, prec); acb_mul_ui(e, d, k+1, prec); acb_mul_ui(e, e, k, prec); acb_div(w, w, e, prec); acb_neg(w, w); acb_set(ck, cknext); acb_set(cknext, w); } acb_addmul(s, ck, xpow, prec); acb_mul_ui(w, cknext, k+1, prec); acb_addmul(s2, w, xpow, prec); acb_mul(xpow, xpow, x, prec); } acb_set(res, s); acb_set(res1, s2); acb_clear(s); acb_clear(s2); acb_clear(w); acb_clear(d); acb_clear(e); acb_clear(xpow); acb_clear(ck); acb_clear(cknext); } void acb_hypgeom_2f1_continuation(acb_t res, acb_t res1, const acb_t a, const acb_t b, const acb_t c, const acb_t y, const acb_t z, const acb_t f0, const acb_t f1, slong prec) { mag_t A, nu, N, w, err, err1, R, T, goal; acb_t x; slong j, k; mag_init(A); mag_init(nu); mag_init(N); mag_init(err); mag_init(err1); mag_init(w); mag_init(R); mag_init(T); mag_init(goal); acb_init(x); bound(A, nu, N, a, b, c, y, f0, f1); acb_sub(x, z, y, prec); /* |T(k)| <= A * binomial(N+k, k) * nu^k * |x|^k */ acb_get_mag(w, x); mag_mul(w, w, nu); /* w = nu |x| */ mag_mul_2exp_si(goal, A, -prec-2); /* bound for T(0) */ mag_set(T, A); mag_inf(R); for (k = 1; k < 100 * prec; k++) { /* T(k) = T(k) * R(k), R(k) = (N+k)/k * w = (1 + N/k) w */ mag_div_ui(R, N, k); mag_add_ui(R, R, 1); mag_mul(R, R, w); /* T(k) */ mag_mul(T, T, R); if (mag_cmp(T, goal) <= 0 && mag_cmp_2exp_si(R, 0) < 0) break; } /* T(k) [1 + R + R^2 + R^3 + ...] */ mag_geom_series(err, R, 0); mag_mul(err, T, err); /* Now compute T, R for the derivative */ /* Coefficients are A * (k+1) * binomial(N+k+1, k+1) */ mag_add_ui(T, N, 1); mag_mul(T, T, A); mag_inf(R); for (j = 1; j <= k; j++) { mag_add_ui(R, N, k + 1); mag_div_ui(R, R, k); mag_mul(R, R, w); mag_mul(T, T, R); } mag_geom_series(err1, R, 0); mag_mul(err1, T, err1); if (mag_is_inf(err)) { acb_indeterminate(res); acb_indeterminate(res1); } else { evaluate_sum(res, res1, a, b, c, y, x, f0, f1, k, prec); acb_add_error_mag(res, err); acb_add_error_mag(res1, err1); } mag_clear(A); mag_clear(nu); mag_clear(N); mag_clear(err); mag_clear(err1); mag_clear(w); mag_clear(R); mag_clear(T); mag_clear(goal); acb_clear(x); } arb-2.8.1/acb_hypgeom/2f1_corner.c000066400000000000000000000045361264125401100166530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_2f1_corner(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec) { acb_t aa, bb, cc, z1, z2, f1, f2; int upper; acb_init(aa); acb_init(bb); acb_init(cc); acb_init(z1); acb_init(z2); acb_init(f1); acb_init(f2); acb_add_ui(aa, a, 1, prec); acb_add_ui(bb, b, 1, prec); acb_add_ui(cc, c, 1, prec); upper = arb_is_positive(acb_imagref(z)); /* 0 -> 0.5 +/- 0.5i -> 0.5 +/- 0.75i -> z */ #if 0 acb_set_d_d(z1, 0.5, upper ? 0.5 : -0.5); acb_set_d_d(z2, 0.5, upper ? 0.75 : -0.75); #else acb_set_d_d(z1, 0.375, upper ? 0.625 : -0.625); acb_set_d_d(z2, 0.5, upper ? 0.8125 : -0.8125); #endif acb_hypgeom_2f1_direct(f1, a, b, c, z1, regularized, prec); acb_hypgeom_2f1_direct(f2, aa, bb, cc, z1, regularized, prec); acb_mul(f2, f2, a, prec); acb_mul(f2, f2, b, prec); if (!regularized) acb_div(f2, f2, c, prec); acb_hypgeom_2f1_continuation(f1, f2, a, b, c, z1, z2, f1, f2, prec); acb_set(z1, z2); acb_set(z2, z); acb_hypgeom_2f1_continuation(f1, f2, a, b, c, z1, z2, f1, f2, prec); acb_set(res, f1); acb_clear(aa); acb_clear(bb); acb_clear(cc); acb_clear(z1); acb_clear(z2); acb_clear(f1); acb_clear(f2); } arb-2.8.1/acb_hypgeom/2f1_direct.c000066400000000000000000000076651264125401100166430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_2f1_direct(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec) { /* 2F1R(a,b,-n,z) = (a)_(n+1) * (b)_(n+1) * z^(n+1) / (n+1)! * 2F1(a+n+1, b+n+1, n+2, z) */ if (regularized && acb_is_int(c) && arf_sgn(arb_midref(acb_realref(c))) <= 0) { if ((acb_is_int(a) && arb_is_nonpositive(acb_realref(a)) && arf_cmp(arb_midref(acb_realref(a)), arb_midref(acb_realref(c))) >= 0) || (acb_is_int(b) && arb_is_nonpositive(acb_realref(b)) && arf_cmp(arb_midref(acb_realref(b)), arb_midref(acb_realref(c))) >= 0)) { acb_zero(res); } else { acb_t n, n1, t, u, v; acb_ptr aa; int p, q; acb_init(n); acb_init(n1); acb_init(t); acb_init(u); acb_init(v); aa = _acb_vec_init(4); acb_neg(n, c); acb_add_ui(n1, n, 1, prec); acb_add(aa, a, n1, prec); acb_add(aa + 1, b, n1, prec); acb_add_ui(aa + 2, n1, 1, prec); if (acb_is_one(aa)) { p = q = 1; acb_swap(aa, aa + 1); } else if (acb_is_one(aa + 1)) { p = q = 1; } else { p = q = 2; acb_one(aa + 3); } acb_hypgeom_pfq_direct(t, aa, p, aa + 2, q, z, -1, prec); /* z^(n+1) */ acb_pow(u, z, n1, prec); acb_mul(t, t, u, prec); acb_rising(u, a, n1, prec); acb_mul(t, t, u, prec); acb_rising(u, b, n1, prec); acb_mul(t, t, u, prec); /* 1/(n+1)! */ acb_rgamma(u, aa + 2, prec); acb_mul(t, t, u, prec); acb_set(res, t); acb_clear(n); acb_clear(n1); acb_clear(t); acb_clear(u); acb_clear(v); _acb_vec_clear(aa, 4); } } else { acb_ptr aa; int p, q; aa = _acb_vec_init(4); acb_set(aa + 2, c); if (acb_is_one(a)) { p = q = 1; acb_set(aa, b); } else if (acb_is_one(b)) { p = q = 1; acb_set(aa, a); } else { p = q = 2; acb_set(aa, a); acb_set(aa + 1, b); acb_one(aa + 3); } acb_hypgeom_pfq_direct(res, aa, p, aa + 2, q, z, -1, prec); if (regularized) { acb_rgamma(aa + 2, aa + 2, prec); acb_mul(res, res, aa + 2, prec); } _acb_vec_clear(aa, 4); } if (!acb_is_finite(res)) acb_indeterminate(res); } arb-2.8.1/acb_hypgeom/2f1_series_direct.c000066400000000000000000000030221264125401100201740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_2f1_series_direct(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t c, const acb_poly_t z, int regularized, slong len, slong prec) { acb_poly_struct aa[4]; aa[0] = *a; aa[1] = *b; aa[2] = *c; acb_poly_init(&aa[3]); acb_poly_one(&aa[3]); acb_hypgeom_pfq_series_direct(res, aa, 2, aa + 2, 2, z, regularized, -1, len, prec); acb_poly_clear(&aa[3]); } arb-2.8.1/acb_hypgeom/2f1_transform.c000066400000000000000000000321461264125401100173740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* which == 0 -- z which == 1 -- z/(z-1) which == 2 -- 1/z which == 3 -- 1/(1-z) which == 4 -- 1-z which == 5 -- 1-1/z */ void _acb_hypgeom_2f1_transform_limit(acb_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t c, const acb_poly_t z, int which, slong prec) { acb_poly_t ba, ca, cb, cab, ac1, bc1, ab1, ba1, w, t, u, v, s; acb_t tt; acb_poly_init(ba); acb_poly_init(ca); acb_poly_init(cb); acb_poly_init(cab); acb_poly_init(ac1); acb_poly_init(bc1); acb_poly_init(ab1); acb_poly_init(ba1); acb_poly_init(w); acb_poly_init(t); acb_poly_init(u); acb_poly_init(v); acb_poly_init(s); acb_init(tt); acb_poly_add_si(s, z, -1, prec); /* s = 1 - z */ acb_poly_neg(s, s); acb_poly_sub(ba, b, a, prec); /* ba = b - a */ acb_poly_sub(ca, c, a, prec); /* ca = c - a */ acb_poly_sub(cb, c, b, prec); /* cb = c - b */ acb_poly_sub(cab, ca, b, prec); /* cab = c - a - b */ acb_poly_add_si(ac1, ca, -1, prec); acb_poly_neg(ac1, ac1); /* ac1 = a - c + 1 */ acb_poly_add_si(bc1, cb, -1, prec); acb_poly_neg(bc1, bc1); /* bc1 = b - c + 1 */ acb_poly_add_si(ab1, ba, -1, prec); acb_poly_neg(ab1, ab1); /* ab1 = a - b + 1 */ acb_poly_add_si(ba1, ba, 1, prec); /* ba1 = b - a + 1 */ /* t = left term, u = right term (DLMF 15.8.1 - 15.8.5) */ if (which == 2) { acb_poly_inv_series(w, z, 2, prec); /* w = 1/z */ acb_hypgeom_2f1_series_direct(t, a, ac1, ab1, w, 1, 2, prec); acb_hypgeom_2f1_series_direct(u, b, bc1, ba1, w, 1, 2, prec); } else if (which == 3) { acb_poly_inv_series(w, s, 2, prec); /* w = 1/(1-z) */ acb_hypgeom_2f1_series_direct(t, a, cb, ab1, w, 1, 2, prec); acb_hypgeom_2f1_series_direct(u, b, ca, ba1, w, 1, 2, prec); } else if (which == 4) { acb_poly_set(w, s); /* w = 1-z */ acb_poly_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_series_direct(t, a, b, v, w, 1, 2, prec); acb_poly_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_hypgeom_2f1_series_direct(u, ca, cb, v, w, 1, 2, prec); } else if (which == 5) { acb_poly_inv_series(w, z, 2, prec); /* w = 1-1/z */ acb_poly_neg(w, w); acb_poly_add_si(w, w, 1, prec); acb_poly_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_series_direct(t, a, ac1, v, w, 1, 2, prec); acb_poly_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_poly_add_si(u, a, -1, prec); /* u = 1-a */ acb_poly_neg(u, u); acb_hypgeom_2f1_series_direct(u, ca, u, v, w, 1, 2, prec); } else { flint_printf("invalid transformation!\n"); abort(); } /* gamma factors */ acb_poly_rgamma_series(v, a, 2, prec); acb_poly_mullow(u, u, v, 2, prec); acb_poly_rgamma_series(v, ca, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_rgamma_series(v, b, 2, prec); if (which == 2 || which == 3) acb_poly_mullow(t, t, v, 2, prec); else acb_poly_mullow(u, u, v, 2, prec); acb_poly_rgamma_series(v, cb, 2, prec); if (which == 2 || which == 3) acb_poly_mullow(u, u, v, 2, prec); else acb_poly_mullow(t, t, v, 2, prec); if (which == 2 || which == 3) { if (which == 2) acb_poly_neg(s, z); /* -z, otherwise 1-z since before */ acb_poly_neg(v, a); acb_poly_pow_series(v, s, v, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_neg(v, b); acb_poly_pow_series(v, s, v, 2, prec); acb_poly_mullow(u, u, v, 2, prec); } else { acb_poly_pow_series(v, s, cab, 2, prec); acb_poly_mullow(u, u, v, 2, prec); if (which == 5) { acb_poly_neg(v, a); acb_poly_pow_series(v, z, v, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_neg(v, ca); acb_poly_pow_series(v, z, v, 2, prec); acb_poly_mullow(u, u, v, 2, prec); } } acb_poly_sub(t, t, u, prec); if (which == 2 || which == 3) acb_poly_sin_pi_series(v, ba, 2, prec); else acb_poly_sin_pi_series(v, cab, 2, prec); acb_poly_get_coeff_acb(tt, t, 1); acb_poly_get_coeff_acb(res, v, 1); acb_div(res, tt, res, prec); acb_const_pi(tt, prec); acb_mul(res, res, tt, prec); acb_poly_clear(ba); acb_poly_clear(ca); acb_poly_clear(cb); acb_poly_clear(cab); acb_poly_clear(ac1); acb_poly_clear(bc1); acb_poly_clear(ab1); acb_poly_clear(ba1); acb_poly_clear(w); acb_poly_clear(t); acb_poly_clear(u); acb_poly_clear(v); acb_poly_clear(s); acb_clear(tt); } void acb_hypgeom_2f1_transform_limit(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, int which, slong prec) { acb_poly_t aa, bb, cc, zz; acb_t t; if (acb_contains_zero(z) || !acb_is_finite(z)) { acb_indeterminate(res); return; } if (arb_contains_si(acb_realref(z), 1) && arb_contains_zero(acb_imagref(z))) { acb_indeterminate(res); return; } if (!regularized) { acb_init(t); acb_gamma(t, c, prec); acb_hypgeom_2f1_transform_limit(res, a, b, c, z, 1, which, prec); acb_mul(res, res, t, prec); acb_clear(t); return; } acb_poly_init(aa); acb_poly_init(bb); acb_poly_init(cc); acb_poly_init(zz); acb_init(t); acb_poly_set_acb(aa, a); acb_poly_set_acb(bb, b); acb_poly_set_acb(cc, c); acb_poly_set_acb(zz, z); if (which == 2 || which == 3) { acb_sub(t, b, a, prec); acb_poly_set_coeff_si(aa, 1, 1); /* prefer b-a nonnegative (either is correct) to avoid expensive operations in the hypergeometric series */ if (arb_is_nonnegative(acb_realref(t))) _acb_hypgeom_2f1_transform_limit(res, aa, bb, cc, zz, which, prec); else _acb_hypgeom_2f1_transform_limit(res, bb, aa, cc, zz, which, prec); } else { acb_poly_set_coeff_si(aa, 1, 1); _acb_hypgeom_2f1_transform_limit(res, aa, bb, cc, zz, which, prec); } acb_poly_clear(aa); acb_poly_clear(bb); acb_poly_clear(cc); acb_poly_clear(zz); acb_clear(t); } void acb_hypgeom_2f1_transform_nolimit(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, int which, slong prec) { acb_t ba, ca, cb, cab, ac1, bc1, ab1, ba1, w, t, u, v, s; if (acb_contains_zero(z) || !acb_is_finite(z)) { acb_indeterminate(res); return; } if (arb_contains_si(acb_realref(z), 1) && arb_contains_zero(acb_imagref(z))) { acb_indeterminate(res); return; } if (!regularized) { acb_init(t); acb_gamma(t, c, prec); acb_hypgeom_2f1_transform_nolimit(res, a, b, c, z, 1, which, prec); acb_mul(res, res, t, prec); acb_clear(t); return; } acb_init(ba); acb_init(ca); acb_init(cb); acb_init(cab); acb_init(ac1); acb_init(bc1); acb_init(ab1); acb_init(ba1); acb_init(w); acb_init(t); acb_init(u); acb_init(v); acb_init(s); acb_add_si(s, z, -1, prec); /* s = 1 - z */ acb_neg(s, s); acb_sub(ba, b, a, prec); /* ba = b - a */ acb_sub(ca, c, a, prec); /* ca = c - a */ acb_sub(cb, c, b, prec); /* cb = c - b */ acb_sub(cab, ca, b, prec); /* cab = c - a - b */ acb_add_si(ac1, ca, -1, prec); acb_neg(ac1, ac1); /* ac1 = a - c + 1 */ acb_add_si(bc1, cb, -1, prec); acb_neg(bc1, bc1); /* bc1 = b - c + 1 */ acb_add_si(ab1, ba, -1, prec); acb_neg(ab1, ab1); /* ab1 = a - b + 1 */ acb_add_si(ba1, ba, 1, prec); /* ba1 = b - a + 1 */ /* t = left term, u = right term (DLMF 15.8.1 - 15.8.5) */ if (which == 2) { acb_inv(w, z, prec); /* w = 1/z */ acb_hypgeom_2f1_direct(t, a, ac1, ab1, w, 1, prec); acb_hypgeom_2f1_direct(u, b, bc1, ba1, w, 1, prec); } else if (which == 3) { acb_inv(w, s, prec); /* w = 1/(1-z) */ acb_hypgeom_2f1_direct(t, a, cb, ab1, w, 1, prec); acb_hypgeom_2f1_direct(u, b, ca, ba1, w, 1, prec); } else if (which == 4) { acb_set(w, s); /* w = 1-z */ acb_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_direct(t, a, b, v, w, 1, prec); acb_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_hypgeom_2f1_direct(u, ca, cb, v, w, 1, prec); } else if (which == 5) { acb_inv(w, z, prec); /* w = 1-1/z */ acb_neg(w, w); acb_add_si(w, w, 1, prec); acb_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_direct(t, a, ac1, v, w, 1, prec); acb_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_add_si(u, a, -1, prec); /* u = 1-a */ acb_neg(u, u); acb_hypgeom_2f1_direct(u, ca, u, v, w, 1, prec); } else { flint_printf("invalid transformation!\n"); abort(); } /* gamma factors */ acb_rgamma(v, a, prec); acb_mul(u, u, v, prec); acb_rgamma(v, ca, prec); acb_mul(t, t, v, prec); acb_rgamma(v, b, prec); if (which == 2 || which == 3) acb_mul(t, t, v, prec); else acb_mul(u, u, v, prec); acb_rgamma(v, cb, prec); if (which == 2 || which == 3) acb_mul(u, u, v, prec); else acb_mul(t, t, v, prec); if (which == 2 || which == 3) { if (which == 2) acb_neg(s, z); /* -z, otherwise 1-z since before */ acb_neg(v, a); acb_pow(v, s, v, prec); acb_mul(t, t, v, prec); acb_neg(v, b); acb_pow(v, s, v, prec); acb_mul(u, u, v, prec); } else { acb_pow(v, s, cab, prec); acb_mul(u, u, v, prec); if (which == 5) { acb_neg(v, a); acb_pow(v, z, v, prec); acb_mul(t, t, v, prec); acb_neg(v, ca); acb_pow(v, z, v, prec); acb_mul(u, u, v, prec); } } acb_sub(t, t, u, prec); if (which == 2 || which == 3) acb_sin_pi(v, ba, prec); else acb_sin_pi(v, cab, prec); acb_div(t, t, v, prec); acb_const_pi(v, prec); acb_mul(t, t, v, prec); acb_set(res, t); acb_clear(ba); acb_clear(ca); acb_clear(cb); acb_clear(cab); acb_clear(ac1); acb_clear(bc1); acb_clear(ab1); acb_clear(ba1); acb_clear(w); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(s); } void acb_hypgeom_2f1_transform(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, int which, slong prec) { if (which == 1) { acb_t t, u, v; acb_init(t); acb_init(u); acb_init(v); acb_sub_ui(t, z, 1, prec); /* t = z-1 */ acb_div(u, z, t, prec); /* u = z/(z-1) */ acb_neg(t, t); acb_neg(v, a); acb_pow(t, t, v, prec); /* t = (1-z)^-a */ acb_sub(v, c, b, prec); /* v = c-b */ /* We cannot use regularized=1 directly, since if c is a nonnegative integer, the transformation formula reads (lhs) * 0 = (rhs) * 0. */ acb_hypgeom_2f1_direct(u, a, v, c, u, 1, prec); if (!regularized) { acb_gamma(v, c, prec); acb_mul(u, u, v, prec); } acb_mul(res, u, t, prec); acb_clear(t); acb_clear(u); acb_clear(v); } else { acb_t d; acb_init(d); if (which == 2 || which == 3) { acb_sub(d, b, a, prec); } else { acb_sub(d, c, a, prec); acb_sub(d, d, b, prec); } if (acb_is_int(d)) acb_hypgeom_2f1_transform_limit(res, a, b, c, z, regularized, which, prec); else acb_hypgeom_2f1_transform_nolimit(res, a, b, c, z, regularized, which, prec); acb_clear(d); } if (!acb_is_finite(res)) acb_indeterminate(res); } arb-2.8.1/acb_hypgeom/airy.c000066400000000000000000000215631264125401100156560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" #include "double_extras.h" #define LOG2 0.69314718055994530942 #define EXP1 2.7182818284590452354 static const double small_log_tab[] = { 0.0, 0.0, 0.693147180559945309, 1.09861228866810969, 1.38629436111989062, 1.60943791243410037, 1.791759469228055, 1.94591014905531331, 2.07944154167983593, 2.19722457733621938, 2.30258509299404568, 2.39789527279837054, 2.48490664978800031, 2.56494935746153674, 2.63905732961525861, 2.70805020110221007, 2.77258872223978124, 2.83321334405621608, 2.89037175789616469, 2.94443897916644046, 2.99573227355399099, 3.044522437723423, 3.09104245335831585, 3.13549421592914969, 3.17805383034794562, 3.21887582486820075, 3.25809653802148205, 3.29583686600432907, 3.33220451017520392, 3.36729582998647403, 3.40119738166215538, 3.43398720448514625, 3.46573590279972655, 3.49650756146648024, 3.52636052461616139, 3.55534806148941368, 3.58351893845611, 3.61091791264422444, 3.63758615972638577, 3.66356164612964643, 3.6888794541139363, 3.7135720667043078, 3.73766961828336831, 3.76120011569356242, 3.78418963391826116, 3.80666248977031976, 3.828641396489095, 3.85014760171005859, 3.87120101090789093, 3.89182029811062661, 3.91202300542814606, 3.93182563272432577, 3.95124371858142735, 3.97029191355212183, 3.98898404656427438, 4.00733318523247092, 4.02535169073514923, 4.04305126783455015, 4.06044301054641934, 4.07753744390571945, 4.09434456222210068, 4.11087386417331125, 4.12713438504509156, 4.14313472639153269, }; static slong asymp_pick_terms(double prec, double logz) { double logk, log2term, log2term_prev; slong k; log2term_prev = 0.0; for (k = 1; ; k++) { logk = k < 64 ? small_log_tab[k] : log(k); log2term = -1.3257480647361593990 - 0.72134752044448170368*logk + k * (-1.8577325401678072259 + 1.4426950408889634074*logk - 2.1640425613334451110*logz); if (log2term > log2term_prev - 0.5) return -1; if (log2term < -prec) return k; } } /* Accurate estimate of log2(|Ai(z)|) or log2(|Bi(z)|), given z = x + yi. Should subtract 0.25*log2(|z| + log2(2*sqrt(pi)) from the output. */ static double estimate_airy(double x, double y, int ai) { double r, t, sgn; r = x; t = x * ((x * x) - 3.0 * (y * y)); y = y * (3.0 * (x * x) - (y * y)); x = t * (1.0 / 9.0); y = y * (1.0 / 9.0); sgn = 1.0; if (r > 0.0 && x > 0.0) { t = sqrt(x * x + y * y) + x; if (ai) sgn = -1.0; } else { x = -x; if (x > 0.0 && x > 1e6 * fabs(y)) t = y * y / (2.0 * x); else t = sqrt(x * x + y * y) - x; } return sgn * sqrt(0.5 * t) * 2.8853900817779268147; } /* error propagation based on derivatives */ void acb_hypgeom_airy_direct_prop(acb_t ai, acb_t aip, acb_t bi, acb_t bip, const acb_t z, slong n, long prec) { mag_t aib, aipb, bib, bipb, zb, rad; acb_t zz; int real; mag_init(aib); mag_init(aipb); mag_init(bib); mag_init(bipb); mag_init(zb); mag_init(rad); acb_init(zz); real = acb_is_real(z); arf_set(arb_midref(acb_realref(zz)), arb_midref(acb_realref(z))); arf_set(arb_midref(acb_imagref(zz)), arb_midref(acb_imagref(z))); mag_hypot(rad, arb_radref(acb_realref(z)), arb_radref(acb_imagref(z))); acb_get_mag(zb, z); acb_hypgeom_airy_bound(aib, aipb, bib, bipb, z); acb_hypgeom_airy_direct(ai, aip, bi, bip, zz, n, prec); if (ai != NULL) { mag_mul(aipb, aipb, rad); if (real) arb_add_error_mag(acb_realref(ai), aipb); else acb_add_error_mag(ai, aipb); } if (aip != NULL) { mag_mul(aib, aib, rad); mag_mul(aib, aib, zb); /* |Ai''(z)| = |z Ai(z)| */ if (real) arb_add_error_mag(acb_realref(aip), aib); else acb_add_error_mag(aip, aib); } if (bi != NULL) { mag_mul(bipb, bipb, rad); if (real) arb_add_error_mag(acb_realref(bi), bipb); else acb_add_error_mag(bi, bipb); } if (bip != NULL) { mag_mul(bib, bib, rad); mag_mul(bib, bib, zb); /* |Bi''(z)| = |z Bi(z)| */ if (real) arb_add_error_mag(acb_realref(bip), bib); else acb_add_error_mag(bip, bib); } mag_clear(aib); mag_clear(aipb); mag_clear(bib); mag_clear(bipb); mag_clear(zb); mag_clear(rad); acb_clear(zz); } void acb_hypgeom_airy(acb_t ai, acb_t aip, acb_t bi, acb_t bip, const acb_t z, long prec) { arf_srcptr re, im; double x, y, t, zmag, z15, term_est, airy_est, abstol; slong n, wp; if (!acb_is_finite(z)) { if (ai != NULL) acb_indeterminate(ai); if (aip != NULL) acb_indeterminate(aip); if (bi != NULL) acb_indeterminate(bi); if (bip != NULL) acb_indeterminate(bip); return; } re = arb_midref(acb_realref(z)); im = arb_midref(acb_imagref(z)); wp = prec * 1.03 + 15; /* tiny input -- use direct method and pick n without underflowing */ if (arf_cmpabs_2exp_si(re, -64) < 0 && arf_cmpabs_2exp_si(im, -64) < 0) { if (arf_cmpabs_2exp_si(re, -wp) < 0 && arf_cmpabs_2exp_si(im, -wp) < 0) { n = 1; /* very tiny input */ } else { if (arf_cmpabs(re, im) > 0) zmag = fmpz_get_d(ARF_EXPREF(re)); else zmag = fmpz_get_d(ARF_EXPREF(im)); zmag = (zmag + 1) * (1.0 / LOG2); n = wp / (-zmag) + 1; } acb_hypgeom_airy_direct(ai, aip, bi, bip, z, n, wp); } /* huge input -- use asymptotics and pick n without overflowing */ else if ((arf_cmpabs_2exp_si(re, 64) > 0 || arf_cmpabs_2exp_si(im, 64) > 0)) { if (arf_cmpabs_2exp_si(re, prec) > 0 || arf_cmpabs_2exp_si(im, prec) > 0) { n = 1; /* very huge input */ } else { x = fmpz_get_d(ARF_EXPREF(re)); y = fmpz_get_d(ARF_EXPREF(im)); zmag = (FLINT_MAX(x, y) - 2) * (1.0 / LOG2); n = asymp_pick_terms(wp, zmag); n = FLINT_MAX(n, 1); } acb_hypgeom_airy_asymp(ai, aip, bi, bip, z, n, wp); } else /* moderate input */ { x = arf_get_d(re, ARF_RND_DOWN); y = arf_get_d(im, ARF_RND_DOWN); zmag = sqrt(x * x + y * y); z15 = zmag * sqrt(zmag); if (zmag >= 4.0 && (n = asymp_pick_terms(wp, log(zmag))) != -1) { acb_hypgeom_airy_asymp(ai, aip, bi, bip, z, n, wp); } else if (zmag <= 1.5) { t = 3 * (wp * LOG2) / (2 * z15 * EXP1); t = (wp * LOG2) / (2 * d_lambertw(t)); n = FLINT_MAX(t + 1, 2); acb_hypgeom_airy_direct(ai, aip, bi, bip, z, n, wp); } else { /* estimate largest term: log2(exp(2(z^3/9)^(1/2))) */ term_est = 0.96179669392597560491 * z15; /* estimate the smaller of Ai and Bi */ airy_est = estimate_airy(x, y, (ai != NULL || aip != NULL)); /* estimate absolute tolerance and necessary working precision */ abstol = airy_est - wp; wp = wp + term_est - airy_est; wp = FLINT_MAX(wp, 10); t = 3 * (-abstol * LOG2) / (2 * z15 * EXP1); t = (-abstol * LOG2) / (2 * d_lambertw(t)); n = FLINT_MAX(t + 1, 2); if (acb_is_exact(z)) acb_hypgeom_airy_direct(ai, aip, bi, bip, z, n, wp); else acb_hypgeom_airy_direct_prop(ai, aip, bi, bip, z, n, wp); } } if (ai != NULL) acb_set_round(ai, ai, prec); if (aip != NULL) acb_set_round(aip, aip, prec); if (bi != NULL) acb_set_round(bi, bi, prec); if (bip != NULL) acb_set_round(bip, bip, prec); } arb-2.8.1/acb_hypgeom/airy_asymp.c000066400000000000000000000407131264125401100170650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_mag_chi(mag_t chi, ulong n); static int arg_lt_2pi3(const acb_t z, const acb_t zeta) { if (arb_is_nonnegative(acb_realref(z))) return 1; if (arb_is_positive(acb_imagref(z)) && arb_is_positive(acb_imagref(zeta))) return 1; if (arb_is_negative(acb_imagref(z)) && arb_is_negative(acb_imagref(zeta))) return 1; return 0; } /* assuming a >= b >= c >= d, e >= f */ void _acb_mul4div2_ui(acb_t x, ulong a, ulong b, ulong c, ulong d, ulong e, ulong f, slong prec) { if (a < (UWORD(1) << (FLINT_BITS / 4))) { acb_mul_ui(x, x, a * b * c * d, prec); } else if (a < (UWORD(1) << (FLINT_BITS / 2))) { acb_mul_ui(x, x, a * b, prec); acb_mul_ui(x, x, c * d, prec); } else { acb_mul_ui(x, x, a, prec); acb_mul_ui(x, x, b, prec); acb_mul_ui(x, x, c, prec); acb_mul_ui(x, x, d, prec); } if (e < (UWORD(1) << (FLINT_BITS / 2))) { acb_div_ui(x, x, e * f, prec); } else { acb_div_ui(x, x, e, prec); acb_div_ui(x, x, f, prec); } } void acb_hypgeom_airy_asymp_sum(acb_t s0even, acb_t s0odd, acb_t s1even, acb_t s1odd, mag_t t0n, mag_t t1n, const acb_t z, const acb_t z2, slong n, slong prec) { slong m, k, j; acb_ptr z2pow; acb_get_mag(t0n, z); mag_mul_ui(t0n, t0n, 72); mag_pow_ui(t0n, t0n, n); mag_one(t1n); for (k = 1; k <= n; k++) { mag_mul_ui(t0n, t0n, 6 * k - 1); mag_mul_ui(t0n, t0n, 6 * k - 5); mag_mul_ui_lower(t1n, t1n, 72 * k); } mag_div(t0n, t0n, t1n); mag_mul_ui(t1n, t0n, 6 * n + 1); mag_div_ui(t1n, t1n, 6 * n - 1); m = n_sqrt(n / 2); m = FLINT_MAX(m, 1); z2pow = _acb_vec_init(m + 1); _acb_vec_set_powers(z2pow, z2, m + 1, prec); if (s0even != NULL) { acb_zero(s0even); for (k = n + (n % 2); k >= 0; k -= 2) { j = (k / 2) % m; if (k < n) acb_add(s0even, s0even, z2pow + j, prec); if (k > 0) { _acb_mul4div2_ui(s0even, 6*k-1, 6*k-5, 6*k-7, 6*k-11, k, k-1, prec); if (j == 0 && k < n) acb_mul(s0even, s0even, z2pow + m, prec); } } } if (s0odd != NULL) { acb_zero(s0odd); for (k = n + 1 + (n % 2); k >= 1; k -= 2) { j = ((k - 1) / 2) % m; if (k < n) acb_add(s0odd, s0odd, z2pow + j, prec); if (k > 1) { _acb_mul4div2_ui(s0odd, 6*k-1, 6*k-5, 6*k-7, 6*k-11, k, k-1, prec); if (j == 0 && k < n) acb_mul(s0odd, s0odd, z2pow + m, prec); } else { acb_mul(s0odd, s0odd, z, prec); acb_mul_ui(s0odd, s0odd, 5, prec); } } } if (s1even != NULL) { acb_zero(s1even); for (k = n + (n % 2); k >= 0; k -= 2) { j = (k / 2) % m; if (k < n) acb_add(s1even, s1even, z2pow + j, prec); if (k > 0) { _acb_mul4div2_ui(s1even, 6*k+1, 6*k-5, 6*k-7, FLINT_ABS(6*k-13), k, k-1, prec); if (k == 2) acb_neg(s1even, s1even); if (j == 0 && k < n) acb_mul(s1even, s1even, z2pow + m, prec); } } } if (s1odd != NULL) { acb_zero(s1odd); for (k = n + 1 + (n % 2); k >= 1; k -= 2) { j = ((k - 1) / 2) % m; if (k < n) acb_add(s1odd, s1odd, z2pow + j, prec); if (k > 1) { _acb_mul4div2_ui(s1odd, 6*k+1, 6*k-5, 6*k-7, 6*k-13, k, k-1, prec); if (j == 0 && k < n) acb_mul(s1odd, s1odd, z2pow + m, prec); } else { acb_mul(s1odd, s1odd, z, prec); acb_mul_si(s1odd, s1odd, -7, prec); } } } _acb_vec_clear(z2pow, m + 1); } void acb_hypgeom_airy_asymp_bound_factor(mag_t bound, const acb_t z, const acb_t zeta, ulong n) { mag_t t, u, v; mag_init(t); mag_init(u); mag_init(v); if (arb_is_nonnegative(acb_realref(z)) && arb_is_nonnegative(acb_realref(zeta))) { /* 2 exp(7 / (36 |zeta|)) */ mag_set_ui_2exp_si(t, 50, -8); /* bound for 7/36 */ acb_get_mag_lower(u, zeta); mag_div(t, t, u); mag_exp(t, t); mag_mul_2exp_si(bound, t, 1); } else { /* 2 exp(7 pi / (72 |zeta|)) */ mag_set_ui_2exp_si(t, 79, -8); /* bound for 7 pi/72 */ acb_get_mag_lower(u, zeta); mag_div(t, t, u); mag_exp(t, t); mag_mul_2exp_si(bound, t, 1); /* 4 exp(7 pi / (36 |re(zeta)|)) / |cos(arg(zeta))|^n */ if (!arg_lt_2pi3(z, zeta)) { arb_get_mag_lower(u, acb_realref(zeta)); arb_get_mag(v, acb_imagref(zeta)); /* 4 exp(7 pi / (36 u)) < exp(157/(256 u)) */ mag_set_ui_2exp_si(t, 157, -8); mag_div(t, t, u); mag_exp(t, t); mag_mul_2exp_si(t, t, 2); /* |1/cos(arg(zeta))| = sqrt(1+(v/u)^2) */ mag_div(v, v, u); mag_mul(v, v, v); mag_one(u); mag_add(v, v, u); mag_sqrt(v, v); mag_pow_ui(v, v, n); mag_mul(t, t, v); mag_max(bound, bound, t); } /* chi(n) */ acb_hypgeom_mag_chi(t, n); mag_mul(bound, bound, t); } mag_clear(t); mag_clear(u); mag_clear(v); } void acb_hypgeom_airy_asymp(acb_t ai, acb_t aip, acb_t bi, acb_t bip, const acb_t z, slong n, slong prec) { acb_t t, u, w, z_root, zeta; acb_t s0even, s0odd, s1even, s1odd, E1, E2; mag_t err1, err2, erru, errv, errtmp; int want_d0, want_d1, is_real, upper; acb_init(t); acb_init(u); acb_init(w); acb_init(z_root); acb_init(zeta); acb_init(s0even); acb_init(s0odd); acb_init(s1even); acb_init(s1odd); acb_init(E1); acb_init(E2); mag_init(err1); mag_init(err2); mag_init(errtmp); mag_init(erru); mag_init(errv); is_real = acb_is_real(z); want_d0 = (ai != NULL) || (bi != NULL); want_d1 = (aip != NULL) || (bip != NULL); /* required for some of the error bounds to be valid */ n = FLINT_MAX(n, 1); /* this is just a heuristic; the sectors are validated later */ if (arf_sgn(arb_midref(acb_realref(z))) >= 0) { /* z_root = z^(1/4), zeta = 2 z^(3/2) / 3 */ acb_sqrt(z_root, z, prec); acb_cube(zeta, z_root, prec); acb_sqrt(z_root, z_root, prec); acb_mul_2exp_si(zeta, zeta, 1); acb_div_ui(zeta, zeta, 3, prec); /* compute bound factor for z = t = z1, zeta = u = zeta1 */ acb_hypgeom_airy_asymp_bound_factor(err1, z, zeta, n); /* this is just a heuristic; the sectors are validated later */ upper = arf_sgn(arb_midref(acb_imagref(z))) >= 0; if (upper) { /* check -pi/3 < arg(z) < pi */ if (arb_is_positive(acb_imagref(z)) || (arb_is_positive(acb_realref(z)) && arb_is_positive(acb_realref(zeta)))) { arb_one(acb_realref(w)); arb_sqrt_ui(acb_imagref(w), 3, prec); acb_mul_2exp_si(w, w, -1); acb_neg(w, w); acb_mul(t, w, z, prec); acb_neg(u, zeta); acb_hypgeom_airy_asymp_bound_factor(err2, t, u, n); } else { mag_inf(err2); } } else { /* check -pi < arg(z) < pi/3 */ if (arb_is_negative(acb_imagref(z)) || (arb_is_positive(acb_realref(z)) && arb_is_positive(acb_realref(zeta)))) { arb_set_si(acb_realref(w), -1); arb_sqrt_ui(acb_imagref(w), 3, prec); acb_mul_2exp_si(w, w, -1); acb_mul(t, w, z, prec); acb_neg(u, zeta); acb_hypgeom_airy_asymp_bound_factor(err2, t, u, n); } else { mag_inf(err2); } } acb_mul_ui(t, zeta, 72, prec); acb_inv(t, t, prec); acb_mul(u, t, t, prec); acb_hypgeom_airy_asymp_sum(want_d0 ? s0even : NULL, want_d0 ? s0odd : NULL, want_d1 ? s1even : NULL, want_d1 ? s1odd : NULL, erru, errv, t, u, n, prec); /* exponentials */ acb_exp_invexp(E2, E1, zeta, prec); /* common prefactor */ acb_const_pi(w, prec); acb_sqrt(w, w, prec); acb_mul_2exp_si(w, w, 1); if (ai != NULL || bi != NULL) { /* t = sum (-1)^k u(k) / (zeta)^k + error */ acb_sub(t, s0even, s0odd, prec); mag_mul(errtmp, err1, erru); acb_add_error_mag(t, errtmp); /* u = sum (-1)^k u(k) / (-zeta)^k = sum u(k) / (zeta)^k + error */ acb_add(u, s0even, s0odd, prec); mag_mul(errtmp, err2, erru); acb_add_error_mag(u, errtmp); if (ai != NULL) { acb_mul(ai, t, E1, prec); } if (bi != NULL) { acb_mul(t, t, E1, prec); acb_mul(u, u, E2, prec); acb_mul_2exp_si(u, u, 1); if (upper) acb_mul_onei(t, t); else acb_div_onei(t, t); acb_add(bi, t, u, prec); } acb_mul(t, w, z_root, prec); acb_inv(t, t, prec); if (ai != NULL) acb_mul(ai, ai, t, prec); if (bi != NULL) acb_mul(bi, bi, t, prec); } if (aip != NULL || bip != NULL) { /* t = sum (-1)^k v(k) / (zeta)^k + error */ acb_sub(t, s1even, s1odd, prec); mag_mul(errtmp, err1, errv); acb_add_error_mag(t, errtmp); /* u = sum (-1)^k v(k) / (-zeta)^k = sum v(k) / (zeta)^k + error */ acb_add(u, s1even, s1odd, prec); mag_mul(errtmp, err2, errv); acb_add_error_mag(u, errtmp); if (aip != NULL) { acb_mul(aip, t, E1, prec); acb_neg(aip, aip); } if (bip != NULL) { acb_mul(t, t, E1, prec); acb_mul(u, u, E2, prec); acb_mul_2exp_si(u, u, 1); if (upper) acb_div_onei(t, t); else acb_mul_onei(t, t); acb_add(bip, t, u, prec); } acb_inv(t, w, prec); acb_mul(t, t, z_root, prec); if (aip != NULL) acb_mul(aip, aip, t, prec); if (bip != NULL) acb_mul(bip, bip, t, prec); } } else { /* z_root = (-z)^(1/4), zeta = 2 (-z)^(3/2) / 3 */ acb_neg(t, z); acb_sqrt(z_root, t, prec); acb_cube(zeta, z_root, prec); acb_sqrt(z_root, z_root, prec); acb_mul_2exp_si(zeta, zeta, 1); acb_div_ui(zeta, zeta, 3, prec); if (arg_lt_2pi3(t, zeta)) { /* compute bound factor for i zeta */ arb_one(acb_realref(w)); arb_sqrt_ui(acb_imagref(w), 3, prec); acb_mul_2exp_si(w, w, -1); acb_mul(t, z, w, prec); acb_neg(t, t); acb_mul_onei(u, zeta); acb_hypgeom_airy_asymp_bound_factor(err1, t, u, n); /* compute bound factor for -i zeta */ acb_conj(w, w); acb_mul(t, z, w, prec); acb_neg(t, t); acb_div_onei(u, zeta); acb_hypgeom_airy_asymp_bound_factor(err2, t, u, n); } else { mag_inf(err1); mag_inf(err2); } /* t = 1/(72 i zeta), u = (1/(72 i zeta))^2 */ acb_mul_onei(t, zeta); acb_mul_ui(t, t, 72, prec); acb_inv(t, t, prec); acb_mul(u, t, t, prec); acb_hypgeom_airy_asymp_sum(want_d0 ? s0even : NULL, want_d0 ? s0odd : NULL, want_d1 ? s1even : NULL, want_d1 ? s1odd : NULL, erru, errv, t, u, n, prec); /* exponentials */ acb_const_pi(t, prec); acb_mul_2exp_si(t, t, -2); acb_sub(t, zeta, t, prec); acb_mul_onei(t, t); acb_exp_invexp(E2, E1, t, prec); /* common prefactor */ acb_const_pi(w, prec); acb_sqrt(w, w, prec); acb_mul_2exp_si(w, w, 1); if (ai != NULL || bi != NULL) { /* t = sum (-1)^k u(k) / (i zeta)^k + error */ acb_sub(t, s0even, s0odd, prec); mag_mul(errtmp, err1, erru); acb_add_error_mag(t, errtmp); /* w = sum (-1)^k u(k) / (-i zeta)^k = sum u(k) / (i zeta)^k + error */ acb_add(u, s0even, s0odd, prec); mag_mul(errtmp, err2, erru); acb_add_error_mag(u, errtmp); if (ai != NULL) { acb_mul(ai, t, E1, prec); acb_addmul(ai, u, E2, prec); } if (bi != NULL) { /* (-i E1) t + (+i E2) u */ acb_mul(bi, u, E2, prec); acb_submul(bi, t, E1, prec); acb_mul_onei(bi, bi); } acb_mul(t, w, z_root, prec); acb_inv(t, t, prec); if (ai != NULL) acb_mul(ai, ai, t, prec); if (bi != NULL) acb_mul(bi, bi, t, prec); } if (aip != NULL || bip != NULL) { /* t = sum (-1)^k v(k) / (i zeta)^k + error */ acb_sub(t, s1even, s1odd, prec); mag_mul(errtmp, err1, errv); acb_add_error_mag(t, errtmp); /* u = sum (-1)^k v(k) / (-i zeta)^k = sum v(k) / (i zeta)^k + error */ acb_add(u, s1even, s1odd, prec); mag_mul(errtmp, err2, errv); acb_add_error_mag(u, errtmp); if (bip != NULL) { acb_mul(bip, t, E1, prec); acb_addmul(bip, u, E2, prec); } if (aip != NULL) { /* i E1 t - i E2 u */ acb_mul(aip, t, E1, prec); acb_submul(aip, u, E2, prec); acb_mul_onei(aip, aip); } acb_inv(t, w, prec); acb_mul(t, t, z_root, prec); if (aip != NULL) acb_mul(aip, aip, t, prec); if (bip != NULL) acb_mul(bip, bip, t, prec); } } if (is_real) { if (ai != NULL) arb_zero(acb_imagref(ai)); if (aip != NULL) arb_zero(acb_imagref(aip)); if (bi != NULL) arb_zero(acb_imagref(bi)); if (bip != NULL) arb_zero(acb_imagref(bip)); } acb_clear(t); acb_clear(u); acb_clear(w); acb_clear(z_root); acb_clear(zeta); acb_clear(s0even); acb_clear(s0odd); acb_clear(s1even); acb_clear(s1odd); acb_clear(E1); acb_clear(E2); mag_clear(err1); mag_clear(err2); mag_clear(errtmp); mag_clear(erru); mag_clear(errv); } arb-2.8.1/acb_hypgeom/airy_bound.c000066400000000000000000000146351264125401100170470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void arb_bound_exp_neg(mag_t b, const arb_t x) { arb_t t; arb_init(t); arf_set_mag(arb_midref(t), arb_radref(x)); arf_sub(arb_midref(t), arb_midref(x), arb_midref(t), MAG_BITS, ARF_RND_FLOOR); arf_neg(arb_midref(t), arb_midref(t)); arb_exp(t, t, MAG_BITS); arb_get_mag(b, t); arb_clear(t); } /* todo -- should be lt in asymp code? */ static int arg_le_2pi3(const acb_t z, const acb_t zeta) { if (arb_is_nonnegative(acb_realref(z))) return 1; if (arb_is_positive(acb_imagref(z)) && arb_is_nonnegative(acb_imagref(zeta))) return 1; if (arb_is_negative(acb_imagref(z)) && arb_is_nonpositive(acb_imagref(zeta))) return 1; return 0; } void acb_hypgeom_airy_bound_9_7_17(mag_t bound, const acb_t z, const acb_t zeta) { mag_t D, t, u, v, zeta_lower; mag_init(D); mag_init(t); mag_init(u); mag_init(v); mag_init(zeta_lower); acb_get_mag_lower(zeta_lower, zeta); /* 2 chi(1) exp(7 pi / (72 |zeta|)) * c_1 */ /* simplified bound */ if (mag_cmp_2exp_si(zeta_lower, -1) >= 0) mag_one(D); else mag_inf(D); if (!arg_le_2pi3(z, zeta)) { arb_get_mag_lower(u, acb_realref(zeta)); arb_get_mag(v, acb_imagref(zeta)); /* exp(7 pi / (36 u)) < exp(5/(8 u)) */ mag_set_ui_2exp_si(t, 5, -3); mag_div(t, t, u); mag_exp(t, t); /* |1/cos(arg(zeta))| = sqrt(1+(v/u)^2) */ mag_div(v, v, u); mag_mul(v, v, v); mag_one(u); mag_add(v, v, u); mag_sqrt(v, v); mag_mul(t, t, v); /* c_1 * 4 chi(1) < 0.62 < 1 -- do nothing */ mag_max(D, D, t); } /* exp(-zeta) / (2 sqrt(pi)) * (1 + D / |zeta|) */ /* t = exp(-zeta) / (2 sqrt(pi)) < exp(-zeta) * (73/256) */ arb_bound_exp_neg(t, acb_realref(zeta)); mag_mul_ui(t, t, 73); mag_mul_2exp_si(t, t, -8); /* u = 1 + D / |zeta| */ mag_div(u, D, zeta_lower); mag_one(v); mag_add(u, u, v); mag_mul(bound, t, u); mag_clear(D); mag_clear(t); mag_clear(u); mag_clear(v); mag_clear(zeta_lower); } void acb_hypgeom_airy_bound(mag_t ai, mag_t aip, mag_t bi, mag_t bip, const acb_t z) { acb_t zeta; acb_t z1, z2; arf_srcptr zre, zim; mag_t A, B, D, zlo, zhi; slong wp; if (acb_contains_zero(z)) { if (ai != NULL) mag_inf(ai); if (aip != NULL) mag_inf(aip); if (bi != NULL) mag_inf(bi); if (bip != NULL) mag_inf(bip); return; } acb_init(zeta); mag_init(A); mag_init(B); mag_init(D); mag_init(zlo); mag_init(zhi); wp = MAG_BITS * 2; zre = arb_midref(acb_realref(z)); zim = arb_midref(acb_imagref(z)); /* near the negative half line, use |Ai(-z)|, |Bi(-z)| <= |Ai(z exp(pi i/3))| + |Ai(z exp(-pi i/3))| */ if (arf_sgn(zre) < 0 && arf_cmpabs(zre, zim) > 0) { acb_init(z1); acb_init(z2); arb_sqrt_ui(acb_imagref(z1), 3, wp); arb_one(acb_realref(z1)); acb_mul_2exp_si(z1, z1, -1); acb_conj(z2, z1); acb_neg_round(zeta, z, wp); acb_mul(z1, z1, zeta, wp); acb_sqrt(zeta, zeta, wp); acb_cube(zeta, zeta, wp); acb_mul_2exp_si(zeta, zeta, 1); acb_div_ui(zeta, zeta, 3, wp); acb_mul_onei(zeta, zeta); acb_hypgeom_airy_bound_9_7_17(A, z1, zeta); /* conjugate symmetry */ if (arb_is_zero(acb_imagref(z))) { mag_mul_2exp_si(A, A, 1); } else { acb_mul(z2, z2, zeta, wp); acb_neg(zeta, zeta); acb_hypgeom_airy_bound_9_7_17(D, z2, zeta); mag_add(A, A, D); } mag_set(B, A); acb_clear(z1); acb_clear(z2); } else { acb_set_round(zeta, z, wp); acb_sqrt(zeta, zeta, wp); acb_cube(zeta, zeta, wp); acb_mul_2exp_si(zeta, zeta, 1); acb_div_ui(zeta, zeta, 3, wp); acb_hypgeom_airy_bound_9_7_17(A, z, zeta); /* Use Bi(z) = w_1 Ai(z) + 2 w_2 Ai(z exp(+/- 2pi i / 3)), where w_1, w_2 are roots of unity */ if (bi != NULL || bip != NULL) { acb_init(z1); arb_sqrt_ui(acb_imagref(z1), 3, wp); arb_set_si(acb_realref(z1), -1); acb_mul_2exp_si(z1, z1, -1); /* multiply by exp(-2 pi i / 3) in upper half plane and by exp(2 pi i / 3) in lower half plane, to stay close to positive reals */ if (arf_sgn(zim) <= 0) acb_conj(z1, z1); acb_mul(z1, z1, z, wp); acb_neg(zeta, zeta); /* same effect regardless of exp(+/-2 pi i/3) */ acb_hypgeom_airy_bound_9_7_17(B, z1, zeta); mag_mul_2exp_si(B, B, 1); mag_add(B, B, A); acb_clear(z1); } } acb_get_mag(zhi, z); acb_get_mag_lower(zlo, z); /* bound |z|^(1/4) */ mag_sqrt(zhi, zhi); mag_sqrt(zhi, zhi); /* bound |z|^(-1/4) */ mag_rsqrt(zlo, zlo); mag_sqrt(zlo, zlo); if (ai != NULL) mag_mul(ai, A, zlo); if (aip != NULL) mag_mul(aip, A, zhi); if (bi != NULL) mag_mul(bi, B, zlo); if (bip != NULL) mag_mul(bip, B, zhi); acb_clear(zeta); mag_clear(A); mag_clear(B); mag_clear(D); mag_clear(zlo); mag_clear(zhi); } arb-2.8.1/acb_hypgeom/airy_direct.c000066400000000000000000000167061264125401100172130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void arb_const_airy_ai0_eval(arb_t y, slong prec) { arb_t t; fmpq_t v; arb_init(t); fmpq_init(v); arb_set_ui(y, 3); arb_root_ui(y, y, 3, prec + 5); arb_mul(y, y, y, prec + 5); fmpq_set_si(v, 2, 3); arb_gamma_fmpq(t, v, prec + 5); arb_mul(y, y, t, prec + 5); arb_inv(y, y, prec); arb_clear(t); fmpq_clear(v); } void arb_const_airy_ai1_eval(arb_t y, slong prec) { arb_t t; fmpq_t v; arb_init(t); fmpq_init(v); arb_set_ui(y, 3); arb_root_ui(y, y, 3, prec + 5); fmpq_set_si(v, 1, 3); arb_gamma_fmpq(t, v, prec + 5); arb_mul(y, y, t, prec + 5); arb_inv(y, y, prec); arb_neg(y, y); arb_clear(t); fmpq_clear(v); } void arb_const_airy_bi0_eval(arb_t y, slong prec) { arb_t t; fmpq_t v; arb_init(t); fmpq_init(v); arb_set_ui(y, 3); arb_root_ui(y, y, 6, prec + 5); fmpq_set_si(v, 2, 3); arb_gamma_fmpq(t, v, prec + 5); arb_mul(y, y, t, prec + 5); arb_inv(y, y, prec); arb_clear(t); fmpq_clear(v); } void arb_const_airy_bi1_eval(arb_t y, slong prec) { arb_t t; fmpq_t v; arb_init(t); fmpq_init(v); arb_set_ui(y, 3); arb_root_ui(y, y, 6, prec + 5); fmpq_set_si(v, 1, 3); arb_gamma_fmpq(t, v, prec + 5); arb_div(y, y, t, prec); arb_clear(t); fmpq_clear(v); } ARB_DEF_CACHED_CONSTANT(arb_const_airy_ai0, arb_const_airy_ai0_eval) ARB_DEF_CACHED_CONSTANT(arb_const_airy_ai1, arb_const_airy_ai1_eval) ARB_DEF_CACHED_CONSTANT(arb_const_airy_bi0, arb_const_airy_bi0_eval) ARB_DEF_CACHED_CONSTANT(arb_const_airy_bi1, arb_const_airy_bi1_eval) static void acb_hypgeom_airy_0f1_sum_inner(acb_t s, acb_srcptr t, slong m, slong n, slong alpha, int real, slong prec) { slong j, k; mp_limb_t c, chi, clo; acb_zero(s); /* not implemented (coefficient overflow) */ if (FLINT_BITS == 32 && n > 37000) { acb_indeterminate(s); return; } c = 1; j = (n - 1) % m; for (k = n - 1; k >= 0; k--) { if (k != 0) { umul_ppmm(chi, clo, c, 3 * k + alpha); if (chi == 0) umul_ppmm(chi, clo, clo, k); if (chi != 0) { acb_div_ui(s, s, c, prec); c = 1; } } if (real) arb_addmul_ui(acb_realref(s), acb_realref(t + j), c, prec); else acb_addmul_ui(s, t + j, c, prec); if (k != 0) { c = c * k * (3 * k + alpha); if (j == 0) { acb_mul(s, s, t + m, prec); j = m - 1; } else { j--; } } } acb_div_ui(s, s, c, prec); } /* s1 = 0F1(1/3, z/3) s2 = 0F1(2/3, z/3) s4 = 0F1(4/3, z/3) s5 = 0F1(5/3, z/3) */ static void acb_hypgeom_airy_0f1_sum(acb_t s1, acb_t s2, acb_t s4, acb_t s5, const acb_t z, slong n, int real, slong prec) { acb_ptr t; slong m; m = 2 * n_sqrt(n); m = FLINT_MAX(m, 1); t = _acb_vec_init(m + 1); _acb_vec_set_powers(t, z, m + 1, prec); if (s1 != NULL) acb_hypgeom_airy_0f1_sum_inner(s1, t, m, n, -2, real, prec); if (s2 != NULL) acb_hypgeom_airy_0f1_sum_inner(s2, t, m, n, -1, real, prec); if (s4 != NULL) acb_hypgeom_airy_0f1_sum_inner(s4, t, m, n, +1, real, prec); if (s5 != NULL) acb_hypgeom_airy_0f1_sum_inner(s5, t, m, n, +2, real, prec); _acb_vec_clear(t, m + 1); } void acb_hypgeom_airy_direct(acb_t ai, acb_t aip, acb_t bi, acb_t bip, const acb_t z, slong n, slong prec) { mag_t err, wmag, tm; int is_real; acb_t s1, s2, s4, s5, t, u; arb_t ai0, ai1, bi0, bi1; mag_init(err); mag_init(wmag); mag_init(tm); acb_init(s1); acb_init(s2); acb_init(s4); acb_init(s5); acb_init(t); acb_init(u); arb_init(ai0); arb_init(ai1); arb_init(bi0); arb_init(bi1); n = FLINT_MAX(n, 2); is_real = acb_is_real(z); acb_get_mag(wmag, z); /* With w = z^3/9, the terms are bounded by 3 w^n / [(n-1)!]^2. 3 w^n w w^2 ---------- [ 1 + --- + ------- + ....] ((n-1)!)^2 n^2 (n+1)^2 */ mag_pow_ui(wmag, wmag, 3); mag_div_ui(wmag, wmag, 9); mag_pow_ui(err, wmag, n); mag_div_ui(tm, wmag, n); mag_div_ui(tm, tm, n); mag_geom_series(tm, tm, 0); mag_mul(err, err, tm); mag_rfac_ui(tm, n - 1); mag_mul(tm, tm, tm); mag_mul(err, err, tm); mag_mul_ui(err, err, 3); acb_cube(t, z, prec); acb_div_ui(t, t, 3, prec); acb_hypgeom_airy_0f1_sum( (aip != NULL || bip != NULL) ? s1 : NULL, (ai != NULL || bi != NULL) ? s2 : NULL, (ai != NULL || bi != NULL) ? s4 : NULL, (aip != NULL || bip != NULL) ? s5 : NULL, t, n, is_real, prec); if (is_real) { arb_add_error_mag(acb_realref(s1), err); arb_add_error_mag(acb_realref(s2), err); arb_add_error_mag(acb_realref(s4), err); arb_add_error_mag(acb_realref(s5), err); } else { acb_add_error_mag(s1, err); acb_add_error_mag(s2, err); acb_add_error_mag(s4, err); acb_add_error_mag(s5, err); } if (ai != NULL || aip != NULL) { arb_const_airy_ai0(ai0, prec); arb_const_airy_ai1(ai1, prec); } if (bi != NULL || bip != NULL) { arb_const_airy_bi0(bi0, prec); arb_const_airy_bi1(bi1, prec); } /* support aliasing with z */ acb_set(t, z); if (ai != NULL || bi != NULL) { acb_mul(u, s4, t, prec); if (ai != NULL) { acb_mul_arb(ai, s2, ai0, prec); acb_addmul_arb(ai, u, ai1, prec); } if (bi != NULL) { acb_mul_arb(bi, s2, bi0, prec); acb_addmul_arb(bi, u, bi1, prec); } } if (aip != NULL || bip != NULL) { acb_mul(u, t, t, prec); acb_mul_2exp_si(u, u, -1); acb_mul(u, u, s5, prec); if (aip != NULL) { acb_mul_arb(aip, s1, ai1, prec); acb_addmul_arb(aip, u, ai0, prec); } if (bip != NULL) { acb_mul_arb(bip, s1, bi1, prec); acb_addmul_arb(bip, u, bi0, prec); } } mag_clear(err); mag_clear(wmag); mag_clear(tm); acb_clear(s1); acb_clear(s2); acb_clear(s4); acb_clear(s5); acb_clear(t); acb_clear(u); arb_clear(ai0); arb_clear(ai1); arb_clear(bi0); arb_clear(bi1); } arb-2.8.1/acb_hypgeom/bessel_i.c000066400000000000000000000122521264125401100164720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014-2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_bessel_i_asymp_prefactors(acb_t A, acb_t B, acb_t C, const acb_t nu, const acb_t z, slong prec) { acb_t t, u; acb_init(t); acb_init(u); /* C = (2 pi z)^(-1/2) */ acb_const_pi(C, prec); acb_mul_2exp_si(C, C, 1); acb_mul(C, C, z, prec); acb_rsqrt(C, C, prec); if (arb_is_positive(acb_imagref(z)) || (arb_is_zero(acb_imagref(z)) && arb_is_negative(acb_realref(z)))) { acb_exp_pi_i(t, nu, prec); acb_mul_onei(t, t); } else if (arb_is_negative(acb_imagref(z)) || (arb_is_zero(acb_imagref(z)) && arb_is_positive(acb_realref(z)))) { acb_neg(t, nu); acb_exp_pi_i(t, t, prec); acb_mul_onei(t, t); acb_neg(t, t); } else { acb_exp_pi_i(t, nu, prec); acb_mul_onei(t, t); acb_neg(u, nu); acb_exp_pi_i(u, u, prec); acb_mul_onei(u, u); acb_neg(u, u); arb_union(acb_realref(t), acb_realref(t), acb_realref(u), prec); arb_union(acb_imagref(t), acb_imagref(t), acb_imagref(u), prec); } acb_exp_invexp(B, A, z, prec); acb_mul(A, A, t, prec); acb_clear(t); acb_clear(u); } void acb_hypgeom_bessel_i_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec) { acb_t A1, A2, C, U1, U2, s, t, u; int is_real, is_imag; acb_init(A1); acb_init(A2); acb_init(C); acb_init(U1); acb_init(U2); acb_init(s); acb_init(t); acb_init(u); is_imag = 0; is_real = acb_is_real(nu) && acb_is_real(z) && (acb_is_int(nu) || arb_is_positive(acb_realref(z))); if (!is_real && arb_is_zero(acb_realref(z)) && acb_is_int(nu)) { acb_mul_2exp_si(t, nu, -1); if (acb_is_int(t)) is_real = 1; else is_imag = 1; } acb_hypgeom_bessel_i_asymp_prefactors(A1, A2, C, nu, z, prec); /* todo: if Ap ~ 2^a and Am = 2^b and U1 ~ U2 ~ 1, change precision? */ if (!acb_is_finite(A1) || !acb_is_finite(A2) || !acb_is_finite(C)) { acb_indeterminate(res); } else { /* s = 1/2 + nu */ acb_one(s); acb_mul_2exp_si(s, s, -1); acb_add(s, s, nu, prec); /* t = 1 + 2 nu */ acb_mul_2exp_si(t, nu, 1); acb_add_ui(t, t, 1, prec); acb_mul_2exp_si(u, z, 1); acb_hypgeom_u_asymp(U1, s, t, u, -1, prec); acb_neg(u, u); acb_hypgeom_u_asymp(U2, s, t, u, -1, prec); acb_mul(res, A1, U1, prec); acb_addmul(res, A2, U2, prec); acb_mul(res, res, C, prec); if (is_real) arb_zero(acb_imagref(res)); if (is_imag) arb_zero(acb_realref(res)); } acb_clear(A1); acb_clear(A2); acb_clear(C); acb_clear(U1); acb_clear(U2); acb_clear(s); acb_clear(t); acb_clear(u); } void acb_hypgeom_bessel_i_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec) { acb_struct b[2]; acb_t w, c, t; if (acb_is_int(nu) && arb_is_negative(acb_realref(nu))) { acb_init(t); acb_neg(t, nu); acb_hypgeom_bessel_i_0f1(res, t, z, prec); acb_clear(t); return; } acb_init(b + 0); acb_init(b + 1); acb_init(w); acb_init(c); acb_init(t); acb_add_ui(b + 0, nu, 1, prec); acb_one(b + 1); /* (z/2)^nu / gamma(nu+1) */ acb_mul_2exp_si(c, z, -1); acb_pow(c, c, nu, prec); acb_rgamma(t, b + 0, prec); acb_mul(c, t, c, prec); /* z^2/4 */ acb_mul(w, z, z, prec); acb_mul_2exp_si(w, w, -2); acb_hypgeom_pfq_direct(t, NULL, 0, b, 2, w, -1, prec); acb_mul(res, t, c, prec); acb_clear(b + 0); acb_clear(b + 1); acb_clear(w); acb_clear(c); acb_clear(t); } void acb_hypgeom_bessel_i(acb_t res, const acb_t nu, const acb_t z, slong prec) { mag_t zmag; mag_init(zmag); acb_get_mag(zmag, z); if (mag_cmp_2exp_si(zmag, 4) < 0 || (mag_cmp_2exp_si(zmag, 64) < 0 && 2 * mag_get_d(zmag) < prec)) acb_hypgeom_bessel_i_0f1(res, nu, z, prec); else acb_hypgeom_bessel_i_asymp(res, nu, z, prec); mag_clear(zmag); } arb-2.8.1/acb_hypgeom/bessel_j.c000066400000000000000000000141231264125401100164720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014-2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* assumes no aliasing */ /* (+/- iz)^(-1/2-v) * z^v * exp(+/- iz) */ void acb_hypgeom_bessel_j_asymp_prefactors_fallback(acb_t Ap, acb_t Am, acb_t C, const acb_t nu, const acb_t z, slong prec) { acb_t t, u, v; acb_init(t); acb_init(u); acb_init(v); /* v = -1/2-nu */ acb_one(v); acb_mul_2exp_si(v, v, -1); acb_add(v, v, nu, prec); acb_neg(v, v); acb_mul_onei(t, z); /* t = iz */ acb_neg(u, t); /* u = -iz */ /* Ap, Am = (+/- iz)^(-1/2-nu) */ acb_pow(Ap, t, v, prec); acb_pow(Am, u, v, prec); /* Ap, Am *= exp(+/- iz) */ acb_exp_invexp(u, v, t, prec); acb_mul(Ap, Ap, u, prec); acb_mul(Am, Am, v, prec); /* z^nu */ acb_pow(t, z, nu, prec); acb_mul(Ap, Ap, t, prec); acb_mul(Am, Am, t, prec); /* (2 pi)^(-1/2) */ acb_const_pi(C, prec); acb_mul_2exp_si(C, C, 1); acb_rsqrt(C, C, prec); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_hypgeom_bessel_j_asymp_prefactors(acb_t Ap, acb_t Am, acb_t C, const acb_t nu, const acb_t z, slong prec) { if (arb_is_positive(acb_realref(z))) { acb_t t, u; acb_init(t); acb_init(u); /* -(2nu+1)/4 * pi + z */ acb_mul_2exp_si(t, nu, 1); acb_add_ui(t, t, 1, prec); acb_mul_2exp_si(t, t, -2); acb_neg(t, t); acb_const_pi(u, prec); acb_mul(t, t, u, prec); acb_add(t, t, z, prec); acb_mul_onei(t, t); acb_exp_invexp(Ap, Am, t, prec); /* (2 pi z)^(-1/2) */ acb_const_pi(C, prec); acb_mul_2exp_si(C, C, 1); acb_mul(C, C, z, prec); acb_rsqrt(C, C, prec); acb_clear(t); acb_clear(u); return; } acb_hypgeom_bessel_j_asymp_prefactors_fallback(Ap, Am, C, nu, z, prec); } void acb_hypgeom_bessel_j_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec) { acb_t A1, A2, C, U1, U2, s, t, u; int is_real, is_imag; acb_init(A1); acb_init(A2); acb_init(C); acb_init(U1); acb_init(U2); acb_init(s); acb_init(t); acb_init(u); is_imag = 0; is_real = acb_is_real(nu) && acb_is_real(z) && (acb_is_int(nu) || arb_is_positive(acb_realref(z))); if (!is_real && arb_is_zero(acb_realref(z)) && acb_is_int(nu)) { acb_mul_2exp_si(t, nu, -1); if (acb_is_int(t)) is_real = 1; else is_imag = 1; } acb_hypgeom_bessel_j_asymp_prefactors(A1, A2, C, nu, z, prec); /* todo: if Ap ~ 2^a and Am = 2^b and U1 ~ U2 ~ 1, change precision? */ if (!acb_is_finite(A1) || !acb_is_finite(A2) || !acb_is_finite(C)) { acb_indeterminate(res); } else { /* s = 1/2 + nu */ acb_one(s); acb_mul_2exp_si(s, s, -1); acb_add(s, s, nu, prec); /* t = 1 + 2 nu */ acb_mul_2exp_si(t, nu, 1); acb_add_ui(t, t, 1, prec); acb_mul_onei(u, z); acb_mul_2exp_si(u, u, 1); acb_hypgeom_u_asymp(U2, s, t, u, -1, prec); acb_neg(u, u); acb_hypgeom_u_asymp(U1, s, t, u, -1, prec); acb_mul(res, A1, U1, prec); acb_addmul(res, A2, U2, prec); acb_mul(res, res, C, prec); if (is_real) arb_zero(acb_imagref(res)); if (is_imag) arb_zero(acb_realref(res)); } acb_clear(A1); acb_clear(A2); acb_clear(C); acb_clear(U1); acb_clear(U2); acb_clear(s); acb_clear(t); acb_clear(u); } void acb_hypgeom_bessel_j_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec) { acb_struct b[2]; acb_t w, c, t; if (acb_is_int(nu) && arb_is_negative(acb_realref(nu))) { acb_init(t); acb_neg(t, nu); acb_hypgeom_bessel_j_0f1(res, t, z, prec); acb_mul_2exp_si(t, t, -1); if (!acb_is_int(t)) acb_neg(res, res); acb_clear(t); return; } acb_init(b + 0); acb_init(b + 1); acb_init(w); acb_init(c); acb_init(t); acb_add_ui(b + 0, nu, 1, prec); acb_one(b + 1); /* (z/2)^nu / gamma(nu+1) */ acb_mul_2exp_si(c, z, -1); acb_pow(c, c, nu, prec); acb_rgamma(t, b + 0, prec); acb_mul(c, t, c, prec); /* -z^2/4 */ acb_mul(w, z, z, prec); acb_mul_2exp_si(w, w, -2); acb_neg(w, w); acb_hypgeom_pfq_direct(t, NULL, 0, b, 2, w, -1, prec); acb_mul(res, t, c, prec); acb_clear(b + 0); acb_clear(b + 1); acb_clear(w); acb_clear(c); acb_clear(t); } /* The asymptotic series can be used roughly when [(1+log(2))/log(2) = 2.44269504088896] * z > p We are a bit more conservative and use the factor 2. */ void acb_hypgeom_bessel_j(acb_t res, const acb_t nu, const acb_t z, slong prec) { mag_t zmag; mag_init(zmag); acb_get_mag(zmag, z); if (mag_cmp_2exp_si(zmag, 4) < 0 || (mag_cmp_2exp_si(zmag, 64) < 0 && 2 * mag_get_d(zmag) < prec)) acb_hypgeom_bessel_j_0f1(res, nu, z, prec); else acb_hypgeom_bessel_j_asymp(res, nu, z, prec); mag_clear(zmag); } arb-2.8.1/acb_hypgeom/bessel_k.c000066400000000000000000000132141264125401100164730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_bessel_k_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec) { acb_t t, a, b, w; acb_init(t); acb_init(a); acb_init(b); acb_init(w); acb_one(a); acb_mul_2exp_si(a, a, -1); acb_add(a, a, nu, prec); acb_mul_2exp_si(b, nu, 1); acb_add_ui(b, b, 1, prec); acb_mul_2exp_si(w, z, 1); acb_hypgeom_u_asymp(t, a, b, w, -1, prec); acb_neg(w, z); acb_exp(w, w, prec); acb_mul(t, t, w, prec); acb_mul_2exp_si(w, z, 1); acb_rsqrt(w, w, prec); acb_mul(res, t, w, prec); arb_const_sqrt_pi(acb_realref(w), prec); acb_mul_arb(res, res, acb_realref(w), prec); acb_clear(t); acb_clear(a); acb_clear(b); acb_clear(w); } void acb_hypgeom_bessel_k_0f1_series(acb_poly_t res, const acb_poly_t nu, const acb_poly_t z, slong len, slong prec) { acb_poly_t s, u, A, B; acb_poly_struct b[2]; arb_t c; slong wlen; int singular; acb_poly_init(s); acb_poly_init(u); acb_poly_init(A); acb_poly_init(B); acb_poly_init(b + 0); acb_poly_init(b + 1); arb_init(c); singular = (nu->length == 0) || acb_is_int(nu->coeffs); wlen = len + (singular != 0); /* A = (z/2)^nu, B = 1/A */ acb_poly_scalar_mul_2exp_si(A, z, -1); acb_poly_pow_series(A, A, nu, wlen, prec); acb_poly_inv_series(B, A, wlen, prec); acb_poly_mullow(u, z, z, wlen, prec); acb_poly_scalar_mul_2exp_si(u, u, -2); acb_poly_one(b + 1); acb_poly_add_si(b + 0, nu, 1, prec); acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec); acb_poly_mullow(A, A, s, wlen, prec); acb_poly_add_si(b + 0, nu, -1, prec); acb_poly_neg(b + 0, b + 0); acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_sub(A, B, A, prec); acb_poly_scalar_mul_2exp_si(A, A, -1); /* multiply by pi csc(pi nu) */ acb_poly_sin_pi_series(B, nu, wlen, prec); if (singular) { acb_poly_shift_right(A, A, 1); acb_poly_shift_right(B, B, 1); } acb_poly_div_series(res, A, B, len, prec); arb_const_pi(c, prec); _acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec); acb_poly_clear(s); acb_poly_clear(u); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(b + 0); acb_poly_clear(b + 1); arb_clear(c); } void acb_hypgeom_bessel_k_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec) { if (acb_is_int(nu)) { acb_poly_t nux, zx, rx; acb_poly_init(nux); acb_poly_init(zx); acb_poly_init(rx); acb_poly_set_coeff_acb(nux, 0, nu); acb_poly_set_coeff_si(nux, 1, 1); acb_poly_set_acb(zx, z); acb_hypgeom_bessel_k_0f1_series(rx, nux, zx, 1, prec); acb_poly_get_coeff_acb(res, rx, 0); acb_poly_clear(nux); acb_poly_clear(zx); acb_poly_clear(rx); } else { acb_t t, u, v, w; acb_struct b[2]; acb_init(t); acb_init(u); acb_init(v); acb_init(w); acb_init(b + 0); acb_init(b + 1); /* u = 0F1(1+nu), v = 0F1(1-nu) */ acb_mul(t, z, z, prec); acb_mul_2exp_si(t, t, -2); acb_add_ui(b, nu, 1, prec); acb_one(b + 1); acb_hypgeom_pfq_direct(u, NULL, 0, b, 2, t, -1, prec); acb_sub_ui(b, nu, 1, prec); acb_neg(b, b); acb_hypgeom_pfq_direct(v, NULL, 0, b, 2, t, -1, prec); /* v = v * gamma(nu) / (z/2)^nu */ acb_mul_2exp_si(t, z, -1); acb_pow(t, t, nu, prec); acb_gamma(w, nu, prec); acb_mul(v, v, w, prec); acb_div(v, v, t, prec); /* u = u * t * pi / (gamma(nu) * nu * sin(pi nu)) */ acb_mul(u, u, t, prec); acb_const_pi(t, prec); acb_mul(u, u, t, prec); acb_sin_pi(t, nu, prec); acb_mul(t, t, w, prec); acb_mul(t, t, nu, prec); acb_div(u, u, t, prec); acb_sub(res, v, u, prec); acb_mul_2exp_si(res, res, -1); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(w); acb_clear(b + 0); acb_clear(b + 1); } } void acb_hypgeom_bessel_k(acb_t res, const acb_t nu, const acb_t z, slong prec) { mag_t zmag; mag_init(zmag); acb_get_mag(zmag, z); if (mag_cmp_2exp_si(zmag, 4) < 0 || (mag_cmp_2exp_si(zmag, 64) < 0 && 2 * mag_get_d(zmag) < prec)) acb_hypgeom_bessel_k_0f1(res, nu, z, prec); else acb_hypgeom_bessel_k_asymp(res, nu, z, prec); mag_clear(zmag); } arb-2.8.1/acb_hypgeom/bessel_y.c000066400000000000000000000056751264125401100165250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" static void phase(acb_t res, const arb_t re, const arb_t im) { if (arb_is_nonnegative(re) || arb_is_negative(im)) { acb_one(res); } else if (arb_is_negative(re) && arb_is_nonnegative(im)) { acb_set_si(res, -3); } else { arb_zero(acb_imagref(res)); /* -1 +/- 2 */ arf_set_si(arb_midref(acb_realref(res)), -1); mag_one(arb_radref(acb_realref(res))); mag_mul_2exp_si(arb_radref(acb_realref(res)), arb_radref(acb_realref(res)), 1); } } void acb_hypgeom_bessel_jy(acb_t res1, acb_t res2, const acb_t nu, const acb_t z, slong prec) { acb_t jnu, t, u, v; acb_init(jnu); acb_init(t); acb_init(u); acb_init(v); acb_hypgeom_bessel_j(jnu, nu, z, prec); if (acb_is_int(nu)) { int is_real = acb_is_real(nu) && acb_is_real(z) && arb_is_positive(acb_realref(z)); acb_mul_onei(t, z); acb_hypgeom_bessel_k(t, nu, t, prec); acb_onei(u); acb_pow(u, u, nu, prec); acb_mul(t, t, u, prec); acb_const_pi(u, prec); acb_div(t, t, u, prec); acb_mul_2exp_si(t, t, 1); acb_neg(t, t); phase(v, acb_realref(z), acb_imagref(z)); acb_mul(u, jnu, v, prec); acb_mul_onei(u, u); acb_sub(res2, t, u, prec); if (is_real) arb_zero(acb_imagref(res2)); } else { acb_sin_cos_pi(t, u, nu, prec); acb_mul(v, jnu, u, prec); acb_neg(u, nu); acb_hypgeom_bessel_j(u, u, z, prec); acb_sub(v, v, u, prec); acb_div(res2, v, t, prec); } if (res1 != NULL) acb_set(res1, jnu); acb_clear(jnu); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_hypgeom_bessel_y(acb_t res, const acb_t nu, const acb_t z, slong prec) { acb_hypgeom_bessel_jy(NULL, res, nu, z, prec); } arb-2.8.1/acb_hypgeom/chebyshev_t.c000066400000000000000000000052161264125401100172120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_chebyshev_t(acb_t res, const acb_t n, const acb_t z, slong prec) { acb_t t; if (acb_is_int(n) && arf_cmpabs_2exp_si(arb_midref(acb_realref(n)), FLINT_BITS - 1) < 0) { slong k = arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN); acb_chebyshev_t_ui(res, FLINT_ABS(k), z, prec); return; } if (acb_is_zero(z)) { acb_mul_2exp_si(res, n, -1); acb_cos_pi(res, res, prec); return; } if (acb_is_one(z)) { acb_one(res); return; } acb_init(t); acb_set_si(t, -1); if (acb_equal(t, z)) { acb_cos_pi(res, n, prec); } else { acb_sub_ui(t, z, 1, prec); if (arf_cmpabs_2exp_si(arb_midref(acb_realref(t)), -2 - prec / 10) < 0 && arf_cmpabs_2exp_si(arb_midref(acb_imagref(t)), -2 - prec / 10) < 0) { acb_t a, c; acb_init(a); acb_init(c); acb_neg(a, n); acb_one(c); acb_mul_2exp_si(c, c, -1); acb_neg(t, t); acb_mul_2exp_si(t, t, -1); acb_hypgeom_2f1(res, a, n, c, t, 0, prec); acb_clear(a); acb_clear(c); } else if (arb_is_nonnegative(acb_realref(t))) { acb_acosh(t, z, prec); acb_mul(t, t, n, prec); acb_cosh(res, t, prec); } else { acb_acos(t, z, prec); acb_mul(t, t, n, prec); acb_cos(res, t, prec); } } acb_clear(t); } arb-2.8.1/acb_hypgeom/chebyshev_u.c000066400000000000000000000065671264125401100172250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_chebyshev_u(acb_t res, const acb_t n, const acb_t z, slong prec) { acb_t t, u; if (acb_is_int(n) && arf_cmpabs_2exp_si(arb_midref(acb_realref(n)), FLINT_BITS - 1) < 0) { slong k = arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN); if (k >= 0) { acb_chebyshev_u_ui(res, k, z, prec); } else if (k == -1) { acb_zero(res); } else { acb_chebyshev_u_ui(res, -2-k, z, prec); acb_neg(res, res); } return; } if (acb_is_zero(z)) { acb_mul_2exp_si(res, n, -1); acb_cos_pi(res, res, prec); return; } if (acb_is_one(z)) { acb_add_ui(res, n, 1, prec); return; } acb_init(t); acb_init(u); acb_add_ui(u, n, 1, prec); acb_sub_ui(t, z, 1, prec); if (arf_cmpabs_2exp_si(arb_midref(acb_realref(t)), -2 - prec / 10) < 0 && arf_cmpabs_2exp_si(arb_midref(acb_imagref(t)), -2 - prec / 10) < 0) { acb_t a, b, c; acb_init(a); acb_init(b); acb_init(c); acb_neg(a, n); acb_add_ui(b, n, 2, prec); acb_set_ui(c, 3); acb_mul_2exp_si(c, c, -1); acb_neg(t, t); acb_mul_2exp_si(t, t, -1); acb_hypgeom_2f1(t, a, b, c, t, 0, prec); acb_mul(res, t, u, prec); acb_clear(a); acb_clear(b); acb_clear(c); } else { if (arb_is_positive(acb_realref(t))) { /* sinh((n+1) acosh(z)) / (sqrt(z-1) sqrt(z+1)); can use one square root when strictly in the right half plane */ acb_mul(t, z, z, prec); acb_sub_ui(t, t, 1, prec); acb_acosh(res, z, prec); acb_mul(res, res, u, prec); acb_sinh(res, res, prec); acb_rsqrt(t, t, prec); acb_mul(res, res, t, prec); } else { acb_mul(t, z, z, prec); acb_sub_ui(t, t, 1, prec); acb_acos(res, z, prec); acb_mul(res, res, u, prec); acb_sin(res, res, prec); acb_neg(t, t); acb_rsqrt(t, t, prec); acb_mul(res, res, t, prec); } } acb_clear(t); acb_clear(u); } arb-2.8.1/acb_hypgeom/chi.c000066400000000000000000000102331264125401100154450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_chi_asymp(acb_t res, const acb_t z, slong prec) { acb_t t, u, v, one; acb_init(t); acb_init(u); acb_init(v); acb_init(one); acb_one(one); /* u = U(1,1,z) */ acb_hypgeom_u_asymp(u, one, one, z, -1, prec); /* v = e^(-z) */ acb_neg(v, z); acb_exp(v, v, prec); acb_mul(t, u, v, prec); if (arb_is_zero(acb_realref(z))) { arb_div(acb_realref(t), acb_imagref(t), acb_imagref(z), prec); arb_zero(acb_imagref(t)); acb_neg(t, t); } else { /* u = U(1,1,-z) */ acb_neg(u, z); acb_hypgeom_u_asymp(u, one, one, u, -1, prec); acb_inv(v, v, prec); acb_submul(t, u, v, prec); acb_div(t, t, z, prec); acb_mul_2exp_si(t, t, -1); acb_neg(t, t); } if (acb_is_real(z)) { if (arb_is_positive(acb_realref(z))) { arb_zero(acb_imagref(t)); } else if (arb_is_negative(acb_realref(z))) { arb_const_pi(acb_imagref(t), prec); } else { /* add [-pi,pi]/2 i */ acb_const_pi(u, prec); arb_zero(acb_imagref(t)); arb_add_error(acb_imagref(t), acb_realref(u)); } } else { /* -pi/2 if positive real or in lower half plane pi/2 if negative real or in upper half plane */ if (arb_is_negative(acb_imagref(z))) { acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_sub(acb_imagref(t), acb_imagref(t), acb_realref(u), prec); } else if (arb_is_positive(acb_imagref(z))) { acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_add(acb_imagref(t), acb_imagref(t), acb_realref(u), prec); } else { /* add [-pi,pi]/2 i */ acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_add_error(acb_imagref(t), acb_realref(u)); } } acb_swap(res, t); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(one); } void acb_hypgeom_chi_2f3(acb_t res, const acb_t z, slong prec) { acb_t a, t, u; acb_struct b[3]; acb_init(a); acb_init(b); acb_init(b + 1); acb_init(b + 2); acb_init(t); acb_init(u); acb_one(a); acb_set_ui(b, 2); acb_set(b + 1, b); acb_set_ui(b + 2, 3); acb_mul_2exp_si(b + 2, b + 2, -1); acb_mul(t, z, z, prec); acb_mul_2exp_si(t, t, -2); acb_hypgeom_pfq_direct(u, a, 1, b, 3, t, -1, prec); acb_mul(u, u, t, prec); acb_log(t, z, prec); acb_add(u, u, t, prec); arb_const_euler(acb_realref(t), prec); arb_add(acb_realref(u), acb_realref(u), acb_realref(t), prec); acb_swap(res, u); acb_clear(a); acb_clear(b); acb_clear(b + 1); acb_clear(b + 2); acb_clear(t); acb_clear(u); } void acb_hypgeom_chi(acb_t res, const acb_t z, slong prec) { if (acb_hypgeom_u_use_asymp(z, prec)) acb_hypgeom_chi_asymp(res, z, prec); else acb_hypgeom_chi_2f3(res, z, prec); } arb-2.8.1/acb_hypgeom/ci.c000066400000000000000000000110321264125401100152730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_ci_asymp(acb_t res, const acb_t z, slong prec) { acb_t t, u, w, v, one; acb_init(t); acb_init(u); acb_init(w); acb_init(v); acb_init(one); acb_one(one); acb_mul_onei(w, z); /* u = U(1,1,iz) */ acb_hypgeom_u_asymp(u, one, one, w, -1, prec); /* v = e^(-iz) */ acb_neg(v, w); acb_exp(v, v, prec); acb_mul(t, u, v, prec); if (acb_is_real(z)) { arb_div(acb_realref(t), acb_imagref(t), acb_realref(z), prec); arb_zero(acb_imagref(t)); acb_neg(t, t); } else { /* u = U(1,1,-iz) */ acb_neg(w, w); acb_hypgeom_u_asymp(u, one, one, w, -1, prec); acb_inv(v, v, prec); acb_submul(t, u, v, prec); acb_div(t, t, w, prec); acb_mul_2exp_si(t, t, -1); } if (arb_is_zero(acb_realref(z))) { if (arb_is_positive(acb_imagref(z))) { arb_const_pi(acb_imagref(t), prec); arb_mul_2exp_si(acb_imagref(t), acb_imagref(t), -1); } else if (arb_is_negative(acb_imagref(z))) { arb_const_pi(acb_imagref(t), prec); arb_mul_2exp_si(acb_imagref(t), acb_imagref(t), -1); arb_neg(acb_imagref(t), acb_imagref(t)); } else { acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_zero(acb_imagref(t)); arb_add_error(acb_imagref(t), acb_realref(u)); } } else { /* 0 if positive or positive imaginary pi if upper left quadrant (including negative real axis) -pi if lower left quadrant (including negative imaginary axis) */ if (arb_is_positive(acb_realref(z))) { /* do nothing */ } else if (arb_is_negative(acb_realref(z)) && arb_is_nonnegative(acb_imagref(z))) { acb_const_pi(u, prec); arb_add(acb_imagref(t), acb_imagref(t), acb_realref(u), prec); } else if (arb_is_nonpositive(acb_realref(z)) && arb_is_negative(acb_imagref(z))) { acb_const_pi(u, prec); arb_sub(acb_imagref(t), acb_imagref(t), acb_realref(u), prec); } else { /* add [-pi,pi] */ acb_const_pi(u, prec); arb_add_error(acb_imagref(t), acb_realref(u)); } } acb_swap(res, t); acb_clear(t); acb_clear(u); acb_clear(w); acb_clear(v); acb_clear(one); } void acb_hypgeom_ci_2f3(acb_t res, const acb_t z, slong prec) { acb_t a, t, u; acb_struct b[3]; acb_init(a); acb_init(b); acb_init(b + 1); acb_init(b + 2); acb_init(t); acb_init(u); acb_one(a); acb_set_ui(b, 2); acb_set(b + 1, b); acb_set_ui(b + 2, 3); acb_mul_2exp_si(b + 2, b + 2, -1); acb_mul(t, z, z, prec); acb_mul_2exp_si(t, t, -2); acb_neg(t, t); acb_hypgeom_pfq_direct(u, a, 1, b, 3, t, -1, prec); acb_mul(u, u, t, prec); acb_log(t, z, prec); acb_add(u, u, t, prec); arb_const_euler(acb_realref(t), prec); arb_add(acb_realref(u), acb_realref(u), acb_realref(t), prec); acb_swap(res, u); acb_clear(a); acb_clear(b); acb_clear(b + 1); acb_clear(b + 2); acb_clear(t); acb_clear(u); } void acb_hypgeom_ci(acb_t res, const acb_t z, slong prec) { if (acb_hypgeom_u_use_asymp(z, prec)) acb_hypgeom_ci_asymp(res, z, prec); else acb_hypgeom_ci_2f3(res, z, prec); } arb-2.8.1/acb_hypgeom/ei.c000066400000000000000000000070031264125401100153000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_ei_asymp(acb_t res, const acb_t z, slong prec) { acb_t t, u; acb_init(t); acb_init(u); acb_one(t); acb_neg(u, z); acb_hypgeom_u_asymp(u, t, t, u, -1, prec); acb_div(u, u, z, prec); acb_exp(t, z, prec); acb_mul(u, u, t, prec); if (arb_is_zero(acb_imagref(z))) { arb_zero(acb_imagref(u)); } else if (arb_is_positive(acb_imagref(z))) { acb_const_pi(t, prec); arb_add(acb_imagref(u), acb_imagref(u), acb_realref(t), prec); } else if (arb_is_negative(acb_imagref(z))) { acb_const_pi(t, prec); arb_sub(acb_imagref(u), acb_imagref(u), acb_realref(t), prec); } else { /* add [-pi,pi] i */ acb_const_pi(t, prec); arb_add_error(acb_imagref(u), acb_realref(t)); } acb_swap(res, u); acb_clear(t); acb_clear(u); } /* Ei(z) = z 2F2(1,1,2,2,z) + 0.5[log(z)-log(1/z)] + gamma */ void acb_hypgeom_ei_2f2(acb_t res, const acb_t z, slong prec) { acb_t a, t; acb_struct b[2]; acb_init(a); acb_init(b); acb_init(b + 1); acb_init(t); acb_one(a); acb_set_ui(b, 2); acb_set_ui(b + 1, 2); acb_hypgeom_pfq_direct(t, a, 1, b, 2, z, -1, prec); acb_mul(t, t, z, prec); arb_const_euler(acb_realref(a), prec); arb_add(acb_realref(t), acb_realref(t), acb_realref(a), prec); if (arb_is_zero(acb_imagref(z))) { if (arb_is_positive(acb_realref(z))) { acb_log(a, z, prec); } else { /* ok if overlapping zero -- will be indeterminate either way */ acb_neg(a, z); acb_log(a, a, prec); arb_zero(acb_imagref(a)); } acb_add(t, t, a, prec); } else if (arb_is_nonzero(acb_imagref(z)) || arb_is_nonnegative(acb_realref(z))) /* not overlapping (-inf,0] */ { acb_log(a, z, prec); acb_add(t, t, a, prec); } else { acb_log(a, z, prec); arb_zero(acb_imagref(a)); acb_const_pi(b, prec); arb_add_error(acb_imagref(a), acb_realref(b)); acb_add(t, t, a, prec); } acb_swap(res, t); acb_clear(a); acb_clear(b); acb_clear(b + 1); acb_clear(t); } void acb_hypgeom_ei(acb_t res, const acb_t z, slong prec) { if (acb_hypgeom_u_use_asymp(z, prec)) acb_hypgeom_ei_asymp(res, z, prec); else acb_hypgeom_ei_2f2(res, z, prec); } arb-2.8.1/acb_hypgeom/erf.c000066400000000000000000000115661264125401100154700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* IMAG: erf(z) = 2z/sqrt(pi) * 1F1(1/2, 3/2, -z^2) */ void acb_hypgeom_erf_1f1a(acb_t res, const acb_t z, slong prec) { acb_t a, t, w; acb_struct b[2]; acb_init(a); acb_init(b); acb_init(b + 1); acb_init(t); acb_init(w); acb_one(a); acb_mul_2exp_si(a, a, -1); acb_set_ui(b, 3); acb_mul_2exp_si(b, b, -1); acb_one(b + 1); acb_mul(w, z, z, prec); acb_neg(w, w); acb_hypgeom_pfq_direct(t, a, 1, b, 2, w, -1, prec); acb_const_pi(w, prec); acb_rsqrt(w, w, prec); acb_mul(t, t, w, prec); acb_mul(t, t, z, prec); acb_mul_2exp_si(res, t, 1); acb_clear(a); acb_clear(b); acb_clear(b + 1); acb_clear(t); acb_clear(w); } /* REAL: erf(x) = 2x/sqrt(pi) * exp(-x^2) 1F1(1, 3/2, x^2) */ void acb_hypgeom_erf_1f1b(acb_t res, const acb_t z, slong prec) { acb_t a, b, t, w; acb_init(a); acb_init(b); acb_init(t); acb_init(w); acb_set_ui(b, 3); acb_mul_2exp_si(b, b, -1); acb_mul(w, z, z, prec); acb_hypgeom_pfq_direct(t, a, 0, b, 1, w, -1, prec); acb_neg(w, w); acb_exp(w, w, prec); acb_mul(t, t, w, prec); acb_const_pi(w, prec); acb_rsqrt(w, w, prec); acb_mul(t, t, w, prec); acb_mul(t, t, z, prec); acb_mul_2exp_si(res, t, 1); acb_clear(a); acb_clear(b); acb_clear(t); acb_clear (w); } void acb_hypgeom_erf_asymp(acb_t res, const acb_t z, slong prec, slong prec2) { acb_t a, t, u; acb_init(a); acb_init(t); acb_init(u); acb_one(a); acb_mul_2exp_si(a, a, -1); acb_mul(t, z, z, prec2); acb_hypgeom_u_asymp(u, a, a, t, -1, prec2); acb_neg(t, t); acb_exp(t, t, prec2); acb_mul(u, u, t, prec2); acb_const_pi(t, prec2); acb_sqrt(t, t, prec2); acb_mul(t, t, z, prec2); acb_div(u, u, t, prec2); /* branch cut term: -1 or 1 */ if (arb_contains_zero(acb_realref(z))) { arb_zero(acb_imagref(t)); arf_zero(arb_midref(acb_realref(t))); mag_one(arb_radref(acb_realref(t))); } else { acb_set_si(t, arf_sgn(arb_midref(acb_realref(z)))); } acb_sub(t, t, u, prec); if (arb_is_zero(acb_imagref(z))) arb_zero(acb_imagref(t)); else if (arb_is_zero(acb_realref(z))) arb_zero(acb_realref(t)); acb_set(res, t); acb_clear(a); acb_clear(t); acb_clear(u); } void acb_hypgeom_erf(acb_t res, const acb_t z, slong prec) { double x, y, absz2, logz; slong prec2; if (!acb_is_finite(z)) { acb_indeterminate(res); return; } if (acb_is_zero(z)) { acb_zero(res); return; } if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 0) < 0 && arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0)) { acb_hypgeom_erf_1f1a(res, z, prec); return; } if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 64) > 0 || arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 64) > 0)) { acb_hypgeom_erf_asymp(res, z, prec, prec); return; } x = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN); y = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN); absz2 = x * x + y * y; logz = 0.5 * log(absz2); if (logz - absz2 < -(prec + 8) * 0.69314718055994530942) { /* If the asymptotic term is small, we can compute with reduced precision */ prec2 = FLINT_MIN(prec + 4 + (y*y - x*x - logz) * 1.4426950408889634074, (double) prec); prec2 = FLINT_MAX(8, prec2); prec2 = FLINT_MIN(prec2, prec); acb_hypgeom_erf_asymp(res, z, prec, prec2); } else if (arf_cmpabs(arb_midref(acb_imagref(z)), arb_midref(acb_realref(z))) > 0) { acb_hypgeom_erf_1f1a(res, z, prec); } else { acb_hypgeom_erf_1f1b(res, z, prec); } } arb-2.8.1/acb_hypgeom/erfc.c000066400000000000000000000032651264125401100156300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_erfc(acb_t res, const acb_t z, slong prec) { if (arb_is_positive(acb_realref(z))) { acb_t t, u; acb_init(t); acb_init(u); acb_set_si(t, 1); acb_mul_2exp_si(t, t, -1); acb_mul(u, z, z, prec); acb_hypgeom_gamma_upper(res, t, u, 0, prec); arb_const_sqrt_pi(acb_realref(t), prec); acb_div_arb(res, res, acb_realref(t), prec); acb_clear(t); acb_clear(u); } else { acb_hypgeom_erf(res, z, prec); acb_sub_ui(res, res, 1, prec); acb_neg(res, res); } } arb-2.8.1/acb_hypgeom/erfi.c000066400000000000000000000024151264125401100156320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_erfi(acb_t res, const acb_t z, slong prec) { acb_mul_onei(res, z); acb_hypgeom_erf(res, res, prec); acb_mul_onei(res, res); acb_neg(res, res); } arb-2.8.1/acb_hypgeom/expint.c000066400000000000000000000024771264125401100162240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_expint(acb_t res, const acb_t s, const acb_t z, slong prec) { acb_t t; acb_init(t); acb_sub_ui(t, s, 1, prec); acb_neg(t, t); acb_hypgeom_gamma_upper(res, t, z, 1, prec); acb_clear(t); } arb-2.8.1/acb_hypgeom/gamma_upper.c000066400000000000000000000163441264125401100172100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_gamma_upper_asymp(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) { acb_t t, u; acb_init(t); acb_init(u); acb_sub_ui(t, s, 1, prec); acb_neg(t, t); acb_hypgeom_u_asymp(u, t, t, z, -1, prec); if (modified) { acb_div(u, u, z, prec); } else { acb_neg(t, t); acb_pow(t, z, t, prec); acb_mul(u, u, t, prec); } acb_neg(t, z); acb_exp(t, t, prec); acb_mul(res, t, u, prec); acb_clear(t); acb_clear(u); } void acb_hypgeom_gamma_upper_1f1a(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) { acb_t a, t, w; acb_struct b[2]; acb_init(a); acb_init(b); acb_init(b + 1); acb_init(t); acb_init(w); acb_set(a, s); acb_add_ui(b, s, 1, prec); acb_one(b + 1); acb_neg(w, z); acb_hypgeom_pfq_direct(t, a, 1, b, 2, w, -1, prec); acb_div(t, t, s, prec); if (modified) { acb_neg(a, s); acb_pow(a, z, a, prec); acb_gamma(b, s, prec); acb_mul(b, b, a, prec); acb_sub(res, b, t, prec); } else { acb_pow(a, z, s, prec); acb_mul(t, t, a, prec); acb_gamma(a, s, prec); acb_sub(res, a, t, prec); } acb_clear(a); acb_clear(b); acb_clear(b + 1); acb_clear(t); acb_clear(w); } void acb_hypgeom_gamma_upper_1f1b(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) { acb_t a, b, t; acb_init(a); acb_init(b); acb_init(t); acb_add_ui(b, s, 1, prec); acb_hypgeom_pfq_direct(t, NULL, 0, b, 1, z, -1, prec); acb_div(t, t, s, prec); acb_neg(a, z); acb_exp(a, a, prec); acb_mul(t, t, a, prec); if (modified) { acb_neg(a, s); acb_pow(a, z, a, prec); acb_gamma(b, s, prec); acb_mul(b, b, a, prec); acb_sub(res, b, t, prec); } else { acb_pow(a, z, s, prec); acb_mul(t, t, a, prec); acb_gamma(a, s, prec); acb_sub(res, a, t, prec); } acb_clear(a); acb_clear(b); acb_clear(t); } /* requires n <= 0 */ void acb_hypgeom_gamma_upper_singular(acb_t res, slong s, const acb_t z, int modified, slong prec) { acb_t A, B, C, t, u; acb_struct a[2]; acb_struct b[2]; arb_t f; slong n; n = -s; acb_init(A); acb_init(B); acb_init(C); acb_init(t); acb_init(u); arb_init(f); acb_init(a + 0); acb_init(a + 1); acb_init(b + 0); acb_init(b + 1); arb_fac_ui(f, n, prec); /* (-1)^n (psi(n+1) - log(z)) / n! */ acb_set_ui(A, n + 1); acb_digamma(A, A, prec); acb_log(t, z, prec); acb_sub(A, A, t, prec); acb_div_arb(A, A, f, prec); if (n % 2) acb_neg(A, A); /* (-1)^n z 2F2(1,1;2,2+n;-z) / (n+1)! */ acb_set_si(a, 1); acb_set_si(b, 2); acb_set_si(b + 1, 2 + n); acb_neg(t, z); acb_hypgeom_pfq_direct(B, a, 1, b, 2, t, -1, prec); acb_mul(B, B, z, prec); arb_mul_ui(f, f, n + 1, prec); acb_div_arb(B, B, f, prec); if (n % 2) acb_neg(B, B); /* -sum((-z)^k / ((k-n) k!), k=0...n-1) */ acb_set_si(a, -n); acb_set_si(b, 1 - n); acb_set_si(b + 1, 1); acb_neg(t, z); if (n == 0) { acb_zero(C); } else { acb_hypgeom_pfq_sum(C, u, a, 1, b, 2, t, n, prec); acb_div_ui(C, C, n, prec); } if (modified) { acb_pow_si(t, z, n, prec); acb_mul(A, A, t, prec); acb_mul(B, B, t, prec); } else { acb_pow_si(t, z, -n, prec); acb_mul(C, C, t, prec); } acb_add(res, A, B, prec); acb_add(res, res, C, prec); acb_clear(A); acb_clear(B); acb_clear(C); acb_clear(t); acb_clear(u); arb_clear(f); acb_clear(a + 0); acb_clear(a + 1); acb_clear(b + 0); acb_clear(b + 1); } void acb_hypgeom_gamma_upper(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) { if (acb_is_zero(z)) { if (modified) { if (arb_is_negative(acb_realref(s))) { acb_inv(res, s, prec); acb_neg(res, res); } else { acb_indeterminate(res); } } else { if (arb_is_positive(acb_realref(s))) acb_gamma(res, s, prec); else acb_indeterminate(res); } } else { slong n = WORD_MAX; if (acb_is_int(s) && arf_cmpabs_2exp_si(arb_midref(acb_realref(s)), 30) < 0) { n = arf_get_si(arb_midref(acb_realref(s)), ARF_RND_DOWN); } if (n >= 1 && n <= 3) { acb_t t, u; acb_init(t); acb_init(u); if (modified) acb_pow_si(u, z, n, prec); if (n == 1) { acb_neg(res, z); acb_exp(res, res, prec); } else if (n == 2) { acb_add_ui(t, z, 1, prec); acb_neg(res, z); acb_exp(res, res, prec); acb_mul(res, res, t, prec); } else if (n == 3) { acb_add_ui(t, z, 2, prec); acb_mul(t, t, z, prec); acb_add_ui(t, t, 2, prec); acb_neg(res, z); acb_exp(res, res, prec); acb_mul(res, res, t, prec); } if (modified) acb_div(res, res, u, prec); acb_clear(t); acb_clear(u); return; } if (acb_hypgeom_u_use_asymp(z, prec)) { acb_hypgeom_gamma_upper_asymp(res, s, z, modified, prec); return; } if (n <= 0 && n > -10 * prec) { acb_hypgeom_gamma_upper_singular(res, n, z, modified, prec); return; } if (arf_sgn(arb_midref(acb_realref(z))) > 0) acb_hypgeom_gamma_upper_1f1b(res, s, z, modified, prec); else acb_hypgeom_gamma_upper_1f1a(res, s, z, modified, prec); } } arb-2.8.1/acb_hypgeom/gegenbauer_c.c000066400000000000000000000063611264125401100173170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* this can be improved */ static int use_recurrence(const acb_t n, const acb_t m, slong prec) { if (!acb_is_int(n) || !arb_is_nonnegative(acb_realref(n))) return 0; if (arf_cmpabs_ui(arb_midref(acb_realref(n)), prec) > 0) return 0; if (arb_is_nonnegative(acb_realref(m))) return 0; return 1; } void acb_hypgeom_gegenbauer_c_ui_recurrence(acb_t res, ulong n, const acb_t m, const acb_t z, slong prec) { acb_t t, u, v; ulong k; if (n == 0) { acb_one(res); return; } if (n == 1) { acb_mul(res, m, z, prec); acb_mul_2exp_si(res, res, 1); return; } acb_init(t); acb_init(u); acb_init(v); acb_one(t); acb_mul(u, m, z, prec); acb_mul_2exp_si(u, u, 1); for (k = 2; k <= n; k++) { acb_mul_2exp_si(v, m, 1); acb_add_ui(v, v, k - 2, prec); acb_mul(t, t, v, prec); acb_add_ui(v, m, k - 1, prec); acb_mul(v, v, z, prec); acb_mul_2exp_si(v, v, 1); acb_mul(v, v, u, prec); acb_sub(t, v, t, prec); acb_div_ui(t, t, k, prec); acb_swap(t, u); } acb_set(res, u); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_hypgeom_gegenbauer_c(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec) { acb_t a, b, c, t; if (use_recurrence(n, m, prec)) { acb_hypgeom_gegenbauer_c_ui_recurrence(res, arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN), m, z, prec); return; } acb_init(a); acb_init(b); acb_init(c); acb_init(t); acb_neg(a, n); acb_mul_2exp_si(b, m, 1); acb_add(b, b, n, prec); acb_one(c); acb_mul_2exp_si(c, c, -1); acb_add(c, c, m, prec); acb_sub_ui(t, z, 1, prec); acb_mul_2exp_si(t, t, -1); acb_neg(t, t); acb_hypgeom_2f1(t, a, b, c, t, 0, prec); acb_mul_2exp_si(b, m, 1); acb_rising(b, b, n, prec); acb_mul(t, t, b, prec); acb_add_ui(b, n, 1, prec); acb_rgamma(b, b, prec); acb_mul(t, t, b, prec); acb_set(res, t); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(t); } arb-2.8.1/acb_hypgeom/hermite_h.c000066400000000000000000000073761264125401100166640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_hermite_h_ui_recurrence(acb_t res, ulong n, const acb_t z, slong prec) { acb_t t, u, v; ulong k; if (n == 0) { acb_one(res); return; } if (n == 1) { acb_set_round(res, z, prec); acb_mul_2exp_si(res, res, 1); return; } acb_init(t); acb_init(u); acb_init(v); acb_one(t); acb_mul_2exp_si(u, z, 1); for (k = 2; k <= n; k++) { acb_mul(v, u, z, prec); acb_submul_ui(v, t, k - 1, prec); acb_mul_2exp_si(v, v, 1); acb_swap(t, u); acb_swap(u, v); } acb_set(res, u); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_hypgeom_hermite_h(acb_t res, const acb_t n, const acb_t z, slong prec) { acb_t a, b, c, t, u, v; int use_asymp; if (acb_is_int(n) && arb_is_nonnegative(acb_realref(n)) && (arf_cmpabs_ui(arb_midref(acb_realref(n)), 30) < 0)) { acb_hypgeom_hermite_h_ui_recurrence(res, arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN), z, prec); return; } acb_init(a); acb_init(b); acb_init(c); acb_init(t); acb_init(u); acb_init(v); acb_mul(t, z, z, prec); use_asymp = arb_is_positive(acb_realref(z)) && acb_hypgeom_u_use_asymp(t, prec); if (use_asymp) { acb_mul_2exp_si(a, n, -1); acb_neg(a, a); acb_one(b); acb_mul_2exp_si(b, b, -1); acb_hypgeom_u_asymp(u, a, b, t, -1, prec); acb_mul_2exp_si(t, z, 1); acb_pow(t, t, n, prec); acb_mul(u, u, t, prec); acb_set(res, u); } else { /* a = (1-n)/2 */ acb_sub_ui(a, n, 1, prec); acb_neg(a, a); acb_mul_2exp_si(a, a, -1); /* c = -n/2 */ acb_mul_2exp_si(c, n, -1); acb_neg(c, c); acb_rgamma(u, a, prec); if (!acb_is_zero(u)) { acb_one(b); acb_mul_2exp_si(b, b, -1); acb_hypgeom_m(v, c, b, t, 0, prec); acb_mul(u, u, v, prec); } acb_rgamma(v, c, prec); if (!acb_is_zero(v)) { acb_set_ui(b, 3); acb_mul_2exp_si(b, b, -1); acb_hypgeom_m(t, a, b, t, 0, prec); acb_mul_2exp_si(t, t, 1); acb_mul(t, t, z, prec); acb_submul(u, v, t, prec); } acb_set_ui(t, 2); acb_pow(t, t, n, prec); acb_mul(u, u, t, prec); acb_const_pi(t, prec); acb_sqrt(t, t, prec); acb_mul(u, u, t, prec); acb_set(res, u); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(t); acb_clear(u); acb_clear(v); } arb-2.8.1/acb_hypgeom/jacobi_p.c000066400000000000000000000065311264125401100164560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* this can be improved */ static int use_recurrence(const acb_t n, const acb_t a, const acb_t b, slong prec) { if (!acb_is_int(n) || !arb_is_nonnegative(acb_realref(n))) return 0; if (arf_cmpabs_ui(arb_midref(acb_realref(n)), prec) > 0) return 0; if (arb_is_nonnegative(acb_realref(a)) || arf_get_d(arb_midref(acb_realref(a)), ARF_RND_DOWN) > -0.9) return 0; return 1; } void acb_hypgeom_jacobi_p_ui_direct(acb_t res, ulong n, const acb_t a, const acb_t b, const acb_t z, slong prec) { acb_ptr terms; acb_t t, u, v; slong k; terms = _acb_vec_init(n + 1); acb_init(t); acb_init(u); acb_init(v); acb_one(terms); acb_add_ui(u, z, 1, prec); for (k = 1; k <= n; k++) { acb_add_ui(t, a, n + 1 - k, prec); acb_mul(t, t, u, prec); acb_div_ui(t, t, 2 * k, prec); acb_mul(terms + k, terms + k - 1, t, prec); } acb_sub_ui(u, z, 1, prec); acb_one(v); for (k = 1; k <= n; k++) { acb_add_ui(t, b, n + 1 - k, prec); acb_mul(t, t, u, prec); acb_div_ui(t, t, 2 * k, prec); acb_mul(v, v, t, prec); acb_mul(terms + n - k, terms + n - k, v, prec); } acb_set(res, terms); for (k = 1; k <= n; k++) acb_add(res, res, terms + k, prec); _acb_vec_clear(terms, n + 1); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_hypgeom_jacobi_p(acb_t res, const acb_t n, const acb_t a, const acb_t b, const acb_t z, slong prec) { acb_t t, u, v, w; if (use_recurrence(n, a, b, prec)) { acb_hypgeom_jacobi_p_ui_direct(res, arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN), a, b, z, prec); return; } acb_init(t); acb_init(u); acb_init(v); acb_init(w); acb_neg(t, n); acb_add_ui(v, a, 1, prec); acb_add(u, n, v, prec); acb_add(u, u, b, prec); acb_sub_ui(w, z, 1, prec); acb_mul_2exp_si(w, w, -1); acb_neg(w, w); acb_hypgeom_2f1(w, t, u, v, w, 0, prec); acb_rising(t, v, n, prec); acb_mul(w, w, t, prec); acb_add_ui(t, n, 1, prec); acb_rgamma(t, t, prec); acb_mul(w, w, t, prec); acb_set(res, w); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(w); } arb-2.8.1/acb_hypgeom/laguerre_l.c000066400000000000000000000061141264125401100170260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* this can be improved */ static int use_recurrence(const acb_t n, const acb_t m, slong prec) { if (!acb_is_int(n) || !arb_is_nonnegative(acb_realref(n))) return 0; if (arf_cmpabs_ui(arb_midref(acb_realref(n)), prec) > 0) return 0; if (arf_cmpabs(arb_midref(acb_realref(n)), arb_midref(acb_realref(m))) >= 0) return 0; return 1; } void acb_hypgeom_laguerre_l_ui_recurrence(acb_t res, ulong n, const acb_t m, const acb_t z, slong prec) { acb_t t, u, v; ulong k; if (n == 0) { acb_one(res); return; } if (n == 1) { acb_sub(res, m, z, prec); acb_add_ui(res, res, 1, prec); return; } acb_init(t); acb_init(u); acb_init(v); acb_one(t); acb_sub(u, m, z, prec); acb_add_ui(u, u, 1, prec); for (k = 2; k <= n; k++) { acb_add_ui(v, m, k - 1, prec); acb_mul(t, t, v, prec); acb_add_ui(v, m, 2 * k - 1, prec); acb_sub(v, v, z, prec); acb_mul(v, v, u, prec); acb_sub(t, v, t, prec); acb_div_ui(t, t, k, prec); acb_swap(t, u); } acb_set(res, u); acb_clear(t); acb_clear(u); acb_clear(v); } void acb_hypgeom_laguerre_l(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec) { acb_t t, u, v; if (use_recurrence(n, m, prec)) { acb_hypgeom_laguerre_l_ui_recurrence(res, arf_get_si(arb_midref(acb_realref(n)), ARF_RND_DOWN), m, z, prec); return; } /* todo: should be a test of whether n contains any negative integer */ if (acb_contains_int(n) && !arb_is_nonnegative(acb_realref(n))) { acb_indeterminate(res); return; } acb_init(t); acb_init(u); acb_init(v); acb_neg(t, n); acb_add_ui(u, m, 1, prec); acb_hypgeom_m(t, t, u, z, 1, prec); acb_add_ui(u, n, 1, prec); acb_rising(u, u, m, prec); acb_mul(res, t, u, prec); acb_clear(t); acb_clear(u); acb_clear(v); } arb-2.8.1/acb_hypgeom/legendre_p.c000066400000000000000000000076421264125401100170200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_legendre_p(acb_t res, const acb_t n, const acb_t m, const acb_t z, int type, slong prec) { acb_t a, b, c, w; if (!acb_is_finite(z)) { acb_indeterminate(res); return; } if (acb_is_int(n) && acb_is_int(m) && arb_is_nonnegative(acb_realref(n)) && arb_is_nonnegative(acb_realref(m)) && type == 0) { arf_srcptr nn = arb_midref(acb_realref(n)); arf_srcptr mm = arb_midref(acb_realref(m)); if (arf_cmpabs(mm, nn) > 0) { acb_zero(res); return; } if (arf_cmpabs_2exp_si(nn, FLINT_BITS - 1) < 0 && arf_cmpabs_2exp_si(mm, FLINT_BITS - 1) < 0) { slong nnn, mmm; nnn = arf_get_si(nn, ARF_RND_DOWN); mmm = arf_get_si(mm, ARF_RND_DOWN); /* we will probably lose all accuracy... */ if (nnn - mmm > 2 * prec) { acb_indeterminate(res); } /* hypergeometric series is faster at high precision, but avoid at 1 */ else if (prec < 500 + nnn * 10.0 || (nnn - mmm) < 10 || (arb_contains_si(acb_realref(z), 1) && arb_contains_zero(acb_imagref(z)))) { if (mmm == 0) { acb_hypgeom_legendre_p_uiui_rec(res, nnn, mmm, z, prec); } else { acb_init(a); acb_init(b); acb_mul(a, z, z, prec); acb_sub_ui(a, a, 1, prec); acb_neg(a, a); acb_mul_2exp_si(b, m, -1); acb_pow(a, a, b, prec); acb_hypgeom_legendre_p_uiui_rec(res, nnn, mmm, z, prec); acb_mul(res, res, a, prec); acb_clear(a); acb_clear(b); } return; } } } acb_init(a); acb_init(b); acb_init(c); acb_init(w); acb_neg(a, n); acb_add_ui(b, n, 1, prec); acb_sub_ui(c, m, 1, prec); acb_neg(c, c); acb_sub_ui(w, z, 1, prec); acb_neg(w, w); acb_mul_2exp_si(w, w, -1); acb_hypgeom_2f1(w, a, b, c, w, 1, prec); if (!acb_is_zero(m)) { acb_add_ui(a, z, 1, prec); acb_sub_ui(b, z, 1, prec); if (type == 0) { acb_neg(b, b); } else if (type != 1) { flint_printf("unsupported 'type' %d for legendre p\n", type); abort(); } acb_mul_2exp_si(c, m, -1); acb_pow(a, a, c, prec); acb_neg(c, c); acb_pow(b, b, c, prec); acb_mul(w, w, a, prec); acb_mul(w, w, b, prec); } acb_set(res, w); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(w); } arb-2.8.1/acb_hypgeom/legendre_p_uiui_rec.c000066400000000000000000000044511264125401100206770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_legendre_p_uiui_rec(acb_t res, ulong n, ulong m, const acb_t z, slong prec) { acb_t t, u, v; slong k; if (!acb_is_finite(z)) { acb_indeterminate(res); return; } if (m > n) { acb_zero(res); return; } if ((n - m) / 4 > prec) { acb_indeterminate(res); return; } acb_init(t); acb_init(u); acb_init(v); /* t = p(m,m) = (-1)^m (2m-1)!! */ if (m == 0) arb_one(acb_realref(t)); else arb_doublefac_ui(acb_realref(t), 2 * m - 1, prec); if (m % 2) arb_neg(acb_realref(t), acb_realref(t)); if (n > m) { /* t = p(m+1,m) = z(2m+1)p(m,m), u = p(m,m) */ acb_mul_ui(u, t, 2 * m + 1, prec); acb_mul(u, u, z, prec); acb_swap(t, u); for (k = m + 2; k <= n; k++) { /* t, u = ((2*k-1)*z*t - (k+m-1)*u) / (k-m), t */ acb_mul(v, t, z, prec); acb_mul_ui(v, v, 2 * k - 1, prec); acb_submul_ui(v, u, k + m - 1, prec); acb_div_ui(u, v, k - m, prec); acb_swap(t, u); } } acb_set(res, t); acb_clear(t); acb_clear(u); acb_clear(v); } arb-2.8.1/acb_hypgeom/legendre_q.c000066400000000000000000000203211264125401100170060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* invalid in (-1,0) */ int _acb_hypgeom_legendre_q_single_valid(const acb_t z) { arb_t t; int ok; if (!arb_contains_zero(acb_imagref(z))) return 1; if (arb_is_positive(acb_imagref(z))) return 1; arb_init(t); arb_one(t); arb_neg(t, t); ok = arb_lt(acb_realref(z), t); arb_clear(t); return ok; } void _acb_hypgeom_legendre_q_double(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec) { acb_t t, u, v; acb_init(t); acb_init(u); acb_init(v); if (acb_is_int(m)) { acb_sub_ui(t, z, 1, prec); acb_mul_2exp_si(u, m, -1); acb_pow(v, t, u, prec); acb_neg(t, t); acb_neg(u, u); acb_pow(t, t, u, prec); acb_mul(t, t, v, prec); acb_hypgeom_legendre_q(u, n, m, z, 0, prec); acb_mul(t, t, u, prec); acb_mul_2exp_si(u, m, -1); if (!acb_is_int(u)) acb_neg(t, t); acb_sub_ui(u, z, 1, prec); acb_sqrt(u, u, prec); acb_sub_ui(v, z, 1, prec); acb_neg(v, v); acb_rsqrt(v, v, prec); acb_mul(u, u, v, prec); acb_hypgeom_legendre_p(v, n, m, z, 1, prec); acb_mul(u, u, v, prec); acb_const_pi(v, prec); acb_mul(u, u, v, prec); acb_mul_2exp_si(u, u, -1); acb_sub(res, t, u, prec); } else { acb_sub(t, n, m, prec); acb_add_ui(t, t, 1, prec); acb_mul_2exp_si(u, m, 1); acb_rising(t, t, u, prec); acb_neg(u, m); acb_hypgeom_legendre_p(u, n, u, z, 1, prec); acb_mul(t, t, u, prec); acb_hypgeom_legendre_p(u, n, m, z, 1, prec); acb_sub(t, u, t, prec); acb_exp_pi_i(u, m, prec); acb_mul(t, t, u, prec); acb_sin_pi(u, m, prec); acb_div(t, t, u, prec); acb_const_pi(u, prec); acb_mul(t, t, u, prec); acb_mul_2exp_si(t, t, -1); acb_set(res, t); } acb_clear(t); acb_clear(u); acb_clear(v); } void _acb_hypgeom_legendre_q_single(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec) { acb_t a, b, c, z2, t, u; acb_init(a); acb_init(b); acb_init(c); acb_init(z2); acb_init(t); acb_init(u); /* invalid in (-1,0) */ if (!_acb_hypgeom_legendre_q_single_valid(z)) { acb_indeterminate(res); return; } acb_pow_si(z2, z, -2, prec); /* z2 = 1/z^2 */ /* t = 2F1r((m+n+1)/2, (m+n)/2+1, n+3/2, 1/z^2) */ acb_add(b, m, n, prec); acb_add_ui(a, b, 1, prec); acb_mul_2exp_si(a, a, -1); acb_mul_2exp_si(b, b, -1); acb_add_ui(b, b, 1, prec); acb_set_ui(c, 3); acb_mul_2exp_si(c, c, -1); acb_add(c, c, n, prec); acb_hypgeom_2f1(t, a, b, c, z2, 1, prec); /* prefactor sqrt(pi) 2^-n (z+1)^(m/2) (z-1)^(m/2) exp(i pi m) */ /* (1/2) gamma(m+n+1) z^(-m-n-1) */ if (!acb_is_zero(m)) { acb_add_ui(z2, z, 1, prec); acb_mul_2exp_si(c, m, -1); acb_pow(z2, z2, c, prec); acb_mul(t, t, z2, prec); acb_sub_ui(z2, z, 1, prec); acb_mul_2exp_si(c, m, -1); acb_pow(z2, z2, c, prec); acb_mul(t, t, z2, prec); acb_exp_pi_i(z2, m, prec); acb_mul(t, t, z2, prec); } acb_set_ui(z2, 2); acb_neg(c, n); acb_pow(z2, z2, c, prec); acb_mul(t, t, z2, prec); acb_add(c, m, n, prec); acb_add_ui(c, c, 1, prec); acb_gamma(z2, c, prec); acb_mul(t, t, z2, prec); acb_neg(c, c); acb_pow(z2, z, c, prec); acb_mul(t, t, z2, prec); acb_mul_2exp_si(t, t, -1); acb_const_pi(u, prec); acb_sqrt(u, u, prec); acb_mul(t, t, u, prec); acb_set(res, t); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(z2); acb_clear(t); acb_clear(u); } void acb_hypgeom_legendre_q(acb_t res, const acb_t n, const acb_t m, const acb_t z, int type, slong prec) { if (type == 0) { /* http://functions.wolfram.com/07.11.26.0033.01 */ /* todo: simplify the gamma quotients and the sqrt pi factor... */ acb_t a, b, c, z2, mn, nm, t, u; acb_init(a); acb_init(b); acb_init(c); acb_init(z2); acb_init(mn); acb_init(nm); acb_init(t); acb_init(u); acb_add(mn, m, n, prec); /* mn = m + n */ acb_sub(nm, n, m, prec); /* nm = n - m */ acb_mul(z2, z, z, prec); /* z2 = z^2 */ /* t = 2F1((1-m-n)/2, (n-m)/2+1, 3/2, z^2) */ acb_sub_ui(a, mn, 1, prec); acb_neg(a, a); acb_mul_2exp_si(a, a, -1); acb_mul_2exp_si(b, nm, -1); acb_add_ui(b, b, 1, prec); acb_set_ui(c, 3); acb_mul_2exp_si(c, c, -1); acb_hypgeom_2f1(t, a, b, c, z2, 0, prec); /* u = 2F1(-(m+n)/2, (n-m+1)/2, 1/2, z^2) */ acb_neg(a, mn); acb_mul_2exp_si(a, a, -1); acb_add_ui(b, nm, 1, prec); acb_mul_2exp_si(b, b, -1); acb_one(c); acb_mul_2exp_si(c, c, -1); acb_hypgeom_2f1(u, a, b, c, z2, 0, prec); /* a = cospi((m+n)/2) gamma((m+n)/2+1) rgamma((n-m+1)/2) z */ /* b = sinpi((m+n)/2) gamma((m+n+1)/2) rgamma((n-m)/2+1) / 2 */ acb_mul_2exp_si(a, mn, -1); acb_sin_cos_pi(b, a, a, prec); acb_mul_2exp_si(c, mn, -1); acb_add_ui(c, c, 1, prec); acb_gamma(c, c, prec); acb_mul(a, a, c, prec); acb_add_ui(c, nm, 1, prec); acb_mul_2exp_si(c, c, -1); acb_rgamma(c, c, prec); acb_mul(a, a, c, prec); acb_mul(a, a, z, prec); acb_add_ui(c, mn, 1, prec); acb_mul_2exp_si(c, c, -1); acb_gamma(c, c, prec); acb_mul(b, b, c, prec); acb_mul_2exp_si(c, nm, -1); acb_add_ui(c, c, 1, prec); acb_rgamma(c, c, prec); acb_mul(b, b, c, prec); acb_mul_2exp_si(b, b, -1); /* at - bu */ acb_mul(t, t, a, prec); acb_mul(u, u, b, prec); acb_sub(t, t, u, prec); /* prefactor sqrt(pi) 2^m (1-z^2)^(-m/2) */ if (!acb_is_zero(m)) { acb_sub_ui(u, z2, 1, prec); acb_neg(u, u); acb_neg(c, m); acb_mul_2exp_si(c, c, -1); acb_pow(u, u, c, prec); acb_set_ui(c, 2); acb_pow(c, c, m, prec); acb_mul(u, u, c, prec); acb_mul(t, t, u, prec); } acb_const_pi(u, prec); acb_sqrt(u, u, prec); acb_mul(t, t, u, prec); acb_set(res, t); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(z2); acb_clear(mn); acb_clear(nm); acb_clear(t); acb_clear(u); } else if (type == 1) { if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -2) < 0 && arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -2) < 0) || !_acb_hypgeom_legendre_q_single_valid(z)) { _acb_hypgeom_legendre_q_double(res, n, m, z, prec); } else { _acb_hypgeom_legendre_q_single(res, n, m, z, prec); } } else { flint_printf("unsupported 'type' %d for legendre q\n", type); abort(); } } arb-2.8.1/acb_hypgeom/li.c000066400000000000000000000042371264125401100153150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" static void _acb_hypgeom_li(acb_t res, const acb_t z, slong prec) { if (acb_is_zero(z)) { acb_zero(res); } else { acb_log(res, z, prec); acb_hypgeom_ei(res, res, prec); } } void _acb_hypgeom_const_li2_eval(arb_t s, slong prec) { acb_t t; acb_init(t); acb_set_ui(t, 2); _acb_hypgeom_li(t, t, prec); arb_set(s, acb_realref(t)); acb_clear(t); } ARB_DEF_CACHED_CONSTANT(_acb_hypgeom_const_li2, _acb_hypgeom_const_li2_eval) static void _acb_hypgeom_li_offset(acb_t res, const acb_t z, slong prec) { if (acb_is_int(z) && arf_cmp_2exp_si(arb_midref(acb_realref(z)), 1) == 0) { acb_zero(res); } else { arb_t t; arb_init(t); _acb_hypgeom_const_li2(t, prec); _acb_hypgeom_li(res, z, prec); arb_sub(acb_realref(res), acb_realref(res), t, prec); arb_clear(t); } } void acb_hypgeom_li(acb_t res, const acb_t z, int offset, slong prec) { if (offset) _acb_hypgeom_li_offset(res, z, prec); else _acb_hypgeom_li(res, z, prec); } arb-2.8.1/acb_hypgeom/m.c000066400000000000000000000117531264125401100151460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_m_asymp(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec) { acb_t t, u, v, c; acb_init(t); acb_init(u); acb_init(v); acb_init(c); acb_sub(c, b, a, prec); acb_neg(v, z); acb_hypgeom_u_asymp(t, a, b, z, -1, prec); acb_hypgeom_u_asymp(u, c, b, v, -1, prec); /* gamma(b-a) */ acb_rgamma(v, c, prec); acb_mul(t, t, v, prec); /* z^(a-b) */ acb_neg(c, c); acb_pow(v, z, c, prec); acb_mul(u, u, v, prec); /* gamma(a) */ acb_rgamma(v, a, prec); acb_mul(u, u, v, prec); /* exp(z) */ acb_exp(v, z, prec); acb_mul(u, u, v, prec); /* (-z)^(-a) */ acb_neg(c, a); acb_neg(v, z); acb_pow(v, v, c, prec); acb_mul(t, t, v, prec); acb_add(t, t, u, prec); if (!regularized) { acb_gamma(v, b, prec); acb_mul(t, t, v, prec); } if (acb_is_real(a) && acb_is_real(b) && acb_is_real(z)) { arb_zero(acb_imagref(t)); } acb_swap(res, t); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(c); } static void _acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec) { if (acb_is_one(a)) { acb_hypgeom_pfq_direct(res, NULL, 0, b, 1, z, -1, prec); } else { acb_struct c[3]; c[0] = *a; c[1] = *b; acb_init(c + 2); acb_one(c + 2); acb_hypgeom_pfq_direct(res, c, 1, c + 1, 2, z, -1, prec); acb_clear(c + 2); } } void acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec) { acb_t t; if (regularized) { acb_init(t); acb_rgamma(t, b, prec); } if (arf_sgn(arb_midref(acb_realref(z))) >= 0 || (acb_is_int(a) && arb_is_nonpositive(acb_realref(a)))) { _acb_hypgeom_m_1f1(res, a, b, z, prec); } else { /* Kummer's transformation */ acb_t u, v; acb_init(u); acb_init(v); acb_sub(u, b, a, prec); acb_neg(v, z); _acb_hypgeom_m_1f1(u, u, b, v, prec); acb_exp(v, z, prec); acb_mul(res, u, v, prec); acb_clear(u); acb_clear(v); } if (regularized) { acb_mul(res, res, t, prec); acb_clear(t); } } void acb_hypgeom_m(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec) { slong m = WORD_MAX; slong n = WORD_MAX; if (acb_is_int(a) && arf_cmpabs_2exp_si(arb_midref(acb_realref(a)), 30) < 0) { m = arf_get_si(arb_midref(acb_realref(a)), ARF_RND_DOWN); } if (acb_is_int(b) && arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0) { n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN); } /* terminating */ if (m <= 0 && m < n && m > -10 * prec && (n > 0 || !regularized)) { acb_hypgeom_m_1f1(res, a, b, z, regularized, prec); return; } /* large */ if (acb_hypgeom_u_use_asymp(z, prec)) { acb_hypgeom_m_asymp(res, a, b, z, regularized, prec); return; } /* remove singularity */ if (n <= 0 && n > -10 * prec && regularized) { acb_t c, d, t, u; acb_init(c); acb_init(d); acb_init(t); acb_init(u); acb_sub(c, a, b, prec); acb_add_ui(c, c, 1, prec); acb_neg(d, b); acb_add_ui(d, d, 2, prec); acb_hypgeom_m_1f1(t, c, d, z, 0, prec); acb_pow_ui(u, z, 1 - n, prec); acb_mul(t, t, u, prec); acb_rising_ui(u, a, 1 - n, prec); acb_mul(t, t, u, prec); arb_fac_ui(acb_realref(u), 1 - n, prec); acb_div_arb(res, t, acb_realref(u), prec); acb_clear(c); acb_clear(d); acb_clear(t); acb_clear(u); } else { acb_hypgeom_m_1f1(res, a, b, z, regularized, prec); } } arb-2.8.1/acb_hypgeom/pfq_bound_factor.c000066400000000000000000000042161264125401100202210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_pfq_bound_factor(mag_t C, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, ulong n) { mag_t t, u; acb_t w; slong i; if (p > q) { mag_inf(C); return; } mag_init(t); mag_init(u); acb_init(w); acb_get_mag(C, z); for (i = 0; i < q; i++) { acb_add_ui(w, b + i, n, MAG_BITS); if (arb_is_positive(acb_realref(w))) { acb_get_mag_lower(u, w); if (i < p) { acb_sub(w, a + i, b + i, MAG_BITS); acb_get_mag(t, w); mag_div(t, t, u); mag_one(u); mag_add(t, t, u); mag_mul(C, C, t); } else { mag_div(C, C, u); } } else { mag_inf(C); } } mag_one(t); mag_sub_lower(u, t, C); if (mag_is_zero(u)) mag_inf(C); else mag_div(C, t, u); mag_clear(t); mag_clear(u); acb_clear(w); } arb-2.8.1/acb_hypgeom/pfq_choose_n.c000066400000000000000000000210021264125401100173410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" double mag_get_log2_d_approx(const mag_t x); #define D_ABS(x) ((x) < 0.0 ? (-x) : (x)) int acb_hypgeom_pfq_choose_n_double(slong * nn, const double * are, const double * aim, slong p, const double * bre, const double * bim, slong q, double log2_z, slong n_skip, slong n_min, slong n_max, slong prec) { double increase, term, term_max, accuracy, accuracy_best, t, u; double required_decrease; slong k, n, n_best; int success; if (p < q) required_decrease = 0.01; else if (p == q) required_decrease = 0.0001; else required_decrease = 0.01; term = term_max = accuracy = accuracy_best = 0.0; success = 0; for (n = n_best = n_skip; n < n_max; n++) { t = 1.0; for (k = 0; k < FLINT_MAX(p, q); k++) { if (k < p) { u = (are[k]+n-1)*(are[k]+n-1) + (aim[k]*aim[k]); t *= D_ABS(u); } if (k < q) { u = (bre[k]+n-1)*(bre[k]+n-1) + (bim[k]*bim[k]); u = D_ABS(u); if (u > 1e-100) t /= u; } } increase = 0.5 * log(t) * 1.4426950408889634074 + log2_z; term += increase; term_max = FLINT_MAX(term_max, term); accuracy = term_max - term; if (accuracy > accuracy_best && n >= n_min && increase < -required_decrease) { n_best = n; accuracy_best = accuracy; } if (accuracy_best > prec + 4) { success = 1; break; } } *nn = n_best; return success; } slong acb_hypgeom_pfq_choose_n(acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong prec) { slong n_skip, n_min, n_max, n_terminating, nint; slong k, n; double log2_z; double * are; double * aim; double * bre; double * bim; mag_t zmag; int success; if (acb_is_zero(z) || !acb_is_finite(z)) return 1; mag_init(zmag); are = flint_malloc(sizeof(double) * 2 * (p + q)); aim = are + p; bre = aim + p; bim = bre + q; acb_get_mag(zmag, z); log2_z = mag_get_log2_d_approx(zmag); n_skip = 1; n_min = 1; n_max = FLINT_MIN(WORD_MAX / 2, 50 + 10.0 * prec); n_terminating = WORD_MAX; for (k = 0; k < p; k++) { are[k] = arf_get_d(arb_midref(acb_realref(a + k)), ARF_RND_DOWN); aim[k] = arf_get_d(arb_midref(acb_imagref(a + k)), ARF_RND_DOWN); /* If the series is terminating, stop at this n. */ if (acb_is_int(a + k) && are[k] <= 0.0) { n_terminating = FLINT_MIN(n_terminating, (slong) (-are[k] + 1)); n_terminating = FLINT_MAX(n_terminating, 1); } else if (are[k] <= 0.01 && D_ABS(aim[k]) < 0.01) { /* If very close to an integer, we don't want to deal with it using doubles, so fast forward (todo: could work with the log2 of the difference instead when this happens). */ nint = floor(are[k] + 0.5); if (D_ABS(nint - are[k]) < 0.01) n_skip = FLINT_MAX(n_skip, 2 - nint); } } n_max = FLINT_MIN(n_max, n_terminating); for (k = 0; k < q; k++) { bre[k] = arf_get_d(arb_midref(acb_realref(b + k)), ARF_RND_DOWN); bim[k] = arf_get_d(arb_midref(acb_imagref(b + k)), ARF_RND_DOWN); if (bre[k] <= 0.25) { n_min = FLINT_MAX(n_min, 2 - bre[k]); /* Also avoid near-integers here (can even allow exact integers when computing regularized hypergeometric functions). */ if (bre[k] <= 0.01 && D_ABS(bim[k]) < 0.01) { nint = floor(bre[k] + 0.5); if (D_ABS(nint - bre[k]) < 0.01) n_skip = FLINT_MAX(n_skip, 2 - nint); } } } success = acb_hypgeom_pfq_choose_n_double(&n, are, aim, p, bre, bim, q, log2_z, n_skip, n_min, n_max, prec); if (!success) { if (n_terminating <= n_max) { n = n_terminating; } else { n = FLINT_MAX(n_min, n); n = FLINT_MIN(n_max, n); } } flint_free(are); mag_clear(zmag); return n; } slong acb_hypgeom_pfq_series_choose_n(const acb_poly_struct * a, slong p, const acb_poly_struct * b, slong q, const acb_poly_t z, slong len, slong prec) { slong n_skip, n_min, n_max, n_terminating, nint; slong k, n; double log2_z; double * are; double * aim; double * bre; double * bim; acb_t t; mag_t zmag; int success; if (z->length == 0) /* todo: check finite */ return 1; mag_init(zmag); acb_init(t); are = flint_malloc(sizeof(double) * 2 * (p + q)); aim = are + p; bre = aim + p; bim = bre + q; acb_get_mag(zmag, z->coeffs); log2_z = mag_get_log2_d_approx(zmag); n_skip = 1; n_min = 1; n_max = FLINT_MIN(WORD_MAX / 2, 50 + 10.0 * prec); n_terminating = WORD_MAX; /* e.g. for exp(x + O(x^100)), make sure that we actually run the recurrence up to order 100. todo: compute correctly based on degrees of inputs */ n_min = FLINT_MAX(n_min, len); n_max = FLINT_MAX(n_max, n_min); for (k = 0; k < p; k++) { acb_poly_get_coeff_acb(t, a + k, 0); are[k] = arf_get_d(arb_midref(acb_realref(t)), ARF_RND_DOWN); aim[k] = arf_get_d(arb_midref(acb_imagref(t)), ARF_RND_DOWN); /* If the series is terminating, stop at this n. */ if (acb_is_int(t) && are[k] <= 0.0 && acb_poly_length(a + k) <= 1) { n_terminating = FLINT_MIN(n_terminating, (slong) (-are[k] + 1)); n_terminating = FLINT_MAX(n_terminating, 1); } else if (are[k] <= 0.01 && D_ABS(aim[k]) < 0.01) { /* If very close to an integer, we don't want to deal with it using doubles, so fast forward (todo: could work with the log2 of the difference instead when this happens). */ nint = floor(are[k] + 0.5); if (D_ABS(nint - are[k]) < 0.01) n_skip = FLINT_MAX(n_skip, 2 - nint); } } n_max = FLINT_MIN(n_max, n_terminating); for (k = 0; k < q; k++) { acb_poly_get_coeff_acb(t, b + k, 0); bre[k] = arf_get_d(arb_midref(acb_realref(t)), ARF_RND_DOWN); bim[k] = arf_get_d(arb_midref(acb_imagref(t)), ARF_RND_DOWN); if (bre[k] <= 0.25) { n_min = FLINT_MAX(n_min, 2 - bre[k]); /* Also avoid near-integers here (can even allow exact integers when computing regularized hypergeometric functions). */ if (bre[k] <= 0.01 && D_ABS(bim[k]) < 0.01) { nint = floor(bre[k] + 0.5); if (D_ABS(nint - bre[k]) < 0.01) n_skip = FLINT_MAX(n_skip, 2 - nint); } } } success = acb_hypgeom_pfq_choose_n_double(&n, are, aim, p, bre, bim, q, log2_z, n_skip, n_min, n_max, prec); if (!success) { if (n_terminating <= n_max) { n = n_terminating; } else { n = FLINT_MAX(n_min, n); n = FLINT_MIN(n_max, n); } } flint_free(are); acb_clear(t); mag_clear(zmag); return n; } arb-2.8.1/acb_hypgeom/pfq_direct.c000066400000000000000000000035761264125401100170360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_pfq_direct(acb_t res, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) { acb_t s, t; mag_t err, C; acb_init(s); acb_init(t); mag_init(err); mag_init(C); if (n < 0) n = acb_hypgeom_pfq_choose_n(a, p, b, q, z, prec); acb_hypgeom_pfq_sum(s, t, a, p, b, q, z, n, prec); if (!acb_is_zero(t)) { acb_hypgeom_pfq_bound_factor(C, a, p, b, q, z, n); acb_get_mag(err, t); mag_mul(err, err, C); if (_acb_vec_is_real(a, p) && _acb_vec_is_real(b, q) && acb_is_real(z)) arb_add_error_mag(acb_realref(s), err); else acb_add_error_mag(s, err); } acb_set(res, s); acb_clear(s); acb_clear(t); mag_clear(err); mag_clear(C); } arb-2.8.1/acb_hypgeom/pfq_series_direct.c000066400000000000000000000262321264125401100204020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void _acb_poly_reciprocal_majorant(arb_ptr res, acb_srcptr vec, slong len, slong prec) { slong i; for (i = 0; i < len; i++) { if (i == 0) { acb_get_abs_lbound_arf(arb_midref(res + i), vec + i, prec); mag_zero(arb_radref(res + i)); } else { acb_get_abs_ubound_arf(arb_midref(res + i), vec + i, prec); arf_neg(arb_midref(res + i), arb_midref(res + i)); mag_zero(arb_radref(res + i)); } } } void acb_poly_reciprocal_majorant(arb_poly_t res, const acb_poly_t poly, slong prec) { arb_poly_fit_length(res, poly->length); _acb_poly_reciprocal_majorant(res->coeffs, poly->coeffs, poly->length, prec); _arb_poly_set_length(res, poly->length); } /* F = 1 + U + U^2 + ... = 1/(1-U) assuming that U[0] is positive; indeterminate if not convergent */ static void arb_poly_geometric_sum(arb_poly_t F, const arb_poly_t U, slong len, slong prec) { if (U->length == 0) { arb_poly_one(F); return; } arb_poly_add_si(F, U, -1, prec); arb_poly_neg(F, F); if (F->length > 0 && arb_is_positive(F->coeffs)) { arb_poly_inv_series(F, F, len, prec); } else { arb_poly_fit_length(F, len); _arb_vec_indeterminate(F->coeffs, len); _arb_poly_set_length(F, len); } } /* F = 1 + U + U^2 + U^3 + ... = 1/(1-U) U = product of (1 + |A-B|/(|B[0] - |B[1:]|) product of (1 / (|B[0] - |B[1:]|)) * |Z| */ void acb_hypgeom_pfq_series_bound_factor(arb_poly_t F, const acb_poly_struct * a, slong p, const acb_poly_struct * b, slong q, const acb_poly_t z, slong n, slong len, slong prec) { slong i; arb_poly_t T, U, V; acb_poly_t BN, AB; /* not convergent */ if (p > q) { arb_poly_fit_length(F, len); _arb_vec_indeterminate(F->coeffs, len); _arb_poly_set_length(F, len); return; } arb_poly_init(T); arb_poly_init(U); arb_poly_init(V); acb_poly_init(BN); acb_poly_init(AB); acb_poly_majorant(U, z, prec); for (i = 0; i < q; i++) { acb_poly_add_si(BN, b + i, n, prec); if (acb_poly_length(BN) != 0 && arb_is_positive(acb_realref(BN->coeffs))) { if (i < p) { /* 1 + |a-b|/reciprocal_majorant(b + n) */ acb_poly_sub(AB, a + i, b + i, prec); acb_poly_majorant(T, AB, prec); acb_poly_reciprocal_majorant(V, BN, prec); arb_poly_div_series(T, T, V, len, prec); arb_poly_add_si(T, T, 1, prec); arb_poly_mullow(U, U, T, len, prec); } else { acb_poly_reciprocal_majorant(T, BN, prec); arb_poly_div_series(U, U, T, len, prec); } } else { arb_poly_fit_length(U, len); _arb_vec_indeterminate(U->coeffs, len); _arb_poly_set_length(U, len); break; } } /* F = 1/(1-U) */ arb_poly_geometric_sum(F, U, len, prec); arb_poly_clear(T); arb_poly_clear(U); arb_poly_clear(V); acb_poly_clear(BN); acb_poly_clear(AB); } void acb_hypgeom_pfq_series_sum_forward(acb_poly_t s, acb_poly_t t, const acb_poly_struct * a, slong p, const acb_poly_struct * b, slong q, const acb_poly_t z, int regularized, slong n, slong len, slong prec) { acb_poly_t u, v; acb_poly_t tmp; slong k, i; acb_poly_init(u); acb_poly_init(v); acb_poly_init(tmp); if (!regularized) { acb_poly_zero(s); acb_poly_one(t); for (k = 0; k < n && acb_poly_length(t) != 0; k++) { acb_poly_add(s, s, t, prec); if (p > 0) { acb_poly_add_si(u, a, k, prec); for (i = 1; i < p; i++) { acb_poly_add_si(v, a + i, k, prec); acb_poly_mullow(u, u, v, len, prec); } acb_poly_mullow(t, t, u, len, prec); } if (q > 0) { acb_poly_add_si(u, b, k, prec); for (i = 1; i < q; i++) { acb_poly_add_si(v, b + i, k, prec); acb_poly_mullow(u, u, v, len, prec); } acb_poly_div_series(t, t, u, len, prec); } acb_poly_mullow(t, t, z, len, prec); } } else { acb_poly_zero(s); for (i = 0; i < q; i++) { if (i == 0) { acb_poly_rgamma_series(t, b + i, len, prec); } else { acb_poly_rgamma_series(u, b + i, len, prec); acb_poly_mullow(tmp, t, u, len, prec); acb_poly_swap(tmp, t); } } for (k = 0; k < n; k++) { acb_poly_add(s, s, t, prec); if (p > 0) { acb_poly_add_si(u, a, k, prec); for (i = 1; i < p; i++) { acb_poly_add_si(v, a + i, k, prec); acb_poly_mullow(tmp, u, v, len, prec); acb_poly_swap(tmp, u); } acb_poly_mullow(tmp, t, u, len, prec); acb_poly_swap(tmp, t); } if (q > 0) { acb_poly_add_si(u, b, k, prec); for (i = 1; i < q; i++) { acb_poly_add_si(v, b + i, k, prec); acb_poly_mullow(tmp, u, v, len, prec); acb_poly_swap(tmp, u); } if (acb_poly_length(u) > 0 && !acb_contains_zero(u->coeffs)) { acb_poly_div_series(tmp, t, u, len, prec); acb_poly_mullow(t, tmp, z, len, prec); } else { /* compute term from scratch */ acb_poly_one(t); for (i = 0; i < p; i++) { acb_poly_rising_ui_series(v, a + i, k + 1, len, prec); acb_poly_mullow(t, t, v, len, prec); } for (i = 0; i < q; i++) { acb_poly_add_si(v, b + i, k + 1, prec); acb_poly_rgamma_series(v, v, len, prec); acb_poly_mullow(t, t, v, len, prec); } acb_poly_pow_ui_trunc_binexp(v, z, k + 1, len, prec); acb_poly_mullow(t, t, v, len, prec); } } else { acb_poly_mullow(tmp, t, z, len, prec); acb_poly_swap(tmp, t); } } } acb_poly_clear(u); acb_poly_clear(v); acb_poly_clear(tmp); } void acb_hypgeom_pfq_series_direct(acb_poly_t res, const acb_poly_struct * a, slong p, const acb_poly_struct * b, slong q, const acb_poly_t z, int regularized, slong n, slong len, slong prec) { acb_poly_t s, t, err; arb_poly_t C, T; slong i; int is_real; int terminating; /* default algorithm to choose number of terms */ if (n < 0) { n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec); } terminating = 0; /* check if it terminates due to a root of the numerator */ for (i = 0; i < p; i++) { if (acb_poly_length(a + i) == 0 && n > 0) { terminating = 1; } else if (acb_poly_length(a + i) == 1) { acb_srcptr c = acb_poly_get_coeff_ptr(a + i, 0); if (acb_is_int(c) && arb_is_negative(acb_realref(c)) && arf_cmpabs_ui(arb_midref(acb_realref(c)), n) < 0) { terminating = 1; } } } /* check if it terminates (to order n) due to z */ /* the following tests could be made stronger... */ if (z->length == 0 && n >= 1) { terminating = 1; } else if (!terminating && z->length > 0 && acb_is_zero(z->coeffs) && n >= len) { if (regularized) { terminating = 1; } else { terminating = 1; for (i = 0; i < q; i++) { acb_srcptr c = acb_poly_get_coeff_ptr(b + i, 0); if (!arb_is_positive(acb_realref(c)) && acb_contains_int(c)) terminating = 0; } } } acb_poly_init(s); acb_poly_init(t); acb_poly_init(err); arb_poly_init(C); arb_poly_init(T); acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec); if (!terminating) { is_real = acb_poly_is_real(z); for (i = 0; i < p; i++) is_real = is_real && acb_poly_is_real(a + i); for (i = 0; i < q; i++) is_real = is_real && acb_poly_is_real(b + i); acb_poly_majorant(T, t, MAG_BITS); acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS); if (!_arb_vec_is_finite(T->coeffs, T->length) || !_arb_vec_is_finite(C->coeffs, C->length)) { arb_poly_fit_length(T, len); _arb_vec_indeterminate(T->coeffs, len); _arb_poly_set_length(T, len); } else { arb_poly_mullow(T, T, C, len, MAG_BITS); } /* create polynomial of errors */ acb_poly_fit_length(err, len); for (i = 0; i < FLINT_MIN(len, T->length); i++) { arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i); if (!is_real) arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i); } _acb_poly_set_length(err, len); _acb_poly_normalise(err); acb_poly_add(s, s, err, prec); } acb_poly_set(res, s); acb_poly_clear(s); acb_poly_clear(t); acb_poly_clear(err); arb_poly_clear(C); arb_poly_clear(T); } arb-2.8.1/acb_hypgeom/pfq_sum.c000066400000000000000000000047101264125401100163570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_pfq_sum(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) { if (n > 4 && prec >= 128 && _acb_vec_bits(a, p) * p + _acb_vec_bits(b, q) * q + 10 < prec / 2) { if (prec >= 256 && acb_bits(z) < prec * 0.01) acb_hypgeom_pfq_sum_bs(s, t, a, p, b, q, z, n, prec); else acb_hypgeom_pfq_sum_rs(s, t, a, p, b, q, z, n, prec); } else if (prec >= 1500 && n >= 30 + 100000 / (prec - 1000)) { acb_hypgeom_pfq_sum_fme(s, t, a, p, b, q, z, n, prec); } else { acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec); } } void acb_hypgeom_pfq_sum_invz(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, const acb_t zinv, slong n, slong prec) { if (n > 4 && prec >= 128 && _acb_vec_bits(a, p) * p + _acb_vec_bits(b, q) * q + 10 < prec / 2) { if (prec >= 256 && acb_bits(zinv) < prec * 0.01) acb_hypgeom_pfq_sum_bs_invz(s, t, a, p, b, q, zinv, n, prec); else acb_hypgeom_pfq_sum_rs(s, t, a, p, b, q, z, n, prec); } else if (prec >= 1500 && n >= 30 + 100000 / (prec - 1000)) { acb_hypgeom_pfq_sum_fme(s, t, a, p, b, q, z, n, prec); } else { acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec); } } arb-2.8.1/acb_hypgeom/pfq_sum_bs.c000066400000000000000000000107241264125401100170450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* [S(k+1)] = [ R(k) 0 ] [S(k)] [T(k+1)] [ 1 1 ] [T(k)] [S(k+1)] = [ P(k) / Q(k) 0 ] [S(k)] [T(k+1)] [ 1 1 ] [T(k)] 1 [ P(k) ] ---- [ ] Q(k) [ Q(k) Q(k) ] [[A2 0] [B2 C2]] . [[A1 0] [B1 C1]] = [[A1 A2 0] [A1 B2 + B1 C2 C1 C2] A1 B2 + B1 B2 = B2 (A1 + B1) -- use to save time? */ static void bsplit(acb_t A1, acb_t B1, acb_t C1, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong aa, slong bb, slong prec, int invz) { if (bb - aa == 1) { slong i; if (p == 0) { if (invz) acb_one(A1); else acb_set(A1, z); } else { acb_add_ui(A1, a, aa, prec); for (i = 1; i < p; i++) { acb_add_ui(B1, a + i, aa, prec); acb_mul(A1, A1, B1, prec); } if (!invz) acb_mul(A1, A1, z, prec); } if (q == 0) { if (invz) acb_set(C1, z); else acb_one(C1); } else { acb_add_ui(C1, b, aa, prec); for (i = 1; i < q; i++) { acb_add_ui(B1, b + i, aa, prec); acb_mul(C1, C1, B1, prec); } if (invz) acb_mul(C1, C1, z, prec); } /* acb_set(B1, C1); but we skip this */ } else { slong m; acb_t A2, B2, C2; acb_init(A2); acb_init(B2); acb_init(C2); m = aa + (bb - aa) / 2; bsplit(A1, B1, C1, a, p, b, q, z, aa, m, prec, invz); bsplit(A2, B2, C2, a, p, b, q, z, m, bb, prec, invz); if (bb - m == 1) /* B2 = C2 */ { if (m - aa == 1) acb_add(B2, A1, C1, prec); else acb_add(B2, A1, B1, prec); acb_mul(B1, B2, C2, prec); } else { if (m - aa == 1) acb_mul(B1, C1, C2, prec); else acb_mul(B1, B1, C2, prec); acb_addmul(B1, A1, B2, prec); } acb_mul(A1, A1, A2, prec); acb_mul(C1, C1, C2, prec); acb_clear(A2); acb_clear(B2); acb_clear(C2); } } void acb_hypgeom_pfq_sum_bs(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) { acb_t u, v, w; if (n < 4) { acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec); return; } acb_init(u); acb_init(v); acb_init(w); bsplit(u, v, w, a, p, b, q, z, 0, n, prec, 0); acb_div(t, u, w, prec); acb_div(s, v, w, prec); acb_clear(u); acb_clear(v); acb_clear(w); } void acb_hypgeom_pfq_sum_bs_invz(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) { acb_t u, v, w; if (n < 4) { acb_init(u); acb_inv(u, z, prec); acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, u, n, prec); acb_clear(u); return; } acb_init(u); acb_init(v); acb_init(w); bsplit(u, v, w, a, p, b, q, z, 0, n, prec, 1); acb_div(t, u, w, prec); acb_div(s, v, w, prec); acb_clear(u); acb_clear(v); acb_clear(w); } arb-2.8.1/acb_hypgeom/pfq_sum_fme.c000066400000000000000000000161051264125401100172070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" static void evaluate(acb_poly_t A, acb_srcptr a, slong p, const acb_t z, slong n, slong prec) { acb_poly_fit_length(A, p + 1); if (p == 1) { acb_add_ui(A->coeffs, a, n, prec); if (z != NULL) acb_mul(A->coeffs, A->coeffs, z, prec); } else if (p == 2) { acb_add(A->coeffs, a + 0, a + 1, prec); acb_add_ui(A->coeffs + 1, A->coeffs, 2 * n, prec); acb_add_ui(A->coeffs, A->coeffs, n, prec); acb_mul_ui(A->coeffs, A->coeffs, n, prec); acb_addmul(A->coeffs, a + 0, a + 1, prec); if (z != NULL) { acb_mul(A->coeffs, A->coeffs, z, prec); acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec); } } else if (p == 3) { acb_t t, u; acb_init(t); acb_init(u); acb_add(t, a + 0, a + 1, prec); acb_add(t, t, a + 2, prec); acb_mul(u, a + 0, a + 1, prec); acb_mul(A->coeffs, u, a + 2, prec); acb_addmul(u, a + 0, a + 2, prec); acb_addmul(u, a + 1, a + 2, prec); /* (a0 + n)(a1 + n)(a2 + n) = a0 a1 a2 + (a0 a1 + a0 a2 + a1 a2) n + (a0 + a1 + a2) n^2 + n^3 (a0 a1 + a0 a2 + a1 a2) + 2 (a0 + a1 + a2) n + 3 n^2 (a0 + a1 + a2) + 3n 1 */ acb_addmul_ui(A->coeffs, u, n, prec); acb_addmul_ui(A->coeffs, t, n * n, prec); acb_add_ui(A->coeffs, A->coeffs, n * n * n, prec); acb_set(A->coeffs + 1, u); acb_addmul_ui(A->coeffs + 1, t, 2 * n, prec); acb_add_ui(A->coeffs + 1, A->coeffs + 1, 3 * n * n, prec); acb_add_ui(A->coeffs + 2, t, 3 * n, prec); if (z != NULL) { acb_mul(A->coeffs + 0, A->coeffs + 0, z, prec); acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec); acb_mul(A->coeffs + 2, A->coeffs + 2, z, prec); } acb_clear(t); acb_clear(u); } else if (p != 0) { abort(); } if (z != NULL) acb_set(A->coeffs + p, z); else acb_one(A->coeffs + p); _acb_poly_set_length(A, p + 1); _acb_poly_normalise(A); } /* todo: do this using underscore methods */ static void bsplit(acb_poly_t A, acb_poly_t B, acb_poly_t C, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong an, slong bn, slong prec) { if (bn - an == 1) { evaluate(A, a, p, z, an, prec); evaluate(B, b, q, NULL, an, prec); acb_poly_set(C, B); } else if (bn - an == 2) /* inlined */ { acb_poly_t A2, B2; acb_poly_init(A2); acb_poly_init(B2); evaluate(A, a, p, z, an, prec); evaluate(A2, a, p, z, an + 1, prec); evaluate(B, b, q, NULL, an, prec); evaluate(B2, b, q, NULL, an + 1, prec); acb_poly_mul(C, B, B2, prec); acb_poly_set(B, C); acb_poly_mul(C, A, B2, prec); acb_poly_add(C, C, B, prec); acb_poly_mul(A2, A, A2, prec); acb_poly_swap(A, A2); acb_poly_clear(A2); acb_poly_clear(B2); } else { slong m = an + (bn - an) / 2; acb_poly_t A2, B2, C2, T; acb_poly_init(A2); acb_poly_init(B2); acb_poly_init(C2); acb_poly_init(T); bsplit(A, B, C, a, p, b, q, z, an, m, prec); bsplit(A2, B2, C2, a, p, b, q, z, m, bn, prec); acb_poly_mul(T, B2, C, prec); acb_poly_mul(C, A, C2, prec); acb_poly_add(C, C, T, prec); acb_poly_mul(C2, B, B2, prec); acb_poly_swap(B, C2); acb_poly_mul(B2, A, A2, prec); acb_poly_swap(A, B2); acb_poly_clear(A2); acb_poly_clear(B2); acb_poly_clear(C2); acb_poly_clear(T); } } void acb_hypgeom_pfq_sum_fme(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) { acb_poly_t A, B, C; acb_ptr ks, As, Bs, Cs; acb_t u, v; acb_ptr * tree; slong i, k, m, w; m = n_sqrt(n) / 4; /* tuning parameter */ w = n / FLINT_MAX(m, 1); if (m < 1 || w < 1 || p > 3 || q > 3) { acb_hypgeom_pfq_sum_forward(s, t, a, p, b, q, z, n, prec); return; } acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_init(u); acb_init(v); ks = _acb_vec_init(w); As = _acb_vec_init(w); Bs = _acb_vec_init(w); Cs = _acb_vec_init(w); bsplit(A, B, C, a, p, b, q, z, 0, m, prec); for (i = 0; i < w; i++) acb_set_ui(ks + i, i * m); tree = _acb_poly_tree_alloc(w); _acb_poly_tree_build(tree, ks, w, prec); _acb_poly_evaluate_vec_fast_precomp(As, A->coeffs, A->length, tree, w, prec); _acb_poly_evaluate_vec_fast_precomp(Bs, B->coeffs, B->length, tree, w, prec); _acb_poly_evaluate_vec_fast_precomp(Cs, C->coeffs, C->length, tree, w, prec); _acb_poly_tree_free(tree, w); /* todo: use binary splitting here for improved numerical stability */ for (i = 1; i < w; i++) { acb_mul(Cs, Cs, Bs + i, prec); acb_addmul(Cs, As, Cs + i, prec); acb_mul(As, As, As + i, prec); acb_mul(Bs, Bs, Bs + i, prec); } acb_div(s, Cs, Bs, prec); acb_div(t, As, Bs, prec); for (k = w * m; k < n && !acb_is_zero(t); k++) { acb_add(s, s, t, prec); if (p > 0) { acb_add_ui(u, a, k, prec); for (i = 1; i < p; i++) { acb_add_ui(v, a + i, k, prec); acb_mul(u, u, v, prec); } acb_mul(t, t, u, prec); } if (q > 0) { acb_add_ui(u, b, k, prec); for (i = 1; i < q; i++) { acb_add_ui(v, b + i, k, prec); acb_mul(u, u, v, prec); } acb_div(t, t, u, prec); } acb_mul(t, t, z, prec); } acb_clear(u); acb_clear(v); _acb_vec_clear(ks, w); _acb_vec_clear(As, w); _acb_vec_clear(Bs, w); _acb_vec_clear(Cs, w); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); } arb-2.8.1/acb_hypgeom/pfq_sum_forward.c000066400000000000000000000040071264125401100201020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_pfq_sum_forward(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) { acb_t u, v; slong k, i; acb_init(u); acb_init(v); acb_zero(s); acb_one(t); for (k = 0; k < n && !acb_is_zero(t); k++) { acb_add(s, s, t, prec); if (p > 0) { acb_add_ui(u, a, k, prec); for (i = 1; i < p; i++) { acb_add_ui(v, a + i, k, prec); acb_mul(u, u, v, prec); } acb_mul(t, t, u, prec); } if (q > 0) { acb_add_ui(u, b, k, prec); for (i = 1; i < q; i++) { acb_add_ui(v, b + i, k, prec); acb_mul(u, u, v, prec); } acb_div(t, t, u, prec); } acb_mul(t, t, z, prec); } acb_clear(u); acb_clear(v); } arb-2.8.1/acb_hypgeom/pfq_sum_rs.c000066400000000000000000000062601264125401100170650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_pfq_sum_rs(acb_t res, acb_t term, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) { acb_ptr zpow; acb_t s, t, u; slong i, j, k, m; mag_t B, C; if (n == 0) { acb_zero(res); acb_one(term); return; } if (n < 0) abort(); m = n_sqrt(n); m = FLINT_MIN(m, 150); mag_init(B); mag_init(C); acb_init(s); acb_init(t); acb_init(u); zpow = _acb_vec_init(m + 1); _acb_vec_set_powers(zpow, z, m + 1, prec); mag_one(B); for (k = n; k >= 0; k--) { j = k % m; if (k < n) acb_add(s, s, zpow + j, prec); if (k > 0) { if (p > 0) { acb_add_ui(u, a, k - 1, prec); for (i = 1; i < p; i++) { acb_add_ui(t, a + i, k - 1, prec); acb_mul(u, u, t, prec); } if (k < n) acb_mul(s, s, u, prec); acb_get_mag(C, u); mag_mul(B, B, C); } if (q > 0) { acb_add_ui(u, b, k - 1, prec); for (i = 1; i < q; i++) { acb_add_ui(t, b + i, k - 1, prec); acb_mul(u, u, t, prec); } if (k < n) acb_div(s, s, u, prec); acb_get_mag_lower(C, u); mag_div(B, B, C); } if (j == 0 && k < n) { acb_mul(s, s, zpow + m, prec); } } } acb_get_mag(C, z); mag_pow_ui(C, C, n); mag_mul(B, B, C); acb_zero(term); if (_acb_vec_is_real(a, p) && _acb_vec_is_real(b, q) && acb_is_real(z)) arb_add_error_mag(acb_realref(term), B); else acb_add_error_mag(term, B); acb_set(res, s); mag_clear(B); mag_clear(C); acb_clear(s); acb_clear(t); acb_clear(u); _acb_vec_clear(zpow, m + 1); } arb-2.8.1/acb_hypgeom/shi.c000066400000000000000000000024131264125401100154660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_shi(acb_t res, const acb_t z, slong prec) { acb_mul_onei(res, z); acb_hypgeom_si(res, res, prec); acb_mul_onei(res, res); acb_neg(res, res); } arb-2.8.1/acb_hypgeom/si.c000066400000000000000000000070031264125401100153160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_si_asymp(acb_t res, const acb_t z, slong prec) { acb_t t, u, w, v, one; acb_init(t); acb_init(u); acb_init(w); acb_init(v); acb_init(one); acb_one(one); acb_mul_onei(w, z); /* u = U(1,1,iz) */ acb_hypgeom_u_asymp(u, one, one, w, -1, prec); /* v = e^(-iz) */ acb_neg(v, w); acb_exp(v, v, prec); acb_mul(t, u, v, prec); if (acb_is_real(z)) { arb_div(acb_realref(t), acb_realref(t), acb_realref(z), prec); arb_zero(acb_imagref(t)); acb_neg(t, t); } else { /* u = U(1,1,-iz) */ acb_neg(w, w); acb_hypgeom_u_asymp(u, one, one, w, -1, prec); acb_inv(v, v, prec); acb_addmul(t, u, v, prec); acb_div(t, t, z, prec); acb_mul_2exp_si(t, t, -1); acb_neg(t, t); } if (arb_is_zero(acb_realref(z))) { /* the function is imaginary */ arb_zero(acb_realref(t)); } else if (arb_is_positive(acb_realref(z))) { acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_add(acb_realref(t), acb_realref(t), acb_realref(u), prec); } else if (arb_is_negative(acb_realref(z))) { acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_sub(acb_realref(t), acb_realref(t), acb_realref(u), prec); } else { /* add [-pi,pi]/2 */ acb_const_pi(u, prec); acb_mul_2exp_si(u, u, -1); arb_add_error(acb_imagref(t), acb_realref(u)); } acb_swap(res, t); acb_clear(t); acb_clear(u); acb_clear(w); acb_clear(v); acb_clear(one); } void acb_hypgeom_si_1f2(acb_t res, const acb_t z, slong prec) { acb_t a, t; acb_struct b[3]; acb_init(a); acb_init(b); acb_init(b + 1); acb_init(b + 2); acb_init(t); acb_one(a); acb_mul_2exp_si(a, a, -1); acb_set_ui(b, 3); acb_mul_2exp_si(b, b, -1); acb_set(b + 1, b); acb_one(b + 2); acb_mul(t, z, z, prec); acb_mul_2exp_si(t, t, -2); acb_neg(t, t); acb_hypgeom_pfq_direct(t, a, 1, b, 3, t, -1, prec); acb_mul(t, t, z, prec); acb_swap(res, t); acb_clear(a); acb_clear(b); acb_clear(b + 1); acb_clear(b + 2); acb_clear(t); } void acb_hypgeom_si(acb_t res, const acb_t z, slong prec) { if (acb_hypgeom_u_use_asymp(z, prec)) acb_hypgeom_si_asymp(res, z, prec); else acb_hypgeom_si_1f2(res, z, prec); } arb-2.8.1/acb_hypgeom/spherical_y.c000066400000000000000000000050131264125401100172040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_spherical_y(acb_t res, slong n, slong m, const acb_t theta, const acb_t phi, slong prec) { acb_t t, u; if (n < 0) { if (m <= n) { acb_zero(res); return; } n = -1-n; } if (m > n || m < -n) { acb_zero(res); return; } if (n > WORD_MAX / 4) { acb_indeterminate(res); return; } acb_init(t); acb_init(u); acb_sin_cos(t, u, theta, prec); /* P_n^m(cos(theta)) */ acb_hypgeom_legendre_p_uiui_rec(u, n, FLINT_ABS(m), u, prec); acb_pow_ui(t, t, FLINT_ABS(m), prec); acb_mul(t, t, u, prec); /* exp(i m phi) */ acb_mul_onei(u, phi); acb_mul_si(u, u, m, prec); acb_exp(u, u, prec); if (m < 0 && m % 2) acb_neg(u, u); acb_mul(t, t, u, prec); /* sqrt((2n+1)/(4pi) (n-m)!/(n+m)!) */ arb_fac_ui(acb_realref(u), n - FLINT_ABS(m), prec); arb_fac_ui(acb_imagref(u), n + FLINT_ABS(m), prec); arb_mul_ui(acb_realref(u), acb_realref(u), 2 * n + 1, prec); arb_div(acb_realref(u), acb_realref(u), acb_imagref(u), prec); arb_const_pi(acb_imagref(u), prec); arb_div(acb_realref(u), acb_realref(u), acb_imagref(u), prec); arb_mul_2exp_si(acb_realref(u), acb_realref(u), -2); arb_sqrt(acb_realref(u), acb_realref(u), prec); acb_mul_arb(t, t, acb_realref(u), prec); acb_set(res, t); acb_clear(t); acb_clear(u); } arb-2.8.1/acb_hypgeom/test/000077500000000000000000000000001264125401100155165ustar00rootroot00000000000000arb-2.8.1/acb_hypgeom/test/t-0f1.c000066400000000000000000000066531264125401100165230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { long iter; flint_rand_t state; flint_printf("0f1...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t a, z, w1, w2; long prec1, prec2; int regularized, ebits; acb_init(a); acb_init(z); acb_init(w1); acb_init(w2); prec1 = 2 + n_randint(state, 700); prec2 = 2 + n_randint(state, 700); if (n_randint(state, 5) == 0) ebits = 100; else ebits = 10; acb_randtest_param(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest_param(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); regularized = n_randint(state, 2); switch (n_randint(state, 3)) { case 0: acb_hypgeom_0f1_asymp(w1, a, z, regularized, prec1); break; case 1: acb_hypgeom_0f1_direct(w1, a, z, regularized, prec1); break; default: acb_hypgeom_0f1(w1, a, z, regularized, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_0f1_asymp(w2, a, z, regularized, prec2); break; case 1: acb_hypgeom_0f1_direct(w2, a, z, regularized, prec2); break; default: acb_hypgeom_0f1(w2, a, z, regularized, prec2); } if (!acb_overlaps(w1, w2)) { flint_printf("FAIL: consistency\n\n"); flint_printf("regularized = %d\n\n", regularized); flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(z); acb_clear(w1); acb_clear(w2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-2f1.c000066400000000000000000000123671264125401100165240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("2f1...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { acb_t a, b, c, z, w1, w2, t; slong prec1, prec2; int reg1, reg2, ebits; int alg1, alg2; acb_init(a); acb_init(b); acb_init(c); acb_init(z); acb_init(w1); acb_init(w2); acb_init(t); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); if (n_randint(state, 20) == 0) ebits = 30; else ebits = 5; switch (n_randint(state, 3)) { case 0: acb_set_si(a, n_randint(state, 500)); acb_set_si(b, n_randint(state, 500)); acb_set_si(c, n_randint(state, 10)); break; case 1: acb_set_si(a, n_randint(state, 200) - 100); acb_set_si(b, n_randint(state, 200) - 100); acb_set_si(c, n_randint(state, 200) - 100); break; default: acb_randtest_param(a, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); acb_randtest_param(b, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); acb_randtest_param(c, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); } acb_randtest_param(z, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); acb_randtest(w1, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); acb_randtest(w2, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); reg1 = n_randint(state, 2); reg2 = n_randint(state, 2); alg1 = n_randint(state, 10); alg2 = n_randint(state, 10); switch (alg1) { case 0: acb_hypgeom_2f1_direct(w1, a, b, c, z, reg1, prec1); break; case 1: case 2: case 3: case 4: case 5: acb_hypgeom_2f1_transform(w1, a, b, c, z, reg1, alg1, prec1); break; case 6: acb_hypgeom_2f1_corner(w1, a, b, c, z, reg1, prec1); break; default: acb_hypgeom_2f1(w1, a, b, c, z, reg1, prec1); } switch (alg2) { case 0: acb_hypgeom_2f1_direct(w2, a, b, c, z, reg2, prec2); break; case 1: case 2: case 3: case 4: case 5: acb_hypgeom_2f1_transform(w2, a, b, c, z, reg2, alg2, prec2); break; case 6: acb_hypgeom_2f1_corner(w2, a, b, c, z, reg2, prec2); break; default: acb_hypgeom_2f1(w2, a, b, c, z, reg2, prec2); } if (reg1 != reg2) { acb_rgamma(t, c, prec2); if (reg1) acb_mul(w2, w2, t, prec2); else acb_mul(w1, w1, t, prec2); } if (!acb_overlaps(w1, w2)) { flint_printf("FAIL: consistency\n\n"); flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2); flint_printf("alg1 = %d, alg2 = %d\n\n", alg1, alg2); flint_printf("reg1 = %d, reg2 = %d\n\n", reg1, reg2); flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(z); acb_clear(w1); acb_clear(w2); acb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-2f1_continuation.c000066400000000000000000000137601264125401100213140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("2f1_continuation...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t a, b, c, z1, z2, f1, f2, g1, g2, h1, h2, aa, bb, cc; mag_t d0, d1, dt; slong prec; int regularized, ebits; acb_init(a); acb_init(b); acb_init(c); acb_init(aa); acb_init(bb); acb_init(cc); acb_init(z1); acb_init(z2); acb_init(f1); acb_init(f2); acb_init(g1); acb_init(g2); acb_init(h1); acb_init(h2); mag_init(d0); mag_init(d1); mag_init(dt); prec = 2 + n_randint(state, 300); ebits = 10; regularized = n_randint(state, 2); acb_randtest_param(a, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits / 2)); acb_randtest_param(b, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits / 2)); acb_randtest_param(c, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits / 2)); acb_randtest(h1, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); acb_randtest(h2, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); do { int left, upper, lower; acb_randtest_param(z1, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); acb_randtest_param(z2, state, 1 + n_randint(state, 400), 1 + n_randint(state, ebits)); /* we test both convergent and non-convergent cases, but try to be more efficient by generating more convergent cases */ if (n_randint(state, 2)) { acb_sub_ui(aa, z1, 1, prec); acb_get_mag(d0, z1); acb_get_mag(d1, aa); acb_get_mag(dt, z2); if (mag_cmp(dt, d0) >= 0 || mag_cmp(dt, d1) >= 0) continue; } acb_add(z2, z1, z2, prec); /* for the test, don't cross the branch cut */ acb_sub_ui(aa, z1, 1, prec); acb_sub_ui(bb, z2, 1, prec); left = arb_is_negative(acb_realref(aa)) && arb_is_negative(acb_realref(bb)); upper = arb_is_positive(acb_imagref(aa)) && arb_is_positive(acb_imagref(bb)); lower = arb_is_nonpositive(acb_imagref(aa)) && arb_is_nonpositive(acb_imagref(bb)); if (left || upper || lower) break; } while (1); acb_add_ui(aa, a, 1, prec); acb_add_ui(bb, b, 1, prec); acb_add_ui(cc, c, 1, prec); acb_hypgeom_2f1(f1, a, b, c, z1, regularized, prec); acb_hypgeom_2f1(f2, aa, bb, cc, z1, regularized, prec); acb_mul(f2, f2, a, prec); acb_mul(f2, f2, b, prec); if (!regularized) acb_div(f2, f2, c, prec); acb_hypgeom_2f1_continuation(h1, h2, a, b, c, z1, z2, f1, f2, prec); if (acb_is_finite(h1) || acb_is_finite(h2)) { acb_hypgeom_2f1(g1, a, b, c, z2, regularized, prec); acb_hypgeom_2f1(g2, aa, bb, cc, z2, regularized, prec); acb_mul(g2, g2, a, prec); acb_mul(g2, g2, b, prec); if (!regularized) acb_div(g2, g2, c, prec); if (!acb_overlaps(g1, h1) || !acb_overlaps(g2, h2)) { flint_printf("FAIL: consistency\n\n"); flint_printf("regularized = %d, prec = %wd\n\n", regularized, prec); flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("c = "); acb_printd(c, 30); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 30); flint_printf("\n\n"); flint_printf("F(a,b,c,z1) and F'(a,b,c,z1):\n"); flint_printf("f1 = "); acb_printd(f1, 30); flint_printf("\n\n"); flint_printf("f2 = "); acb_printd(f2, 30); flint_printf("\n\n"); flint_printf("F(a,b,c,z2) and F'(a,b,c,z2):\n"); flint_printf("g1 = "); acb_printd(g1, 30); flint_printf("\n\n"); flint_printf("g2 = "); acb_printd(g2, 30); flint_printf("\n\n"); flint_printf("Computed F and F':\n"); flint_printf("h1 = "); acb_printd(h1, 30); flint_printf("\n\n"); flint_printf("h2 = "); acb_printd(h2, 30); flint_printf("\n\n"); abort(); } } acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(aa); acb_clear(bb); acb_clear(cc); acb_clear(z1); acb_clear(z2); acb_clear(f1); acb_clear(f2); acb_clear(g1); acb_clear(g2); acb_clear(h1); acb_clear(h2); mag_clear(d0); mag_clear(d1); mag_clear(dt); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-airy.c000066400000000000000000000147721264125401100171020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("airy...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t z, t, w; acb_t ai1, aip1, bi1, bip1; acb_t ai2, aip2, bi2, bip2; slong n1, n2, prec1, prec2; unsigned int mask; acb_init(z); acb_init(t); acb_init(w); acb_init(ai1); acb_init(aip1); acb_init(bi1); acb_init(bip1); acb_init(ai2); acb_init(aip2); acb_init(bi2); acb_init(bip2); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); n1 = n_randint(state, 300); n2 = n_randint(state, 300); acb_randtest_param(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest_param(t, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_add(z, z, t, 1000); acb_sub(z, z, t, 1000); switch (n_randint(state, 3)) { case 0: acb_hypgeom_airy_direct(ai1, aip1, bi1, bip1, z, n1, prec1); break; case 1: acb_hypgeom_airy_asymp(ai1, aip1, bi1, bip1, z, n1, prec1); break; default: acb_hypgeom_airy(ai1, aip1, bi1, bip1, z, prec1); break; } switch (n_randint(state, 3)) { case 0: acb_hypgeom_airy_direct(ai2, aip2, bi2, bip2, z, n2, prec2); break; case 1: acb_hypgeom_airy_asymp(ai2, aip2, bi2, bip2, z, n2, prec2); break; default: acb_hypgeom_airy(ai2, aip2, bi2, bip2, z, prec2); break; } if (!acb_overlaps(ai1, ai2)) { flint_printf("FAIL: consistency (Ai)\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("ai1 = "); acb_printd(ai1, 30); flint_printf("\n\n"); flint_printf("ai2 = "); acb_printd(ai2, 30); flint_printf("\n\n"); abort(); } if (!acb_overlaps(aip1, aip2)) { flint_printf("FAIL: consistency (Ai')\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("aip1 = "); acb_printd(aip1, 30); flint_printf("\n\n"); flint_printf("aip2 = "); acb_printd(aip2, 30); flint_printf("\n\n"); abort(); } if (!acb_overlaps(bi1, bi2)) { flint_printf("FAIL: consistency (Bi)\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("bi1 = "); acb_printd(bi1, 30); flint_printf("\n\n"); flint_printf("bi2 = "); acb_printd(bi2, 30); flint_printf("\n\n"); abort(); } if (!acb_overlaps(bip1, bip2)) { flint_printf("FAIL: consistency (Bi')\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("bip1 = "); acb_printd(bip1, 30); flint_printf("\n\n"); flint_printf("bip2 = "); acb_printd(bip2, 30); flint_printf("\n\n"); abort(); } acb_mul(w, ai1, bip1, prec1); acb_submul(w, bi1, aip1, prec1); acb_const_pi(t, prec1); acb_inv(t, t, prec1); if (!acb_overlaps(w, t)) { flint_printf("FAIL: wronskian\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("ai1 = "); acb_printd(ai1, 30); flint_printf("\n\n"); flint_printf("aip1 = "); acb_printd(aip1, 30); flint_printf("\n\n"); flint_printf("bi1 = "); acb_printd(bi1, 30); flint_printf("\n\n"); flint_printf("bip1 = "); acb_printd(bip1, 30); flint_printf("\n\n"); flint_printf("w = "); acb_printd(w, 30); flint_printf("\n\n"); abort(); } mask = n_randlimb(state); acb_hypgeom_airy((mask & 1) ? ai2 : NULL, (mask & 2) ? aip2 : NULL, (mask & 4) ? bi2 : NULL, (mask & 8) ? bip2 : NULL, z, prec2); if (!acb_overlaps(ai1, ai2) || !acb_overlaps(aip1, aip2) || !acb_overlaps(bi1, bi2) || !acb_overlaps(bip1, bip2)) { flint_printf("FAIL: consistency (mask)\n\n"); flint_printf("mask = %u\n\n", mask); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("ai1 = "); acb_printd(ai1, 30); flint_printf("\n\n"); flint_printf("ai2 = "); acb_printd(ai2, 30); flint_printf("\n\n"); flint_printf("aip1 = "); acb_printd(aip1, 30); flint_printf("\n\n"); flint_printf("aip2 = "); acb_printd(aip2, 30); flint_printf("\n\n"); flint_printf("bi1 = "); acb_printd(bi1, 30); flint_printf("\n\n"); flint_printf("bi2 = "); acb_printd(bi2, 30); flint_printf("\n\n"); flint_printf("bip1 = "); acb_printd(bip1, 30); flint_printf("\n\n"); flint_printf("bip2 = "); acb_printd(bip2, 30); flint_printf("\n\n"); abort(); } acb_clear(z); acb_clear(t); acb_clear(w); acb_clear(ai1); acb_clear(aip1); acb_clear(bi1); acb_clear(bip1); acb_clear(ai2); acb_clear(aip2); acb_clear(bi2); acb_clear(bip2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-airy_bound.c000066400000000000000000000136411264125401100202630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("airy_bound...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t ai, aip, bi, bip, z1, z2; slong prec; mag_t aib, aipb, bib, bipb, aim, aipm, bim, bipm; acb_init(ai); acb_init(aip); acb_init(bi); acb_init(bip); acb_init(z1); acb_init(z2); mag_init(aib); mag_init(aipb); mag_init(bib); mag_init(bipb); mag_init(aim); mag_init(aipm); mag_init(bim); mag_init(bipm); acb_randtest(z1, state, 1 + n_randint(state, 200), 1 + n_randint(state, 10)); arb_mul_ui(acb_realref(z1), acb_realref(z1), n_randint(state, 300), 1 + n_randint(state, 200)); arb_mul_ui(acb_imagref(z1), acb_imagref(z1), n_randint(state, 300), 1 + n_randint(state, 200)); acb_zero(z2); arf_set_mag(arb_midref(acb_realref(z2)), arb_radref(acb_realref(z1))); arf_set_mag(arb_midref(acb_imagref(z2)), arb_radref(acb_imagref(z1))); switch (n_randint(state, 5)) { case 0: arf_add(arb_midref(acb_realref(z2)), arb_midref(acb_realref(z1)), arb_midref(acb_realref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); arf_add(arb_midref(acb_imagref(z2)), arb_midref(acb_imagref(z1)), arb_midref(acb_imagref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); break; case 1: arf_add(arb_midref(acb_realref(z2)), arb_midref(acb_realref(z1)), arb_midref(acb_realref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); arf_sub(arb_midref(acb_imagref(z2)), arb_midref(acb_imagref(z1)), arb_midref(acb_imagref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); break; case 2: arf_sub(arb_midref(acb_realref(z2)), arb_midref(acb_realref(z1)), arb_midref(acb_realref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); arf_add(arb_midref(acb_imagref(z2)), arb_midref(acb_imagref(z1)), arb_midref(acb_imagref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); break; case 3: arf_sub(arb_midref(acb_realref(z2)), arb_midref(acb_realref(z1)), arb_midref(acb_realref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); arf_sub(arb_midref(acb_imagref(z2)), arb_midref(acb_imagref(z1)), arb_midref(acb_imagref(z2)), ARF_PREC_EXACT, ARF_RND_DOWN); break; default: arf_set(arb_midref(acb_realref(z2)), arb_midref(acb_realref(z1))); arf_set(arb_midref(acb_imagref(z2)), arb_midref(acb_imagref(z1))); } acb_hypgeom_airy_bound(aib, aipb, bib, bipb, z1); prec = MAG_BITS + 10; do { acb_hypgeom_airy(ai, aip, bi, bip, z2, prec); if (acb_rel_accuracy_bits(ai) >= MAG_BITS && acb_rel_accuracy_bits(aip) >= MAG_BITS && acb_rel_accuracy_bits(bi) >= MAG_BITS && acb_rel_accuracy_bits(bip) >= MAG_BITS) break; prec *= 2; } while (1); acb_get_mag(aim, ai); acb_get_mag(aipm, aip); acb_get_mag(bim, bi); acb_get_mag(bipm, bip); if (mag_cmp(aim, aib) > 0 || mag_cmp(aipm, aipb) > 0 || mag_cmp(bim, bib) > 0 || mag_cmp(aipm, bipb) > 0) { printf("FAIL\n"); flint_printf("z1 = "); acb_printd(z1, 20); flint_printf("\n"); flint_printf("z2 = "); acb_printd(z2, 20); flint_printf("\n\n"); flint_printf("ai = "); acb_printd(ai, 20); flint_printf("\n"); flint_printf("aim = "); mag_printd(aim, 10); printf("\n"); flint_printf("aib = "); mag_printd(aib, 10); printf("\n\n"); flint_printf("api = "); acb_printd(aip, 20); flint_printf("\n"); flint_printf("aipm = "); mag_printd(aipm, 10); printf("\n"); flint_printf("aipb = "); mag_printd(aipb, 10); printf("\n\n"); flint_printf("bi = "); acb_printd(bi, 20); flint_printf("\n"); flint_printf("bim = "); mag_printd(bim, 10); printf("\n"); flint_printf("bib = "); mag_printd(bib, 10); printf("\n\n"); flint_printf("bpi = "); acb_printd(bip, 20); flint_printf("\n"); flint_printf("bipm = "); mag_printd(bipm, 10); printf("\n"); flint_printf("bipb = "); mag_printd(bipb, 10); printf("\n\n"); abort(); } acb_clear(ai); acb_clear(aip); acb_clear(bi); acb_clear(bip); acb_clear(z1); acb_clear(z2); mag_clear(aib); mag_clear(aipb); mag_clear(bib); mag_clear(bipb); mag_clear(aim); mag_clear(aipm); mag_clear(bim); mag_clear(bipm); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-bessel_i.c000066400000000000000000000177141264125401100177220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("bessel_i...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t nu, z, jv, iv, t; slong prec; acb_init(nu); acb_init(z); acb_init(jv); acb_init(iv); acb_init(t); prec = 2 + n_randint(state, 500); acb_randtest_param(nu, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_i_asymp(iv, nu, z, prec); break; case 1: acb_hypgeom_bessel_i_0f1(iv, nu, z, prec); break; default: acb_hypgeom_bessel_i(iv, nu, z, prec); } acb_mul_onei(t, z); acb_hypgeom_bessel_j(jv, nu, t, prec); acb_pow(t, z, nu, prec); acb_mul(jv, jv, t, prec); acb_mul_onei(t, z); acb_pow(t, t, nu, prec); acb_div(jv, jv, t, prec); if (!acb_overlaps(iv, jv)) { flint_printf("FAIL: consistency with bessel_j\n\n"); flint_printf("nu = "); acb_printd(nu, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("iv = "); acb_printd(iv, 30); flint_printf("\n\n"); flint_printf("jv = "); acb_printd(jv, 30); flint_printf("\n\n"); abort(); } acb_clear(nu); acb_clear(z); acb_clear(jv); acb_clear(iv); acb_clear(t); } for (iter = 0; iter < 2000; iter++) { acb_t nu0, nu1, nu2, z, w0, w1, w2, t, u; slong prec0, prec1, prec2; acb_init(nu0); acb_init(nu1); acb_init(nu2); acb_init(z); acb_init(w0); acb_init(w1); acb_init(w2); acb_init(t); acb_init(u); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_randtest_param(nu0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_sub_ui(nu1, nu0, 1, prec0); acb_sub_ui(nu2, nu0, 2, prec0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_i_asymp(w0, nu0, z, prec0); break; case 1: acb_hypgeom_bessel_i_0f1(w0, nu0, z, prec0); break; default: acb_hypgeom_bessel_i(w0, nu0, z, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_i_asymp(w1, nu0, z, prec1); break; case 1: acb_hypgeom_bessel_i_0f1(w1, nu0, z, prec1); break; default: acb_hypgeom_bessel_i(w1, nu0, z, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_i_asymp(w1, nu1, z, prec1); break; case 1: acb_hypgeom_bessel_i_0f1(w1, nu1, z, prec1); break; default: acb_hypgeom_bessel_i(w1, nu1, z, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_i_asymp(w2, nu2, z, prec2); break; case 1: acb_hypgeom_bessel_i_0f1(w2, nu2, z, prec2); break; default: acb_hypgeom_bessel_i(w2, nu2, z, prec2); } acb_mul(t, w1, nu1, prec0); acb_mul_2exp_si(t, t, 1); acb_submul(t, w2, z, prec0); acb_addmul(t, w0, z, prec0); if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_neg(t, nu0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_i_asymp(w2, t, z, prec2); break; case 1: acb_hypgeom_bessel_i_0f1(w2, t, z, prec2); break; default: acb_hypgeom_bessel_i(w2, t, z, prec2); } acb_mul(w1, w1, w2, prec2); acb_neg(t, nu1); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_i_asymp(w2, t, z, prec2); break; case 1: acb_hypgeom_bessel_i_0f1(w2, t, z, prec2); break; default: acb_hypgeom_bessel_i(w2, t, z, prec2); } acb_mul(w0, w0, w2, prec2); acb_sub(w0, w1, w0, prec2); acb_sin_pi(t, nu0, prec2); acb_const_pi(u, prec2); acb_mul(u, u, z, prec2); acb_div(t, t, u, prec2); acb_mul_2exp_si(t, t, 1); if (!acb_overlaps(w0, t)) { flint_printf("FAIL: wronskian\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_clear(nu0); acb_clear(nu1); acb_clear(nu2); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(w2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-bessel_j.c000066400000000000000000000146421264125401100177200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("bessel_j...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t nu0, nu1, nu2, z, w0, w1, w2, t, u; slong prec0, prec1, prec2; acb_init(nu0); acb_init(nu1); acb_init(nu2); acb_init(z); acb_init(w0); acb_init(w1); acb_init(w2); acb_init(t); acb_init(u); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_randtest_param(nu0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_sub_ui(nu1, nu0, 1, prec0); acb_sub_ui(nu2, nu0, 2, prec0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w0, nu0, z, prec0); break; case 1: acb_hypgeom_bessel_j_0f1(w0, nu0, z, prec0); break; default: acb_hypgeom_bessel_j(w0, nu0, z, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w1, nu0, z, prec1); break; case 1: acb_hypgeom_bessel_j_0f1(w1, nu0, z, prec1); break; default: acb_hypgeom_bessel_j(w1, nu0, z, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w1, nu1, z, prec1); break; case 1: acb_hypgeom_bessel_j_0f1(w1, nu1, z, prec1); break; default: acb_hypgeom_bessel_j(w1, nu1, z, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w2, nu2, z, prec2); break; case 1: acb_hypgeom_bessel_j_0f1(w2, nu2, z, prec2); break; default: acb_hypgeom_bessel_j(w2, nu2, z, prec2); } acb_mul(t, w1, nu1, prec0); acb_mul_2exp_si(t, t, 1); acb_submul(t, w2, z, prec0); acb_submul(t, w0, z, prec0); if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_neg(t, nu0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w2, t, z, prec2); break; case 1: acb_hypgeom_bessel_j_0f1(w2, t, z, prec2); break; default: acb_hypgeom_bessel_j(w2, t, z, prec2); } acb_mul(w1, w1, w2, prec2); acb_neg(t, nu1); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_j_asymp(w2, t, z, prec2); break; case 1: acb_hypgeom_bessel_j_0f1(w2, t, z, prec2); break; default: acb_hypgeom_bessel_j(w2, t, z, prec2); } acb_mul(w0, w0, w2, prec2); acb_add(w0, w0, w1, prec2); acb_sin_pi(t, nu0, prec2); acb_const_pi(u, prec2); acb_mul(u, u, z, prec2); acb_div(t, t, u, prec2); acb_mul_2exp_si(t, t, 1); if (!acb_overlaps(w0, t)) { flint_printf("FAIL: wronskian\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_clear(nu0); acb_clear(nu1); acb_clear(nu2); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(w2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-bessel_k.c000066400000000000000000000121141264125401100177110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("bessel_k...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t nu0, nu1, nu2, z, w0, w1, w2, t, u; slong prec0, prec1, prec2; acb_init(nu0); acb_init(nu1); acb_init(nu2); acb_init(z); acb_init(w0); acb_init(w1); acb_init(w2); acb_init(t); acb_init(u); prec0 = 2 + n_randint(state, 700); prec1 = 2 + n_randint(state, 700); prec2 = 2 + n_randint(state, 700); acb_randtest_param(nu0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); if (n_randint(state, 4) == 0) arb_zero(acb_imagref(z)); acb_sub_ui(nu1, nu0, 1, prec0); acb_sub_ui(nu2, nu0, 2, prec0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_k_asymp(w0, nu0, z, prec0); break; case 1: acb_hypgeom_bessel_k_0f1(w0, nu0, z, prec0); break; default: acb_hypgeom_bessel_k(w0, nu0, z, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_k_asymp(w1, nu0, z, prec1); break; case 1: acb_hypgeom_bessel_k_0f1(w1, nu0, z, prec1); break; default: acb_hypgeom_bessel_k(w1, nu0, z, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_k_asymp(w1, nu1, z, prec1); break; case 1: acb_hypgeom_bessel_k_0f1(w1, nu1, z, prec1); break; default: acb_hypgeom_bessel_k(w1, nu1, z, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_bessel_k_asymp(w2, nu2, z, prec2); break; case 1: acb_hypgeom_bessel_k_0f1(w2, nu2, z, prec2); break; default: acb_hypgeom_bessel_k(w2, nu2, z, prec2); } acb_mul(t, w1, nu1, prec0); acb_mul_2exp_si(t, t, 1); acb_addmul(t, w2, z, prec0); acb_submul(t, w0, z, prec0); if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation\n\n"); flint_printf("nu = "); acb_printd(nu0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_clear(nu0); acb_clear(nu1); acb_clear(nu2); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(w2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-bessel_y.c000066400000000000000000000113401264125401100177270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("bessel_y...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t nu, nu1, z, jv, jv1, yv, yv1, r, s; slong prec, n; acb_init(nu); acb_init(nu1); acb_init(z); acb_init(jv); acb_init(jv1); acb_init(yv); acb_init(yv1); acb_init(r); acb_init(s); prec = 2 + n_randint(state, 500); acb_randtest_param(nu, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); if (n_randint(state, 4) == 0) arb_zero(acb_imagref(z)); acb_add_ui(nu1, nu, 1, prec); if (n_randint(state, 2)) { acb_hypgeom_bessel_j(jv, nu, z, prec); acb_hypgeom_bessel_y(yv, nu, z, prec); } else { acb_hypgeom_bessel_jy(jv, yv, nu, z, prec); } if (n_randint(state, 2)) { acb_hypgeom_bessel_j(jv1, nu1, z, prec); acb_hypgeom_bessel_y(yv1, nu1, z, prec); } else { acb_hypgeom_bessel_jy(jv1, yv1, nu1, z, prec); } acb_mul(r, jv1, yv, prec); acb_submul(r, jv, yv1, prec); acb_mul(r, r, z, prec); acb_const_pi(s, prec); acb_mul(r, r, s, prec); acb_sub_ui(r, r, 2, prec); if (!acb_contains_zero(r)) { flint_printf("FAIL: wronskian\n\n"); flint_printf("nu = "); acb_printd(nu, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("yv = "); acb_printd(yv, 30); flint_printf("\n\n"); flint_printf("yv1 = "); acb_printd(yv1, 30); flint_printf("\n\n"); flint_printf("jv = "); acb_printd(jv, 30); flint_printf("\n\n"); flint_printf("jv1 = "); acb_printd(jv1, 30); flint_printf("\n\n"); flint_printf("r = "); acb_printd(r, 30); flint_printf("\n\n"); abort(); } /* Y_n(-z) = (-1)^n [Y_n(z) - (2/pi) [log(z) - log(-z)] J_v(z)] */ n = n_randint(state, 20) - 10; acb_set_si(nu, n); acb_hypgeom_bessel_y(yv, nu, z, prec); acb_hypgeom_bessel_j(jv, nu, z, prec); acb_log(r, z, prec); acb_neg(s, z); acb_log(s, s, prec); acb_sub(r, r, s, prec); acb_mul(jv, jv, r, prec); acb_const_pi(r, prec); acb_div(jv, jv, r, prec); acb_mul_2exp_si(jv, jv, 1); acb_sub(r, yv, jv, prec); if (n % 2) acb_neg(r, r); acb_neg(yv1, z); acb_hypgeom_bessel_y(yv1, nu, yv1, prec); if (!acb_overlaps(r, yv1)) { flint_printf("FAIL: reflection formula\n\n"); flint_printf("nu = "); acb_printd(nu, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("yv = "); acb_printd(yv, 30); flint_printf("\n\n"); flint_printf("yv1 = "); acb_printd(yv1, 30); flint_printf("\n\n"); flint_printf("jv = "); acb_printd(jv, 30); flint_printf("\n\n"); flint_printf("r = "); acb_printd(r, 30); flint_printf("\n\n"); abort(); } acb_clear(nu); acb_clear(nu1); acb_clear(z); acb_clear(jv); acb_clear(jv1); acb_clear(yv); acb_clear(yv1); acb_clear(r); acb_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-chebyshev_t.c000066400000000000000000000057661264125401100204440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("chebyshev_t...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t n, z, a, b, c, t, res1, res2; slong prec; acb_init(n); acb_init(z); acb_init(a); acb_init(b); acb_init(c); acb_init(t); acb_init(res1); acb_init(res2); prec = 2 + n_randint(state, 300); acb_randtest_param(n, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_randtest_param(z, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_randtest_param(res1, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_randtest_param(res2, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_hypgeom_chebyshev_t(res1, n, z, prec); acb_neg(a, n); acb_set(b, n); acb_one(c); acb_mul_2exp_si(c, c, -1); acb_sub_ui(t, z, 1, prec); acb_neg(t, t); acb_mul_2exp_si(t, t, -1); acb_hypgeom_2f1(res2, a, b, c, t, 0, 2 + n_randint(state, 300)); if (!acb_overlaps(res1, res2)) { flint_printf("FAIL: consistency\n\n"); flint_printf("iter = %wd\n\n", iter); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(z); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(t); acb_clear(res1); acb_clear(res2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-chebyshev_u.c000066400000000000000000000061211264125401100204270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("chebyshev_u...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t n, z, a, b, c, t, res1, res2; slong prec; acb_init(n); acb_init(z); acb_init(a); acb_init(b); acb_init(c); acb_init(t); acb_init(res1); acb_init(res2); prec = 2 + n_randint(state, 300); acb_randtest_param(n, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_randtest_param(z, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_randtest_param(res1, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_randtest_param(res2, state, 1 + n_randint(state, 400), 1 + n_randint(state, 10)); acb_hypgeom_chebyshev_u(res1, n, z, prec); acb_neg(a, n); acb_add_ui(b, n, 2, prec); acb_set_ui(c, 3); acb_mul_2exp_si(c, c, -1); acb_sub_ui(t, z, 1, prec); acb_neg(t, t); acb_mul_2exp_si(t, t, -1); acb_hypgeom_2f1(res2, a, b, c, t, 0, 2 + n_randint(state, 300)); acb_add_ui(t, n, 1, prec); acb_mul(res2, res2, t, prec); if (!acb_overlaps(res1, res2)) { flint_printf("FAIL: consistency\n\n"); flint_printf("iter = %wd\n\n", iter); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(z); acb_clear(a); acb_clear(b); acb_clear(c); acb_clear(t); acb_clear(res1); acb_clear(res2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-chi.c000066400000000000000000000062351264125401100166740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("chi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t z0, z1, w0, w1; slong prec0, prec1; acb_init(z0); acb_init(z1); acb_init(w0); acb_init(w1); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); acb_randtest(z0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 10)); acb_set(z1, z0); if (n_randint(state, 2)) { acb_add(z1, z1, w0, prec0); acb_sub(z1, z1, w0, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_chi_2f3(w0, z0, prec0); break; case 1: acb_hypgeom_chi_asymp(w0, z0, prec0); break; default: acb_hypgeom_chi(w0, z0, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_chi_2f3(w1, z1, prec1); break; case 1: acb_hypgeom_chi_asymp(w1, z1, prec1); break; default: acb_hypgeom_chi(w1, z1, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("z0 = "); acb_printd(z0, 30); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } acb_clear(z0); acb_clear(z1); acb_clear(w0); acb_clear(w1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-ci.c000066400000000000000000000062311264125401100165200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("ci...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t z0, z1, w0, w1; slong prec0, prec1; acb_init(z0); acb_init(z1); acb_init(w0); acb_init(w1); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); acb_randtest(z0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_set(z1, z0); if (n_randint(state, 2)) { acb_add(z1, z1, w0, prec0); acb_sub(z1, z1, w0, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_ci_2f3(w0, z0, prec0); break; case 1: acb_hypgeom_ci_asymp(w0, z0, prec0); break; default: acb_hypgeom_ci(w0, z0, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_ci_2f3(w1, z1, prec1); break; case 1: acb_hypgeom_ci_asymp(w1, z1, prec1); break; default: acb_hypgeom_ci(w1, z1, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("z0 = "); acb_printd(z0, 30); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } acb_clear(z0); acb_clear(z1); acb_clear(w0); acb_clear(w1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-ei.c000066400000000000000000000076101264125401100165240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_ei_fallback(acb_t res, const acb_t z, slong prec) { acb_t t, u; acb_init(t); acb_init(u); acb_zero(t); acb_neg(u, z); acb_hypgeom_gamma_upper(u, t, u, 0, prec); acb_neg(u, u); acb_log(t, z, prec); acb_mul_2exp_si(t, t, -1); acb_add(u, u, t, prec); acb_inv(t, z, prec); acb_log(t, t, prec); acb_mul_2exp_si(t, t, -1); acb_sub(u, u, t, prec); acb_neg(t, z); acb_log(t, t, prec); acb_sub(u, u, t, prec); acb_swap(res, u); acb_clear(t); acb_clear(u); } int main() { slong iter; flint_rand_t state; flint_printf("ei...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { acb_t z0, z1, w0, w1; slong prec0, prec1; acb_init(z0); acb_init(z1); acb_init(w0); acb_init(w1); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); acb_randtest(z0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_set(z1, z0); if (n_randint(state, 2)) { acb_add(z1, z1, w0, prec0); acb_sub(z1, z1, w0, prec0); } switch (n_randint(state, 4)) { case 0: acb_hypgeom_ei_2f2(w0, z0, prec0); break; case 1: acb_hypgeom_ei_asymp(w0, z0, prec0); break; case 2: acb_hypgeom_ei(w0, z0, prec0); break; default: acb_hypgeom_ei_fallback(w0, z0, prec0); } switch (n_randint(state, 4)) { case 0: acb_hypgeom_ei_2f2(w1, z1, prec1); break; case 1: acb_hypgeom_ei_asymp(w1, z1, prec1); break; case 2: acb_hypgeom_ei(w1, z1, prec1); break; default: acb_hypgeom_ei_fallback(w1, z1, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("z0 = "); acb_printd(z0, 30); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } acb_clear(z0); acb_clear(z1); acb_clear(w0); acb_clear(w1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-erf.c000066400000000000000000000062311264125401100167010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("erf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t a, b, c; slong prec1, prec2, prec3, prec4; prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); prec3 = 2 + n_randint(state, 1000); prec4 = 2 + n_randint(state, 1000); acb_init(a); acb_init(b); acb_init(c); acb_randtest_special(a, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest_special(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest_special(c, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); switch (n_randint(state, 4)) { case 0: acb_hypgeom_erf_asymp(b, a, prec1, prec3); break; case 1: acb_hypgeom_erf_1f1a(b, a, prec1); break; case 2: acb_hypgeom_erf_1f1b(b, a, prec1); break; default: acb_hypgeom_erf(b, a, prec1); } switch (n_randint(state, 4)) { case 0: acb_hypgeom_erf_asymp(c, a, prec2, prec4); break; case 1: acb_hypgeom_erf_1f1a(c, a, prec2); break; case 2: acb_hypgeom_erf_1f1b(c, a, prec2); break; default: acb_hypgeom_erf(c, a, prec2); } if (!acb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("b = "); acb_print(b); flint_printf("\n\n"); flint_printf("c = "); acb_print(c); flint_printf("\n\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-gamma_upper.c000066400000000000000000000123471264125401100204270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma_upper...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t a0, a1, b, z, w0, w1, t, u; slong prec0, prec1; int modified; acb_init(a0); acb_init(a1); acb_init(b); acb_init(z); acb_init(w0); acb_init(w1); acb_init(t); acb_init(u); modified = n_randint(state, 2); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); acb_randtest_param(a0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_add_ui(a1, a0, 1, prec0); switch (n_randint(state, 4)) { case 0: acb_hypgeom_gamma_upper_asymp(w0, a0, z, modified, prec0); break; case 1: acb_hypgeom_gamma_upper_1f1a(w0, a0, z, modified, prec0); break; case 2: acb_hypgeom_gamma_upper_1f1b(w0, a0, z, modified, prec0); break; default: acb_hypgeom_gamma_upper(w0, a0, z, modified, prec0); } switch (n_randint(state, 4)) { case 0: acb_hypgeom_gamma_upper_asymp(w1, a0, z, modified, prec1); break; case 1: acb_hypgeom_gamma_upper_1f1a(w1, a0, z, modified, prec1); break; case 2: acb_hypgeom_gamma_upper_1f1b(w1, a0, z, modified, prec1); break; default: acb_hypgeom_gamma_upper(w1, a0, z, modified, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("nu = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 4)) { case 0: acb_hypgeom_gamma_upper_asymp(w1, a1, z, modified, prec1); break; case 1: acb_hypgeom_gamma_upper_1f1a(w1, a1, z, modified, prec1); break; case 2: acb_hypgeom_gamma_upper_1f1b(w1, a1, z, modified, prec1); break; default: acb_hypgeom_gamma_upper(w1, a1, z, modified, prec1); } /* a Gamma(a,z) + exp(-z) z^a = Gamma(a+1,z) */ if (modified) acb_one(t); else acb_pow(t, z, a0, prec0); acb_neg(u, z); acb_exp(u, u, prec0); acb_mul(t, t, u, prec0); if (modified) { acb_mul(b, w1, z, prec0); acb_addmul(t, a0, w0, prec0); acb_sub(t, t, b, prec0); } else { acb_addmul(t, a0, w0, prec0); acb_sub(t, t, w1, prec0); } if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation\n\n"); flint_printf("nu = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_clear(a0); acb_clear(a1); acb_clear(b); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-gegenbauer_c.c000066400000000000000000000063771264125401100205460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("gegenbauer_c...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t n, m, z, t, u, res1, res2; slong prec1, prec2; acb_init(n); acb_init(m); acb_init(z); acb_init(t); acb_init(u); acb_init(res1); acb_init(res2); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); if (n_randint(state, 2)) { acb_set_si(m, n_randint(state, 20) - 10); acb_set_si(n, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), 10); acb_randtest_param(m, state, 1 + n_randint(state, 400), 10); } acb_randtest_param(z, state, 1 + n_randint(state, 400), 10); acb_hypgeom_gegenbauer_c(res1, n, m, z, prec1); acb_one(t); acb_mul_2exp_si(t, t, -1); acb_sub(t, m, t, prec2); acb_hypgeom_jacobi_p(res2, n, t, t, z, prec2); acb_add_ui(t, t, 1, prec2); acb_rising(t, t, n, prec2); acb_div(res2, res2, t, prec2); acb_mul_2exp_si(t, m, 1); acb_rising(t, t, n, prec2); acb_mul(res2, res2, t, prec2); if (!acb_overlaps(res1, res2)) { flint_printf("FAIL: consistency 1\n\n"); flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(m); acb_clear(z); acb_clear(t); acb_clear(u); acb_clear(res1); acb_clear(res2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-hermite_h.c000066400000000000000000000061641264125401100200760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("hermite_h...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t n, n1, n2, z, res1, res2, res3, s; slong prec1, prec2, prec3; acb_init(n); acb_init(n1); acb_init(n2); acb_init(z); acb_init(res1); acb_init(res2); acb_init(res3); acb_init(s); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); prec3 = 2 + n_randint(state, 300); acb_randtest_param(n, state, 1 + n_randint(state, 400), 10); acb_sub_ui(n1, n, 1, prec1); acb_sub_ui(n2, n, 2, prec1); acb_randtest_param(z, state, 1 + n_randint(state, 400), 10); acb_randtest_param(res1, state, 1 + n_randint(state, 400), 10); acb_hypgeom_hermite_h(res1, n, z, prec1); acb_hypgeom_hermite_h(res2, n1, z, prec2); acb_hypgeom_hermite_h(res3, n2, z, prec3); acb_mul(s, res2, z, prec1); acb_submul(s, res3, n1, prec1); acb_mul_2exp_si(s, s, 1); if (!acb_overlaps(res1, s)) { flint_printf("FAIL: consistency\n\n"); flint_printf("iter = %wd\n\n", iter); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n"); flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(n1); acb_clear(n2); acb_clear(z); acb_clear(res1); acb_clear(res2); acb_clear(res3); acb_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-jacobi_p.c000066400000000000000000000072111264125401100176720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("jacobi_p...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t n, a, b, n1, a1, b1, z, res1, res2, res3, s; slong prec; acb_init(n); acb_init(a); acb_init(b); acb_init(n1); acb_init(a1); acb_init(b1); acb_init(z); acb_init(res1); acb_init(res2); acb_init(res3); acb_init(s); prec = 2 + n_randint(state, 300); if (n_randint(state, 2)) { acb_set_si(n, n_randint(state, 20) - 10); acb_set_si(a, n_randint(state, 20) - 10); acb_set_si(b, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), 10); acb_randtest_param(a, state, 1 + n_randint(state, 400), 10); acb_randtest_param(b, state, 1 + n_randint(state, 400), 10); } acb_randtest_param(z, state, 1 + n_randint(state, 400), 10); acb_sub_ui(n1, n, 1, prec); acb_sub_ui(a1, a, 1, prec); acb_sub_ui(b1, b, 1, prec); acb_hypgeom_jacobi_p(res1, n, a, b1, z, prec); acb_hypgeom_jacobi_p(res2, n, a1, b, z, 2 + n_randint(state, 300)); acb_hypgeom_jacobi_p(res3, n1, a, b, z, 2 + n_randint(state, 300)); acb_sub(s, res1, res2, prec); if (!acb_overlaps(s, res3)) { flint_printf("FAIL: consistency\n\n"); flint_printf("iter = %wd\n\n", iter); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n"); flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(a); acb_clear(b); acb_clear(n1); acb_clear(a1); acb_clear(b1); acb_clear(z); acb_clear(res1); acb_clear(res2); acb_clear(res3); acb_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-laguerre_l.c000066400000000000000000000065451264125401100202560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("laguerre_l...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t n, m, n1, m1, z, res1, res2, res3, s; slong prec; acb_init(n); acb_init(m); acb_init(n1); acb_init(m1); acb_init(z); acb_init(res1); acb_init(res2); acb_init(res3); acb_init(s); prec = 2 + n_randint(state, 200); if (n_randint(state, 2)) { acb_set_si(n, n_randint(state, 20) - 10); acb_set_si(m, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), 10); acb_randtest_param(m, state, 1 + n_randint(state, 400), 10); } acb_randtest_param(z, state, 1 + n_randint(state, 400), 10); acb_sub_ui(n1, n, 1, prec); acb_sub_ui(m1, m, 1, prec); acb_hypgeom_laguerre_l(res1, n, m, z, prec); acb_hypgeom_laguerre_l(res2, n1, m, z, 2 + n_randint(state, 200)); acb_hypgeom_laguerre_l(res3, n, m1, z, 2 + n_randint(state, 200)); acb_add(s, res2, res3, prec); if (acb_is_finite(res1) && acb_is_finite(s) && !acb_overlaps(res1, s)) { flint_printf("FAIL: consistency\n\n"); flint_printf("iter = %wd\n\n", iter); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n"); flint_printf("s = "); acb_printd(s, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(m); acb_clear(n1); acb_clear(m1); acb_clear(z); acb_clear(res1); acb_clear(res2); acb_clear(res3); acb_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-legendre_p.c000066400000000000000000000077201264125401100202350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("legendre_p...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t n, na, nb, m, z, res1, res2, res3, t, u; slong prec1, prec2, ebits; int type; acb_init(n); acb_init(na); acb_init(nb); acb_init(m); acb_init(z); acb_init(res1); acb_init(res2); acb_init(res3); acb_init(t); acb_init(u); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); ebits = 1 + n_randint(state, 10); if (n_randint(state, 2)) { acb_set_si(m, n_randint(state, 20) - 10); acb_set_si(n, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits); acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits); } acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits); acb_sub_ui(na, n, 1, prec2); acb_add_ui(nb, n, 1, prec2); type = n_randint(state, 2); acb_hypgeom_legendre_p(res1, n, m, z, type, prec1); acb_hypgeom_legendre_p(res2, na, m, z, type, prec2); acb_hypgeom_legendre_p(res3, nb, m, z, type, prec2); acb_add(t, n, m, prec2); acb_mul(t, t, res2, prec2); acb_sub(u, n, m, prec2); acb_add_ui(u, u, 1, prec2); acb_mul(u, u, res3, prec2); acb_add(t, t, u, prec2); acb_mul_2exp_si(u, n, 1); acb_add_ui(u, u, 1, prec2); acb_mul(u, u, z, prec2); acb_mul(u, u, res1, prec2); if (!acb_overlaps(t, u)) { flint_printf("FAIL: consistency\n\n"); flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2); flint_printf("type = %d\n\n", type); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); flint_printf("res3 = "); acb_printd(res3, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); flint_printf("u = "); acb_printd(u, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(na); acb_clear(nb); acb_clear(m); acb_clear(z); acb_clear(res1); acb_clear(res2); acb_clear(res3); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-legendre_q.c000066400000000000000000000135711264125401100202370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* these functions are not public for now */ void _acb_hypgeom_legendre_q_single(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec); void _acb_hypgeom_legendre_q_double(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec); int main() { slong iter; flint_rand_t state; flint_printf("legendre_q...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t n, m, z, res1, res2; slong prec1, prec2, ebits; acb_init(n); acb_init(m); acb_init(z); acb_init(res1); acb_init(res2); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); ebits = 1 + n_randint(state, 10); if (n_randint(state, 2)) { acb_set_si(m, n_randint(state, 20) - 10); acb_set_si(n, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits); acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits); } acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits); _acb_hypgeom_legendre_q_single(res1, n, m, z, prec1); _acb_hypgeom_legendre_q_double(res2, n, m, z, prec2); if (!acb_overlaps(res1, res2)) { flint_printf("FAIL: consistency 1\n\n"); flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2); flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n"); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(m); acb_clear(z); acb_clear(res1); acb_clear(res2); } for (iter = 0; iter < 2000; iter++) { acb_t n, m, z, res1, res2, t, u; slong prec1, prec2, ebits; int type; acb_init(n); acb_init(m); acb_init(z); acb_init(res1); acb_init(res2); acb_init(t); acb_init(u); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); ebits = 1 + n_randint(state, 10); if (n_randint(state, 2)) { acb_set_si(m, n_randint(state, 20) - 10); acb_set_si(n, n_randint(state, 20) - 10); } else { acb_randtest_param(n, state, 1 + n_randint(state, 400), ebits); acb_randtest_param(m, state, 1 + n_randint(state, 400), ebits); } acb_randtest_param(z, state, 1 + n_randint(state, 400), ebits); type = n_randint(state, 2); acb_hypgeom_legendre_q(res1, n, m, z, type, prec1); acb_neg(t, m); acb_hypgeom_legendre_p(res2, n, t, z, type, prec2); acb_add(u, m, n, prec2); acb_add_ui(u, u, 1, prec2); acb_gamma(u, u, prec2); acb_mul(res2, res2, u, prec2); acb_sub(u, n, m, prec2); acb_add_ui(u, u, 1, prec2); acb_rgamma(u, u, prec2); acb_mul(res2, res2, u, prec2); acb_hypgeom_legendre_p(t, n, m, z, type, prec2); if (type == 0) { acb_cos_pi(u, m, prec2); acb_mul(t, t, u, prec2); } acb_sub(res2, t, res2, prec2); if (type == 1) { acb_exp_pi_i(t, m, prec2); acb_mul(res2, res2, t, prec2); } acb_sin_pi(t, m, prec2); if (acb_contains_zero(t)) acb_indeterminate(res2); else acb_div(res2, res2, t, prec2); acb_const_pi(t, prec2); acb_mul(res2, res2, t, prec2); acb_mul_2exp_si(res2, res2, -1); if (!acb_overlaps(res1, res2)) { flint_printf("FAIL: consistency 2\n\n"); flint_printf("iter = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, prec1, prec2); flint_printf("type = %d\n\n", type); flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n"); flint_printf("n = "); acb_printd(n, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("res1 = "); acb_printd(res1, 30); flint_printf("\n\n"); flint_printf("res2 = "); acb_printd(res2, 30); flint_printf("\n\n"); abort(); } acb_clear(n); acb_clear(m); acb_clear(z); acb_clear(res1); acb_clear(res2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-m.c000066400000000000000000000215271264125401100163660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("m...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t a0, a1, a2, b, z, w0, w1, w2, t, u; slong prec0, prec1, prec2; int regularized, ebits; acb_init(a0); acb_init(a1); acb_init(a2); acb_init(b); acb_init(z); acb_init(w0); acb_init(w1); acb_init(w2); acb_init(t); acb_init(u); prec0 = 2 + n_randint(state, 700); prec1 = 2 + n_randint(state, 700); prec2 = 2 + n_randint(state, 700); if (n_randint(state, 5) == 0) ebits = 100; else ebits = 10; acb_randtest_param(a0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest_param(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, ebits)); regularized = n_randint(state, 2); acb_add_ui(a1, a0, 1, prec0); acb_add_ui(a2, a0, 2, prec0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_m_asymp(w0, a0, b, z, regularized, prec0); break; case 1: acb_hypgeom_m_1f1(w0, a0, b, z, regularized, prec0); break; default: acb_hypgeom_m(w0, a0, b, z, regularized, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_m_asymp(w1, a0, b, z, regularized, prec1); break; case 1: acb_hypgeom_m_1f1(w1, a0, b, z, regularized, prec1); break; default: acb_hypgeom_m(w1, a0, b, z, regularized, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("regularized = %d\n\n", regularized); flint_printf("a = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_m_asymp(w1, a1, b, z, regularized, prec1); break; case 1: acb_hypgeom_m_1f1(w1, a1, b, z, regularized, prec1); break; default: acb_hypgeom_m(w1, a1, b, z, regularized, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_m_asymp(w2, a2, b, z, regularized, prec2); break; case 1: acb_hypgeom_m_1f1(w2, a2, b, z, regularized, prec2); break; default: acb_hypgeom_m(w2, a2, b, z, regularized, prec2); } /* 1F1(a,b,z) * (a-b+1) */ acb_sub(u, a1, b, prec0); acb_mul(t, w0, u, prec0); /* 1F1(a+1,b,z) * (2a - b + z + 2) */ acb_mul_2exp_si(u, a0, 1); acb_sub(u, u, b, prec0); acb_add(u, u, z, prec0); acb_add_ui(u, u, 2, prec0); acb_submul(t, w1, u, prec0); /* 1F1(a+2,b,z) * -(a+1) */ acb_addmul(t, w2, a1, prec0); if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation\n\n"); flint_printf("a = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_add_ui(a1, b, 1, prec0); acb_add_ui(a2, b, 2, prec0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_m_asymp(w1, a0, a1, z, regularized, prec1); break; case 1: acb_hypgeom_m_1f1(w1, a0, a1, z, regularized, prec1); break; default: acb_hypgeom_m(w1, a0, a1, z, regularized, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_m_asymp(w2, a0, a2, z, regularized, prec2); break; case 1: acb_hypgeom_m_1f1(w2, a0, a2, z, regularized, prec2); break; default: acb_hypgeom_m(w2, a0, a2, z, regularized, prec2); } if (regularized) { acb_set(t, w0); acb_add(u, b, z, prec0); acb_submul(t, w1, u, prec0); acb_sub(u, a0, a1, prec0); acb_mul(u, u, z, prec0); acb_submul(t, w2, u, prec0); } else { acb_mul(t, w0, b, prec0); acb_mul(t, t, a1, prec0); acb_add(u, b, z, prec0); acb_mul(u, u, a1, prec0); acb_submul(t, w1, u, prec0); acb_sub(u, a0, a1, prec0); acb_mul(u, u, z, prec0); acb_submul(t, w2, u, prec0); } if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation 2\n\n"); flint_printf("a = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_m(a0, a0, b, z, regularized, prec0); acb_set(t, a0); break; case 1: acb_hypgeom_m(b, a0, b, z, regularized, prec0); acb_set(t, b); break; default: acb_hypgeom_m(z, a0, b, z, regularized, prec2); acb_set(t, z); } if (!acb_overlaps(t, w0)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_clear(a0); acb_clear(a1); acb_clear(a2); acb_clear(b); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(w2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-pfq_series_direct.c000066400000000000000000000101011264125401100216060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("pfq_series_direct...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_poly_struct a[4], b[4]; acb_poly_t z, s1, s2; slong i, p, q, len1, len2, n1, n2, prec1, prec2; int regularized; p = n_randint(state, 3); q = n_randint(state, 3); len1 = n_randint(state, 8); len2 = n_randint(state, 8); prec1 = 2 + n_randint(state, 400); prec2 = 2 + n_randint(state, 400); if (n_randint(state, 2)) n1 = -1; else n1 = n_randint(state, 50); if (n_randint(state, 2)) n2 = -1; else n2 = n_randint(state, 50); regularized = n_randint(state, 2); acb_poly_init(z); acb_poly_init(s1); acb_poly_init(s2); for (i = 0; i < p; i++) acb_poly_init(a + i); for (i = 0; i < q; i++) acb_poly_init(b + i); acb_poly_randtest(z, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 10); for (i = 0; i < p; i++) acb_poly_randtest(a + i, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 3); for (i = 0; i < q; i++) acb_poly_randtest(b + i, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 3); acb_hypgeom_pfq_series_direct(s1, a, p, b, q, z, regularized, n1, len1, prec1); acb_hypgeom_pfq_series_direct(s2, a, p, b, q, z, regularized, n2, len2, prec2); acb_poly_truncate(s1, FLINT_MIN(len1, len2)); acb_poly_truncate(s2, FLINT_MIN(len1, len2)); if (!acb_poly_overlaps(s1, s2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("iter = %wd\n", iter); flint_printf("n1 = %wd, n2 = %wd prec1 = %wd, prec2 = %wd\n\n", n1, n2, prec1, prec2); flint_printf("p = %wd, q = %wd\n\n", p, q); flint_printf("z = "); acb_poly_printd(z, 15); flint_printf("\n\n"); for (i = 0; i < p; i++) { flint_printf("a[%wd] = ", i); acb_poly_printd(a + i, 15); flint_printf("\n\n"); } for (i = 0; i < q; i++) { flint_printf("b[%wd] = ", i); acb_poly_printd(b + i, 15); flint_printf("\n\n"); } flint_printf("s1 = "); acb_poly_printd(s1, 15); flint_printf("\n\n"); flint_printf("s2 = "); acb_poly_printd(s2, 15); flint_printf("\n\n"); acb_poly_sub(s1, s1, s2, prec1); flint_printf("diff = "); acb_poly_printd(s1, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(z); acb_poly_clear(s1); acb_poly_clear(s2); for (i = 0; i < p; i++) acb_poly_clear(a + i); for (i = 0; i < q; i++) acb_poly_clear(b + i); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-pfq_sum_bs.c000066400000000000000000000065221264125401100202660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("pfq_sum_bs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_ptr a, b; acb_t z, s1, s2, t1, t2; slong i, p, q, n, prec1, prec2; p = n_randint(state, 5); q = n_randint(state, 5); n = n_randint(state, 300); prec1 = 2 + n_randint(state, 500); prec2 = 2 + n_randint(state, 500); acb_init(z); acb_init(s1); acb_init(s2); acb_init(t1); acb_init(t2); acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(s1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(t1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(s2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(t2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); a = _acb_vec_init(p); b = _acb_vec_init(q); for (i = 0; i < p; i++) acb_randtest(a + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10)); for (i = 0; i < q; i++) acb_randtest(b + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10)); acb_hypgeom_pfq_sum_forward(s1, t1, a, p, b, q, z, n, prec1); acb_hypgeom_pfq_sum_bs(s2, t2, a, p, b, q, z, n, prec2); if (!acb_overlaps(s1, s2) || !acb_overlaps(t1, t2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("z = "); acb_print(a); flint_printf("\n\n"); flint_printf("s1 = "); acb_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); acb_print(s2); flint_printf("\n\n"); flint_printf("t1 = "); acb_print(t1); flint_printf("\n\n"); flint_printf("t2 = "); acb_print(t2); flint_printf("\n\n"); abort(); } _acb_vec_clear(a, p); _acb_vec_clear(b, q); acb_clear(z); acb_clear(s1); acb_clear(s2); acb_clear(t1); acb_clear(t2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-pfq_sum_fme.c000066400000000000000000000064371264125401100204360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("pfq_sum_fme...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { acb_ptr a, b; acb_t z, s1, s2, t1, t2; slong i, p, q, n, prec1, prec2; p = n_randint(state, 4); q = n_randint(state, 4); n = n_randint(state, 100); prec1 = 2 + n_randint(state, 500); prec2 = 2 + n_randint(state, 500); acb_init(z); acb_init(s1); acb_init(s2); acb_init(t1); acb_init(t2); acb_randtest(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 5)); acb_randtest(s1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 5)); acb_randtest(t1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 5)); acb_randtest(s2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 5)); acb_randtest(t2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 5)); a = _acb_vec_init(p); b = _acb_vec_init(q); for (i = 0; i < p; i++) acb_randtest(a + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 5)); for (i = 0; i < q; i++) acb_randtest(b + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 5)); acb_hypgeom_pfq_sum_forward(s1, t1, a, p, b, q, z, n, prec1); acb_hypgeom_pfq_sum_fme(s2, t2, a, p, b, q, z, n, prec2); if (!acb_overlaps(s1, s2) || !acb_overlaps(t1, t2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("z = "); acb_print(a); flint_printf("\n\n"); flint_printf("s1 = "); acb_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); acb_print(s2); flint_printf("\n\n"); flint_printf("t1 = "); acb_print(t1); flint_printf("\n\n"); flint_printf("t2 = "); acb_print(t2); flint_printf("\n\n"); abort(); } _acb_vec_clear(a, p); _acb_vec_clear(b, q); acb_clear(z); acb_clear(s1); acb_clear(s2); acb_clear(t1); acb_clear(t2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-pfq_sum_invz.c000066400000000000000000000072051264125401100206470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("pfq_sum_invz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_ptr a, b; acb_t z, zinv, s1, s2, t1, t2; slong i, p, q, n, prec1, prec2; p = n_randint(state, 5); q = n_randint(state, 5); n = n_randint(state, 300); prec1 = 2 + n_randint(state, 500); prec2 = 2 + n_randint(state, 500); acb_init(z); acb_init(zinv); acb_init(s1); acb_init(s2); acb_init(t1); acb_init(t2); acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(s1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(t1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(s2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(t2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_inv(zinv, z, 1 + n_randint(state, 500)); a = _acb_vec_init(p); b = _acb_vec_init(q); for (i = 0; i < p; i++) acb_randtest(a + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10)); for (i = 0; i < q; i++) acb_randtest(b + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10)); if (n_randint(state, 2)) acb_hypgeom_pfq_sum_invz(s1, t1, a, p, b, q, zinv, z, n, prec1); else acb_hypgeom_pfq_sum_bs_invz(s1, t1, a, p, b, q, z, n, prec1); acb_hypgeom_pfq_sum(s2, t2, a, p, b, q, zinv, n, prec2); if (!acb_overlaps(s1, s2) || !acb_overlaps(t1, t2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wd\n\n", n); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("s1 = "); acb_printd(s1, 15); flint_printf("\n\n"); flint_printf("s2 = "); acb_printd(s2, 15); flint_printf("\n\n"); flint_printf("t1 = "); acb_printd(t1, 15); flint_printf("\n\n"); flint_printf("t2 = "); acb_printd(t2, 15); flint_printf("\n\n"); abort(); } _acb_vec_clear(a, p); _acb_vec_clear(b, q); acb_clear(z); acb_clear(zinv); acb_clear(s1); acb_clear(s2); acb_clear(t1); acb_clear(t2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-pfq_sum_rs.c000066400000000000000000000065221264125401100203060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("pfq_sum_rs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_ptr a, b; acb_t z, s1, s2, t1, t2; slong i, p, q, n, prec1, prec2; p = n_randint(state, 5); q = n_randint(state, 5); n = n_randint(state, 300); prec1 = 2 + n_randint(state, 500); prec2 = 2 + n_randint(state, 500); acb_init(z); acb_init(s1); acb_init(s2); acb_init(t1); acb_init(t2); acb_randtest_special(z, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(s1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(t1, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(s2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); acb_randtest_special(t2, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100)); a = _acb_vec_init(p); b = _acb_vec_init(q); for (i = 0; i < p; i++) acb_randtest(a + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10)); for (i = 0; i < q; i++) acb_randtest(b + i, state, 1 + n_randint(state, 100), 1 + n_randint(state, 10)); acb_hypgeom_pfq_sum_forward(s1, t1, a, p, b, q, z, n, prec1); acb_hypgeom_pfq_sum_rs(s2, t2, a, p, b, q, z, n, prec2); if (!acb_overlaps(s1, s2) || !acb_overlaps(t1, t2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("z = "); acb_print(a); flint_printf("\n\n"); flint_printf("s1 = "); acb_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); acb_print(s2); flint_printf("\n\n"); flint_printf("t1 = "); acb_print(t1); flint_printf("\n\n"); flint_printf("t2 = "); acb_print(t2); flint_printf("\n\n"); abort(); } _acb_vec_clear(a, p); _acb_vec_clear(b, q); acb_clear(z); acb_clear(s1); acb_clear(s2); acb_clear(t1); acb_clear(t2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-si.c000066400000000000000000000062311264125401100165400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t z0, z1, w0, w1; slong prec0, prec1; acb_init(z0); acb_init(z1); acb_init(w0); acb_init(w1); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); acb_randtest(z0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_set(z1, z0); if (n_randint(state, 2)) { acb_add(z1, z1, w0, prec0); acb_sub(z1, z1, w0, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_si_1f2(w0, z0, prec0); break; case 1: acb_hypgeom_si_asymp(w0, z0, prec0); break; default: acb_hypgeom_si(w0, z0, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_si_1f2(w1, z1, prec1); break; case 1: acb_hypgeom_si_asymp(w1, z1, prec1); break; default: acb_hypgeom_si(w1, z1, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("z0 = "); acb_printd(z0, 30); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } acb_clear(z0); acb_clear(z1); acb_clear(w0); acb_clear(w1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-spherical_y.c000066400000000000000000000122401264125401100204240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* generated with mpmath */ static const double testdata[] = { 0.0, 0.0, -0.02701626593453869896, 0.06085851132589568114, 0.092391418427377575111, 0.29443833672801130076, 0.65131374739365937388, 0.37063665572827331764, 0.83847032733386007862, -0.28730577566514336534, -0.14750357092078405673, -0.30269451746476217073, -0.048646822931479694311, 0.038926542608778397121, 0.0048197328091099892156, 0.003641138129582944611, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.027574808444335508972, 0.11025410152651193448, 0.35400136349600893569, 0.24420566191536183849, 0.67425312681608106523, -0.11728998324910652574, -0.069322941709900597259, -0.18037674817459565026, -0.018729775699827662658, 0.013254956213452933465, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.14771800806690767222, 0.11532328561497280466, 0.50057392828327004059, -0.029559886614345590592, -0.02552211332726607337, -0.080244885187214384683, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.28209479177387814347, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.28209479177387814347, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.14771800806690767222, 0.11532328561497280466, 0.50057392828327004059, -0.029559886614345590592, -0.02552211332726607337, -0.080244885187214384683, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.027574808444335508972, 0.11025410152651193448, 0.35400136349600893569, 0.24420566191536183849, 0.67425312681608106523, -0.11728998324910652574, -0.069322941709900597259, -0.18037674817459565026, -0.018729775699827662658, 0.013254956213452933465, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.02701626593453869896, 0.06085851132589568114, 0.092391418427377575111, 0.29443833672801130076, 0.65131374739365937388, 0.37063665572827331764, 0.83847032733386007862, -0.28730577566514336534, -0.14750357092078405673, -0.30269451746476217073, -0.048646822931479694311, 0.038926542608778397121, 0.0048197328091099892156, 0.003641138129582944611, 0.0, 0.0, -0.033798002071615353821, 0.018033964330683617275, -0.071988993423855434033, 0.19195223773954952294, 0.23381678888295549361, 0.58288246446413288682, 1.0666048448920927459, 0.45816450098677839043, 0.99160821344691798668, -0.56670953266315770842, -0.27930640165163989333, -0.44051756827083040505, -0.092578419347396006256, 0.086641542063743427664, 0.015474322098595795308, 0.010316287906840124695, 0.00051935757617903067671, -0.0014726339944978705874, }; int main() { flint_printf("spherical_y...."); fflush(stdout); { slong i, n, m; acb_t z, w, x, y; acb_init(z); acb_init(w); acb_init(x); acb_init(y); i = 0; arb_set_str(acb_realref(x), "0.2", 64); arb_set_str(acb_imagref(x), "0.3", 64); arb_set_str(acb_realref(y), "0.3", 64); arb_set_str(acb_imagref(y), "0.4", 64); for (n = -4; n <= 4; n++) { for (m = -4; m <= 4; m++) { acb_hypgeom_spherical_y(z, n, m, x, y, 64); acb_set_d_d(w, testdata[2 * i], testdata[2 * i + 1]); mag_set_d(arb_radref(acb_realref(w)), 1e-13); mag_set_d(arb_radref(acb_imagref(w)), 1e-13); if (!acb_overlaps(z, w)) { flint_printf("FAIL: value\n\n"); flint_printf("n = %wd, m = %wd\n", n, m); flint_printf("z = "); acb_printd(z, 20); flint_printf("\n\n"); flint_printf("w = "); acb_printd(w, 20); flint_printf("\n\n"); abort(); } i++; } } acb_clear(z); acb_clear(w); acb_clear(x); acb_clear(y); } flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-u.c000066400000000000000000000132171264125401100163730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_u_asymp_proper(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec) { acb_t t; acb_init(t); acb_pow(t, z, a, prec); acb_hypgeom_u_asymp(res, a, b, z, -1, prec); acb_div(res, res, t, prec); acb_clear(t); } int main() { slong iter; flint_rand_t state; flint_printf("u...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t a0, a1, a2, b, z, w0, w1, w2, t, u; slong prec0, prec1, prec2; acb_init(a0); acb_init(a1); acb_init(a2); acb_init(b); acb_init(z); acb_init(w0); acb_init(w1); acb_init(w2); acb_init(t); acb_init(u); prec0 = 2 + n_randint(state, 700); prec1 = 2 + n_randint(state, 700); prec2 = 2 + n_randint(state, 700); acb_randtest_param(a0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest_param(b, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w0, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w1, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_randtest(w2, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); acb_add_ui(a1, a0, 1, prec0); acb_add_ui(a2, a0, 2, prec0); switch (n_randint(state, 3)) { case 0: acb_hypgeom_u_asymp_proper(w0, a0, b, z, prec0); break; case 1: acb_hypgeom_u_1f1(w0, a0, b, z, prec0); break; default: acb_hypgeom_u(w0, a0, b, z, prec0); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_u_asymp_proper(w1, a0, b, z, prec1); break; case 1: acb_hypgeom_u_1f1(w1, a0, b, z, prec1); break; default: acb_hypgeom_u(w1, a0, b, z, prec1); } if (!acb_overlaps(w0, w1)) { flint_printf("FAIL: consistency\n\n"); flint_printf("a = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); abort(); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_u_asymp_proper(w1, a1, b, z, prec1); break; case 1: acb_hypgeom_u_1f1(w1, a1, b, z, prec1); break; default: acb_hypgeom_u(w1, a1, b, z, prec1); } switch (n_randint(state, 3)) { case 0: acb_hypgeom_u_asymp_proper(w2, a2, b, z, prec2); break; case 1: acb_hypgeom_u_1f1(w2, a2, b, z, prec2); break; default: acb_hypgeom_u(w2, a2, b, z, prec2); } acb_set(t, w0); acb_mul_2exp_si(u, a0, 1); acb_sub(u, u, b, prec0); acb_add(u, u, z, prec0); acb_add_ui(u, u, 2, prec0); acb_submul(t, w1, u, prec0); acb_sub(u, a2, b, prec0); acb_mul(u, u, a1, prec0); acb_addmul(t, w2, u, prec0); if (!acb_contains_zero(t)) { flint_printf("FAIL: contiguous relation\n\n"); flint_printf("a = "); acb_printd(a0, 30); flint_printf("\n\n"); flint_printf("b = "); acb_printd(b, 30); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w0 = "); acb_printd(w0, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 30); flint_printf("\n\n"); abort(); } acb_clear(a0); acb_clear(a1); acb_clear(a2); acb_clear(b); acb_clear(z); acb_clear(w0); acb_clear(w1); acb_clear(w2); acb_clear(t); acb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/test/t-u_asymp.c000066400000000000000000000172551264125401100176120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int main() { slong iter; flint_rand_t state; flint_printf("u_asymp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t a, b, a2, b2, z, U1, U2, t, u, M1, M2, am; acb_struct bm[2]; ulong n1, n2; slong prec0, prec1, prec2; acb_init(a); acb_init(b); acb_init(a2); acb_init(b2); acb_init(z); acb_init(U1); acb_init(U2); acb_init(t); acb_init(u); acb_init(M1); acb_init(M2); acb_init(am); acb_init(bm); acb_init(bm + 1); if (n_randint(state, 4) == 0) { n1 = n_randint(state, 200); n2 = n_randint(state, 200); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); } else { n1 = n_randint(state, 40); n2 = n_randint(state, 40); prec0 = 2 + n_randint(state, 300); prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); } acb_randtest_param(a, state, prec0, 1 + n_randint(state, 20)); if (n_randint(state, 4) == 0) acb_add_ui(b, a, n_randint(state, 10), prec0); else acb_randtest_param(b, state, prec0, 1 + n_randint(state, 20)); acb_randtest(z, state, prec0, 1 + n_randint(state, 20)); /* Test Kummer's transformation */ acb_sub(a2, a, b, prec0); acb_add_ui(a2, a2, 1, prec0); acb_sub_ui(b2, b, 2, prec0); acb_neg(b2, b2); acb_hypgeom_u_asymp(U1, a, b, z, n1, prec1); acb_hypgeom_u_asymp(U2, a2, b2, z, n2, prec2); if (!acb_overlaps(U1, U2)) { flint_printf("FAIL (Kummer transformation)\n"); flint_printf("iter = %wd\n", iter); flint_printf("a = "); acb_printd(a, 50); flint_printf("\n"); flint_printf("b = "); acb_printd(b, 50); flint_printf("\n"); flint_printf("z = "); acb_printd(z, 50); flint_printf("\n"); flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2); flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n"); flint_printf("U2 = "); acb_printd(U2, 100); flint_printf("\n"); abort(); } /* Check contiguous relation (b-a-1)U(a,b-1,z) + z U(a,b+1,z) + (1-b-z) U(a,b,z) = 0 */ acb_one(t); acb_sub(t, t, b, prec0); acb_sub(t, t, z, prec0); acb_mul(u, U1, t, prec1); acb_add_ui(b2, b, 1, prec0); acb_hypgeom_u_asymp(U2, a, b2, z, n2, prec2); acb_addmul(u, U2, z, prec1); acb_sub_ui(b2, b, 1, prec0); acb_hypgeom_u_asymp(U2, a, b2, z, n2, prec2); acb_sub(t, b, a, prec0); acb_sub_ui(t, t, 1, prec0); acb_mul(t, t, U2, prec0); acb_add(t, t, u, prec0); if (!acb_contains_zero(t)) { flint_printf("FAIL (contiguous relation)\n"); flint_printf("iter = %wd\n", iter); flint_printf("a = "); acb_printd(a, 50); flint_printf("\n"); flint_printf("b = "); acb_printd(b, 50); flint_printf("\n"); flint_printf("z = "); acb_printd(z, 50); flint_printf("\n"); flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2); flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n"); flint_printf("t = "); acb_printd(t, 100); flint_printf("\n"); abort(); } /* Test U(a,b,z) = gamma(1-b)/gamma(a-b+1) M(a,b,z) + gamma(b-1)/gamma(a) z^(1-b) M(a-b+1,2-b,z) */ acb_set(am, a); acb_set(bm, b); acb_one(bm + 1); acb_hypgeom_pfq_direct(M1, am, 1, bm, 2, z, n2, prec2); acb_sub(am, a, b, prec2); acb_add_ui(am, am, 1, prec2); acb_sub_ui(bm, b, 2, prec2); acb_neg(bm, bm); acb_one(bm + 1); acb_hypgeom_pfq_direct(M2, am, 1, bm, 2, z, n2, prec2); acb_sub(am, a, b, prec2); acb_add_ui(am, am, 1, prec2); acb_rgamma(am, am, prec2); acb_mul(M1, M1, am, prec2); acb_sub_ui(am, b, 1, prec2); acb_neg(am, am); acb_gamma(am, am, prec2); acb_mul(M1, M1, am, prec2); acb_rgamma(am, a, prec2); acb_mul(M2, M2, am, prec2); acb_sub_ui(am, b, 1, prec2); acb_gamma(am, am, prec2); acb_mul(M2, M2, am, prec2); acb_sub_ui(am, b, 1, prec2); acb_neg(am, am); acb_pow(am, z, am, prec2); acb_mul(M2, M2, am, prec2); acb_add(U2, M1, M2, prec2); acb_pow(am, z, a, prec2); acb_mul(U2, U2, am, prec2); if (!acb_overlaps(U1, U2)) { flint_printf("FAIL (U in terms of M)\n"); flint_printf("iter = %wd\n", iter); flint_printf("a = "); acb_printd(a, 50); flint_printf("\n"); flint_printf("b = "); acb_printd(b, 50); flint_printf("\n"); flint_printf("z = "); acb_printd(z, 50); flint_printf("\n"); flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2); flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n"); flint_printf("U2 = "); acb_printd(U2, 100); flint_printf("\n"); abort(); } /* Test special value: b = a+1 */ acb_add_ui(b, a, 1, prec0); acb_hypgeom_u_asymp(U1, a, b, z, n1, prec1); acb_one(U2); if (!acb_overlaps(U1, U2)) { flint_printf("FAIL (special value)\n"); flint_printf("iter = %wd\n", iter); flint_printf("a = "); acb_printd(a, 50); flint_printf("\n"); flint_printf("b = "); acb_printd(b, 50); flint_printf("\n"); flint_printf("z = "); acb_printd(z, 50); flint_printf("\n"); flint_printf("n1 = %wd, n2 = %wd, prec1 = %wd, prec2 = %wd\n", n1, n2, prec1, prec2); flint_printf("U1 = "); acb_printd(U1, 100); flint_printf("\n"); flint_printf("U2 = "); acb_printd(U2, 100); flint_printf("\n"); abort(); } acb_clear(a); acb_clear(b); acb_clear(a2); acb_clear(b2); acb_clear(z); acb_clear(U1); acb_clear(U2); acb_clear(t); acb_clear(u); acb_clear(M1); acb_clear(M2); acb_clear(am); acb_clear(bm); acb_clear(bm + 1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_hypgeom/u.c000066400000000000000000000126461264125401100151600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" void acb_hypgeom_u_1f1_series(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t z, slong len, slong prec) { acb_poly_t s, u, A, B; acb_poly_struct aa[3]; arb_t c; slong wlen; int singular; acb_poly_init(s); acb_poly_init(u); acb_poly_init(A); acb_poly_init(B); acb_poly_init(aa + 0); acb_poly_init(aa + 1); acb_poly_init(aa + 2); arb_init(c); singular = (b->length == 0) || acb_is_int(b->coeffs); wlen = len + (singular != 0); /* A = rgamma(a-b+1) * 1F~1(a,b,z) */ acb_poly_sub(u, a, b, prec); acb_poly_add_si(u, u, 1, prec); acb_poly_rgamma_series(A, u, wlen, prec); /* todo: handle a = 1 efficiently */ acb_poly_set(aa, a); acb_poly_set(aa + 1, b); acb_poly_one(aa + 2); acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec); acb_poly_mullow(A, A, s, wlen, prec); /* B = rgamma(a) * 1F~1(a-b+1,2-b,z) * z^(1-b) */ acb_poly_set(aa, u); acb_poly_add_si(aa + 1, b, -2, prec); acb_poly_neg(aa + 1, aa + 1); acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec); acb_poly_rgamma_series(B, a, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_add_si(u, b, -1, prec); acb_poly_neg(u, u); acb_poly_pow_series(s, z, u, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_sub(A, A, B, prec); /* multiply by pi csc(pi b) */ acb_poly_sin_pi_series(B, b, wlen, prec); if (singular) { acb_poly_shift_right(A, A, 1); acb_poly_shift_right(B, B, 1); } acb_poly_div_series(res, A, B, len, prec); arb_const_pi(c, prec); _acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec); acb_poly_clear(s); acb_poly_clear(u); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(aa + 0); acb_poly_clear(aa + 1); acb_poly_clear(aa + 2); arb_clear(c); } void acb_hypgeom_u_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec) { if (acb_is_int(b)) { acb_poly_t aa, bb, zz; acb_poly_init(aa); acb_poly_init(bb); acb_poly_init(zz); acb_poly_set_acb(aa, a); acb_poly_set_coeff_acb(bb, 0, b); acb_poly_set_coeff_si(bb, 1, 1); acb_poly_set_acb(zz, z); acb_hypgeom_u_1f1_series(zz, aa, bb, zz, 1, prec); acb_poly_get_coeff_acb(res, zz, 0); acb_poly_clear(aa); acb_poly_clear(bb); acb_poly_clear(zz); } else { acb_t t, u, v; acb_struct aa[3]; acb_init(t); acb_init(u); acb_init(v); acb_init(aa + 0); acb_init(aa + 1); acb_init(aa + 2); acb_set(aa, a); acb_set(aa + 1, b); acb_one(aa + 2); acb_hypgeom_pfq_direct(u, aa, 1, aa + 1, 2, z, -1, prec); acb_sub(aa, a, b, prec); acb_add_ui(aa, aa, 1, prec); acb_sub_ui(aa + 1, b, 2, prec); acb_neg(aa + 1, aa + 1); acb_hypgeom_pfq_direct(v, aa, 1, aa + 1, 2, z, -1, prec); acb_sub_ui(aa + 1, b, 1, prec); /* rgamma(a-b+1) * gamma(1-b) * u */ acb_rgamma(t, aa, prec); acb_mul(u, u, t, prec); acb_neg(t, aa + 1); acb_gamma(t, t, prec); acb_mul(u, u, t, prec); /* rgamma(a) * gamma(b-1) * z^(1-b) * v */ acb_rgamma(t, a, prec); acb_mul(v, v, t, prec); acb_gamma(t, aa + 1, prec); acb_mul(v, v, t, prec); acb_neg(t, aa + 1); acb_pow(t, z, t, prec); acb_mul(v, v, t, prec); acb_add(res, u, v, prec); acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(aa + 0); acb_clear(aa + 1); acb_clear(aa + 2); } } void acb_hypgeom_u(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec) { acb_t t; acb_init(t); acb_sub(t, a, b, prec); acb_add_ui(t, t, 1, prec); if ((acb_is_int(a) && arf_sgn(arb_midref(acb_realref(a))) <= 0) || (acb_is_int(t) && arf_sgn(arb_midref(acb_realref(t))) <= 0) || acb_hypgeom_u_use_asymp(z, prec)) { acb_neg(t, a); acb_pow(t, z, t, prec); acb_hypgeom_u_asymp(res, a, b, z, -1, prec); acb_mul(res, res, t, prec); } else { acb_hypgeom_u_1f1(res, a, b, z, prec); } acb_clear(t); } arb-2.8.1/acb_hypgeom/u_asymp.c000066400000000000000000000164251264125401100163700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" /* computes the factors that are independent of n (all are upper bounds) */ void acb_hypgeom_u_asymp_bound_factors(int * R, mag_t alpha, mag_t nu, mag_t sigma, mag_t rho, mag_t zinv, const acb_t a, const acb_t b, const acb_t z) { mag_t r, u, zre, zim, zlo, sigma_prime; acb_t t; mag_init(r); mag_init(u); mag_init(zre); mag_init(zim); mag_init(zlo); mag_init(sigma_prime); acb_init(t); /* lower bounds for |re(z)|, |im(z)|, |z| */ arb_get_mag_lower(zre, acb_realref(z)); arb_get_mag_lower(zim, acb_imagref(z)); acb_get_mag_lower(zlo, z); /* todo: hypot */ /* upper bound for 1/|z| */ mag_one(u); mag_div(zinv, u, zlo); /* upper bound for r = |b - 2a| */ acb_mul_2exp_si(t, a, 1); acb_sub(t, b, t, MAG_BITS); acb_get_mag(r, t); /* determine region */ *R = 0; if (mag_cmp(zlo, r) >= 0) { int znonneg = arb_is_nonnegative(acb_realref(z)); if (znonneg && mag_cmp(zre, r) >= 0) { *R = 1; } else if (mag_cmp(zim, r) >= 0 || znonneg) { *R = 2; } else { mag_mul_2exp_si(u, r, 1); if (mag_cmp(zlo, u) >= 0) *R = 3; } } if (R == 0) { mag_inf(alpha); mag_inf(nu); mag_inf(sigma); mag_inf(rho); } else { /* sigma = |(b-2a)/z| */ mag_mul(sigma, r, zinv); /* nu = (1/2 + 1/2 sqrt(1-4 sigma^2))^(-1/2) <= 1 + 2 sigma^2 */ if (mag_cmp_2exp_si(sigma, -1) <= 0) { mag_mul(nu, sigma, sigma); mag_mul_2exp_si(nu, nu, 1); mag_one(u); mag_add(nu, nu, u); } else { mag_inf(nu); } /* modified sigma for alpha, beta, rho when in R3 */ if (*R == 3) mag_mul(sigma_prime, sigma, nu); else mag_set(sigma_prime, sigma); /* alpha = 1/(1-sigma') */ mag_one(alpha); mag_sub_lower(alpha, alpha, sigma_prime); mag_one(u); mag_div(alpha, u, alpha); /* rho = |2a^2-2ab+b|/2 + sigma'*(1+sigma'/4)/(1-sigma')^2 */ mag_mul_2exp_si(rho, sigma_prime, -2); mag_one(u); mag_add(rho, rho, u); mag_mul(rho, rho, sigma_prime); mag_mul(rho, rho, alpha); mag_mul(rho, rho, alpha); acb_sub(t, a, b, MAG_BITS); acb_mul(t, t, a, MAG_BITS); acb_mul_2exp_si(t, t, 1); acb_add(t, t, b, MAG_BITS); acb_get_mag(u, t); mag_mul_2exp_si(u, u, -1); mag_add(rho, rho, u); } mag_clear(r); mag_clear(u); mag_clear(zre); mag_clear(zim); mag_clear(zlo); mag_clear(sigma_prime); acb_clear(t); } void acb_hypgeom_mag_chi(mag_t chi, ulong n) { mag_t p, q; ulong k; mag_init(p); mag_init(q); if (n % 2 == 0) { mag_one(p); mag_one(q); } else { /* upper bound for pi/2 */ mag_set_ui_2exp_si(p, 843314857, -28); mag_one(q); } for (k = n; k >= 2; k -= 2) { mag_mul_ui(p, p, k); mag_mul_ui_lower(q, q, k - 1); } mag_div(chi, p, q); mag_clear(p); mag_clear(q); } void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong n, slong prec) { mag_t C1, Cn, alpha, nu, sigma, rho, zinv, tmp, err; acb_struct aa[3]; acb_t s, t, w, winv; int R, p, q, is_real; if (!acb_is_finite(a) || !acb_is_finite(b) || !acb_is_finite(z)) { acb_indeterminate(res); return; } mag_init(C1); mag_init(Cn); mag_init(alpha); mag_init(nu); mag_init(sigma); mag_init(rho); mag_init(zinv); mag_init(tmp); mag_init(err); acb_init(aa); acb_init(aa + 1); acb_init(aa + 2); acb_init(s); acb_init(t); acb_init(w); acb_init(winv); /* special case, for incomplete gamma [todo: also when they happen to be exact and with difference 1...] */ if (a == b) { acb_set(aa, a); p = 1; q = 0; } else { acb_set(aa, a); acb_sub(aa + 1, a, b, prec); acb_add_ui(aa + 1, aa + 1, 1, prec); acb_one(aa + 2); p = 2; q = 1; } is_real = acb_is_real(a) && acb_is_real(b) && acb_is_real(z) && arb_is_positive(acb_realref(z)); acb_neg(w, z); acb_inv(w, w, prec); acb_neg(winv, z); if (n < 0) n = acb_hypgeom_pfq_choose_n(aa, p, aa + p, q, w, prec); /* todo: handle the exact polynomial case better... */ acb_hypgeom_u_asymp_bound_factors(&R, alpha, nu, sigma, rho, zinv, a, b, z); if (R == 0) { acb_indeterminate(res); } else { acb_hypgeom_pfq_sum_invz(s, t, aa, p, aa + p, q, w, winv, n, prec); if (R == 1) { mag_one(C1); mag_one(Cn); } else { acb_hypgeom_mag_chi(C1, 1); acb_hypgeom_mag_chi(Cn, n); if (R == 3) { mag_mul(tmp, nu, nu); mag_mul(tmp, tmp, sigma); mag_add(C1, C1, tmp); mag_mul(C1, C1, nu); mag_mul_ui(tmp, tmp, n); mag_add(Cn, Cn, tmp); mag_pow_ui(tmp, nu, n); mag_mul(Cn, Cn, tmp); } } mag_mul(tmp, C1, rho); mag_mul(tmp, tmp, alpha); mag_mul(tmp, tmp, zinv); mag_mul_2exp_si(tmp, tmp, 1); mag_exp(err, tmp); mag_mul(err, err, Cn); mag_mul(err, err, alpha); mag_mul_2exp_si(err, err, 1); /* nth term * factor */ acb_get_mag(tmp, t); mag_mul(err, err, tmp); if (is_real) arb_add_error_mag(acb_realref(s), err); else acb_add_error_mag(s, err); acb_set(res, s); } mag_clear(C1); mag_clear(Cn); mag_clear(alpha); mag_clear(nu); mag_clear(sigma); mag_clear(rho); mag_clear(zinv); mag_clear(tmp); mag_clear(err); acb_clear(aa); acb_clear(aa + 1); acb_clear(aa + 2); acb_clear(s); acb_clear(t); acb_clear(w); acb_clear(winv); } arb-2.8.1/acb_hypgeom/u_use_asymp.c000066400000000000000000000032511264125401100172350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_hypgeom.h" int acb_hypgeom_u_use_asymp(const acb_t z, slong prec) { double x, y; if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 0) < 0 && arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0)) { return 0; } if ((arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 64) > 0 || arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 64) > 0)) { return 1; } x = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN); y = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN); return sqrt(x * x + y * y) > prec * 0.69314718055994530942; } arb-2.8.1/acb_mat.h000066400000000000000000000214651264125401100140310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef ACB_MAT_H #define ACB_MAT_H #ifdef ACB_MAT_INLINES_C #define ACB_MAT_INLINE #else #define ACB_MAT_INLINE static __inline__ #endif #include "arb.h" #include "acb.h" #include "fmpz_mat.h" #include "fmpq_mat.h" #include "arb_mat.h" #include "acb_poly.h" #ifdef __cplusplus extern "C" { #endif typedef struct { acb_ptr entries; slong r; slong c; acb_ptr * rows; } acb_mat_struct; typedef acb_mat_struct acb_mat_t[1]; #define acb_mat_entry(mat,i,j) ((mat)->rows[i] + (j)) #define acb_mat_nrows(mat) ((mat)->r) #define acb_mat_ncols(mat) ((mat)->c) ACB_MAT_INLINE acb_ptr acb_mat_entry_ptr(acb_mat_t mat, slong i, slong j) { return acb_mat_entry(mat, i, j); } /* Memory management */ void acb_mat_init(acb_mat_t mat, slong r, slong c); void acb_mat_clear(acb_mat_t mat); ACB_MAT_INLINE void acb_mat_swap(acb_mat_t mat1, acb_mat_t mat2) { acb_mat_struct t = *mat1; *mat1 = *mat2; *mat2 = t; } /* Conversions */ void acb_mat_set(acb_mat_t dest, const acb_mat_t src); void acb_mat_set_fmpz_mat(acb_mat_t dest, const fmpz_mat_t src); void acb_mat_set_round_fmpz_mat(acb_mat_t dest, const fmpz_mat_t src, slong prec); void acb_mat_set_fmpq_mat(acb_mat_t dest, const fmpq_mat_t src, slong prec); void acb_mat_set_arb_mat(acb_mat_t dest, const arb_mat_t src); void acb_mat_set_round_arb_mat(acb_mat_t dest, const arb_mat_t src, slong prec); /* Random generation */ void acb_mat_randtest(acb_mat_t mat, flint_rand_t state, slong prec, slong mag_bits); /* I/O */ void acb_mat_printd(const acb_mat_t mat, slong digits); /* Comparisons */ int acb_mat_eq(const acb_mat_t mat1, const acb_mat_t mat2); int acb_mat_ne(const acb_mat_t mat1, const acb_mat_t mat2); int acb_mat_equal(const acb_mat_t mat1, const acb_mat_t mat2); int acb_mat_overlaps(const acb_mat_t mat1, const acb_mat_t mat2); int acb_mat_contains(const acb_mat_t mat1, const acb_mat_t mat2); int acb_mat_contains_fmpq_mat(const acb_mat_t mat1, const fmpq_mat_t mat2); int acb_mat_contains_fmpz_mat(const acb_mat_t mat1, const fmpz_mat_t mat2); int acb_mat_is_real(const acb_mat_t mat); /* Special matrices */ void acb_mat_zero(acb_mat_t mat); void acb_mat_one(acb_mat_t mat); void acb_mat_transpose(acb_mat_t mat1, const acb_mat_t mat2); /* Norms */ void acb_mat_bound_inf_norm(mag_t b, const acb_mat_t A); /* Arithmetic */ void acb_mat_neg(acb_mat_t dest, const acb_mat_t src); void acb_mat_add(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec); void acb_mat_sub(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec); void acb_mat_mul(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec); void acb_mat_sqr(acb_mat_t res, const acb_mat_t mat, slong prec); void acb_mat_pow_ui(acb_mat_t B, const acb_mat_t A, ulong exp, slong prec); /* Scalar arithmetic */ ACB_MAT_INLINE void acb_mat_scalar_mul_2exp_si(acb_mat_t B, const acb_mat_t A, slong c) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_mul_2exp_si(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c); } ACB_MAT_INLINE void acb_mat_scalar_addmul_si(acb_mat_t B, const acb_mat_t A, slong c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_addmul_si(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_mul_si(acb_mat_t B, const acb_mat_t A, slong c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_mul_si(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_div_si(acb_mat_t B, const acb_mat_t A, slong c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_div_si(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_addmul_fmpz(acb_mat_t B, const acb_mat_t A, const fmpz_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_addmul_fmpz(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_mul_fmpz(acb_mat_t B, const acb_mat_t A, const fmpz_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_mul_fmpz(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_div_fmpz(acb_mat_t B, const acb_mat_t A, const fmpz_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_div_fmpz(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_addmul_acb(acb_mat_t B, const acb_mat_t A, const acb_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_addmul(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_mul_acb(acb_mat_t B, const acb_mat_t A, const acb_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_mul(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_div_acb(acb_mat_t B, const acb_mat_t A, const acb_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_div(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_addmul_arb(acb_mat_t B, const acb_mat_t A, const arb_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_addmul_arb(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_mul_arb(acb_mat_t B, const acb_mat_t A, const arb_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_mul_arb(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } ACB_MAT_INLINE void acb_mat_scalar_div_arb(acb_mat_t B, const acb_mat_t A, const arb_t c, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(A); i++) for (j = 0; j < acb_mat_ncols(A); j++) acb_div_arb(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), c, prec); } /* Solving */ ACB_MAT_INLINE void acb_mat_swap_rows(acb_mat_t mat, slong * perm, slong r, slong s) { if (r != s) { acb_ptr u; slong t; if (perm != NULL) { t = perm[s]; perm[s] = perm[r]; perm[r] = t; } u = mat->rows[s]; mat->rows[s] = mat->rows[r]; mat->rows[r] = u; } } slong acb_mat_find_pivot_partial(const acb_mat_t mat, slong start_row, slong end_row, slong c); int acb_mat_lu(slong * P, acb_mat_t LU, const acb_mat_t A, slong prec); void acb_mat_solve_lu_precomp(acb_mat_t X, const slong * perm, const acb_mat_t A, const acb_mat_t B, slong prec); int acb_mat_solve(acb_mat_t X, const acb_mat_t A, const acb_mat_t B, slong prec); int acb_mat_inv(acb_mat_t X, const acb_mat_t A, slong prec); void acb_mat_det(acb_t det, const acb_mat_t A, slong prec); /* Special functions */ void acb_mat_exp(acb_mat_t B, const acb_mat_t A, slong prec); void _acb_mat_charpoly(acb_ptr cp, const acb_mat_t mat, slong prec); void acb_mat_charpoly(acb_poly_t cp, const acb_mat_t mat, slong prec); void acb_mat_trace(acb_t trace, const acb_mat_t mat, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/acb_mat/000077500000000000000000000000001264125401100136505ustar00rootroot00000000000000arb-2.8.1/acb_mat/add.c000066400000000000000000000026661264125401100145560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_add(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) acb_add(acb_mat_entry(res, i, j), acb_mat_entry(mat1, i, j), acb_mat_entry(mat2, i, j), prec); } arb-2.8.1/acb_mat/bound_inf_norm.c000066400000000000000000000031241264125401100170120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_bound_inf_norm(mag_t b, const acb_mat_t A) { slong i, j, r, c; mag_t s, t; r = acb_mat_nrows(A); c = acb_mat_ncols(A); mag_zero(b); if (r == 0 || c == 0) return; mag_init(s); mag_init(t); for (i = 0; i < r; i++) { mag_zero(s); for (j = 0; j < c; j++) { acb_get_mag(t, acb_mat_entry(A, i, j)); mag_add(s, s, t); } mag_max(b, b, s); } mag_clear(s); mag_clear(t); } arb-2.8.1/acb_mat/charpoly.c000066400000000000000000000061641264125401100156440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Sebastian Pancratz ******************************************************************************/ #include "acb_mat.h" void _acb_mat_charpoly(acb_ptr cp, const acb_mat_t mat, slong prec) { const slong n = mat->r; if (n == 0) { acb_one(cp); } else if (n == 1) { acb_neg(cp + 0, acb_mat_entry(mat, 0, 0)); acb_one(cp + 1); } else { slong i, j, k, t; acb_ptr a, A, s; a = _acb_vec_init(n * n); A = a + (n - 1) * n; _acb_vec_zero(cp, n + 1); acb_neg(cp + 0, acb_mat_entry(mat, 0, 0)); for (t = 1; t < n; t++) { for (i = 0; i <= t; i++) { acb_set(a + 0 * n + i, acb_mat_entry(mat, i, t)); } acb_set(A + 0, acb_mat_entry(mat, t, t)); for (k = 1; k < t; k++) { for (i = 0; i <= t; i++) { s = a + k * n + i; acb_zero(s); for (j = 0; j <= t; j++) acb_addmul(s, acb_mat_entry(mat, i, j), a + (k - 1) * n + j, prec); } acb_set(A + k, a + k * n + t); } acb_zero(A + t); for (j = 0; j <= t; j++) acb_addmul(A + t, acb_mat_entry(mat, t, j), a + (t - 1) * n + j, prec); for (k = 0; k <= t; k++) { for (j = 0; j < k; j++) acb_submul(cp + k, A + j, cp + (k - j - 1), prec); acb_sub(cp + k, cp + k, A + k, prec); } } /* Shift all coefficients up by one */ for (i = n; i > 0; i--) acb_swap(cp + i, cp + (i - 1)); acb_one(cp + 0); _acb_poly_reverse(cp, cp, n + 1, n + 1); _acb_vec_clear(a, n * n); } } void acb_mat_charpoly(acb_poly_t cp, const acb_mat_t mat, slong prec) { if (mat->r != mat->c) { flint_printf("Exception (acb_mat_charpoly). Non-square matrix.\n"); abort(); } acb_poly_fit_length(cp, mat->r + 1); _acb_poly_set_length(cp, mat->r + 1); _acb_mat_charpoly(cp->coeffs, mat, prec); } arb-2.8.1/acb_mat/clear.c000066400000000000000000000023741264125401100151100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_clear(acb_mat_t mat) { if (mat->entries != NULL) { _acb_vec_clear(mat->entries, mat->r * mat->c); flint_free(mat->rows); } } arb-2.8.1/acb_mat/contains.c000066400000000000000000000030131264125401100156270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_contains(const acb_mat_t mat1, const acb_mat_t mat2) { slong i, j; if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) || (acb_mat_ncols(mat1) != acb_mat_ncols(mat2))) return 0; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) if (!acb_contains(acb_mat_entry(mat1, i, j), acb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/acb_mat/contains_fmpq_mat.c000066400000000000000000000030531264125401100175170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_contains_fmpq_mat(const acb_mat_t mat1, const fmpq_mat_t mat2) { slong i, j; if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) || (acb_mat_ncols(mat1) != acb_mat_ncols(mat2))) return 0; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) if (!acb_contains_fmpq(acb_mat_entry(mat1, i, j), fmpq_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/acb_mat/contains_fmpz_mat.c000066400000000000000000000030531264125401100175300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_contains_fmpz_mat(const acb_mat_t mat1, const fmpz_mat_t mat2) { slong i, j; if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) || (acb_mat_ncols(mat1) != acb_mat_ncols(mat2))) return 0; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) if (!acb_contains_fmpz(acb_mat_entry(mat1, i, j), fmpz_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/acb_mat/det.c000066400000000000000000000103271264125401100145730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" slong acb_mat_gauss_partial(acb_mat_t A, slong prec) { acb_t e; acb_ptr * a; slong j, m, n, r, rank, row, col, sign; m = A->r; n = A->c; a = A->rows; rank = row = col = 0; sign = 1; acb_init(e); while (row < m && col < n) { r = acb_mat_find_pivot_partial(A, row, m, col); if (r == -1) { break; } else if (r != row) { acb_mat_swap_rows(A, NULL, row, r); sign *= -1; } rank++; for (j = row + 1; j < m; j++) { acb_div(e, a[j] + col, a[row] + col, prec); acb_neg(e, e); _acb_vec_scalar_addmul(a[j] + col + 1, a[row] + col + 1, n - col - 1, e, prec); } row++; col++; } acb_clear(e); return rank * sign; } void acb_vec_get_arf_2norm_squared_bound(arf_t s, acb_srcptr vec, slong len, slong prec) { slong i; arf_t t; arf_init(t); arf_zero(s); for (i = 0; i < len; i++) { arb_get_abs_ubound_arf(t, acb_realref(vec + i), prec); arf_addmul(s, t, t, prec, ARF_RND_UP); arb_get_abs_ubound_arf(t, acb_imagref(vec + i), prec); arf_addmul(s, t, t, prec, ARF_RND_UP); } arf_clear(t); } void acb_mat_det_inplace(acb_t det, acb_mat_t A, slong prec) { slong i, n, sign, rank; int is_real; n = acb_mat_nrows(A); rank = acb_mat_gauss_partial(A, prec); sign = (rank < 0) ? -1 : 1; rank = FLINT_ABS(rank); acb_set_si(det, sign); for (i = 0; i < rank; i++) acb_mul(det, det, acb_mat_entry(A, i, i), prec); /* bound unreduced part using Hadamard's inequality */ if (rank < n) { arf_t t; arf_t d; acb_t e; arf_init(t); arf_init(d); acb_init(e); arf_one(d); is_real = acb_mat_is_real(A); for (i = rank; i < n; i++) { acb_vec_get_arf_2norm_squared_bound(t, A->rows[i] + rank, n - rank, MAG_BITS); arf_mul(d, d, t, MAG_BITS, ARF_RND_UP); } /* now d contains the absolute value of the determinant */ arf_sqrt(d, d, MAG_BITS, ARF_RND_UP); /* multiply by disc with radius d */ if (is_real) { arb_add_error_arf(acb_realref(e), d); } else { arb_add_error_arf(acb_realref(e), d); arb_add_error_arf(acb_imagref(e), d); } acb_mul(det, det, e, prec); acb_clear(e); arf_clear(d); arf_clear(t); } } void acb_mat_det(acb_t det, const acb_mat_t A, slong prec) { slong n = acb_mat_nrows(A); if (n == 0) { acb_one(det); } else if (n == 1) { acb_set(det, acb_mat_entry(A, 0, 0)); } else if (n == 2) { acb_mul(det, acb_mat_entry(A, 0, 0), acb_mat_entry(A, 1, 1), prec); acb_submul(det, acb_mat_entry(A, 0, 1), acb_mat_entry(A, 1, 0), prec); } else { acb_mat_t T; acb_mat_init(T, acb_mat_nrows(A), acb_mat_ncols(A)); acb_mat_set(T, A); acb_mat_det_inplace(det, T, prec); acb_mat_clear(T); } } arb-2.8.1/acb_mat/eq.c000066400000000000000000000030131264125401100144160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "acb_mat.h" int acb_mat_eq(const acb_mat_t mat1, const acb_mat_t mat2) { slong i, j; if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) || (acb_mat_ncols(mat1) != acb_mat_ncols(mat2))) return 0; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) if (!acb_eq(acb_mat_entry(mat1, i, j), acb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/acb_mat/equal.c000066400000000000000000000030251264125401100151230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_equal(const acb_mat_t mat1, const acb_mat_t mat2) { slong i, j; if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) || (acb_mat_ncols(mat1) != acb_mat_ncols(mat2))) return 0; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) if (!acb_equal(acb_mat_entry(mat1, i, j), acb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/acb_mat/exp.c000066400000000000000000000124631264125401100146160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "double_extras.h" #include "acb_mat.h" slong _arb_mat_exp_choose_N(const mag_t norm, slong prec); /* evaluates the truncated Taylor series (assumes no aliasing) */ void _acb_mat_exp_taylor(acb_mat_t S, const acb_mat_t A, slong N, slong prec) { if (N == 1) { acb_mat_one(S); } else if (N == 2) { acb_mat_one(S); acb_mat_add(S, S, A, prec); } else if (N == 3) { acb_mat_t T; acb_mat_init(T, acb_mat_nrows(A), acb_mat_nrows(A)); acb_mat_sqr(T, A, prec); acb_mat_scalar_mul_2exp_si(T, T, -1); acb_mat_add(S, A, T, prec); acb_mat_one(T); acb_mat_add(S, S, T, prec); acb_mat_clear(T); } else { slong i, lo, hi, m, w, dim; acb_mat_struct * pows; acb_mat_t T, U; fmpz_t c, f; dim = acb_mat_nrows(A); m = n_sqrt(N); w = (N + m - 1) / m; fmpz_init(c); fmpz_init(f); pows = flint_malloc(sizeof(acb_mat_t) * (m + 1)); acb_mat_init(T, dim, dim); acb_mat_init(U, dim, dim); for (i = 0; i <= m; i++) { acb_mat_init(pows + i, dim, dim); if (i == 0) acb_mat_one(pows + i); else if (i == 1) acb_mat_set(pows + i, A); else acb_mat_mul(pows + i, pows + i - 1, A, prec); } acb_mat_zero(S); fmpz_one(f); for (i = w - 1; i >= 0; i--) { lo = i * m; hi = FLINT_MIN(N - 1, lo + m - 1); acb_mat_zero(T); fmpz_one(c); while (hi >= lo) { acb_mat_scalar_addmul_fmpz(T, pows + hi - lo, c, prec); if (hi != 0) fmpz_mul_ui(c, c, hi); hi--; } acb_mat_mul(U, pows + m, S, prec); acb_mat_scalar_mul_fmpz(S, T, f, prec); acb_mat_add(S, S, U, prec); fmpz_mul(f, f, c); } acb_mat_scalar_div_fmpz(S, S, f, prec); fmpz_clear(c); fmpz_clear(f); for (i = 0; i <= m; i++) acb_mat_clear(pows + i); flint_free(pows); acb_mat_clear(T); acb_mat_clear(U); } } void acb_mat_exp(acb_mat_t B, const acb_mat_t A, slong prec) { slong i, j, dim, wp, N, q, r; mag_t norm, err; acb_mat_t T; int is_real; dim = acb_mat_nrows(A); if (dim != acb_mat_ncols(A)) { flint_printf("acb_mat_exp: a square matrix is required!\n"); abort(); } if (dim == 0) { return; } else if (dim == 1) { acb_exp(acb_mat_entry(B, 0, 0), acb_mat_entry(A, 0, 0), prec); return; } is_real = acb_mat_is_real(A); wp = prec + 3 * FLINT_BIT_COUNT(prec); mag_init(norm); mag_init(err); acb_mat_init(T, dim, dim); acb_mat_bound_inf_norm(norm, A); if (mag_is_zero(norm)) { acb_mat_one(B); } else { q = pow(wp, 0.25); /* wanted magnitude */ if (mag_cmp_2exp_si(norm, 2 * wp) > 0) /* too big */ r = 2 * wp; else if (mag_cmp_2exp_si(norm, -q) < 0) /* tiny, no need to reduce */ r = 0; else r = FLINT_MAX(0, q + MAG_EXP(norm)); /* reduce to magnitude 2^(-r) */ acb_mat_scalar_mul_2exp_si(T, A, -r); mag_mul_2exp_si(norm, norm, -r); N = _arb_mat_exp_choose_N(norm, wp); mag_exp_tail(err, norm, N); _acb_mat_exp_taylor(B, T, N, wp); if (is_real) { for (i = 0; i < dim; i++) for (j = 0; j < dim; j++) arb_add_error_mag(acb_realref(acb_mat_entry(B, i, j)), err); } else { for (i = 0; i < dim; i++) for (j = 0; j < dim; j++) acb_add_error_mag(acb_mat_entry(B, i, j), err); } for (i = 0; i < r; i++) { acb_mat_sqr(T, B, wp); acb_mat_swap(T, B); } for (i = 0; i < dim; i++) for (j = 0; j < dim; j++) acb_set_round(acb_mat_entry(B, i, j), acb_mat_entry(B, i, j), prec); } mag_clear(norm); mag_clear(err); acb_mat_clear(T); } arb-2.8.1/acb_mat/find_pivot_partial.c000066400000000000000000000042541264125401100176760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_cmpabs_approx(const acb_t x, const acb_t y) { const arf_struct *xm, *ym; if (arf_cmpabs(arb_midref(acb_realref(x)), arb_midref(acb_imagref(x))) >= 0) xm = arb_midref(acb_realref(x)); else xm = arb_midref(acb_imagref(x)); if (arf_cmpabs(arb_midref(acb_realref(y)), arb_midref(acb_imagref(y))) >= 0) ym = arb_midref(acb_realref(y)); else ym = arb_midref(acb_imagref(y)); return arf_cmpabs(xm, ym); } slong acb_mat_find_pivot_partial(const acb_mat_t mat, slong start_row, slong end_row, slong c) { slong best_row, i; best_row = -1; for (i = start_row; i < end_row; i++) { if (!acb_contains_zero(acb_mat_entry(mat, i, c))) { if (best_row == -1) { best_row = i; } /* todo: should take the radius into account */ else if (acb_cmpabs_approx(acb_mat_entry(mat, i, c), acb_mat_entry(mat, best_row, c)) > 0) { best_row = i; } } } return best_row; } arb-2.8.1/acb_mat/init.c000066400000000000000000000027161264125401100147650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_init(acb_mat_t mat, slong r, slong c) { if (r != 0 && c != 0) { slong i; mat->entries = _acb_vec_init(r * c); mat->rows = (acb_ptr *) flint_malloc(r * sizeof(acb_ptr)); for (i = 0; i < r; i++) mat->rows[i] = mat->entries + i * c; } else mat->entries = NULL; mat->r = r; mat->c = c; } arb-2.8.1/acb_mat/inlines.c000066400000000000000000000021601264125401100154540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define ACB_MAT_INLINES_C #include "acb_mat.h" arb-2.8.1/acb_mat/inv.c000066400000000000000000000026761264125401100146230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_inv(acb_mat_t X, const acb_mat_t A, slong prec) { if (X == A) { int r; acb_mat_t T; acb_mat_init(T, acb_mat_nrows(A), acb_mat_ncols(A)); r = acb_mat_inv(T, A, prec); acb_mat_swap(T, X); acb_mat_clear(T); return r; } acb_mat_one(X); return acb_mat_solve(X, A, X, prec); } arb-2.8.1/acb_mat/is_real.c000066400000000000000000000025231264125401100154340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_is_real(const acb_mat_t mat) { slong i, j; for (i = 0; i < acb_mat_nrows(mat); i++) for (j = 0; j < acb_mat_ncols(mat); j++) if (!acb_is_real(acb_mat_entry(mat, i, j))) return 0; return 1; } arb-2.8.1/acb_mat/lu.c000066400000000000000000000042451264125401100144410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_lu(slong * P, acb_mat_t LU, const acb_mat_t A, slong prec) { acb_t d, e; acb_ptr * a; slong i, j, m, n, r, row, col; int result; m = acb_mat_nrows(A); n = acb_mat_ncols(A); result = 1; if (m == 0 || n == 0) return result; acb_mat_set(LU, A); a = LU->rows; row = col = 0; for (i = 0; i < m; i++) P[i] = i; acb_init(d); acb_init(e); while (row < m && col < n) { r = acb_mat_find_pivot_partial(LU, row, m, col); if (r == -1) { result = 0; break; } else if (r != row) acb_mat_swap_rows(LU, P, row, r); acb_set(d, a[row] + col); for (j = row + 1; j < m; j++) { acb_div(e, a[j] + col, d, prec); acb_neg(e, e); _acb_vec_scalar_addmul(a[j] + col, a[row] + col, n - col, e, prec); acb_zero(a[j] + col); acb_neg(a[j] + row, e); } row++; col++; } acb_clear(d); acb_clear(e); return result; } arb-2.8.1/acb_mat/mul.c000066400000000000000000000043001264125401100146060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_mul(acb_mat_t C, const acb_mat_t A, const acb_mat_t B, slong prec) { slong ar, ac, br, bc, i, j, k; ar = acb_mat_nrows(A); ac = acb_mat_ncols(A); br = acb_mat_nrows(B); bc = acb_mat_ncols(B); if (ac != br || ar != acb_mat_nrows(C) || bc != acb_mat_ncols(C)) { flint_printf("acb_mat_mul: incompatible dimensions\n"); abort(); } if (br == 0) { acb_mat_zero(C); return; } if (A == C || B == C) { acb_mat_t T; acb_mat_init(T, ar, bc); acb_mat_mul(T, A, B, prec); acb_mat_swap(T, C); acb_mat_clear(T); return; } for (i = 0; i < ar; i++) { for (j = 0; j < bc; j++) { acb_mul(acb_mat_entry(C, i, j), acb_mat_entry(A, i, 0), acb_mat_entry(B, 0, j), prec); for (k = 1; k < br; k++) { acb_addmul(acb_mat_entry(C, i, j), acb_mat_entry(A, i, k), acb_mat_entry(B, k, j), prec); } } } } arb-2.8.1/acb_mat/ne.c000066400000000000000000000030121264125401100144120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "acb_mat.h" int acb_mat_ne(const acb_mat_t mat1, const acb_mat_t mat2) { slong i, j; if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) || (acb_mat_ncols(mat1) != acb_mat_ncols(mat2))) return 1; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) if (acb_ne(acb_mat_entry(mat1, i, j), acb_mat_entry(mat2, i, j))) return 1; return 0; } arb-2.8.1/acb_mat/neg.c000066400000000000000000000025311264125401100145660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_neg(acb_mat_t dest, const acb_mat_t src) { slong i, j; for (i = 0; i < acb_mat_nrows(src); i++) for (j = 0; j < acb_mat_ncols(src); j++) acb_neg(acb_mat_entry(dest, i, j), acb_mat_entry(src, i, j)); } arb-2.8.1/acb_mat/one.c000066400000000000000000000025711264125401100146020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_one(acb_mat_t mat) { slong i, j; for (i = 0; i < acb_mat_nrows(mat); i++) for (j = 0; j < acb_mat_ncols(mat); j++) if (i == j) acb_one(acb_mat_entry(mat, i, j)); else acb_zero(acb_mat_entry(mat, i, j)); } arb-2.8.1/acb_mat/overlaps.c000066400000000000000000000030131264125401100156440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_overlaps(const acb_mat_t mat1, const acb_mat_t mat2) { slong i, j; if ((acb_mat_nrows(mat1) != acb_mat_nrows(mat2)) || (acb_mat_ncols(mat1) != acb_mat_ncols(mat2))) return 0; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) if (!acb_overlaps(acb_mat_entry(mat1, i, j), acb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/acb_mat/pow_ui.c000066400000000000000000000041371264125401100153230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_pow_ui(acb_mat_t B, const acb_mat_t A, ulong exp, slong prec) { slong d = acb_mat_nrows(A); if (exp <= 2 || d <= 1) { if (exp == 0 || d == 0) { acb_mat_one(B); } else if (d == 1) { acb_pow_ui(acb_mat_entry(B, 0, 0), acb_mat_entry(A, 0, 0), exp, prec); } else if (exp == 1) { acb_mat_set(B, A); } else if (exp == 2) { acb_mat_sqr(B, A, prec); } } else { acb_mat_t T, U; slong i; acb_mat_init(T, d, d); acb_mat_set(T, A); acb_mat_init(U, d, d); for (i = ((slong) FLINT_BIT_COUNT(exp)) - 2; i >= 0; i--) { acb_mat_sqr(U, T, prec); if (exp & (WORD(1) << i)) acb_mat_mul(T, U, A, prec); else acb_mat_swap(T, U); } acb_mat_swap(B, T); acb_mat_clear(T); acb_mat_clear(U); } } arb-2.8.1/acb_mat/printd.c000066400000000000000000000027451264125401100153240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_printd(const acb_mat_t mat, slong digits) { slong i, j; for (i = 0; i < acb_mat_nrows(mat); i++) { flint_printf("["); for (j = 0; j < acb_mat_ncols(mat); j++) { acb_printd(acb_mat_entry(mat, i, j), digits); if (j < acb_mat_ncols(mat) - 1) flint_printf(", "); } flint_printf("]\n"); } } arb-2.8.1/acb_mat/randtest.c000066400000000000000000000031311264125401100156360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_randtest(acb_mat_t mat, flint_rand_t state, slong prec, slong mag_bits) { slong i, j; if (n_randint(state, 2)) for (i = 0; i < acb_mat_nrows(mat); i++) for (j = 0; j < acb_mat_ncols(mat); j++) acb_randtest(acb_mat_entry(mat, i, j), state, prec, mag_bits); else for (i = 0; i < acb_mat_nrows(mat); i++) for (j = 0; j < acb_mat_ncols(mat); j++) acb_randtest_precise(acb_mat_entry(mat, i, j), state, prec, mag_bits); } arb-2.8.1/acb_mat/set.c000066400000000000000000000026451264125401100146160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_set(acb_mat_t dest, const acb_mat_t src) { slong i, j; if (dest != src && acb_mat_ncols(src) != 0) { for (i = 0; i < acb_mat_nrows(src); i++) for (j = 0; j < acb_mat_ncols(src); j++) acb_set(acb_mat_entry(dest, i, j), acb_mat_entry(src, i, j)); } } arb-2.8.1/acb_mat/set_arb_mat.c000066400000000000000000000026411264125401100162770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "acb_mat.h" void acb_mat_set_arb_mat(acb_mat_t dest, const arb_mat_t src) { slong i, j; if (acb_mat_ncols(dest) != 0) { for (i = 0; i < acb_mat_nrows(dest); i++) for (j = 0; j < acb_mat_ncols(dest); j++) acb_set_arb(acb_mat_entry(dest, i, j), arb_mat_entry(src, i, j)); } } arb-2.8.1/acb_mat/set_fmpq_mat.c000066400000000000000000000026731264125401100165030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_set_fmpq_mat(acb_mat_t dest, const fmpq_mat_t src, slong prec) { slong i, j; if (acb_mat_ncols(dest) != 0) { for (i = 0; i < acb_mat_nrows(dest); i++) for (j = 0; j < acb_mat_ncols(dest); j++) acb_set_fmpq(acb_mat_entry(dest, i, j), fmpq_mat_entry(src, i, j), prec); } } arb-2.8.1/acb_mat/set_fmpz_mat.c000066400000000000000000000026511264125401100165100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_set_fmpz_mat(acb_mat_t dest, const fmpz_mat_t src) { slong i, j; if (acb_mat_ncols(dest) != 0) { for (i = 0; i < acb_mat_nrows(dest); i++) for (j = 0; j < acb_mat_ncols(dest); j++) acb_set_fmpz(acb_mat_entry(dest, i, j), fmpz_mat_entry(src, i, j)); } } arb-2.8.1/acb_mat/set_round_arb_mat.c000066400000000000000000000026771264125401100175170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "acb_mat.h" void acb_mat_set_round_arb_mat(acb_mat_t dest, const arb_mat_t src, slong prec) { slong i, j; if (acb_mat_ncols(dest) != 0) { for (i = 0; i < acb_mat_nrows(dest); i++) for (j = 0; j < acb_mat_ncols(dest); j++) acb_set_round_arb(acb_mat_entry(dest, i, j), arb_mat_entry(src, i, j), prec); } } arb-2.8.1/acb_mat/set_round_fmpz_mat.c000066400000000000000000000027031264125401100177150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "acb_mat.h" void acb_mat_set_round_fmpz_mat(acb_mat_t dest, const fmpz_mat_t src, slong prec) { slong i, j; if (acb_mat_ncols(dest) != 0) { for (i = 0; i < acb_mat_nrows(dest); i++) for (j = 0; j < acb_mat_ncols(dest); j++) acb_set_round_fmpz(acb_mat_entry(dest, i, j), fmpz_mat_entry(src, i, j), prec); } } arb-2.8.1/acb_mat/solve.c000066400000000000000000000030671264125401100151520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int acb_mat_solve(acb_mat_t X, const acb_mat_t A, const acb_mat_t B, slong prec) { int result; slong n, m, *perm; acb_mat_t LU; n = acb_mat_nrows(A); m = acb_mat_ncols(X); if (n == 0 || m == 0) return 1; perm = _perm_init(n); acb_mat_init(LU, n, n); result = acb_mat_lu(perm, LU, A, prec); if (result) acb_mat_solve_lu_precomp(X, perm, LU, B, prec); acb_mat_clear(LU); _perm_clear(perm); return result; } arb-2.8.1/acb_mat/solve_lu_precomp.c000066400000000000000000000050201264125401100173660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_solve_lu_precomp(acb_mat_t X, const slong * perm, const acb_mat_t A, const acb_mat_t B, slong prec) { slong i, j, c, n, m; n = acb_mat_nrows(X); m = acb_mat_ncols(X); if (X == B) { acb_ptr tmp = flint_malloc(sizeof(acb_struct) * n); for (c = 0; c < m; c++) { for (i = 0; i < n; i++) tmp[i] = B->rows[perm[i]][c]; for (i = 0; i < n; i++) X->rows[i][c] = tmp[i]; } flint_free(tmp); } else { for (c = 0; c < m; c++) { for (i = 0; i < n; i++) { acb_set(acb_mat_entry(X, i, c), acb_mat_entry(B, perm[i], c)); } } } for (c = 0; c < m; c++) { /* solve Ly = b */ for (i = 1; i < n; i++) { for (j = 0; j < i; j++) { acb_submul(acb_mat_entry(X, i, c), acb_mat_entry(A, i, j), acb_mat_entry(X, j, c), prec); } } /* solve Ux = y */ for (i = n - 1; i >= 0; i--) { for (j = i + 1; j < n; j++) { acb_submul(acb_mat_entry(X, i, c), acb_mat_entry(A, i, j), acb_mat_entry(X, j, c), prec); } acb_div(acb_mat_entry(X, i, c), acb_mat_entry(X, i, c), acb_mat_entry(A, i, i), prec); } } } arb-2.8.1/acb_mat/sqr.c000066400000000000000000000065221264125401100146260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "acb_mat.h" void acb_mat_sqr(acb_mat_t B, const acb_mat_t A, slong prec) { slong n, i, j, k; acb_t p, s; n = acb_mat_nrows(A); if (acb_mat_ncols(A) != n || acb_mat_nrows(B) != n || acb_mat_ncols(B) != n) { flint_printf("acb_mat_sqr: incompatible dimensions\n"); abort(); } if (n == 0) { acb_mat_zero(B); return; } if (n == 1) { acb_mul(acb_mat_entry(B, 0, 0), acb_mat_entry(A, 0, 0), acb_mat_entry(A, 0, 0), prec); return; } if (A == B) { acb_mat_t T; acb_mat_init(T, n, n); acb_mat_sqr(T, A, prec); acb_mat_swap(T, B); acb_mat_clear(T); return; } acb_init(p); acb_init(s); /* contribution of diagonal of A to diagonal of B */ for (i = 0; i < n; i++) { acb_mul(acb_mat_entry(B, i, i), acb_mat_entry(A, i, i), acb_mat_entry(A, i, i), prec); } for (i = 0; i < n; i++) { for (j = 0; j < i; j++) { /* contribution of off-diagonal of A to diagonal of B */ acb_mul(p, acb_mat_entry(A, i, j), acb_mat_entry(A, j, i), prec); acb_add(acb_mat_entry(B, i, i), acb_mat_entry(B, i, i), p, prec); acb_add(acb_mat_entry(B, j, j), acb_mat_entry(B, j, j), p, prec); /* contribution of diagonal of A to off-diagonal of B */ acb_add(s, acb_mat_entry(A, i, i), acb_mat_entry(A, j, j), prec); acb_mul(acb_mat_entry(B, i, j), acb_mat_entry(A, i, j), s, prec); acb_mul(acb_mat_entry(B, j, i), acb_mat_entry(A, j, i), s, prec); } } /* contribution of off-diagonal of A to off-diagonal of B */ if (n > 2) { for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { for (k = 0; k < n; k++) { if (i != j && j != k && k != i) { acb_addmul(acb_mat_entry(B, i, j), acb_mat_entry(A, i, k), acb_mat_entry(A, k, j), prec); } } } } } acb_clear(p); acb_clear(s); } arb-2.8.1/acb_mat/sub.c000066400000000000000000000026661264125401100146170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_sub(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec) { slong i, j; for (i = 0; i < acb_mat_nrows(mat1); i++) for (j = 0; j < acb_mat_ncols(mat1); j++) acb_sub(acb_mat_entry(res, i, j), acb_mat_entry(mat1, i, j), acb_mat_entry(mat2, i, j), prec); } arb-2.8.1/acb_mat/test/000077500000000000000000000000001264125401100146275ustar00rootroot00000000000000arb-2.8.1/acb_mat/test/t-charpoly.c000066400000000000000000000052321264125401100170570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int main(void) { slong iter; flint_rand_t state; flint_printf("charpoly...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_mat_t A, B, C, D; acb_poly_t f, g; slong m, n; m = n_randint(state, 8); n = m; acb_mat_init(A, m, n); acb_mat_init(B, m, n); acb_mat_init(C, m, m); acb_mat_init(D, n, n); acb_poly_init(f); acb_poly_init(g); acb_mat_randtest(A, state, 1 + n_randint(state, 1000), 10); acb_mat_randtest(B, state, 1 + n_randint(state, 1000), 10); acb_mat_mul(C, A, B, 2 + n_randint(state, 1000)); acb_mat_mul(D, B, A, 2 + n_randint(state, 1000)); acb_mat_charpoly(f, C, 2 + n_randint(state, 1000)); acb_mat_charpoly(g, D, 2 + n_randint(state, 1000)); if (!acb_poly_overlaps(f, g)) { flint_printf("FAIL: charpoly(AB) != charpoly(BA).\n"); flint_printf("Matrix A:\n"), acb_mat_printd(A, 15), flint_printf("\n"); flint_printf("Matrix B:\n"), acb_mat_printd(B, 15), flint_printf("\n"); flint_printf("cp(AB) = "), acb_poly_printd(f, 15), flint_printf("\n"); flint_printf("cp(BA) = "), acb_poly_printd(g, 15), flint_printf("\n"); abort(); } acb_mat_clear(A); acb_mat_clear(B); acb_mat_clear(C); acb_mat_clear(D); acb_poly_clear(f); acb_poly_clear(g); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/acb_mat/test/t-det.c000066400000000000000000000061111264125401100160070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("det...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q; fmpq_t Qdet; acb_mat_t A; acb_t Adet, imagunit; slong n, qbits, prec; int imaginary; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 200); imaginary = n_randint(state, 2); fmpq_mat_init(Q, n, n); fmpq_init(Qdet); acb_mat_init(A, n, n); acb_init(Adet); acb_init(imagunit); fmpq_mat_randtest(Q, state, qbits); fmpq_mat_det(Qdet, Q); acb_mat_set_fmpq_mat(A, Q, prec); if (imaginary) { acb_onei(imagunit); acb_mat_scalar_mul_acb(A, A, imagunit, prec); } acb_mat_det(Adet, A, prec); if (imaginary) { acb_onei(imagunit); acb_inv(imagunit, imagunit, prec); acb_pow_ui(imagunit, imagunit, n, prec); acb_mul(Adet, Adet, imagunit, prec); } if (!acb_contains_fmpq(Adet, Qdet)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("Qdet = \n"); fmpq_print(Qdet); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Adet = \n"); acb_printd(Adet, 15); flint_printf("\n\n"); flint_printf("Adet = \n"); acb_print(Adet); flint_printf("\n\n"); abort(); } fmpq_mat_clear(Q); fmpq_clear(Qdet); acb_mat_clear(A); acb_clear(Adet); acb_clear(imagunit); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-exp.c000066400000000000000000000061471264125401100160400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("exp...."); fflush(stdout); flint_randinit(state); /* check exp(A)*exp(c*A) = exp((1+c)*A) */ for (iter = 0; iter < 500; iter++) { acb_mat_t A, E, F, EF, G; fmpq_mat_t Q; acb_t c, d; slong n, qbits, prec; n = n_randint(state, 5); qbits = 2 + n_randint(state, 300); prec = 2 + n_randint(state, 300); acb_init(c); acb_init(d); fmpq_mat_init(Q, n, n); acb_mat_init(A, n, n); acb_mat_init(E, n, n); acb_mat_init(F, n, n); acb_mat_init(EF, n, n); acb_mat_init(G, n, n); fmpq_mat_randtest(Q, state, qbits); acb_mat_set_fmpq_mat(A, Q, prec); acb_mat_exp(E, A, prec); acb_randtest(c, state, prec, 10); acb_mat_scalar_mul_acb(F, A, c, prec); acb_mat_exp(F, F, prec); acb_add_ui(d, c, 1, prec); acb_mat_scalar_mul_acb(G, A, d, prec); acb_mat_exp(G, G, prec); acb_mat_mul(EF, E, F, prec); if (!acb_mat_overlaps(EF, G)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("c = \n"); acb_printd(c, 15); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("E = \n"); acb_mat_printd(E, 15); flint_printf("\n\n"); flint_printf("F = \n"); acb_mat_printd(F, 15); flint_printf("\n\n"); flint_printf("E*F = \n"); acb_mat_printd(EF, 15); flint_printf("\n\n"); flint_printf("G = \n"); acb_mat_printd(G, 15); flint_printf("\n\n"); abort(); } acb_clear(c); acb_clear(d); fmpq_mat_clear(Q); acb_mat_clear(A); acb_mat_clear(E); acb_mat_clear(F); acb_mat_clear(EF); acb_mat_clear(G); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-inv.c000066400000000000000000000106671264125401100160420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("inv...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q, Qinv; acb_mat_t A, Ainv; slong n, qbits, prec; int q_invertible, r_invertible, r_invertible2; n = n_randint(state, 8); qbits = 1 + n_randint(state, 30); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_mat_init(Qinv, n, n); acb_mat_init(A, n, n); acb_mat_init(Ainv, n, n); fmpq_mat_randtest(Q, state, qbits); q_invertible = fmpq_mat_inv(Qinv, Q); if (!q_invertible) { acb_mat_set_fmpq_mat(A, Q, prec); r_invertible = acb_mat_inv(Ainv, A, prec); if (r_invertible) { flint_printf("FAIL: matrix is singular over Q but not over R\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n"); abort(); } } else { /* now this must converge */ while (1) { acb_mat_set_fmpq_mat(A, Q, prec); r_invertible = acb_mat_inv(Ainv, A, prec); if (r_invertible) { break; } else { if (prec > 10000) { flint_printf("FAIL: failed to converge at 10000 bits\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); abort(); } prec *= 2; } } if (!acb_mat_contains_fmpq_mat(Ainv, Qinv)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("Qinv = \n"); fmpq_mat_print(Qinv); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n"); abort(); } /* test aliasing */ r_invertible2 = acb_mat_inv(A, A, prec); if (!acb_mat_equal(A, Ainv) || r_invertible != r_invertible2) { flint_printf("FAIL (aliasing)\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Ainv = \n"); acb_mat_printd(Ainv, 15); flint_printf("\n\n"); abort(); } } fmpq_mat_clear(Q); fmpq_mat_clear(Qinv); acb_mat_clear(A); acb_mat_clear(Ainv); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-lu.c000066400000000000000000000116201264125401100156540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int fmpq_mat_is_invertible(const fmpq_mat_t A) { int r; fmpq_t t; fmpq_init(t); fmpq_mat_det(t, A); r = !fmpq_is_zero(t); fmpq_clear(t); return r; } int main() { slong iter; flint_rand_t state; flint_printf("lu...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q; acb_mat_t A, LU, P, L, U, T; slong i, j, n, qbits, prec, *perm; int q_invertible, r_invertible; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 202); fmpq_mat_init(Q, n, n); acb_mat_init(A, n, n); acb_mat_init(LU, n, n); acb_mat_init(P, n, n); acb_mat_init(L, n, n); acb_mat_init(U, n, n); acb_mat_init(T, n, n); perm = _perm_init(n); fmpq_mat_randtest(Q, state, qbits); q_invertible = fmpq_mat_is_invertible(Q); if (!q_invertible) { acb_mat_set_fmpq_mat(A, Q, prec); r_invertible = acb_mat_lu(perm, LU, A, prec); if (r_invertible) { flint_printf("FAIL: matrix is singular over Q but not over R\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("LU = \n"); acb_mat_printd(LU, 15); flint_printf("\n\n"); } } else { /* now this must converge */ while (1) { acb_mat_set_fmpq_mat(A, Q, prec); r_invertible = acb_mat_lu(perm, LU, A, prec); if (r_invertible) { break; } else { if (prec > 10000) { flint_printf("FAIL: failed to converge at 10000 bits\n"); abort(); } prec *= 2; } } acb_mat_one(L); for (i = 0; i < n; i++) for (j = 0; j < i; j++) acb_set(acb_mat_entry(L, i, j), acb_mat_entry(LU, i, j)); for (i = 0; i < n; i++) for (j = i; j < n; j++) acb_set(acb_mat_entry(U, i, j), acb_mat_entry(LU, i, j)); for (i = 0; i < n; i++) acb_one(acb_mat_entry(P, perm[i], i)); acb_mat_mul(T, P, L, prec); acb_mat_mul(T, T, U, prec); if (!acb_mat_contains_fmpq_mat(T, Q)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("LU = \n"); acb_mat_printd(LU, 15); flint_printf("\n\n"); flint_printf("L = \n"); acb_mat_printd(L, 15); flint_printf("\n\n"); flint_printf("U = \n"); acb_mat_printd(U, 15); flint_printf("\n\n"); flint_printf("P*L*U = \n"); acb_mat_printd(T, 15); flint_printf("\n\n"); abort(); } } fmpq_mat_clear(Q); acb_mat_clear(A); acb_mat_clear(LU); acb_mat_clear(P); acb_mat_clear(L); acb_mat_clear(U); acb_mat_clear(T); _perm_clear(perm); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-mul.c000066400000000000000000000223711264125401100160360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void _acb_mat_init_randtest(acb_mat_t mat, slong r, slong c, flint_rand_t state) { acb_mat_init(mat, r, c); acb_mat_randtest(mat, state, 2 + n_randint(state, 200), 10); } void _acb_mat_nprintd(const char * name, acb_mat_t mat) { flint_printf("%s = ", name); acb_mat_printd(mat, 15); flint_printf("\n\n"); } int main() { slong iter; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, k, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_mat_t A, B, C; acb_mat_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); k = n_randint(state, 10); fmpq_mat_init(A, m, n); fmpq_mat_init(B, n, k); fmpq_mat_init(C, m, k); acb_mat_init(a, m, n); acb_mat_init(b, n, k); acb_mat_init(c, m, k); acb_mat_init(d, m, k); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_randtest(B, state, qbits2); fmpq_mat_mul(C, A, B); acb_mat_set_fmpq_mat(a, A, rbits1); acb_mat_set_fmpq_mat(b, B, rbits2); acb_mat_mul(c, a, b, rbits3); if (!acb_mat_contains_fmpq_mat(c, C)) { flint_printf("FAIL\n\n"); flint_printf("m = %wd, n = %wd, k = %wd, bits3 = %wd\n", m, n, k, rbits3); flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_mat_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_mat_printd(c, 15); flint_printf("\n\n"); abort(); } /* test aliasing with a */ if (acb_mat_nrows(a) == acb_mat_nrows(c) && acb_mat_ncols(a) == acb_mat_ncols(c)) { acb_mat_set(d, a); acb_mat_mul(d, d, b, rbits3); if (!acb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } } /* test aliasing with b */ if (acb_mat_nrows(b) == acb_mat_nrows(c) && acb_mat_ncols(b) == acb_mat_ncols(c)) { acb_mat_set(d, b); acb_mat_mul(d, a, d, rbits3); if (!acb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(C); acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); acb_mat_clear(d); } /* check algebraic properties like associativity and distributivity */ for (iter = 0; iter < 1000; iter++) { slong m, n, k, l; slong rbits; acb_mat_t a, b, c, d, ab, ac, bd, cd, s; rbits = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); k = n_randint(state, 10); l = n_randint(state, 10); _acb_mat_init_randtest(a, m, n, state); _acb_mat_init_randtest(b, n, k, state); _acb_mat_init_randtest(c, n, k, state); _acb_mat_init_randtest(d, k, l, state); acb_mat_init(ab, m, k); acb_mat_init(ac, m, k); acb_mat_init(bd, n, l); acb_mat_init(cd, n, l); acb_mat_init(s, n, k); acb_mat_mul(ab, a, b, rbits); acb_mat_mul(ac, a, c, rbits); acb_mat_mul(bd, b, d, rbits); acb_mat_mul(cd, c, d, rbits); acb_mat_add(s, b, c, rbits); /* check associativity of multiplication */ /* (A*B)*D = A*(B*D) */ { acb_mat_t lhs, rhs; acb_mat_init(lhs, m, l); acb_mat_init(rhs, m, l); acb_mat_mul(lhs, ab, d, rbits); acb_mat_mul(rhs, a, bd, rbits); if (!acb_mat_overlaps(lhs, rhs)) { flint_printf("FAIL\n\n"); flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("a", a); _acb_mat_nprintd("b", b); _acb_mat_nprintd("d", d); _acb_mat_nprintd("(a*b)*d", lhs); _acb_mat_nprintd("a*(b*d)", rhs); abort(); } acb_mat_clear(lhs); acb_mat_clear(rhs); } /* check left distributivity of multiplication over addition */ /* A*(B + C) = A*B + A*C */ { acb_mat_t lhs, rhs; acb_mat_init(lhs, m, k); acb_mat_init(rhs, m, k); acb_mat_mul(lhs, a, s, rbits); acb_mat_add(rhs, ab, ac, rbits); if (!acb_mat_overlaps(lhs, rhs)) { flint_printf("FAIL\n\n"); flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("a", a); _acb_mat_nprintd("b", b); _acb_mat_nprintd("c", c); _acb_mat_nprintd("a*(b + c)", lhs); _acb_mat_nprintd("a*b + b*c", rhs); abort(); } acb_mat_clear(lhs); acb_mat_clear(rhs); } /* check right distributivity of multiplication over addition */ /* (B + C)*D = B*D + C*D */ { acb_mat_t lhs, rhs; acb_mat_init(lhs, n, l); acb_mat_init(rhs, n, l); acb_mat_mul(lhs, s, d, rbits); acb_mat_add(rhs, bd, cd, rbits); if (!acb_mat_overlaps(lhs, rhs)) { flint_printf("FAIL\n\n"); flint_printf("m, n, k, l = %wd, %wd, %wd, %wd\n", m, n, k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("b", b); _acb_mat_nprintd("c", c); _acb_mat_nprintd("d", d); _acb_mat_nprintd("(b + c)*d", lhs); _acb_mat_nprintd("b*d + c*d", rhs); abort(); } acb_mat_clear(lhs); acb_mat_clear(rhs); } /* check left multiplicative identity I*D = D */ { acb_mat_t one, lhs; acb_mat_init(one, k, k); acb_mat_init(lhs, k, l); acb_mat_one(one); acb_mat_mul(lhs, one, d, rbits); if (!acb_mat_contains(lhs, d)) { flint_printf("FAIL\n\n"); flint_printf("k = %wd, l = %wd\n", k, l); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("identity * d", lhs); _acb_mat_nprintd("d", d); abort(); } acb_mat_clear(one); acb_mat_clear(lhs); } /* check right multiplicative identity A*I = A */ { acb_mat_t one, lhs; acb_mat_init(one, n, n); acb_mat_init(lhs, m, n); acb_mat_one(one); acb_mat_mul(lhs, a, one, rbits); if (!acb_mat_contains(lhs, a)) { flint_printf("FAIL\n\n"); flint_printf("m = %wd, n = %wd\n", m, n); flint_printf("rbits = %wd\n", rbits); _acb_mat_nprintd("a * identity", lhs); _acb_mat_nprintd("a", a); abort(); } acb_mat_clear(one); acb_mat_clear(lhs); } acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); acb_mat_clear(d); acb_mat_clear(ab); acb_mat_clear(ac); acb_mat_clear(bd); acb_mat_clear(cd); acb_mat_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-solve.c000066400000000000000000000122551264125401100163710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("solve...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q, QX, QB; acb_mat_t A, X, B; slong n, m, qbits, prec; int q_invertible, r_invertible, r_invertible2; n = n_randint(state, 8); m = n_randint(state, 8); qbits = 1 + n_randint(state, 30); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_mat_init(QX, n, m); fmpq_mat_init(QB, n, m); acb_mat_init(A, n, n); acb_mat_init(X, n, m); acb_mat_init(B, n, m); fmpq_mat_randtest(Q, state, qbits); fmpq_mat_randtest(QB, state, qbits); q_invertible = fmpq_mat_solve_fraction_free(QX, Q, QB); if (!q_invertible) { acb_mat_set_fmpq_mat(A, Q, prec); r_invertible = acb_mat_solve(X, A, B, prec); if (r_invertible) { flint_printf("FAIL: matrix is singular over Q but not over R\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n"); flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); abort(); } } else { /* now this must converge */ while (1) { acb_mat_set_fmpq_mat(A, Q, prec); acb_mat_set_fmpq_mat(B, QB, prec); r_invertible = acb_mat_solve(X, A, B, prec); if (r_invertible) { break; } else { if (prec > 10000) { flint_printf("FAIL: failed to converge at 10000 bits\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n"); flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); abort(); } prec *= 2; } } if (!acb_mat_contains_fmpq_mat(X, QX)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n"); flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("B = \n"); acb_mat_printd(B, 15); flint_printf("\n\n"); flint_printf("X = \n"); acb_mat_printd(X, 15); flint_printf("\n\n"); abort(); } /* test aliasing */ r_invertible2 = acb_mat_solve(B, A, B, prec); if (!acb_mat_equal(X, B) || r_invertible != r_invertible2) { flint_printf("FAIL (aliasing)\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("B = \n"); acb_mat_printd(B, 15); flint_printf("\n\n"); flint_printf("X = \n"); acb_mat_printd(X, 15); flint_printf("\n\n"); abort(); } } fmpq_mat_clear(Q); fmpq_mat_clear(QB); fmpq_mat_clear(QX); acb_mat_clear(A); acb_mat_clear(B); acb_mat_clear(X); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-sqr.c000066400000000000000000000054051264125401100160450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "acb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("sqr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong n, qbits1, rbits1, rbits2; fmpq_mat_t A, B; acb_mat_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = n_randint(state, 10); fmpq_mat_init(A, n, n); fmpq_mat_init(B, n, n); acb_mat_init(a, n, n); acb_mat_init(b, n, n); acb_mat_init(c, n, n); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_mul(B, A, A); acb_mat_set_fmpq_mat(a, A, rbits1); acb_mat_sqr(b, a, rbits2); if (!acb_mat_contains_fmpq_mat(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_mat_printd(b, 15); flint_printf("\n\n"); abort(); } /* test aliasing */ acb_mat_set(c, a); acb_mat_sqr(c, c, rbits2); if (!acb_mat_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-trace.c000066400000000000000000000104501264125401100163320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "acb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("trace...."); fflush(stdout); flint_randinit(state); /* check that the acb trace contains the fmpq trace */ for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q; fmpq_t Qtrace; acb_mat_t A; acb_t Atrace; slong n, qbits, prec; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_init(Qtrace); acb_mat_init(A, n, n); acb_init(Atrace); fmpq_mat_randtest(Q, state, qbits); fmpq_mat_trace(Qtrace, Q); acb_mat_set_fmpq_mat(A, Q, prec); acb_mat_trace(Atrace, A, prec); if (!acb_contains_fmpq(Atrace, Qtrace)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("Qtrace = \n"); fmpq_print(Qtrace); flint_printf("\n\n"); flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Atrace = \n"); acb_printd(Atrace, 15); flint_printf("\n\n"); flint_printf("Atrace = \n"); acb_print(Atrace); flint_printf("\n\n"); abort(); } fmpq_mat_clear(Q); fmpq_clear(Qtrace); acb_mat_clear(A); acb_clear(Atrace); } /* check trace(A*B) = trace(B*A) */ for (iter = 0; iter < 10000; iter++) { slong m, n, prec; acb_mat_t a, b, ab, ba; acb_t trab, trba; prec = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); acb_mat_init(a, m, n); acb_mat_init(b, n, m); acb_mat_init(ab, m, m); acb_mat_init(ba, n, n); acb_init(trab); acb_init(trba); acb_mat_randtest(a, state, 2 + n_randint(state, 100), 10); acb_mat_randtest(b, state, 2 + n_randint(state, 100), 10); acb_mat_mul(ab, a, b, prec); acb_mat_mul(ba, b, a, prec); acb_mat_trace(trab, ab, prec); acb_mat_trace(trba, ba, prec); if (!acb_overlaps(trab, trba)) { flint_printf("FAIL (overlap, iter = %wd)\n", iter); flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec); flint_printf("\n"); flint_printf("a = \n"); acb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = \n"); acb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("ab = \n"); acb_mat_printd(ab, 15); flint_printf("\n\n"); flint_printf("ba = \n"); acb_mat_printd(ba, 15); flint_printf("\n\n"); flint_printf("trace(ab) = \n"); acb_printd(trab, 15); flint_printf("\n\n"); flint_printf("trace(ba) = \n"); acb_printd(trba, 15); flint_printf("\n\n"); } acb_clear(trab); acb_clear(trba); acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(ab); acb_mat_clear(ba); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/test/t-transpose.c000066400000000000000000000045661264125401100172650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("transpose...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n; acb_mat_t a, b, c; m = n_randint(state, 10); n = n_randint(state, 10); acb_mat_init(a, m, n); acb_mat_init(b, n, m); acb_mat_init(c, m, n); acb_mat_randtest(a, state, 2 + n_randint(state, 100), 10); acb_mat_randtest(b, state, 2 + n_randint(state, 100), 10); acb_mat_randtest(c, state, 2 + n_randint(state, 100), 10); acb_mat_transpose(b, a); acb_mat_transpose(c, b); if (!acb_mat_equal(c, a)) { flint_printf("FAIL\n\n"); flint_printf("m = %wd, n = %wd\n", m, n); abort(); } if (acb_mat_nrows(a) == acb_mat_ncols(a)) { acb_mat_transpose(c, a); acb_mat_transpose(a, a); if (!acb_mat_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } } acb_mat_clear(a); acb_mat_clear(b); acb_mat_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_mat/trace.c000066400000000000000000000026561264125401100151230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "acb_mat.h" void acb_mat_trace(acb_t trace, const acb_mat_t mat, slong prec) { slong i, n = acb_mat_nrows(mat); if (n == 0) { acb_zero(trace); } else { acb_set(trace, acb_mat_entry(mat, 0, 0)); for (i = 1; i < n; i++) { acb_add(trace, trace, acb_mat_entry(mat, i, i), prec); } } } arb-2.8.1/acb_mat/transpose.c000066400000000000000000000037371264125401100160440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "acb_mat.h" void acb_mat_transpose(acb_mat_t B, const acb_mat_t A) { acb_struct tmp; slong i, j; if (acb_mat_nrows(B) != acb_mat_ncols(A) || acb_mat_ncols(B) != acb_mat_nrows(A)) { flint_printf("Exception (acb_mat_transpose). Incompatible dimensions.\n"); abort(); } if (A == B) /* In-place, guaranteed to be square */ { for (i = 0; i < acb_mat_nrows(A) - 1; i++) { for (j = i + 1; j < acb_mat_ncols(A); j++) { tmp = *acb_mat_entry(A, i, j); *acb_mat_entry(A, i, j) = *acb_mat_entry(A, j, i); *acb_mat_entry(A, j, i) = tmp; } } } else /* Not aliased; general case */ { for (i = 0; i < acb_mat_nrows(B); i++) for (j = 0; j < acb_mat_ncols(B); j++) acb_set(acb_mat_entry(B, i, j), acb_mat_entry(A, j, i)); } } arb-2.8.1/acb_mat/zero.c000066400000000000000000000024321264125401100147740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_mat.h" void acb_mat_zero(acb_mat_t mat) { slong i, j; for (i = 0; i < acb_mat_nrows(mat); i++) for (j = 0; j < acb_mat_ncols(mat); j++) acb_zero(acb_mat_entry(mat, i, j)); } arb-2.8.1/acb_modular.h000066400000000000000000000134031264125401100147040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #ifndef ACB_MODULAR_H #define ACB_MODULAR_H #include "acb.h" #ifdef __cplusplus extern "C" { #endif typedef struct { fmpz a; fmpz b; fmpz c; fmpz d; } psl2z_struct; typedef psl2z_struct psl2z_t[1]; static __inline__ void psl2z_init(psl2z_t g) { fmpz_init(&g->a); fmpz_init(&g->b); fmpz_init(&g->c); fmpz_init(&g->d); fmpz_one(&g->a); fmpz_one(&g->d); } static __inline__ void psl2z_clear(psl2z_t g) { fmpz_clear(&g->a); fmpz_clear(&g->b); fmpz_clear(&g->c); fmpz_clear(&g->d); } static __inline__ void psl2z_swap(psl2z_t f, psl2z_t g) { psl2z_struct h = *f; *f = *g; *g = h; } static __inline__ void psl2z_set(psl2z_t h, const psl2z_t g) { fmpz_set(&h->a, &g->a); fmpz_set(&h->b, &g->b); fmpz_set(&h->c, &g->c); fmpz_set(&h->d, &g->d); } static __inline__ void psl2z_one(psl2z_t g) { fmpz_one(&g->a); fmpz_zero(&g->b); fmpz_zero(&g->c); fmpz_one(&g->d); } static __inline__ void psl2z_print(const psl2z_t g) { flint_printf("["); fmpz_print(&g->a); flint_printf(" "); fmpz_print(&g->b); flint_printf("; "); fmpz_print(&g->c); flint_printf(" "); fmpz_print(&g->d); flint_printf("]"); } static __inline__ int psl2z_equal(const psl2z_t f, const psl2z_t g) { return fmpz_equal(&f->a, &g->a) && fmpz_equal(&f->b, &g->b) && fmpz_equal(&f->c, &g->c) && fmpz_equal(&f->d, &g->d); } void psl2z_mul(psl2z_t h, const psl2z_t f, const psl2z_t g); void psl2z_inv(psl2z_t h, const psl2z_t g); int psl2z_is_one(const psl2z_t g); int psl2z_is_correct(const psl2z_t g); void psl2z_randtest(psl2z_t g, flint_rand_t state, slong bits); void acb_modular_transform(acb_t w, const psl2z_t g, const acb_t z, slong prec); void acb_modular_fundamental_domain_approx_d(psl2z_t g, double x, double y, double one_minus_eps); void acb_modular_fundamental_domain_approx_arf(psl2z_t g, const arf_t xx, const arf_t yy, const arf_t one_minus_eps, slong prec); void acb_modular_fundamental_domain_approx(acb_t w, psl2z_t g, const acb_t z, const arf_t one_minus_eps, slong prec); int acb_modular_is_in_fundamental_domain(const acb_t z, const arf_t tol, slong prec); void acb_modular_addseq_theta(slong * exponents, slong * aindex, slong * bindex, slong num); void acb_modular_addseq_eta(slong * exponents, slong * aindex, slong * bindex, slong num); void acb_modular_fill_addseq(slong * tab, slong len); void acb_modular_theta_transform(int * R, int * S, int * C, const psl2z_t g); void acb_modular_theta_const_sum(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong prec); void acb_modular_theta_const_sum_basecase(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec); void acb_modular_theta_const_sum_rs(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec); void acb_modular_theta_sum(acb_ptr theta1, acb_ptr theta2, acb_ptr theta3, acb_ptr theta4, const acb_t w, int w_is_unit, const acb_t q, slong len, slong prec); void acb_modular_theta_notransform(acb_t theta1, acb_t theta2, acb_t theta3, acb_t theta4, const acb_t z, const acb_t tau, slong prec); void acb_modular_theta(acb_t theta1, acb_t theta2, acb_t theta3, acb_t theta4, const acb_t z, const acb_t tau, slong prec); void acb_modular_j(acb_t z, const acb_t tau, slong prec); int acb_modular_epsilon_arg(const psl2z_t g); void acb_modular_eta_sum(acb_t eta, const acb_t q, slong prec); void acb_modular_eta(acb_t z, const acb_t tau, slong prec); void acb_modular_lambda(acb_t r, const acb_t tau, slong prec); void acb_modular_delta(acb_t r, const acb_t tau, slong prec); void acb_modular_eisenstein(acb_ptr r, const acb_t tau, slong len, slong prec); void acb_modular_elliptic_p(acb_t r, const acb_t z, const acb_t tau, slong prec); void acb_modular_elliptic_p_zpx(acb_ptr r, const acb_t z, const acb_t tau, slong len, slong prec); void acb_modular_elliptic_k(acb_t k, const acb_t m, slong prec); void acb_modular_elliptic_k_cpx(acb_ptr w, const acb_t m, slong len, slong prec); void acb_modular_elliptic_e(acb_t res, const acb_t m, slong prec); void acb_modular_hilbert_class_poly(fmpz_poly_t res, slong D); /* this is a performance hack until the main arb/acb functions improve */ static __inline__ void acb_mul_approx(acb_t z, acb_t tmp1, acb_t tmp2, const acb_t x, const acb_t y, slong wprec, slong prec) { if (prec <= 1024) { acb_mul(z, x, y, wprec); } else if (x == y) { acb_set_round(tmp1, x, wprec); acb_mul(z, tmp1, tmp1, wprec); } else { acb_set_round(tmp1, x, wprec); acb_set_round(tmp2, y, wprec); acb_mul(z, tmp1, tmp2, wprec); } } #ifdef __cplusplus } #endif #endif arb-2.8.1/acb_modular/000077500000000000000000000000001264125401100145325ustar00rootroot00000000000000arb-2.8.1/acb_modular/addseq.c000066400000000000000000000101531264125401100161370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" static slong bisect(slong needle, const slong * haystack, slong len) { slong a, b, mid; a = 0; b = len - 1; while (a < b) { mid = (a + b) / 2; if (haystack[mid] < needle) a = mid + 1; else b = mid; } if (a == b && haystack[a] == needle) { return a; } return -1; } /* write p = 2a with a in P */ static int write_as_2a(slong * i1, slong * i2, slong p, const slong * P, slong Plen) { if (p % 2 == 0) { slong i = bisect(p / 2, P, Plen); if (i != -1) { *i1 = *i2 = i; return 1; } } return 0; } /* write p = a + b with a, b in P */ static int write_as_a_b(slong * i1, slong * i2, slong p, const slong * P, slong Plen) { slong i, j, pi; for (i = 0; i < Plen; i++) { pi = P[i]; j = bisect(p - pi, P, Plen); if (j != -1) { *i1 = i; *i2 = j; return 1; } } return 0; } /* write p = 2a + b with a, b in P */ static int write_as_2a_b(slong * i1, slong * i2, slong p, const slong * P, slong Plen) { slong i, j, pi; for (i = 0; i < Plen; i++) { pi = P[i]; if (2 * pi > p) break; j = bisect(p - 2*pi, P, Plen); if (j != -1) { *i1 = i; *i2 = j; return 1; } } return 0; } void acb_modular_addseq_theta(slong * exponents, slong * aindex, slong * bindex, slong num) { slong i; slong c; for (i = 0; i < num; i++) { if (i == 0) { exponents[i] = 1; aindex[i] = 0; bindex[i] = 0; continue; } else { c = ((i + 2) * (i + 2)) / 4; exponents[i] = c; if (write_as_2a(aindex + i, bindex + i, c, exponents, i)) continue; if (write_as_a_b(aindex + i, bindex + i, c, exponents, i)) continue; if (write_as_2a_b(aindex + i, bindex + i, c, exponents, i)) continue; flint_printf("i = %wd, c = %wu: bad addition sequence!\n", i, c); abort(); } } } void acb_modular_addseq_eta(slong * exponents, slong * aindex, slong * bindex, slong num) { slong i; slong c; for (i = 0; i < num; i++) { if (i == 0) { exponents[i] = 1; aindex[i] = 0; bindex[i] = 0; continue; } else { c = ((i + 2) / 2) * ((3 * i + 5) / 2) / 2; exponents[i] = c; if (write_as_2a(aindex + i, bindex + i, c, exponents, i)) continue; if (write_as_a_b(aindex + i, bindex + i, c, exponents, i)) continue; if (write_as_2a_b(aindex + i, bindex + i, c, exponents, i)) continue; flint_printf("i = %wd, c = %wu: bad addition sequence!\n", i, c); abort(); } } } arb-2.8.1/acb_modular/delta.c000066400000000000000000000043741264125401100157770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_delta(acb_t z, const acb_t tau, slong prec) { psl2z_t g; arf_t one_minus_eps; acb_t tau_prime, t1, t2, t3, t4, q; psl2z_init(g); arf_init(one_minus_eps); acb_init(tau_prime); acb_init(t1); acb_init(t2); acb_init(t3); acb_init(t4); acb_init(q); arf_set_ui_2exp_si(one_minus_eps, 63, -6); acb_modular_fundamental_domain_approx(tau_prime, g, tau, one_minus_eps, prec); acb_exp_pi_i(q, tau_prime, prec); acb_modular_theta_const_sum(t2, t3, t4, q, prec); /* (t2 t3 t4) ^ 8 * q^2 */ acb_mul(t1, t2, t3, prec); acb_mul(t1, t1, t4, prec); acb_mul(t1, t1, t1, prec); acb_mul(t1, t1, t1, prec); acb_mul(t1, t1, q, prec); acb_mul(t1, t1, t1, prec); acb_mul_2exp_si(t1, t1, -8); if (!fmpz_is_zero(&g->c)) { acb_mul_fmpz(t2, tau, &g->c, prec); acb_add_fmpz(t2, t2, &g->d, prec); acb_pow_ui(t2, t2, 12, prec); acb_div(t1, t1, t2, prec); } acb_set(z, t1); psl2z_clear(g); arf_clear(one_minus_eps); acb_clear(tau_prime); acb_clear(t1); acb_clear(t2); acb_clear(t3); acb_clear(t4); acb_clear(q); } arb-2.8.1/acb_modular/eisenstein.c000066400000000000000000000101241264125401100170420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_eisenstein(acb_ptr r, const acb_t tau, slong len, slong prec) { psl2z_t g; arf_t one_minus_eps; acb_t tau_prime, t1, t2, t3, t4, q; slong m, n; if (len < 1) return; psl2z_init(g); arf_init(one_minus_eps); acb_init(tau_prime); acb_init(t1); acb_init(t2); acb_init(t3); acb_init(t4); acb_init(q); arf_set_ui_2exp_si(one_minus_eps, 63, -6); acb_modular_fundamental_domain_approx(tau_prime, g, tau, one_minus_eps, prec); acb_exp_pi_i(q, tau_prime, prec); acb_modular_theta_const_sum(t2, t3, t4, q, prec); /* fourth powers of the theta functions (a, b, c) */ acb_mul(t2, t2, t2, prec); acb_mul(t2, t2, t2, prec); acb_mul(t2, t2, q, prec); acb_mul(t3, t3, t3, prec); acb_mul(t3, t3, t3, prec); acb_mul(t4, t4, t4, prec); acb_mul(t4, t4, t4, prec); /* c2 = pi^4 * (a^8 + b^8 + c^8) / 30 */ /* c3 = pi^6 * (b^12 + c^12 - 3a^8 * (b^4+c^4)) / 180 */ /* r = a^8 */ acb_mul(r, t2, t2, prec); if (len > 1) { /* r[1] = -3 a^8 * (b^4 + c^4) */ acb_add(r + 1, t3, t4, prec); acb_mul(r + 1, r + 1, r, prec); acb_mul_si(r + 1, r + 1, -3, prec); } /* b^8 */ acb_mul(t1, t3, t3, prec); acb_add(r, r, t1, prec); /* b^12 */ if (len > 1) acb_addmul(r + 1, t1, t3, prec); /* c^8 */ acb_mul(t1, t4, t4, prec); acb_add(r, r, t1, prec); /* c^12 */ if (len > 1) acb_addmul(r + 1, t1, t4, prec); acb_const_pi(t1, prec); acb_mul(t1, t1, t1, prec); acb_mul(t2, t1, t1, prec); acb_mul(r, r, t2, prec); acb_div_ui(r, r, 30, prec); if (len > 1) { acb_mul(t2, t2, t1, prec); acb_mul(r + 1, r + 1, t2, prec); acb_div_ui(r + 1, r + 1, 189, prec); } /* apply modular transformation */ if (!fmpz_is_zero(&g->c)) { acb_mul_fmpz(t1, tau, &g->c, prec); acb_add_fmpz(t1, t1, &g->d, prec); acb_inv(t1, t1, prec); acb_mul(t1, t1, t1, prec); acb_mul(t2, t1, t1, prec); acb_mul(r, r, t2, prec); if (len > 1) { acb_mul(t2, t1, t2, prec); acb_mul(r + 1, r + 1, t2, prec); } } /* compute more coefficients using recurrence */ for (n = 4; n < len + 2; n++) { acb_zero(r + n - 2); m = 2; for (m = 2; m * 2 < n; m++) acb_addmul(r + n - 2, r + m - 2, r + n - m - 2, prec); acb_mul_2exp_si(r + n - 2, r + n - 2, 1); if (n % 2 == 0) acb_addmul(r + n - 2, r + n / 2 - 2, r + n / 2 - 2, prec); acb_mul_ui(r + n - 2, r + n - 2, 3, prec); acb_div_ui(r + n - 2, r + n - 2, (2 * n + 1) * (n - 3), prec); } /* convert c's to G's */ for (n = 0; n < len; n++) acb_div_ui(r + n, r + n, 2 * n + 3, prec); psl2z_clear(g); arf_clear(one_minus_eps); acb_clear(tau_prime); acb_clear(t1); acb_clear(t2); acb_clear(t3); acb_clear(t4); acb_clear(q); } arb-2.8.1/acb_modular/elliptic_e.c000066400000000000000000000033631264125401100170140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_elliptic_e(acb_t res, const acb_t m, slong prec) { if (acb_is_zero(m)) { acb_const_pi(res, prec); acb_mul_2exp_si(res, res, -1); } else if (acb_is_one(m)) { acb_one(res); } else { acb_struct t[2]; acb_init(t + 0); acb_init(t + 1); acb_modular_elliptic_k_cpx(t, m, 2, prec); acb_mul(t + 1, t + 1, m, prec); acb_mul_2exp_si(t + 1, t + 1, 1); acb_add(t, t, t + 1, prec); acb_sub_ui(t + 1, m, 1, prec); acb_mul(res, t, t + 1, prec); acb_neg(res, res); acb_clear(t + 0); acb_clear(t + 1); } } arb-2.8.1/acb_modular/elliptic_k.c000066400000000000000000000026131264125401100170170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_elliptic_k(acb_t k, const acb_t m, slong prec) { acb_t t; acb_init(t); acb_sub_ui(t, m, 1, prec); acb_neg(t, t); acb_sqrt(t, t, prec); acb_agm1(k, t, prec); acb_const_pi(t, prec); acb_div(k, t, k, prec); acb_mul_2exp_si(k, k, -1); acb_clear(t); } arb-2.8.1/acb_modular/elliptic_k_cpx.c000066400000000000000000000054051264125401100176730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_elliptic_k_cpx(acb_ptr w, const acb_t m, slong len, slong prec) { acb_t t, u, msub1m, m2sub1; slong k, n; if (len < 1) return; if (len == 1) { acb_modular_elliptic_k(w, m, prec); return; } if (acb_is_zero(m)) { acb_const_pi(w, prec); acb_mul_2exp_si(w, w, -1); for (k = 1; k < len; k++) { acb_mul_ui(w + k, w + k - 1, (2 * k - 1) * (2 * k - 1), prec); acb_div_ui(w + k, w + k, 4 * k * k, prec); } return; } acb_init(t); acb_init(u); acb_init(msub1m); acb_init(m2sub1); acb_sub_ui(msub1m, m, 1, prec); acb_neg(t, msub1m); acb_sqrt(t, t, prec); acb_mul(msub1m, msub1m, m, prec); acb_mul_2exp_si(m2sub1, m, 1); acb_sub_ui(m2sub1, m2sub1, 1, prec); acb_agm1_cpx(w, t, 2, prec); /* pi M'(t) / (4 t M(t)^2) */ acb_mul(u, w, w, prec); acb_mul(t, t, u, prec); acb_div(w + 1, w + 1, t, prec); acb_const_pi(u, prec); acb_mul(w + 1, w + 1, u, prec); acb_mul_2exp_si(w + 1, w + 1, -2); /* pi / (2 M(t)) */ acb_const_pi(u, prec); acb_div(w, u, w, prec); acb_mul_2exp_si(w, w, -1); acb_inv(t, msub1m, prec); for (k = 2; k < len; k++) { n = k - 2; acb_mul_ui(w + k, w + n, (2 * n + 1) * (2 * n + 1), prec); acb_mul(u, w + n + 1, m2sub1, prec); acb_addmul_ui(w + k, u, (n + 1) * (n + 1) * 4, prec); acb_mul(w + k, w + k, t, prec); acb_div_ui(w + k, w + k, 4 * (n + 1) * (n + 2), prec); acb_neg(w + k, w + k); } acb_clear(t); acb_clear(u); acb_clear(msub1m); acb_clear(m2sub1); } arb-2.8.1/acb_modular/elliptic_p.c000066400000000000000000000037601264125401100170300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_elliptic_p(acb_t r, const acb_t z, const acb_t tau, slong prec) { acb_struct t0[4], tz[4]; acb_t t; int i; acb_init(t); for (i = 0; i < 4; i++) { acb_init(t0 + i); acb_init(tz + i); } acb_modular_theta(tz + 0, tz + 1, tz + 2, tz + 3, z, tau, prec); acb_zero(t); acb_modular_theta(t0 + 0, t0 + 1, t0 + 2, t0 + 3, t, tau, prec); acb_mul(t, t0 + 1, t0 + 2, prec); acb_mul(t, t, tz + 3, prec); acb_div(t, t, tz + 0, prec); acb_mul(t, t, t, prec); acb_pow_ui(t0 + 1, t0 + 1, 4, prec); acb_pow_ui(t0 + 2, t0 + 2, 4, prec); acb_add(r, t0 + 1, t0 + 2, prec); acb_div_ui(r, r, 3, prec); acb_sub(r, t, r, prec); acb_const_pi(t, prec); acb_mul(t, t, t, prec); acb_mul(r, r, t, prec); acb_clear(t); for (i = 0; i < 4; i++) { acb_clear(t0 + i); acb_clear(tz + i); } } arb-2.8.1/acb_modular/elliptic_p_zpx.c000066400000000000000000000066251264125401100177340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" #include "acb_poly.h" void acb_modular_theta_zpx_notransform(acb_ptr theta1, acb_ptr theta2, acb_ptr theta3, acb_ptr theta4, const acb_t z, const acb_t tau, slong len, slong prec) { acb_t q, q4, w; int w_is_unit; acb_init(q); acb_init(q4); acb_init(w); /* compute q_{1/4}, q */ acb_mul_2exp_si(q4, tau, -2); acb_exp_pi_i(q4, q4, prec); acb_pow_ui(q, q4, 4, prec); /* compute w */ acb_exp_pi_i(w, z, prec); w_is_unit = arb_is_zero(acb_imagref(z)); /* evaluate theta functions */ acb_modular_theta_sum(theta1, theta2, theta3, theta4, w, w_is_unit, q, len, prec); _acb_vec_scalar_mul(theta1, theta1, len, q4, prec); _acb_vec_scalar_mul(theta2, theta2, len, q4, prec); acb_clear(q); acb_clear(q4); acb_clear(w); } void acb_modular_elliptic_p_zpx(acb_ptr r, const acb_t z, const acb_t tau, slong len, slong prec) { acb_t t01, t02, t03, t04; acb_ptr tz1, tz2, tz3, tz4; acb_t t; if (len < 1) return; if (len == 1) { acb_modular_elliptic_p(r, z, tau, prec); return; } acb_init(t); acb_init(t01); acb_init(t02); acb_init(t03); acb_init(t04); tz1 = _acb_vec_init(len); tz2 = _acb_vec_init(len); tz3 = _acb_vec_init(len); tz4 = _acb_vec_init(len); acb_modular_theta_zpx_notransform(tz1, tz2, tz3, tz4, z, tau, len, prec); /* [theta_4(z) / theta_1(z)]^2 */ _acb_poly_div_series(tz2, tz4, len, tz1, len, len, prec); _acb_poly_mullow(tz1, tz2, len, tz2, len, len, prec); acb_zero(t); acb_modular_theta_notransform(t01, t02, t03, t04, t, tau, prec); /* [theta_2(0) * theta_3(0)] ^2 */ acb_mul(t, t02, t03, prec); acb_mul(t, t, t, prec); _acb_vec_scalar_mul(tz1, tz1, len, t, prec); /* - [theta_2(0)^4 + theta_3(0)^4] / 3 */ acb_pow_ui(t02, t02, 4, prec); acb_pow_ui(t03, t03, 4, prec); acb_add(t, t02, t03, prec); acb_div_ui(t, t, 3, prec); acb_sub(tz1, tz1, t, prec); /* times pi^2 */ acb_const_pi(t, prec); acb_mul(t, t, t, prec); _acb_vec_scalar_mul(r, tz1, len, t, prec); acb_clear(t); acb_clear(t01); acb_clear(t02); acb_clear(t03); acb_clear(t04); _acb_vec_clear(tz1, len); _acb_vec_clear(tz2, len); _acb_vec_clear(tz3, len); _acb_vec_clear(tz4, len); } arb-2.8.1/acb_modular/epsilon_arg.c000066400000000000000000000050231264125401100172000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" static int fmpz_kronecker(const fmpz_t a, const fmpz_t b) { if (fmpz_sgn(b) < 0) { int r; fmpz_t t; fmpz_init(t); fmpz_neg(t, b); r = fmpz_kronecker(a, t); fmpz_clear(t); return r; } else if (fmpz_is_one(b)) { return 1; } else { return fmpz_jacobi(a, b); } } int acb_modular_epsilon_arg(const psl2z_t g) { #define a (&g->a) #define b (&g->b) #define c (&g->c) #define d (&g->d) if (fmpz_is_zero(c)) { return fmpz_fdiv_ui(b, 24); } else { int aa, bb, cc, dd; int u; aa = fmpz_fdiv_ui(a, 24); bb = fmpz_fdiv_ui(b, 24); cc = fmpz_fdiv_ui(c, 24); dd = fmpz_fdiv_ui(d, 24); if (cc % 2 == 1) { u = fmpz_kronecker(a, c); aa = aa*bb + 2*aa*cc - 3*cc + cc*dd*(1-aa*aa); } else { u = fmpz_kronecker(c, a); aa = aa*bb - aa*cc + 3*aa - 3 + cc*dd*(1-aa*aa); } if (u == -1) { aa += 12; } else if (u != 1) { flint_printf("bad kronecker input\n"); abort(); } /* mod 24 */ if (aa < 0) { aa = 24 - ((-aa) % 24); if (aa == 24) aa = 0; } else aa = aa % 24; return aa; } #undef a #undef b #undef c #undef d } arb-2.8.1/acb_modular/eta.c000066400000000000000000000044041264125401100154510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_eta(acb_t z, const acb_t tau, slong prec) { psl2z_t g; fmpq_t t; arf_t one_minus_eps; acb_t tau_prime, eta, q, q24; psl2z_init(g); fmpq_init(t); arf_init(one_minus_eps); acb_init(tau_prime); acb_init(eta); acb_init(q); acb_init(q24); arf_set_ui_2exp_si(one_minus_eps, 63, -6); acb_modular_fundamental_domain_approx(tau_prime, g, tau, one_minus_eps, prec); acb_div_ui(q24, tau_prime, 12, prec); acb_exp_pi_i(q24, q24, prec); acb_pow_ui(q, q24, 24, prec); acb_modular_eta_sum(eta, q, prec); acb_mul(eta, eta, q24, prec); /* epsilon^-1 */ fmpq_set_si(t, -acb_modular_epsilon_arg(g), 12); arb_sin_cos_pi_fmpq(acb_imagref(q), acb_realref(q), t, prec); acb_mul(eta, eta, q, prec); /* (c*tau+d)^(-1/2) */ if (!fmpz_is_zero(&g->c)) { acb_mul_fmpz(q, tau, &g->c, prec); acb_add_fmpz(q, q, &g->d, prec); acb_rsqrt(q, q, prec); acb_mul(eta, eta, q, prec); } acb_set(z, eta); psl2z_clear(g); fmpq_clear(t); arf_clear(one_minus_eps); acb_clear(tau_prime); acb_clear(eta); acb_clear(q); acb_clear(q24); } arb-2.8.1/acb_modular/eta_sum.c000066400000000000000000000171241264125401100163400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" double mag_get_log2_d_approx(const mag_t x); static const int pentagonal_best_m[] = { 2, 5, 7, 11, 13, 17, 19, 23, 25, 35, 55, 65, 77, 91, 119, 133, 143, 175, 275, 325, 385, 455, 595, 665, 715, 935, 1001, 1309, 1463, 1547, 1729, 1925, 2275, 2975, 3325, 3575, 4675, 5005, 6545, 7315, 7735, 8645, 10465, 11305, 12155, 13585, 16445, 17017, 19019, 23023, 24871, 25025, 32725, 36575, 38675, 43225, 52325, 56525, 60775, 67925, 82225, 85085, 95095, 115115, 124355, 145145, 146965, 168245, 177905, 198835, 224315, 230945, 279565, 312455, 323323, 391391, 425425, 475475, 575575, 621775, 725725, 734825, 841225, 889525, 994175, 0 }; static const int pentagonal_best_m_residues[] = { 2, 3, 4, 6, 7, 9, 10, 12, 11, 12, 18, 21, 24, 28, 36, 40, 42, 44, 66, 77, 72, 84, 108, 120, 126, 162, 168, 216, 240, 252, 280, 264, 308, 396, 440, 462, 594, 504, 648, 720, 756, 840, 1008, 1080, 1134, 1260, 1512, 1512, 1680, 2016, 2160, 1848, 2376, 2640, 2772, 3080, 3696, 3960, 4158, 4620, 5544, 4536, 5040, 6048, 6480, 7560, 7560, 8640, 9072, 10080, 11340, 11340, 13608, 15120, 15120, 18144, 16632, 18480, 22176, 23760, 27720, 27720, 31680, 33264, 36960, 0 }; slong acb_modular_rs_optimal_m(const int * best_ms, const int * num_residues, slong N); #define PENTAGONAL(N) ((((N)+2)/2) * ((3*(N)+5)/2)/2) void _acb_modular_eta_sum_basecase(acb_t eta, const acb_t q, double log2q_approx, slong N, slong prec) { slong e, e1, e2, k, k1, k2, num, term_prec; slong *exponents, *aindex, *bindex; acb_ptr qpow; acb_t tmp1, tmp2; double log2term_approx; if (N <= 5) { if (N <= 1) { acb_set_ui(eta, N != 0); } else if (N == 2) { acb_sub_ui(eta, q, 1, prec); acb_neg(eta, eta); } else { acb_mul(eta, q, q, prec); acb_add(eta, eta, q, prec); acb_neg(eta, eta); acb_add_ui(eta, eta, 1, prec); } return; } num = 1; while (PENTAGONAL(num) < N) num++; acb_init(tmp1); acb_init(tmp2); exponents = flint_malloc(sizeof(slong) * 3 * num); aindex = exponents + num; bindex = aindex + num; qpow = _acb_vec_init(num); acb_modular_addseq_eta(exponents, aindex, bindex, num); acb_set_round(qpow + 0, q, prec); acb_zero(eta); for (k = 0; k < num; k++) { e = exponents[k]; log2term_approx = e * log2q_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); if (k > 0) { k1 = aindex[k]; k2 = bindex[k]; e1 = exponents[k1]; e2 = exponents[k2]; if (e == e1 + e2) { acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k1, qpow + k2, term_prec, prec); } else if (e == 2 * e1 + e2) { acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k1, qpow + k1, term_prec, prec); acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k, qpow + k2, term_prec, prec); } else { flint_printf("exponent not in addition sequence!\n"); abort(); } } if (k % 4 <= 1) acb_sub(eta, eta, qpow + k, prec); else acb_add(eta, eta, qpow + k, prec); } acb_add_ui(eta, eta, 1, prec); flint_free(exponents); _acb_vec_clear(qpow, num); acb_clear(tmp1); acb_clear(tmp2); } void _acb_modular_eta_sum_rs(acb_t eta, const acb_t q, double log2q_approx, slong N, slong prec) { slong * tab; slong k, term_prec, i, e, eprev; slong m, num_pentagonal; double log2term_approx; acb_ptr qpow; acb_t tmp1, tmp2; acb_init(tmp1); acb_init(tmp2); /* choose rectangular splitting parameters */ m = acb_modular_rs_optimal_m(pentagonal_best_m, pentagonal_best_m_residues, N); /* build addition sequence */ tab = flint_calloc(m + 1, sizeof(slong)); for (k = 0; PENTAGONAL(k) < N; k++) tab[PENTAGONAL(k) % m] = -1; num_pentagonal = k; tab[m] = -1; /* compute powers in addition sequence */ qpow = _acb_vec_init(m + 1); acb_modular_fill_addseq(tab, m + 1); for (k = 0; k < m + 1; k++) { if (k == 0) { acb_one(qpow + k); } else if (k == 1) { acb_set_round(qpow + k, q, prec); } else if (tab[k] != 0) { log2term_approx = k * log2q_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); acb_mul_approx(qpow + k, tmp1, tmp2, qpow + tab[k], qpow + k - tab[k], term_prec, prec); } } /* compute eta */ acb_zero(eta); term_prec = prec; for (k = num_pentagonal - 1; k >= 0; k--) { e = PENTAGONAL(k); /* exponent */ eprev = PENTAGONAL(k+1); log2term_approx = e * log2q_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); /* giant steps */ for (i = e / m; i < eprev / m; i++) { if (!acb_is_zero(eta)) acb_mul_approx(eta, tmp1, tmp2, eta, qpow + m, term_prec, prec); } if (k % 4 <= 1) acb_sub(eta, eta, qpow + (e % m), prec); else acb_add(eta, eta, qpow + (e % m), prec); } acb_add_ui(eta, eta, 1, prec); acb_clear(tmp1); acb_clear(tmp2); _acb_vec_clear(qpow, m + 1); flint_free(tab); } void acb_modular_eta_sum(acb_t eta, const acb_t q, slong prec) { mag_t err, qmag; double log2q_approx; int q_is_real; slong N; mag_init(err); mag_init(qmag); q_is_real = arb_is_zero(acb_imagref(q)); acb_get_mag(qmag, q); log2q_approx = mag_get_log2_d_approx(qmag); if (log2q_approx >= 0.0) { N = 1; mag_inf(err); } else /* Pick N and compute error bound */ { N = 0; while (0.05 * N * N < prec) { if (log2q_approx * PENTAGONAL(N) < -prec - 2) break; N++; } N = PENTAGONAL(N); mag_geom_series(err, qmag, N); if (mag_is_inf(err)) N = 1; } if (N < 400) _acb_modular_eta_sum_basecase(eta, q, log2q_approx, N, prec); else _acb_modular_eta_sum_rs(eta, q, log2q_approx, N, prec); if (q_is_real) arb_add_error_mag(acb_realref(eta), err); else acb_add_error_mag(eta, err); mag_clear(err); mag_clear(qmag); } arb-2.8.1/acb_modular/fill_addseq.c000066400000000000000000000047301264125401100171510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_fill_addseq(slong * tab, slong len) { slong i, j; for (i = 2; i < len; i++) { if (tab[i] == -1) { /* prefer doubling (squaring) */ if ((i % 2) == 0 && tab[i / 2] != 0) { tab[i] = i / 2; } else { /* check if it can be written as a sum */ /* prefer unbalanced, because one power will have low precision */ #if 1 for (j = 1; 2 * j <= i; j++) #else for (j = i / 2; j >= 1; j--) #endif { if (tab[j] != 0 && tab[i-j] != 0) { tab[i] = j; break; } } /* extend and start over */ if (tab[i] == -1) { tab[i] = i / 2; if (tab[i / 2] == 0) tab[i / 2] = -1; if (tab[i - i / 2] == 0) tab[i - i / 2] = -1; i = 1; } } } } /* prefer squaring (extra entries may have been inserted) */ for (i = 2; i < len; i += 2) { if (tab[i] != 0 && tab[i] != i / 2) { if (tab[i / 2] != 0) tab[i] = i / 2; } } } arb-2.8.1/acb_modular/fundamental_domain_approx.c000066400000000000000000000064201264125401100221160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" static int good_enough(const acb_t z, const arf_t one_minus_eps, slong prec) { arf_t m; int res; if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -1) > 0) return 0; if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) >= 0) return 1; arf_init(m); arf_mul(m, arb_midref(acb_realref(z)), arb_midref(acb_realref(z)), prec, ARF_RND_DOWN); arf_addmul(m, arb_midref(acb_imagref(z)), arb_midref(acb_imagref(z)), prec, ARF_RND_DOWN); res = (arf_cmp(m, one_minus_eps) >= 0); arf_clear(m); return res; } void acb_modular_fundamental_domain_approx(acb_t w, psl2z_t g, const acb_t z, const arf_t one_minus_eps, slong prec) { acb_t t; psl2z_one(g); /* we must be in the upper half-plane */ if (!acb_is_finite(z) || arf_sgn(arb_midref(acb_imagref(z))) <= 0) { acb_set(w, z); return; } /* too large real-value shift */ if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), prec) > 0) { acb_set(w, z); return; } /* y >= 1: just shift x */ if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) >= 0) { arf_get_fmpz(&g->b, arb_midref(acb_realref(z)), ARF_RND_NEAR); acb_sub_fmpz(w, z, &g->b, prec); fmpz_neg(&g->b, &g->b); return; } acb_init(t); /* try using doubles */ if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -40) > 0 && arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 40) < 0) { double zred, zimd; zred = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN); zimd = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN); acb_modular_fundamental_domain_approx_d(g, zred, zimd, arf_get_d(one_minus_eps, ARF_RND_UP)); acb_modular_transform(t, g, z, prec); if (good_enough(t, one_minus_eps, prec)) { acb_swap(w, t); acb_clear(t); return; } } /* try with full precision */ acb_modular_fundamental_domain_approx_arf(g, arb_midref(acb_realref(z)), arb_midref(acb_imagref(z)), one_minus_eps, prec); acb_modular_transform(t, g, z, prec); acb_swap(w, t); acb_clear(t); } arb-2.8.1/acb_modular/fundamental_domain_approx_arf.c000066400000000000000000000060421264125401100227460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_fundamental_domain_approx_arf(psl2z_t g, const arf_t xx, const arf_t yy, const arf_t one_minus_eps, slong prec) { slong i; arf_t x, y, t; fmpz_t n; psl2z_one(g); /* we must be in the upper half-plane */ if (!arf_is_finite(xx) || !arf_is_finite(yy) || arf_sgn(yy) <= 0) return; arf_init(x); arf_init(y); arf_init(t); fmpz_init(n); arf_set_round(x, xx, prec, ARF_RND_DOWN); arf_set_round(y, yy, prec, ARF_RND_DOWN); for (i = 0; i < 10 + prec / 4; i++) { /* too large shift */ if (arf_cmpabs_2exp_si(x, prec) > 0) { psl2z_one(g); break; } if (fmpz_bits(&g->a) > prec || fmpz_bits(&g->b) > prec || fmpz_bits(&g->c) > prec || fmpz_bits(&g->d) > prec) { psl2z_one(g); break; } /* shift */ if (arf_cmpabs_2exp_si(x, -1) > 0) { arf_get_fmpz(n, x, ARF_RND_NEAR); arf_sub_fmpz(x, x, n, prec, ARF_RND_DOWN); fmpz_submul(&g->a, &g->c, n); fmpz_submul(&g->b, &g->d, n); continue; } arf_mul(t, x, x, prec, ARF_RND_DOWN); arf_addmul(t, y, y, prec, ARF_RND_DOWN); /* inversion */ if (arf_cmp(t, one_minus_eps) < 0) { arf_div(x, x, t, prec, ARF_RND_DOWN); arf_neg(x, x); arf_div(y, y, t, prec, ARF_RND_DOWN); fmpz_swap(&g->a, &g->c); fmpz_swap(&g->b, &g->d); fmpz_neg(&g->a, &g->a); fmpz_neg(&g->b, &g->b); continue; } /* we're good */ break; } if (fmpz_sgn(&g->c) < 0 || (fmpz_is_zero(&g->c) && fmpz_sgn(&g->d) < 0)) { fmpz_neg(&g->a, &g->a); fmpz_neg(&g->b, &g->b); fmpz_neg(&g->c, &g->c); fmpz_neg(&g->d, &g->d); } arf_clear(x); arf_clear(y); arf_clear(t); fmpz_clear(n); } arb-2.8.1/acb_modular/fundamental_domain_approx_d.c000066400000000000000000000050761264125401100224270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" static __inline__ int d_is_ok(double x) { return (x > -1e15) && (x < 1e15); } void acb_modular_fundamental_domain_approx_d(psl2z_t g, double x, double y, double one_minus_eps) { double a, b, c, d, aa, bb, t; int i; a = d = 1; b = c = 0; for (i = 0; i < 20; i++) { if (!d_is_ok(x) || !d_is_ok(y) || !(y > 0.0)) { psl2z_one(g); return; } /* shift */ if (x < -0.5 || x > 0.5) { t = floor(x + 0.5); x -= t; a -= t * c; b -= t * d; /* too large to guarantee exactness */ if (!d_is_ok(a) || !d_is_ok(b)) { psl2z_one(g); return; } continue; } t = x*x + y*y; /* can't divide by a too small number */ if (t < 1e-30) { psl2z_one(g); break; } /* inversion */ if (t < one_minus_eps) { t = 1.0 / t; x *= -t; y *= t; aa = a; bb = b; a = -c; b = -d; c = aa; d = bb; continue; } /* we're good */ break; } if (c < 0 || (c == 0 && d < 0)) { a = -a; b = -b; c = -c; d = -d; } fmpz_set_d(&g->a, a); fmpz_set_d(&g->b, b); fmpz_set_d(&g->c, c); fmpz_set_d(&g->d, d); } arb-2.8.1/acb_modular/hilbert_class_poly.c000066400000000000000000000122061264125401100205600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #include "acb_modular.h" static void bsplit(arb_poly_t pol, const arb_t sqrtD, const slong * qbf, slong a, slong b, slong prec) { if (b - a == 0) { arb_poly_one(pol); } else if (b - a == 1) { acb_t z; acb_init(z); /* j((-b+sqrt(-D))/(2a)) */ arb_set_si(acb_realref(z), -FLINT_ABS(qbf[3 * a + 1])); arb_set(acb_imagref(z), sqrtD); acb_div_si(z, z, 2 * qbf[3 * a], prec); acb_modular_j(z, z, prec); if (qbf[3 * a + 1] < 0) { /* (x^2 - 2re(j) x + |j|^2) */ arb_poly_fit_length(pol, 3); arb_mul(pol->coeffs, acb_realref(z), acb_realref(z), prec); arb_addmul(pol->coeffs, acb_imagref(z), acb_imagref(z), prec); arb_mul_2exp_si(pol->coeffs + 1, acb_realref(z), 1); arb_neg(pol->coeffs + 1, pol->coeffs + 1); arb_one(pol->coeffs + 2); _arb_poly_set_length(pol, 3); } else { /* (x-j) */ arb_poly_fit_length(pol, 2); arb_neg(pol->coeffs, acb_realref(z)); arb_one(pol->coeffs + 1); _arb_poly_set_length(pol, 2); } acb_clear(z); } else { arb_poly_t tmp; arb_poly_init(tmp); bsplit(pol, sqrtD, qbf, a, a + (b - a) / 2, prec); bsplit(tmp, sqrtD, qbf, a + (b - a) / 2, b, prec); arb_poly_mul(pol, pol, tmp, prec); arb_poly_clear(tmp); } } int _acb_modular_hilbert_class_poly(fmpz_poly_t res, slong D, const slong * qbf, slong qbf_len, slong prec) { arb_t sqrtD; arb_poly_t pol; int success; arb_init(sqrtD); arb_poly_init(pol); arb_set_si(sqrtD, -D); arb_sqrt(sqrtD, sqrtD, prec); bsplit(pol, sqrtD, qbf, 0, qbf_len, prec); success = arb_poly_get_unique_fmpz_poly(res, pol); arb_clear(sqrtD); arb_poly_clear(pol); return success; } void acb_modular_hilbert_class_poly(fmpz_poly_t res, slong D) { slong i, a, b, c, ac, h, qbf_alloc, qbf_len, prec; slong * qbf; double lgh; if (D >= 0 || ((D & 3) > 1)) { fmpz_poly_zero(res); return; } qbf_alloc = qbf_len = 0; qbf = NULL; b = D & 1; h = 0; /* Cohen algorithm 5.3.5 */ do { ac = (b*b - D) / 4; a = FLINT_MAX(b, 1); do { if (ac % a == 0 && n_gcd_full(n_gcd(a, b), ac/a) == 1) { c = ac / a; if (qbf_len >= qbf_alloc) { qbf_alloc = FLINT_MAX(4, FLINT_MAX(qbf_len + 1, qbf_alloc * 2)); qbf = flint_realloc(qbf, qbf_alloc * 3 * sizeof(slong)); } if (a == b || a*a == ac || b == 0) { qbf[3 * qbf_len + 0] = a; qbf[3 * qbf_len + 1] = b; qbf[3 * qbf_len + 2] = c; h += 1; } else { /* -b indicates that we have both b and -b */ qbf[3 * qbf_len + 0] = a; qbf[3 * qbf_len + 1] = -b; qbf[3 * qbf_len + 2] = c; h += 2; } qbf_len++; } a++; } while (a*a <= ac); b += 2; } while (3*b*b <= -D); /* Estimate precision - see p.7 in http://hal.inria.fr/inria-00001040 */ lgh = 0.0; for (i = 0; i < qbf_len; i++) { if (qbf[3 * i + 1] < 0) lgh += 2.0 / qbf[3 * i]; else lgh += 1.0 / qbf[3 * i]; } lgh = 3.141593 * sqrt(-D) * lgh; #if 0 lgh += 3.012 * h; prec = lgh * 1.442696; prec = prec + 10; #else prec = lgh * 1.442696; /* heuristic, but more accurate */ prec = prec * 1.005 + 20; #endif while (!_acb_modular_hilbert_class_poly(res, D, qbf, qbf_len, prec)) { flint_printf("hilbert_class_poly failed at %wd bits of precision\n", prec); prec = prec * 1.2 + 10; } flint_free(qbf); } arb-2.8.1/acb_modular/is_in_fundamental_domain.c000066400000000000000000000037141264125401100217110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int acb_modular_is_in_fundamental_domain(const acb_t z, const arf_t tol, slong prec) { arb_t t; arb_init(t); /* require re(w) + 1/2 >= 0 */ arb_set_ui(t, 1); arb_mul_2exp_si(t, t, -1); arb_add(t, t, acb_realref(z), prec); arb_add_arf(t, t, tol, prec); if (!arb_is_nonnegative(t)) { arb_clear(t); return 0; } /* require re(w) - 1/2 <= 0 */ arb_set_ui(t, 1); arb_mul_2exp_si(t, t, -1); arb_sub(t, acb_realref(z), t, prec); arb_sub_arf(t, t, tol, prec); if (!arb_is_nonpositive(t)) { arb_clear(t); return 0; } /* require |w| >= 1 - tol, i.e. |w| - 1 + tol >= 0 */ acb_abs(t, z, prec); arb_sub_ui(t, t, 1, prec); arb_add_arf(t, t, tol, prec); if (!arb_is_nonnegative(t)) { arb_clear(t); return 0; } arb_clear(t); return 1; } arb-2.8.1/acb_modular/j.c000066400000000000000000000044771264125401100151430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_j(acb_t z, const acb_t tau, slong prec) { psl2z_t g; arf_t one_minus_eps; acb_t tau_prime, t2, t3, t4, q; psl2z_init(g); arf_init(one_minus_eps); acb_init(tau_prime); acb_init(t2); acb_init(t3); acb_init(t4); acb_init(q); arf_set_ui_2exp_si(one_minus_eps, 63, -6); acb_modular_fundamental_domain_approx(tau_prime, g, tau, one_minus_eps, prec); acb_exp_pi_i(q, tau_prime, prec); acb_modular_theta_const_sum(t2, t3, t4, q, prec); /* theta2 ^ 8 */ acb_mul(t2, t2, t2, prec); acb_mul(t2, t2, t2, prec); acb_mul(t2, t2, q, prec); acb_mul(t2, t2, t2, prec); /* theta3 ^ 8 */ acb_mul(t3, t3, t3, prec); acb_mul(t3, t3, t3, prec); acb_mul(t3, t3, t3, prec); /* theta4 ^ 8 */ acb_mul(t4, t4, t4, prec); acb_mul(t4, t4, t4, prec); acb_mul(t4, t4, t4, prec); acb_mul(z, t2, t3, prec); acb_mul(z, z, t4, prec); acb_add(t2, t2, t3, prec); acb_add(t2, t2, t4, prec); acb_cube(t2, t2, prec); acb_div(z, t2, z, prec); acb_mul_2exp_si(z, z, 5); psl2z_clear(g); arf_clear(one_minus_eps); acb_clear(tau_prime); acb_clear(t2); acb_clear(t3); acb_clear(t4); acb_clear(q); } arb-2.8.1/acb_modular/lambda.c000066400000000000000000000047431264125401100161260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_lambda(acb_t r, const acb_t tau, slong prec) { psl2z_t g; arf_t one_minus_eps; acb_t tau_prime, q; acb_struct thetas[4]; int R[4], S[4], C; int Rsum, qpower; psl2z_init(g); arf_init(one_minus_eps); acb_init(tau_prime); acb_init(q); acb_init(thetas + 0); acb_init(thetas + 1); acb_init(thetas + 2); acb_init(thetas + 3); arf_set_ui_2exp_si(one_minus_eps, 63, -6); acb_modular_fundamental_domain_approx(tau_prime, g, tau, one_minus_eps, prec); acb_modular_theta_transform(R, S, &C, g); acb_exp_pi_i(q, tau_prime, prec); acb_modular_theta_const_sum(thetas + 1, thetas + 2, thetas + 3, q, prec); acb_zero(thetas + 0); /* divide the transformation factors */ Rsum = 4 * (R[1] - R[2]); /* possible factor [q^(+/- 1/4)]^4 needed for theta_1^4 or theta_2^4 */ qpower = (S[1] == 0 || S[1] == 1) - (S[2] == 0 || S[2] == 1); acb_div(r, thetas + S[1], thetas + S[2], prec); acb_mul(r, r, r, prec); acb_mul(r, r, r, prec); if ((Rsum & 7) == 4) acb_neg(r, r); if (qpower == 1) acb_mul(r, r, q, prec); else if (qpower == -1) acb_div(r, r, q, prec); psl2z_clear(g); arf_clear(one_minus_eps); acb_clear(tau_prime); acb_clear(q); acb_clear(thetas + 0); acb_clear(thetas + 1); acb_clear(thetas + 2); acb_clear(thetas + 3); } arb-2.8.1/acb_modular/psl2z_inv.c000066400000000000000000000026531264125401100166320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void psl2z_inv(psl2z_t h, const psl2z_t g) { if (h != g) psl2z_set(h, g); if (fmpz_is_zero(&h->c) && fmpz_sgn(&h->a) > 0) { fmpz_neg(&h->b, &h->b); fmpz_swap(&h->d, &h->a); } else { fmpz_swap(&h->a, &h->d); fmpz_neg(&h->a, &h->a); fmpz_neg(&h->d, &h->d); } } arb-2.8.1/acb_modular/psl2z_is_correct.c000066400000000000000000000026511264125401100201700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int psl2z_is_correct(const psl2z_t g) { int res; fmpz_t t; if (fmpz_sgn(&g->c) < 0) return 0; if (fmpz_is_zero(&g->c) && fmpz_sgn(&g->d) <= 0) return 0; fmpz_init(t); fmpz_mul(t, &g->a, &g->d); fmpz_submul(t, &g->b, &g->c); res = fmpz_is_one(t); fmpz_clear(t); return res; } arb-2.8.1/acb_modular/psl2z_is_one.c000066400000000000000000000023601264125401100173050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int psl2z_is_one(const psl2z_t g) { return fmpz_is_one(&g->a) && fmpz_is_zero(&g->b) && fmpz_is_zero(&g->c) && fmpz_is_one(&g->d); } arb-2.8.1/acb_modular/psl2z_mul.c000066400000000000000000000035131264125401100166270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void psl2z_mul(psl2z_t h, const psl2z_t f, const psl2z_t g) { if (h == f || h == g) { psl2z_t t; psl2z_init(t); psl2z_mul(t, f, g); psl2z_swap(t, h); psl2z_clear(t); return; } fmpz_mul(&h->a, &f->a, &g->a); fmpz_addmul(&h->a, &f->b, &g->c); fmpz_mul(&h->b, &f->a, &g->b); fmpz_addmul(&h->b, &f->b, &g->d); fmpz_mul(&h->c, &f->c, &g->a); fmpz_addmul(&h->c, &f->d, &g->c); fmpz_mul(&h->d, &f->c, &g->b); fmpz_addmul(&h->d, &f->d, &g->d); if (fmpz_sgn(&h->c) < 0 || (fmpz_is_zero(&h->c) && fmpz_sgn(&h->d) < 0)) { fmpz_neg(&h->a, &h->a); fmpz_neg(&h->b, &h->b); fmpz_neg(&h->c, &h->c); fmpz_neg(&h->d, &h->d); } } arb-2.8.1/acb_modular/psl2z_randtest.c000066400000000000000000000036161264125401100176620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void psl2z_randtest(psl2z_t g, flint_rand_t state, slong bits) { bits = FLINT_MAX(bits, 1); fmpz_randtest(&g->a, state, bits); fmpz_randtest(&g->b, state, bits); if (fmpz_is_zero(&g->a) && fmpz_is_zero(&g->b)) { psl2z_one(g); } else { fmpz_t t; fmpz_init(t); fmpz_xgcd(t, &g->d, &g->c, &g->a, &g->b); fmpz_divexact(&g->a, &g->a, t); fmpz_divexact(&g->b, &g->b, t); if (fmpz_sgn(&g->c) < 0) fmpz_neg(&g->c, &g->c); else fmpz_neg(&g->b, &g->b); if (fmpz_is_zero(&g->c) && fmpz_sgn(&g->d) < 0) { fmpz_neg(&g->a, &g->a); fmpz_neg(&g->b, &g->b); fmpz_neg(&g->c, &g->c); fmpz_neg(&g->d, &g->d); } fmpz_clear(t); } } arb-2.8.1/acb_modular/test/000077500000000000000000000000001264125401100155115ustar00rootroot00000000000000arb-2.8.1/acb_modular/test/t-delta.c000066400000000000000000000054501264125401100172130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" #include "profiler.h" int main() { slong iter; flint_rand_t state; flint_printf("delta...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t tau, z1, z2; slong e0, prec0, prec1, prec2; acb_init(tau); acb_init(z1); acb_init(z2); e0 = 1 + n_randint(state, 10); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_randtest(tau, state, prec0, e0); acb_randtest(z1, state, prec0, e0); acb_randtest(z2, state, prec0, e0); /* compare with eta */ acb_modular_delta(z1, tau, prec1); acb_modular_eta(z2, tau, prec2); acb_pow_ui(z2, z2, 24, prec2); if (!acb_overlaps(z1, z2)) { flint_printf("FAIL (overlap)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); abort(); } acb_modular_delta(tau, tau, prec1); if (!acb_overlaps(z1, tau)) { flint_printf("FAIL (aliasing)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); abort(); } acb_clear(tau); acb_clear(z1); acb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-eisenstein.c000066400000000000000000000064451264125401100202750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("eisenstein...."); fflush(stdout); flint_randinit(state); /* Test functional equation */ for (iter = 0; iter < 10000; iter++) { acb_t tau1, tau2, t; acb_ptr r1, r2; slong e0, prec0, prec1, prec2, len1, len2, i; psl2z_t g; psl2z_init(g); acb_init(tau1); acb_init(tau2); acb_init(t); e0 = 1 + n_randint(state, 200); prec0 = 2 + n_randint(state, 2000); prec1 = 2 + n_randint(state, 2000); prec2 = 2 + n_randint(state, 2000); len1 = n_randint(state, 20); len2 = n_randint(state, 20); r1 = _acb_vec_init(len1); r2 = _acb_vec_init(len2); acb_randtest(tau1, state, prec0, e0); acb_randtest(tau2, state, prec0, e0); psl2z_randtest(g, state, 1 + n_randint(state, 200)); acb_modular_transform(tau2, g, tau1, prec0); acb_modular_eisenstein(r1, tau1, len1, prec1); acb_modular_eisenstein(r2, tau2, len2, prec2); for (i = 0; i < FLINT_MIN(len1, len2); i++) { acb_mul_fmpz(t, tau1, &g->c, prec1); acb_add_fmpz(t, t, &g->d, prec1); acb_pow_ui(t, t, 2 * i + 4, prec1); acb_mul(t, t, r1 + i, prec1); if (!acb_overlaps(t, r2 + i)) { flint_printf("FAIL (overlap)\n"); flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n"); flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n\n"); flint_printf("r1 = "); acb_printd(r1 + i, 15); flint_printf("\n\n"); flint_printf("r2 = "); acb_printd(r2 + i, 15); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n"); abort(); } } acb_clear(tau1); acb_clear(tau2); acb_clear(t); _acb_vec_clear(r1, len1); _acb_vec_clear(r2, len2); psl2z_clear(g); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-elliptic_e.c000066400000000000000000000056761264125401100202450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("elliptic_e...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 500; iter++) { acb_t m, w, K, Kp, E, Ep, r, pi2; slong prec; acb_init(m); acb_init(w); acb_init(K); acb_init(Kp); acb_init(E); acb_init(Ep); acb_init(r); acb_init(pi2); prec = 2 + n_randint(state, 1000); acb_randtest(m, state, prec, 1 + n_randint(state, 100)); acb_sub_ui(w, m, 1, prec); acb_neg(w, w); acb_const_pi(pi2, prec); acb_mul_2exp_si(pi2, pi2, -1); acb_modular_elliptic_k(K, m, prec); acb_modular_elliptic_k(Kp, w, prec); acb_modular_elliptic_e(E, m, prec); acb_modular_elliptic_e(Ep, w, prec); acb_mul(r, K, Ep, prec); acb_addmul(r, E, Kp, prec); acb_submul(r, K, Kp, prec); if (!acb_overlaps(r, pi2)) { flint_printf("FAIL (overlap)\n\n"); flint_printf("m = "); acb_printd(m, 30); flint_printf("\n\n"); flint_printf("w = "); acb_printd(w, 30); flint_printf("\n\n"); flint_printf("K = "); acb_printd(K, 30); flint_printf("\n\n"); flint_printf("Kp = "); acb_printd(Kp, 30); flint_printf("\n\n"); flint_printf("E = "); acb_printd(E, 30); flint_printf("\n\n"); flint_printf("Ep = "); acb_printd(Ep, 30); flint_printf("\n\n"); flint_printf("r = "); acb_printd(r, 30); flint_printf("\n\n"); abort(); } acb_clear(m); acb_clear(w); acb_clear(K); acb_clear(Kp); acb_clear(E); acb_clear(Ep); acb_clear(r); acb_clear(pi2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-elliptic_k.c000066400000000000000000000145161264125401100202440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" #define EPS 1e-13 #define NUM_DERIVS 4 #define NUM_TESTS 7 const double k_testdata[NUM_TESTS][10] = { {0.0, 0.0, 1.5707963267948966192, 0.0, 0.39269908169872415481, 0.0, 0.22089323345553233708, 0.0, 0.15339807878856412297, 0.0}, {0.5, 0.0, 1.8540746773013719184, 0.0, 0.84721308479397908661, 0.0, 0.92703733865068595922, 0.0, 1.2708196271909686299, 0.0}, {-1.0, 0.0, 1.3110287771460599052, 0.0, 0.17798966494456595038, 0.0, 0.051552950136795718707, 0.0, 0.018179887959689603011, 0.0}, {2.0, 0.0, 1.3110287771460599052, -1.3110287771460599052, -0.47752472362846400224, 0.17798966494456595038, 0.2762042441497192576, -0.051552950136795718707, -0.18666835846938225718, 0.018179887959689603011}, {-3.0, 0.0, 1.0782578237498216177, 0.0, 0.078788301660931975886, 0.0, 0.011748068987044517782, 0.0, 0.0021065590680576326689, 0.0}, {1.0, 1.0, 1.5092369540512728293, 0.62514641520269688427, -0.079689518666051625811, 0.40903679001382547524, -0.23159955416582020342, -0.028627375924621981072, 0.014191044435751759097, -0.16030448214657194629}, {-2.0, -3.0, 1.0408718798817036, -0.24497111630480680352, 0.04401149835588265436, -0.060184042863324675054, -0.0012755513109907959184, -0.01044301570409968822, -0.0013811810360989366762, -0.0011248246747562196271} }; int main() { slong iter; flint_rand_t state; flint_printf("elliptic_k...."); fflush(stdout); flint_randinit(state); /* check particular values against table */ { acb_t z, t; acb_ptr w1; slong i, j, prec, cnj; acb_init(z); acb_init(t); w1 = _acb_vec_init(NUM_DERIVS); for (prec = 32; prec <= 512; prec *= 4) { for (i = 0; i < NUM_TESTS; i++) { for (cnj = 0; cnj < 2; cnj++) { if (cnj == 1 && k_testdata[i][0] > 1 && k_testdata[i][1] == 0) continue; acb_zero(z); arf_set_d(arb_midref(acb_realref(z)), k_testdata[i][0]); arf_set_d(arb_midref(acb_imagref(z)), cnj ? -k_testdata[i][1] : k_testdata[i][1]); acb_modular_elliptic_k_cpx(w1, z, NUM_DERIVS, prec); for (j = 0; j < NUM_DERIVS; j++) { arf_set_d(arb_midref(acb_realref(t)), k_testdata[i][2+2*j]); mag_set_d(arb_radref(acb_realref(t)), fabs(k_testdata[i][2+2*j]) * EPS); arf_set_d(arb_midref(acb_imagref(t)), cnj ? -k_testdata[i][2+2*j+1] : k_testdata[i][2+2*j+1]); mag_set_d(arb_radref(acb_imagref(t)), fabs(k_testdata[i][2+2*j+1]) * EPS); if (!acb_overlaps(w1 + j, t)) { flint_printf("FAIL\n\n"); flint_printf("j = %wd\n\n", j); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1 + j, 15); flint_printf("\n\n"); abort(); } } } } } _acb_vec_clear(w1, NUM_DERIVS); acb_clear(z); acb_clear(t); } /* self-consistency test */ for (iter = 0; iter < 500; iter++) { acb_ptr m1, m2; acb_t z1, z2, t; slong i, len1, len2, prec1, prec2; len1 = n_randint(state, 10); len2 = n_randint(state, 10); prec1 = 2 + n_randint(state, 2000); prec2 = 2 + n_randint(state, 2000); m1 = _acb_vec_init(len1); m2 = _acb_vec_init(len2); acb_init(z1); acb_init(z2); acb_init(t); acb_randtest(z1, state, prec1, 1 + n_randint(state, 100)); if (n_randint(state, 2)) { acb_set(z2, z1); } else { acb_randtest(t, state, prec2, 1 + n_randint(state, 100)); acb_add(z2, z1, t, prec2); acb_sub(z2, z2, t, prec2); } acb_modular_elliptic_k_cpx(m1, z1, len1, prec1); acb_modular_elliptic_k_cpx(m2, z2, len2, prec2); for (i = 0; i < FLINT_MIN(len1, len2); i++) { if (!acb_overlaps(m1 + i, m2 + i)) { flint_printf("FAIL (overlap)\n\n"); flint_printf("iter = %wd, i = %wd, len1 = %wd, len2 = %wd, prec1 = %wd, prec2 = %wd\n\n", iter, i, len1, len2, prec1, prec2); flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 30); flint_printf("\n\n"); flint_printf("m1 = "); acb_printd(m1, 30); flint_printf("\n\n"); flint_printf("m2 = "); acb_printd(m2, 30); flint_printf("\n\n"); abort(); } } _acb_vec_clear(m1, len1); _acb_vec_clear(m2, len2); acb_clear(z1); acb_clear(z2); acb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-elliptic_p.c000066400000000000000000000126611264125401100202500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" #define NUM_TESTS 6 #define EPS 1e-13 /* z, tau, p(z, tau) checked with Mathematica: N[{z, tau, WeierstrassP[z, WeierstrassInvariants[{1, tau}/2]]}, 20] */ const double testdata[NUM_TESTS][6] = { { 1.4142135623730950488, 1.7320508075688772935, 2.2360679774997896964, 2.6457513110645905905, -3.3440423818409419071, 0.1143522489547216990 }, { -3.0, -2.0, -7.0, 3.0, -3.3640051024505898616, 0.0 }, { 0.1, 0.0, 0.6, 0.2, 99.322596953997138519, 2.258818666973309701 }, { 0.0, 0.1, 0.6, 0.2, -99.322596953997138519, -2.258818666973309701 }, { 0.5, 0.0, 0.333333333333333333, 20.0, 6.5797362673929057459, 0.0 }, { 3.6666666666666667, 2014.0, -3.1415926535897932385, 0.1, -36.988356711748296440, -102.242185767588750178 } }; static void acb_set_dddd(acb_t z, double a, double ar, double b, double br) { arf_set_d(arb_midref(acb_realref(z)), a); mag_set_d(arb_radref(acb_realref(z)), ar); arf_set_d(arb_midref(acb_imagref(z)), b); mag_set_d(arb_radref(acb_imagref(z)), br); } int main() { slong iter; flint_rand_t state; flint_printf("elliptic_p...."); fflush(stdout); flint_randinit(state); /* check test values */ for (iter = 0; iter < 100; iter++) { slong i; acb_t z, tau, p1, p2; acb_init(z); acb_init(tau); acb_init(p1); acb_init(p2); for (i = 0; i < NUM_TESTS; i++) { acb_set_dddd(z, testdata[i][0], 0.0, testdata[i][1], 0.0); acb_set_dddd(tau, testdata[i][2], 0.0, testdata[i][3], 0.0); acb_set_dddd(p2, testdata[i][4], EPS, testdata[i][5], EPS); acb_modular_elliptic_p(p1, z, tau, 2 + n_randint(state, 1000)); if (!acb_overlaps(p1, p2)) { flint_printf("FAIL (test value)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("p1 = "); acb_printd(p1, 15); flint_printf("\n\n"); flint_printf("p2 = "); acb_printd(p2, 15); flint_printf("\n\n"); abort(); } } acb_clear(z); acb_clear(tau); acb_clear(p1); acb_clear(p2); } /* Test periods */ for (iter = 0; iter < 2000; iter++) { acb_t tau, z1, z2, p1, p2; slong m, n, e0, prec0, prec1, prec2; acb_init(tau); acb_init(z1); acb_init(z2); acb_init(p1); acb_init(p2); e0 = 1 + n_randint(state, 10); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_randtest(tau, state, prec0, e0); if (arf_sgn(arb_midref(acb_imagref(tau))) < 0) acb_neg(tau, tau); acb_randtest(z1, state, prec0, e0); acb_randtest(p1, state, prec0, e0); acb_randtest(p2, state, prec0, e0); /* z2 = z1 + m + n*tau */ m = n_randint(state, 10); n = n_randint(state, 10); acb_add_ui(z2, z1, m, prec0); acb_addmul_ui(z2, tau, n, prec0); acb_modular_elliptic_p(p1, z1, tau, prec1); acb_modular_elliptic_p(p2, z2, tau, prec2); if (!acb_overlaps(p1, p2)) { flint_printf("FAIL (overlap)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); flint_printf("p1 = "); acb_printd(p1, 15); flint_printf("\n\n"); flint_printf("p2 = "); acb_printd(p2, 15); flint_printf("\n\n"); abort(); } acb_modular_elliptic_p(z1, z1, tau, prec1); if (!acb_overlaps(z1, p1)) { flint_printf("FAIL (aliasing)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("p1 = "); acb_printd(p1, 15); flint_printf("\n\n"); abort(); } acb_clear(tau); acb_clear(z1); acb_clear(z2); acb_clear(p1); acb_clear(p2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-elliptic_p_zpx.c000066400000000000000000000113361264125401100211470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("elliptic_p_zpx...."); fflush(stdout); flint_randinit(state); /* Test differential equation */ for (iter = 0; iter < 5000; iter++) { acb_t tau, z; acb_ptr g, wp, wp3, wpd, wpd2; slong prec, len, i; len = 1 + n_randint(state, 15); prec = 2 + n_randint(state, 1000); acb_init(tau); acb_init(z); g = _acb_vec_init(2); wp = _acb_vec_init(len + 1); wp3 = _acb_vec_init(len); wpd = _acb_vec_init(len); wpd2 = _acb_vec_init(len); acb_randtest(tau, state, prec, 10); acb_randtest(z, state, prec, 10); acb_modular_elliptic_p_zpx(wp, z, tau, len + 1, prec); acb_modular_eisenstein(g, tau, 2, prec); acb_mul_ui(g, g, 60, prec); acb_mul_ui(g + 1, g + 1, 140, prec); _acb_poly_derivative(wpd, wp, len + 1, prec); _acb_poly_mullow(wpd2, wpd, len, wpd, len, len, prec); _acb_poly_pow_ui_trunc_binexp(wp3, wp, len, 3, len, prec); _acb_vec_scalar_mul_ui(wp3, wp3, len, 4, prec); _acb_vec_scalar_submul(wp3, wp, len, g, prec); acb_sub(wp3, wp3, g + 1, prec); for (i = 0; i < len; i++) { if (!acb_overlaps(wpd2 + i, wp3 + i)) { flint_printf("FAIL (overlap)\n"); flint_printf("i = %wd len = %wd prec = %wd\n\n", i, len, prec); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("wp = "); acb_printd(wp + i, 15); flint_printf("\n\n"); flint_printf("wpd = "); acb_printd(wpd + i, 15); flint_printf("\n\n"); flint_printf("wp3 = "); acb_printd(wp3 + i, 15); flint_printf("\n\n"); abort(); } } acb_clear(tau); acb_clear(z); _acb_vec_clear(g, 2); _acb_vec_clear(wp, len + 1); _acb_vec_clear(wp3, len); _acb_vec_clear(wpd, len); _acb_vec_clear(wpd2, len); } /* Consistency test */ for (iter = 0; iter < 5000; iter++) { acb_t tau, z; acb_ptr wp1, wp2; slong prec1, prec2, len1, len2, i; len1 = n_randint(state, 15); len2 = n_randint(state, 15); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_init(tau); acb_init(z); wp1 = _acb_vec_init(len1); wp2 = _acb_vec_init(len2); acb_randtest(tau, state, prec1, 10); acb_randtest(z, state, prec1, 10); acb_modular_elliptic_p_zpx(wp1, z, tau, len1, prec1); acb_modular_elliptic_p_zpx(wp2, z, tau, len2, prec2); for (i = 0; i < FLINT_MIN(len1, len2); i++) { if (!acb_overlaps(wp1 + i, wp2 + i)) { flint_printf("FAIL (overlap)\n"); flint_printf("i = %wd len1 = %wd len2 = %wd\n\n", i, len1, len2); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("wp1 = "); acb_printd(wp1 + i, 15); flint_printf("\n\n"); flint_printf("wp2 = "); acb_printd(wp2 + i, 15); flint_printf("\n\n"); abort(); } } acb_clear(tau); acb_clear(z); _acb_vec_clear(wp1, len1); _acb_vec_clear(wp2, len2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-epsilon_arg.c000066400000000000000000000060021264125401100204160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" #include "arith.h" static void acb_modular_epsilon_arg_naive(fmpq_t arg, const psl2z_t g) { #define a (&g->a) #define b (&g->b) #define c (&g->c) #define d (&g->d) if (fmpz_is_zero(c)) { fmpz_set(fmpq_numref(arg), b); fmpz_set_ui(fmpq_denref(arg), 12); fmpq_canonicalise(arg); } else { fmpq_t t; fmpq_init(t); fmpz_add(fmpq_numref(arg), a, d); fmpz_submul_ui(fmpq_numref(arg), c, 3); fmpz_mul_ui(fmpq_denref(arg), c, 12); fmpq_canonicalise(arg); arith_dedekind_sum(t, d, c); fmpq_sub(arg, arg, t); fmpq_clear(t); } #undef a #undef b #undef c #undef d } int main() { slong iter; flint_rand_t state; flint_printf("eta_epsilon_arg...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { psl2z_t g; fmpq_t x, y; acb_t a, b; psl2z_init(g); fmpq_init(x); fmpq_init(y); acb_init(a); acb_init(b); psl2z_randtest(g, state, n_randint(state, 200)); fmpq_randtest(x, state, 100); fmpq_randtest(y, state, 100); fmpq_set_si(x, acb_modular_epsilon_arg(g), 12); acb_modular_epsilon_arg_naive(y, g); arb_sin_cos_pi_fmpq(acb_imagref(a), acb_realref(a), x, 200); arb_sin_cos_pi_fmpq(acb_imagref(b), acb_realref(b), x, 200); if (!acb_overlaps(a, b)) { flint_printf("FAIL\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n"); abort(); } psl2z_clear(g); fmpq_clear(x); fmpq_clear(y); acb_clear(a); acb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-eta.c000066400000000000000000000115331264125401100166720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("eta...."); fflush(stdout); flint_randinit(state); /* Test functional equation */ for (iter = 0; iter < 10000; iter++) { acb_t tau1, tau2, z1, z2, z3, t; fmpq_t arg; slong e0, prec0, prec1, prec2; psl2z_t g; psl2z_init(g); fmpq_init(arg); acb_init(tau1); acb_init(tau2); acb_init(z1); acb_init(z2); acb_init(z3); acb_init(t); e0 = 1 + n_randint(state, 200); prec0 = 2 + n_randint(state, 2000); prec1 = 2 + n_randint(state, 2000); prec2 = 2 + n_randint(state, 2000); acb_randtest(tau1, state, prec0, e0); acb_randtest(tau2, state, prec0, e0); acb_randtest(z1, state, prec0, e0); acb_randtest(z2, state, prec0, e0); psl2z_randtest(g, state, 1 + n_randint(state, 200)); acb_modular_transform(tau2, g, tau1, prec0); acb_modular_eta(z1, tau1, prec1); acb_modular_eta(z2, tau2, prec2); /* apply transformation */ fmpq_set_si(arg, acb_modular_epsilon_arg(g), 12); arb_sin_cos_pi_fmpq(acb_imagref(t), acb_realref(t), arg, prec1); acb_mul(z3, z1, t, prec1); acb_mul_fmpz(t, tau1, &g->c, prec1); acb_add_fmpz(t, t, &g->d, prec1); acb_sqrt(t, t, prec1); acb_mul(z3, z3, t, prec1); if (!acb_overlaps(z3, z2)) { flint_printf("FAIL (overlap)\n"); flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n"); flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); flint_printf("z3 = "); acb_printd(z3, 15); flint_printf("\n\n"); abort(); } acb_modular_eta(tau1, tau1, prec2); if (!acb_overlaps(z1, tau1)) { flint_printf("FAIL (aliasing)\n"); flint_printf("tau1 = "); acb_print(tau1); flint_printf("\n\n"); flint_printf("tau2 = "); acb_print(tau2); flint_printf("\n\n"); flint_printf("z1 = "); acb_print(z1); flint_printf("\n\n"); flint_printf("z2 = "); acb_print(z2); flint_printf("\n\n"); abort(); } acb_clear(tau1); acb_clear(tau2); acb_clear(z1); acb_clear(z2); acb_clear(z3); acb_clear(t); psl2z_clear(g); fmpq_clear(arg); } /* Test special values */ for (iter = 0; iter < 100; iter++) { acb_t tau, z; arb_t t, u; slong prec; acb_init(tau); acb_init(z); arb_init(t); arb_init(u); prec = 2 + n_randint(state, 10000); acb_randtest(z, state, prec, 10); acb_onei(tau); acb_modular_eta(z, tau, prec); arb_one(t); arb_mul_2exp_si(t, t, -2); arb_gamma(t, t, prec); arb_const_pi(u, prec); arb_root_ui(u, u, 4, prec); arb_pow_ui(u, u, 3, prec); arb_div(t, t, u, prec); arb_mul_2exp_si(t, t, -1); if (!arb_overlaps(acb_realref(z), t) || !arb_contains_zero(acb_imagref(z))) { flint_printf("FAIL (value 1)\n"); flint_printf("tau = "); acb_print(tau); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); abort(); } acb_clear(tau); acb_clear(z); arb_clear(t); arb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-fundamental_domain_approx.c000066400000000000000000000116611264125401100233410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("fundamental_domain_approx...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpq_t x, y; psl2z_t g; arf_t one_minus_eps, tol; acb_t z, w, w2; arb_t t; slong prec; fmpq_init(x); fmpq_init(y); psl2z_init(g); acb_init(z); acb_init(w); acb_init(w2); arf_init(one_minus_eps); arf_init(tol); arb_init(t); /* pick an exact point in the upper half plane */ fmpq_randtest(x, state, 1 + n_randint(state, 500)); do { fmpq_randtest(y, state, 1 + n_randint(state, 500)); } while (fmpz_sgn(fmpq_numref(y)) <= 0); /* pick a tolerance */ arf_set_ui_2exp_si(tol, 1, -(slong) n_randint(state, 500)); /* now increase the precision until convergence */ for (prec = 32; ; prec *= 2) { if (prec > 16384) { flint_printf("FAIL (no convergence)\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n"); flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n\n"); abort(); } arb_set_fmpq(acb_realref(z), x, prec); arb_set_fmpq(acb_imagref(z), y, prec); arf_set_ui_2exp_si(one_minus_eps, 1, -prec / 4); arf_sub_ui(one_minus_eps, one_minus_eps, 1, prec, ARF_RND_DOWN); arf_neg(one_minus_eps, one_minus_eps); acb_modular_fundamental_domain_approx(w, g, z, one_minus_eps, prec); acb_modular_transform(w2, g, z, prec); if (!psl2z_is_correct(g) || !acb_overlaps(w, w2)) { flint_printf("FAIL (incorrect transformation)\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n"); flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n\n"); abort(); } /* success */ if (acb_modular_is_in_fundamental_domain(w, tol, prec)) break; } /* check that g^(-1) * w contains x+yi */ psl2z_inv(g, g); acb_modular_transform(w2, g, w, 2 + n_randint(state, 1000)); if (!arb_contains_fmpq(acb_realref(w2), x) || !arb_contains_fmpq(acb_imagref(w2), y)) { flint_printf("FAIL (inverse containment)\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n"); flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n\n"); abort(); } fmpq_clear(x); fmpq_clear(y); psl2z_clear(g); acb_clear(z); acb_clear(w); acb_clear(w2); arf_clear(one_minus_eps); arf_clear(tol); arb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-hilbert_class_poly.c000066400000000000000000000201231264125401100217750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "fmpz_poly.h" #include "acb_modular.h" /* reference values h_(-d)(2015) mod 31337 computed using sage */ static const short hilbert_poly_values[1000] = { 0, 0, 0, 2015, 287, 0, 0, 5390, 25352, 0, 0, 3446, 10689, 0, 0, 7571, 27889, 0, 0, 9315, 17503, 0, 0, 20694, 1734, 0, 0, 5911, 29250, 0, 0, 6194, 3783, 0, 0, 6982, 30449, 0, 0, 10645, 11069, 0, 0, 494, 29262, 0, 0, 10595, 22835, 0, 0, 18309, 24632, 0, 0, 6433, 5042, 0, 0, 9174, 24082, 0, 0, 3463, 30027, 0, 0, 11406, 22491, 0, 0, 16831, 8457, 0, 0, 21721, 19275, 0, 0, 23777, 28295, 0, 0, 13585, 26717, 0, 0, 632, 20965, 0, 0, 9886, 852, 0, 0, 18674, 12461, 0, 0, 17204, 23887, 0, 0, 132, 11124, 0, 0, 29609, 2760, 0, 0, 29227, 28978, 0, 0, 29543, 20831, 0, 0, 12260, 15153, 0, 0, 18215, 29267, 0, 0, 13864, 4648, 0, 0, 9591, 3948, 0, 0, 29683, 20283, 0, 0, 30212, 23760, 0, 0, 10290, 17465, 0, 0, 31207, 21341, 0, 0, 19076, 29310, 0, 0, 740, 11697, 0, 0, 20446, 7258, 0, 0, 16515, 29406, 0, 0, 19948, 20065, 0, 0, 8576, 19014, 0, 0, 1647, 1354, 0, 0, 19468, 6933, 0, 0, 2065, 17883, 0, 0, 19430, 5539, 0, 0, 5738, 25233, 0, 0, 21651, 6815, 0, 0, 23927, 28399, 0, 0, 3108, 23302, 0, 0, 17409, 7911, 0, 0, 26800, 31051, 0, 0, 14360, 11091, 0, 0, 10984, 11954, 0, 0, 26389, 3557, 0, 0, 3298, 18516, 0, 0, 22211, 2972, 0, 0, 22613, 5274, 0, 0, 27799, 13362, 0, 0, 8002, 23366, 0, 0, 31122, 20593, 0, 0, 356, 19130, 0, 0, 10024, 2373, 0, 0, 19390, 28768, 0, 0, 25504, 4440, 0, 0, 14798, 8726, 0, 0, 6180, 7623, 0, 0, 12941, 31038, 0, 0, 14370, 29147, 0, 0, 166, 10994, 0, 0, 8397, 354, 0, 0, 26973, 17435, 0, 0, 21128, 5064, 0, 0, 20453, 30343, 0, 0, 25679, 6503, 0, 0, 28364, 4924, 0, 0, 6341, 11339, 0, 0, 10624, 17028, 0, 0, 28001, 192, 0, 0, 27052, 28470, 0, 0, 10034, 12162, 0, 0, 25236, 6842, 0, 0, 19334, 7593, 0, 0, 29159, 26694, 0, 0, 14719, 26199, 0, 0, 9382, 25741, 0, 0, 31174, 8440, 0, 0, 4218, 17722, 0, 0, 11574, 8090, 0, 0, 9938, 4982, 0, 0, 22701, 6931, 0, 0, 29372, 29088, 0, 0, 28, 24186, 0, 0, 23852, 7521, 0, 0, 18508, 9883, 0, 0, 2392, 30611, 0, 0, 26103, 11926, 0, 0, 27676, 24118, 0, 0, 7495, 15441, 0, 0, 12681, 20030, 0, 0, 8106, 3260, 0, 0, 25626, 24143, 0, 0, 17471, 9620, 0, 0, 24315, 24991, 0, 0, 25966, 12488, 0, 0, 9839, 25896, 0, 0, 14932, 27863, 0, 0, 20652, 11663, 0, 0, 1779, 5540, 0, 0, 2066, 24758, 0, 0, 23522, 20408, 0, 0, 26357, 2423, 0, 0, 14671, 18184, 0, 0, 16904, 264, 0, 0, 27879, 30997, 0, 0, 1506, 23000, 0, 0, 1236, 13243, 0, 0, 24917, 2346, 0, 0, 2397, 14849, 0, 0, 21298, 15702, 0, 0, 9627, 8103, 0, 0, 26185, 6738, 0, 0, 2476, 21350, 0, 0, 7578, 9859, 0, 0, 19157, 5329, 0, 0, 401, 3223, 0, 0, 30337, 21258, 0, 0, 25707, 14593, 0, 0, 8611, 15496, 0, 0, 12225, 1505, 0, 0, 23534, 16704, 0, 0, 13230, 19926, 0, 0, 12220, 19104, 0, 0, 6130, 12697, 0, 0, 19881, 6864, 0, 0, 25044, 7436, 0, 0, 29137, 14435, 0, 0, 20628, 26292, 0, 0, 30933, 8606, 0, 0, 28752, 23603, 0, 0, 11633, 21739, 0, 0, 22592, 18621, 0, 0, 20125, 1595, 0, 0, 25306, 15723, 0, 0, 1643, 16444, 0, 0, 11825, 27858, 0, 0, 13835, 4948, 0, 0, 29003, 12298, 0, 0, 16479, 12920, 0, 0, 25238, 15558, 0, 0, 4102, 16578, 0, 0, 10456, 546, 0, 0, 3738, 28968, 0, 0, 20266, 8035, 0, 0, 9779, 25941, 0, 0, 5911, 20127, 0, 0, 18291, 28982, 0, 0, 18831, 29846, 0, 0, 21272, 11493, 0, 0, 24427, 28574, 0, 0, 22664, 14849, 0, 0, 30445, 20996, 0, 0, 13612, 18604, 0, 0, 19880, 19227, 0, 0, 6230, 17398, 0, 0, 29192, 29933, 0, 0, 25046, 14031, 0, 0, 24100, 463, 0, 0, 19254, 17038, 0, 0, 19912, 10339, 0, 0, 12475, 24909, 0, 0, 3292, 18482, 0, 0, 1542, 24603, 0, 0, 24850, 2332, 0, 0, 22262, 14510, 0, 0, 16526, 18396, 0, 0, 30544, 14396, 0, 0, 2788, 18461, 0, 0, 17619, 14749, 0, 0, 29832, 24740, 0, 0, 19298, 20355, 0, 0, 538, 18003, 0, 0, 4225, 4401, 0, 0, 28095, 1371, 0, 0, 2724, 353, 0, 0, 8917, 943, 0, 0, 4998, 2384, 0, 0, 14677, 9528, 0, 0, 7351, 13960, 0, 0, 4467, 8153, 0, 0, 16711, 8606, 0, 0, 24590, 1061, 0, 0, 7678, 5647, 0, 0, 27940, 3563, 0, 0, 11137, 29574, 0, 0, 15623, 29261, 0, 0, 15422, 3266, 0, 0, 26284, 9039, 0, 0, 9616, 21817, 0, 0, 2661, 8479, 0, 0, 19882, 5965, 0, 0, 13459, 2231, 0, 0, 10839, 22085, 0, 0, 23581, 14883, 0, 0, 7516, 20147, 0, 0, 7072, 16192, 0, 0, 26870, 29168, 0, 0, 5724, 19808, 0, 0, 25458, 21905, 0, 0, 28942, 29586, 0, 0, 13256, 6359, 0, 0, 15267, 8726, 0, 0, 29008, 24734, 0, 0, 2786, 716, 0, 0, 29798, 3021, 0, 0, 1388, 28017, 0, 0, 26001, 11541, 0, 0, 19326, 2630, 0, 0, 5326, 1153, 0, 0, 12367, 12089, 0, 0, 15701, 7816, 0, 0, 28096, 13980, 0, 0, 15683, 16412, 0, 0, 29609, 21907, 0, 0, 2266, 30126, 0, 0, 26922, 29563, 0, 0, 27024, 11031, 0, 0, 28714, 4013, 0, 0, 20446, 30395, 0, 0, 1980, 26546, 0, 0, 26413, 13346, 0, 0, 4083, 837, 0, 0, 7134, 251, 0, 0, 29540, 6521, 0, 0, 18515, 2436, 0, 0, 21198, 24291, 0, 0, 26451, 28377, 0, 0, 18689, 15300, 0, 0, 8527, 27153, 0, 0, 18586, 30431, 0, 0, 28981, 13795, 0, 0, 11286, 26207, 0, 0, 11870, 2833, 0, 0, 6996, 19018, 0, 0, 22638, 18958, 0, 0, 10333, 12804, 0, 0, 13618, 8212, 0, 0, 30926, 11947, 0, 0, 6681 }; static const int hilbert_poly_values_2[] = { -2000, 13490, -1999, 10172, -4000, 2042, -3999, 16478, -8000, 14919, -7999, 15365, -16000, 8190, -15999, 30928, -32000, 10486, -31999, 2808, -64000, 26310, -63999, 23551, /* slow -128000, 30815, -127999, 2144, -256000, 5257, -255999, 18151, -512000, 31288, -511999, 30227, -1024000, 14241, -1023999, 16711, */ 0, 0, }; int main() { flint_printf("hilbert_class_poly...."); fflush(stdout); { slong i; mp_limb_t c; fmpz_poly_t hd; nmod_poly_t hdp; fmpz_poly_init(hd); nmod_poly_init(hdp, 31337); for (i = 0; i < 1000; i++) { acb_modular_hilbert_class_poly(hd, -i); fmpz_poly_get_nmod_poly(hdp, hd); c = nmod_poly_evaluate_nmod(hdp, 2015); if (c != hilbert_poly_values[i]) { flint_printf("FAIL!\n"); flint_printf("D = %wd\n", -i); flint_printf("c = %wu\n", c); flint_printf("expected = %d\n", (int) hilbert_poly_values[i]); abort(); } } for (i = 0; hilbert_poly_values_2[2 * i] != 0; i++) { acb_modular_hilbert_class_poly(hd, hilbert_poly_values_2[2 * i]); fmpz_poly_get_nmod_poly(hdp, hd); c = nmod_poly_evaluate_nmod(hdp, 2015); if (c != hilbert_poly_values_2[2 * i + 1]) { flint_printf("FAIL!\n"); flint_printf("D = %wd\n", -i); flint_printf("c = %wu\n", c); flint_printf("expected = %d\n", (int) hilbert_poly_values_2[2*i+1]); abort(); } } fmpz_poly_clear(hd); nmod_poly_clear(hdp); } flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-j.c000066400000000000000000000102661264125401100163540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("j...."); fflush(stdout); flint_randinit(state); /* Test SL2Z invariance */ for (iter = 0; iter < 10000; iter++) { acb_t tau1, tau2, z1, z2; slong e0, prec0, prec1, prec2; psl2z_t g; psl2z_init(g); acb_init(tau1); acb_init(tau2); acb_init(z1); acb_init(z2); e0 = 1 + n_randint(state, 100); prec0 = 2 + n_randint(state, 2000); prec1 = 2 + n_randint(state, 2000); prec2 = 2 + n_randint(state, 2000); acb_randtest(tau1, state, prec0, e0); acb_randtest(tau2, state, prec0, e0); acb_randtest(z1, state, prec0, e0); acb_randtest(z2, state, prec0, e0); psl2z_randtest(g, state, 1 + n_randint(state, 200)); acb_modular_transform(tau2, g, tau1, prec0); acb_modular_j(z1, tau1, prec1); acb_modular_j(z2, tau2, prec2); if (!acb_overlaps(z1, z2)) { flint_printf("FAIL (overlap)\n"); flint_printf("tau1 = "); acb_print(tau1); flint_printf("\n\n"); flint_printf("tau2 = "); acb_print(tau2); flint_printf("\n\n"); flint_printf("z1 = "); acb_print(z1); flint_printf("\n\n"); flint_printf("z2 = "); acb_print(z2); flint_printf("\n\n"); abort(); } acb_modular_j(tau1, tau1, prec2); if (!acb_overlaps(z1, tau1)) { flint_printf("FAIL (aliasing)\n"); flint_printf("tau1 = "); acb_print(tau1); flint_printf("\n\n"); flint_printf("tau2 = "); acb_print(tau2); flint_printf("\n\n"); flint_printf("z1 = "); acb_print(z1); flint_printf("\n\n"); flint_printf("z2 = "); acb_print(z2); flint_printf("\n\n"); abort(); } acb_clear(tau1); acb_clear(tau2); acb_clear(z1); acb_clear(z2); psl2z_clear(g); } /* Test special values */ for (iter = 0; iter < 100; iter++) { acb_t tau, z; slong prec; acb_init(tau); acb_init(z); prec = 2 + n_randint(state, 2000); acb_randtest(z, state, prec, 10); acb_onei(tau); acb_modular_j(z, tau, prec); acb_sub_ui(z, z, 1728, prec); if (!acb_contains_zero(z)) { flint_printf("FAIL (value 1)\n"); flint_printf("tau = "); acb_print(tau); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); abort(); } acb_set_ui(tau, 2); acb_div_ui(tau, tau, 3, prec); acb_exp_pi_i(tau, tau, prec); acb_modular_j(z, tau, prec); if (!acb_contains_zero(z)) { flint_printf("FAIL (value 2)\n"); flint_printf("tau = "); acb_print(tau); flint_printf("\n\n"); flint_printf("z = "); acb_print(z); flint_printf("\n\n"); abort(); } acb_clear(tau); acb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-lambda.c000066400000000000000000000101341264125401100173350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("lambda...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_t tau1, tau2, z1, z2, z3, t; slong e0, prec0, prec1, prec2, step; acb_init(tau1); acb_init(tau2); acb_init(z1); acb_init(z2); acb_init(z3); acb_init(t); e0 = 1 + n_randint(state, 100); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_randtest(tau1, state, prec0, e0); acb_randtest(tau2, state, prec0, e0); acb_randtest(z1, state, prec0, e0); acb_randtest(z2, state, prec0, e0); acb_set(tau2, tau1); step = n_randint(state, 10); /* Test invariance */ while (step --> 0) { if (n_randint(state, 2)) { acb_add_ui(tau2, tau2, 2, prec0); } else { acb_mul_si(z1, tau2, -2, prec0); acb_add_ui(z1, z1, 1, prec0); acb_div(tau2, tau2, z1, prec0); } } acb_modular_lambda(z1, tau1, prec1); acb_modular_lambda(z2, tau2, prec2); /* Compare with eta */ acb_mul_2exp_si(tau1, tau1, -1); acb_modular_eta(z3, tau1, prec2); acb_mul_2exp_si(tau1, tau1, 2); acb_modular_eta(t, tau1, prec2); acb_mul(t, t, t, prec2); acb_mul(z3, z3, t, prec2); acb_mul_2exp_si(tau1, tau1, -1); acb_modular_eta(t, tau1, prec2); acb_pow_ui(t, t, 3, prec2); acb_div(z3, z3, t, prec2); acb_pow_ui(z3, z3, 8, prec2); acb_mul_2exp_si(z3, z3, 4); if (!acb_overlaps(z1, z2) || !acb_overlaps(z1, z3)) { flint_printf("FAIL (overlap)\n"); flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n"); flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); flint_printf("z3 = "); acb_printd(z3, 15); flint_printf("\n\n"); abort(); } acb_modular_lambda(tau1, tau1, prec2); if (!acb_overlaps(z1, tau1)) { flint_printf("FAIL (aliasing)\n"); flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n"); flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); abort(); } acb_clear(tau1); acb_clear(tau2); acb_clear(z1); acb_clear(z2); acb_clear(z3); acb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-psl2z_inv.c000066400000000000000000000050521264125401100200460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("psl2z_inv...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { psl2z_t f, g, h, i; psl2z_init(f); psl2z_init(g); psl2z_init(h); psl2z_init(i); psl2z_randtest(f, state, n_randint(state, 100)); psl2z_randtest(g, state, n_randint(state, 100)); psl2z_randtest(h, state, n_randint(state, 100)); psl2z_inv(g, f); psl2z_mul(h, f, g); psl2z_one(i); if (!psl2z_equal(h, i) || !psl2z_is_correct(g)) { flint_printf("FAIL\n"); flint_printf("f = "); psl2z_print(f); flint_printf("\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n"); flint_printf("h = "); psl2z_print(h); flint_printf("\n"); flint_printf("i = "); psl2z_print(i); flint_printf("\n"); abort(); } psl2z_inv(f, f); if (!psl2z_equal(f, g) || !psl2z_is_correct(f)) { flint_printf("FAIL (aliasing)\n"); flint_printf("f = "); psl2z_print(f); flint_printf("\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n"); abort(); } psl2z_clear(f); psl2z_clear(g); psl2z_clear(h); psl2z_clear(i); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-psl2z_mul.c000066400000000000000000000051011264125401100200420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("psl2z_mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { psl2z_t f, g, h, u, v; psl2z_init(f); psl2z_init(g); psl2z_init(h); psl2z_init(u); psl2z_init(v); psl2z_randtest(f, state, n_randint(state, 100)); psl2z_randtest(g, state, n_randint(state, 100)); psl2z_randtest(h, state, n_randint(state, 100)); psl2z_randtest(u, state, n_randint(state, 100)); psl2z_randtest(v, state, n_randint(state, 100)); /* test (f*g)*h = f*(g*h) */ psl2z_mul(u, f, g); psl2z_mul(u, u, h); psl2z_mul(v, g, h); psl2z_mul(v, f, v); if (!psl2z_equal(u, v) || !psl2z_is_correct(u) || !psl2z_is_correct(v)) { flint_printf("FAIL\n"); flint_printf("f = "); psl2z_print(f); flint_printf("\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n"); flint_printf("h = "); psl2z_print(h); flint_printf("\n"); flint_printf("u = "); psl2z_print(u); flint_printf("\n"); flint_printf("v = "); psl2z_print(v); flint_printf("\n"); abort(); } psl2z_clear(f); psl2z_clear(g); psl2z_clear(h); psl2z_clear(u); psl2z_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-theta.c000066400000000000000000000063621264125401100172320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("theta...."); fflush(stdout); flint_randinit(state); /* Test consistency with/without transform */ for (iter = 0; iter < 10000; iter++) { acb_t t1, t2, t3, t4, t1b, t2b, t3b, t4b, z, tau; slong prec0, prec1, prec2, e0; acb_init(t1); acb_init(t2); acb_init(t3); acb_init(t4); acb_init(t1b); acb_init(t2b); acb_init(t3b); acb_init(t4b); acb_init(z); acb_init(tau); prec0 = 2 + n_randint(state, 2000); prec1 = 2 + n_randint(state, 2000); prec2 = 2 + n_randint(state, 2000); e0 = 1 + n_randint(state, 100); acb_randtest(tau, state, prec0, e0); acb_randtest(z, state, prec0, e0); acb_modular_theta(t1, t2, t3, t4, z, tau, prec1); acb_modular_theta_notransform(t1b, t2b, t3b, t4b, z, tau, prec2); if (!acb_overlaps(t1, t1b) || !acb_overlaps(t2, t2b) || !acb_overlaps(t3, t3b) || !acb_overlaps(t4, t4b)) { flint_printf("FAIL (overlap)\n"); flint_printf("z = "); acb_printd(z, 25); flint_printf("\n\n"); flint_printf("tau = "); acb_printd(tau, 25); flint_printf("\n\n"); flint_printf("t1 = "); acb_printd(t1, 15); flint_printf("\n\n"); flint_printf("t1b = "); acb_printd(t1b, 15); flint_printf("\n\n"); flint_printf("t2 = "); acb_printd(t2, 15); flint_printf("\n\n"); flint_printf("t2b = "); acb_printd(t2b, 15); flint_printf("\n\n"); flint_printf("t3 = "); acb_printd(t3, 15); flint_printf("\n\n"); flint_printf("t3b = "); acb_printd(t3b, 15); flint_printf("\n\n"); flint_printf("t4 = "); acb_printd(t4, 15); flint_printf("\n\n"); flint_printf("t4b = "); acb_printd(t4b, 15); flint_printf("\n\n"); abort(); } acb_clear(t1); acb_clear(t2); acb_clear(t3); acb_clear(t4); acb_clear(t1b); acb_clear(t2b); acb_clear(t3b); acb_clear(t4b); acb_clear(z); acb_clear(tau); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-theta_const_sum_rs.c000066400000000000000000000061631264125401100220270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("theta_const_sum_rs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { acb_t q, t2a, t2b, t3a, t3b, t4a, t4b; slong prec1, prec2, N; acb_init(q); acb_init(t2a); acb_init(t2b); acb_init(t3a); acb_init(t3b); acb_init(t4a); acb_init(t4b); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); N = n_randint(state, 300); acb_randtest(q, state, prec1, 3); acb_randtest(t2a, state, prec1, 3); acb_randtest(t2b, state, prec1, 3); acb_randtest(t3a, state, prec1, 3); acb_randtest(t3b, state, prec1, 3); acb_randtest(t4a, state, prec1, 3); acb_randtest(t4b, state, prec1, 3); acb_modular_theta_const_sum_basecase(t2a, t3a, t4a, q, N, prec1); acb_modular_theta_const_sum_rs(t2b, t3b, t4b, q, N, prec2); if (!acb_overlaps(t2a, t2b) || !acb_overlaps(t3a, t3b) || !acb_overlaps(t4a, t4b)) { flint_printf("FAIL (overlap) iter = %wd\n", iter); flint_printf("N = %wd\n", N); flint_printf("q = "); acb_printd(q, 50); flint_printf("\n\n"); flint_printf("t2a = "); acb_printd(t2a, 50); flint_printf("\n\n"); flint_printf("t2b = "); acb_printd(t2b, 50); flint_printf("\n\n"); flint_printf("t3a = "); acb_printd(t3a, 50); flint_printf("\n\n"); flint_printf("t3b = "); acb_printd(t3b, 50); flint_printf("\n\n"); flint_printf("t4a = "); acb_printd(t4a, 50); flint_printf("\n\n"); flint_printf("t4b = "); acb_printd(t4b, 50); flint_printf("\n\n"); abort(); } acb_clear(q); acb_clear(t2a); acb_clear(t2b); acb_clear(t3a); acb_clear(t3b); acb_clear(t4a); acb_clear(t4b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-theta_sum.c000066400000000000000000000120241264125401100201060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("theta_sum...."); fflush(stdout); flint_randinit(state); /* Very weak test, just testing the error bounds and not that we compute the right functions */ for (iter = 0; iter < 10000; iter++) { acb_ptr t1a, t1b, t2a, t2b, t3a, t3b, t4a, t4b; acb_t w, q; int w_is_unit; slong prec0, e0, prec1, prec2, len1, len2, i; acb_init(w); acb_init(q); e0 = 1 + n_randint(state, 100); prec0 = 2 + n_randint(state, 3000); prec1 = 2 + n_randint(state, 3000); prec2 = 2 + n_randint(state, 3000); len1 = 1 + n_randint(state, 30); len2 = 1 + n_randint(state, 30); t1a = _acb_vec_init(len1); t2a = _acb_vec_init(len1); t3a = _acb_vec_init(len1); t4a = _acb_vec_init(len1); t1b = _acb_vec_init(len2); t2b = _acb_vec_init(len2); t3b = _acb_vec_init(len2); t4b = _acb_vec_init(len2); if (n_randint(state, 2)) { arb_randtest(acb_realref(q), state, prec0, e0); arb_zero(acb_imagref(q)); acb_exp_pi_i(w, q, prec0); w_is_unit = n_randint(state, 2); } else { acb_randtest(w, state, prec0, e0); w_is_unit = 0; } acb_randtest(q, state, prec0, e0); for (i = 0; i < len1; i++) { acb_randtest(t1a + i, state, prec0, e0); acb_randtest(t2a + i, state, prec0, e0); acb_randtest(t3a + i, state, prec0, e0); acb_randtest(t4a + i, state, prec0, e0); } for (i = 0; i < len2; i++) { acb_randtest(t1b + i, state, prec0, e0); acb_randtest(t2b + i, state, prec0, e0); acb_randtest(t3b + i, state, prec0, e0); acb_randtest(t4b + i, state, prec0, e0); } acb_modular_theta_sum(t1a, t2a, t3a, t4a, w, w_is_unit, q, len1, prec1); acb_modular_theta_sum(t1b, t2b, t3b, t4b, w, w_is_unit & n_randint(state, 2), q, len2, prec2); for (i = 0; i < FLINT_MIN(len1, len2); i++) { if (!acb_overlaps(t1a + i, t1b + i) || !acb_overlaps(t2a + i, t2b + i) || !acb_overlaps(t3a + i, t3b + i) || !acb_overlaps(t4a + i, t4b + i)) { flint_printf("FAIL (overlap) iter = %wd\n", iter); flint_printf("len1 = %wd, len2 = %wd, prec1 = %wd, prec2 = %wd\n\n", len1, len2, prec1, prec2); flint_printf("i = %wd\n\n", i); flint_printf("q = "); acb_printd(q, 50); flint_printf("\n\n"); flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n"); flint_printf("t1a = "); acb_printd(t1a + i, 50); flint_printf("\n\n"); flint_printf("t1b = "); acb_printd(t1b + i, 50); flint_printf("\n\n"); flint_printf("t2a = "); acb_printd(t2a + i, 50); flint_printf("\n\n"); flint_printf("t2b = "); acb_printd(t2b + i, 50); flint_printf("\n\n"); flint_printf("t3a = "); acb_printd(t3a + i, 50); flint_printf("\n\n"); flint_printf("t3b = "); acb_printd(t3b + i, 50); flint_printf("\n\n"); flint_printf("t4a = "); acb_printd(t4a + i, 50); flint_printf("\n\n"); flint_printf("t4b = "); acb_printd(t4b + i, 50); flint_printf("\n\n"); abort(); } } _acb_vec_clear(t1a, len1); _acb_vec_clear(t2a, len1); _acb_vec_clear(t3a, len1); _acb_vec_clear(t4a, len1); _acb_vec_clear(t1b, len2); _acb_vec_clear(t2b, len2); _acb_vec_clear(t3b, len2); _acb_vec_clear(t4b, len2); acb_clear(w); acb_clear(q); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/test/t-transform.c000066400000000000000000000052731264125401100201400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" int main() { slong iter; flint_rand_t state; flint_printf("transform...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { psl2z_t g; acb_t z, w1, w2, t; slong prec; psl2z_init(g); acb_init(z); acb_init(w1); acb_init(w2); acb_init(t); psl2z_randtest(g, state, n_randint(state, 20)); acb_randtest(z, state, 1 + n_randint(state, 200), 1 + n_randint(state, 20)); acb_randtest(w1, state, 1 + n_randint(state, 200), 1 + n_randint(state, 20)); acb_randtest(w2, state, 1 + n_randint(state, 200), 1 + n_randint(state, 20)); acb_modular_transform(w1, g, z, 2 + n_randint(state, 200)); prec = 2 + n_randint(state, 200); acb_mul_fmpz(t, z, &g->a, prec); acb_add_fmpz(t, t, &g->b, prec); acb_mul_fmpz(w2, z, &g->c, prec); acb_add_fmpz(w2, w2, &g->d, prec); acb_div(w2, t, w2, prec); if (!acb_overlaps(w1, w2)) { flint_printf("FAIL\n"); flint_printf("g = "); psl2z_print(g); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 30); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1, 30); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2, 30); flint_printf("\n\n"); abort(); } psl2z_clear(g); acb_clear(z); acb_clear(w1); acb_clear(w2); acb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_modular/theta.c000066400000000000000000000122671264125401100160130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" static void acb_mul_4th_root(acb_t y, const acb_t x, int r, slong prec) { r &= 7; if (r == 0) { acb_set(y, x); } else if (r == 4) { acb_neg(y, x); } else if (r == 2) { acb_mul_onei(y, x); } else if (r == 6) { acb_mul_onei(y, x); acb_neg(y, y); } else { fmpq_t t; fmpq_init(t); fmpq_set_si(t, r, 4); arb_sin_cos_pi_fmpq(acb_imagref(y), acb_realref(y), t, prec); acb_mul(y, y, x, prec); fmpq_clear(t); } } void acb_modular_theta(acb_t theta1, acb_t theta2, acb_t theta3, acb_t theta4, const acb_t z, const acb_t tau, slong prec) { fmpq_t t; psl2z_t g; arf_t one_minus_eps; acb_t z_prime, tau_prime, q, q4, w, A, B; acb_struct thetas[4]; int w_is_unit, R[4], S[4], C; psl2z_init(g); fmpq_init(t); arf_init(one_minus_eps); acb_init(z_prime); acb_init(tau_prime); acb_init(q); acb_init(q4); acb_init(w); acb_init(thetas + 0); acb_init(thetas + 1); acb_init(thetas + 2); acb_init(thetas + 3); acb_init(A); acb_init(B); /* move tau to the fundamental domain */ arf_set_ui_2exp_si(one_minus_eps, 63, -6); acb_modular_fundamental_domain_approx(tau_prime, g, tau, one_minus_eps, prec); /* compute transformation parameters */ acb_modular_theta_transform(R, S, &C, g); if (C == 0) { acb_set(z_prime, z); } else { /* B = 1/(c*tau+d) (temporarily) */ acb_mul_fmpz(B, tau, &g->c, prec); acb_add_fmpz(B, B, &g->d, prec); acb_inv(B, B, prec); /* -z/(c*tau+d) */ acb_mul(z_prime, z, B, prec); acb_neg(z_prime, z_prime); /* A = sqrt(i/(c*tau+d)) */ acb_mul_onei(A, B); acb_sqrt(A, A, prec); /* B = exp(-pi i c z^2/(c*tau+d)) */ if (acb_is_zero(z)) { acb_one(B); } else { acb_mul(B, z_prime, z, prec); acb_mul_fmpz(B, B, &g->c, prec); acb_exp_pi_i(B, B, prec); } } /* compute q_{1/4}, q */ acb_mul_2exp_si(q4, tau_prime, -2); acb_exp_pi_i(q4, q4, prec); acb_pow_ui(q, q4, 4, prec); /* compute w */ acb_exp_pi_i(w, z_prime, prec); w_is_unit = arb_is_zero(acb_imagref(z_prime)); /* evaluate theta functions of transformed variables */ acb_modular_theta_sum(thetas + 0, thetas + 1, thetas + 2, thetas + 3, w, w_is_unit, q, 1, prec); acb_mul(thetas + 0, thetas + 0, q4, prec); acb_mul(thetas + 1, thetas + 1, q4, prec); /* multiply by roots of unity */ acb_mul_4th_root(theta1, thetas + S[0], R[0], prec); acb_mul_4th_root(theta2, thetas + S[1], R[1], prec); acb_mul_4th_root(theta3, thetas + S[2], R[2], prec); acb_mul_4th_root(theta4, thetas + S[3], R[3], prec); if (C != 0) { acb_mul(A, A, B, prec); acb_mul(theta1, theta1, A, prec); acb_mul(theta2, theta2, A, prec); acb_mul(theta3, theta3, A, prec); acb_mul(theta4, theta4, A, prec); } psl2z_clear(g); fmpq_clear(t); arf_clear(one_minus_eps); acb_clear(z_prime); acb_clear(tau_prime); acb_clear(q); acb_clear(q4); acb_clear(w); acb_clear(thetas + 0); acb_clear(thetas + 1); acb_clear(thetas + 2); acb_clear(thetas + 3); acb_clear(A); acb_clear(B); } void acb_modular_theta_notransform(acb_t theta1, acb_t theta2, acb_t theta3, acb_t theta4, const acb_t z, const acb_t tau, slong prec) { acb_t q, q4, w; int w_is_unit; acb_init(q); acb_init(q4); acb_init(w); /* compute q_{1/4}, q */ acb_mul_2exp_si(q4, tau, -2); acb_exp_pi_i(q4, q4, prec); acb_pow_ui(q, q4, 4, prec); /* compute w */ acb_exp_pi_i(w, z, prec); w_is_unit = arb_is_zero(acb_imagref(z)); /* evaluate theta functions */ acb_modular_theta_sum(theta1, theta2, theta3, theta4, w, w_is_unit, q, 1, prec); acb_mul(theta1, theta1, q4, prec); acb_mul(theta2, theta2, q4, prec); acb_clear(q); acb_clear(q4); acb_clear(w); } arb-2.8.1/acb_modular/theta_const_sum.c000066400000000000000000000051131264125401100200750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" double mag_get_log2_d_approx(const mag_t x); void acb_modular_theta_const_sum(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong prec) { mag_t qmag, err; double log2q_approx; int is_real, is_real_or_imag; slong N; mag_init(qmag); mag_init(err); acb_get_mag(qmag, q); log2q_approx = mag_get_log2_d_approx(qmag); is_real = arb_is_zero(acb_imagref(q)); is_real_or_imag = is_real || arb_is_zero(acb_realref(q)); if (log2q_approx >= 0.0) { N = 1; mag_inf(err); } else { N = 0; while (0.05 * N * N < prec) { if (log2q_approx * ((N+2)*(N+2)/4) < -prec - 2) break; N++; } N = (N+2)*(N+2)/4; mag_geom_series(err, qmag, N); mag_mul_2exp_si(err, err, 1); /* each term is taken twice */ if (mag_is_inf(err)) N = 1; } if (N < 1800) acb_modular_theta_const_sum_basecase(theta2, theta3, theta4, q, N, prec); else acb_modular_theta_const_sum_rs(theta2, theta3, theta4, q, N, prec); if (is_real_or_imag) arb_add_error_mag(acb_realref(theta2), err); else acb_add_error_mag(theta2, err); if (is_real) { arb_add_error_mag(acb_realref(theta3), err); arb_add_error_mag(acb_realref(theta4), err); } else { acb_add_error_mag(theta3, err); acb_add_error_mag(theta4, err); } mag_clear(qmag); mag_clear(err); } arb-2.8.1/acb_modular/theta_const_sum_basecase.c000066400000000000000000000124061264125401100217260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" double mag_get_log2_d_approx(const mag_t x); void acb_modular_theta_const_sum_basecase(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec) { slong * tab; slong k, term_prec; double log2q_approx, log2term_approx; mag_t qmag; acb_ptr qpow; acb_t s1, s2, s3, t1, t2; if (N < 2) { acb_set_ui(theta2, 2 * (N > 0)); acb_set_ui(theta3, N > 0); acb_set(theta4, theta3); return; } if (N < 25) { acb_t q1, q2, q4, q8, q16; acb_init(q1); acb_init(q2); acb_init(q4); acb_init(q8); acb_init(q16); acb_set_round(q1, q, prec); if (N > 2) acb_mul(q2, q1, q1, prec); if (N > 4) acb_mul(q4, q2, q2, prec); if (N > 9) acb_mul(q8, q4, q4, prec); if (N > 16) acb_mul(q16, q8, q8, prec); /* theta2 = 2 + 2q^2 + 2q^4 [2q^2 + 2q^8 + 2q^16] */ if (N > 6) { if (N > 12) { acb_add(theta2, q2, q8, prec); if (N > 20) acb_add(theta2, theta2, q16, prec); acb_mul(theta2, theta2, q4, prec); } else { acb_mul(theta2, q2, q4, prec); } acb_add(theta2, theta2, q2, prec); acb_add_ui(theta2, theta2, 1, prec); } else if (N > 2) acb_add_ui(theta2, q2, 1, prec); else acb_one(theta2); acb_mul_2exp_si(theta2, theta2, 1); /* theta3 = [1 + 2q^4 + 2q^16] + [2q + 2q^9] */ /* theta4 = [1 + 2q^4 + 2q^16] - [2q + 2q^9] */ if (N > 4) { if (N > 16) acb_add(q4, q4, q16, prec); acb_mul_2exp_si(q4, q4, 1); acb_add_ui(q4, q4, 1, prec); if (N > 9) acb_addmul(q1, q1, q8, prec); acb_mul_2exp_si(q1, q1, 1); acb_add(theta3, q4, q1, prec); acb_sub(theta4, q4, q1, prec); } else { acb_mul_2exp_si(q1, q1, 1); acb_add_ui(theta3, q1, 1, prec); acb_sub_ui(theta4, q1, 1, prec); acb_neg(theta4, theta4); } acb_clear(q1); acb_clear(q2); acb_clear(q4); acb_clear(q8); acb_clear(q16); return; } mag_init(qmag); acb_init(s1); acb_init(s2); acb_init(s3); acb_init(t1); acb_init(t2); tab = flint_calloc(N, sizeof(slong)); qpow = _acb_vec_init(N); for (k = 0; k*(k+1) < N; k++) tab[k*(k+1)] = -1; for (k = 0; 4*k*k < N; k++) tab[4*k*k] = -1; for (k = 0; 4*k*(k+1) + 1 < N; k++) tab[4*k*(k+1)] = -1; if (N > 0) tab[0] = 0; if (N > 1) tab[1] = 1; acb_modular_fill_addseq(tab, N); acb_get_mag(qmag, q); log2q_approx = mag_get_log2_d_approx(qmag); for (k = 0; k < N; k++) { if (k == 0) { acb_one(qpow + k); } else if (k == 1) { acb_set_round(qpow + k, q, prec); } else if (tab[k] != 0) { log2term_approx = k * log2q_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); acb_mul_approx(qpow + k, t1, t2, qpow + tab[k], qpow + k - tab[k], term_prec, prec); } } for (k = 0; k*(k+1) < N; k++) acb_add(s1, s1, qpow + k*(k+1), prec); for (k = 1; 4*k*k < N; k++) acb_add(s2, s2, qpow + 4*k*k, prec); for (k = 0; 4*k*(k+1) + 1 < N; k++) acb_add(s3, s3, qpow + 4*k*(k+1), prec); /* theta2 = 2 + 2q^2 + 2q^6 + 2q^12 + 2q^20 + 2q^30 + ... theta3 = 1 + 2 (q^4 + q^16 + ...) + 2q (1 + q^8 + q^24 + ...) theta4 = 1 + 2 (q^4 + q^16 + ...) - 2q (1 + q^8 + q^24 + ...) */ acb_mul(s3, s3, q, prec); acb_mul_2exp_si(s3, s3, 1); acb_mul_2exp_si(s2, s2, 1); acb_add(theta3, s2, s3, prec); acb_sub(theta4, s2, s3, prec); acb_add_ui(theta3, theta3, 1, prec); acb_add_ui(theta4, theta4, 1, prec); acb_mul_2exp_si(theta2, s1, 1); _acb_vec_clear(qpow, N); flint_free(tab); acb_clear(s1); acb_clear(s2); acb_clear(s3); acb_clear(t1); acb_clear(t2); mag_clear(qmag); } arb-2.8.1/acb_modular/theta_const_sum_rs.c000066400000000000000000000153431264125401100206070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" double mag_get_log2_d_approx(const mag_t x); static const int square_best_m[] = { 2, 3, 4, 8, 12, 16, 32, 48, 80, 96, 112, 144, 240, 288, 336, 480, 560, 576, 720, 1008, 1440, 1680, 2016, 2640, 2880, 3600, 4032, 5040, 7920, 9360, 10080, 15840, 18480, 20160, 25200, 31680, 37440, 39600, 44352, 50400, 55440, 65520, 85680, 95760, 102960, 110880, 131040, 171360, 191520, 205920, 221760, 262080, 277200, 327600, 383040, 411840, 514800, 554400, 655200, 720720, 942480, 0 }; static const int square_best_m_residues[] = { 2, 2, 2, 3, 4, 4, 7, 8, 12, 14, 16, 16, 24, 28, 32, 42, 48, 48, 48, 64, 84, 96, 112, 144, 144, 176, 192, 192, 288, 336, 336, 504, 576, 576, 704, 864, 1008, 1056, 1152, 1232, 1152, 1344, 1728, 1920, 2016, 2016, 2352, 3024, 3360, 3528, 3456, 4032, 4224, 4928, 5760, 6048, 7392, 7392, 8624, 8064, 10368, 0 }; static const int trigonal_best_m[] = { 2, 6, 10, 14, 18, 30, 42, 66, 70, 90, 126, 198, 210, 330, 390, 450, 630, 990, 1170, 1386, 1638, 2142, 2310, 2730, 3150, 4950, 5850, 6930, 8190, 10710, 11970, 12870, 16830, 18018, 23562, 26334, 27846, 30030, 34650, 40950, 53550, 59850, 64350, 84150, 90090, 117810, 131670, 139230, 155610, 188370, 203490, 218790, 244530, 270270, 296010, 306306, 342342, 414414, 447678, 450450, 589050, 658350, 696150, 778050, 941850, 0 }; static const int trigonal_best_m_residues[] = { 1, 2, 3, 4, 4, 6, 8, 12, 12, 12, 16, 24, 24, 36, 42, 44, 48, 72, 84, 96, 112, 144, 144, 168, 176, 264, 308, 288, 336, 432, 480, 504, 648, 672, 864, 960, 1008, 1008, 1056, 1232, 1584, 1760, 1848, 2376, 2016, 2592, 2880, 3024, 3360, 4032, 4320, 4536, 5040, 5544, 6048, 6048, 6720, 8064, 8640, 7392, 9504, 10560, 11088, 12320, 14784, 0, }; slong acb_modular_rs_optimal_m(const int * best_ms, const int * num_residues, slong N) { slong i, m, cost, best_i, best_m, best_cost; best_i = 0; best_m = best_ms[0]; best_cost = WORD_MAX; for (i = 0; (m = best_ms[i]) != 0; i++) { cost = N / m + num_residues[i]; if (i == 0 || cost < best_cost) { best_i = i; best_cost = cost; best_m = m; } } /* flint_printf("N = %wd, best_m = %wd, best_cost = %wd, s(m) = %d\n", N, best_m, best_cost, num_residues[best_i]); */ i = best_i; return best_m; } void acb_modular_theta_const_sum_rs(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec) { slong * tab; slong k, term_prec, i, e, eprev; slong M, m2, m3, num_square, num_trigonal; double log2q_approx, log2term_approx; acb_ptr qpow; acb_t tmp1, tmp2; mag_t qmag; mag_init(qmag); acb_get_mag(qmag, q); log2q_approx = mag_get_log2_d_approx(qmag); mag_clear(qmag); acb_init(tmp1); acb_init(tmp2); /* choose rectangular splitting parameters */ m2 = acb_modular_rs_optimal_m(trigonal_best_m, trigonal_best_m_residues, N); m3 = acb_modular_rs_optimal_m(square_best_m, square_best_m_residues, N); M = FLINT_MAX(m2, m3) + 1; /* build addition sequence */ tab = flint_calloc(M, sizeof(slong)); for (k = 0; k*(k+1) < N; k++) tab[(k*(k+1)) % m2] = -1; num_trigonal = k; for (k = 0; k*k < N; k++) tab[(k*k) % m3] = -1; num_square = k; tab[m2] = -1; tab[m3] = -1; /* compute powers in addition sequence */ qpow = _acb_vec_init(M); acb_modular_fill_addseq(tab, M); for (k = 0; k < M; k++) { if (k == 0) { acb_one(qpow + k); } else if (k == 1) { acb_set_round(qpow + k, q, prec); } else if (tab[k] != 0) { log2term_approx = k * log2q_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); acb_mul_approx(qpow + k, tmp1, tmp2, qpow + tab[k], qpow + k - tab[k], term_prec, prec); } } /* compute theta2 */ acb_zero(theta2); term_prec = prec; for (k = num_trigonal - 1; k >= 0; k--) { e = k * (k + 1); /* exponent */ eprev = (k + 1) * (k + 2); log2term_approx = e * log2q_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); /* giant steps */ for (i = e / m2; i < eprev / m2; i++) { if (!acb_is_zero(theta2)) acb_mul_approx(theta2, tmp1, tmp2, theta2, qpow + m2, term_prec, prec); } acb_add(theta2, theta2, qpow + (e % m2), prec); } acb_mul_2exp_si(theta2, theta2, 1); /* compute theta3, theta4 */ acb_zero(theta3); acb_zero(theta4); term_prec = prec; for (k = num_square - 1; k >= 0; k--) { e = k * k; /* exponent */ eprev = (k + 1) * (k + 1); log2term_approx = e * log2q_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); /* giant steps */ for (i = e / m3; i < eprev / m3; i++) { if (!acb_is_zero(theta3)) acb_mul_approx(theta3, tmp1, tmp2, theta3, qpow + m3, term_prec, prec); if (!acb_is_zero(theta4)) acb_mul_approx(theta4, tmp1, tmp2, theta4, qpow + m3, term_prec, prec); } if (k == 0) { acb_mul_2exp_si(theta3, theta3, 1); acb_mul_2exp_si(theta4, theta4, 1); } acb_add(theta3, theta3, qpow + (e % m3), prec); if (k % 2 == 0) acb_add(theta4, theta4, qpow + (e % m3), prec); else acb_sub(theta4, theta4, qpow + (e % m3), prec); } acb_clear(tmp1); acb_clear(tmp2); _acb_vec_clear(qpow, M); flint_free(tab); } arb-2.8.1/acb_modular/theta_sum.c000066400000000000000000000351531264125401100166760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" double mag_get_log2_d_approx(const mag_t x) { if (mag_is_zero(x)) { return COEFF_MIN; } else if (mag_is_inf(x)) { return COEFF_MAX; } else if (COEFF_IS_MPZ(MAG_EXP(x))) { if (fmpz_sgn(MAG_EXPREF(x)) < 0) return COEFF_MIN; else return COEFF_MAX; } else { slong e = MAG_EXP(x); if (e < -20 || e > 20) return e; else return e + 1.4426950408889634074 * mag_d_log_upper_bound(MAG_MAN(x) * ldexp(1.0, -MAG_BITS)); } } void acb_modular_theta_sum(acb_ptr theta1, acb_ptr theta2, acb_ptr theta3, acb_ptr theta4, const acb_t w, int w_is_unit, const acb_t q, slong len, slong prec) { mag_t qmag, wmag, vmag; mag_ptr err; double log2q_approx, log2w_approx, log2term_approx; slong e, e1, e2, k, k1, k2, r, n, N, WN, term_prec; slong *exponents, *aindex, *bindex; acb_ptr qpow, wpow, vpow; acb_t tmp1, tmp2, v; int q_is_real, w_is_one; q_is_real = arb_is_zero(acb_imagref(q)); w_is_one = acb_is_one(w); if (w_is_one && len == 1) { acb_modular_theta_const_sum(theta2, theta3, theta4, q, prec); acb_zero(theta1); return; } mag_init(qmag); mag_init(wmag); mag_init(vmag); acb_init(tmp1); acb_init(tmp2); acb_init(v); err = _mag_vec_init(len); if (w_is_one) acb_one(v); else if (w_is_unit) acb_conj(v, w); else acb_inv(v, w, prec); acb_get_mag(qmag, q); log2q_approx = mag_get_log2_d_approx(qmag); if (w_is_unit) { mag_one(wmag); mag_one(vmag); log2w_approx = 0.0; } else { acb_get_mag(wmag, w); acb_get_mag(vmag, v); mag_max(wmag, wmag, vmag); log2w_approx = mag_get_log2_d_approx(wmag); } if (log2q_approx >= 0.0) { N = 1; for (r = 0; r < len; r++) mag_inf(err + r); } else /* Pick N and compute error bound */ { mag_t den, cmag, dmag; mag_init(den); mag_init(cmag); mag_init(dmag); N = 1; while (0.05 * N * N < prec) { log2term_approx = log2q_approx * ((N+2)*(N+2)/4) + (N+2)*log2w_approx; if (log2term_approx < -prec - 2) break; N++; } if (len == 1) { if (w_is_unit) { mag_one(den); mag_sub_lower(den, den, qmag); /* 1 - |q| is good enough */ } else /* denominator: 1 - |q|^(floor((N+1)/2)+1) * max(|w|,1/|w|) */ { mag_pow_ui(err, qmag, (N + 1) / 2 + 1); mag_mul(err, err, wmag); mag_one(den); mag_sub_lower(den, den, err); } /* no convergence */ if (mag_is_zero(den)) { N = 1; mag_inf(err); } else if (w_is_unit) { mag_pow_ui(err, qmag, ((N + 2) * (N + 2)) / 4); mag_div(err, err, den); mag_mul_2exp_si(err, err, 1); } else { mag_pow_ui(err, qmag, ((N + 2) * (N + 2)) / 4); mag_pow_ui(vmag, wmag, N + 2); mag_mul(err, err, vmag); mag_div(err, err, den); mag_mul_2exp_si(err, err, 1); } } else { /* numerator: 2 |q|^E * max(|w|,|v|)^(N+2) * (N+2)^r */ mag_pow_ui(err, qmag, ((N + 2) * (N + 2)) / 4); if (!w_is_one) { mag_pow_ui(vmag, wmag, N + 2); mag_mul(err, err, vmag); } mag_mul_2exp_si(err, err, 1); for (r = 1; r < len; r++) mag_mul_ui(err + r, err + r - 1, N + 2); /* den: 1 - |q|^floor((N+1)/2+1) * max(|w|,|v|) * exp(r/(N+2)) */ mag_pow_ui(cmag, qmag, (N + 1) / 2 + 1); mag_mul(cmag, cmag, wmag); for (r = 0; r < len; r++) { mag_set_ui(dmag, r); mag_div_ui(dmag, dmag, N + 2); mag_exp(dmag, dmag); mag_mul(dmag, cmag, dmag); mag_one(den); mag_sub_lower(den, den, dmag); if (mag_is_zero(den)) mag_inf(err + r); else mag_div(err + r, err + r, den); } } /* don't do work if we can't determine the zeroth derivative */ if (mag_is_inf(err)) N = 1; mag_clear(den); mag_clear(cmag); mag_clear(dmag); } exponents = flint_malloc(sizeof(slong) * 3 * N); aindex = exponents + N; bindex = aindex + N; qpow = _acb_vec_init(N); acb_modular_addseq_theta(exponents, aindex, bindex, N); acb_set_round(qpow + 0, q, prec); _acb_vec_zero(theta1, len); _acb_vec_zero(theta2, len); _acb_vec_zero(theta3, len); _acb_vec_zero(theta4, len); WN = (N + 3) / 2; /* compute powers of w^2 and 1/w^2 */ /* todo: conjugates... */ if (!w_is_one) { wpow = _acb_vec_init(WN); vpow = _acb_vec_init(WN + 1); acb_mul(tmp1, w, w, prec); acb_mul(tmp2, v, v, prec); _acb_vec_set_powers(wpow, tmp1, WN, prec); _acb_vec_set_powers(vpow, tmp2, WN + 1, prec); } else { wpow = vpow = NULL; } for (k = 0; k < N; k++) { e = exponents[k]; log2term_approx = e * log2q_approx + (k+2) * log2w_approx; term_prec = FLINT_MIN(FLINT_MAX(prec + log2term_approx + 16.0, 16.0), prec); if (k > 0) { k1 = aindex[k]; k2 = bindex[k]; e1 = exponents[k1]; e2 = exponents[k2]; if (e == e1 + e2) { acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k1, qpow + k2, term_prec, prec); } else if (e == 2 * e1 + e2) { acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k1, qpow + k1, term_prec, prec); acb_mul_approx(qpow + k, tmp1, tmp2, qpow + k, qpow + k2, term_prec, prec); } else { flint_printf("exponent not in addition sequence!\n"); abort(); } } if (w_is_one && len == 1) { if (k % 2 == 0) { acb_add(theta3, theta3, qpow + k, prec); if (k % 4 == 0) acb_sub(theta4, theta4, qpow + k, prec); else acb_add(theta4, theta4, qpow + k, prec); } else { acb_add(theta2, theta2, qpow + k, prec); } } else { n = k / 2 + 1; if (k % 2 == 0) { acb_ptr term; if (w_is_one) { acb_mul_2exp_si(tmp1, qpow + k, 1); acb_zero(tmp2); } else { /* tmp1 = w^(2n) + v^(2n) ~= 2 cos(2n) */ acb_add(tmp1, wpow + n, vpow + n, term_prec); acb_mul(tmp1, qpow + k, tmp1, term_prec); /* tmp2 = w^(2n) - v^(2n) ~= 2 sin(2n) */ if (len > 1) { acb_sub(tmp2, wpow + n, vpow + n, term_prec); acb_mul(tmp2, qpow + k, tmp2, term_prec); } } /* compute all the derivatives */ for (r = 0; r < len; r++) { term = (r % 2 == 0) ? tmp1 : tmp2; if (r == 1) acb_mul_ui(term, term, 2 * n, term_prec); else if (r > 1) acb_mul_ui(term, term, 4 * n * n, term_prec); acb_add(theta3 + r, theta3 + r, term, prec); if (k % 4 == 0) acb_sub(theta4 + r, theta4 + r, term, prec); else acb_add(theta4 + r, theta4 + r, term, prec); } } else { acb_ptr term; if (w_is_one) { acb_mul_2exp_si(tmp1, qpow + k, 1); acb_zero(tmp2); } else { /* tmp1 = w^(2n) + v^(2n+2) ~= 2 cos(2n+1) / w */ acb_add(tmp1, wpow + n, vpow + n + 1, term_prec); acb_mul(tmp1, qpow + k, tmp1, term_prec); /* tmp2 = w^(2n) - v^(2n+2) ~= 2 sin(2n+1) / w */ acb_sub(tmp2, wpow + n, vpow + n + 1, term_prec); acb_mul(tmp2, qpow + k, tmp2, term_prec); } /* compute all the derivatives */ for (r = 0; r < len; r++) { if (r > 0) { acb_mul_ui(tmp1, tmp1, 2 * n + 1, term_prec); acb_mul_ui(tmp2, tmp2, 2 * n + 1, term_prec); } term = (r % 2 == 0) ? tmp2 : tmp1; if (k % 4 == 1) acb_sub(theta1 + r, theta1 + r, term, prec); else acb_add(theta1 + r, theta1 + r, term, prec); term = (r % 2 == 0) ? tmp1 : tmp2; acb_add(theta2 + r, theta2 + r, term, prec); } } } } if (w_is_one && len == 1) { acb_mul_2exp_si(theta2, theta2, 1); acb_mul_2exp_si(theta3, theta3, 1); acb_mul_2exp_si(theta4, theta4, 1); } /* theta1: w * sum + 2 sin */ /* theta2: w * sum + 2 cos */ if (!w_is_one) { _acb_vec_scalar_mul(theta1, theta1, len, w, prec); _acb_vec_scalar_mul(theta2, theta2, len, w, prec); acb_add(tmp1, w, v, prec); acb_sub(tmp2, w, v, prec); } else { acb_set_ui(tmp1, 2); acb_zero(tmp2); } for (r = 0; r < len; r++) { acb_add(theta1 + r, theta1 + r, (r % 2 == 0) ? tmp2 : tmp1, prec); acb_add(theta2 + r, theta2 + r, (r % 2 == 0) ? tmp1 : tmp2, prec); } /* Coefficient r in the z-expansion gains a factor: pi^r / r! times a sign: + 2 cos = +1 * (exp + 1/exp) - 2 sin = +i * (exp - 1/exp) - 2 cos = -1 * (exp + 1/exp) + 2 sin = -i * (exp - 1/exp) ... */ acb_mul_onei(theta1, theta1); acb_neg(theta1, theta1); for (r = 1; r < len; r++) { if (r % 4 == 0) { acb_mul_onei(theta1 + r, theta1 + r); acb_neg(theta1 + r, theta1 + r); } else if (r % 4 == 1) { acb_mul_onei(theta2 + r, theta2 + r); acb_mul_onei(theta3 + r, theta3 + r); acb_mul_onei(theta4 + r, theta4 + r); } else if (r % 4 == 2) { acb_mul_onei(theta1 + r, theta1 + r); acb_neg(theta2 + r, theta2 + r); acb_neg(theta3 + r, theta3 + r); acb_neg(theta4 + r, theta4 + r); } else { acb_neg(theta1 + r, theta1 + r); acb_mul_onei(theta2 + r, theta2 + r); acb_mul_onei(theta3 + r, theta3 + r); acb_mul_onei(theta4 + r, theta4 + r); acb_neg(theta2 + r, theta2 + r); acb_neg(theta3 + r, theta3 + r); acb_neg(theta4 + r, theta4 + r); } } /* Add error bound. Note that this must be done after the rearrangements above, and before scaling by pi^r / r! below. */ for (r = 0; r < len; r++) { if (q_is_real && w_is_unit) /* result must be real */ { arb_add_error_mag(acb_realref(theta1 + r), err + r); arb_add_error_mag(acb_realref(theta2 + r), err + r); arb_add_error_mag(acb_realref(theta3 + r), err + r); arb_add_error_mag(acb_realref(theta4 + r), err + r); } else { acb_add_error_mag(theta1 + r, err + r); acb_add_error_mag(theta2 + r, err + r); acb_add_error_mag(theta3 + r, err + r); acb_add_error_mag(theta4 + r, err + r); } } if (len > 1) { arb_t c, d; arb_init(c); arb_init(d); arb_const_pi(c, prec); arb_set(d, c); for (r = 1; r < len; r++) { acb_mul_arb(theta1 + r, theta1 + r, d, prec); acb_mul_arb(theta2 + r, theta2 + r, d, prec); acb_mul_arb(theta3 + r, theta3 + r, d, prec); acb_mul_arb(theta4 + r, theta4 + r, d, prec); if (r + 1 < len) { arb_mul(d, d, c, prec); arb_div_ui(d, d, r + 1, prec); } } arb_clear(c); arb_clear(d); } acb_add_ui(theta3, theta3, 1, prec); acb_add_ui(theta4, theta4, 1, prec); if (!w_is_one) { _acb_vec_clear(wpow, WN); _acb_vec_clear(vpow, WN + 1); } flint_free(exponents); _acb_vec_clear(qpow, N); acb_clear(tmp1); acb_clear(tmp2); acb_clear(v); mag_clear(qmag); mag_clear(wmag); mag_clear(vmag); _mag_vec_clear(err, len); } arb-2.8.1/acb_modular/theta_transform.c000066400000000000000000000060201264125401100200740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" /* convert theta_{m,n} to theta_i */ static int swappy1(int m, int n) { m = m & 1; n = n & 1; if (m == 0 && n == 0) return 2; if (m == 0 && n == 1) return 3; if (m == 1 && n == 0) return 1; return 0; } /* extra phase shift picked up: a factor (-1)^n when m is congruent to 2,3 (mod 4), and possibly a factor i = sqrt(-1) when converting from theta_1 to theta_{1,1} */ static int swappy2(int m, int n) { m = m & 3; n = n & 1; if (m == 1 && n == 1) return 2; /* i */ if (m == 2 && n == 1) return 4; /* (-1)^n */ if (m == 3 && n == 1) return 6; /* (-1)^n * i */ return 0; } void acb_modular_theta_transform(int * R, int * S, int * C, const psl2z_t g) { R[0] = 0; R[1] = 0; R[2] = 0; R[3] = 0; S[0] = 0; S[1] = 1; S[2] = 2; S[3] = 3; if (fmpz_is_zero(&g->c)) { C[0] = 0; if (fmpz_is_odd(&g->b)) { S[2] = 3; S[3] = 2; } /* -b mod 8 */ R[0] = (- (int) fmpz_fdiv_ui(&g->b, 8)) & 7; R[1] = R[0]; } else { int a, b, c, d, e1, e2; psl2z_t h; psl2z_init(h); psl2z_inv(h, g); e1 = acb_modular_epsilon_arg(h); e2 = acb_modular_epsilon_arg(g); psl2z_clear(h); C[0] = 1; a = fmpz_fdiv_ui(&g->a, 8); b = fmpz_fdiv_ui(&g->b, 8); c = fmpz_fdiv_ui(&g->c, 8); d = fmpz_fdiv_ui(&g->d, 8); R[0] = e1 + 1; R[1] = -e2 + 5 + (2 - c) * a; R[2] = -e2 + 4 + (c - d - 2) * (b - a); R[3] = -e2 + 3 - (2 + d) * b; S[1] = swappy1(1 - c, 1 + a); R[1] += swappy2(1 - c, 1 + a); S[2] = swappy1(1 + d - c, 1 - b + a); R[2] += swappy2(1 + d - c, 1 - b + a); S[3] = swappy1(1 + d, 1 - b); R[3] += swappy2(1 + d, 1 - b); /* floor mod by 8 */ R[0] &= 7; R[1] &= 7; R[2] &= 7; R[3] &= 7; } } arb-2.8.1/acb_modular/transform.c000066400000000000000000000061041264125401100167120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_modular.h" void acb_modular_transform(acb_t w, const psl2z_t g, const acb_t z, slong prec) { #define a (&g->a) #define b (&g->b) #define c (&g->c) #define d (&g->d) #define x acb_realref(z) #define y acb_imagref(z) if (fmpz_is_zero(c)) { /* (az+b)/d, where we must have a = d = 1 */ acb_add_fmpz(w, z, b, prec); } else if (fmpz_is_zero(a)) { /* b/(cz+d), where -bc = 1, c = 1 => -1/(z+d) */ acb_add_fmpz(w, z, d, prec); acb_inv(w, w, prec); acb_neg(w, w); } else if (0) { acb_t t, u; acb_init(t); acb_init(u); acb_set_fmpz(t, b); acb_addmul_fmpz(t, z, a, prec); acb_set_fmpz(u, d); acb_addmul_fmpz(u, z, c, prec); acb_div(w, t, u, prec); acb_clear(t); acb_clear(u); } else { /* (az+b)/(cz+d) = (re+im*i)/den where re = bd + (bc+ad)x + ac(x^2+y^2) im = (ad-bc)y den = c^2(x^2+y^2) + 2cdx + d^2 */ fmpz_t t; arb_t re, im, den; arb_init(re); arb_init(im); arb_init(den); fmpz_init(t); arb_mul(im, x, x, prec); arb_addmul(im, y, y, prec); fmpz_mul(t, b, d); arb_set_fmpz(re, t); fmpz_mul(t, b, c); fmpz_addmul(t, a, d); arb_addmul_fmpz(re, x, t, prec); fmpz_mul(t, a, c); arb_addmul_fmpz(re, im, t, prec); fmpz_mul(t, d, d); arb_set_fmpz(den, t); fmpz_mul(t, c, d); fmpz_mul_2exp(t, t, 1); arb_addmul_fmpz(den, x, t, prec); fmpz_mul(t, c, c); arb_addmul_fmpz(den, im, t, prec); fmpz_mul(t, a, d); fmpz_submul(t, b, c); arb_mul_fmpz(im, y, t, prec); arb_div(acb_realref(w), re, den, prec); arb_div(acb_imagref(w), im, den, prec); arb_clear(re); arb_clear(im); arb_clear(den); fmpz_clear(t); } #undef a #undef b #undef c #undef d #undef x #undef y } arb-2.8.1/acb_poly.h000066400000000000000000000601201264125401100142220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef ACB_POLY_H #define ACB_POLY_H #ifdef ACB_POLY_INLINES_C #define ACB_POLY_INLINE #else #define ACB_POLY_INLINE static __inline__ #endif #include "acb.h" #include "arb_poly.h" #ifdef __cplusplus extern "C" { #endif typedef struct { acb_ptr coeffs; slong length; slong alloc; } acb_poly_struct; typedef acb_poly_struct acb_poly_t[1]; /* Memory management */ void acb_poly_init(acb_poly_t poly); void acb_poly_init2(acb_poly_t poly, slong len); void acb_poly_clear(acb_poly_t poly); void acb_poly_fit_length(acb_poly_t poly, slong len); void _acb_poly_set_length(acb_poly_t poly, slong len); void _acb_poly_normalise(acb_poly_t poly); ACB_POLY_INLINE void acb_poly_swap(acb_poly_t poly1, acb_poly_t poly2) { acb_poly_struct t = *poly1; *poly1 = *poly2; *poly2 = t; } ACB_POLY_INLINE slong acb_poly_length(const acb_poly_t poly) { return poly->length; } ACB_POLY_INLINE slong acb_poly_degree(const acb_poly_t poly) { return poly->length - 1; } ACB_POLY_INLINE void acb_poly_zero(acb_poly_t poly) { poly->length = 0; } ACB_POLY_INLINE void acb_poly_one(acb_poly_t poly) { acb_poly_fit_length(poly, 1); acb_one(poly->coeffs); _acb_poly_set_length(poly, 1); } void acb_poly_set_coeff_si(acb_poly_t poly, slong n, slong x); void acb_poly_set_coeff_acb(acb_poly_t poly, slong n, const acb_t x); void acb_poly_get_coeff_acb(acb_t x, const acb_poly_t poly, slong n); #define acb_poly_get_coeff_ptr(poly, n) \ ((n) < (poly)->length ? (poly)->coeffs + (n) : NULL) void _acb_poly_shift_right(acb_ptr res, acb_srcptr poly, slong len, slong n); void acb_poly_shift_right(acb_poly_t res, const acb_poly_t poly, slong n); void _acb_poly_shift_left(acb_ptr res, acb_srcptr poly, slong len, slong n); void acb_poly_shift_left(acb_poly_t res, const acb_poly_t poly, slong n); ACB_POLY_INLINE void acb_poly_truncate(acb_poly_t poly, slong newlen) { if (poly->length > newlen) { slong i; for (i = newlen; i < poly->length; i++) acb_zero(poly->coeffs + i); poly->length = newlen; _acb_poly_normalise(poly); } } void _acb_poly_majorant(arb_ptr res, acb_srcptr vec, slong len, slong prec); void acb_poly_majorant(arb_poly_t res, const acb_poly_t poly, slong prec); void acb_poly_printd(const acb_poly_t poly, slong digits); void _acb_poly_evaluate_horner(acb_t res, acb_srcptr f, slong len, const acb_t a, slong prec); void acb_poly_evaluate_horner(acb_t res, const acb_poly_t f, const acb_t a, slong prec); void _acb_poly_evaluate_rectangular(acb_t y, acb_srcptr poly, slong len, const acb_t x, slong prec); void acb_poly_evaluate_rectangular(acb_t res, const acb_poly_t f, const acb_t a, slong prec); void _acb_poly_evaluate(acb_t res, acb_srcptr f, slong len, const acb_t a, slong prec); void acb_poly_evaluate(acb_t res, const acb_poly_t f, const acb_t a, slong prec); void _acb_poly_evaluate2_horner(acb_t y, acb_t z, acb_srcptr f, slong len, const acb_t x, slong prec); void acb_poly_evaluate2_horner(acb_t y, acb_t z, const acb_poly_t f, const acb_t x, slong prec); void _acb_poly_evaluate2_rectangular(acb_t y, acb_t z, acb_srcptr f, slong len, const acb_t x, slong prec); void acb_poly_evaluate2_rectangular(acb_t y, acb_t z, const acb_poly_t f, const acb_t x, slong prec); void _acb_poly_evaluate2(acb_t y, acb_t z, acb_srcptr f, slong len, const acb_t x, slong prec); void acb_poly_evaluate2(acb_t y, acb_t z, const acb_poly_t f, const acb_t x, slong prec); void _acb_poly_derivative(acb_ptr res, acb_srcptr poly, slong len, slong prec); void acb_poly_derivative(acb_poly_t res, const acb_poly_t poly, slong prec); void _acb_poly_integral(acb_ptr res, acb_srcptr poly, slong len, slong prec); void acb_poly_integral(acb_poly_t res, const acb_poly_t poly, slong prec); void acb_poly_set(acb_poly_t dest, const acb_poly_t src); void acb_poly_set_round(acb_poly_t dest, const acb_poly_t src, slong prec); void acb_poly_set_arb_poly(acb_poly_t poly, const arb_poly_t re); void acb_poly_set2_arb_poly(acb_poly_t poly, const arb_poly_t re, const arb_poly_t im); void acb_poly_set_fmpq_poly(acb_poly_t poly, const fmpq_poly_t re, slong prec); void acb_poly_set2_fmpq_poly(acb_poly_t poly, const fmpq_poly_t re, const fmpq_poly_t im, slong prec); void acb_poly_set_fmpz_poly(acb_poly_t poly, const fmpz_poly_t src, slong prec); void acb_poly_set2_fmpz_poly(acb_poly_t poly, const fmpz_poly_t re, const fmpz_poly_t im, slong prec); int acb_poly_get_unique_fmpz_poly(fmpz_poly_t res, const acb_poly_t src); ACB_POLY_INLINE void acb_poly_set_acb(acb_poly_t poly, const acb_t c) { acb_poly_fit_length(poly, 1); acb_set(poly->coeffs, c); _acb_poly_set_length(poly, !acb_is_zero(poly->coeffs)); } void acb_poly_set_si(acb_poly_t poly, slong c); void acb_poly_randtest(acb_poly_t poly, flint_rand_t state, slong len, slong prec, slong mag_bits); int acb_poly_equal(const acb_poly_t A, const acb_poly_t B); int acb_poly_contains_fmpz_poly(const acb_poly_t poly1, const fmpz_poly_t poly2); int acb_poly_contains_fmpq_poly(const acb_poly_t poly1, const fmpq_poly_t poly2); int _acb_poly_overlaps(acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2); int acb_poly_overlaps(const acb_poly_t poly1, const acb_poly_t poly2); int acb_poly_contains(const acb_poly_t poly1, const acb_poly_t poly2); ACB_POLY_INLINE int acb_poly_is_real(const acb_poly_t poly) { return _acb_vec_is_real(poly->coeffs, poly->length); } void _acb_poly_add(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec); void acb_poly_add(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec); void acb_poly_add_si(acb_poly_t res, const acb_poly_t poly, slong c, slong prec); void _acb_poly_sub(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec); void acb_poly_sub(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec); ACB_POLY_INLINE void acb_poly_neg(acb_poly_t res, const acb_poly_t poly) { acb_poly_fit_length(res, poly->length); _acb_vec_neg(res->coeffs, poly->coeffs, poly->length); _acb_poly_set_length(res, poly->length); } ACB_POLY_INLINE void acb_poly_scalar_mul_2exp_si(acb_poly_t res, const acb_poly_t poly, slong c) { acb_poly_fit_length(res, poly->length); _acb_vec_scalar_mul_2exp_si(res->coeffs, poly->coeffs, poly->length, c); _acb_poly_set_length(res, poly->length); } void acb_poly_mullow_classical(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec); void _acb_poly_mullow_classical(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec); void _acb_poly_mullow_transpose(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec); void acb_poly_mullow_transpose(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec); void _acb_poly_mullow_transpose_gauss(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec); void acb_poly_mullow_transpose_gauss(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec); void _acb_poly_mullow(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec); void acb_poly_mullow(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec); void _acb_poly_mul(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec); void acb_poly_mul(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec); ACB_POLY_INLINE void _acb_poly_mul_monic(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) { if (len1 + len2 - 2 > 0) _acb_poly_mullow(res, poly1, len1, poly2, len2, len1 + len2 - 2, prec); acb_one(res + len1 + len2 - 2); } void _acb_poly_inv_series(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong len, slong prec); void acb_poly_inv_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec); void _acb_poly_div_series(acb_ptr Q, acb_srcptr A, slong Alen, acb_srcptr B, slong Blen, slong n, slong prec); void acb_poly_div_series(acb_poly_t Q, const acb_poly_t A, const acb_poly_t B, slong n, slong prec); void _acb_poly_reverse(acb_ptr res, acb_srcptr poly, slong len, slong n); void _acb_poly_div(acb_ptr Q, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec); void _acb_poly_divrem(acb_ptr Q, acb_ptr R, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec); void _acb_poly_rem(acb_ptr R, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec); int acb_poly_divrem(acb_poly_t Q, acb_poly_t R, const acb_poly_t A, const acb_poly_t B, slong prec); void _acb_poly_div_root(acb_ptr Q, acb_t R, acb_srcptr A, slong len, const acb_t c, slong prec); /* Composition */ void _acb_poly_compose(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec); void acb_poly_compose(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec); void _acb_poly_compose_horner(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec); void acb_poly_compose_horner(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec); void _acb_poly_compose_divconquer(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec); void acb_poly_compose_divconquer(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec); void _acb_poly_compose_series_horner(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec); void acb_poly_compose_series_horner(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec); void _acb_poly_compose_series_brent_kung(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec); void acb_poly_compose_series_brent_kung(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec); void _acb_poly_compose_series(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec); void acb_poly_compose_series(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec); /* Reversion */ void _acb_poly_revert_series_lagrange(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec); void acb_poly_revert_series_lagrange(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec); void _acb_poly_revert_series_newton(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec); void acb_poly_revert_series_newton(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec); void _acb_poly_revert_series_lagrange_fast(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec); void acb_poly_revert_series_lagrange_fast(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec); void _acb_poly_revert_series(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec); void acb_poly_revert_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec); void _acb_poly_evaluate_vec_fast_precomp(acb_ptr vs, acb_srcptr poly, slong plen, acb_ptr * tree, slong len, slong prec); void _acb_poly_evaluate_vec_fast(acb_ptr ys, acb_srcptr poly, slong plen, acb_srcptr xs, slong n, slong prec); void acb_poly_evaluate_vec_fast(acb_ptr ys, const acb_poly_t poly, acb_srcptr xs, slong n, slong prec); void _acb_poly_evaluate_vec_iter(acb_ptr ys, acb_srcptr poly, slong plen, acb_srcptr xs, slong n, slong prec); void acb_poly_evaluate_vec_iter(acb_ptr ys, const acb_poly_t poly, acb_srcptr xs, slong n, slong prec); void _acb_poly_interpolate_barycentric(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec); void acb_poly_interpolate_barycentric(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec); void _acb_poly_interpolation_weights(acb_ptr w, acb_ptr * tree, slong len, slong prec); void _acb_poly_interpolate_fast_precomp(acb_ptr poly, acb_srcptr ys, acb_ptr * tree, acb_srcptr weights, slong len, slong prec); void _acb_poly_interpolate_fast(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong len, slong prec); void acb_poly_interpolate_fast(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec); void _acb_poly_interpolate_newton(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec); void acb_poly_interpolate_newton(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec); void _acb_poly_product_roots(acb_ptr poly, acb_srcptr xs, slong n, slong prec); void acb_poly_product_roots(acb_poly_t poly, acb_srcptr xs, slong n, slong prec); acb_ptr * _acb_poly_tree_alloc(slong len); void _acb_poly_tree_free(acb_ptr * tree, slong len); void _acb_poly_tree_build(acb_ptr * tree, acb_srcptr roots, slong len, slong prec); void _acb_poly_root_inclusion(acb_t r, const acb_t m, acb_srcptr poly, acb_srcptr polyder, slong len, slong prec); slong _acb_poly_validate_roots(acb_ptr roots, acb_srcptr poly, slong len, slong prec); void _acb_poly_refine_roots_durand_kerner(acb_ptr roots, acb_srcptr poly, slong len, slong prec); slong _acb_poly_find_roots(acb_ptr roots, acb_srcptr poly, acb_srcptr initial, slong len, slong maxiter, slong prec); slong acb_poly_find_roots(acb_ptr roots, const acb_poly_t poly, acb_srcptr initial, slong maxiter, slong prec); void _acb_poly_root_bound_fujiwara(mag_t bound, acb_srcptr poly, slong len); void acb_poly_root_bound_fujiwara(mag_t bound, acb_poly_t poly); int _acb_poly_validate_real_roots(acb_srcptr roots, acb_srcptr poly, slong len, slong prec); int acb_poly_validate_real_roots(acb_srcptr roots, const acb_poly_t poly, slong prec); /* Special functions */ void _acb_poly_pow_ui_trunc_binexp(acb_ptr res, acb_srcptr f, slong flen, ulong exp, slong len, slong prec); void acb_poly_pow_ui_trunc_binexp(acb_poly_t res, const acb_poly_t poly, ulong exp, slong len, slong prec); void _acb_poly_pow_ui(acb_ptr res, acb_srcptr f, slong flen, ulong exp, slong prec); void acb_poly_pow_ui(acb_poly_t res, const acb_poly_t poly, ulong exp, slong prec); void _acb_poly_rsqrt_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_rsqrt_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_sqrt_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_sqrt_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_log_series(acb_ptr res, acb_srcptr f, slong flen, slong n, slong prec); void acb_poly_log_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec); void _acb_poly_atan_series(acb_ptr res, acb_srcptr f, slong flen, slong n, slong prec); void acb_poly_atan_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec); void _acb_poly_exp_series_basecase(acb_ptr f, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_exp_series_basecase(acb_poly_t f, const acb_poly_t h, slong n, slong prec); void _acb_poly_exp_series(acb_ptr f, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_exp_series(acb_poly_t f, const acb_poly_t h, slong n, slong prec); void _acb_poly_sin_cos_series_basecase(acb_ptr s, acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec, int times_pi); void acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec, int times_pi); void _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c, const acb_srcptr h, slong hlen, slong len, slong prec, int times_pi); void acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec, int times_pi); void _acb_poly_sin_cos_series(acb_ptr s, acb_ptr c, const acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_sin_cos_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec); void _acb_poly_sin_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_sin_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_cos_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_cos_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_sin_cos_pi_series(acb_ptr s, acb_ptr c, const acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec); void _acb_poly_sin_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_sin_pi_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_cos_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_cos_pi_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_cot_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_cot_pi_series(acb_poly_t res, const acb_poly_t f, slong len, slong prec); void _acb_poly_tan_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_tan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_gamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_gamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec); void _acb_poly_rgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_rgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec); void _acb_poly_lgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_lgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec); void _acb_poly_digamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec); void acb_poly_digamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec); void _acb_poly_rising_ui_series(acb_ptr res, acb_srcptr f, slong flen, ulong r, slong trunc, slong prec); void acb_poly_rising_ui_series(acb_poly_t res, const acb_poly_t f, ulong r, slong trunc, slong prec); void _acb_poly_pow_acb_series(acb_ptr h, acb_srcptr f, slong flen, const acb_t g, slong len, slong prec); void acb_poly_pow_acb_series(acb_poly_t h, const acb_poly_t f, const acb_t g, slong len, slong prec); void _acb_poly_pow_series(acb_ptr h, acb_srcptr f, slong flen, acb_srcptr g, slong glen, slong len, slong prec); void acb_poly_pow_series(acb_poly_t h, const acb_poly_t f, const acb_poly_t g, slong len, slong prec); void _acb_poly_binomial_pow_acb_series(acb_ptr h, acb_srcptr f, slong flen, const acb_t g, slong len, slong prec); /* TODO: document */ ACB_POLY_INLINE void _acb_poly_acb_pow_cpx(acb_ptr w, const acb_t a, const acb_t b, slong len, slong prec) { if (len == 1) { acb_pow(w, a, b, prec); } else { acb_t log_a; slong k; acb_init(log_a); acb_log(log_a, a, prec); acb_mul(w, log_a, b, prec); acb_exp(w, w, prec); for (k = 1; k < len; k++) { acb_mul(w + k, w + k - 1, log_a, prec); acb_div_ui(w + k, w + k, k, prec); } acb_clear(log_a); } } #define _acb_poly_pow_cpx _acb_poly_acb_pow_cpx /* TODO: document */ void _acb_poly_acb_invpow_cpx(acb_ptr res, const acb_t N, const acb_t c, slong trunc, slong prec); /* TODO: document */ void _acb_poly_mullow_cpx(acb_ptr res, acb_srcptr src, slong len, const acb_t c, slong trunc, slong prec); void _acb_poly_powsum_series_naive(acb_ptr z, const acb_t s, const acb_t a, const acb_t q, slong n, slong len, slong prec); void _acb_poly_powsum_series_naive_threaded(acb_ptr z, const acb_t s, const acb_t a, const acb_t q, slong n, slong len, slong prec); void _acb_poly_powsum_one_series_sieved(acb_ptr z, const acb_t s, slong n, slong len, slong prec); void _acb_poly_zeta_em_sum(acb_ptr z, const acb_t s, const acb_t a, int deflate, ulong N, ulong M, slong d, slong prec); void _acb_poly_zeta_em_choose_param(mag_t bound, ulong * N, ulong * M, const acb_t s, const acb_t a, slong d, slong target, slong prec); void _acb_poly_zeta_em_bound1(mag_t bound, const acb_t s, const acb_t a, slong N, slong M, slong d, slong wp); void _acb_poly_zeta_em_bound(arb_ptr vec, const acb_t s, const acb_t a, ulong N, ulong M, slong d, slong wp); void _acb_poly_zeta_em_tail_naive(acb_ptr sum, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong len, slong prec); void _acb_poly_zeta_em_tail_bsplit(acb_ptr z, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong len, slong prec); void _acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate, slong d, slong prec); void _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int deflate, slong len, slong prec); void acb_poly_zeta_series(acb_poly_t res, const acb_poly_t f, const acb_t a, int deflate, slong n, slong prec); void _acb_poly_polylog_cpx_zeta(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec); void _acb_poly_polylog_cpx_small(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec); void _acb_poly_polylog_cpx(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec); void _acb_poly_polylog_series(acb_ptr res, acb_srcptr s, slong slen, const acb_t z, slong len, slong prec); void acb_poly_polylog_series(acb_poly_t res, const acb_poly_t s, const acb_t z, slong n, slong prec); void _acb_poly_agm1_series(acb_ptr res, acb_srcptr z, slong zlen, slong len, slong prec); void acb_poly_agm1_series(acb_poly_t res, const acb_poly_t z, slong n, slong prec); void _acb_poly_elliptic_k_series(acb_ptr res, acb_srcptr z, slong zlen, slong len, slong prec); void acb_poly_elliptic_k_series(acb_poly_t res, const acb_poly_t z, slong n, slong prec); void _acb_poly_elliptic_p_series(acb_ptr res, acb_srcptr z, slong zlen, const acb_t tau, slong len, slong prec); void acb_poly_elliptic_p_series(acb_poly_t res, const acb_poly_t z, const acb_t tau, slong n, slong prec); void _acb_poly_erf_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_erf_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec); void _acb_poly_gamma_upper_series(acb_ptr g, const acb_t s, acb_srcptr h, slong hlen, slong n, slong prec); void acb_poly_gamma_upper_series(acb_poly_t g, const acb_t s, const acb_poly_t h, slong n, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/acb_poly/000077500000000000000000000000001264125401100140525ustar00rootroot00000000000000arb-2.8.1/acb_poly/add.c000066400000000000000000000035641264125401100147560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_add(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) { slong i, min = FLINT_MIN(len1, len2); for (i = 0; i < min; i++) acb_add(res + i, poly1 + i, poly2 + i, prec); for (i = min; i < len1; i++) acb_set_round(res + i, poly1 + i, prec); for (i = min; i < len2; i++) acb_set_round(res + i, poly2 + i, prec); } void acb_poly_add(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) { slong max = FLINT_MAX(poly1->length, poly2->length); acb_poly_fit_length(res, max); _acb_poly_add(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); _acb_poly_set_length(res, max); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/add_si.c000066400000000000000000000031731264125401100154450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_add_si(acb_poly_t res, const acb_poly_t x, slong y, slong prec) { slong len = x->length; if (len == 0) { acb_poly_set_si(res, y); } else { acb_poly_fit_length(res, len); if (y >= 0) acb_add_ui(res->coeffs, x->coeffs, y, prec); else acb_sub_ui(res->coeffs, x->coeffs, -y, prec); if (res != x) _acb_vec_set(res->coeffs + 1, x->coeffs + 1, len - 1); _acb_poly_set_length(res, len); _acb_poly_normalise(res); } } arb-2.8.1/acb_poly/agm1_series.c000066400000000000000000000040401264125401100164130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_agm1_series(acb_ptr res, acb_srcptr z, slong zlen, slong len, slong prec) { acb_ptr t, u; zlen = FLINT_MIN(zlen, len); t = _acb_vec_init(len); u = _acb_vec_init(len); acb_agm1_cpx(t, z, len, prec); /* compose with nonconstant part */ acb_zero(u); _acb_vec_set(u + 1, z + 1, zlen - 1); _acb_poly_compose_series(res, t, len, u, zlen, len, prec); _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void acb_poly_agm1_series(acb_poly_t res, const acb_poly_t z, slong n, slong prec) { if (n == 0) { acb_poly_zero(res); return; } acb_poly_fit_length(res, n); if (z->length == 0) { acb_t t; acb_init(t); _acb_poly_agm1_series(res->coeffs, t, 1, n, prec); acb_clear(t); } else { _acb_poly_agm1_series(res->coeffs, z->coeffs, z->length, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/atan_series.c000066400000000000000000000043561264125401100165230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_atan_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) { acb_t c; acb_init(c); acb_atan(c, h, prec); hlen = FLINT_MIN(hlen, n); if (hlen == 1) { _acb_vec_zero(g + 1, n - 1); } else { acb_ptr t, u; slong ulen; t = _acb_vec_init(n); u = _acb_vec_init(n); /* atan(h(x)) = integral(h'(x)/(1+h(x)^2)) */ ulen = FLINT_MIN(n, 2 * hlen - 1); _acb_poly_mullow(u, h, hlen, h, hlen, ulen, prec); acb_add_ui(u, u, 1, prec); _acb_poly_derivative(t, h, hlen, prec); _acb_poly_div_series(g, t, hlen - 1, u, ulen, n, prec); _acb_poly_integral(g, g, n, prec); _acb_vec_clear(t, n); _acb_vec_clear(u, n); } acb_swap(g, c); acb_clear(c); } void acb_poly_atan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { acb_poly_zero(g); return; } acb_poly_fit_length(g, n); _acb_poly_atan_series(g->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/clear.c000066400000000000000000000023701264125401100153060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_clear(acb_poly_t poly) { slong i; for (i = 0; i < poly->alloc; i++) acb_clear(poly->coeffs + i); flint_free(poly->coeffs); } arb-2.8.1/acb_poly/compose.c000066400000000000000000000061601264125401100156660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 William Hart Copyright (C) 2012 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_compose(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) { if (len2 == 1) { _acb_poly_evaluate(res, poly1, len1, poly2, prec); } else if (_acb_vec_is_zero(poly2, len2 - 1)) /* poly2 is a monomial */ { slong i; acb_t t; acb_init(t); acb_set(t, poly2 + len2 - 1); acb_set_round(res, poly1, prec); for (i = 1; i < len1; i++) { acb_mul(res + i * (len2 - 1), poly1 + i, t, prec); if (i + 1 < len1) acb_mul(t, t, poly2 + len2 - 1, prec); _acb_vec_zero(res + (i - 1) * (len2 - 1) + 1, len2 - 2); } acb_clear(t); } else if (len1 <= 7) { _acb_poly_compose_horner(res, poly1, len1, poly2, len2, prec); } else { _acb_poly_compose_divconquer(res, poly1, len1, poly2, len2, prec); } } void acb_poly_compose(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) { const slong len1 = poly1->length; const slong len2 = poly2->length; if (len1 == 0) { acb_poly_zero(res); } else if (len1 == 1 || len2 == 0) { acb_poly_set_acb(res, poly1->coeffs); } else { const slong lenr = (len1 - 1) * (len2 - 1) + 1; if (res != poly1 && res != poly2) { acb_poly_fit_length(res, lenr); _acb_poly_compose(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); } else { acb_poly_t t; acb_poly_init2(t, lenr); _acb_poly_compose(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); acb_poly_swap(res, t); acb_poly_clear(t); } _acb_poly_set_length(res, lenr); _acb_poly_normalise(res); } } arb-2.8.1/acb_poly/compose_divconquer.c000066400000000000000000000131041264125401100201210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 William Hart Copyright (C) 2012 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_compose_divconquer(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) { slong i, j, k, n; slong *hlen, alloc, powlen; acb_ptr v, pow, temp; acb_ptr * h; if (len1 == 1) { acb_set(res, poly1); return; } if (len2 == 1) { _acb_poly_evaluate(res, poly1, len1, poly2, prec); return; } if (len1 == 2) { _acb_poly_compose_horner(res, poly1, len1, poly2, len2, prec); return; } /* Initialisation */ hlen = (slong *) flint_malloc(((len1 + 1) / 2) * sizeof(slong)); for (k = 1; (2 << k) < len1; k++) ; hlen[0] = hlen[1] = ((1 << k) - 1) * (len2 - 1) + 1; for (i = k - 1; i > 0; i--) { slong hi = (len1 + (1 << i) - 1) / (1 << i); for (n = (hi + 1) / 2; n < hi; n++) hlen[n] = ((1 << i) - 1) * (len2 - 1) + 1; } powlen = (1 << k) * (len2 - 1) + 1; alloc = 0; for (i = 0; i < (len1 + 1) / 2; i++) alloc += hlen[i]; v = _acb_vec_init(alloc + 2 * powlen); h = (acb_ptr *) flint_malloc(((len1 + 1) / 2) * sizeof(acb_ptr)); h[0] = v; for (i = 0; i < (len1 - 1) / 2; i++) { h[i + 1] = h[i] + hlen[i]; hlen[i] = 0; } hlen[(len1 - 1) / 2] = 0; pow = v + alloc; temp = pow + powlen; /* Let's start the actual work */ for (i = 0, j = 0; i < len1 / 2; i++, j += 2) { if (!acb_is_zero(poly1 + j + 1)) { _acb_vec_scalar_mul(h[i], poly2, len2, poly1 + j + 1, prec); acb_add(h[i], h[i], poly1 + j, prec); hlen[i] = len2; } else if (!acb_is_zero(poly1 + j)) { acb_set(h[i], poly1 + j); hlen[i] = 1; } } if ((len1 & WORD(1))) { if (!acb_is_zero(poly1 + j)) { acb_set(h[i], poly1 + j); hlen[i] = 1; } } _acb_poly_mul(pow, poly2, len2, poly2, len2, prec); powlen = 2 * len2 - 1; for (n = (len1 + 1) / 2; n > 2; n = (n + 1) / 2) { if (hlen[1] > 0) { slong templen = powlen + hlen[1] - 1; _acb_poly_mul(temp, pow, powlen, h[1], hlen[1], prec); _acb_poly_add(h[0], temp, templen, h[0], hlen[0], prec); hlen[0] = FLINT_MAX(hlen[0], templen); } for (i = 1; i < n / 2; i++) { if (hlen[2*i + 1] > 0) { _acb_poly_mul(h[i], pow, powlen, h[2*i + 1], hlen[2*i + 1], prec); hlen[i] = hlen[2*i + 1] + powlen - 1; } else hlen[i] = 0; _acb_poly_add(h[i], h[i], hlen[i], h[2*i], hlen[2*i], prec); hlen[i] = FLINT_MAX(hlen[i], hlen[2*i]); } if ((n & WORD(1))) { _acb_vec_set(h[i], h[2*i], hlen[2*i]); hlen[i] = hlen[2*i]; } _acb_poly_mul(temp, pow, powlen, pow, powlen, prec); powlen += powlen - 1; { acb_ptr t = pow; pow = temp; temp = t; } } _acb_poly_mul(res, pow, powlen, h[1], hlen[1], prec); _acb_vec_add(res, res, h[0], hlen[0], prec); _acb_vec_clear(v, alloc + 2 * powlen); flint_free(h); flint_free(hlen); } void acb_poly_compose_divconquer(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) { const slong len1 = poly1->length; const slong len2 = poly2->length; if (len1 == 0) { acb_poly_zero(res); } else if (len1 == 1 || len2 == 0) { acb_poly_set_acb(res, poly1->coeffs); } else { const slong lenr = (len1 - 1) * (len2 - 1) + 1; if (res != poly1 && res != poly2) { acb_poly_fit_length(res, lenr); _acb_poly_compose_divconquer(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); } else { acb_poly_t t; acb_poly_init2(t, lenr); _acb_poly_compose_divconquer(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); acb_poly_swap(res, t); acb_poly_clear(t); } _acb_poly_set_length(res, lenr); _acb_poly_normalise(res); } } arb-2.8.1/acb_poly/compose_horner.c000066400000000000000000000070441264125401100172450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 William Hart Copyright (C) 2012 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_compose_horner(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) { if (len1 == 1) { acb_set(res, poly1); } else if (len2 == 1) { _acb_poly_evaluate(res, poly1, len1, poly2, prec); } else if (len1 == 2) { _acb_vec_scalar_mul(res, poly2, len2, poly1 + 1, prec); acb_add(res, res, poly1, prec); } else { const slong alloc = (len1 - 1) * (len2 - 1) + 1; slong i = len1 - 1, lenr = len2; acb_ptr t, t1, t2; t = _acb_vec_init(alloc); if (len1 % 2 == 0) { t1 = res; t2 = t; } else { t1 = t; t2 = res; } /* Perform the first two steps as one, "res = a(m) * poly2 + a(m-1)". */ { _acb_vec_scalar_mul(t1, poly2, len2, poly1 + i, prec); i--; acb_add(t1 + 0, t1 + 0, poly1 + i, prec); } while (i--) { _acb_poly_mul(t2, t1, lenr, poly2, len2, prec); lenr += len2 - 1; { void *t_ = t1; t1 = t2; t2 = t_; } acb_add(t1 + 0, t1 + 0, poly1 + i, prec); } _acb_vec_clear(t, alloc); } } void acb_poly_compose_horner(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) { const slong len1 = poly1->length; const slong len2 = poly2->length; if (len1 == 0) { acb_poly_zero(res); } else if (len1 == 1 || len2 == 0) { acb_poly_set_acb(res, poly1->coeffs); } else { const slong lenr = (len1 - 1) * (len2 - 1) + 1; if (res != poly1 && res != poly2) { acb_poly_fit_length(res, lenr); _acb_poly_compose_horner(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); } else { acb_poly_t t; acb_poly_init2(t, lenr); _acb_poly_compose_horner(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); acb_poly_swap(res, t); acb_poly_clear(t); } _acb_poly_set_length(res, lenr); _acb_poly_normalise(res); } } arb-2.8.1/acb_poly/compose_series.c000066400000000000000000000071141264125401100172400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_compose_series(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { if (len2 == 1) { acb_set_round(res, poly1, prec); _acb_vec_zero(res + 1, n - 1); } else if (_acb_vec_is_zero(poly2 + 1, len2 - 2)) /* poly2 is a monomial */ { slong i, j; acb_t t; acb_init(t); acb_set(t, poly2 + len2 - 1); acb_set_round(res, poly1, prec); for (i = 1, j = len2 - 1; i < len1 && j < n; i++, j += len2 - 1) { acb_mul(res + j, poly1 + i, t, prec); if (i + 1 < len1 && j + len2 - 1 < n) acb_mul(t, t, poly2 + len2 - 1, prec); } if (len2 != 2) for (i = 1; i < n; i++) if (i % (len2 - 1) != 0) acb_zero(res + i); acb_clear(t); } else if (len1 < 6 || n < 6) { _acb_poly_compose_series_horner(res, poly1, len1, poly2, len2, n, prec); } else { _acb_poly_compose_series_brent_kung(res, poly1, len1, poly2, len2, n, prec); } } void acb_poly_compose_series(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) { slong len1 = poly1->length; slong len2 = poly2->length; slong lenr; if (len2 != 0 && !acb_is_zero(poly2->coeffs)) { flint_printf("exception: compose_series: inner " "polynomial must have zero constant term\n"); abort(); } if (len1 == 0 || n == 0) { acb_poly_zero(res); return; } if (len2 == 0 || len1 == 1) { acb_poly_set_acb(res, poly1->coeffs); return; } lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n); len1 = FLINT_MIN(len1, lenr); len2 = FLINT_MIN(len2, lenr); if ((res != poly1) && (res != poly2)) { acb_poly_fit_length(res, lenr); _acb_poly_compose_series(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _acb_poly_set_length(res, lenr); _acb_poly_normalise(res); } else { acb_poly_t t; acb_poly_init2(t, lenr); _acb_poly_compose_series(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _acb_poly_set_length(t, lenr); _acb_poly_normalise(t); acb_poly_swap(res, t); acb_poly_clear(t); } } arb-2.8.1/acb_poly/compose_series_brent_kung.c000066400000000000000000000075231264125401100214620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #include "acb_mat.h" void _acb_poly_compose_series_brent_kung(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { acb_mat_t A, B, C; acb_ptr t, h; slong i, m; if (n == 1) { acb_set(res, poly1); return; } m = n_sqrt(n) + 1; acb_mat_init(A, m, n); acb_mat_init(B, m, m); acb_mat_init(C, m, n); h = _acb_vec_init(n); t = _acb_vec_init(n); /* Set rows of B to the segments of poly1 */ for (i = 0; i < len1 / m; i++) _acb_vec_set(B->rows[i], poly1 + i*m, m); _acb_vec_set(B->rows[i], poly1 + i*m, len1 % m); /* Set rows of A to powers of poly2 */ acb_set_ui(A->rows[0] + 0, UWORD(1)); _acb_vec_set(A->rows[1], poly2, len2); for (i = 2; i < m; i++) _acb_poly_mullow(A->rows[i], A->rows[(i + 1) / 2], n, A->rows[i / 2], n, n, prec); acb_mat_mul(C, B, A, prec); /* Evaluate block composition using the Horner scheme */ _acb_vec_set(res, C->rows[m - 1], n); _acb_poly_mullow(h, A->rows[m - 1], n, poly2, len2, n, prec); for (i = m - 2; i >= 0; i--) { _acb_poly_mullow(t, res, n, h, n, n, prec); _acb_poly_add(res, t, n, C->rows[i], n, prec); } _acb_vec_clear(h, n); _acb_vec_clear(t, n); acb_mat_clear(A); acb_mat_clear(B); acb_mat_clear(C); } void acb_poly_compose_series_brent_kung(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) { slong len1 = poly1->length; slong len2 = poly2->length; slong lenr; if (len2 != 0 && !acb_is_zero(poly2->coeffs)) { flint_printf("exception: compose_series: inner " "polynomial must have zero constant term\n"); abort(); } if (len1 == 0 || n == 0) { acb_poly_zero(res); return; } if (len2 == 0 || len1 == 1) { acb_poly_set_acb(res, poly1->coeffs); return; } lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n); len1 = FLINT_MIN(len1, lenr); len2 = FLINT_MIN(len2, lenr); if ((res != poly1) && (res != poly2)) { acb_poly_fit_length(res, lenr); _acb_poly_compose_series_brent_kung(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _acb_poly_set_length(res, lenr); _acb_poly_normalise(res); } else { acb_poly_t t; acb_poly_init2(t, lenr); _acb_poly_compose_series_brent_kung(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _acb_poly_set_length(t, lenr); _acb_poly_normalise(t); acb_poly_swap(res, t); acb_poly_clear(t); } } arb-2.8.1/acb_poly/compose_series_horner.c000066400000000000000000000066771264125401100206320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_compose_series_horner(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { if (n == 1) { acb_set(res, poly1); } else { slong i = len1 - 1; slong lenr; acb_ptr t = _acb_vec_init(n); lenr = len2; _acb_vec_scalar_mul(res, poly2, len2, poly1 + i, prec); i--; acb_add(res, res, poly1 + i, prec); while (i > 0) { i--; if (lenr + len2 - 1 < n) { _acb_poly_mul(t, res, lenr, poly2, len2, prec); lenr = lenr + len2 - 1; } else { _acb_poly_mullow(t, res, lenr, poly2, len2, n, prec); lenr = n; } _acb_poly_add(res, t, lenr, poly1 + i, 1, prec); } _acb_vec_zero(res + lenr, n - lenr); _acb_vec_clear(t, n); } } void acb_poly_compose_series_horner(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) { slong len1 = poly1->length; slong len2 = poly2->length; slong lenr; if (len2 != 0 && !acb_is_zero(poly2->coeffs)) { flint_printf("exception: compose_series: inner " "polynomial must have zero constant term\n"); abort(); } if (len1 == 0 || n == 0) { acb_poly_zero(res); return; } if (len2 == 0 || len1 == 1) { acb_poly_set_acb(res, poly1->coeffs); return; } lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n); len1 = FLINT_MIN(len1, lenr); len2 = FLINT_MIN(len2, lenr); if ((res != poly1) && (res != poly2)) { acb_poly_fit_length(res, lenr); _acb_poly_compose_series_horner(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _acb_poly_set_length(res, lenr); _acb_poly_normalise(res); } else { acb_poly_t t; acb_poly_init2(t, lenr); _acb_poly_compose_series_horner(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _acb_poly_set_length(t, lenr); _acb_poly_normalise(t); acb_poly_swap(res, t); acb_poly_clear(t); } } arb-2.8.1/acb_poly/contains.c000066400000000000000000000030011264125401100160260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int acb_poly_contains(const acb_poly_t poly1, const acb_poly_t poly2) { slong i; if (poly2->length > poly1->length) return 0; for (i = 0; i < poly2->length; i++) { if (!acb_contains(poly1->coeffs + i, poly2->coeffs + i)) return 0; } for (i = poly2->length; i < poly1->length; i++) if (!acb_contains_zero(poly1->coeffs + i)) return 0; return 1; } arb-2.8.1/acb_poly/contains_fmpq_poly.c000066400000000000000000000032241264125401100201230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int acb_poly_contains_fmpq_poly(const acb_poly_t poly1, const fmpq_poly_t poly2) { slong i; fmpq_t t; if (poly2->length > poly1->length) return 0; fmpq_init(t); for (i = 0; i < poly2->length; i++) { fmpq_poly_get_coeff_fmpq(t, poly2, i); if (!acb_contains_fmpq(poly1->coeffs + i, t)) { fmpq_clear(t); return 0; } } fmpq_clear(t); for (i = poly2->length; i < poly1->length; i++) if (!acb_contains_zero(poly1->coeffs + i)) return 0; return 1; } arb-2.8.1/acb_poly/contains_fmpz_poly.c000066400000000000000000000030061264125401100201320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int acb_poly_contains_fmpz_poly(const acb_poly_t poly1, const fmpz_poly_t poly2) { slong i; if (poly2->length > poly1->length) return 0; for (i = 0; i < poly2->length; i++) if (!acb_contains_fmpz(poly1->coeffs + i, poly2->coeffs + i)) return 0; for (i = poly2->length; i < poly1->length; i++) if (!acb_contains_zero(poly1->coeffs + i)) return 0; return 1; } arb-2.8.1/acb_poly/cos_pi_series.c000066400000000000000000000042701264125401100170470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_cos_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { acb_cos_pi(g, h, prec); _acb_vec_zero(g + 1, n - 1); } else if (n == 2) { acb_t t; acb_init(t); acb_sin_cos_pi(t, g, h, prec); acb_neg(t, t); acb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ acb_const_pi(t, prec); acb_mul(g + 1, g + 1, t, prec); acb_clear(t); } else { acb_ptr t = _acb_vec_init(n); _acb_poly_sin_cos_pi_series(t, g, h, hlen, n, prec); _acb_vec_clear(t, n); } } void acb_poly_cos_pi_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(g); return; } if (hlen == 0) { acb_poly_one(g); return; } if (hlen == 1) n = 1; acb_poly_fit_length(g, n); _acb_poly_cos_pi_series(g->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/cos_series.c000066400000000000000000000041371264125401100163610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_cos_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { acb_cos(g, h, prec); _acb_vec_zero(g + 1, n - 1); } else if (n == 2) { acb_t t; acb_init(t); acb_sin_cos(t, g, h, prec); acb_neg(t, t); acb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ acb_clear(t); } else { acb_ptr t = _acb_vec_init(n); _acb_poly_sin_cos_series(t, g, h, hlen, n, prec); _acb_vec_clear(t, n); } } void acb_poly_cos_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(g); return; } if (hlen == 0) { acb_poly_one(g); return; } if (hlen == 1) n = 1; acb_poly_fit_length(g, n); _acb_poly_cos_series(g->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/cot_pi_series.c000066400000000000000000000064751264125401100170610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_cot_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); if (hlen == 1) { acb_cot_pi(g, h, prec); _acb_vec_zero(g + 1, len - 1); } else { acb_ptr t, u; t = _acb_vec_init(len); u = _acb_vec_init(len); if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(h)), 0) < 0) { _acb_poly_sin_cos_pi_series(t, u, h, hlen, len, prec); _acb_poly_div_series(g, u, len, t, len, len, prec); } else { _acb_vec_scalar_mul_2exp_si(t, h, hlen, 1); if (arf_sgn(arb_midref(acb_imagref(h))) > 0) { acb_const_pi(u, prec); acb_mul_onei(u, u); _acb_vec_scalar_mul(t, t, hlen, u, prec); _acb_poly_exp_series(t, t, hlen, len, prec); acb_sub_ui(u, t, 1, prec); _acb_vec_set(u + 1, t + 1, len - 1); _acb_poly_div_series(g, t, len, u, len, len, prec); _acb_vec_scalar_mul_2exp_si(g, g, len, 1); acb_sub_ui(g, g, 1, prec); _acb_vec_scalar_mul_onei(g, g, len); } else { acb_const_pi(u, prec); acb_div_onei(u, u); _acb_vec_scalar_mul(t, t, hlen, u, prec); _acb_poly_exp_series(t, t, hlen, len, prec); acb_sub_ui(u, t, 1, prec); _acb_vec_set(u + 1, t + 1, len - 1); _acb_poly_div_series(g, t, len, u, len, len, prec); _acb_vec_scalar_mul_2exp_si(g, g, len, 1); acb_sub_ui(g, g, 1, prec); _acb_vec_scalar_mul_onei(g, g, len); _acb_vec_neg(g, g, len); } } _acb_vec_clear(t, len); _acb_vec_clear(u, len); } } void acb_poly_cot_pi_series(acb_poly_t res, const acb_poly_t f, slong len, slong prec) { acb_poly_fit_length(res, len); if (f->length == 0 || len == 0) _acb_vec_indeterminate(res->coeffs, len); else _acb_poly_cot_pi_series(res->coeffs, f->coeffs, f->length, len, prec); _acb_poly_set_length(res, len); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/derivative.c000066400000000000000000000031431264125401100163610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_derivative(acb_ptr res, acb_srcptr poly, slong len, slong prec) { slong i; for (i = 1; i < len; i++) acb_mul_ui(res + i - 1, poly + i, i, prec); } void acb_poly_derivative(acb_poly_t res, const acb_poly_t poly, slong prec) { slong len = poly->length; if (len < 2) { acb_poly_zero(res); } else { acb_poly_fit_length(res, len - 1); _acb_poly_derivative(res->coeffs, poly->coeffs, len, prec); _acb_poly_set_length(res, len - 1); } } arb-2.8.1/acb_poly/digamma_series.c000066400000000000000000000113511264125401100171700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const acb_t x, int use_reflect, int digamma, slong prec); void _acb_poly_gamma_stirling_eval(acb_ptr res, const acb_t z, slong n, slong num, slong prec); void _acb_poly_gamma_stirling_eval2(acb_ptr res, const acb_t z, slong n, slong num, int diff, slong prec); void _acb_poly_digamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec) { int reflect; slong i, r, n, rflen, wp; acb_t zr; acb_ptr t, u, v; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { acb_digamma(res, h, prec); if (acb_is_finite(res)) _acb_vec_zero(res + 1, len - 1); else _acb_vec_indeterminate(res + 1, len - 1); return; } /* use real code for real input */ if (_acb_vec_is_real(h, hlen)) { arb_ptr tmp = _arb_vec_init(len); for (i = 0; i < hlen; i++) arb_set(tmp + i, acb_realref(h + i)); _arb_poly_digamma_series(tmp, tmp, hlen, len, prec); for (i = 0; i < len; i++) acb_set_arb(res + i, tmp + i); _arb_vec_clear(tmp, len); return; } wp = prec + FLINT_BIT_COUNT(prec); t = _acb_vec_init(len + 1); u = _acb_vec_init(len + 1); v = _acb_vec_init(len + 1); acb_init(zr); /* use Stirling series */ acb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 1, wp); /* psi(x) = psi((1-x)+r) - h(1-x,r) - pi*cot(pi*x) */ if (reflect) { if (r != 0) /* otherwise t = 0 */ { acb_sub_ui(v, h, 1, wp); acb_neg(v, v); acb_one(v + 1); rflen = FLINT_MIN(len + 1, r + 1); _acb_poly_rising_ui_series(u, v, 2, r, rflen, wp); _acb_poly_derivative(v, u, rflen, wp); _acb_poly_div_series(t, v, rflen - 1, u, rflen, len, wp); for (i = 1; i < len; i += 2) acb_neg(t + i, t + i); } acb_sub_ui(zr, h, r + 1, wp); acb_neg(zr, zr); _acb_poly_gamma_stirling_eval2(u, zr, n, len + 1, 1, wp); for (i = 1; i < len; i += 2) acb_neg(u + i, u + i); _acb_vec_sub(u, u, t, len, wp); acb_set(t, h); acb_one(t + 1); _acb_poly_cot_pi_series(t, t, 2, len, wp); acb_const_pi(v, wp); _acb_vec_scalar_mul(t, t, len, v, wp); _acb_vec_sub(u, u, t, len, wp); } else { if (r == 0) { acb_add_ui(zr, h, r, wp); _acb_poly_gamma_stirling_eval2(u, zr, n, len + 1, 1, wp); } else { acb_set(v, h); acb_one(v + 1); rflen = FLINT_MIN(len + 1, r + 1); _acb_poly_rising_ui_series(u, v, 2, r, rflen, wp); _acb_poly_derivative(v, u, rflen, wp); _acb_poly_div_series(t, v, rflen - 1, u, rflen, len, wp); acb_add_ui(zr, h, r, wp); _acb_poly_gamma_stirling_eval2(u, zr, n, len + 1, 1, wp); _acb_vec_sub(u, u, t, len, wp); } } /* compose with nonconstant part */ acb_zero(t); _acb_vec_set(t + 1, h + 1, hlen - 1); _acb_poly_compose_series(res, u, len, t, hlen, len, prec); acb_clear(zr); _acb_vec_clear(t, len + 1); _acb_vec_clear(u, len + 1); _acb_vec_clear(v, len + 1); } void acb_poly_digamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec) { acb_poly_fit_length(res, n); if (f->length == 0 || n == 0) _acb_vec_indeterminate(res->coeffs, n); else _acb_poly_digamma_series(res->coeffs, f->coeffs, f->length, n, prec); _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/div_root.c000066400000000000000000000033701264125401100160460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 William Hart Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_div_root(acb_ptr Q, acb_t R, acb_srcptr A, slong len, const acb_t c, slong prec) { acb_t r, t; slong i; if (len < 2) { acb_zero(R); return; } acb_init(r); acb_init(t); acb_set(t, A + len - 2); acb_set(Q + len - 2, A + len - 1); acb_set(r, Q + len - 2); /* TODO: avoid the extra assignments (but still support aliasing) */ for (i = len - 2; i > 0; i--) { acb_mul(r, r, c, prec); acb_add(r, r, t, prec); acb_set(t, A + i - 1); acb_set(Q + i - 1, r); } acb_mul(r, r, c, prec); acb_add(R, r, t, prec); } arb-2.8.1/acb_poly/div_series.c000066400000000000000000000055171264125401100163620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_div_series(acb_ptr Q, acb_srcptr A, slong Alen, acb_srcptr B, slong Blen, slong n, slong prec) { Alen = FLINT_MIN(Alen, n); Blen = FLINT_MIN(Blen, n); if (Blen == 1) { _acb_vec_scalar_div(Q, A, Alen, B, prec); _acb_vec_zero(Q + Alen, n - Alen); } else if (n == 2) { if (Alen == 1) { acb_div(Q, A, B, prec); acb_div(Q + 1, Q, B, prec); acb_mul(Q + 1, Q + 1, B + 1, prec); acb_neg(Q + 1, Q + 1); } else { acb_div(Q, A, B, prec); acb_mul(Q + 1, Q, B + 1, prec); acb_sub(Q + 1, A + 1, Q + 1, prec); acb_div(Q + 1, Q + 1, B, prec); } } else { acb_ptr Binv; Binv = _acb_vec_init(n); _acb_poly_inv_series(Binv, B, Blen, n, prec); _acb_poly_mullow(Q, Binv, n, A, Alen, n, prec); _acb_vec_clear(Binv, n); } } void acb_poly_div_series(acb_poly_t Q, const acb_poly_t A, const acb_poly_t B, slong n, slong prec) { if (n == 0) { acb_poly_zero(Q); return; } if (B->length == 0) { acb_poly_fit_length(Q, n); _acb_vec_indeterminate(Q->coeffs, n); _acb_poly_set_length(Q, n); return; } if (A->length == 0) { acb_poly_zero(Q); return; } if (Q == A || Q == B) { acb_poly_t t; acb_poly_init(t); acb_poly_div_series(t, A, B, n, prec); acb_poly_swap(Q, t); acb_poly_clear(t); return; } acb_poly_fit_length(Q, n); _acb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec); _acb_poly_set_length(Q, n); _acb_poly_normalise(Q); } arb-2.8.1/acb_poly/divrem.c000066400000000000000000000071641264125401100155140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 William Hart Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" /* TODO: tighten this code */ void _acb_poly_div(acb_ptr Q, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) { slong lenQ, lenB2; acb_ptr Arev, Brev; lenQ = lenA - lenB + 1; Arev = _acb_vec_init(2 * lenQ); Brev = Arev + lenQ; _acb_poly_reverse(Arev, A + (lenA - lenQ), lenQ, lenQ); if (lenB >= lenQ) { _acb_poly_reverse(Brev, B + (lenB - lenQ), lenQ, lenQ); lenB2 = lenQ; } else { _acb_poly_reverse(Brev, B, lenB, lenB); lenB2 = lenB; } _acb_poly_div_series(Q, Arev, lenQ, Brev, lenB2, lenQ, prec); _acb_poly_reverse(Q, Q, lenQ, lenQ); _acb_vec_clear(Arev, 2 * lenQ); } void _acb_poly_divrem(acb_ptr Q, acb_ptr R, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) { const slong lenQ = lenA - lenB + 1; _acb_poly_div(Q, A, lenA, B, lenB, prec); if (lenB > 1) { if (lenQ >= lenB - 1) _acb_poly_mullow(R, Q, lenQ, B, lenB - 1, lenB - 1, prec); else _acb_poly_mullow(R, B, lenB - 1, Q, lenQ, lenB - 1, prec); _acb_vec_sub(R, A, R, lenB - 1, prec); } } void _acb_poly_rem(acb_ptr R, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) { const slong lenQ = lenA - lenB + 1; acb_ptr Q = _acb_vec_init(lenQ); _acb_poly_divrem(Q, R, A, lenA, B, lenB, prec); _acb_vec_clear(Q, lenQ); } int acb_poly_divrem(acb_poly_t Q, acb_poly_t R, const acb_poly_t A, const acb_poly_t B, slong prec) { const slong lenA = A->length, lenB = B->length; if (lenB == 0 || acb_contains_zero(B->coeffs + lenB - 1)) { return 0; } if (lenA < lenB) { acb_poly_set(R, A); acb_poly_zero(Q); return 1; } if (Q == A || Q == B) { acb_poly_t T; acb_poly_init(T); acb_poly_divrem(T, R, A, B, prec); acb_poly_swap(Q, T); acb_poly_clear(T); return 1; } if (R == A || R == B) { acb_poly_t U; acb_poly_init(U); acb_poly_divrem(Q, U, A, B, prec); acb_poly_swap(R, U); acb_poly_clear(U); return 1; } acb_poly_fit_length(Q, lenA - lenB + 1); acb_poly_fit_length(R, lenB - 1); _acb_poly_divrem(Q->coeffs, R->coeffs, A->coeffs, lenA, B->coeffs, lenB, prec); _acb_poly_set_length(Q, lenA - lenB + 1); _acb_poly_set_length(R, lenB - 1); _acb_poly_normalise(R); return 1; } arb-2.8.1/acb_poly/elliptic_k_series.c000066400000000000000000000041371264125401100177140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #include "acb_modular.h" void _acb_poly_elliptic_k_series(acb_ptr res, acb_srcptr z, slong zlen, slong len, slong prec) { acb_ptr t, u; zlen = FLINT_MIN(zlen, len); t = _acb_vec_init(len); u = _acb_vec_init(len); acb_modular_elliptic_k_cpx(t, z, len, prec); /* compose with nonconstant part */ acb_zero(u); _acb_vec_set(u + 1, z + 1, zlen - 1); _acb_poly_compose_series(res, t, len, u, zlen, len, prec); _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void acb_poly_elliptic_k_series(acb_poly_t res, const acb_poly_t z, slong n, slong prec) { if (n == 0) { acb_poly_zero(res); return; } acb_poly_fit_length(res, n); if (z->length == 0) { acb_t t; acb_init(t); _acb_poly_elliptic_k_series(res->coeffs, t, 1, n, prec); acb_clear(t); } else { _acb_poly_elliptic_k_series(res->coeffs, z->coeffs, z->length, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/elliptic_p_series.c000066400000000000000000000042201264125401100177120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #include "acb_modular.h" void _acb_poly_elliptic_p_series(acb_ptr res, acb_srcptr z, slong zlen, const acb_t tau, slong len, slong prec) { acb_ptr t, u; zlen = FLINT_MIN(zlen, len); t = _acb_vec_init(len); u = _acb_vec_init(len); acb_modular_elliptic_p_zpx(t, z, tau, len, prec); /* compose with nonconstant part */ acb_zero(u); _acb_vec_set(u + 1, z + 1, zlen - 1); _acb_poly_compose_series(res, t, len, u, zlen, len, prec); _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void acb_poly_elliptic_p_series(acb_poly_t res, const acb_poly_t z, const acb_t tau, slong n, slong prec) { if (n == 0) { acb_poly_zero(res); return; } acb_poly_fit_length(res, n); if (z->length == 0) { acb_t t; acb_init(t); _acb_poly_elliptic_p_series(res->coeffs, t, 1, tau, n, prec); acb_clear(t); } else { _acb_poly_elliptic_p_series(res->coeffs, z->coeffs, z->length, tau, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/equal.c000066400000000000000000000025271264125401100153330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int acb_poly_equal(const acb_poly_t A, const acb_poly_t B) { slong i; if (A->length != B->length) return 0; for (i = 0; i < A->length; i++) if (!acb_equal(A->coeffs + i, B->coeffs + i)) return 0; return 1; } arb-2.8.1/acb_poly/erf_series.c000066400000000000000000000050521264125401100163460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #include "acb_hypgeom.h" void _acb_poly_erf_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) { acb_t c; acb_init(c); acb_hypgeom_erf(c, h, prec); hlen = FLINT_MIN(hlen, n); if (hlen == 1) { _acb_vec_zero(g + 1, n - 1); } else { acb_ptr t, u; slong ulen; t = _acb_vec_init(n); u = _acb_vec_init(n); /* erf(h(x)) = integral(h'(x) exp(-h(x)^2)) * (2/sqrt(pi)) */ ulen = FLINT_MIN(n, 2 * hlen - 1); _acb_poly_mullow(u, h, hlen, h, hlen, ulen, prec); _acb_vec_neg(u, u, ulen); _acb_poly_exp_series(u, u, ulen, n, prec); _acb_poly_derivative(t, h, hlen, prec); _acb_poly_mullow(g, u, n, t, hlen - 1, n, prec); _acb_poly_integral(g, g, n, prec); arb_const_sqrt_pi(acb_realref(t), prec); arb_inv(acb_realref(t), acb_realref(t), prec); arb_mul_2exp_si(acb_realref(t), acb_realref(t), 1); _acb_vec_scalar_mul_arb(g, g, n, acb_realref(t), prec); _acb_vec_clear(t, n); _acb_vec_clear(u, n); } acb_swap(g, c); acb_clear(c); } void acb_poly_erf_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { acb_poly_zero(g); return; } acb_poly_fit_length(g, n); _acb_poly_erf_series(g->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/evaluate.c000066400000000000000000000032361264125401100160300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_evaluate(acb_t res, acb_srcptr f, slong len, const acb_t x, slong prec) { if ((prec >= 1024) && (len >= 5 + 20000 / prec)) { slong fbits; fbits = _acb_vec_bits(f, len); if (fbits <= prec / 2) { _acb_poly_evaluate_rectangular(res, f, len, x, prec); return; } } _acb_poly_evaluate_horner(res, f, len, x, prec); } void acb_poly_evaluate(acb_t res, const acb_poly_t f, const acb_t a, slong prec) { _acb_poly_evaluate(res, f->coeffs, f->length, a, prec); } arb-2.8.1/acb_poly/evaluate2.c000066400000000000000000000032311264125401100161050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_evaluate2(acb_t y, acb_t z, acb_srcptr f, slong len, const acb_t x, slong prec) { if ((prec >= 1024) && (len >= 5 + 20000 / prec)) { slong fbits; fbits = _acb_vec_bits(f, len); if (fbits <= prec / 2) { _acb_poly_evaluate2_rectangular(y, z, f, len, x, prec); return; } } _acb_poly_evaluate2_horner(y, z, f, len, x, prec); } void acb_poly_evaluate2(acb_t r, acb_t s, const acb_poly_t f, const acb_t a, slong prec) { _acb_poly_evaluate2(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/acb_poly/evaluate2_horner.c000066400000000000000000000045031264125401100174650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_evaluate2_horner(acb_t y, acb_t z, acb_srcptr poly, slong len, const acb_t x, slong prec) { if (len == 0) { acb_zero(y); acb_zero(z); } else if (len == 1) { acb_set_round(y, poly + 0, prec); acb_zero(z); } else if (acb_is_zero(x)) { acb_set_round(y, poly + 0, prec); acb_set_round(z, poly + 1, prec); } else if (len == 2) { acb_mul(y, x, poly + 1, prec); acb_add(y, y, poly + 0, prec); acb_set_round(z, poly + 1, prec); } else { acb_t t, u, v; slong i; acb_init(t); acb_init(u); acb_init(v); acb_set_round(u, poly + len - 1, prec); acb_zero(v); for (i = len - 2; i >= 0; i--) { acb_mul(t, v, x, prec); acb_add(v, u, t, prec); acb_mul(t, u, x, prec); acb_add(u, t, poly + i, prec); } acb_swap(y, u); acb_swap(z, v); acb_clear(t); acb_clear(u); acb_clear(v); } } void acb_poly_evaluate2_horner(acb_t r, acb_t s, const acb_poly_t f, const acb_t a, slong prec) { _acb_poly_evaluate2_horner(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/acb_poly/evaluate2_rectangular.c000066400000000000000000000062351264125401100205030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_evaluate2_rectangular(acb_t y, acb_t z, acb_srcptr poly, slong len, const acb_t x, slong prec) { slong i, j, m, r; acb_ptr xs; acb_t s, t, c; if (len < 3) { if (len == 0) { acb_zero(y); acb_zero(z); } else if (len == 1) { acb_set_round(y, poly + 0, prec); acb_zero(z); } else if (len == 2) { acb_mul(y, x, poly + 1, prec); acb_add(y, y, poly + 0, prec); acb_set_round(z, poly + 1, prec); } return; } m = n_sqrt(len) + 1; m *= 1; r = (len + m - 1) / m; xs = _acb_vec_init(m + 1); acb_init(s); acb_init(t); acb_init(c); _acb_vec_set_powers(xs, x, m + 1, prec); acb_set(y, poly + (r - 1) * m); for (j = 1; (r - 1) * m + j < len; j++) acb_addmul(y, xs + j, poly + (r - 1) * m + j, prec); for (i = r - 2; i >= 0; i--) { acb_set(s, poly + i * m); for (j = 1; j < m; j++) acb_addmul(s, xs + j, poly + i * m + j, prec); acb_mul(y, y, xs + m, prec); acb_add(y, y, s, prec); } len -= 1; r = (len + m - 1) / m; acb_mul_ui(z, poly + (r - 1) * m + 1, (r - 1) * m + 1, ARF_PREC_EXACT); for (j = 1; (r - 1) * m + j < len; j++) { acb_mul_ui(c, poly + (r - 1) * m + j + 1, (r - 1) * m + j + 1, ARF_PREC_EXACT); acb_addmul(z, xs + j, c, prec); } for (i = r - 2; i >= 0; i--) { acb_mul_ui(s, poly + i * m + 1, i * m + 1, ARF_PREC_EXACT); for (j = 1; j < m; j++) { acb_mul_ui(c, poly + i * m + j + 1, i * m + j + 1, ARF_PREC_EXACT); acb_addmul(s, xs + j, c, prec); } acb_mul(z, z, xs + m, prec); acb_add(z, z, s, prec); } _acb_vec_clear(xs, m + 1); acb_clear(s); acb_clear(t); acb_clear(c); } void acb_poly_evaluate2_rectangular(acb_t r, acb_t s, const acb_poly_t f, const acb_t a, slong prec) { _acb_poly_evaluate2_rectangular(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/acb_poly/evaluate_horner.c000066400000000000000000000037531264125401100174110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_evaluate_horner(acb_t y, acb_srcptr f, slong len, const acb_t x, slong prec) { if (len == 0) { acb_zero(y); } else if (len == 1 || acb_is_zero(x)) { acb_set_round(y, f, prec); } else if (len == 2) { acb_mul(y, x, f + 1, prec); acb_add(y, y, f + 0, prec); } else { slong i = len - 1; acb_t t, u; acb_init(t); acb_init(u); acb_set(u, f + i); for (i = len - 2; i >= 0; i--) { acb_mul(t, u, x, prec); acb_add(u, f + i, t, prec); } acb_swap(y, u); acb_clear(t); acb_clear(u); } } void acb_poly_evaluate_horner(acb_t res, const acb_poly_t f, const acb_t a, slong prec) { _acb_poly_evaluate_horner(res, f->coeffs, f->length, a, prec); } arb-2.8.1/acb_poly/evaluate_rectangular.c000066400000000000000000000046051264125401100204200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_evaluate_rectangular(acb_t y, acb_srcptr poly, slong len, const acb_t x, slong prec) { slong i, j, m, r; acb_ptr xs; acb_t s, t, c; if (len < 3) { if (len == 0) { acb_zero(y); } else if (len == 1) { acb_set_round(y, poly + 0, prec); } else if (len == 2) { acb_mul(y, x, poly + 1, prec); acb_add(y, y, poly + 0, prec); } return; } m = n_sqrt(len) + 1; r = (len + m - 1) / m; xs = _acb_vec_init(m + 1); acb_init(s); acb_init(t); acb_init(c); _acb_vec_set_powers(xs, x, m + 1, prec); acb_set(y, poly + (r - 1) * m); for (j = 1; (r - 1) * m + j < len; j++) acb_addmul(y, xs + j, poly + (r - 1) * m + j, prec); for (i = r - 2; i >= 0; i--) { acb_set(s, poly + i * m); for (j = 1; j < m; j++) acb_addmul(s, xs + j, poly + i * m + j, prec); acb_mul(y, y, xs + m, prec); acb_add(y, y, s, prec); } _acb_vec_clear(xs, m + 1); acb_clear(s); acb_clear(t); acb_clear(c); } void acb_poly_evaluate_rectangular(acb_t res, const acb_poly_t f, const acb_t a, slong prec) { _acb_poly_evaluate_rectangular(res, f->coeffs, f->length, a, prec); } arb-2.8.1/acb_poly/evaluate_vec_fast.c000066400000000000000000000102171264125401100176770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" /* This gives some speedup for small lengths. */ static __inline__ void _acb_poly_rem_2(acb_ptr r, acb_srcptr a, slong al, acb_srcptr b, slong bl, slong prec) { if (al == 2) { acb_mul(r + 0, a + 1, b + 0, prec); acb_sub(r + 0, a + 0, r + 0, prec); } else { _acb_poly_rem(r, a, al, b, bl, prec); } } void _acb_poly_evaluate_vec_fast_precomp(acb_ptr vs, acb_srcptr poly, slong plen, acb_ptr * tree, slong len, slong prec) { slong height, i, j, pow, left; slong tree_height; slong tlen; acb_ptr t, u, swap, pa, pb, pc; /* avoid worrying about some degenerate cases */ if (len < 2 || plen < 2) { if (len == 1) { acb_t tmp; acb_init(tmp); acb_neg(tmp, tree[0] + 0); _acb_poly_evaluate(vs + 0, poly, plen, tmp, prec); acb_clear(tmp); } else if (len != 0 && plen == 0) { _acb_vec_zero(vs, len); } else if (len != 0 && plen == 1) { for (i = 0; i < len; i++) acb_set(vs + i, poly + 0); } return; } t = _acb_vec_init(len); u = _acb_vec_init(len); left = len; /* Initial reduction. We allow the polynomial to be larger or smaller than the number of points. */ height = FLINT_BIT_COUNT(plen - 1) - 1; tree_height = FLINT_CLOG2(len); while (height >= tree_height) height--; pow = WORD(1) << height; for (i = j = 0; i < len; i += pow, j += (pow + 1)) { tlen = ((i + pow) <= len) ? pow : len % pow; _acb_poly_rem(t + i, poly, plen, tree[height] + j, tlen + 1, prec); } for (i = height - 1; i >= 0; i--) { pow = WORD(1) << i; left = len; pa = tree[i]; pb = t; pc = u; while (left >= 2 * pow) { _acb_poly_rem_2(pc, pb, 2 * pow, pa, pow + 1, prec); _acb_poly_rem_2(pc + pow, pb, 2 * pow, pa + pow + 1, pow + 1, prec); pa += 2 * pow + 2; pb += 2 * pow; pc += 2 * pow; left -= 2 * pow; } if (left > pow) { _acb_poly_rem(pc, pb, left, pa, pow + 1, prec); _acb_poly_rem(pc + pow, pb, left, pa + pow + 1, left - pow + 1, prec); } else if (left > 0) _acb_vec_set(pc, pb, left); swap = t; t = u; u = swap; } _acb_vec_set(vs, t, len); _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void _acb_poly_evaluate_vec_fast(acb_ptr ys, acb_srcptr poly, slong plen, acb_srcptr xs, slong n, slong prec) { acb_ptr * tree; tree = _acb_poly_tree_alloc(n); _acb_poly_tree_build(tree, xs, n, prec); _acb_poly_evaluate_vec_fast_precomp(ys, poly, plen, tree, n, prec); _acb_poly_tree_free(tree, n); } void acb_poly_evaluate_vec_fast(acb_ptr ys, const acb_poly_t poly, acb_srcptr xs, slong n, slong prec) { _acb_poly_evaluate_vec_fast(ys, poly->coeffs, poly->length, xs, n, prec); } arb-2.8.1/acb_poly/evaluate_vec_iter.c000066400000000000000000000030371264125401100177070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_evaluate_vec_iter(acb_ptr ys, acb_srcptr poly, slong plen, acb_srcptr xs, slong n, slong prec) { slong i; for (i = 0; i < n; i++) _acb_poly_evaluate(ys + i, poly, plen, xs + i, prec); } void acb_poly_evaluate_vec_iter(acb_ptr ys, const acb_poly_t poly, acb_srcptr xs, slong n, slong prec) { _acb_poly_evaluate_vec_iter(ys, poly->coeffs, poly->length, xs, n, prec); } arb-2.8.1/acb_poly/exp_series.c000066400000000000000000000123561264125401100163730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define NEWTON_EXP_CUTOFF 120 /* with inverse=1 simultaneously computes g = exp(-x) to length n with inverse=0 uses g as scratch space, computing g = exp(-x) only to length (n+1)/2 */ static void _acb_poly_exp_series_newton(acb_ptr f, acb_ptr g, acb_srcptr h, slong len, slong prec, int inverse, slong cutoff) { slong alloc; acb_ptr T, U, hprime; alloc = 3 * len; T = _acb_vec_init(alloc); U = T + len; hprime = U + len; _acb_poly_derivative(hprime, h, len, prec); acb_zero(hprime + len - 1); NEWTON_INIT(cutoff, len) /* f := exp(h) + O(x^m), g := exp(-h) + O(x^m2) */ NEWTON_BASECASE(n) _acb_poly_exp_series_basecase(f, h, n, n, prec); _acb_poly_inv_series(g, f, (n + 1) / 2, (n + 1) / 2, prec); NEWTON_END_BASECASE /* extend from length m to length n */ NEWTON_LOOP(m, n) slong m2 = (m + 1) / 2; slong l = m - 1; /* shifted for derivative */ /* g := exp(-h) + O(x^m) */ _acb_poly_mullow(T, f, m, g, m2, m, prec); _acb_poly_mullow(g + m2, g, m2, T + m2, m - m2, m - m2, prec); _acb_vec_neg(g + m2, g + m2, m - m2); /* U := h' + g (f' - f h') + O(x^(n-1)) Note: should replace h' by h' mod x^(m-1) */ _acb_vec_zero(f + m, n - m); _acb_poly_mullow(T, f, n, hprime, n, n, prec); /* should be mulmid */ _acb_poly_derivative(U, f, n, prec); acb_zero(U + n - 1); /* should skip low terms */ _acb_vec_sub(U + l, U + l, T + l, n - l, prec); _acb_poly_mullow(T + l, g, n - m, U + l, n - m, n - m, prec); _acb_vec_add(U + l, hprime + l, T + l, n - m, prec); /* f := f + f * (h - int U) + O(x^n) = exp(h) + O(x^n) */ _acb_poly_integral(U, U, n, prec); /* should skip low terms */ _acb_vec_sub(U + m, h + m, U + m, n - m, prec); _acb_poly_mullow(f + m, f, n - m, U + m, n - m, n - m, prec); /* g := exp(-h) + O(x^n) */ /* not needed if we only want exp(x) */ if (n == len && inverse) { _acb_poly_mullow(T, f, n, g, m, n, prec); _acb_poly_mullow(g + m, g, m, T + m, n - m, n - m, prec); _acb_vec_neg(g + m, g + m, n - m); } NEWTON_END_LOOP NEWTON_END _acb_vec_clear(T, alloc); } void _acb_poly_exp_series(acb_ptr f, acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { acb_exp(f, h, prec); _acb_vec_zero(f + 1, n - 1); } else if (n == 2) { acb_exp(f, h, prec); acb_mul(f + 1, f, h + 1, prec); /* safe since hlen >= 2 */ } else if (_acb_vec_is_zero(h + 1, hlen - 2)) /* h = a + bx^d */ { slong i, j, d = hlen - 1; acb_t t; acb_init(t); acb_set(t, h + d); acb_exp(f, h, prec); for (i = 1, j = d; j < n; j += d, i++) { acb_mul(f + j, f + j - d, t, prec); acb_div_ui(f + j, f + j, i, prec); _acb_vec_zero(f + j - d + 1, hlen - 2); } _acb_vec_zero(f + j - d + 1, n - (j - d + 1)); acb_clear(t); } else if (hlen <= NEWTON_EXP_CUTOFF) { _acb_poly_exp_series_basecase(f, h, hlen, n, prec); } else { acb_ptr g, t; acb_t u; int fix; g = _acb_vec_init((n + 1) / 2); fix = (hlen < n || h == f || !acb_is_zero(h)); if (fix) { t = _acb_vec_init(n); _acb_vec_set(t + 1, h + 1, hlen - 1); } else t = (acb_ptr) h; acb_init(u); acb_exp(u, h, prec); _acb_poly_exp_series_newton(f, g, t, n, prec, 0, NEWTON_EXP_CUTOFF); if (!acb_is_one(u)) _acb_vec_scalar_mul(f, f, n, u, prec); _acb_vec_clear(g, (n + 1) / 2); if (fix) _acb_vec_clear(t, n); acb_clear(u); } } void acb_poly_exp_series(acb_poly_t f, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(f); return; } if (hlen == 0) { acb_poly_one(f); return; } if (hlen == 1) n = 1; acb_poly_fit_length(f, n); _acb_poly_exp_series(f->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(f, n); _acb_poly_normalise(f); } arb-2.8.1/acb_poly/exp_series_basecase.c000066400000000000000000000057571264125401100202300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define MUL_CUTOFF 24 static void _acb_poly_exp_series_basecase_rec(acb_ptr f, acb_ptr a, acb_srcptr h, slong hlen, slong n, slong prec) { slong j, k; acb_t s; acb_init(s); acb_exp(f, h, prec); for (k = 1; k < hlen; k++) acb_mul_ui(a + k, h + k, k, prec); for (k = 1; k < n; k++) { acb_zero(s); for (j = 1; j < FLINT_MIN(k + 1, hlen); j++) acb_addmul(s, a + j, f + k - j, prec); acb_div_ui(f + k, s, k, prec); } acb_clear(s); } void _acb_poly_exp_series_basecase(acb_ptr f, acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(n, hlen); if (n < MUL_CUTOFF || hlen < 0.9 * n) { acb_ptr t = _acb_vec_init(hlen); _acb_poly_exp_series_basecase_rec(f, t, h, hlen, n, prec); _acb_vec_clear(t, hlen); } else { slong m, v; acb_ptr t, u; m = (n + 2) / 3; v = m * 2; t = _acb_vec_init(n); u = _acb_vec_init(n - m); _acb_poly_mullow(t, h + m, hlen - m, h + m, hlen - m, n - v, prec); _acb_vec_scalar_mul_2exp_si(t, t, n - v, -1); _acb_vec_set(u, h + m, v - m); _acb_poly_add(u + v - m, t, n - v, h + v, hlen - v, prec); _acb_poly_exp_series_basecase_rec(f, t, h, m, n, prec); _acb_poly_mullow(t, f, n, u, n - m, n - m, prec); _acb_poly_add(f + m, f + m, n - m, t, n - m, prec); _acb_vec_clear(t, n); _acb_vec_clear(u, n - m); } } void acb_poly_exp_series_basecase(acb_poly_t f, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(f); return; } if (hlen == 0) { acb_poly_one(f); return; } acb_poly_fit_length(f, n); _acb_poly_exp_series_basecase(f->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(f, n); _acb_poly_normalise(f); } arb-2.8.1/acb_poly/find_roots.c000066400000000000000000000112171264125401100163660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" slong _acb_get_mid_mag(const acb_t z) { slong rm, im; rm = arf_abs_bound_lt_2exp_si(arb_midref(acb_realref(z))); im = arf_abs_bound_lt_2exp_si(arb_midref(acb_imagref(z))); return FLINT_MAX(rm, im); } slong _acb_get_rad_mag(const acb_t z) { slong rm, im; /* TODO: write mag function */ arf_t t; arf_init(t); arf_set_mag(t, arb_radref(acb_realref(z))); rm = arf_abs_bound_lt_2exp_si(t); arf_set_mag(t, arb_radref(acb_imagref(z))); im = arf_abs_bound_lt_2exp_si(t); arf_clear(t); return FLINT_MAX(rm, im); } void _acb_poly_roots_initial_values(acb_ptr roots, slong deg, slong prec) { slong i; fmpq_t q; fmpq_init(q); fmpq_set_si(q, 4, 10); arb_set_fmpq(acb_realref(roots + 0), q, prec); mag_zero(arb_radref(acb_realref(roots + 0))); fmpq_set_si(q, 9, 10); arb_set_fmpq(acb_imagref(roots + 0), q, prec); mag_zero(arb_radref(acb_imagref(roots + 0))); fmpq_clear(q); for (i = 1; i < deg; i++) { acb_mul(roots + i, roots + i - 1, roots + 0, prec); mag_zero(arb_radref(acb_realref(roots + i))); mag_zero(arb_radref(acb_imagref(roots + i))); } } slong _acb_poly_find_roots(acb_ptr roots, acb_srcptr poly, acb_srcptr initial, slong len, slong maxiter, slong prec) { slong iter, i, deg; slong rootmag, max_rootmag, correction, max_correction; deg = len - 1; if (deg == 0) { return 0; } else if (acb_contains_zero(poly + len - 1)) { /* if the leading coefficient contains zero, roots can be anywhere */ for (i = 0; i < deg; i++) { arb_zero_pm_inf(acb_realref(roots + i)); arb_zero_pm_inf(acb_imagref(roots + i)); } return 0; } else if (deg == 1) { acb_inv(roots + 0, poly + 1, prec); acb_mul(roots + 0, roots + 0, poly + 0, prec); acb_neg(roots + 0, roots + 0); return 1; } if (initial == NULL) _acb_poly_roots_initial_values(roots, deg, prec); else _acb_vec_set(roots, initial, deg); if (maxiter == 0) maxiter = 2 * deg + n_sqrt(prec); for (iter = 0; iter < maxiter; iter++) { max_rootmag = -ARF_PREC_EXACT; for (i = 0; i < deg; i++) { rootmag = _acb_get_mid_mag(roots + i); max_rootmag = FLINT_MAX(rootmag, max_rootmag); } _acb_poly_refine_roots_durand_kerner(roots, poly, len, prec); max_correction = -ARF_PREC_EXACT; for (i = 0; i < deg; i++) { correction = _acb_get_rad_mag(roots + i); max_correction = FLINT_MAX(correction, max_correction); } /* estimate the correction relative to the whole set of roots */ max_correction -= max_rootmag; /* flint_printf("ITER %wd MAX CORRECTION: %wd\n", iter, max_correction); */ if (max_correction < -prec / 2) maxiter = FLINT_MIN(maxiter, iter + 2); else if (max_correction < -prec / 3) maxiter = FLINT_MIN(maxiter, iter + 3); else if (max_correction < -prec / 4) maxiter = FLINT_MIN(maxiter, iter + 4); } return _acb_poly_validate_roots(roots, poly, len, prec); } slong acb_poly_find_roots(acb_ptr roots, const acb_poly_t poly, acb_srcptr initial, slong maxiter, slong prec) { slong len = poly->length; if (len == 0) { flint_printf("find_roots: expected a nonzero polynomial"); abort(); } return _acb_poly_find_roots(roots, poly->coeffs, initial, len, maxiter, prec); } arb-2.8.1/acb_poly/fit_length.c000066400000000000000000000027271264125401100163510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_fit_length(acb_poly_t poly, slong len) { slong i; if (len > poly->alloc) { if (len < 2 * poly->alloc) len = 2 * poly->alloc; poly->coeffs = flint_realloc(poly->coeffs, len * sizeof(acb_struct)); for (i = poly->alloc; i < len; i++) acb_init(poly->coeffs + i); poly->alloc = len; } } arb-2.8.1/acb_poly/gamma_series.c000066400000000000000000000226761264125401100166670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_gamma_stirling_bound(mag_ptr err, const acb_t x, slong k0, slong knum, slong n); void acb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const acb_t x, int use_reflect, int digamma, slong prec); void arb_gamma_stirling_coeff(arb_t b, ulong k, int digamma, slong prec); static void bsplit(acb_ptr Q, acb_ptr T, const acb_t z, slong a, slong b, slong num, slong prec) { if (b - a == 1) { arb_gamma_stirling_coeff(acb_realref(T), a, 0, prec); arb_zero(acb_imagref(T)); if (a == 1) { /* (z + t) */ acb_set(Q, z); if (num > 1) acb_one(Q + 1); if (num > 2) acb_zero(Q + 2); } else { /* (z + t)^2 */ acb_mul(Q, z, z, prec); /* TODO: precompute */ if (num > 1) acb_mul_2exp_si(Q + 1, z, 1); if (num > 2) acb_one(Q + 2); } } else { slong m, n1, n2, q1len, q2len, t1len, t2len, qlen, tlen, alloc; acb_ptr Q1, T1, Q2, T2; m = a + (b - a) / 2; n1 = m - a; n2 = b - m; q1len = FLINT_MIN(2 * n1 + 1, num); t1len = FLINT_MIN(2 * n1 - 1, num); q2len = FLINT_MIN(2 * n2 + 1, num); t2len = FLINT_MIN(2 * n2 - 1, num); qlen = FLINT_MIN(q1len + q2len - 1, num); tlen = FLINT_MIN(t1len + q2len - 1, num); alloc = q1len + q2len + t1len + t2len; Q1 = _acb_vec_init(alloc); Q2 = Q1 + q1len; T1 = Q2 + q2len; T2 = T1 + t1len; bsplit(Q1, T1, z, a, m, num, prec); bsplit(Q2, T2, z, m, b, num, prec); _acb_poly_mullow(Q, Q2, q2len, Q1, q1len, qlen, prec); _acb_poly_mullow(T, Q2, q2len, T1, t1len, tlen, prec); _acb_poly_add(T, T, tlen, T2, t2len, prec); _acb_vec_clear(Q1, alloc); } } void _acb_poly_log_cpx_series(acb_ptr res, const acb_t c, slong num, slong prec) { slong i; for (i = 0; i < num; i++) { if (i == 0) acb_log(res + i, c, prec); else if (i == 1) acb_inv(res + i, c, prec); else acb_mul(res + i, res + i - 1, res + 1, prec); } for (i = 2; i < num; i++) { acb_div_ui(res + i, res + i, i, prec); if (i % 2 == 0) acb_neg(res + i, res + i); } } void _acb_poly_gamma_stirling_eval2(acb_ptr res, const acb_t z, slong n, slong num, int diff, slong prec) { slong k, tlen, qlen; acb_ptr T, Q; mag_ptr err; acb_t c; T = _acb_vec_init(num); Q = _acb_vec_init(num); err = _mag_vec_init(num); acb_init(c); acb_gamma_stirling_bound(err, z, 0, num, n); if (n <= 1) { _acb_vec_zero(res, num); } else { qlen = FLINT_MIN(2 * (n - 1) + 1, num); tlen = FLINT_MIN(2 * (n - 1) - 1, num); bsplit(Q, T, z, 1, n, num, prec); _acb_poly_div_series(res, T, tlen, Q, qlen, num, prec); } if (diff) { _acb_vec_add_error_mag_vec(res, err, num); _acb_poly_derivative(res, res, num, prec); if (num > 1) { /* add log(z+x) - 1/(2(z+x)) */ acb_inv(c, z, prec); _acb_vec_set_powers(T, c, num, prec); for (k = 1; k < num - 1; k++) { acb_mul_2exp_si(T, z, 1); acb_div_ui(T, T, k, prec); acb_add_ui(T, T, 1, prec); acb_mul_2exp_si(T, T, -1); if (k % 2 == 0) acb_submul(res + k, T, T + k + 1, prec); else acb_addmul(res + k, T, T + k + 1, prec); } acb_mul_2exp_si(c, c, -1); acb_sub(res, res, c, prec); acb_log(c, z, prec); acb_add(res, res, c, prec); } } else { /* ((z-1/2) + t) * log(z+t) */ _acb_poly_log_cpx_series(T, z, num, prec); acb_one(c); acb_mul_2exp_si(c, c, -1); acb_sub(c, z, c, prec); _acb_poly_mullow_cpx(T, T, num, c, num, prec); /* constant term */ arb_const_log_sqrt2pi(acb_realref(c), prec); arb_zero(acb_imagref(c)); acb_add(T, T, c, prec); /* subtract (z+t) */ acb_sub(T, T, z, prec); if (num > 1) acb_sub_ui(T + 1, T + 1, 1, prec); _acb_vec_add(res, res, T, num, prec); _acb_vec_add_error_mag_vec(res, err, num); } _acb_vec_clear(T, num); _acb_vec_clear(Q, num); _mag_vec_clear(err, num); acb_clear(c); } void _acb_poly_gamma_stirling_eval(acb_ptr res, const acb_t z, slong n, slong num, slong prec) { _acb_poly_gamma_stirling_eval2(res, z, n, num, 0, prec); } void _acb_poly_gamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec) { int reflect; slong i, rflen, r, n, wp; acb_ptr t, u, v; acb_struct f[2]; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { acb_gamma(res, h, prec); if (acb_is_finite(res)) _acb_vec_zero(res + 1, len - 1); else _acb_vec_indeterminate(res + 1, len - 1); return; } /* use real code for real input */ if (_acb_vec_is_real(h, hlen)) { arb_ptr tmp = _arb_vec_init(len); for (i = 0; i < hlen; i++) arb_set(tmp + i, acb_realref(h + i)); _arb_poly_gamma_series(tmp, tmp, hlen, len, prec); for (i = 0; i < len; i++) acb_set_arb(res + i, tmp + i); _arb_vec_clear(tmp, len); return; } wp = prec + FLINT_BIT_COUNT(prec); t = _acb_vec_init(len); u = _acb_vec_init(len); v = _acb_vec_init(len); acb_init(f); acb_init(f + 1); /* use Stirling series */ acb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 0, wp); /* gamma(h) = (rf(1-h, r) * pi) / (gamma(1-h+r) sin(pi h)), h = h0 + t*/ if (reflect) { /* u = 1/gamma(r+1-h) */ acb_sub_ui(f, h, r + 1, wp); acb_neg(f, f); _acb_poly_gamma_stirling_eval(t, f, n, len, wp); _acb_vec_neg(t, t, len); _acb_poly_exp_series(u, t, len, len, wp); for (i = 1; i < len; i += 2) acb_neg(u + i, u + i); /* v = 1/sin(pi x) */ acb_set(f, h); acb_one(f + 1); _acb_poly_sin_pi_series(t, f, 2, len, wp); _acb_poly_inv_series(v, t, len, len, wp); _acb_poly_mullow(t, u, len, v, len, len, wp); /* rf(1-h,r) * pi */ if (r == 0) { rflen = 1; acb_const_pi(u, wp); } else { acb_sub_ui(f, h, 1, wp); acb_neg(f, f); acb_set_si(f + 1, -1); rflen = FLINT_MIN(len, r + 1); _acb_poly_rising_ui_series(u, f, FLINT_MIN(2, len), r, rflen, wp); acb_const_pi(v, wp); _acb_vec_scalar_mul(u, u, rflen, v, wp); } /* multiply by rising factorial */ _acb_poly_mullow(v, t, len, u, rflen, len, wp); } else { /* gamma(h) = gamma(h+r) / rf(h,r) */ if (r == 0) { acb_add_ui(f, h, r, wp); _acb_poly_gamma_stirling_eval(t, f, n, len, wp); _acb_poly_exp_series(v, t, len, len, wp); } else { /* TODO: div_series may be better (once it has a good basecase), if the rising factorial is short */ acb_set(f, h); acb_one(f + 1); rflen = FLINT_MIN(len, r + 1); _acb_poly_rising_ui_series(u, f, FLINT_MIN(2, len), r, rflen, wp); _acb_poly_inv_series(t, u, rflen, len, wp); acb_add_ui(f, h, r, wp); _acb_poly_gamma_stirling_eval(v, f, n, len, wp); _acb_poly_exp_series(u, v, len, len, wp); _acb_poly_mullow(v, u, len, t, len, len, wp); } } /* compose with nonconstant part */ acb_zero(t); _acb_vec_set(t + 1, h + 1, hlen - 1); _acb_poly_compose_series(res, v, len, t, hlen, len, prec); acb_clear(f); acb_clear(f + 1); _acb_vec_clear(t, len); _acb_vec_clear(u, len); _acb_vec_clear(v, len); } void acb_poly_gamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec) { acb_poly_fit_length(res, n); if (f->length == 0 || n == 0) _acb_vec_indeterminate(res->coeffs, n); else _acb_poly_gamma_series(res->coeffs, f->coeffs, f->length, n, prec); _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/gamma_upper_series.c000066400000000000000000000052511264125401100200700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #include "acb_hypgeom.h" void _acb_poly_gamma_upper_series(acb_ptr g, const acb_t s, acb_srcptr h, slong hlen, slong n, slong prec) { acb_t c; acb_init(c); acb_hypgeom_gamma_upper(c, s, h, 0, prec); hlen = FLINT_MIN(hlen, n); if (hlen == 1) { _acb_vec_zero(g + 1, n - 1); } else { acb_ptr t, u, v; t = _acb_vec_init(n); u = _acb_vec_init(n); v = _acb_vec_init(n); /* Gamma(s, h(x)) = -integral(h'(x) h(x)^(s-1) exp(-h(x)) */ acb_sub_ui(u, s, 1, prec); _acb_poly_pow_acb_series(t, h, hlen, u, n, prec); _acb_poly_derivative(u, h, hlen, prec); _acb_poly_mullow(v, t, n, u, hlen - 1, n, prec); _acb_vec_neg(t, h, hlen); _acb_poly_exp_series(t, t, hlen, n, prec); _acb_poly_mullow(g, v, n, t, n, n, prec); _acb_poly_integral(g, g, n, prec); _acb_vec_neg(g, g, n); _acb_vec_clear(t, n); _acb_vec_clear(u, n); _acb_vec_clear(v, n); } acb_swap(g, c); acb_clear(c); } void acb_poly_gamma_upper_series(acb_poly_t g, const acb_t s, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(g); return; } acb_poly_fit_length(g, n); if (hlen == 0) { acb_t t; acb_init(t); _acb_poly_gamma_upper_series(g->coeffs, s, t, 1, n, prec); acb_clear(t); } else { _acb_poly_gamma_upper_series(g->coeffs, s, h->coeffs, hlen, n, prec); } _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/get_coeff_acb.c000066400000000000000000000023771264125401100167550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_get_coeff_acb(acb_t x, const acb_poly_t poly, slong n) { if (n < poly->length) acb_set(x, poly->coeffs + n); else acb_zero(x); } arb-2.8.1/acb_poly/get_unique_fmpz_poly.c000066400000000000000000000026261264125401100204700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int acb_poly_get_unique_fmpz_poly(fmpz_poly_t res, const acb_poly_t src) { int success; fmpz_poly_fit_length(res, src->length); success = _acb_vec_get_unique_fmpz_vec(res->coeffs, src->coeffs, src->length); _fmpz_poly_set_length(res, src->length); _fmpz_poly_normalise(res); return success; } arb-2.8.1/acb_poly/init.c000066400000000000000000000024651264125401100151700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_init(acb_poly_t poly) { poly->coeffs = NULL; poly->length = 0; poly->alloc = 0; } void acb_poly_init2(acb_poly_t poly, slong len) { acb_poly_init(poly); acb_poly_fit_length(poly, len); } arb-2.8.1/acb_poly/inlines.c000066400000000000000000000021621264125401100156600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define ACB_POLY_INLINES_C #include "acb_poly.h" arb-2.8.1/acb_poly/integral.c000066400000000000000000000031031264125401100160200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_integral(acb_ptr res, acb_srcptr poly, slong len, slong prec) { slong k = len - 1; for (k = len - 1; k > 0; k--) acb_div_ui(res + k, poly + k - 1, k, prec); acb_zero(res); } void acb_poly_integral(acb_poly_t res, const acb_poly_t poly, slong prec) { acb_poly_fit_length(res, poly->length + 1); _acb_poly_integral(res->coeffs, poly->coeffs, poly->length + 1, prec); _acb_poly_set_length(res, poly->length + 1); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/interpolate_barycentric.c000066400000000000000000000047171264125401100211420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_interpolate_barycentric(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) { acb_ptr P, Q, w; acb_t t; slong i, j; if (n == 1) { acb_set(poly, ys); return; } P = _acb_vec_init(n + 1); Q = _acb_vec_init(n); w = _acb_vec_init(n); acb_init(t); _acb_poly_product_roots(P, xs, n, prec); for (i = 0; i < n; i++) { acb_one(w + i); for (j = 0; j < n; j++) { if (i != j) { acb_sub(t, xs + i, xs + j, prec); acb_mul(w + i, w + i, t, prec); } } acb_inv(w + i, w + i, prec); } _acb_vec_zero(poly, n); for (i = 0; i < n; i++) { _acb_poly_div_root(Q, t, P, n + 1, xs + i, prec); acb_mul(t, w + i, ys + i, prec); _acb_vec_scalar_addmul(poly, Q, n, t, prec); } _acb_vec_clear(P, n + 1); _acb_vec_clear(Q, n); _acb_vec_clear(w, n); acb_clear(t); } void acb_poly_interpolate_barycentric(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) { if (n == 0) { acb_poly_zero(poly); } else { acb_poly_fit_length(poly, n); _acb_poly_set_length(poly, n); _acb_poly_interpolate_barycentric(poly->coeffs, xs, ys, n, prec); _acb_poly_normalise(poly); } } arb-2.8.1/acb_poly/interpolate_fast.c000066400000000000000000000072521264125401100175670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_interpolation_weights(acb_ptr w, acb_ptr * tree, slong len, slong prec) { acb_ptr tmp; slong i, n, height; if (len == 0) return; if (len == 1) { acb_one(w); return; } tmp = _acb_vec_init(len + 1); height = FLINT_CLOG2(len); n = WORD(1) << (height - 1); _acb_poly_mul_monic(tmp, tree[height-1], n + 1, tree[height-1] + (n + 1), (len - n + 1), prec); _acb_poly_derivative(tmp, tmp, len + 1, prec); _acb_poly_evaluate_vec_fast_precomp(w, tmp, len, tree, len, prec); for (i = 0; i < len; i++) acb_inv(w + i, w + i, prec); _acb_vec_clear(tmp, len + 1); } void _acb_poly_interpolate_fast_precomp(acb_ptr poly, acb_srcptr ys, acb_ptr * tree, acb_srcptr weights, slong len, slong prec) { acb_ptr t, u, pa, pb; slong i, pow, left; if (len == 0) return; t = _acb_vec_init(len); u = _acb_vec_init(len); for (i = 0; i < len; i++) acb_mul(poly + i, weights + i, ys + i, prec); for (i = 0; i < FLINT_CLOG2(len); i++) { pow = (WORD(1) << i); pa = tree[i]; pb = poly; left = len; while (left >= 2 * pow) { _acb_poly_mul(t, pa, pow + 1, pb + pow, pow, prec); _acb_poly_mul(u, pa + pow + 1, pow + 1, pb, pow, prec); _acb_vec_add(pb, t, u, 2 * pow, prec); left -= 2 * pow; pa += 2 * pow + 2; pb += 2 * pow; } if (left > pow) { _acb_poly_mul(t, pa, pow + 1, pb + pow, left - pow, prec); _acb_poly_mul(u, pb, pow, pa + pow + 1, left - pow + 1, prec); _acb_vec_add(pb, t, u, left, prec); } } _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void _acb_poly_interpolate_fast(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong len, slong prec) { acb_ptr * tree; acb_ptr w; tree = _acb_poly_tree_alloc(len); _acb_poly_tree_build(tree, xs, len, prec); w = _acb_vec_init(len); _acb_poly_interpolation_weights(w, tree, len, prec); _acb_poly_interpolate_fast_precomp(poly, ys, tree, w, len, prec); _acb_vec_clear(w, len); _acb_poly_tree_free(tree, len); } void acb_poly_interpolate_fast(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) { if (n == 0) { acb_poly_zero(poly); } else { acb_poly_fit_length(poly, n); _acb_poly_set_length(poly, n); _acb_poly_interpolate_fast(poly->coeffs, xs, ys, n, prec); _acb_poly_normalise(poly); } } arb-2.8.1/acb_poly/interpolate_newton.c000066400000000000000000000056221264125401100201430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" static void _interpolate_newton(acb_ptr ys, acb_srcptr xs, slong n, slong prec) { acb_t p, q, t; slong i, j; acb_init(p); acb_init(q); acb_init(t); for (i = 1; i < n; i++) { acb_set(t, ys + i - 1); for (j = i; j < n; j++) { acb_sub(p, ys + j, t, prec); acb_sub(q, xs + j, xs + j - i, prec); acb_set(t, ys + j); acb_div(ys + j, p, q, prec); } } acb_clear(p); acb_clear(q); acb_clear(t); } static void _newton_to_monomial(acb_ptr ys, acb_srcptr xs, slong n, slong prec) { acb_t t, u; slong i, j; acb_init(t); acb_init(u); for (i = n - 2; i >= 0; i--) { acb_set(t, ys + i); acb_set(ys + i, ys + i + 1); for (j = i + 1; j < n - 1; j++) { acb_mul(u, ys + j, xs + i, prec); acb_sub(ys + j, ys + j + 1, u, prec); } acb_mul(u, ys + n - 1, xs + i, prec); acb_sub(ys + n - 1, t, u, prec); } _acb_poly_reverse(ys, ys, n, n); acb_clear(t); acb_clear(u); } void _acb_poly_interpolate_newton(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) { if (n == 1) { acb_set(poly, ys); } else { _acb_vec_set(poly, ys, n); _interpolate_newton(poly, xs, n, prec); while (n > 0 && acb_is_zero(poly + n - 1)) n--; _newton_to_monomial(poly, xs, n, prec); } } void acb_poly_interpolate_newton(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) { if (n == 0) { acb_poly_zero(poly); } else { acb_poly_fit_length(poly, n); _acb_poly_set_length(poly, n); _acb_poly_interpolate_newton(poly->coeffs, xs, ys, n, prec); _acb_poly_normalise(poly); } } arb-2.8.1/acb_poly/inv_series.c000066400000000000000000000055031264125401100163670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define MULLOW(z, x, xn, y, yn, nn, prec) \ if ((xn) >= (yn)) \ _acb_poly_mullow(z, x, xn, y, yn, nn, prec); \ else \ _acb_poly_mullow(z, y, yn, x, xn, nn, prec); \ void _acb_poly_inv_series(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong len, slong prec) { acb_inv(Qinv, Q, prec); if (Qlen == 1) { _acb_vec_zero(Qinv + 1, len - 1); } else if (len == 2) { acb_div(Qinv + 1, Qinv, Q, prec); acb_mul(Qinv + 1, Qinv + 1, Q + 1, prec); acb_neg(Qinv + 1, Qinv + 1); } else { slong Qnlen, Wlen, W2len; acb_ptr W; W = _acb_vec_init(len); NEWTON_INIT(1, len) NEWTON_LOOP(m, n) Qnlen = FLINT_MIN(Qlen, n); Wlen = FLINT_MIN(Qnlen + m - 1, n); W2len = Wlen - m; MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec); MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec); _acb_vec_neg(Qinv + m, Qinv + m, n - m); NEWTON_END_LOOP NEWTON_END _acb_vec_clear(W, len); } } void acb_poly_inv_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec) { if (n == 0) { acb_poly_zero(Qinv); return; } if (Q->length == 0) { acb_poly_fit_length(Qinv, n); _acb_vec_indeterminate(Qinv->coeffs, n); _acb_poly_set_length(Qinv, n); return; } if (Qinv == Q) { acb_poly_t t; acb_poly_init(t); acb_poly_inv_series(t, Q, n, prec); acb_poly_swap(Qinv, t); acb_poly_clear(t); return; } acb_poly_fit_length(Qinv, n); _acb_poly_inv_series(Qinv->coeffs, Q->coeffs, Q->length, n, prec); _acb_poly_set_length(Qinv, n); _acb_poly_normalise(Qinv); } arb-2.8.1/acb_poly/lgamma_series.c000066400000000000000000000124151264125401100170310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_log_rising_correct_branch(acb_t t, const acb_t t_wrong, const acb_t z, ulong r, slong prec); void acb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const acb_t x, int use_reflect, int digamma, slong prec); void _acb_poly_gamma_stirling_eval(acb_ptr res, const acb_t z, slong n, slong num, slong prec); static __inline__ void _log_rising_ui_series(acb_ptr t, const acb_t x, slong r, slong len, slong prec) { acb_struct f[2]; slong rflen; acb_init(f); acb_init(f + 1); acb_set(f, x); acb_one(f + 1); rflen = FLINT_MIN(len, r + 1); _acb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, prec); _acb_poly_log_series(t, t, rflen, len, prec); _acb_log_rising_correct_branch(t, t, x, r, prec); acb_clear(f); acb_clear(f + 1); } void _acb_poly_lgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec) { int reflect; slong i, r, n, wp; acb_t zr; acb_ptr t, u; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { acb_lgamma(res, h, prec); if (acb_is_finite(res)) _acb_vec_zero(res + 1, len - 1); else _acb_vec_indeterminate(res + 1, len - 1); return; } if (len == 2) { acb_t v; acb_init(v); acb_set(v, h + 1); acb_digamma(res + 1, h, prec); acb_lgamma(res, h, prec); acb_mul(res + 1, res + 1, v, prec); acb_clear(v); return; } /* use real code for real input and output */ if (_acb_vec_is_real(h, hlen) && arb_is_positive(acb_realref(h))) { arb_ptr tmp = _arb_vec_init(len); for (i = 0; i < hlen; i++) arb_set(tmp + i, acb_realref(h + i)); _arb_poly_lgamma_series(tmp, tmp, hlen, len, prec); for (i = 0; i < len; i++) acb_set_arb(res + i, tmp + i); _arb_vec_clear(tmp, len); return; } wp = prec + FLINT_BIT_COUNT(prec); t = _acb_vec_init(len); u = _acb_vec_init(len); acb_init(zr); /* use Stirling series */ acb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 0, wp); if (reflect) { /* log gamma(h+x) = log rf(1-(h+x), r) - log gamma(1-(h+x)+r) - log sin(pi (h+x)) + log(pi) */ if (r != 0) /* otherwise t = 0 */ { acb_sub_ui(u, h, 1, wp); acb_neg(u, u); _log_rising_ui_series(t, u, r, len, wp); for (i = 1; i < len; i += 2) acb_neg(t + i, t + i); } acb_sub_ui(u, h, 1, wp); acb_neg(u, u); acb_add_ui(zr, u, r, wp); _acb_poly_gamma_stirling_eval(u, zr, n, len, wp); for (i = 1; i < len; i += 2) acb_neg(u + i, u + i); _acb_vec_sub(t, t, u, len, wp); /* log(sin) is unstable with large imaginary parts; cot_pi is implemented in a numerically stable way */ acb_set(u, h); acb_one(u + 1); _acb_poly_cot_pi_series(u, u, 2, len - 1, wp); _acb_poly_integral(u, u, len, wp); acb_const_pi(u, wp); _acb_vec_scalar_mul(u + 1, u + 1, len - 1, u, wp); acb_log_sin_pi(u, h, wp); _acb_vec_sub(u, t, u, len, wp); acb_const_pi(t, wp); /* todo: constant for log pi */ acb_log(t, t, wp); acb_add(u, u, t, wp); } else { /* log gamma(x) = log gamma(x+r) - log rf(x,r) */ acb_add_ui(zr, h, r, wp); _acb_poly_gamma_stirling_eval(u, zr, n, len, wp); if (r != 0) { _log_rising_ui_series(t, h, r, len, wp); _acb_vec_sub(u, u, t, len, wp); } } /* compose with nonconstant part */ acb_zero(t); _acb_vec_set(t + 1, h + 1, hlen - 1); _acb_poly_compose_series(res, u, len, t, hlen, len, prec); acb_clear(zr); _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void acb_poly_lgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec) { acb_poly_fit_length(res, n); if (f->length == 0 || n == 0) _acb_vec_indeterminate(res->coeffs, n); else _acb_poly_lgamma_series(res->coeffs, f->coeffs, f->length, n, prec); _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/log_series.c000066400000000000000000000060101264125401100163460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_log_series(acb_ptr res, acb_srcptr f, slong flen, slong n, slong prec) { flen = FLINT_MIN(flen, n); if (flen == 1) { acb_log(res, f, prec); _acb_vec_zero(res + 1, n - 1); } else if (n == 2) { acb_div(res + 1, f + 1, f + 0, prec); /* safe since hlen >= 2 */ acb_log(res, f, prec); } else if (_acb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */ { slong i, j, d = flen - 1; for (i = 1, j = d; j < n; j += d, i++) { if (i == 1) acb_div(res + j, f + d, f + 0, prec); else acb_mul(res + j, res + j - d, res + d, prec); _acb_vec_zero(res + j - d + 1, flen - 2); } _acb_vec_zero(res + j - d + 1, n - (j - d + 1)); for (i = 2, j = 2 * d; j < n; j += d, i++) acb_div_si(res + j, res + j, i % 2 ? i : -i, prec); acb_log(res, f, prec); /* done last to allow aliasing */ } else { acb_ptr f_diff, f_inv; acb_t a; slong alloc; alloc = n + flen - 1; f_inv = _acb_vec_init(alloc); f_diff = f_inv + n; acb_init(a); acb_log(a, f, prec); _acb_poly_derivative(f_diff, f, flen, prec); _acb_poly_inv_series(f_inv, f, flen, n, prec); _acb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec); _acb_poly_integral(res, res, n, prec); acb_swap(res, a); acb_clear(a); _acb_vec_clear(f_inv, alloc); } } void acb_poly_log_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec) { if (n == 0) { acb_poly_zero(res); return; } acb_poly_fit_length(res, n); if (f->length == 0) _acb_vec_indeterminate(res->coeffs, n); else _acb_poly_log_series(res->coeffs, f->coeffs, f->length, n, prec); _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/majorant.c000066400000000000000000000030721264125401100160330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_majorant(arb_ptr res, acb_srcptr vec, slong len, slong prec) { slong i; for (i = 0; i < len; i++) { acb_get_abs_ubound_arf(arb_midref(res + i), vec + i, prec); mag_zero(arb_radref(res + i)); } } void acb_poly_majorant(arb_poly_t res, const acb_poly_t poly, slong prec) { arb_poly_fit_length(res, poly->length); _acb_poly_majorant(res->coeffs, poly->coeffs, poly->length, prec); _arb_poly_set_length(res, poly->length); } arb-2.8.1/acb_poly/mul.c000066400000000000000000000041621264125401100150160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_mul(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) { _acb_poly_mullow(C, A, lenA, B, lenB, lenA + lenB - 1, prec); } void acb_poly_mul(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) { slong len_out; if ((poly1->length == 0) || (poly2->length == 0)) { acb_poly_zero(res); return; } len_out = poly1->length + poly2->length - 1; if (res == poly1 || res == poly2) { acb_poly_t temp; acb_poly_init2(temp, len_out); _acb_poly_mul(temp->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); acb_poly_swap(res, temp); acb_poly_clear(temp); } else { acb_poly_fit_length(res, len_out); _acb_poly_mul(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); } _acb_poly_set_length(res, len_out); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/mullow.c000066400000000000000000000046601264125401100155430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define CUTOFF 4 void _acb_poly_mullow(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { if (n < CUTOFF || len1 < CUTOFF || len2 < CUTOFF) _acb_poly_mullow_classical(res, poly1, len1, poly2, len2, n, prec); else _acb_poly_mullow_transpose(res, poly1, len1, poly2, len2, n, prec); } void acb_poly_mullow(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) { slong len1, len2; len1 = poly1->length; len2 = poly2->length; if (len1 == 0 || len2 == 0 || n == 0) { acb_poly_zero(res); return; } n = FLINT_MIN((len1 + len2 - 1), n); len1 = FLINT_MIN(len1, n); len2 = FLINT_MIN(len2, n); if (res == poly1 || res == poly2) { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_mullow(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, n, prec); acb_poly_swap(res, t); acb_poly_clear(t); } else { acb_poly_fit_length(res, n); _acb_poly_mullow(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/mullow_classical.c000066400000000000000000000070151264125401100175560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2008, 2009 William Hart Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_mullow_classical(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { len1 = FLINT_MIN(len1, n); len2 = FLINT_MIN(len2, n); if (n == 1) { acb_mul(res, poly1, poly2, prec); } else if (poly1 == poly2 && len1 == len2) { slong i; _acb_vec_scalar_mul(res, poly1, FLINT_MIN(len1, n), poly1, prec); _acb_vec_scalar_mul(res + len1, poly1 + 1, n - len1, poly1 + len1 - 1, prec); for (i = 1; i < len1 - 1; i++) _acb_vec_scalar_addmul(res + i + 1, poly1 + 1, FLINT_MIN(i - 1, n - (i + 1)), poly1 + i, prec); for (i = 1; i < FLINT_MIN(2 * len1 - 2, n); i++) acb_mul_2exp_si(res + i, res + i, 1); for (i = 1; i < FLINT_MIN(len1 - 1, (n + 1) / 2); i++) acb_addmul(res + 2 * i, poly1 + i, poly1 + i, prec); } else { slong i; _acb_vec_scalar_mul(res, poly1, FLINT_MIN(len1, n), poly2, prec); if (n > len1) _acb_vec_scalar_mul(res + len1, poly2 + 1, n - len1, poly1 + len1 - 1, prec); for (i = 0; i < FLINT_MIN(len1, n) - 1; i++) _acb_vec_scalar_addmul(res + i + 1, poly2 + 1, FLINT_MIN(len2, n - i) - 1, poly1 + i, prec); } } void acb_poly_mullow_classical(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) { slong len_out; if (poly1->length == 0 || poly2->length == 0 || n == 0) { acb_poly_zero(res); return; } len_out = poly1->length + poly2->length - 1; if (n > len_out) n = len_out; if (res == poly1 || res == poly2) { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_mullow_classical(t->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, prec); acb_poly_swap(res, t); acb_poly_clear(t); } else { acb_poly_fit_length(res, n); _acb_poly_mullow_classical(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/mullow_transpose.c000066400000000000000000000070451264125401100176410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_mullow_transpose(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { arb_ptr a, b, c, d, e, f, w; arb_ptr t; slong i; len1 = FLINT_MIN(len1, n); len2 = FLINT_MIN(len2, n); w = flint_malloc(sizeof(arb_struct) * (2 * (len1 + len2 + n))); a = w; b = a + len1; c = b + len1; d = c + len2; e = d + len2; f = e + n; /* (e+fi) = (a+bi)(c+di) = (ac - bd) + (ad + bc)i */ t = _arb_vec_init(n); for (i = 0; i < len1; i++) { a[i] = *acb_realref(poly1 + i); b[i] = *acb_imagref(poly1 + i); } for (i = 0; i < len2; i++) { c[i] = *acb_realref(poly2 + i); d[i] = *acb_imagref(poly2 + i); } for (i = 0; i < n; i++) { e[i] = *acb_realref(res + i); f[i] = *acb_imagref(res + i); } _arb_poly_mullow(e, a, len1, c, len2, n, prec); _arb_poly_mullow(t, b, len1, d, len2, n, prec); _arb_vec_sub(e, e, t, n, prec); _arb_poly_mullow(f, a, len1, d, len2, n, prec); /* squaring */ if (poly1 == poly2 && len1 == len2) { _arb_vec_scalar_mul_2exp_si(f, f, n, 1); } else { _arb_poly_mullow(t, b, len1, c, len2, n, prec); _arb_vec_add(f, f, t, n, prec); } for (i = 0; i < n; i++) { *acb_realref(res + i) = e[i]; *acb_imagref(res + i) = f[i]; } _arb_vec_clear(t, n); flint_free(w); } void acb_poly_mullow_transpose(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) { slong len1, len2; len1 = poly1->length; len2 = poly2->length; if (len1 == 0 || len2 == 0 || n == 0) { acb_poly_zero(res); return; } n = FLINT_MIN((len1 + len2 - 1), n); len1 = FLINT_MIN(len1, n); len2 = FLINT_MIN(len2, n); if (res == poly1 || res == poly2) { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_mullow_transpose(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, n, prec); acb_poly_swap(res, t); acb_poly_clear(t); } else { acb_poly_fit_length(res, n); _acb_poly_mullow_transpose(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/mullow_transpose_gauss.c000066400000000000000000000070351264125401100210420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_mullow_transpose_gauss(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) { arb_ptr a, b, c, d, e, f, w; arb_ptr t, u, v; slong i; len1 = FLINT_MIN(len1, n); len2 = FLINT_MIN(len2, n); w = flint_malloc(sizeof(arb_struct) * (2 * (len1 + len2 + n))); a = w; b = a + len1; c = b + len1; d = c + len2; e = d + len2; f = e + n; t = _arb_vec_init(n); u = _arb_vec_init(n); v = _arb_vec_init(n); for (i = 0; i < len1; i++) { a[i] = *acb_realref(poly1 + i); b[i] = *acb_imagref(poly1 + i); } for (i = 0; i < len2; i++) { c[i] = *acb_realref(poly2 + i); d[i] = *acb_imagref(poly2 + i); } for (i = 0; i < n; i++) { e[i] = *acb_realref(res + i); f[i] = *acb_imagref(res + i); } _arb_vec_add(t, a, b, len1, prec); _arb_vec_add(u, c, d, len2, prec); _arb_poly_mullow(v, t, len1, u, len2, n, prec); _arb_poly_mullow(t, a, len1, c, len2, n, prec); _arb_poly_mullow(u, b, len1, d, len2, n, prec); _arb_vec_sub(e, t, u, n, prec); _arb_vec_sub(f, v, t, n, prec); _arb_vec_sub(f, f, u, n, prec); for (i = 0; i < n; i++) { *acb_realref(res + i) = e[i]; *acb_imagref(res + i) = f[i]; } _arb_vec_clear(t, n); _arb_vec_clear(u, n); _arb_vec_clear(v, n); flint_free(w); } void acb_poly_mullow_transpose_gauss(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) { slong len1, len2; len1 = poly1->length; len2 = poly2->length; if (len1 == 0 || len2 == 0 || n == 0) { acb_poly_zero(res); return; } n = FLINT_MIN((len1 + len2 - 1), n); len1 = FLINT_MIN(len1, n); len2 = FLINT_MIN(len2, n); if (res == poly1 || res == poly2) { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_mullow_transpose_gauss(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, n, prec); acb_poly_swap(res, t); acb_poly_clear(t); } else { acb_poly_fit_length(res, n); _acb_poly_mullow_transpose_gauss(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/normalise.c000066400000000000000000000024061264125401100162110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_normalise(acb_poly_t poly) { slong i; for (i = poly->length - 1; (i >= 0) && acb_is_zero(poly->coeffs + i); i--); poly->length = i + 1; } arb-2.8.1/acb_poly/overlaps.c000066400000000000000000000033431264125401100160540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int _acb_poly_overlaps(acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2) { slong i; for (i = 0; i < len2; i++) if (!acb_overlaps(poly1 + i, poly2 + i)) return 0; for (i = len2; i < len1; i++) if (!acb_contains_zero(poly1 + i)) return 0; return 1; } int acb_poly_overlaps(const acb_poly_t poly1, const acb_poly_t poly2) { slong len1 = poly1->length; slong len2 = poly2->length; if (len1 >= len2) return _acb_poly_overlaps(poly1->coeffs, len1, poly2->coeffs, len2); else return _acb_poly_overlaps(poly2->coeffs, len2, poly1->coeffs, len1); } arb-2.8.1/acb_poly/polylog_series.c000066400000000000000000000203471264125401100172630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" /* note: will not return a wrong value, as arf_get_si aborts on overflow */ slong arb_get_si_lower(const arb_t x) { arf_t t; slong v; arf_init(t); arf_set_mag(t, arb_radref(x)); arf_sub(t, arb_midref(x), t, 2 * FLINT_BITS, ARF_RND_FLOOR); v = arf_get_si(t, ARF_RND_FLOOR); arf_clear(t); return v; } slong polylog_choose_terms(mag_t err, slong sigma, const mag_t z, slong d, slong prec) { slong N; for (N = 3; ; N = FLINT_MAX(N+3, N*1.1)) { mag_polylog_tail(err, z, sigma, d, N); /* TODO: do something else when |Li_s(z)| is very small/very large? */ if (mag_cmp_2exp_si(err, -prec) < 0) break; if (N > 100 * prec) { N = 3; mag_inf(err); break; } } return N; } int polylog_is_real(const acb_t s, const acb_t z) { if (!arb_is_zero(acb_imagref(s))) { return 0; } else if (!arb_is_zero(acb_imagref(z))) { return 0; } else { fmpz_t one; int res; fmpz_init(one); fmpz_one(one); if (arb_contains_fmpz(acb_realref(z), one)) res = 0; else res = (arf_cmp_2exp_si(arb_midref(acb_realref(z)), 0) < 0); fmpz_clear(one); return res; } } void _acb_poly_polylog_cpx_zeta(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec) { acb_ptr e1, e2, z1, z2, e1z1, e2z2; acb_t t, u, v; slong k, len2; int deflate_zeta, deflate_gamma; if (!acb_is_finite(s) || !acb_is_finite(z)) { _acb_vec_indeterminate(w, len); return; } acb_init(t); acb_init(u); acb_init(v); /* v = 1-s */ acb_one(v); acb_sub(v, v, s, prec); /* pole of zeta */ deflate_zeta = acb_is_one(v); /* poles of gamma at nonpositive integer v */ deflate_gamma = (arb_is_zero(acb_imagref(v)) && arb_is_int(acb_realref(v)) && arf_sgn(arb_midref(acb_realref(v))) <= 0); len2 = len + deflate_gamma; e1 = _acb_vec_init(len + 1); e2 = _acb_vec_init(len + 1); z1 = _acb_vec_init(len + 1); z2 = _acb_vec_init(len + 1); e1z1 = _acb_vec_init(len + 1); e2z2 = _acb_vec_init(len + 1); /* u = log(-z)/(pi*i) */ acb_neg(t, z); acb_log(t, t, prec); acb_const_pi(u, prec); acb_mul_onei(u, u); acb_div(u, t, u, prec); /* z1 = zeta(v+x, 1/2 + log(-z)/(2*pi*i)) */ acb_one(t); acb_add(t, t, u, prec); acb_mul_2exp_si(t, t, -1); _acb_poly_zeta_cpx_series(z1, v, t, deflate_zeta, len2, prec); /* z2 = zeta(v+x, 1/2 - log(-z)/(2*pi*i)) */ acb_one(t); acb_sub(t, t, u, prec); acb_mul_2exp_si(t, t, -1); _acb_poly_zeta_cpx_series(z2, v, t, deflate_zeta, len2, prec); /* e1 = (i/(2pi))^(v+x) */ acb_onei(t); acb_const_pi(u, prec); acb_div(t, t, u, prec); acb_mul_2exp_si(t, t, -1); _acb_poly_acb_pow_cpx(e1, t, v, len + (deflate_zeta || deflate_gamma), prec); /* e2 = (1/(2 pi i))^(v+x) */ acb_conj(t, t); _acb_poly_acb_pow_cpx(e2, t, v, len + (deflate_zeta || deflate_gamma), prec); _acb_poly_mullow(e1z1, e1, len2, z1, len2, len2, prec); _acb_poly_mullow(e2z2, e2, len2, z2, len2, len2, prec); _acb_vec_add(z1, e1z1, e2z2, len2, prec); if (deflate_gamma) { /* gamma(v+x) = pi/sin(pi(v+x)) * 1/gamma(1-v-x) */ /* TODO: write a csc function? */ acb_zero(e1); acb_const_pi(e1 + 1, prec); acb_mul_2exp_si(e2, v, -1); if (!arb_is_int(acb_realref(e2))) acb_neg(e1 + 1, e1 + 1); _acb_poly_sin_series(e2, e1, 2, len2, prec); _acb_poly_inv_series(e1, e2 + 1, len, len, prec); acb_const_pi(e2, prec); _acb_vec_scalar_mul(e1, e1, len, e2, prec); acb_set(z2, s); acb_set_si(z2 + 1, -1); _acb_poly_rgamma_series(e2, z2, 2, len, prec); _acb_poly_mullow(z2, e1, len, e2, len, len, prec); _acb_poly_mullow(w, z1 + 1, len, z2, len, len, prec); } else { if (deflate_zeta) { for (k = 0; k < len; k++) { arb_mul_2exp_si(acb_realref(e1 + k + 1), acb_realref(e1 + k + 1), 1); arb_add(acb_realref(z1 + k), acb_realref(z1 + k), acb_realref(e1 + k + 1), prec); } } /* gamma(v+x) */ acb_set(e1, v); if (len > 1) acb_one(e1 + 1); _acb_poly_gamma_series(z2, e1, FLINT_MIN(len, 2), len, prec); _acb_poly_mullow(w, z2, len, z1, len, len, prec); } /* correct signs (from s -> 1-s) */ for (k = 1; k < len; k += 2) acb_neg(w + k, w + k); _acb_vec_clear(e1, len + 1); _acb_vec_clear(e2, len + 1); _acb_vec_clear(z1, len + 1); _acb_vec_clear(z2, len + 1); _acb_vec_clear(e1z1, len + 1); _acb_vec_clear(e2z2, len + 1); acb_clear(t); acb_clear(u); acb_clear(v); } void _acb_poly_polylog_cpx_small(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec) { slong k, N, sigma; int is_real; mag_t zmag, err, errf; acb_t a; acb_init(a); mag_init(zmag); mag_init(err); mag_init(errf); is_real = polylog_is_real(s, z); acb_get_mag(zmag, z); sigma = arb_get_si_lower(acb_realref(s)); N = polylog_choose_terms(err, sigma, zmag, len - 1, prec); /* TODO: allow threading */ acb_one(a); _acb_poly_powsum_series_naive(w, s, a, z, N - 1, len, prec); _acb_vec_scalar_mul(w, w, len, z, prec); for (k = 0; k < len; k++) { mag_polylog_tail(err, zmag, sigma, k, N); mag_rfac_ui(errf, k); mag_mul(err, err, errf); if (is_real) arb_add_error_mag(acb_realref(w + k), err); else acb_add_error_mag(w + k, err); } acb_clear(a); mag_clear(zmag); mag_clear(err); mag_clear(errf); } void _acb_poly_polylog_cpx(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec) { mag_t zmag; mag_init(zmag); acb_get_mag(zmag, z); if (mag_cmp_2exp_si(zmag, -1) < 0) _acb_poly_polylog_cpx_small(w, s, z, len, prec); else _acb_poly_polylog_cpx_zeta(w, s, z, len, prec); mag_clear(zmag); } void _acb_poly_polylog_series(acb_ptr res, acb_srcptr s, slong slen, const acb_t z, slong len, slong prec) { acb_ptr t, u; slen = FLINT_MIN(slen, len); t = _acb_vec_init(len); u = _acb_vec_init(len); _acb_poly_polylog_cpx(t, s, z, len, prec); /* compose with nonconstant part */ acb_zero(u); _acb_vec_set(u + 1, s + 1, slen - 1); _acb_poly_compose_series(res, t, len, u, slen, len, prec); _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void acb_poly_polylog_series(acb_poly_t res, const acb_poly_t s, const acb_t z, slong n, slong prec) { if (n == 0) { acb_poly_zero(res); return; } acb_poly_fit_length(res, n); if (s->length == 0) { acb_t t; acb_init(t); _acb_poly_polylog_series(res->coeffs, t, 1, z, n, prec); acb_clear(t); } else { _acb_poly_polylog_series(res->coeffs, s->coeffs, s->length, z, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/pow_acb_series.c000066400000000000000000000107511264125401100172060ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" /* (a + bx^c)^g where a = f[0] and b = f[flen-1] */ void _acb_poly_binomial_pow_acb_series(acb_ptr h, acb_srcptr f, slong flen, const acb_t g, slong len, slong prec) { slong i, j, d; acb_t t; acb_init(t); d = flen - 1; acb_pow(h, f, g, prec); acb_div(t, f + d, f, prec); for (i = 1, j = d; j < len; i++, j += d) { acb_sub_ui(h + j, g, i - 1, prec); acb_mul(h + j, h + j, h + j - d, prec); acb_mul(h + j, h + j, t, prec); acb_div_ui(h + j, h + j, i, prec); } if (d > 1) { for (i = 1; i < len; i++) if (i % d != 0) acb_zero(h + i); } acb_clear(t); return; } void _acb_poly_pow_acb_series(acb_ptr h, acb_srcptr f, slong flen, const acb_t g, slong len, slong prec) { int f_binomial, g_exact, g_int; while (flen > 0 && acb_is_zero(f + flen - 1)) flen--; if (flen <= 1) { acb_pow(h, f, g, prec); _acb_vec_zero(h + 1, len - 1); return; } g_exact = acb_is_exact(g); g_int = acb_is_real(g) && arb_is_int(acb_realref(g)); f_binomial = _acb_vec_is_zero(f + 1, flen - 2); /* g = small integer */ if (g_exact && g_int && arf_cmpabs_2exp_si(arb_midref(acb_realref(g)), FLINT_BITS - 1) < 0) { slong e, hlen; e = arf_get_si(arb_midref(acb_realref(g)), ARF_RND_DOWN); hlen = poly_pow_length(flen, FLINT_ABS(e), len); if (e >= 0) { _acb_poly_pow_ui_trunc_binexp(h, f, flen, e, hlen, prec); _acb_vec_zero(h + hlen, len - hlen); return; } else if (!f_binomial) { acb_ptr t; t = _acb_vec_init(hlen); _acb_poly_pow_ui_trunc_binexp(t, f, flen, -e, hlen, prec); _acb_poly_inv_series(h, t, hlen, len, prec); _acb_vec_clear(t, hlen); return; } } /* (a + bx^c)^g */ if (f_binomial) { _acb_poly_binomial_pow_acb_series(h, f, flen, g, len, prec); return; } /* g = +/- 1/2 */ if (g_exact && acb_is_real(g) && arf_cmpabs_2exp_si(arb_midref(acb_realref(g)), -1) == 0) { if (arf_sgn(arb_midref(acb_realref(g))) > 0) _acb_poly_sqrt_series(h, f, flen, len, prec); else _acb_poly_rsqrt_series(h, f, flen, len, prec); return; } /* f^g = exp(g*log(f)) */ _acb_poly_log_series(h, f, flen, len, prec); _acb_vec_scalar_mul(h, h, len, g, prec); _acb_poly_exp_series(h, h, len, len, prec); } void acb_poly_pow_acb_series(acb_poly_t h, const acb_poly_t f, const acb_t g, slong len, slong prec) { slong flen; flen = f->length; flen = FLINT_MIN(flen, len); if (len == 0) { acb_poly_zero(h); return; } if (acb_is_zero(g)) { acb_poly_one(h); return; } if (flen == 0) { acb_poly_zero(h); return; } if (f == h) { acb_poly_t t; acb_poly_init2(t, len); _acb_poly_pow_acb_series(t->coeffs, f->coeffs, flen, g, len, prec); _acb_poly_set_length(t, len); _acb_poly_normalise(t); acb_poly_swap(t, h); acb_poly_clear(t); } else { acb_poly_fit_length(h, len); _acb_poly_pow_acb_series(h->coeffs, f->coeffs, flen, g, len, prec); _acb_poly_set_length(h, len); _acb_poly_normalise(h); } } arb-2.8.1/acb_poly/pow_series.c000066400000000000000000000060261264125401100164010ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_pow_series(acb_ptr h, acb_srcptr f, slong flen, acb_srcptr g, slong glen, slong len, slong prec) { if (glen == 1) { _acb_poly_pow_acb_series(h, f, flen, g, len, prec); return; } /* f^g = exp(g * log(f)) */ if (flen == 1) { acb_t t; acb_init(t); acb_log(t, f, prec); _acb_vec_scalar_mul(h, g, glen, t, prec); _acb_poly_exp_series(h, h, glen, len, prec); acb_clear(t); } else { acb_ptr t; t = _acb_vec_init(len); _acb_poly_log_series(t, f, flen, len, prec); _acb_poly_mullow(h, t, len, g, glen, len, prec); _acb_poly_exp_series(h, h, len, len, prec); _acb_vec_clear(t, len); } } void acb_poly_pow_series(acb_poly_t h, const acb_poly_t f, const acb_poly_t g, slong len, slong prec) { slong flen, glen; flen = f->length; glen = g->length; flen = FLINT_MIN(flen, len); glen = FLINT_MIN(glen, len); if (len == 0) { acb_poly_zero(h); return; } if (glen == 0) { acb_poly_one(h); return; } if (flen == 0) { acb_poly_zero(h); return; } if (flen == 1 && glen == 1) { acb_poly_fit_length(h, 1); acb_pow(h->coeffs, f->coeffs, g->coeffs, prec); _acb_poly_set_length(h, 1); _acb_poly_normalise(h); return; } if (f == h || g == h) { acb_poly_t t; acb_poly_init2(t, len); _acb_poly_pow_series(t->coeffs, f->coeffs, flen, g->coeffs, glen, len, prec); _acb_poly_set_length(t, len); _acb_poly_normalise(t); acb_poly_swap(t, h); acb_poly_clear(t); } else { acb_poly_fit_length(h, len); _acb_poly_pow_series(h->coeffs, f->coeffs, flen, g->coeffs, glen, len, prec); _acb_poly_set_length(h, len); _acb_poly_normalise(h); } } arb-2.8.1/acb_poly/pow_ui.c000066400000000000000000000042221264125401100155200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_pow_ui(acb_ptr res, acb_srcptr f, slong flen, ulong exp, slong prec) { _acb_poly_pow_ui_trunc_binexp(res, f, flen, exp, exp * (flen - 1) + 1, prec); } void acb_poly_pow_ui(acb_poly_t res, const acb_poly_t poly, ulong exp, slong prec) { slong flen, rlen; flen = poly->length; if (exp == 0) { acb_poly_one(res); } else if (flen == 0) { acb_poly_zero(res); } else { rlen = exp * (flen - 1) + 1; if (res != poly) { acb_poly_fit_length(res, rlen); _acb_poly_pow_ui(res->coeffs, poly->coeffs, flen, exp, prec); _acb_poly_set_length(res, rlen); _acb_poly_normalise(res); } else { acb_poly_t t; acb_poly_init2(t, rlen); _acb_poly_pow_ui(t->coeffs, poly->coeffs, flen, exp, prec); _acb_poly_set_length(t, rlen); _acb_poly_normalise(t); acb_poly_swap(res, t); acb_poly_clear(t); } } } arb-2.8.1/acb_poly/pow_ui_trunc_binexp.c000066400000000000000000000076221264125401100203070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define MUL(z, zlen, x, xlen, y, ylen, trunc, prec) \ do { \ slong slen = FLINT_MIN(xlen + ylen - 1, trunc); \ _acb_poly_mullow(z, x, xlen, y, ylen, slen, prec); \ zlen = slen; \ } while (0) void _acb_poly_pow_ui_trunc_binexp(acb_ptr res, acb_srcptr f, slong flen, ulong exp, slong len, slong prec) { acb_ptr v, R, S, T; slong rlen; ulong bit; if (exp <= 1) { if (exp == 0) acb_one(res); else if (exp == 1) _acb_vec_set_round(res, f, len, prec); return; } /* (f * x^r)^m = x^(rm) * f^m */ while (flen > 1 && acb_is_zero(f)) { if (((ulong) len) > exp) { _acb_vec_zero(res, exp); len -= exp; res += exp; } else { _acb_vec_zero(res, len); return; } f++; flen--; } if (exp == 2) { _acb_poly_mullow(res, f, flen, f, flen, len, prec); return; } if (flen == 1) { acb_pow_ui(res, f, exp, prec); return; } v = _acb_vec_init(len); bit = UWORD(1) << (FLINT_BIT_COUNT(exp) - 2); if (n_zerobits(exp) % 2) { R = res; S = v; } else { R = v; S = res; } MUL(R, rlen, f, flen, f, flen, len, prec); if (bit & exp) { MUL(S, rlen, R, rlen, f, flen, len, prec); T = R; R = S; S = T; } while (bit >>= 1) { if (bit & exp) { MUL(S, rlen, R, rlen, R, rlen, len, prec); MUL(R, rlen, S, rlen, f, flen, len, prec); } else { MUL(S, rlen, R, rlen, R, rlen, len, prec); T = R; R = S; S = T; } } _acb_vec_clear(v, len); } void acb_poly_pow_ui_trunc_binexp(acb_poly_t res, const acb_poly_t poly, ulong exp, slong len, slong prec) { slong flen, rlen; flen = poly->length; if (exp == 0 && len != 0) { acb_poly_one(res); } else if (flen == 0 || len == 0) { acb_poly_zero(res); } else { rlen = poly_pow_length(flen, exp, len); if (res != poly) { acb_poly_fit_length(res, rlen); _acb_poly_pow_ui_trunc_binexp(res->coeffs, poly->coeffs, flen, exp, rlen, prec); _acb_poly_set_length(res, rlen); _acb_poly_normalise(res); } else { acb_poly_t t; acb_poly_init2(t, rlen); _acb_poly_pow_ui_trunc_binexp(t->coeffs, poly->coeffs, flen, exp, rlen, prec); _acb_poly_set_length(t, rlen); _acb_poly_normalise(t); acb_poly_swap(res, t); acb_poly_clear(t); } } } arb-2.8.1/acb_poly/powsum_one_series_sieved.c000066400000000000000000000110731264125401100213240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define POWER(_k) (powers + (((_k)-1)/2) * (len)) #define DIVISOR(_k) (divisors[((_k)-1)/2]) #define COMPUTE_POWER(t, k, kprev) \ do { \ if (integer) \ { \ arb_neg(w, acb_realref(s)); \ arb_set_ui(v, k); \ arb_pow(acb_realref(t), v, w, prec); \ arb_zero(acb_imagref(t)); \ if (len != 1) \ { \ arb_log_ui_from_prev(logk, k, logk, kprev, prec); \ kprev = k; \ arb_neg(logk, logk); \ } \ } \ else \ { \ arb_log_ui_from_prev(logk, k, logk, kprev, prec); \ kprev = k; \ arb_neg(logk, logk); \ arb_mul(w, logk, acb_imagref(s), prec); \ arb_sin_cos(acb_imagref(t), acb_realref(t), w, prec); \ if (critical_line) \ { \ arb_rsqrt_ui(w, k, prec); \ acb_mul_arb(t, t, w, prec); \ } \ else \ { \ arb_mul(w, acb_realref(s), logk, prec); \ arb_exp(w, w, prec); \ acb_mul_arb(t, t, w, prec); \ } \ } \ for (i = 1; i < len; i++) \ { \ acb_mul_arb(t + i, t + i - 1, logk, prec); \ acb_div_ui(t + i, t + i, i, prec); \ } \ arb_neg(logk, logk); \ } while (0); \ void _acb_poly_powsum_one_series_sieved(acb_ptr z, const acb_t s, slong n, slong len, slong prec) { slong * divisors; slong powers_alloc; slong i, j, k, ibound, kprev, power_of_two, horner_point; int critical_line, integer; acb_ptr powers; acb_ptr t, u, x; acb_ptr p1, p2; arb_t logk, v, w; critical_line = arb_is_exact(acb_realref(s)) && (arf_cmp_2exp_si(arb_midref(acb_realref(s)), -1) == 0); integer = arb_is_zero(acb_imagref(s)) && arb_is_int(acb_realref(s)); divisors = flint_calloc(n / 2 + 1, sizeof(slong)); powers_alloc = (n / 6 + 1) * len; powers = _acb_vec_init(powers_alloc); ibound = n_sqrt(n); for (i = 3; i <= ibound; i += 2) if (DIVISOR(i) == 0) for (j = i * i; j <= n; j += 2 * i) DIVISOR(j) = i; t = _acb_vec_init(len); u = _acb_vec_init(len); x = _acb_vec_init(len); arb_init(logk); arb_init(v); arb_init(w); power_of_two = 1; while (power_of_two * 2 <= n) power_of_two *= 2; horner_point = n / power_of_two; _acb_vec_zero(z, len); kprev = 0; COMPUTE_POWER(x, 2, kprev); for (k = 1; k <= n; k += 2) { /* t = k^(-s) */ if (DIVISOR(k) == 0) { COMPUTE_POWER(t, k, kprev); } else { p1 = POWER(DIVISOR(k)); p2 = POWER(k / DIVISOR(k)); if (len == 1) acb_mul(t, p1, p2, prec); else _acb_poly_mullow(t, p1, len, p2, len, len, prec); } if (k * 3 <= n) _acb_vec_set(POWER(k), t, len); _acb_vec_add(u, u, t, len, prec); while (k == horner_point && power_of_two != 1) { _acb_poly_mullow(t, z, len, x, len, len, prec); _acb_vec_add(z, t, u, len, prec); power_of_two /= 2; horner_point = n / power_of_two; horner_point -= (horner_point % 2 == 0); } } _acb_poly_mullow(t, z, len, x, len, len, prec); _acb_vec_add(z, t, u, len, prec); flint_free(divisors); _acb_vec_clear(powers, powers_alloc); _acb_vec_clear(t, len); _acb_vec_clear(u, len); _acb_vec_clear(x, len); arb_clear(logk); arb_clear(v); arb_clear(w); } arb-2.8.1/acb_poly/powsum_series_naive.c000066400000000000000000000056151264125401100203130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_acb_invpow_cpx(acb_ptr res, const acb_t N, const acb_t c, slong trunc, slong prec) { slong i; acb_t logN; acb_init(logN); acb_log(logN, N, prec); acb_mul(res + 0, logN, c, prec); acb_neg(res + 0, res + 0); acb_exp(res + 0, res + 0, prec); for (i = 1; i < trunc; i++) { acb_mul(res + i, res + i - 1, logN, prec); acb_div_si(res + i, res + i, -i, prec); } acb_clear(logN); } void _acb_poly_powsum_series_naive(acb_ptr z, const acb_t s, const acb_t a, const acb_t q, slong n, slong len, slong prec) { slong k, i; int q_one, s_int; acb_t ak, logak, t, qpow, negs; acb_init(ak); acb_init(logak); acb_init(t); acb_init(qpow); acb_init(negs); _acb_vec_zero(z, len); acb_one(qpow); acb_neg(negs, s); q_one = acb_is_one(q); s_int = arb_is_int(acb_realref(s)) && arb_is_zero(acb_imagref(s)); for (k = 0; k < n; k++) { acb_add_ui(ak, a, k, prec); if (len == 1) { acb_pow(t, ak, negs, prec); } else { acb_log(logak, ak, prec); if (s_int) { acb_pow(t, ak, negs, prec); } else { acb_mul(t, logak, negs, prec); acb_exp(t, t, prec); } } if (!q_one) { acb_mul(t, t, qpow, prec); if (k < n - 1) acb_mul(qpow, qpow, q, prec); } acb_add(z, z, t, prec); for (i = 1; i < len; i++) { acb_mul(t, t, logak, prec); acb_div_si(t, t, -i, prec); acb_add(z + i, z + i, t, prec); } } acb_clear(ak); acb_clear(logak); acb_clear(t); acb_clear(qpow); acb_clear(negs); } arb-2.8.1/acb_poly/powsum_series_naive_threaded.c000066400000000000000000000120001264125401100221350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include #include "acb_poly.h" typedef struct { acb_ptr z; acb_srcptr s; acb_srcptr a; acb_srcptr q; slong n0; slong n1; slong d0; slong len; slong prec; } powsum_arg_t; void * _acb_zeta_powsum_evaluator(void * arg_ptr) { powsum_arg_t arg = *((powsum_arg_t *) arg_ptr); slong i, k; int q_one, s_int; acb_t t, u, v, ak, qpow, negs; arb_t f; acb_init(t); acb_init(u); acb_init(v); acb_init(ak); acb_init(qpow); acb_init(negs); arb_init(f); _acb_vec_zero(arg.z, arg.len); q_one = acb_is_one(arg.q); s_int = arb_is_int(acb_realref(arg.s)) && arb_is_zero(acb_imagref(arg.s)); if (!q_one) acb_pow_ui(qpow, arg.q, arg.n0, arg.prec); acb_neg(negs, arg.s); arb_fac_ui(f, arg.d0, arg.prec); for (k = arg.n0; k < arg.n1; k++) { acb_add_ui(ak, arg.a, k, arg.prec); if (arg.d0 == 0 && arg.len == 1) { /* u = (a+k)^(-s) */ acb_pow(u, ak, negs, arg.prec); } else { /* t = log(a+k) */ acb_log(t, ak, arg.prec); /* u = (a+k)^(-s) */ if (s_int) { acb_pow(u, ak, negs, arg.prec); } else { acb_mul(u, t, negs, arg.prec); acb_exp(u, u, arg.prec); } } /* u = u * q^k */ if (!q_one) { acb_mul(u, u, qpow, arg.prec); if (k < arg.n1 - 1) acb_mul(qpow, qpow, arg.q, arg.prec); } /* forward: u *= (-1)^d * log(a+k)^d / d! */ if (arg.d0 != 0) { acb_pow_ui(v, t, arg.d0, arg.prec); acb_mul(u, u, v, arg.prec); arb_div(acb_realref(u), acb_realref(u), f, arg.prec); arb_div(acb_imagref(u), acb_imagref(u), f, arg.prec); if (arg.d0 % 2) acb_neg(u, u); } acb_add(arg.z, arg.z, u, arg.prec); for (i = 1; i < arg.len; i++) { acb_mul(u, u, t, arg.prec); acb_div_si(u, u, -(arg.d0 + i), arg.prec); acb_add(arg.z + i, arg.z + i, u, arg.prec); } } acb_clear(t); acb_clear(u); acb_clear(v); acb_clear(ak); acb_clear(qpow); acb_clear(negs); arb_clear(f); flint_cleanup(); return NULL; } void _acb_poly_powsum_series_naive_threaded(acb_ptr z, const acb_t s, const acb_t a, const acb_t q, slong n, slong len, slong prec) { pthread_t * threads; powsum_arg_t * args; slong i, num_threads; int split_each_term; num_threads = flint_get_num_threads(); threads = flint_malloc(sizeof(pthread_t) * num_threads); args = flint_malloc(sizeof(powsum_arg_t) * num_threads); split_each_term = (len > 1000); for (i = 0; i < num_threads; i++) { args[i].s = s; args[i].a = a; args[i].q = q; if (split_each_term) { slong n0, n1; n0 = (len * i) / num_threads; n1 = (len * (i + 1)) / num_threads; args[i].z = z + n0; args[i].n0 = 0; args[i].n1 = n; args[i].d0 = n0; args[i].len = n1 - n0; } else { args[i].z = _acb_vec_init(len); args[i].n0 = (n * i) / num_threads; args[i].n1 = (n * (i + 1)) / num_threads; args[i].d0 = 0; args[i].len = len; } args[i].prec = prec; pthread_create(&threads[i], NULL, _acb_zeta_powsum_evaluator, &args[i]); } for (i = 0; i < num_threads; i++) { pthread_join(threads[i], NULL); } if (!split_each_term) { _acb_vec_zero(z, len); for (i = 0; i < num_threads; i++) { _acb_vec_add(z, z, args[i].z, len, prec); _acb_vec_clear(args[i].z, len); } } flint_free(threads); flint_free(args); } arb-2.8.1/acb_poly/printd.c000066400000000000000000000025661264125401100155270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_printd(const acb_poly_t poly, slong digits) { slong i; flint_printf("["); for (i = 0; i < poly->length; i++) { acb_printd(poly->coeffs + i, digits); if (i + 1 < poly->length) flint_printf("\n"); } flint_printf("]"); } arb-2.8.1/acb_poly/product_roots.c000066400000000000000000000041171264125401100171270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 William Hart Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_product_roots(acb_ptr poly, acb_srcptr xs, slong n, slong prec) { if (n == 0) { acb_one(poly); } else if (n == 1) { acb_neg(poly, xs); acb_one(poly + 1); } else if (n == 2) { acb_mul(poly, xs + 0, xs + 1, prec); acb_add(poly + 1, xs + 0, xs + 1, prec); acb_neg(poly + 1, poly + 1); acb_one(poly + 2); } else { const slong m = (n + 1) / 2; acb_ptr tmp; tmp = _acb_vec_init(n + 2); _acb_poly_product_roots(tmp, xs, m, prec); _acb_poly_product_roots(tmp + m + 1, xs + m, n - m, prec); _acb_poly_mul_monic(poly, tmp, m + 1, tmp + m + 1, n - m + 1, prec); _acb_vec_clear(tmp, n + 2); } } void acb_poly_product_roots(acb_poly_t poly, acb_srcptr xs, slong n, slong prec) { acb_poly_fit_length(poly, n + 1); _acb_poly_product_roots(poly->coeffs, xs, n, prec); _acb_poly_set_length(poly, n + 1); } arb-2.8.1/acb_poly/randtest.c000066400000000000000000000034621264125401100160470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_randtest(acb_poly_t poly, flint_rand_t state, slong len, slong prec, slong mag_bits) { slong i; acb_poly_fit_length(poly, len); if (n_randint(state, 2)) { for (i = 0; i < len; i++) { arb_randtest(acb_realref(poly->coeffs + i), state, prec, mag_bits); arb_randtest(acb_imagref(poly->coeffs + i), state, prec, mag_bits); } } else { for (i = 0; i < len; i++) { arb_randtest_precise(acb_realref(poly->coeffs + i), state, prec, mag_bits); arb_randtest_precise(acb_imagref(poly->coeffs + i), state, prec, mag_bits); } } _acb_poly_set_length(poly, len); _acb_poly_normalise(poly); } arb-2.8.1/acb_poly/refine_roots_durand_kerner.c000066400000000000000000000101621264125401100216170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" /* we don't need any error bounding, so we define a few helper functions that ignore the radii */ static __inline__ void acb_sub_mid(acb_t z, const acb_t x, const acb_t y, slong prec) { arf_sub(arb_midref(acb_realref(z)), arb_midref(acb_realref(x)), arb_midref(acb_realref(y)), prec, ARF_RND_DOWN); arf_sub(arb_midref(acb_imagref(z)), arb_midref(acb_imagref(x)), arb_midref(acb_imagref(y)), prec, ARF_RND_DOWN); } static __inline__ void acb_add_mid(acb_t z, const acb_t x, const acb_t y, slong prec) { arf_add(arb_midref(acb_realref(z)), arb_midref(acb_realref(x)), arb_midref(acb_realref(y)), prec, ARF_RND_DOWN); arf_add(arb_midref(acb_imagref(z)), arb_midref(acb_imagref(x)), arb_midref(acb_imagref(y)), prec, ARF_RND_DOWN); } static __inline__ void acb_mul_mid(acb_t z, const acb_t x, const acb_t y, slong prec) { #define a arb_midref(acb_realref(x)) #define b arb_midref(acb_imagref(x)) #define c arb_midref(acb_realref(y)) #define d arb_midref(acb_imagref(y)) #define e arb_midref(acb_realref(z)) #define f arb_midref(acb_imagref(z)) arf_complex_mul(e, f, a, b, c, d, prec, ARF_RND_DOWN); #undef a #undef b #undef c #undef d #undef e #undef f } static __inline__ void acb_inv_mid(acb_t z, const acb_t x, slong prec) { arf_t t; arf_init(t); #define a arb_midref(acb_realref(x)) #define b arb_midref(acb_imagref(x)) #define e arb_midref(acb_realref(z)) #define f arb_midref(acb_imagref(z)) arf_mul(t, a, a, prec, ARF_RND_DOWN); arf_addmul(t, b, b, prec, ARF_RND_DOWN); arf_div(e, a, t, prec, ARF_RND_DOWN); arf_div(f, b, t, prec, ARF_RND_DOWN); arf_neg(f, f); #undef a #undef b #undef e #undef f arf_clear(t); } void _acb_poly_evaluate_mid(acb_t res, acb_srcptr f, slong len, const acb_t a, slong prec) { slong i = len - 1; acb_t t; acb_init(t); acb_set(res, f + i); for (i = len - 2; i >= 0; i--) { acb_mul_mid(t, res, a, prec); acb_add_mid(res, f + i, t, prec); } acb_clear(t); } void _acb_poly_refine_roots_durand_kerner(acb_ptr roots, acb_srcptr poly, slong len, slong prec) { slong i, j; acb_t x, y, t; acb_init(x); acb_init(y); acb_init(t); for (i = 0; i < len - 1; i++) { _acb_poly_evaluate_mid(x, poly, len, roots + i, prec); acb_set(y, poly + len - 1); for (j = 0; j < len - 1; j++) { if (i != j) { acb_sub_mid(t, roots + i, roots + j, prec); acb_mul_mid(y, y, t, prec); } } mag_zero(arb_radref(acb_realref(y))); mag_zero(arb_radref(acb_imagref(y))); acb_inv_mid(t, y, prec); acb_mul_mid(t, t, x, prec); acb_sub_mid(roots + i, roots + i, t, prec); arf_get_mag(arb_radref(acb_realref(roots + i)), arb_midref(acb_realref(t))); arf_get_mag(arb_radref(acb_imagref(roots + i)), arb_midref(acb_imagref(t))); } acb_clear(x); acb_clear(y); acb_clear(t); } arb-2.8.1/acb_poly/reverse.c000066400000000000000000000032141264125401100156710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_reverse(acb_ptr res, acb_srcptr poly, slong len, slong n) { if (res == poly) { slong i; for (i = 0; i < n / 2; i++) { acb_struct t = res[i]; res[i] = res[n - 1 - i]; res[n - 1 - i] = t; } for (i = 0; i < n - len; i++) acb_zero(res + i); } else { slong i; for (i = 0; i < n - len; i++) acb_zero(res + i); for (i = 0; i < len; i++) acb_set(res + (n - len) + i, poly + (len - 1) - i); } } arb-2.8.1/acb_poly/revert_series.c000066400000000000000000000041121264125401100170750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_revert_series(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec) { _acb_poly_revert_series_lagrange_fast(Qinv, Q, Qlen, n, prec); } void acb_poly_revert_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !acb_is_zero(Q->coeffs) || acb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (acb_poly_revert_series). Input must \n" "have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { acb_poly_fit_length(Qinv, n); _acb_poly_revert_series(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_revert_series(t->coeffs, Q->coeffs, Qlen, n, prec); acb_poly_swap(Qinv, t); acb_poly_clear(t); } _acb_poly_set_length(Qinv, n); _acb_poly_normalise(Qinv); } arb-2.8.1/acb_poly/revert_series_lagrange.c000066400000000000000000000054121264125401100207410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_revert_series_lagrange(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec) { slong i; acb_ptr R, S, T, tmp; if (n <= 2) { if (n >= 1) acb_zero(Qinv); if (n == 2) acb_inv(Qinv + 1, Q + 1, prec); return; } R = _acb_vec_init(n - 1); S = _acb_vec_init(n - 1); T = _acb_vec_init(n - 1); acb_zero(Qinv); acb_inv(Qinv + 1, Q + 1, prec); _acb_poly_inv_series(R, Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec); _acb_vec_set(S, R, n - 1); for (i = 2; i < n; i++) { _acb_poly_mullow(T, S, n - 1, R, n - 1, n - 1, prec); acb_div_ui(Qinv + i, T + i - 1, i, prec); tmp = S; S = T; T = tmp; } _acb_vec_clear(R, n - 1); _acb_vec_clear(S, n - 1); _acb_vec_clear(T, n - 1); } void acb_poly_revert_series_lagrange(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !acb_is_zero(Q->coeffs) || acb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (acb_poly_revert_series_lagrange). Input must \n" "have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { acb_poly_fit_length(Qinv, n); _acb_poly_revert_series_lagrange(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_revert_series_lagrange(t->coeffs, Q->coeffs, Qlen, n, prec); acb_poly_swap(Qinv, t); acb_poly_clear(t); } _acb_poly_set_length(Qinv, n); _acb_poly_normalise(Qinv); } arb-2.8.1/acb_poly/revert_series_lagrange_fast.c000066400000000000000000000067421264125401100217650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" /* pointer to (x/Q)^i */ #define Ri(ii) (R + (n-1)*((ii)-1)) void _acb_poly_revert_series_lagrange_fast(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec) { slong i, j, k, m; acb_ptr R, S, T, tmp; acb_t t; if (n <= 2) { if (n >= 1) acb_zero(Qinv); if (n == 2) acb_inv(Qinv + 1, Q + 1, prec); return; } m = n_sqrt(n); acb_init(t); R = _acb_vec_init((n - 1) * m); S = _acb_vec_init(n - 1); T = _acb_vec_init(n - 1); acb_zero(Qinv); acb_inv(Qinv + 1, Q + 1, prec); _acb_poly_inv_series(Ri(1), Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec); for (i = 2; i <= m; i++) _acb_poly_mullow(Ri(i), Ri((i + 1) / 2), n - 1, Ri(i / 2), n - 1, n - 1, prec); for (i = 2; i < m; i++) acb_div_ui(Qinv + i, Ri(i) + i - 1, i, prec); _acb_vec_set(S, Ri(m), n - 1); for (i = m; i < n; i += m) { acb_div_ui(Qinv + i, S + i - 1, i, prec); for (j = 1; j < m && i + j < n; j++) { acb_mul(t, S + 0, Ri(j) + i + j - 1, prec); for (k = 1; k <= i + j - 1; k++) acb_addmul(t, S + k, Ri(j) + i + j - 1 - k, prec); acb_div_ui(Qinv + i + j, t, i + j, prec); } if (i + 1 < n) { _acb_poly_mullow(T, S, n - 1, Ri(m), n - 1, n - 1, prec); tmp = S; S = T; T = tmp; } } acb_clear(t); _acb_vec_clear(R, (n - 1) * m); _acb_vec_clear(S, n - 1); _acb_vec_clear(T, n - 1); } void acb_poly_revert_series_lagrange_fast(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !acb_is_zero(Q->coeffs) || acb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (acb_poly_revert_series_lagrange_fast). Input \n" "must have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { acb_poly_fit_length(Qinv, n); _acb_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n, prec); acb_poly_swap(Qinv, t); acb_poly_clear(t); } _acb_poly_set_length(Qinv, n); _acb_poly_normalise(Qinv); } arb-2.8.1/acb_poly/revert_series_newton.c000066400000000000000000000060671264125401100205020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define CUTOFF 5 void _acb_poly_revert_series_newton(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong n, slong prec) { slong i, k, a[FLINT_BITS]; acb_ptr T, U, V; if (n <= 2) { if (n >= 1) acb_zero(Qinv); if (n == 2) acb_inv(Qinv + 1, Q + 1, prec); return; } T = _acb_vec_init(n); U = _acb_vec_init(n); V = _acb_vec_init(n); k = n; for (i = 1; (WORD(1) << i) < k; i++); a[i = 0] = k; while (k >= CUTOFF) a[++i] = (k = (k + 1) / 2); _acb_poly_revert_series_lagrange(Qinv, Q, Qlen, k, prec); _acb_vec_zero(Qinv + k, n - k); for (i--; i >= 0; i--) { k = a[i]; _acb_poly_compose_series(T, Q, FLINT_MIN(Qlen, k), Qinv, k, k, prec); _acb_poly_derivative(U, T, k, prec); acb_zero(U + k - 1); acb_zero(T + 1); _acb_poly_div_series(V, T, k, U, k, k, prec); _acb_poly_derivative(T, Qinv, k, prec); _acb_poly_mullow(U, V, k, T, k, k, prec); _acb_vec_sub(Qinv, Qinv, U, k, prec); } _acb_vec_clear(T, n); _acb_vec_clear(U, n); _acb_vec_clear(V, n); } void acb_poly_revert_series_newton(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !acb_is_zero(Q->coeffs) || acb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (acb_poly_revert_series_newton). Input must \n" "have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { acb_poly_fit_length(Qinv, n); _acb_poly_revert_series_newton(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { acb_poly_t t; acb_poly_init2(t, n); _acb_poly_revert_series_newton(t->coeffs, Q->coeffs, Qlen, n, prec); acb_poly_swap(Qinv, t); acb_poly_clear(t); } _acb_poly_set_length(Qinv, n); _acb_poly_normalise(Qinv); } arb-2.8.1/acb_poly/rgamma_series.c000066400000000000000000000117221264125401100170370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const acb_t x, int use_reflect, int digamma, slong prec); void _acb_poly_gamma_stirling_eval(acb_ptr res, const acb_t z, slong n, slong num, slong prec); void _acb_poly_rgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong len, slong prec) { int reflect; slong i, rflen, r, n, wp; acb_ptr t, u, v; acb_struct f[2]; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { acb_rgamma(res, h, prec); _acb_vec_zero(res + 1, len - 1); return; } /* use real code for real input */ if (_acb_vec_is_real(h, hlen)) { arb_ptr tmp = _arb_vec_init(len); for (i = 0; i < hlen; i++) arb_set(tmp + i, acb_realref(h + i)); _arb_poly_rgamma_series(tmp, tmp, hlen, len, prec); for (i = 0; i < len; i++) acb_set_arb(res + i, tmp + i); _arb_vec_clear(tmp, len); return; } wp = prec + FLINT_BIT_COUNT(prec); t = _acb_vec_init(len); u = _acb_vec_init(len); v = _acb_vec_init(len); acb_init(f); acb_init(f + 1); /* otherwise use Stirling series */ acb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 0, wp); /* rgamma(h) = (gamma(1-h+r) sin(pi h)) / (rf(1-h, r) * pi), h = h0 + t*/ if (reflect) { /* u = gamma(r+1-h) */ acb_sub_ui(f, h, r + 1, wp); acb_neg(f, f); _acb_poly_gamma_stirling_eval(t, f, n, len, wp); _acb_poly_exp_series(u, t, len, len, wp); for (i = 1; i < len; i += 2) acb_neg(u + i, u + i); /* v = sin(pi x) */ acb_set(f, h); acb_one(f + 1); _acb_poly_sin_pi_series(v, f, 2, len, wp); _acb_poly_mullow(t, u, len, v, len, len, wp); /* rf(1-h,r) * pi */ if (r == 0) { acb_const_pi(u, wp); _acb_vec_scalar_div(v, t, len, u, wp); } else { acb_sub_ui(f, h, 1, wp); acb_neg(f, f); acb_set_si(f + 1, -1); rflen = FLINT_MIN(len, r + 1); _acb_poly_rising_ui_series(v, f, FLINT_MIN(2, len), r, rflen, wp); acb_const_pi(u, wp); _acb_vec_scalar_mul(v, v, rflen, u, wp); /* divide by rising factorial */ /* TODO: might better to use div_series, when it has a good basecase */ _acb_poly_inv_series(u, v, rflen, len, wp); _acb_poly_mullow(v, t, len, u, len, len, wp); } } else { /* rgamma(h) = rgamma(h+r) rf(h,r) */ if (r == 0) { acb_add_ui(f, h, r, wp); _acb_poly_gamma_stirling_eval(t, f, n, len, wp); _acb_vec_neg(t, t, len); _acb_poly_exp_series(v, t, len, len, wp); } else { acb_set(f, h); acb_one(f + 1); rflen = FLINT_MIN(len, r + 1); _acb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, wp); acb_add_ui(f, h, r, wp); _acb_poly_gamma_stirling_eval(v, f, n, len, wp); _acb_vec_neg(v, v, len); _acb_poly_exp_series(u, v, len, len, wp); _acb_poly_mullow(v, u, len, t, rflen, len, wp); } } /* compose with nonconstant part */ acb_zero(t); _acb_vec_set(t + 1, h + 1, hlen - 1); _acb_poly_compose_series(res, v, len, t, hlen, len, prec); acb_clear(f); acb_clear(f + 1); _acb_vec_clear(t, len); _acb_vec_clear(u, len); _acb_vec_clear(v, len); } void acb_poly_rgamma_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec) { if (f->length == 0 || n == 0) { acb_poly_zero(res); } else { acb_poly_fit_length(res, n); _acb_poly_rgamma_series(res->coeffs, f->coeffs, f->length, n, prec); _acb_poly_set_length(res, n); _acb_poly_normalise(res); } } arb-2.8.1/acb_poly/rising_ui_series.c000066400000000000000000000062411264125401100175630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" static void _acb_poly_rising_ui_series_bsplit(acb_ptr res, acb_srcptr f, slong flen, ulong a, ulong b, slong trunc, slong prec) { flen = FLINT_MIN(flen, trunc); if (b - a == 1) { acb_add_ui(res, f, a, prec); _acb_vec_set(res + 1, f + 1, flen - 1); } else { acb_ptr L, R; slong len1, len2; slong m = a + (b - a) / 2; len1 = poly_pow_length(flen, m - a, trunc); len2 = poly_pow_length(flen, b - m, trunc); L = _acb_vec_init(len1 + len2); R = L + len1; _acb_poly_rising_ui_series_bsplit(L, f, flen, a, m, trunc, prec); _acb_poly_rising_ui_series_bsplit(R, f, flen, m, b, trunc, prec); _acb_poly_mullow(res, L, len1, R, len2, FLINT_MIN(trunc, len1 + len2 - 1), prec); _acb_vec_clear(L, len1 + len2); } } void _acb_poly_rising_ui_series(acb_ptr res, acb_srcptr f, slong flen, ulong r, slong trunc, slong prec) { if (trunc == 1 || flen == 1) { acb_rising_ui(res, f, r, prec); _acb_vec_zero(res + 1, trunc - 1); } else if (trunc == 2) { acb_rising2_ui(res, res + 1, f, r, prec); acb_mul(res + 1, res + 1, f + 1, prec); } else { _acb_poly_rising_ui_series_bsplit(res, f, flen, 0, r, trunc, prec); } } void acb_poly_rising_ui_series(acb_poly_t res, const acb_poly_t f, ulong r, slong trunc, slong prec) { slong len; if ((f->length == 0 && r != 0) || trunc == 0) { acb_poly_zero(res); return; } if (r == 0) { acb_poly_one(res); return; } len = poly_pow_length(f->length, r, trunc); if (f == res) { acb_poly_t tmp; acb_poly_init(tmp); acb_poly_rising_ui_series(tmp, f, r, len, prec); acb_poly_swap(tmp, res); acb_poly_clear(tmp); } else { acb_poly_fit_length(res, len); _acb_poly_rising_ui_series(res->coeffs, f->coeffs, f->length, r, len, prec); _acb_poly_set_length(res, len); _acb_poly_normalise(res); } } arb-2.8.1/acb_poly/root_bound_fujiwara.c000066400000000000000000000036241264125401100202650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_root_bound_fujiwara(mag_t bound, acb_srcptr poly, slong len) { mag_t t, u, v; slong i; if (len <= 1) { mag_inf(bound); return; } mag_init(t); mag_init(u); mag_init(v); /* u = 1/leading */ acb_get_mag_lower(t, poly + len - 1); mag_one(u); mag_div(u, u, t); mag_zero(v); for (i = 0; i < len - 1; i++) { acb_get_mag(t, poly + len - 2 - i); mag_mul(t, t, u); if (i == len - 2) mag_mul_2exp_si(t, t, -1); mag_root(t, t, i + 1); mag_max(v, v, t); } mag_mul_2exp_si(bound, v, 1); mag_clear(t); mag_clear(u); mag_clear(v); } void acb_poly_root_bound_fujiwara(mag_t bound, acb_poly_t poly) { _acb_poly_root_bound_fujiwara(bound, poly->coeffs, poly->length); } arb-2.8.1/acb_poly/root_inclusion.c000066400000000000000000000040241264125401100172640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_root_inclusion(acb_t r, const acb_t m, acb_srcptr poly, acb_srcptr polyder, slong len, slong prec) { acb_t t; arf_t u, v; acb_init(t); arf_init(u); arf_init(v); acb_set(r, m); mag_zero(arb_radref(acb_realref(r))); mag_zero(arb_radref(acb_imagref(r))); _acb_poly_evaluate(t, poly, len, r, prec); acb_get_abs_ubound_arf(u, t, MAG_BITS); /* it could happen that we have an exact root, in which case we should avoid dividing by the derivative */ if (!arf_is_zero(u)) { _acb_poly_evaluate(t, polyder, len - 1, r, prec); acb_inv(t, t, MAG_BITS); acb_get_abs_ubound_arf(v, t, MAG_BITS); arf_mul(u, u, v, MAG_BITS, ARF_RND_UP); arf_mul_ui(u, u, len - 1, MAG_BITS, ARF_RND_UP); } arf_get_mag(arb_radref(acb_realref(r)), u); arf_get_mag(arb_radref(acb_imagref(r)), u); arf_clear(u); arf_clear(v); acb_clear(t); } arb-2.8.1/acb_poly/rsqrt_series.c000066400000000000000000000060011264125401100167400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_rsqrt_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); while (hlen > 0 && acb_is_zero(h + hlen - 1)) hlen--; if (hlen <= 1) { acb_rsqrt(g, h, prec); _acb_vec_zero(g + 1, len - 1); } else if (len == 2) { acb_rsqrt(g, h, prec); acb_div(g + 1, h + 1, h, prec); acb_mul(g + 1, g + 1, g, prec); acb_mul_2exp_si(g + 1, g + 1, -1); acb_neg(g + 1, g + 1); } else if (_acb_vec_is_zero(h + 1, hlen - 2)) { acb_t t; acb_init(t); arf_set_si_2exp_si(arb_midref(acb_realref(t)), -1, -1); _acb_poly_binomial_pow_acb_series(g, h, hlen, t, len, prec); acb_clear(t); } else { acb_ptr t, u; slong tlen; t = _acb_vec_init(2 * len); u = t + len; acb_rsqrt(g, h, prec); NEWTON_INIT(1, len) NEWTON_LOOP(m, n) tlen = FLINT_MIN(2 * m - 1, n); _acb_poly_mullow(t, g, m, g, m, tlen, prec); _acb_poly_mullow(u, g, m, t, tlen, n, prec); _acb_poly_mullow(t, u, n, h, hlen, n, prec); _acb_vec_scalar_mul_2exp_si(g + m, t + m, n - m, -1); _acb_vec_neg(g + m, g + m, n - m); NEWTON_END_LOOP NEWTON_END _acb_vec_clear(t, 2 * len); } } void acb_poly_rsqrt_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { if (n == 0) { acb_poly_zero(g); return; } if (g == h) { acb_poly_t t; acb_poly_init(t); acb_poly_rsqrt_series(t, h, n, prec); acb_poly_swap(g, t); acb_poly_clear(t); return; } acb_poly_fit_length(g, n); if (h->length == 0) _acb_vec_indeterminate(g->coeffs, n); else _acb_poly_rsqrt_series(g->coeffs, h->coeffs, h->length, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/set.c000066400000000000000000000024671264125401100150220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set(acb_poly_t dest, const acb_poly_t src) { slong len = acb_poly_length(src); acb_poly_fit_length(dest, len); _acb_vec_set(dest->coeffs, src->coeffs, len); _acb_poly_set_length(dest, len); } arb-2.8.1/acb_poly/set2_arb_poly.c000066400000000000000000000041001264125401100167550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set_arb_poly(acb_poly_t poly, const arb_poly_t re) { slong i, len; len = arb_poly_length(re); acb_poly_fit_length(poly, len); for (i = 0; i < len; i++) { arb_set(acb_realref(poly->coeffs + i), re->coeffs + i); arb_zero(acb_imagref(poly->coeffs + i)); } _acb_poly_set_length(poly, len); } void acb_poly_set2_arb_poly(acb_poly_t poly, const arb_poly_t re, const arb_poly_t im) { slong i, rlen, ilen, len; rlen = arb_poly_length(re); ilen = arb_poly_length(im); len = FLINT_MAX(rlen, ilen); acb_poly_fit_length(poly, len); for (i = 0; i < rlen; i++) arb_set(acb_realref(poly->coeffs + i), re->coeffs + i); for (i = rlen; i < len; i++) arb_zero(acb_realref(poly->coeffs + i)); for (i = 0; i < ilen; i++) arb_set(acb_imagref(poly->coeffs + i), im->coeffs + i); for (i = ilen; i < len; i++) arb_zero(acb_imagref(poly->coeffs + i)); _acb_poly_set_length(poly, len); } arb-2.8.1/acb_poly/set2_fmpq_poly.c000066400000000000000000000032151264125401100171620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set_fmpq_poly(acb_poly_t poly, const fmpq_poly_t re, slong prec) { arb_poly_t t; arb_poly_init(t); arb_poly_set_fmpq_poly(t, re, prec); acb_poly_set_arb_poly(poly, t); arb_poly_clear(t); } void acb_poly_set2_fmpq_poly(acb_poly_t poly, const fmpq_poly_t re, const fmpq_poly_t im, slong prec) { arb_poly_t t, u; arb_poly_init(t); arb_poly_init(u); arb_poly_set_fmpq_poly(t, re, prec); arb_poly_set_fmpq_poly(u, im, prec); acb_poly_set2_arb_poly(poly, t, u); arb_poly_clear(t); arb_poly_clear(u); } arb-2.8.1/acb_poly/set2_fmpz_poly.c000066400000000000000000000026551264125401100172020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set2_fmpz_poly(acb_poly_t poly, const fmpz_poly_t re, const fmpz_poly_t im, slong prec) { arb_poly_t t, u; arb_poly_init(t); arb_poly_init(u); arb_poly_set_fmpz_poly(t, re, prec); arb_poly_set_fmpz_poly(u, im, prec); acb_poly_set2_arb_poly(poly, t, u); arb_poly_clear(t); arb_poly_clear(u); } arb-2.8.1/acb_poly/set_coeff_acb.c000066400000000000000000000026301264125401100167610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set_coeff_acb(acb_poly_t poly, slong n, const acb_t x) { acb_poly_fit_length(poly, n + 1); if (n + 1 > poly->length) { _acb_vec_zero(poly->coeffs + poly->length, n - poly->length); poly->length = n + 1; } acb_set(poly->coeffs + n, x); _acb_poly_normalise(poly); } arb-2.8.1/acb_poly/set_coeff_si.c000066400000000000000000000026241264125401100166520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set_coeff_si(acb_poly_t poly, slong n, slong x) { acb_poly_fit_length(poly, n + 1); if (n + 1 > poly->length) { _acb_vec_zero(poly->coeffs + poly->length, n - poly->length); poly->length = n + 1; } acb_set_si(poly->coeffs + n, x); _acb_poly_normalise(poly); } arb-2.8.1/acb_poly/set_fmpz_poly.c000066400000000000000000000026031264125401100171110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set_fmpz_poly(acb_poly_t poly, const fmpz_poly_t src, slong prec) { slong i, len = fmpz_poly_length(src); acb_poly_fit_length(poly, len); _acb_poly_set_length(poly, len); for (i = 0; i < len; i++) acb_set_round_fmpz(poly->coeffs + i, src->coeffs + i, prec); } arb-2.8.1/acb_poly/set_length.c000066400000000000000000000024651264125401100163610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_set_length(acb_poly_t poly, slong len) { slong i; if (poly->length > len) { for (i = len; i < poly->length; i++) acb_zero(poly->coeffs + i); } poly->length = len; } arb-2.8.1/acb_poly/set_round.c000066400000000000000000000025251264125401100162240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set_round(acb_poly_t dest, const acb_poly_t src, slong prec) { slong len = acb_poly_length(src); acb_poly_fit_length(dest, len); _acb_vec_set_round(dest->coeffs, src->coeffs, len, prec); _acb_poly_set_length(dest, len); } arb-2.8.1/acb_poly/set_si.c000066400000000000000000000025131264125401100155050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void acb_poly_set_si(acb_poly_t poly, slong c) { if (c == 0) { acb_poly_zero(poly); } else { acb_poly_fit_length(poly, 1); acb_set_si(poly->coeffs, c); _acb_poly_set_length(poly, 1); } } arb-2.8.1/acb_poly/shift_left.c000066400000000000000000000037501264125401100163520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2008, 2009 William Hart Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_shift_left(acb_ptr res, acb_srcptr poly, slong len, slong n) { slong i; /* Copy in reverse to avoid writing over unshifted coefficients */ if (res != poly) { for (i = len; i--; ) acb_set(res + n + i, poly + i); } else { for (i = len; i--; ) acb_swap(res + n + i, res + i); } for (i = 0; i < n; i++) acb_zero(res + i); } void acb_poly_shift_left(acb_poly_t res, const acb_poly_t poly, slong n) { if (n == 0) { acb_poly_set(res, poly); return; } if (poly->length == 0) { acb_poly_zero(res); return; } acb_poly_fit_length(res, poly->length + n); _acb_poly_shift_left(res->coeffs, poly->coeffs, poly->length, n); _acb_poly_set_length(res, poly->length + n); } arb-2.8.1/acb_poly/shift_right.c000066400000000000000000000037141264125401100165350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2008, 2009 William Hart Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_shift_right(acb_ptr res, acb_srcptr poly, slong len, slong n) { slong i; /* Copy in forward order to avoid writing over unshifted coefficients */ if (res != poly) { for (i = 0; i < len - n; i++) acb_set(res + i, poly + n + i); } else { for (i = 0; i < len - n; i++) acb_swap(res + i, res + n + i); } } void acb_poly_shift_right(acb_poly_t res, const acb_poly_t poly, slong n) { if (n == 0) { acb_poly_set(res, poly); return; } if (poly->length <= n) { acb_poly_zero(res); return; } acb_poly_fit_length(res, poly->length - n); _acb_poly_shift_right(res->coeffs, poly->coeffs, poly->length, n); _acb_poly_set_length(res, poly->length - n); } arb-2.8.1/acb_poly/sin_cos_pi_series.c000066400000000000000000000050121264125401100177130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define TANGENT_CUTOFF 80 void _acb_poly_sin_cos_pi_series(acb_ptr s, acb_ptr c, const acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { acb_sin_cos_pi(s, c, h, prec); _acb_vec_zero(s + 1, n - 1); _acb_vec_zero(c + 1, n - 1); } else if (n == 2) { acb_t t; acb_init(t); acb_const_pi(t, prec); acb_mul(t, t, h + 1, prec); acb_sin_cos_pi(s, c, h, prec); acb_mul(s + 1, c, t, prec); acb_neg(t, t); acb_mul(c + 1, s, t, prec); acb_clear(t); } else if (hlen < TANGENT_CUTOFF) _acb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 1); else _acb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 1); } void acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(s); acb_poly_zero(c); return; } if (hlen == 0) { acb_poly_zero(s); acb_poly_one(c); return; } if (hlen == 1) n = 1; acb_poly_fit_length(s, n); acb_poly_fit_length(c, n); _acb_poly_sin_cos_pi_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(s, n); _acb_poly_normalise(s); _acb_poly_set_length(c, n); _acb_poly_normalise(c); } arb-2.8.1/acb_poly/sin_cos_series.c000066400000000000000000000047231264125401100172330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define TANGENT_CUTOFF 80 void _acb_poly_sin_cos_series(acb_ptr s, acb_ptr c, const acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { acb_sin_cos(s, c, h, prec); _acb_vec_zero(s + 1, n - 1); _acb_vec_zero(c + 1, n - 1); } else if (n == 2) { acb_t t; acb_init(t); acb_set(t, h + 1); acb_sin_cos(s, c, h, prec); acb_mul(s + 1, c, t, prec); acb_neg(t, t); acb_mul(c + 1, s, t, prec); acb_clear(t); } else if (hlen < TANGENT_CUTOFF) _acb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 0); else _acb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 0); } void acb_poly_sin_cos_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(s); acb_poly_zero(c); return; } if (hlen == 0) { acb_poly_zero(s); acb_poly_one(c); return; } if (hlen == 1) n = 1; acb_poly_fit_length(s, n); acb_poly_fit_length(c, n); _acb_poly_sin_cos_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(s, n); _acb_poly_normalise(s); _acb_poly_set_length(c, n); _acb_poly_normalise(c); } arb-2.8.1/acb_poly/sin_cos_series_basecase.c000066400000000000000000000054421264125401100210600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_sin_cos_series_basecase(acb_ptr s, acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec, int times_pi) { slong j, k, alen = FLINT_MIN(n, hlen); acb_ptr a; acb_t t, u; if (times_pi) acb_sin_cos_pi(s, c, h, prec); else acb_sin_cos(s, c, h, prec); if (hlen == 1) { _acb_vec_zero(s + 1, n - 1); _acb_vec_zero(c + 1, n - 1); return; } acb_init(t); acb_init(u); a = _acb_vec_init(alen); for (k = 1; k < alen; k++) acb_mul_ui(a + k, h + k, k, prec); if (times_pi) { acb_const_pi(t, prec); _acb_vec_scalar_mul(a + 1, a + 1, alen - 1, t, prec); } for (k = 1; k < n; k++) { acb_zero(t); acb_zero(u); for (j = 1; j < FLINT_MIN(k + 1, hlen); j++) { acb_submul(t, a + j, s + k - j, prec); acb_addmul(u, a + j, c + k - j, prec); } acb_div_ui(c + k, t, k, prec); acb_div_ui(s + k, u, k, prec); } acb_clear(t); acb_clear(u); _acb_vec_clear(a, alen); } void acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec, int times_pi) { slong hlen = h->length; if (n == 0) { acb_poly_zero(s); acb_poly_zero(c); return; } if (hlen == 0) { acb_poly_zero(s); acb_poly_one(c); return; } acb_poly_fit_length(s, n); acb_poly_fit_length(c, n); _acb_poly_sin_cos_series_basecase(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi); _acb_poly_set_length(s, n); _acb_poly_normalise(s); _acb_poly_set_length(c, n); _acb_poly_normalise(c); } arb-2.8.1/acb_poly/sin_cos_series_tangent.c000066400000000000000000000073141264125401100207520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c, const acb_srcptr h, slong hlen, slong len, slong prec, int times_pi) { acb_ptr t, u, v; acb_t s0, c0; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { if (times_pi) acb_sin_cos_pi(s, c, h, prec); else acb_sin_cos(s, c, h, prec); _acb_vec_zero(s + 1, len - 1); _acb_vec_zero(c + 1, len - 1); return; } /* sin(x) = 2*tan(x/2)/(1+tan(x/2)^2) cos(x) = (1-tan(x/2)^2)/(1+tan(x/2)^2) */ acb_init(s0); acb_init(c0); t = _acb_vec_init(3 * len); u = t + len; v = u + len; /* sin, cos of h0 */ if (times_pi) acb_sin_cos_pi(s0, c0, h, prec); else acb_sin_cos(s0, c0, h, prec); /* t = tan((h-h0)/2) */ acb_zero(u); _acb_vec_scalar_mul_2exp_si(u + 1, h + 1, hlen - 1, -1); if (times_pi) { acb_const_pi(t, prec); _acb_vec_scalar_mul(u + 1, u + 1, hlen - 1, t, prec); } _acb_poly_tan_series(t, u, hlen, len, prec); /* v = 1 + t^2 */ _acb_poly_mullow(v, t, len, t, len, len, prec); acb_add_ui(v, v, 1, prec); /* u = 1/(1+t^2) */ _acb_poly_inv_series(u, v, len, len, prec); /* sine */ _acb_poly_mullow(s, t, len, u, len, len, prec); _acb_vec_scalar_mul_2exp_si(s, s, len, 1); /* cosine */ acb_sub_ui(v, v, 2, prec); _acb_vec_neg(v, v, len); _acb_poly_mullow(c, v, len, u, len, len, prec); /* sin(h0 + h1) = cos(h0) sin(h1) + sin(h0) cos(h1) cos(h0 + h1) = cos(h0) cos(h1) - sin(h0) sin(h1) */ if (!acb_is_zero(s0)) { _acb_vec_scalar_mul(t, s, len, c0, prec); _acb_vec_scalar_mul(u, c, len, s0, prec); _acb_vec_scalar_mul(v, s, len, s0, prec); _acb_vec_add(s, t, u, len, prec); _acb_vec_scalar_mul(t, c, len, c0, prec); _acb_vec_sub(c, t, v, len, prec); } _acb_vec_clear(t, 3 * len); acb_clear(s0); acb_clear(c0); } void acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec, int times_pi) { slong hlen = h->length; if (n == 0) { acb_poly_zero(s); acb_poly_zero(c); return; } if (hlen == 0) { acb_poly_zero(s); acb_poly_one(c); return; } acb_poly_fit_length(s, n); acb_poly_fit_length(c, n); _acb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi); _acb_poly_set_length(s, n); _acb_poly_normalise(s); _acb_poly_set_length(c, n); _acb_poly_normalise(c); } arb-2.8.1/acb_poly/sin_pi_series.c000066400000000000000000000041451264125401100170550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_sin_pi_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { acb_sin_pi(g, h, prec); _acb_vec_zero(g + 1, n - 1); } else if (n == 2) { acb_t t; acb_init(t); acb_sin_cos_pi(g, t, h, prec); acb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ acb_const_pi(t, prec); acb_mul(g + 1, g + 1, t, prec); acb_clear(t); } else { acb_ptr t = _acb_vec_init(n); _acb_poly_sin_cos_pi_series(g, t, h, hlen, n, prec); _acb_vec_clear(t, n); } } void acb_poly_sin_pi_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { acb_poly_zero(g); return; } if (hlen == 1) n = 1; acb_poly_fit_length(g, n); _acb_poly_sin_pi_series(g->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/sin_series.c000066400000000000000000000040141264125401100163600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_sin_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { acb_sin(g, h, prec); _acb_vec_zero(g + 1, n - 1); } else if (n == 2) { acb_t t; acb_init(t); acb_sin_cos(g, t, h, prec); acb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ acb_clear(t); } else { acb_ptr t = _acb_vec_init(n); _acb_poly_sin_cos_series(g, t, h, hlen, n, prec); _acb_vec_clear(t, n); } } void acb_poly_sin_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { acb_poly_zero(g); return; } if (hlen == 1) n = 1; acb_poly_fit_length(g, n); _acb_poly_sin_series(g->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/sqrt_series.c000066400000000000000000000051421264125401100165630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_sqrt_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); while (hlen > 0 && acb_is_zero(h + hlen - 1)) hlen--; if (hlen <= 1) { acb_sqrt(g, h, prec); _acb_vec_zero(g + 1, len - 1); } else if (len == 2) { acb_sqrt(g, h, prec); acb_div(g + 1, h + 1, h, prec); acb_mul(g + 1, g + 1, g, prec); acb_mul_2exp_si(g + 1, g + 1, -1); } else if (_acb_vec_is_zero(h + 1, hlen - 2)) { acb_t t; acb_init(t); arf_set_si_2exp_si(arb_midref(acb_realref(t)), 1, -1); _acb_poly_binomial_pow_acb_series(g, h, hlen, t, len, prec); acb_clear(t); } else { acb_ptr t; t = _acb_vec_init(len); _acb_poly_rsqrt_series(t, h, hlen, len, prec); _acb_poly_mullow(g, t, len, h, hlen, len, prec); _acb_vec_clear(t, len); } } void acb_poly_sqrt_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { if (n == 0) { acb_poly_zero(g); return; } if (g == h) { acb_poly_t t; acb_poly_init(t); acb_poly_sqrt_series(t, h, n, prec); acb_poly_swap(g, t); acb_poly_clear(t); return; } acb_poly_fit_length(g, n); if (h->length == 0) _acb_vec_indeterminate(g->coeffs, n); else _acb_poly_sqrt_series(g->coeffs, h->coeffs, h->length, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/sub.c000066400000000000000000000035641264125401100150170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_sub(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) { slong i, min = FLINT_MIN(len1, len2); for (i = 0; i < min; i++) acb_sub(res + i, poly1 + i, poly2 + i, prec); for (i = min; i < len1; i++) acb_set_round(res + i, poly1 + i, prec); for (i = min; i < len2; i++) acb_neg_round(res + i, poly2 + i, prec); } void acb_poly_sub(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) { slong max = FLINT_MAX(poly1->length, poly2->length); acb_poly_fit_length(res, max); _acb_poly_sub(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); _acb_poly_set_length(res, max); _acb_poly_normalise(res); } arb-2.8.1/acb_poly/tan_series.c000066400000000000000000000054651264125401100163640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define TAN_NEWTON_CUTOFF 20 void _acb_poly_tan_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); if (hlen == 1) { acb_tan(g, h, prec); _acb_vec_zero(g + 1, len - 1); } else if (len == 2) { acb_t t; acb_init(t); acb_tan(g, h, prec); acb_mul(t, g, g, prec); acb_add_ui(t, t, 1, prec); acb_mul(g + 1, t, h + 1, prec); /* safe since hlen >= 2 */ acb_clear(t); } else { acb_ptr t, u; t = _acb_vec_init(2 * len); u = t + len; NEWTON_INIT(TAN_NEWTON_CUTOFF, len) NEWTON_BASECASE(n) _acb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec, 0); _acb_poly_div_series(g, t, n, u, n, n, prec); NEWTON_END_BASECASE NEWTON_LOOP(m, n) _acb_poly_mullow(u, g, m, g, m, n, prec); acb_add_ui(u, u, 1, prec); _acb_poly_atan_series(t, g, m, n, prec); _acb_poly_sub(t + m, h + m, FLINT_MAX(0, hlen - m), t + m, n - m, prec); _acb_poly_mullow(g + m, u, n, t + m, n - m, n - m, prec); NEWTON_END_LOOP NEWTON_END _acb_vec_clear(t, 2 * len); } } void acb_poly_tan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) { if (h->length == 0 || n == 0) { acb_poly_zero(g); return; } if (g == h) { acb_poly_t t; acb_poly_init(t); acb_poly_tan_series(t, h, n, prec); acb_poly_swap(g, t); acb_poly_clear(t); return; } acb_poly_fit_length(g, n); _acb_poly_tan_series(g->coeffs, h->coeffs, h->length, n, prec); _acb_poly_set_length(g, n); _acb_poly_normalise(g); } arb-2.8.1/acb_poly/test/000077500000000000000000000000001264125401100150315ustar00rootroot00000000000000arb-2.8.1/acb_poly/test/t-add.c000066400000000000000000000070161264125401100161720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_add(C, A, B); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_add(c, a, b, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_add(d, d, b, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_add(d, a, d, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-add_si.c000066400000000000000000000047511264125401100166700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("add_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_poly_t a, b, c, d; slong v; acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); acb_poly_randtest(b, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); acb_poly_randtest(c, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); acb_poly_randtest(d, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); v = n_randtest(state); acb_poly_set_si(b, v); acb_poly_add(c, a, b, 2 + n_randint(state, 200)); acb_poly_add_si(d, a, v, 2 + n_randint(state, 200)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); abort(); } acb_poly_add_si(a, a, v, 2 + n_randint(state, 200)); if (!acb_poly_overlaps(a, d)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-agm1_series.c000066400000000000000000000054451264125401100176450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("agm1_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 10); n1 = 1 + n_randint(state, 10); n2 = 1 + n_randint(state, 10); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_poly_agm1_series(A, S, n1, bits2); acb_poly_agm1_series(B, S, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_agm1_series(S, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-atan_series.c000066400000000000000000000066701264125401100177440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("atan_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; acb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); fmpq_poly_set_coeff_si(A, 0, 0); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_atan_series(b, a, n, rbits2); /* Check 2 atan(x) = atan(2x/(1-x^2)) + C */ acb_poly_mullow(c, a, a, n, rbits2); acb_poly_one(d); acb_poly_sub(c, d, c, rbits2); acb_poly_add(d, a, a, rbits2); if (acb_poly_length(c) != 0) { acb_poly_div_series(c, d, c, n, rbits2); acb_poly_atan_series(c, c, n, rbits2); acb_poly_add(d, b, b, rbits2); /* TODO: also check the first coefficient */ acb_poly_set_coeff_si(c, 0, 0); acb_poly_set_coeff_si(d, 0, 0); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } } acb_poly_atan_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-compose.c000066400000000000000000000067511264125401100171140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 20), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_compose(C, A, B); acb_poly_randtest(c, state, 1 + n_randint(state, 20), rbits1, 4); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_compose(c, a, b, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_compose(d, d, b, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_compose(d, a, d, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-compose_divconquer.c000066400000000000000000000067121264125401100213500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_divconquer...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 20), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_compose(C, A, B); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_compose_divconquer(c, a, b, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_compose_divconquer(d, d, b, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_compose_divconquer(d, a, d, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-compose_horner.c000066400000000000000000000066721264125401100204730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 20), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_compose(C, A, B); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_compose_horner(c, a, b, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_compose_horner(d, d, b, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_compose_horner(d, a, d, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-compose_series.c000066400000000000000000000071661264125401100204670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, n; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 25), qbits2); fmpq_poly_set_coeff_ui(B, 0, 0); fmpq_poly_compose_series(C, A, B, n); acb_poly_randtest(c, state, 1 + n_randint(state, 20), rbits1, 4); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_compose_series(c, a, b, n, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits3 = %wd\n", n, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_compose_series(d, d, b, n, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_compose_series(d, a, d, n, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-compose_series_brent_kung.c000066400000000000000000000071271264125401100227020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_series_brent_kung...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, n; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 25), qbits2); fmpq_poly_set_coeff_ui(B, 0, 0); fmpq_poly_compose_series(C, A, B, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_compose_series_brent_kung(c, a, b, n, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits3 = %wd\n", n, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_compose_series_brent_kung(d, d, b, n, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_compose_series_brent_kung(d, a, d, n, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-compose_series_horner.c000066400000000000000000000071071264125401100220370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_series_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, n; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 25), qbits2); fmpq_poly_set_coeff_ui(B, 0, 0); fmpq_poly_compose_series(C, A, B, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_compose_series_horner(c, a, b, n, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits3 = %wd\n", n, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_compose_series_horner(d, d, b, n, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_compose_series_horner(d, a, d, n, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-cos_pi_series.c000066400000000000000000000057231264125401100202730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("cos_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; acb_t pi; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_init(pi); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_poly_cos_pi_series(A, S, n1, bits2); acb_const_pi(pi, bits3); acb_poly_set_acb(B, pi); acb_poly_mul(B, S, B, bits3); acb_poly_cos_series(B, B, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_cos_pi_series(S, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); acb_clear(pi); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-cot_pi_series.c000066400000000000000000000053001264125401100202630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("cot_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, bits1, bits2, bits3; acb_poly_t S, A, B, C; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_randtest(S, state, m, bits1, 10); acb_poly_randtest(A, state, m, bits1, 10); acb_poly_randtest(B, state, m, bits1, 10); acb_poly_cot_pi_series(A, S, n1, bits2); acb_poly_sin_cos_pi_series(B, C, S, n1, bits3); acb_poly_div_series(B, C, B, n1, bits3); if (!acb_poly_overlaps(A, B)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_cot_pi_series(S, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-digamma_series.c000066400000000000000000000067501264125401100204170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("digamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 300); rbits2 = 2 + n_randint(state, 300); rbits3 = 2 + n_randint(state, 300); m = n_randint(state, 25); n1 = n_randint(state, 25); n2 = n_randint(state, 25); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_digamma_series(b, a, n1, rbits2); acb_poly_digamma_series(c, a, n2, rbits3); acb_poly_set(d, b); acb_poly_truncate(d, FLINT_MIN(n1, n2)); acb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); acb_poly_printd(a, 50); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 50); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 50); flint_printf("\n\n"); abort(); } /* check psi(a) + 1/a = psi(a+1) */ acb_poly_inv_series(c, a, n1, rbits2); acb_poly_add(c, b, c, rbits2); acb_poly_add_si(d, a, 1, rbits2); acb_poly_digamma_series(d, d, n1, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_digamma_series(a, a, n1, rbits2); if (!acb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-div_series.c000066400000000000000000000073321264125401100175770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("div_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, p, qbits, rbits1, rbits2; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); p = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); do { fmpq_poly_randtest_not_zero(B, state, n, qbits); } while (B->coeffs[0] == 0); fmpq_poly_div_series(C, A, B, p); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits1); acb_poly_div_series(c, a, b, p, rbits2); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_div_series(d, d, b, p, rbits2); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_div_series(d, a, d, p, rbits2); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_div_series(c, d, d, p, rbits2); acb_poly_div_series(d, d, d, p, rbits2); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 3)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-divrem.c000066400000000000000000000101171264125401100167240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("divrem...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong m, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, Q, R; acb_poly_t a, b, q, r; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(Q); fmpq_poly_init(R); acb_poly_init(a); acb_poly_init(b); acb_poly_init(q); acb_poly_init(r); fmpq_poly_randtest(A, state, m, qbits1); fmpq_poly_randtest_not_zero(B, state, n, qbits2); fmpq_poly_divrem(Q, R, A, B); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_divrem(q, r, a, b, rbits3); if (!acb_poly_contains_fmpq_poly(q, Q) || !acb_poly_contains_fmpq_poly(r, R)) { flint_printf("FAIL\n\n"); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("Q = "); fmpq_poly_print(Q); flint_printf("\n\n"); flint_printf("R = "); fmpq_poly_print(R); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("q = "); acb_poly_printd(q, 15); flint_printf("\n\n"); flint_printf("r = "); acb_poly_printd(r, 15); flint_printf("\n\n"); abort(); } acb_poly_divrem(a, r, a, b, rbits3); if (!acb_poly_equal(a, q)) { flint_printf("FAIL (aliasing q, a)\n\n"); } acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_divrem(b, r, a, b, rbits3); if (!acb_poly_equal(b, q)) { flint_printf("FAIL (aliasing q, b)\n\n"); abort(); } acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_divrem(q, a, a, b, rbits3); if (!acb_poly_equal(a, r)) { flint_printf("FAIL (aliasing r, a)\n\n"); abort(); } acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_divrem(q, b, a, b, rbits3); if (!acb_poly_equal(b, r)) { flint_printf("FAIL (aliasing r, b)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(Q); fmpq_poly_clear(R); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(q); acb_poly_clear(r); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-elliptic_k_series.c000066400000000000000000000054751264125401100211420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("elliptic_k_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 10); n1 = 1 + n_randint(state, 10); n2 = 1 + n_randint(state, 10); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_poly_elliptic_k_series(A, S, n1, bits2); acb_poly_elliptic_k_series(B, S, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_elliptic_k_series(S, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-elliptic_p_series.c000066400000000000000000000057671264125401100211530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("elliptic_p_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; acb_t z; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 10); n1 = 1 + n_randint(state, 10); n2 = 1 + n_randint(state, 10); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_init(z); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_randtest(z, state, bits1, 3); acb_poly_elliptic_p_series(A, S, z, n1, bits2); acb_poly_elliptic_p_series(B, S, z, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_elliptic_p_series(S, S, z, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); acb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-erf_series.c000066400000000000000000000054411264125401100175700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("erf_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 10); n1 = 1 + n_randint(state, 10); n2 = 1 + n_randint(state, 10); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_poly_erf_series(A, S, n1, bits2); acb_poly_erf_series(B, S, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_erf_series(S, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate.c000066400000000000000000000060371264125401100172520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq_t X, Y; acb_poly_t f; acb_t x, y; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(F); fmpq_init(X); fmpq_init(Y); acb_poly_init(f); acb_init(x); acb_init(y); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); fmpq_randtest(X, state, qbits2); fmpq_poly_evaluate_fmpq(Y, F, X); acb_poly_set_fmpq_poly(f, F, rbits1); acb_set_fmpq(x, X, rbits2); acb_poly_evaluate(y, f, x, rbits3); if (!acb_contains_fmpq(y, Y)) { flint_printf("FAIL\n\n"); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y); flint_printf("\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); acb_printd(y, 15); flint_printf("\n\n"); abort(); } /* aliasing */ acb_poly_evaluate(x, f, x, rbits3); if (!acb_contains_fmpq(x, Y)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(F); fmpq_clear(X); fmpq_clear(Y); acb_poly_clear(f); acb_clear(x); acb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate2.c000066400000000000000000000055541264125401100173370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate2...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_poly_t f, g; acb_t x, y1, z1, y2, z2; acb_init(x); acb_init(y1); acb_init(z1); acb_init(y2); acb_init(z2); acb_poly_init(f); acb_poly_init(g); acb_randtest(x, state, 2 + n_randint(state, 1000), 5); acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); acb_poly_derivative(g, f, 2 + n_randint(state, 1000)); acb_poly_evaluate2(y1, z1, f, x, 2 + n_randint(state, 1000)); acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); acb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000)); if (!acb_overlaps(y1, y2) || !acb_overlaps(z1, z2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); acb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(f); acb_poly_clear(g); acb_clear(x); acb_clear(y1); acb_clear(z1); acb_clear(y2); acb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate2_horner.c000066400000000000000000000055721264125401100207140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate2_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_poly_t f, g; acb_t x, y1, z1, y2, z2; acb_init(x); acb_init(y1); acb_init(z1); acb_init(y2); acb_init(z2); acb_poly_init(f); acb_poly_init(g); acb_randtest(x, state, 2 + n_randint(state, 1000), 5); acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); acb_poly_derivative(g, f, 2 + n_randint(state, 1000)); acb_poly_evaluate2_horner(y1, z1, f, x, 2 + n_randint(state, 1000)); acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); acb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000)); if (!acb_overlaps(y1, y2) || !acb_overlaps(z1, z2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); acb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(f); acb_poly_clear(g); acb_clear(x); acb_clear(y1); acb_clear(z1); acb_clear(y2); acb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate2_rectangular.c000066400000000000000000000056041264125401100217220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate2_rectangular...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_poly_t f, g; acb_t x, y1, z1, y2, z2; acb_init(x); acb_init(y1); acb_init(z1); acb_init(y2); acb_init(z2); acb_poly_init(f); acb_poly_init(g); acb_randtest(x, state, 2 + n_randint(state, 1000), 5); acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); acb_poly_derivative(g, f, 2 + n_randint(state, 1000)); acb_poly_evaluate2_rectangular(y1, z1, f, x, 2 + n_randint(state, 1000)); acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); acb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000)); if (!acb_overlaps(y1, y2) || !acb_overlaps(z1, z2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); acb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(f); acb_poly_clear(g); acb_clear(x); acb_clear(y1); acb_clear(z1); acb_clear(y2); acb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate_horner.c000066400000000000000000000060641264125401100206270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq_t X, Y; acb_poly_t f; acb_t x, y; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(F); fmpq_init(X); fmpq_init(Y); acb_poly_init(f); acb_init(x); acb_init(y); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); fmpq_randtest(X, state, qbits2); fmpq_poly_evaluate_fmpq(Y, F, X); acb_poly_set_fmpq_poly(f, F, rbits1); acb_set_fmpq(x, X, rbits2); acb_poly_evaluate_horner(y, f, x, rbits3); if (!acb_contains_fmpq(y, Y)) { flint_printf("FAIL\n\n"); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y); flint_printf("\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); acb_printd(y, 15); flint_printf("\n\n"); abort(); } /* aliasing */ acb_poly_evaluate_horner(x, f, x, rbits3); if (!acb_contains_fmpq(x, Y)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(F); fmpq_clear(X); fmpq_clear(Y); acb_poly_clear(f); acb_clear(x); acb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate_rectangular.c000066400000000000000000000045311264125401100216360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_rectangular...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_poly_t f; acb_t x, y1, y2; acb_init(x); acb_init(y1); acb_init(y2); acb_poly_init(f); acb_randtest(x, state, 2 + n_randint(state, 1000), 5); acb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); acb_poly_evaluate_rectangular(y1, f, x, 2 + n_randint(state, 1000)); acb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); if (!acb_overlaps(y1, y2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n"); flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(f); acb_clear(x); acb_clear(y1); acb_clear(y2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate_vec_fast.c000066400000000000000000000063541264125401100211260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_vec_fast...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq * X, * Y; acb_poly_t f; acb_ptr x, y; qbits1 = 2 + n_randint(state, 100); qbits2 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = n_randint(state, 10); fmpq_poly_init(F); X = _fmpq_vec_init(n); Y = _fmpq_vec_init(n); acb_poly_init(f); x = _acb_vec_init(n); y = _acb_vec_init(n); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); for (i = 0; i < n; i++) fmpq_randtest(X + i, state, qbits2); for (i = 0; i < n; i++) fmpq_poly_evaluate_fmpq(Y + i, F, X + i); acb_poly_set_fmpq_poly(f, F, rbits1); for (i = 0; i < n; i++) acb_set_fmpq(x + i, X + i, rbits2); acb_poly_evaluate_vec_fast(y, f, x, n, rbits3); for (i = 0; i < n; i++) { if (!acb_contains_fmpq(y + i, Y + i)) { flint_printf("FAIL (%wd of %wd)\n\n", i, n); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X + i); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y + i); flint_printf("\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x + i, 15); flint_printf("\n\n"); flint_printf("y = "); acb_printd(y + i, 15); flint_printf("\n\n"); abort(); } } fmpq_poly_clear(F); _fmpq_vec_clear(X, n); _fmpq_vec_clear(Y, n); acb_poly_clear(f); _acb_vec_clear(x, n); _acb_vec_clear(y, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-evaluate_vec_iter.c000066400000000000000000000063541264125401100211340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_vec_iter...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq * X, * Y; acb_poly_t f; acb_ptr x, y; qbits1 = 2 + n_randint(state, 100); qbits2 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = n_randint(state, 10); fmpq_poly_init(F); X = _fmpq_vec_init(n); Y = _fmpq_vec_init(n); acb_poly_init(f); x = _acb_vec_init(n); y = _acb_vec_init(n); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); for (i = 0; i < n; i++) fmpq_randtest(X + i, state, qbits2); for (i = 0; i < n; i++) fmpq_poly_evaluate_fmpq(Y + i, F, X + i); acb_poly_set_fmpq_poly(f, F, rbits1); for (i = 0; i < n; i++) acb_set_fmpq(x + i, X + i, rbits2); acb_poly_evaluate_vec_iter(y, f, x, n, rbits3); for (i = 0; i < n; i++) { if (!acb_contains_fmpq(y + i, Y + i)) { flint_printf("FAIL (%wd of %wd)\n\n", i, n); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X + i); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y + i); flint_printf("\n\n"); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x + i, 15); flint_printf("\n\n"); flint_printf("y = "); acb_printd(y + i, 15); flint_printf("\n\n"); abort(); } } fmpq_poly_clear(F); _fmpq_vec_clear(X, n); _fmpq_vec_clear(Y, n); acb_poly_clear(f); _acb_vec_clear(x, n); _acb_vec_clear(y, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-exp_series.c000066400000000000000000000060001264125401100176000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, bits1, bits2, bits3; acb_poly_t a, b, c, d; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); if (n_randint(state, 100) == 0) { m = 1 + n_randint(state, 400); n = 1 + n_randint(state, 400); } else { m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); } acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, bits1, 10); acb_poly_randtest(b, state, m, bits1, 10); acb_poly_randtest(c, state, 1 + n_randint(state, 300), bits1, 10); acb_poly_randtest(d, state, 1 + n_randint(state, 300), bits1, 10); /* check exp(a+b) = exp(a) exp(b) */ acb_poly_exp_series(c, a, n, bits2); acb_poly_exp_series(d, b, n, bits2); acb_poly_mullow(c, c, d, n, bits2); acb_poly_add(d, a, b, bits3); acb_poly_exp_series(d, d, n, bits3); /* also aliasing test */ if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-exp_series_basecase.c000066400000000000000000000053221264125401100214340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_series_basecase...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, bits1, bits2, bits3; acb_poly_t a, b, c, d; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 40); n = 1 + n_randint(state, 40); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, bits1, 10); acb_poly_randtest(b, state, m, bits1, 10); /* check exp(a+b) = exp(a) exp(b) */ acb_poly_exp_series_basecase(c, a, n, bits2); acb_poly_exp_series_basecase(d, b, n, bits2); acb_poly_mullow(c, c, d, n, bits2); acb_poly_add(d, a, b, bits3); acb_poly_exp_series_basecase(d, d, n, bits3); /* also aliasing test */ if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-find_roots.c000066400000000000000000000063671264125401100176200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("find_roots...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_poly_t A; acb_poly_t B; acb_poly_t C; acb_t t; acb_ptr roots; slong i, deg, isolated; slong prec = 10 + n_randint(state, 400); acb_init(t); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); do { acb_poly_randtest(A, state, 2 + n_randint(state, 15), prec, 5); } while (A->length == 0); deg = A->length - 1; roots = _acb_vec_init(deg); isolated = acb_poly_find_roots(roots, A, NULL, 0, prec); if (isolated == deg) { acb_poly_fit_length(B, 1); acb_set(B->coeffs, A->coeffs + deg); _acb_poly_set_length(B, 1); for (i = 0; i < deg; i++) { acb_poly_fit_length(C, 2); acb_one(C->coeffs + 1); acb_neg(C->coeffs + 0, roots + i); _acb_poly_set_length(C, 2); acb_poly_mul(B, B, C, prec); } if (!acb_poly_contains(B, A)) { flint_printf("FAIL: product does not equal polynomial\n"); acb_poly_printd(A, 15); flint_printf("\n\n"); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } } for (i = 0; i < isolated; i++) { acb_poly_evaluate(t, A, roots + i, prec); if (!acb_contains_zero(t)) { flint_printf("FAIL: poly(root) does not contain zero\n"); acb_poly_printd(A, 15); flint_printf("\n\n"); acb_printd(roots + i, 15); flint_printf("\n\n"); acb_printd(t, 15); flint_printf("\n\n"); abort(); } } _acb_vec_clear(roots, deg); acb_clear(t); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-gamma_series.c000066400000000000000000000071361264125401100201010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 25); n1 = 1 + n_randint(state, 25); n2 = 1 + n_randint(state, 25); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, rbits1, 3); acb_poly_randtest(b, state, m, rbits1, 3); acb_poly_randtest(c, state, m, rbits1, 3); acb_poly_gamma_series(b, a, n1, rbits2); acb_poly_gamma_series(c, a, n2, rbits3); acb_poly_set(d, b); acb_poly_truncate(d, FLINT_MIN(n1, n2)); acb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check gamma(a) * a = gamma(a+1) */ acb_poly_mullow(c, b, a, n1, rbits2); acb_poly_set(d, a); acb_add_ui(d->coeffs, d->coeffs, 1, rbits2); acb_poly_gamma_series(d, d, n1, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation, n1 = %wd)\n\n", n1); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_gamma_series(a, a, n1, rbits2); if (!acb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-gamma_upper_series.c000066400000000000000000000075051264125401100213140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma_upper_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; acb_t s, t; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 10); n1 = 1 + n_randint(state, 10); n2 = 1 + n_randint(state, 10); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_init(s); acb_init(t); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_randtest(s, state, bits1, 3); acb_poly_gamma_upper_series(A, s, S, n1, bits2); acb_poly_gamma_upper_series(B, s, S, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL (consistency)\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_derivative(C, S, bits2); acb_poly_neg(B, S); acb_poly_exp_series(B, B, n1, bits2); acb_poly_mullow(C, C, B, n1, bits2); acb_sub_ui(t, s, 1, bits2); acb_poly_pow_acb_series(B, S, t, n1, bits2); acb_poly_mullow(C, C, B, n1, bits2); acb_poly_neg(C, C); acb_poly_truncate(C, n1 - 1); acb_poly_derivative(B, A, bits2); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL (derivative)\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); flint_printf("C = "); acb_poly_printd(C, 15); flint_printf("\n\n"); abort(); } acb_poly_gamma_upper_series(S, s, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); acb_clear(s); acb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-get_coeff_ptr.c000066400000000000000000000042201264125401100202420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main(void) { int i, result; flint_rand_t state; flint_printf("get_coeff_ptr...."); fflush(stdout); flint_randinit(state); for (i = 0; i < 1000; i++) { acb_poly_t A; acb_t a; slong n = n_randint(state, 100); acb_poly_init(A); acb_poly_randtest(A, state, n_randint(state, 100), 100, 10); acb_init(a); acb_poly_get_coeff_acb(a, A, n); result = n < acb_poly_length(A) ? acb_equal(a, acb_poly_get_coeff_ptr(A, n)) : acb_poly_get_coeff_ptr(A, n) == NULL; if (!result) { flint_printf("FAIL:\n"); flint_printf("A = "), acb_poly_printd(A, 10), flint_printf("\n\n"); flint_printf("a = "), acb_print(a), flint_printf("\n\n"); flint_printf("n = %wd\n\n", n); abort(); } acb_poly_clear(A); acb_clear(a); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/acb_poly/test/t-get_set_coeff_fmprb.c000066400000000000000000000044511264125401100214240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2009 William Hart Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main(void) { int i, j, result; flint_rand_t state; flint_printf("get/set_coeff_acb...."); fflush(stdout); flint_randinit(state); for (i = 0; i < 100; i++) { acb_poly_t a; acb_t x1, x2; slong coeff, len; acb_poly_init(a); acb_init(x1); acb_init(x2); len = n_randint(state, 100) + 1; for (j = 0; j < 100; j++) { acb_randtest(x1, state, 2 + n_randint(state, 200), 10); coeff = n_randint(state, len); acb_poly_set_coeff_acb(a, coeff, x1); acb_poly_get_coeff_acb(x2, a, coeff); result = (acb_equal(x1, x2)); if (!result) { flint_printf("FAIL:\n"); flint_printf("x1 = "), acb_print(x1), flint_printf("\n"); flint_printf("x2 = "), acb_print(x2), flint_printf("\n"); flint_printf("coeff = %wd, length = %wd\n", coeff, len); abort(); } } acb_clear(x1); acb_clear(x2); acb_poly_clear(a); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/acb_poly/test/t-get_unique_fmpz_poly.c000066400000000000000000000056601264125401100217110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("get_unique_fmpz_poly...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong prec, c; fmpz_poly_t A, B, C; acb_poly_t a, b; fmpz_poly_init(A); fmpz_poly_init(B); fmpz_poly_init(C); acb_poly_init(a); acb_poly_init(b); fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); fmpz_poly_randtest(B, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); fmpz_poly_randtest(C, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); c = 1 + n_randint(state, 1000); prec = 2 + n_randint(state, 100); for ( ; ; ) { acb_poly_set_fmpz_poly(a, A, prec); acb_poly_set2_fmpz_poly(b, B, C, prec); acb_poly_scalar_mul_2exp_si(b, b, -c); acb_poly_add(a, a, b, prec); acb_poly_sub(a, a, b, prec); if (acb_poly_get_unique_fmpz_poly(B, a)) { if (!fmpz_poly_equal(A, B)) { flint_printf("FAIL\n\n"); flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); abort(); } break; } else { prec *= 2; } } fmpz_poly_clear(A); fmpz_poly_clear(B); fmpz_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-interpolate_barycentric.c000066400000000000000000000061761264125401100223630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("interpolate_barycentric...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t P; acb_poly_t R, S; fmpq_t t, u; acb_ptr xs, ys; fmpq_poly_init(P); acb_poly_init(R); acb_poly_init(S); fmpq_init(t); fmpq_init(u); qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 5); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1); n = P->length; xs = _acb_vec_init(n); ys = _acb_vec_init(n); acb_poly_set_fmpq_poly(R, P, rbits1); if (n > 0) { fmpq_randtest(t, state, qbits2); acb_set_fmpq(xs, t, rbits2); for (i = 1; i < n; i++) { fmpq_randtest_not_zero(u, state, qbits2); fmpq_abs(u, u); fmpq_add(t, t, u); acb_set_fmpq(xs + i, t, rbits2); } } for (i = 0; i < n; i++) acb_poly_evaluate(ys + i, R, xs + i, rbits2); acb_poly_interpolate_barycentric(S, xs, ys, n, rbits3); if (!acb_poly_contains_fmpq_poly(S, P)) { flint_printf("FAIL:\n"); flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n"); flint_printf("R = "); acb_poly_printd(R, 15); flint_printf("\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(P); acb_poly_clear(R); acb_poly_clear(S); fmpq_clear(t); fmpq_clear(u); _acb_vec_clear(xs, n); _acb_vec_clear(ys, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-interpolate_fast.c000066400000000000000000000061601264125401100210040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("interpolate_fast...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t P; acb_poly_t R, S; fmpq_t t, u; acb_ptr xs, ys; fmpq_poly_init(P); acb_poly_init(R); acb_poly_init(S); fmpq_init(t); fmpq_init(u); qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 5); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1); n = P->length; xs = _acb_vec_init(n); ys = _acb_vec_init(n); acb_poly_set_fmpq_poly(R, P, rbits1); if (n > 0) { fmpq_randtest(t, state, qbits2); acb_set_fmpq(xs, t, rbits2); for (i = 1; i < n; i++) { fmpq_randtest_not_zero(u, state, qbits2); fmpq_abs(u, u); fmpq_add(t, t, u); acb_set_fmpq(xs + i, t, rbits2); } } for (i = 0; i < n; i++) acb_poly_evaluate(ys + i, R, xs + i, rbits2); acb_poly_interpolate_fast(S, xs, ys, n, rbits3); if (!acb_poly_contains_fmpq_poly(S, P)) { flint_printf("FAIL:\n"); flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n"); flint_printf("R = "); acb_poly_printd(R, 15); flint_printf("\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(P); acb_poly_clear(R); acb_poly_clear(S); fmpq_clear(t); fmpq_clear(u); _acb_vec_clear(xs, n); _acb_vec_clear(ys, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-interpolate_newton.c000066400000000000000000000061641264125401100213650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("interpolate_newton...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t P; acb_poly_t R, S; fmpq_t t, u; acb_ptr xs, ys; fmpq_poly_init(P); acb_poly_init(R); acb_poly_init(S); fmpq_init(t); fmpq_init(u); qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 5); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1); n = P->length; xs = _acb_vec_init(n); ys = _acb_vec_init(n); acb_poly_set_fmpq_poly(R, P, rbits1); if (n > 0) { fmpq_randtest(t, state, qbits2); acb_set_fmpq(xs, t, rbits2); for (i = 1; i < n; i++) { fmpq_randtest_not_zero(u, state, qbits2); fmpq_abs(u, u); fmpq_add(t, t, u); acb_set_fmpq(xs + i, t, rbits2); } } for (i = 0; i < n; i++) acb_poly_evaluate(ys + i, R, xs + i, rbits2); acb_poly_interpolate_newton(S, xs, ys, n, rbits3); if (!acb_poly_contains_fmpq_poly(S, P)) { flint_printf("FAIL:\n"); flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n"); flint_printf("R = "); acb_poly_printd(R, 15); flint_printf("\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(P); acb_poly_clear(R); acb_poly_clear(S); fmpq_clear(t); fmpq_clear(u); _acb_vec_clear(xs, n); _acb_vec_clear(ys, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-inv_series.c000066400000000000000000000077141264125401100176150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("inv_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; acb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (A->coeffs[0] == 0); fmpq_poly_inv_series(B, A, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_inv_series(b, a, n, rbits2); if (!acb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } acb_poly_inv_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); } /* check f * f^-1 = 1 */ for (iter = 0; iter < 10000; iter++) { slong bits, trunc; acb_poly_t a, b, ab; fmpq_poly_t id; bits = 2 + n_randint(state, 200); trunc = 1 + n_randint(state, 10); acb_poly_init(a); acb_poly_init(b); acb_poly_init(ab); fmpq_poly_init(id); do { acb_poly_randtest(a, state, 1 + n_randint(state, 10), bits, 5); } while (a->length == 0 || acb_contains_zero(a->coeffs + 0)); acb_poly_inv_series(b, a, trunc, bits); acb_poly_mullow(ab, a, b, trunc, bits); fmpq_poly_set_ui(id, 1); if (!acb_poly_contains_fmpq_poly(ab, id)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("ab = "); acb_poly_printd(ab, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(ab); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-lgamma_series.c000066400000000000000000000105721264125401100202530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("lgamma_series...."); fflush(stdout); flint_randinit(state); /* special accuracy test case */ { acb_poly_t a; acb_t c; acb_init(c); acb_poly_init(a); arb_set_str(acb_realref(c), "-20.25", 53); arb_set_str(acb_imagref(c), "1e1000", 53); acb_poly_set_coeff_acb(a, 0, c); acb_poly_set_coeff_si(a, 1, 1); acb_poly_lgamma_series(a, a, 3, 53); if (acb_rel_accuracy_bits(a->coeffs) < 40 || acb_rel_accuracy_bits(a->coeffs + 1) < 40 || acb_rel_accuracy_bits(a->coeffs + 2) < 40) { flint_printf("FAIL: accuracy (reflection formula)\n\n"); acb_poly_printd(a, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_clear(c); } for (iter = 0; iter < 500; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_randtest(b, state, m, rbits1, 10); acb_poly_randtest(c, state, m, rbits1, 10); acb_poly_lgamma_series(b, a, n1, rbits2); acb_poly_lgamma_series(c, a, n2, rbits3); acb_poly_set(d, b); acb_poly_truncate(d, FLINT_MIN(n1, n2)); acb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check loggamma(a) + log(a) = loggamma(a+1) */ acb_poly_log_series(c, a, n1, rbits2); acb_poly_add(c, b, c, rbits2); acb_poly_set(d, a); acb_add_ui(d->coeffs, d->coeffs, 1, rbits2); acb_poly_lgamma_series(d, d, n1, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_lgamma_series(a, a, n1, rbits2); if (!acb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-log_series.c000066400000000000000000000127121264125401100175740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("log_series...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; acb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); fmpq_poly_randtest_not_zero(A, state, m, qbits); fmpq_poly_set_coeff_ui(A, 0, UWORD(1)); fmpq_poly_log_series(B, A, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); acb_poly_log_series(b, a, n, rbits2); if (!acb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); } /* test aliasing */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; acb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); acb_poly_init(a); acb_poly_init(b); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (fmpz_sgn(A->coeffs + 0) <= 0); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_log_series(b, a, n, rbits2); acb_poly_log_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); acb_poly_clear(a); acb_poly_clear(b); } /* test that exp(log(f)) contains f */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; acb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (fmpz_sgn(A->coeffs + 0) <= 0); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); acb_poly_log_series(b, a, n, rbits2); acb_poly_exp_series_basecase(c, b, n, rbits3); fmpq_poly_truncate(A, n); if (!acb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-mullow.c000066400000000000000000000133701264125401100167610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mullow...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mullow(C, A, B, trunc); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_mullow(c, a, b, trunc, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_mullow(d, d, b, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_mullow(d, a, d, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ acb_poly_set(b, a); acb_poly_mullow(c, a, b, trunc, rbits3); acb_poly_mullow(d, a, a, trunc, rbits3); if (!acb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_mullow(a, a, a, trunc, rbits3); if (!acb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } /* compare with classical */ for (iter = 0; iter < 10000; iter++) { slong bits, trunc; acb_poly_t a, b, ab, ab2; bits = 2 + n_randint(state, 200); trunc = n_randint(state, 10); acb_poly_init(a); acb_poly_init(b); acb_poly_init(ab); acb_poly_init(ab2); acb_poly_randtest(a, state, 1 + n_randint(state, 10), bits, 5); acb_poly_randtest(b, state, 1 + n_randint(state, 10), bits, 5); acb_poly_mullow_classical(ab, a, b, trunc, bits); acb_poly_mullow(ab2, a, b, trunc, bits); if (!acb_poly_overlaps(ab, ab2)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("ab = "); acb_poly_printd(ab, 15); flint_printf("\n\n"); flint_printf("ab2 = "); acb_poly_printd(ab2, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(ab); acb_poly_clear(ab2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-mullow_classical.c000066400000000000000000000145401264125401100207770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mullow_classical...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mullow(C, A, B, trunc); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_mullow_classical(c, a, b, trunc, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_mullow_classical(d, d, b, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_mullow_classical(d, a, d, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ acb_poly_set(b, a); acb_poly_mullow_classical(c, a, b, trunc, rbits3); acb_poly_mullow_classical(d, a, a, trunc, rbits3); if (!acb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_mullow_classical(a, a, a, trunc, rbits3); if (!acb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } /* check a*(b+c) = a*b+a*c */ for (iter = 0; iter < 10000; iter++) { slong bits, trunc; acb_poly_t a, b, c, bc, abc, ab, ac, abac; bits = 2 + n_randint(state, 200); trunc = n_randint(state, 10); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(bc); acb_poly_init(abc); acb_poly_init(ab); acb_poly_init(ac); acb_poly_init(abac); acb_poly_randtest(a, state, 1 + n_randint(state, 10), bits, 5); acb_poly_randtest(b, state, 1 + n_randint(state, 10), bits, 5); acb_poly_randtest(c, state, 1 + n_randint(state, 10), bits, 5); acb_poly_add(bc, b, c, bits); acb_poly_mullow_classical(abc, a, bc, trunc, bits); acb_poly_mullow_classical(ab, a, b, trunc, bits); acb_poly_mullow_classical(ac, a, c, trunc, bits); acb_poly_add(abac, ab, ac, bits); if (!acb_poly_overlaps(abc, abac)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("abc = "); acb_poly_printd(abc, 15); flint_printf("\n\n"); flint_printf("abac = "); acb_poly_printd(abac, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(bc); acb_poly_clear(abc); acb_poly_clear(ab); acb_poly_clear(ac); acb_poly_clear(abac); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-mullow_transpose.c000066400000000000000000000135101264125401100210530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mullow_transpose...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mullow(C, A, B, trunc); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_mullow_transpose(c, a, b, trunc, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_mullow_transpose(d, d, b, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_mullow_transpose(d, a, d, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ acb_poly_set(b, a); acb_poly_mullow_transpose(c, a, b, trunc, rbits3); acb_poly_mullow_transpose(d, a, a, trunc, rbits3); if (!acb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_mullow_transpose(a, a, a, trunc, rbits3); if (!acb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } /* compare with classical */ for (iter = 0; iter < 10000; iter++) { slong bits, trunc; acb_poly_t a, b, ab, ab2; bits = 2 + n_randint(state, 200); trunc = n_randint(state, 10); acb_poly_init(a); acb_poly_init(b); acb_poly_init(ab); acb_poly_init(ab2); acb_poly_randtest(a, state, 1 + n_randint(state, 10), bits, 5); acb_poly_randtest(b, state, 1 + n_randint(state, 10), bits, 5); acb_poly_mullow_classical(ab, a, b, trunc, bits); acb_poly_mullow_transpose(ab2, a, b, trunc, bits); if (!acb_poly_overlaps(ab, ab2)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("ab = "); acb_poly_printd(ab, 15); flint_printf("\n\n"); flint_printf("ab2 = "); acb_poly_printd(ab2, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(ab); acb_poly_clear(ab2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-mullow_transpose_gauss.c000066400000000000000000000135701264125401100222630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mullow_transpose_gauss...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mullow(C, A, B, trunc); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_mullow_transpose_gauss(c, a, b, trunc, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_mullow_transpose_gauss(d, d, b, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_mullow_transpose_gauss(d, a, d, trunc, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ acb_poly_set(b, a); acb_poly_mullow_transpose_gauss(c, a, b, trunc, rbits3); acb_poly_mullow_transpose_gauss(d, a, a, trunc, rbits3); if (!acb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_mullow_transpose_gauss(a, a, a, trunc, rbits3); if (!acb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } /* compare with classical */ for (iter = 0; iter < 10000; iter++) { slong bits, trunc; acb_poly_t a, b, ab, ab2; bits = 2 + n_randint(state, 200); trunc = n_randint(state, 10); acb_poly_init(a); acb_poly_init(b); acb_poly_init(ab); acb_poly_init(ab2); acb_poly_randtest(a, state, 1 + n_randint(state, 10), bits, 5); acb_poly_randtest(b, state, 1 + n_randint(state, 10), bits, 5); acb_poly_mullow_classical(ab, a, b, trunc, bits); acb_poly_mullow_transpose_gauss(ab2, a, b, trunc, bits); if (!acb_poly_overlaps(ab, ab2)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("ab = "); acb_poly_printd(ab, 15); flint_printf("\n\n"); flint_printf("ab2 = "); acb_poly_printd(ab2, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(ab); acb_poly_clear(ab2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-polylog_cpx.c000066400000000000000000000331571264125401100200060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #define EPS 1e-13 #define NUM_DERIVS 3 #define NUM_TESTS 56 const double polylog_testdata[NUM_TESTS][10] = { {-2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2.0, 0.0, -0.5, 0.0, -0.0740740740740740741, 0.0, -0.158799035455864473, 0.0, 0.00278425812292977954, 0.0}, {-2.0, 0.0, 0.99609375, 0.0, 33358080.0, 0.0, -215693527.719090182, 0.0, 703924885.809675425, 0.0}, {-2.0, 0.0, 1.00390625, 0.0, -33751296.0, 0.0, 218367905.967311029, -106032823.56283664, -546519337.1290267, 686023009.262281684}, {-2.0, 0.0, -4.25, 0.0, 0.0954540546377281071, 0.0, -0.0297817299750221174, 0.0, -0.196648773789941696, 0.0}, {-2.0, 0.0, 3.5, 0.0, -1.008, 0.0, 0.691243661008350802, -3.19575256895409845, 4.53340070033764442, 2.22882281653983385}, {-2.0, 0.0, 0.0, -1.0, 0.0, 0.5, -0.852556797635011582, -0.25189536315108886, 0.345626503121598963, -0.46292146649778986}, {-2.0, 0.0, 0.125, 0.125, 0.071424, 0.280832, 0.0646851488459364134, -0.118051747326526959, -0.0396751348737248634, 0.0452067417426917285}, {-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-1.0, 0.0, -0.5, 0.0, -0.222222222222222222, 0.0, -0.131883201632587537, 0.0, 0.0199225628389378777, 0.0}, {-1.0, 0.0, 0.99609375, 0.0, 65280.0, 0.0, -389461.499432291984, 0.0, 1182814.77437627002, 0.0}, {-1.0, 0.0, 1.00390625, 0.0, 65792.0, 0.0, -392773.095775796478, 206691.925664168516, 868954.597422132011, -1233932.55215831045}, {-1.0, 0.0, -4.25, 0.0, -0.154195011337868481, 0.0, -0.474824989764482489, 0.0, -0.21428706813151403, 0.0}, {-1.0, 0.0, 3.5, 0.0, 0.56, 0.0, -0.322735710701998933, 2.00176023742981729, -3.09698193717149541, -0.395213225234415973}, {-1.0, 0.0, 0.0, -1.0, -0.5, 0.0, -0.183855151549436048, -0.58312180806163756, 0.254077251327014729, 0.0351429519611278982}, {-1.0, 0.0, 0.125, 0.125, 0.1088, 0.1984, 0.0192018441183911, -0.0548368329876085499, -0.0115465156713130216, 0.020954643261003461}, {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {0.0, 0.0, -0.5, 0.0, -0.333333333333333333, 0.0, -0.0904116649848191551, 0.0, 0.0199028637728058217, 0.0}, {0.0, 0.0, 0.99609375, 0.0, 255.0, 0.0, -1269.73106874463507, 0.0, 3359.60296533314103, 0.0}, {0.0, 0.0, 1.00390625, 0.0, -257.0, 0.0, 1273.86116119868176, -805.817494984366455, -2113.9649224353639, 4004.84182305521042}, {0.0, 0.0, -4.25, 0.0, -0.809523809523809524, 0.0, -0.795769271870623909, 0.0, -0.0965372637237445457, 0.0}, {0.0, 0.0, 3.5, 0.0, -1.4, 0.0, -1.78816683065098841, -2.50773109725857055, 1.83790031889197745, -2.01262260402527512}, {0.0, 0.0, 0.0, -1.0, -0.5, -0.5, 0.120782237635245222, -0.391594392706836776, 0.0669079578849868665, 0.116416441749488305}, {0.0, 0.0, 0.125, 0.125, 0.12, 0.16, 0.00583206536388767829, -0.0256940749384562616, -0.00344424777009813297, 0.00965046958017889366}, {-0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-0.5, 0.0, -0.5, 0.0, -0.283012810746506023, 0.0, -0.111080563146094489, 0.0, 0.0211430885590715694, 0.0}, {-0.5, 0.0, 0.99609375, 0.0, 3619.14124113924805, 0.0, -20195.2825251289493, 0.0, 58032.3050555790807, 0.0}, {-0.5, 0.0, 1.00390625, 0.0, -0.207985517845521836, 3640.61848390552728, -11437.7014354502895, -20327.8206114649109, 63861.4335397379033, 40487.2831296029499}, {-0.5, 0.0, -4.25, 0.0, -0.441427843410865187, 0.0, -0.665497904840929966, 0.0, -0.162969337925229287, 0.0}, {-0.5, 0.0, 3.5, 0.0, -0.232043460812781422, 0.63203565652521718, -2.44367789279529917, 0.119367210264842707, -0.763914228371074801, -2.81228485141461073}, {-0.5, 0.0, 0.0, -1.0, -0.537549381115898973, -0.27517974122882025, 0.0158915835170861709, -0.505981074388456133, 0.147999289996985447, 0.105632732120539676}, {-0.5, 0.0, 0.125, 0.125, 0.116021225799463628, 0.175602658223910358, 0.0105539353881710306, -0.0374742285737420805, -0.0062875342272019156, 0.0142081398192247589}, {1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {1.0, 0.0, -0.5, 0.0, -0.405465108108164382, 0.0, -0.0556552111040376179, 0.0, 0.0145754167941056437, 0.0}, {1.0, 0.0, 0.99609375, 0.0, 5.54517744447956248, 0.0, -13.0766609768056118, 0.0, 24.0940545588450487, 0.0}, {1.0, 0.0, 1.00390625, 0.0, 5.54517744447956248, -3.14159265358979324, -8.16844417312495553, 15.6134381896777968, -0.38789687903338657, -36.2148484363837508}, {1.0, 0.0, -4.25, 0.0, -1.65822807660353238, 0.0, -0.861140718490863904, 0.0, 0.0240108114276114004, 0.0}, {1.0, 0.0, 3.5, 0.0, -0.916290731874155065, -3.14159265358979324, 2.57284574234941582, -2.52133906787958123, 1.44241441233798233, 1.57208443290129947}, {1.0, 0.0, 0.0, -1.0, -0.346573590279972655, -0.78539816339744831, 0.160292055087885226, -0.192901316796912429, -0.0115066749133700615, 0.0770708622146679417}, {1.0, 0.0, 0.125, 0.125, 0.123430038965762899, 0.141897054604163923, 0.00180689203856968544, -0.0122114794810442984, -0.00105066979284378462, 0.00449853805632375062}, {2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {2.0, 0.0, -0.5, 0.0, -0.448414206923646202, 0.0, -0.0320237060779612787, 0.0, 0.0092536571135294828, 0.0}, {2.0, 0.0, 0.99609375, 0.0, 1.61932072927810507, 0.0, -0.863010139919679163, 0.0, 0.825515949454683347, 0.0}, {2.0, 0.0, 1.00390625, 0.0, 1.6704551616562229, -0.0122479400888173039, -0.992661633138610541, 0.0731191212424626706, 1.04852574935488925, -0.214307793003452771}, {2.0, 0.0, -4.25, 0.0, -2.46898738747224279, 0.0, -0.739287387997829118, 0.0, 0.0874470644522297429, 0.0}, {2.0, 0.0, 3.5, 0.0, 2.1959348115757808, -3.93567093851438969, 2.87640729249480637, 0.777030723254221356, -0.81939570865486996, 1.19241843763256774}, {2.0, 0.0, 0.0, -1.0, -0.205616758356028305, -0.915965594177219015, 0.117193531789480469, -0.0815807361165927951, -0.0255408233794369879, 0.0372076062178391175}, {2.0, 0.0, 0.125, 0.125, 0.124500148439393858, 0.133240721203487057, 0.000569113907620539642, -0.00588251562210034232, -0.000326714635669985778, 0.00213086661076891839}, {-2.0, 2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, {-2.0, 2.0, -0.5, 0.0, -0.132203419506655614, -0.390689361106274866, -0.256343261725123592, 0.106175177622871437, 0.0749290443999118563, 0.0319207027895210173}, {-2.0, 2.0, 0.99609375, 0.0, 13841369.6929212372, -8339597.62269406988, -87251051.2148652244, 65225350.0315463319, 273254167.909661771, -247710863.316563213}, {-2.0, 2.0, 1.00390625, 0.0, -26028.6661639721745, 15961.1559569935978, 113847.512122984734, -206358.723605581203, 6578.40068463757013, 908971.828153761815}, {-2.0, 2.0, -4.25, 0.0, 1.26205464628714387, 0.274313692011971484, 0.442242006131113713, -1.61799252235272836, -0.927785295033312282, -0.172205994085466244}, {-2.0, 2.0, 3.5, 0.0, 0.0870998538268457367, 0.0980699787750225838, 0.152937181587789832, -0.0211963252018165386, 0.0431921445114569281, -0.0695183434413184998}, {-2.0, 2.0, 0.0, -1.0, 0.199312975007554535, -0.0775592701795263651, -0.0210851901426345675, -0.167326332453265841, -0.0632997708310078762, -0.0392019115527122943}, {-2.0, 2.0, 0.125, 0.125, 0.315234332693229892, 0.165559827416958489, -0.16530664867351669, -0.0392852937947218337, 0.0780220225006149953, 0.0215283250955342792}, }; int main() { slong iter; flint_rand_t state; flint_printf("polylog_cpx...."); fflush(stdout); flint_randinit(state); /* check particular values against table */ { acb_t s, z, t; acb_ptr w1, w2; slong i, j, prec; acb_init(s); acb_init(z); acb_init(t); w1 = _acb_vec_init(NUM_DERIVS); w2 = _acb_vec_init(NUM_DERIVS); for (prec = 32; prec <= 512; prec *= 4) { for (i = 0; i < NUM_TESTS; i++) { acb_zero(s); arf_set_d(arb_midref(acb_realref(s)), polylog_testdata[i][0]); arf_set_d(arb_midref(acb_imagref(s)), polylog_testdata[i][1]); acb_zero(z); arf_set_d(arb_midref(acb_realref(z)), polylog_testdata[i][2]); arf_set_d(arb_midref(acb_imagref(z)), polylog_testdata[i][3]); _acb_poly_polylog_cpx_small(w1, s, z, NUM_DERIVS, prec); _acb_poly_polylog_cpx_zeta(w2, s, z, NUM_DERIVS, prec); for (j = 0; j < NUM_DERIVS; j++) { arf_set_d(arb_midref(acb_realref(t)), polylog_testdata[i][4+2*j]); mag_set_d(arb_radref(acb_realref(t)), fabs(polylog_testdata[i][4+2*j]) * EPS); arf_set_d(arb_midref(acb_imagref(t)), polylog_testdata[i][4+2*j+1]); mag_set_d(arb_radref(acb_imagref(t)), fabs(polylog_testdata[i][4+2*j+1]) * EPS); if (!acb_overlaps(w1 + j, t) || !acb_overlaps(w2 + j, t) || !acb_overlaps(w1 + j, w2 + j)) { flint_printf("FAIL\n\n"); flint_printf("s = "); acb_printd(s, 15); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1 + j, 15); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2 + j, 15); flint_printf("\n\n"); abort(); } } } } _acb_vec_clear(w1, NUM_DERIVS); _acb_vec_clear(w2, NUM_DERIVS); acb_clear(s); acb_clear(z); acb_clear(t); } for (iter = 0; iter < 250; iter++) { acb_t s, z; acb_ptr w1, w2; slong i, len1, len2, prec1, prec2; acb_init(s); acb_init(z); if (n_randint(state, 2)) acb_randtest(s, state, 1 + n_randint(state, 300), 3); else acb_set_si(s, n_randint(state, 20) - 10); switch (n_randint(state, 3)) { case 0: acb_randtest(z, state, 1 + n_randint(state, 300), 10); break; case 1: arb_randtest(acb_realref(z), state, 1 + n_randint(state, 300), 10); break; case 2: acb_one(z); break; } prec1 = 2 + n_randint(state, 300); prec2 = prec1 + 30; len1 = 1 + n_randint(state, 20); len2 = 1 + n_randint(state, 20); w1 = _acb_vec_init(len1); w2 = _acb_vec_init(len2); switch (n_randint(state, 5)) { case 0: _acb_poly_polylog_cpx_small(w1, s, z, len1, prec1); break; case 1: _acb_poly_polylog_cpx_zeta(w1, s, z, len1, prec1); break; default: _acb_poly_polylog_cpx(w1, s, z, len1, prec1); break; } switch (n_randint(state, 5)) { case 0: _acb_poly_polylog_cpx_small(w2, s, z, len2, prec2); break; case 1: _acb_poly_polylog_cpx_zeta(w2, s, z, len2, prec2); break; default: _acb_poly_polylog_cpx(w2, s, z, len2, prec2); break; } for (i = 0; i < FLINT_MIN(len1, len2); i++) { if (!acb_overlaps(w1 + i, w2 + i)) { flint_printf("FAIL: overlap\n\n"); flint_printf("iter = %wd\n", iter); flint_printf("len1 = %wd, len2 = %wd, i = %wd\n\n", len1, len2, i); flint_printf("s = "); acb_printd(s, prec1 / 3.33); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, prec1 / 3.33); flint_printf("\n\n"); flint_printf("w1 = "); acb_printd(w1 + i, prec1 / 3.33); flint_printf("\n\n"); flint_printf("w2 = "); acb_printd(w2 + i, prec2 / 3.33); flint_printf("\n\n"); abort(); } } acb_clear(s); acb_clear(z); _acb_vec_clear(w1, len1); _acb_vec_clear(w2, len2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-polylog_series.c000066400000000000000000000057531264125401100205070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("polylog_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; acb_t z; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 10); n1 = 1 + n_randint(state, 10); n2 = 1 + n_randint(state, 10); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_init(z); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_randtest(z, state, bits1, 3); acb_poly_polylog_series(A, S, z, n1, bits2); acb_poly_polylog_series(B, S, z, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_polylog_series(S, S, z, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); acb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-pow_acb_series.c000066400000000000000000000065151264125401100204310ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_acb_series...."); fflush(stdout); flint_randinit(state); /* compare with exp/log */ for (iter = 0; iter < 10000; iter++) { slong prec, trunc; acb_poly_t f, g, h1, h2; acb_t c; prec = 2 + n_randint(state, 200); trunc = n_randint(state, 20); acb_poly_init(f); acb_poly_init(g); acb_poly_init(h1); acb_poly_init(h2); acb_init(c); /* generate binomials */ if (n_randint(state, 20) == 0) { acb_randtest(c, state, prec, 10); acb_poly_set_coeff_acb(f, 0, c); acb_randtest(c, state, prec, 10); acb_poly_set_coeff_acb(f, 1 + n_randint(state, 20), c); } else { acb_poly_randtest(f, state, 1 + n_randint(state, 20), prec, 10); } acb_poly_randtest(h1, state, 1 + n_randint(state, 20), prec, 10); acb_randtest(c, state, prec, 10); acb_poly_set_acb(g, c); /* f^c */ acb_poly_pow_acb_series(h1, f, c, trunc, prec); /* f^c = exp(c*log(f)) */ acb_poly_log_series(h2, f, trunc, prec); acb_poly_mullow(h2, h2, g, trunc, prec); acb_poly_exp_series(h2, h2, trunc, prec); if (!acb_poly_overlaps(h1, h2)) { flint_printf("FAIL\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("trunc = %wd\n", trunc); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("c = "); acb_printd(c, 15); flint_printf("\n\n"); flint_printf("h1 = "); acb_poly_printd(h1, 15); flint_printf("\n\n"); flint_printf("h2 = "); acb_poly_printd(h2, 15); flint_printf("\n\n"); abort(); } acb_poly_pow_acb_series(f, f, c, trunc, prec); if (!acb_poly_overlaps(f, h1)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(f); acb_poly_clear(g); acb_poly_clear(h1); acb_poly_clear(h2); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-pow_series.c000066400000000000000000000070071264125401100176210ustar00rootroot00000000000000/*============================================================================= This file is part of acb. acb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. acb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with acb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong rbits1, rbits2, len; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); len = n_randint(state, 25); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); if (n_randint(state, 4) == 0) acb_poly_randtest(a, state, 1, rbits1, 25); else acb_poly_randtest(a, state, 1 + n_randint(state, 20), rbits1, 5); if (n_randint(state, 4) == 0) acb_poly_randtest(b, state, 1, rbits1, 25); else acb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); acb_poly_randtest(c, state, 1 + n_randint(state, 20), rbits1, 5); acb_poly_pow_series(c, a, b, len, rbits2); /* a^b = exp(b log a) */ acb_poly_log_series(d, a, len, rbits2); acb_poly_mullow(d, d, b, len, rbits2); acb_poly_exp_series(d, d, len, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (iter %wd)\n\n", iter); flint_printf("bits2 = %wd\n", rbits2); flint_printf("len = %wd\n", len); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } /* check aliasing */ if (iter < 5000) { acb_poly_set(d, a); acb_poly_pow_series(d, d, b, len, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (aliasing 1)\n"); abort(); } acb_poly_set(d, b); acb_poly_pow_series(d, a, d, len, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (aliasing 2)\n"); abort(); } } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-pow_ui.c000066400000000000000000000054131264125401100167430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_ui...."); fflush(stdout); flint_randinit(state); /* compare with fmpz_poly */ for (iter = 0; iter < 10000; iter++) { slong zbits1, rbits1, rbits2; ulong e; fmpz_poly_t A, B; acb_poly_t a, b; zbits1 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); e = n_randint(state, 30); fmpz_poly_init(A); fmpz_poly_init(B); acb_poly_init(a); acb_poly_init(b); fmpz_poly_randtest(A, state, 1 + n_randint(state, 8), zbits1); fmpz_poly_pow(B, A, e); acb_poly_set_fmpz_poly(a, A, rbits1); acb_poly_pow_ui(b, a, e, rbits2); if (!acb_poly_contains_fmpz_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("e = %wu\n", e); flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } acb_poly_pow_ui(a, a, e, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpz_poly_clear(A); fmpz_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-pow_ui_trunc_binexp.c000066400000000000000000000056551264125401100215330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_ui_trunc_binexp...."); fflush(stdout); flint_randinit(state); /* compare with fmpz_poly */ for (iter = 0; iter < 10000; iter++) { slong zbits1, rbits1, rbits2, trunc; ulong e; fmpz_poly_t A, B; acb_poly_t a, b; zbits1 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); e = n_randint(state, 50); trunc = n_randint(state, 40); fmpz_poly_init(A); fmpz_poly_init(B); acb_poly_init(a); acb_poly_init(b); fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), zbits1); fmpz_poly_pow_trunc(B, A, e, trunc); acb_poly_set_fmpz_poly(a, A, rbits1); acb_poly_pow_ui_trunc_binexp(b, a, e, trunc, rbits2); if (!acb_poly_contains_fmpz_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("e = %wu\n", e); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } acb_poly_pow_ui_trunc_binexp(a, a, e, trunc, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpz_poly_clear(A); fmpz_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-powsum_one_series_sieved.c000066400000000000000000000060461264125401100225500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("powsum_one_series_sieved...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t s, a, q; acb_ptr z1, z2; slong i, n, len, prec; acb_init(s); acb_init(a); acb_init(q); if (n_randint(state, 2)) { acb_randtest(s, state, 1 + n_randint(state, 200), 3); } else { arb_set_ui(acb_realref(s), 1); arb_mul_2exp_si(acb_realref(s), acb_realref(s), -1); arb_randtest(acb_imagref(s), state, 1 + n_randint(state, 200), 4); } acb_one(a); acb_one(q); prec = 2 + n_randint(state, 200); n = n_randint(state, 100); len = 1 + n_randint(state, 10); z1 = _acb_vec_init(len); z2 = _acb_vec_init(len); _acb_poly_powsum_series_naive(z1, s, a, q, n, len, prec); _acb_poly_powsum_one_series_sieved(z2, s, n, len, prec); for (i = 0; i < len; i++) { if (!acb_overlaps(z1 + i, z2 + i)) { flint_printf("FAIL: overlap\n\n"); flint_printf("iter = %wd\n", iter); flint_printf("n = %wd, prec = %wd, len = %wd, i = %wd\n\n", n, prec, len, i); flint_printf("s = "); acb_printd(s, prec / 3.33); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, prec / 3.33); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1 + i, prec / 3.33); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2 + i, prec / 3.33); flint_printf("\n\n"); abort(); } } acb_clear(a); acb_clear(s); acb_clear(q); _acb_vec_clear(z1, len); _acb_vec_clear(z2, len); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-powsum_series_naive_threaded.c000066400000000000000000000066551264125401100234000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("powsum_series_naive_threaded...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { acb_t s, a, q; acb_ptr z1, z2; slong i, n, len, prec; acb_init(s); acb_init(a); acb_init(q); if (n_randint(state, 2)) { acb_randtest(s, state, 1 + n_randint(state, 200), 3); } else { arb_set_ui(acb_realref(s), 1); arb_mul_2exp_si(acb_realref(s), acb_realref(s), -1); arb_randtest(acb_imagref(s), state, 1 + n_randint(state, 200), 4); } if (n_randint(state, 2)) acb_one(a); else acb_randtest(a, state, 1 + n_randint(state, 200), 3); if (n_randint(state, 2)) acb_one(q); else acb_randtest(q, state, 1 + n_randint(state, 200), 3); prec = 2 + n_randint(state, 200); n = n_randint(state, 100); len = 1 + n_randint(state, 10); z1 = _acb_vec_init(len); z2 = _acb_vec_init(len); _acb_poly_powsum_series_naive(z1, s, a, q, n, len, prec); flint_set_num_threads(1 + n_randint(state, 3)); _acb_poly_powsum_series_naive_threaded(z2, s, a, q, n, len, prec); for (i = 0; i < len; i++) { if (!acb_overlaps(z1 + i, z2 + i)) { flint_printf("FAIL: overlap\n\n"); flint_printf("iter = %wd\n", iter); flint_printf("n = %wd, prec = %wd, len = %wd, i = %wd\n\n", n, prec, len, i); flint_printf("s = "); acb_printd(s, prec / 3.33); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, prec / 3.33); flint_printf("\n\n"); flint_printf("q = "); acb_printd(q, prec / 3.33); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1 + i, prec / 3.33); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2 + i, prec / 3.33); flint_printf("\n\n"); abort(); } } acb_clear(a); acb_clear(s); acb_clear(q); _acb_vec_clear(z1, len); _acb_vec_clear(z2, len); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-revert_series.c000066400000000000000000000056651264125401100203330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; acb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_revert_series(b, a, n, rbits2); if (!acb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } acb_poly_set(c, a); acb_poly_revert_series(c, c, n, rbits2); if (!acb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-revert_series_lagrange.c000066400000000000000000000057201264125401100221630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series_lagrange...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; acb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_revert_series_lagrange(b, a, n, rbits2); if (!acb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } acb_poly_set(c, a); acb_poly_revert_series_lagrange(c, c, n, rbits2); if (!acb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-revert_series_lagrange_fast.c000066400000000000000000000057371264125401100232100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series_lagrange_fast...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; acb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_revert_series_lagrange_fast(b, a, n, rbits2); if (!acb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } acb_poly_set(c, a); acb_poly_revert_series_lagrange_fast(c, c, n, rbits2); if (!acb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-revert_series_newton.c000066400000000000000000000057121264125401100217160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series_newton...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; acb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_revert_series_newton(b, a, n, rbits2); if (!acb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } acb_poly_set(c, a); acb_poly_revert_series_newton(c, c, n, rbits2); if (!acb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-rgamma_series.c000066400000000000000000000070721264125401100202620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rgamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, rbits1, 3); acb_poly_randtest(b, state, m, rbits1, 3); acb_poly_randtest(c, state, m, rbits1, 3); acb_poly_rgamma_series(b, a, n1, rbits2); acb_poly_rgamma_series(c, a, n2, rbits3); acb_poly_set(d, b); acb_poly_truncate(d, FLINT_MIN(n1, n2)); acb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check rgamma(a) = a gamma(a+1) */ acb_poly_add_si(d, a, 1, rbits2); acb_poly_rgamma_series(d, d, n1, rbits2); acb_poly_mullow(c, d, a, n1, rbits2); if (!acb_poly_overlaps(b, c)) { flint_printf("FAIL (functional equation, n1 = %wd)\n\n", n1); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_rgamma_series(a, a, n1, rbits2); if (!acb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-rising_ui_series.c000066400000000000000000000077311264125401100210100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_series...."); fflush(stdout); flint_randinit(state); /* check rf(f, a) * rf(f + a, b) = rf(f, a + b) */ for (iter = 0; iter < 1000; iter++) { slong bits, trunc; ulong a, b; acb_poly_t f, g, h1, h2, h1h2, h3; bits = 2 + n_randint(state, 200); trunc = 1 + n_randint(state, 20); a = n_randint(state, 10); b = n_randint(state, 10); acb_poly_init(f); acb_poly_init(g); acb_poly_init(h1); acb_poly_init(h2); acb_poly_init(h1h2); acb_poly_init(h3); acb_poly_randtest(f, state, 1 + n_randint(state, 20), bits, 4); acb_poly_set(g, f); /* g = f + 1 */ if (g->length == 0) { acb_poly_fit_length(g, 1); acb_set_ui(g->coeffs, a); _acb_poly_set_length(g, 1); _acb_poly_normalise(g); } else { acb_add_ui(g->coeffs, g->coeffs, a, bits); _acb_poly_normalise(g); } acb_poly_rising_ui_series(h1, f, a, trunc, bits); acb_poly_rising_ui_series(h2, g, b, trunc, bits); acb_poly_rising_ui_series(h3, f, a + b, trunc, bits); acb_poly_mullow(h1h2, h1, h2, trunc, bits); if (!acb_poly_overlaps(h1h2, h3)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = %wu\n", a); flint_printf("b = %wu\n", a); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); acb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("h1 = "); acb_poly_printd(h1, 15); flint_printf("\n\n"); flint_printf("h2 = "); acb_poly_printd(h2, 15); flint_printf("\n\n"); flint_printf("h1h2 = "); acb_poly_printd(h1h2, 15); flint_printf("\n\n"); flint_printf("h3 = "); acb_poly_printd(h3, 15); flint_printf("\n\n"); abort(); } acb_poly_rising_ui_series(f, f, a, trunc, bits); if (!acb_poly_equal(f, h1)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = %wu\n", a); flint_printf("b = %wu\n", a); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("h1 = "); acb_poly_printd(h1, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(f); acb_poly_clear(g); acb_poly_clear(h1); acb_poly_clear(h2); acb_poly_clear(h1h2); acb_poly_clear(h3); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-root_bound_fujiwara.c000066400000000000000000000057641264125401100215140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("root_bound_fujiwara...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { acb_poly_t a; acb_ptr roots; acb_t t; mag_t mag1, mag2; slong i, deg, prec; prec = 10 + n_randint(state, 400); deg = n_randint(state, 10); acb_init(t); acb_poly_init(a); mag_init(mag1); mag_init(mag2); roots = _acb_vec_init(deg); for (i = 0; i < deg; i++) acb_randtest(roots + i, state, prec, 1 + n_randint(state, 20)); acb_poly_product_roots(a, roots, deg, prec); acb_randtest(t, state, prec, 1 + n_randint(state, 20)); _acb_vec_scalar_mul(a->coeffs, a->coeffs, a->length, t, prec); acb_poly_root_bound_fujiwara(mag1, a); for (i = 0; i < deg; i++) { acb_get_mag(mag2, roots + i); /* acb_get_mag gives an upper bound which due to rounding could be larger than mag1, so we pick a slightly smaller number */ mag_mul_ui(mag2, mag2, 10000); mag_div_ui(mag2, mag2, 10001); if (mag_cmp(mag2, mag1) > 0) { flint_printf("FAIL\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("root = "); acb_printd(roots + i, 15); flint_printf("\n\n"); flint_printf("mag1 = "); mag_printd(mag1, 10); flint_printf("\n\n"); flint_printf("mag2 = "); mag_printd(mag2, 10); flint_printf("\n\n"); abort(); } } _acb_vec_clear(roots, deg); acb_clear(t); acb_poly_clear(a); mag_clear(mag1); mag_clear(mag2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-rsqrt_series.c000066400000000000000000000056721264125401100201750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rsqrt_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; acb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); fmpq_poly_randtest_not_zero(A, state, m, qbits); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5); acb_poly_rsqrt_series(b, a, n, rbits2); /* Check 1/((1/sqrt(a))^2) = a */ acb_poly_mullow(c, b, b, n, rbits2); acb_poly_inv_series(c, c, n, rbits2); fmpq_poly_truncate(A, n); if (!acb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_rsqrt_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-shift_left_right.c000066400000000000000000000070551264125401100207710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2009 William Hart Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main(void) { int i, result; flint_rand_t state; flint_printf("shift_left/right...."); fflush(stdout); flint_randinit(state); /* Check aliasing of a and b for left shift */ for (i = 0; i < 1000; i++) { acb_poly_t a, b; slong shift = n_randint(state, 100); acb_poly_init(a); acb_poly_init(b); acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); acb_poly_shift_left(b, a, shift); acb_poly_shift_left(a, a, shift); result = (acb_poly_equal(a, b)); if (!result) { flint_printf("FAIL:\n"); acb_poly_printd(a, 10), flint_printf("\n\n"); acb_poly_printd(b, 10), flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); } /* Check aliasing of a and b for right shift */ for (i = 0; i < 1000; i++) { acb_poly_t a, b; slong shift = n_randint(state, 100); acb_poly_init(a); acb_poly_init(b); acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); acb_poly_shift_right(b, a, shift); acb_poly_shift_right(a, a, shift); result = (acb_poly_equal(a, b)); if (!result) { flint_printf("FAIL:\n"); acb_poly_printd(a, 10), flint_printf("\n\n"); acb_poly_printd(b, 10), flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); } /* Check shift left then right does nothing */ for (i = 0; i < 1000; i++) { acb_poly_t a, b, c; slong shift = n_randint(state, 100); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); acb_poly_shift_left(b, a, shift); acb_poly_shift_right(c, b, shift); result = (acb_poly_equal(c, a)); if (!result) { flint_printf("FAIL:\n"); acb_poly_printd(a, 10), flint_printf("\n\n"); acb_poly_printd(b, 10), flint_printf("\n\n"); acb_poly_printd(c, 10), flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/acb_poly/test/t-sin_cos_pi_series.c000066400000000000000000000066071264125401100211460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; acb_poly_t a, b, c, d, e; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_sin_cos_pi_series(b, c, a, n, rbits2); /* Check sin(x)^2 + cos(x)^2 = 1 */ acb_poly_mullow(d, b, b, n, rbits2); acb_poly_mullow(e, c, c, n, rbits2); acb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!acb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_pi_series(d, c, d, n, rbits2); if (!acb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_pi_series(b, d, d, n, rbits2); if (!acb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); acb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-sin_cos_series.c000066400000000000000000000062311264125401100204470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n, rbits1, rbits2; fmpq_poly_t B; acb_poly_t a, b, c, d, e; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_init(e); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_sin_cos_series(b, c, a, n, rbits2); /* Check sin(x)^2 + cos(x)^2 = 1 */ acb_poly_mullow(d, b, b, n, rbits2); acb_poly_mullow(e, c, c, n, rbits2); acb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!acb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series(d, c, d, n, rbits2); if (!acb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series(b, d, d, n, rbits2); if (!acb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); acb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-sin_cos_series_basecase.c000066400000000000000000000064311264125401100222770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_series_basecase...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n, rbits1, rbits2; fmpq_poly_t B; acb_poly_t a, b, c, d, e; int times_pi; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); times_pi = n_randint(state, 2); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_init(e); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_sin_cos_series_basecase(b, c, a, n, rbits2, times_pi); /* Check sin(x)^2 + cos(x)^2 = 1 */ acb_poly_mullow(d, b, b, n, rbits2); acb_poly_mullow(e, c, c, n, rbits2); acb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!acb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series_basecase(d, c, d, n, rbits2, times_pi); if (!acb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series_basecase(b, d, d, n, rbits2, times_pi); if (!acb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); acb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-sin_cos_series_tangent.c000066400000000000000000000064251264125401100221740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_series_tangent...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n, rbits1, rbits2; fmpq_poly_t B; acb_poly_t a, b, c, d, e; int times_pi; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); times_pi = n_randint(state, 2); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_init(e); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_sin_cos_series_tangent(b, c, a, n, rbits2, times_pi); /* Check sin(x)^2 + cos(x)^2 = 1 */ acb_poly_mullow(d, b, b, n, rbits2); acb_poly_mullow(e, c, c, n, rbits2); acb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!acb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series_tangent(d, c, d, n, rbits2, times_pi); if (!acb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series_tangent(b, d, d, n, rbits2, times_pi); if (!acb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); acb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-sin_pi_series.c000066400000000000000000000057231264125401100203000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, bits1, bits2, bits3; acb_poly_t S, A, B, C; acb_t pi; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_init(pi); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_poly_sin_pi_series(A, S, n1, bits2); acb_const_pi(pi, bits3); acb_poly_set_acb(B, pi); acb_poly_mul(B, S, B, bits3); acb_poly_sin_series(B, B, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_sin_pi_series(S, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); acb_clear(pi); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-sin_series_cos_series.c000066400000000000000000000062711264125401100220250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_series/cos_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n, rbits1, rbits2; fmpq_poly_t B; acb_poly_t a, b, c, d, e; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_init(e); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_sin_series(b, a, n, rbits2); acb_poly_cos_series(c, a, n, rbits2); /* Check sin(x)^2 + cos(x)^2 = 1 */ acb_poly_mullow(d, b, b, n, rbits2); acb_poly_mullow(e, c, c, n, rbits2); acb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!acb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_series(d, d, n, rbits2); if (!acb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, a); acb_poly_cos_series(d, d, n, rbits2); if (!acb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); acb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-sqrt_series.c000066400000000000000000000054661264125401100200140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; acb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); fmpq_poly_randtest_not_zero(A, state, m, qbits); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_sqrt_series(b, a, n, rbits2); /* Check sqrt(a)^2 = a */ acb_poly_mullow(c, b, b, n, rbits2); fmpq_poly_truncate(A, n); if (!acb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_sqrt_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-sub.c000066400000000000000000000070161264125401100162330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sub...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_sub(C, A, B); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_sub(c, a, b, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sub(d, d, b, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_sub(d, a, d, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-tan_series.c000066400000000000000000000057241264125401100176020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("tan_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { slong m, n, rbits1, rbits2; acb_poly_t a, b, c, d, e; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 50); n = 1 + n_randint(state, 50); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_init(e); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_set_coeff_si(a, 0, 0); /* TODO: implement complex atan */ acb_poly_tan_series(b, a, n, rbits2); /* check tan(x) = 2*tan(x/2)/(1-tan(x/2)^2) */ acb_poly_scalar_mul_2exp_si(c, a, -1); acb_poly_tan_series(c, c, n, rbits2); acb_poly_mullow(d, c, c, n, rbits2); acb_poly_one(e); acb_poly_sub(e, e, d, rbits2); acb_poly_div_series(c, c, e, n, rbits2); acb_poly_scalar_mul_2exp_si(c, c, 1); if (!acb_poly_overlaps(b, c)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_tan_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); acb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-zeta_cpx_series.c000066400000000000000000000065601264125401100206340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_cpx_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t s, a; acb_ptr z1, z2; slong i, len, prec1, prec2; int deflate; acb_init(s); acb_init(a); if (n_randint(state, 2)) { acb_randtest(s, state, 1 + n_randint(state, 300), 3); } else { arb_set_ui(acb_realref(s), 1); arb_mul_2exp_si(acb_realref(s), acb_realref(s), -1); arb_randtest(acb_imagref(s), state, 1 + n_randint(state, 300), 4); } switch (n_randint(state, 3)) { case 0: acb_randtest(a, state, 1 + n_randint(state, 300), 3); break; case 1: arb_randtest(acb_realref(a), state, 1 + n_randint(state, 300), 3); break; case 2: acb_one(a); break; } prec1 = 2 + n_randint(state, 300); prec2 = prec1 + 30; len = 1 + n_randint(state, 20); deflate = n_randint(state, 2); z1 = _acb_vec_init(len); z2 = _acb_vec_init(len); _acb_poly_zeta_cpx_series(z1, s, a, deflate, len, prec1); _acb_poly_zeta_cpx_series(z2, s, a, deflate, len, prec2); for (i = 0; i < len; i++) { if (!acb_overlaps(z1 + i, z2 + i)) { flint_printf("FAIL: overlap\n\n"); flint_printf("iter = %wd\n", iter); flint_printf("deflate = %d, len = %wd, i = %wd\n\n", deflate, len, i); flint_printf("s = "); acb_printd(s, prec1 / 3.33); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, prec1 / 3.33); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1 + i, prec1 / 3.33); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2 + i, prec2 / 3.33); flint_printf("\n\n"); abort(); } } acb_clear(a); acb_clear(s); _acb_vec_clear(z1, len); _acb_vec_clear(z2, len); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-zeta_em_tail_bsplit.c000066400000000000000000000054551264125401100214610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_em_tail_bsplit...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { acb_t Na, s; acb_ptr z1, z2, Nasx; slong i, M, len, prec; prec = 2 + n_randint(state, 400); len = 1 + n_randint(state, 30); M = n_randint(state, 40); acb_init(Na); acb_init(s); Nasx = _acb_vec_init(len); z1 = _acb_vec_init(len); z2 = _acb_vec_init(len); acb_randtest(Na, state, prec, 4); acb_randtest(s, state, prec, 4); _acb_poly_acb_invpow_cpx(Nasx, Na, s, len, prec); _acb_poly_zeta_em_tail_naive(z1, s, Na, Nasx, M, len, prec); _acb_poly_zeta_em_tail_bsplit(z2, s, Na, Nasx, M, len, prec); for (i = 0; i < len; i++) { if (!acb_overlaps(z1 + i, z2 + i)) { flint_printf("FAIL: overlap\n\n"); flint_printf("iter = %wd\n", iter); flint_printf("prec = %wd, len = %wd, M = %wd\n", prec, len, M); flint_printf("s = "); acb_printd(s, prec / 3.33); flint_printf("\n\n"); flint_printf("Na = "); acb_printd(Na, prec / 3.33); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1 + i, prec / 3.33); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2 + i, prec / 3.33); flint_printf("\n\n"); abort(); } } acb_clear(Na); acb_clear(s); _acb_vec_clear(z1, len); _acb_vec_clear(z2, len); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/test/t-zeta_series.c000066400000000000000000000103501264125401100177520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 400; iter++) { slong m, n1, n2, bits1, bits2, bits3; int deflate; acb_poly_t S, A, B, C, D, E, F; acb_t a, a1; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 25); n1 = 1 + n_randint(state, 25); n2 = 1 + n_randint(state, 25); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_init(D); acb_poly_init(E); acb_poly_init(F); acb_init(a); acb_init(a1); deflate = n_randint(state, 2); acb_poly_randtest(S, state, m, bits1, 3); arb_randtest_precise(acb_realref(a), state, bits1, 3); arb_randtest_precise(acb_imagref(a), state, bits1, 3); acb_poly_set_coeff_acb(S, 0, a); if (n_randint(state, 2)) acb_randtest(a, state, bits1, 3); else acb_one(a); acb_poly_zeta_series(A, S, a, deflate, n1, bits2); acb_poly_zeta_series(B, S, a, deflate, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, FLINT_MIN(n1, n2)); acb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } /* check zeta(s,a) = zeta(s,a+1) + a^(-s) */ acb_poly_set_acb(D, a); acb_poly_log_series(D, D, n1, bits2); acb_poly_mullow(D, D, S, n1, bits2); acb_poly_neg(D, D); acb_poly_exp_series(D, D, n1, bits2); acb_add_ui(a1, a, 1, bits2); acb_poly_zeta_series(E, S, a1, deflate, n1, bits2); acb_poly_add(E, E, D, bits2); if (!acb_poly_overlaps(A, E)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("a = "); acb_printd(a, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("E = "); acb_poly_printd(A, 15); flint_printf("\n\n"); abort(); } acb_poly_zeta_series(S, S, a, deflate, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); acb_poly_clear(D); acb_poly_clear(E); acb_poly_clear(F); acb_clear(a); acb_clear(a1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/acb_poly/tree.c000066400000000000000000000062701264125401100151620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" acb_ptr * _acb_poly_tree_alloc(slong len) { acb_ptr * tree = NULL; if (len) { slong i, height = FLINT_CLOG2(len); tree = flint_malloc(sizeof(acb_ptr) * (height + 1)); for (i = 0; i <= height; i++) tree[i] = _acb_vec_init(len + (len >> i) + 1); } return tree; } void _acb_poly_tree_free(acb_ptr * tree, slong len) { if (len) { slong i, height = FLINT_CLOG2(len); for (i = 0; i <= height; i++) _acb_vec_clear(tree[i], len + (len >> i) + 1); flint_free(tree); } } void _acb_poly_tree_build(acb_ptr * tree, acb_srcptr roots, slong len, slong prec) { slong height, pow, left, i; acb_ptr pa, pb; acb_srcptr a, b; if (len == 0) return; height = FLINT_CLOG2(len); /* zeroth level, (x-a) */ for (i = 0; i < len; i++) { acb_one(tree[0] + (2 * i + 1)); acb_neg(tree[0] + (2 * i), roots + i); } /* first level, (x-a)(x-b) = x^2 + (-a-b)*x + a*b */ if (height > 1) { pa = tree[1]; for (i = 0; i < len / 2; i++) { a = (acb_srcptr) (roots + (2 * i)); b = (acb_srcptr) (roots + (2 * i + 1)); acb_mul(pa + (3 * i), a, b, prec); acb_add(pa + (3 * i + 1), a, b, prec); acb_neg(pa + (3 * i + 1), pa + (3 * i + 1)); acb_one(pa + (3 * i + 2)); } if (len & 1) { acb_neg(pa + (3 * (len / 2)), roots + len - 1); acb_one(pa + (3 * (len / 2) + 1)); } } for (i = 1; i < height - 1; i++) { left = len; pow = WORD(1) << i; pa = tree[i]; pb = tree[i + 1]; while (left >= 2 * pow) { _acb_poly_mul_monic(pb, pa, pow + 1, pa + pow + 1, pow + 1, prec); left -= 2 * pow; pa += 2 * pow + 2; pb += 2 * pow + 1; } if (left > pow) { _acb_poly_mul_monic(pb, pa, pow + 1, pa + pow + 1, left - pow + 1, prec); } else if (left > 0) _acb_vec_set(pb, pa, left + 1); } } arb-2.8.1/acb_poly/validate_real_roots.c000066400000000000000000000101561264125401100202430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #ifndef __compar_fn_t typedef int (*__compar_fn_t) (__const void *, __const void *); #endif int arb_cmp_mid(const arb_t a, const arb_t b) { return arf_cmp(arb_midref(a), arb_midref(b)); } void _arb_vec_sort_mid(arb_ptr vec, slong len) { qsort(vec, len, sizeof(arb_struct), (__compar_fn_t) arb_cmp_mid); } int _acb_poly_validate_real_roots(acb_srcptr roots, acb_srcptr poly, slong len, slong prec) { slong i, deg, num_real; arb_ptr real; int result; deg = len - 1; num_real = 0; result = 1; if (deg <= 1) return 1; real = _arb_vec_init(deg); /* pick out the candidate real roots */ for (i = 0; i < deg; i++) { if (arb_contains_zero(acb_imagref(roots + i))) { arb_set(real + num_real, acb_realref(roots + i)); num_real++; } } /* number of real roots must be even if the polynomial is even, and odd if the polynomial is odd (unless there are repeated roots... in which case the input is invalid) */ if ((num_real % 2) != (deg % 2)) { result = 0; } else if (num_real > 0) { int sign_neg_inf, sign_pos_inf, prev_sign; acb_t t; acb_init(t); /* by assumption that the roots are real and isolated, the lead coefficient really must be known to be either positive or negative */ sign_pos_inf = arb_is_positive(acb_realref(poly + deg)) ? 1 : -1; sign_neg_inf = (deg % 2) ? -sign_pos_inf : sign_pos_inf; /* now we check that there's a sign change between each root */ _arb_vec_sort_mid(real, num_real); prev_sign = sign_neg_inf; for (i = 0; i < num_real - 1; i++) { /* set t to the midpoint between the midpoints */ arb_zero(acb_imagref(t)); arf_add(arb_midref(acb_realref(t)), arb_midref(real + i), arb_midref(real + i + 1), prec, ARF_RND_DOWN); arf_mul_2exp_si(arb_midref(acb_realref(t)), arb_midref(acb_realref(t)), -1); mag_zero(arb_radref(acb_realref(t))); /* check that this point really is between both intervals (one interval could be much wider than the other */ if (arb_lt(real + i, acb_realref(t)) && arb_lt(acb_realref(t), real + i + 1)) { /* check sign change */ _acb_poly_evaluate(t, poly, len, t, prec); if (prev_sign == 1) result = arb_is_negative(acb_realref(t)); else result = arb_is_positive(acb_realref(t)); if (!result) break; prev_sign = -prev_sign; } else { result = 0; break; } } acb_clear(t); } _arb_vec_clear(real, deg); return result; } int acb_poly_validate_real_roots(acb_srcptr roots, const acb_poly_t poly, slong prec) { return _acb_poly_validate_real_roots(roots, poly->coeffs, poly->length, prec); } arb-2.8.1/acb_poly/validate_roots.c000066400000000000000000000051371264125401100172430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" slong _acb_poly_validate_roots(acb_ptr roots, acb_srcptr poly, slong len, slong prec) { slong i, j, deg; slong isolated, nonisolated, total_isolated; acb_ptr deriv; acb_ptr tmp; int *overlap; deg = len - 1; deriv = _acb_vec_init(deg); overlap = flint_calloc(deg, sizeof(int)); tmp = flint_malloc(sizeof(acb_struct) * deg); _acb_poly_derivative(deriv, poly, len, prec); /* compute an inclusion interval for each point */ for (i = 0; i < deg; i++) { _acb_poly_root_inclusion(roots + i, roots + i, poly, deriv, len, prec); } /* find which points do not overlap with any other points */ for (i = 0; i < deg; i++) { for (j = i + 1; j < deg; j++) { if (acb_overlaps(roots + i, roots + j)) { overlap[i] = overlap[j] = 1; } } } /* count and move all isolated roots to the front of the array */ total_isolated = 0; for (i = 0; i < deg; i++) total_isolated += (overlap[i] == 0); for (i = 0; i < deg; i++) tmp[i] = roots[i]; isolated = 0; nonisolated = 0; for (i = 0; i < deg; i++) { if (overlap[i] == 0) { roots[isolated] = tmp[i]; isolated++; } else { roots[total_isolated + nonisolated] = tmp[i]; nonisolated++; } } _acb_vec_clear(deriv, deg); flint_free(tmp); flint_free(overlap); return isolated; } arb-2.8.1/acb_poly/zeta_em_bound.c000066400000000000000000000122461264125401100170360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" static void bound_I(arb_ptr I, const arb_t A, const arb_t B, const arb_t C, slong len, slong wp) { slong k; arb_t D, Dk, L, T, Bm1; arb_init(D); arb_init(Dk); arb_init(Bm1); arb_init(T); arb_init(L); arb_sub_ui(Bm1, B, 1, wp); arb_one(L); /* T = 1 / (A^Bm1 * Bm1) */ arb_inv(T, A, wp); arb_pow(T, T, Bm1, wp); arb_div(T, T, Bm1, wp); if (len > 1) { arb_log(D, A, wp); arb_add(D, D, C, wp); arb_mul(D, D, Bm1, wp); arb_set(Dk, D); } for (k = 0; k < len; k++) { if (k > 0) { arb_mul_ui(L, L, k, wp); arb_add(L, L, Dk, wp); arb_mul(Dk, Dk, D, wp); } arb_mul(I + k, L, T, wp); arb_div(T, T, Bm1, wp); } arb_clear(D); arb_clear(Dk); arb_clear(Bm1); arb_clear(T); arb_clear(L); } /* 0.5*(B/AN)^2 + |B|/AN */ static void bound_C(arb_t C, const arb_t AN, const arb_t B, slong wp) { arb_t t; arb_init(t); arb_abs(t, B); arb_div(t, t, AN, wp); arb_mul_2exp_si(C, t, -1); arb_add_ui(C, C, 1, wp); arb_mul(C, C, t, wp); arb_clear(t); } static void bound_K(arb_t C, const arb_t AN, const arb_t B, const arb_t T, slong wp) { if (arb_is_zero(B) || arb_is_zero(T)) { arb_one(C); } else { arb_div(C, B, AN, wp); /* TODO: atan is dumb, should also bound by pi/2 */ arb_atan(C, C, wp); arb_mul(C, C, T, wp); if (arb_is_nonpositive(C)) arb_one(C); else arb_exp(C, C, wp); } } static void bound_rfac(arb_ptr F, const acb_t s, ulong n, slong len, slong wp) { if (len == 1) { acb_rising_ui_get_mag(arb_radref(F), s, n); arf_set_mag(arb_midref(F), arb_radref(F)); mag_zero(arb_radref(F + 0)); } else { arb_struct sx[2]; arb_init(sx + 0); arb_init(sx + 1); acb_abs(sx + 0, s, wp); arb_one(sx + 1); _arb_vec_zero(F, len); _arb_poly_rising_ui_series(F, sx, 2, n, len, wp); arb_clear(sx + 0); arb_clear(sx + 1); } } void _acb_poly_zeta_em_bound(arb_ptr bound, const acb_t s, const acb_t a, ulong N, ulong M, slong len, slong wp) { arb_t K, C, AN, S2M; arb_ptr F, R; slong k; arb_srcptr alpha = acb_realref(a); arb_srcptr beta = acb_imagref(a); arb_srcptr sigma = acb_realref(s); arb_srcptr tau = acb_imagref(s); arb_init(AN); arb_init(S2M); /* require alpha + N > 1, sigma + 2M > 1 */ arb_add_ui(AN, alpha, N - 1, wp); arb_add_ui(S2M, sigma, 2*M - 1, wp); if (!arb_is_positive(AN) || !arb_is_positive(S2M) || N < 1 || M < 1) { arb_clear(AN); arb_clear(S2M); for (k = 0; k < len; k++) arb_pos_inf(bound + k); return; } /* alpha + N, sigma + 2M */ arb_add_ui(AN, AN, 1, wp); arb_add_ui(S2M, S2M, 1, wp); R = _arb_vec_init(len); F = _arb_vec_init(len); arb_init(K); arb_init(C); /* bound for power integral */ bound_C(C, AN, beta, wp); bound_K(K, AN, beta, tau, wp); bound_I(R, AN, S2M, C, len, wp); for (k = 0; k < len; k++) { arb_mul(R + k, R + k, K, wp); arb_div_ui(K, K, k + 1, wp); } /* bound for rising factorial */ bound_rfac(F, s, 2*M, len, wp); /* product (TODO: only need upper bound; write a function for this) */ _arb_poly_mullow(bound, F, len, R, len, len, wp); /* bound for bernoulli polynomials, 4 / (2pi)^(2M) */ arb_const_pi(C, wp); arb_mul_2exp_si(C, C, 1); arb_pow_ui(C, C, 2 * M, wp); arb_ui_div(C, 4, C, wp); _arb_vec_scalar_mul(bound, bound, len, C, wp); arb_clear(K); arb_clear(C); arb_clear(AN); arb_clear(S2M); _arb_vec_clear(R, len); _arb_vec_clear(F, len); } void _acb_poly_zeta_em_bound1(mag_t bound, const acb_t s, const acb_t a, slong N, slong M, slong len, slong wp) { arb_ptr vec = _arb_vec_init(len); _acb_poly_zeta_em_bound(vec, s, a, N, M, len, wp); _arb_vec_get_mag(bound, vec, len); _arb_vec_clear(vec, len); } arb-2.8.1/acb_poly/zeta_em_choose_param.c000066400000000000000000000054041264125401100203650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" static ulong choose_M(ulong N, slong target) { return FLINT_MIN(N, target + N / 100); } void _acb_poly_zeta_em_choose_param(mag_t bound, ulong * N, ulong * M, const acb_t s, const acb_t a, slong d, slong target, slong prec) { ulong A, B, C, limit; mag_t Abound, Bbound, Cbound, tol; mag_init(Abound); mag_init(Bbound); mag_init(Cbound); mag_init(tol); mag_one(tol); mag_mul_2exp_si(tol, tol, -target); A = 1; B = 2; /* Hack: allow evaluation very high up in the critical strip... */ if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(s)), 10) > 0) limit = UWORD_MAX / 4; else limit = 100 * target; /* but normally, fail more quickly */ _acb_poly_zeta_em_bound1(Bbound, s, a, B, choose_M(B, target), d, prec); if (mag_cmp(Bbound, tol) > 0) { while (mag_cmp(Bbound, tol) > 0 && B <= limit) { mag_set(Abound, Bbound); A *= 2; B *= 2; if (B == 0) abort(); _acb_poly_zeta_em_bound1(Bbound, s, a, B, choose_M(B, target), d, prec); } /* bisect (-A, B] */ while (B > A + 4) { C = A + (B - A) / 2; _acb_poly_zeta_em_bound1(Cbound, s, a, C, choose_M(C, target), d, prec); if (mag_cmp(Cbound, tol) < 0) { B = C; mag_set(Bbound, Cbound); } else { A = C; mag_set(Abound, Cbound); } } } mag_set(bound, Bbound); *N = B; *M = choose_M(B, target); mag_clear(Abound); mag_clear(Bbound); mag_clear(Cbound); mag_clear(tol); } arb-2.8.1/acb_poly/zeta_em_sum.c000066400000000000000000000111151264125401100165250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" /* res = src * (c + x) */ void _acb_poly_mullow_cpx(acb_ptr res, acb_srcptr src, slong len, const acb_t c, slong trunc, slong prec) { slong i; if (len < trunc) acb_set(res + len, src + len - 1); for (i = len - 1; i > 0; i--) { acb_mul(res + i, src + i, c, prec); acb_add(res + i, res + i, src + i - 1, prec); } acb_mul(res, src, c, prec); } void _acb_poly_zeta_em_sum(acb_ptr z, const acb_t s, const acb_t a, int deflate, ulong N, ulong M, slong d, slong prec) { acb_ptr t, u, v, term, sum; acb_t Na, one; slong i; t = _acb_vec_init(d + 1); u = _acb_vec_init(d); v = _acb_vec_init(d); term = _acb_vec_init(d); sum = _acb_vec_init(d); acb_init(Na); acb_init(one); prec += 2 * (FLINT_BIT_COUNT(N) + FLINT_BIT_COUNT(d)); acb_one(one); /* sum 1/(k+a)^(s+x) */ if (acb_is_one(a) && d <= 3) _acb_poly_powsum_one_series_sieved(sum, s, N, d, prec); else if (N > 50 && flint_get_num_threads() > 1) _acb_poly_powsum_series_naive_threaded(sum, s, a, one, N, d, prec); else _acb_poly_powsum_series_naive(sum, s, a, one, N, d, prec); /* t = 1/(N+a)^(s+x); we might need one extra term for deflation */ acb_add_ui(Na, a, N, prec); _acb_poly_acb_invpow_cpx(t, Na, s, d + 1, prec); /* sum += (N+a) * 1/((s+x)-1) * t */ if (!deflate) { /* u = (N+a)^(1-(s+x)) */ acb_sub_ui(v, s, 1, prec); _acb_poly_acb_invpow_cpx(u, Na, v, d, prec); /* divide by 1/((s-1) + x) */ acb_sub_ui(v, s, 1, prec); acb_div(u, u, v, prec); for (i = 1; i < d; i++) { acb_sub(u + i, u + i, u + i - 1, prec); acb_div(u + i, u + i, v, prec); } _acb_vec_add(sum, sum, u, d, prec); } /* sum += ((N+a)^(1-(s+x)) - 1) / ((s+x) - 1) */ else { /* at s = 1, this becomes (N*t - 1)/x, i.e. just remove one coeff */ if (acb_is_one(s)) { for (i = 0; i < d; i++) acb_mul(u + i, t + i + 1, Na, prec); _acb_vec_add(sum, sum, u, d, prec); } else { /* TODO: this is numerically unstable for large derivatives, and divides by zero if s contains 1. We want a good way to evaluate the power series ((N+a)^y - 1) / y where y has nonzero constant term, without doing a division. How is this best done? */ _acb_vec_scalar_mul(t, t, d, Na, prec); acb_sub_ui(t + 0, t + 0, 1, prec); acb_sub_ui(u + 0, s, 1, prec); acb_inv(u + 0, u + 0, prec); for (i = 1; i < d; i++) acb_mul(u + i, u + i - 1, u + 0, prec); for (i = 1; i < d; i += 2) acb_neg(u + i, u + i); _acb_poly_mullow(v, u, d, t, d, d, prec); _acb_vec_add(sum, sum, v, d, prec); _acb_poly_acb_invpow_cpx(t, Na, s, d, prec); } } /* sum += u = 1/2 * t */ _acb_vec_scalar_mul_2exp_si(u, t, d, -WORD(1)); _acb_vec_add(sum, sum, u, d, prec); /* Euler-Maclaurin formula tail */ if (d < 5 || d < M / 10) _acb_poly_zeta_em_tail_naive(u, s, Na, t, M, d, prec); else _acb_poly_zeta_em_tail_bsplit(u, s, Na, t, M, d, prec); _acb_vec_add(z, sum, u, d, prec); _acb_vec_clear(t, d + 1); _acb_vec_clear(u, d); _acb_vec_clear(v, d); _acb_vec_clear(term, d); _acb_vec_clear(sum, d); acb_clear(Na); acb_clear(one); } arb-2.8.1/acb_poly/zeta_em_tail_bsplit.c000066400000000000000000000076311264125401100202370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #include "bernoulli.h" static void bsplit(acb_ptr P, acb_ptr T, const acb_t s, const acb_t Na, slong a, slong b, int cont, slong len, slong prec) { slong plen = FLINT_MIN(2 * (b - a) + 1, len); if (b - a == 1) { slong j = a; fmpz_t t; fmpz_init(t); if (j == 0) { acb_set(P, s); if (len > 1) acb_one(P + 1); if (len > 2) acb_zero(P + 2); } else { /* P = ((s+x)+2j-1)(s+x)+2j) */ /* constant term = s^2 + (4j-1)s + (4j^2-2j)*/ acb_mul(P, s, s, prec); acb_addmul_ui(P, s, 4*j-1, prec); fmpz_set_ui(t, 2*j); fmpz_mul_ui(t, t, 2*j-1); acb_add_fmpz(P, P, t, prec); /* x term = (2s+4j-1) */ if (len > 1) { acb_mul_ui(P + 1, s, 2, prec); acb_add_ui(P + 1, P + 1, 4*j-1, prec); } /* x^2 term = 1 */ if (len > 2) acb_one(P + 2); } /* P = P / ((2j+1)*(2j+2)) */ fmpz_set_ui(t, 2*j+1); fmpz_mul_ui(t, t, 2*j+2); _acb_vec_scalar_div_fmpz(P, P, plen, t, prec); /* P = P / Na or P / Na^2 */ if (j == 0) acb_set(T, Na); else acb_mul(T, Na, Na, prec); _acb_vec_scalar_div(P, P, plen, T, prec); /* T = P * B_{2j+2} */ _acb_vec_scalar_mul_fmpz(T, P, plen, fmpq_numref(bernoulli_cache + 2 * j + 2), prec); _acb_vec_scalar_div_fmpz(T, T, plen, fmpq_denref(bernoulli_cache + 2 * j + 2), prec); fmpz_clear(t); } else { slong m, len1, len2, alloc; acb_ptr P1, T1, P2, T2; m = a + (b - a) / 2; len1 = FLINT_MIN(2 * (m - a) + 1, len); len2 = FLINT_MIN(2 * (b - m) + 1, len); alloc = 2 * len1 + 2 * len2; P1 = _acb_vec_init(alloc); T1 = P1 + len1; P2 = T1 + len1; T2 = P2 + len2; bsplit(P1, T1, s, Na, a, m, 1, len, prec); bsplit(P2, T2, s, Na, m, b, 1, len, prec); /* P = P1 * P2 */ if (cont) _acb_poly_mullow(P, P2, len2, P1, len1, plen, prec); /* T = T1 + P1 * T2 */ _acb_poly_mullow(T, T2, len2, P1, len1, plen, prec); _acb_vec_add(T, T, T1, len1, prec); _acb_vec_clear(P1, alloc); } } void _acb_poly_zeta_em_tail_bsplit(acb_ptr z, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong len, slong prec) { acb_ptr P, T; if (M < 1) { _acb_vec_zero(z, len); return; } BERNOULLI_ENSURE_CACHED(2 * M); P = _acb_vec_init(len); T = _acb_vec_init(len); bsplit(P, T, s, Na, 0, M, 0, len, prec); _acb_poly_mullow(z, T, len, Nasx, len, len, prec); _acb_vec_clear(P, len); _acb_vec_clear(T, len); } arb-2.8.1/acb_poly/zeta_em_tail_naive.c000066400000000000000000000065451264125401100200470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" #include "bernoulli.h" void _acb_poly_mullow_cpx(acb_ptr res, acb_srcptr src, slong len, const acb_t c, slong trunc, slong prec); void _acb_poly_zeta_em_tail_naive(acb_ptr sum, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong d, slong prec) { acb_ptr u, term; acb_t Na2, splus, rec; arb_t x; fmpz_t c; int aint; slong r; BERNOULLI_ENSURE_CACHED(2 * M); u = _acb_vec_init(d); term = _acb_vec_init(d); acb_init(splus); acb_init(rec); acb_init(Na2); arb_init(x); fmpz_init(c); _acb_vec_zero(sum, d); /* u = 1/2 * Nasx */ _acb_vec_scalar_mul_2exp_si(u, Nasx, d, -WORD(1)); /* term = u * (s+x) / (N+a) */ _acb_poly_mullow_cpx(u, u, d, s, d, prec); _acb_vec_scalar_div(term, u, d, Na, prec); /* (N+a)^2 or 1/(N+a)^2 */ acb_mul(Na2, Na, Na, prec); aint = acb_is_int(Na2); if (!aint) acb_inv(Na2, Na2, prec); for (r = 1; r <= M; r++) { /* flint_printf("sum 2: %wd %wd\n", r, M); */ /* sum += bernoulli number * term */ arb_set_round_fmpz(x, fmpq_numref(bernoulli_cache + 2 * r), prec); arb_div_fmpz(x, x, fmpq_denref(bernoulli_cache + 2 * r), prec); _acb_vec_scalar_mul_arb(u, term, d, x, prec); _acb_vec_add(sum, sum, u, d, prec); /* multiply term by ((s+x)+2r-1)((s+x)+2r) / ((N+a)^2 * (2*r+1)*(2*r+2)) */ acb_set(splus, s); arb_add_ui(acb_realref(splus), acb_realref(splus), 2*r-1, prec); _acb_poly_mullow_cpx(term, term, d, splus, d, prec); arb_add_ui(acb_realref(splus), acb_realref(splus), 1, prec); _acb_poly_mullow_cpx(term, term, d, splus, d, prec); /* TODO: combine with previous multiplication? */ if (aint) { arb_mul_ui(x, acb_realref(Na2), 2*r+1, prec); arb_mul_ui(x, x, 2*r+2, prec); _acb_vec_scalar_div_arb(term, term, d, x, prec); } else { fmpz_set_ui(c, 2*r+1); fmpz_mul_ui(c, c, 2*r+2); acb_div_fmpz(rec, Na2, c, prec); _acb_vec_scalar_mul(term, term, d, rec, prec); } } _acb_vec_clear(u, d); _acb_vec_clear(term, d); acb_clear(splus); acb_clear(rec); acb_clear(Na2); arb_clear(x); fmpz_clear(c); } arb-2.8.1/acb_poly/zeta_series.c000066400000000000000000000125521264125401100165400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "acb_poly.h" void _acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate, slong d, slong prec) { ulong M, N; slong i; mag_t bound; arb_ptr vb; int is_real, const_is_real; if (d < 1) return; if (!acb_is_finite(s) || !acb_is_finite(a)) { _acb_vec_indeterminate(z, d); return; } is_real = const_is_real = 0; if (acb_is_real(s) && acb_is_real(a)) { if (arb_is_positive(acb_realref(a))) { is_real = const_is_real = 1; } else if (arb_is_int(acb_realref(a)) && arb_is_int(acb_realref(s)) && arb_is_nonpositive(acb_realref(s))) { const_is_real = 1; } } mag_init(bound); vb = _arb_vec_init(d); _acb_poly_zeta_em_choose_param(bound, &N, &M, s, a, FLINT_MIN(d, 2), prec, MAG_BITS); _acb_poly_zeta_em_bound(vb, s, a, N, M, d, MAG_BITS); _acb_poly_zeta_em_sum(z, s, a, deflate, N, M, d, prec); for (i = 0; i < d; i++) { arb_get_mag(bound, vb + i); arb_add_error_mag(acb_realref(z + i), bound); if (!is_real && !(i == 0 && const_is_real)) arb_add_error_mag(acb_imagref(z + i), bound); } mag_clear(bound); _arb_vec_clear(vb, d); } void _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int deflate, slong len, slong prec) { slong i; acb_ptr t, u; hlen = FLINT_MIN(hlen, len); t = _acb_vec_init(len); u = _acb_vec_init(len); /* use reflection formula */ if (arf_sgn(arb_midref(acb_realref(h))) < 0 && acb_is_one(a)) { /* zeta(s) = (2*pi)**s * sin(pi*s/2) / pi * gamma(1-s) * zeta(1-s) */ acb_t pi; acb_ptr f, s1, s2, s3, s4; acb_init(pi); f = _acb_vec_init(2); s1 = _acb_vec_init(len); s2 = _acb_vec_init(len); s3 = _acb_vec_init(len); s4 = _acb_vec_init(len); acb_const_pi(pi, prec); /* s1 = (2*pi)**s */ acb_mul_2exp_si(pi, pi, 1); _acb_poly_pow_cpx(s1, pi, h, len, prec); acb_mul_2exp_si(pi, pi, -1); /* s2 = sin(pi*s/2) / pi */ acb_set(f, h); acb_one(f + 1); acb_mul_2exp_si(f, f, -1); acb_mul_2exp_si(f + 1, f + 1, -1); _acb_poly_sin_pi_series(s2, f, 2, len, prec); _acb_vec_scalar_div(s2, s2, len, pi, prec); /* s3 = gamma(1-s) */ acb_sub_ui(f, h, 1, prec); acb_neg(f, f); acb_set_si(f + 1, -1); _acb_poly_gamma_series(s3, f, 2, len, prec); /* s4 = zeta(1-s) */ acb_sub_ui(f, h, 1, prec); acb_neg(f, f); _acb_poly_zeta_cpx_series(s4, f, a, 0, len, prec); for (i = 1; i < len; i += 2) acb_neg(s4 + i, s4 + i); _acb_poly_mullow(u, s1, len, s2, len, len, prec); _acb_poly_mullow(s1, s3, len, s4, len, len, prec); _acb_poly_mullow(t, u, len, s1, len, len, prec); /* add 1/(1-(s+t)) = 1/(1-s) + t/(1-s)^2 + ... */ if (deflate) { acb_sub_ui(u, h, 1, prec); acb_neg(u, u); acb_inv(u, u, prec); for (i = 1; i < len; i++) acb_mul(u + i, u + i - 1, u, prec); _acb_vec_add(t, t, u, len, prec); } acb_clear(pi); _acb_vec_clear(f, 2); _acb_vec_clear(s1, len); _acb_vec_clear(s2, len); _acb_vec_clear(s3, len); _acb_vec_clear(s4, len); } else { _acb_poly_zeta_cpx_series(t, h, a, deflate, len, prec); } /* compose with nonconstant part */ acb_zero(u); _acb_vec_set(u + 1, h + 1, hlen - 1); _acb_poly_compose_series(res, t, len, u, hlen, len, prec); _acb_vec_clear(t, len); _acb_vec_clear(u, len); } void acb_poly_zeta_series(acb_poly_t res, const acb_poly_t f, const acb_t a, int deflate, slong n, slong prec) { if (n == 0) { acb_poly_zero(res); return; } acb_poly_fit_length(res, n); if (f->length == 0) { acb_t t; acb_init(t); _acb_poly_zeta_series(res->coeffs, t, 1, a, deflate, n, prec); acb_clear(t); } else { _acb_poly_zeta_series(res->coeffs, f->coeffs, f->length, a, deflate, n, prec); } _acb_poly_set_length(res, n); _acb_poly_normalise(res); } arb-2.8.1/arb.h000066400000000000000000000756751264125401100132230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #ifndef ARB_H #define ARB_H #ifdef ARB_INLINES_C #define ARB_INLINE #else #define ARB_INLINE static __inline__ #endif #include "fmprb.h" #include "mag.h" #include "arf.h" #ifdef __cplusplus extern "C" { #endif extern const char * arb_version; typedef struct { arf_struct mid; mag_struct rad; } arb_struct; typedef arb_struct arb_t[1]; typedef arb_struct * arb_ptr; typedef const arb_struct * arb_srcptr; #define arb_midref(x) (&(x)->mid) #define arb_radref(x) (&(x)->rad) #define ARB_IS_LAGOM(x) (ARF_IS_LAGOM(arb_midref(x)) && MAG_IS_LAGOM(arb_radref(x))) #define ARB_RND ARF_RND_DOWN ARB_INLINE void arb_init(arb_t x) { arf_init(arb_midref(x)); mag_init(arb_radref(x)); } ARB_INLINE void arb_clear(arb_t x) { arf_clear(arb_midref(x)); mag_clear(arb_radref(x)); } ARB_INLINE arb_ptr _arb_vec_init(slong n) { slong i; arb_ptr v = (arb_ptr) flint_malloc(sizeof(arb_struct) * n); for (i = 0; i < n; i++) arb_init(v + i); return v; } ARB_INLINE void _arb_vec_clear(arb_ptr v, slong n) { slong i; for (i = 0; i < n; i++) arb_clear(v + i); flint_free(v); } ARB_INLINE void arb_set_fmprb(arb_t x, const fmprb_t y) { arf_set_fmpr(arb_midref(x), fmprb_midref(y)); mag_set_fmpr(arb_radref(x), fmprb_radref(y)); } ARB_INLINE void arb_get_fmprb(fmprb_t x, const arb_t y) { arf_get_fmpr(fmprb_midref(x), arb_midref(y)); mag_get_fmpr(fmprb_radref(x), arb_radref(y)); } ARB_INLINE arf_ptr arb_mid_ptr(arb_t z) { return arb_midref(z); } ARB_INLINE mag_ptr arb_rad_ptr(arb_t z) { return arb_radref(z); } ARB_INLINE int arb_is_exact(const arb_t x) { return mag_is_zero(arb_radref(x)); } ARB_INLINE int arb_equal(const arb_t x, const arb_t y) { return arf_equal(arb_midref(x), arb_midref(y)) && mag_equal(arb_radref(x), arb_radref(y)); } int arb_eq(const arb_t x, const arb_t y); int arb_ne(const arb_t x, const arb_t y); int arb_lt(const arb_t x, const arb_t y); int arb_le(const arb_t x, const arb_t y); int arb_gt(const arb_t x, const arb_t y); int arb_ge(const arb_t x, const arb_t y); ARB_INLINE void arb_zero(arb_t x) { arf_zero(arb_midref(x)); mag_zero(arb_radref(x)); } ARB_INLINE int arb_is_zero(const arb_t x) { return arf_is_zero(arb_midref(x)) && mag_is_zero(arb_radref(x)); } ARB_INLINE void arb_pos_inf(arb_t x) { arf_pos_inf(arb_midref(x)); mag_zero(arb_radref(x)); } ARB_INLINE void arb_neg_inf(arb_t x) { arf_neg_inf(arb_midref(x)); mag_zero(arb_radref(x)); } ARB_INLINE void arb_zero_pm_inf(arb_t x) { arf_zero(arb_midref(x)); mag_inf(arb_radref(x)); } ARB_INLINE void arb_indeterminate(arb_t x) { arf_nan(arb_midref(x)); mag_inf(arb_radref(x)); } ARB_INLINE int arb_is_finite(const arb_t x) { return arf_is_finite(arb_midref(x)) && mag_is_finite(arb_radref(x)); } void arb_set(arb_t x, const arb_t y); ARB_INLINE void arb_swap(arb_t x, arb_t y) { arb_struct t = *x; *x = *y; *y = t; } void arb_set_round(arb_t z, const arb_t x, slong prec); void arb_trim(arb_t y, const arb_t x); void arb_neg(arb_t y, const arb_t x); void arb_neg_round(arb_t x, const arb_t y, slong prec); void arb_abs(arb_t y, const arb_t x); void _arb_digits_round_inplace(char * s, mp_bitcnt_t * shift, fmpz_t error, slong n, arf_rnd_t rnd); int arb_set_str(arb_t res, const char * inp, slong prec); #define ARB_STR_MORE UWORD(1) #define ARB_STR_NO_RADIUS UWORD(2) #define ARB_STR_CONDENSE UWORD(16) char * arb_get_str(const arb_t x, slong n, ulong flags); ARB_INLINE void arb_set_arf(arb_t x, const arf_t y) { arf_set(arb_midref(x), y); mag_zero(arb_radref(x)); } ARB_INLINE void arb_set_si(arb_t x, slong y) { arf_set_si(arb_midref(x), y); mag_zero(arb_radref(x)); } ARB_INLINE void arb_set_ui(arb_t x, ulong y) { arf_set_ui(arb_midref(x), y); mag_zero(arb_radref(x)); } ARB_INLINE void arb_set_d(arb_t x, double y) { arf_set_d(arb_midref(x), y); mag_zero(arb_radref(x)); } ARB_INLINE void arb_set_fmpz(arb_t x, const fmpz_t y) { arf_set_fmpz(arb_midref(x), y); mag_zero(arb_radref(x)); } ARB_INLINE void arb_set_fmpz_2exp(arb_t x, const fmpz_t y, const fmpz_t exp) { arf_set_fmpz_2exp(arb_midref(x), y, exp); mag_zero(arb_radref(x)); } void arb_set_round_fmpz_2exp(arb_t y, const fmpz_t x, const fmpz_t exp, slong prec); void arb_set_round_fmpz(arb_t y, const fmpz_t x, slong prec); ARB_INLINE int arb_is_one(const arb_t f) { return arf_is_one(arb_midref(f)) && mag_is_zero(arb_radref(f)); } ARB_INLINE void arb_one(arb_t f) { arf_one(arb_midref(f)); mag_zero(arb_radref(f)); } void arb_print(const arb_t x); void arb_printd(const arb_t x, slong digits); void arb_printn(const arb_t x, slong digits, ulong flags); ARB_INLINE void arb_mul_2exp_si(arb_t y, const arb_t x, slong e) { arf_mul_2exp_si(arb_midref(y), arb_midref(x), e); mag_mul_2exp_si(arb_radref(y), arb_radref(x), e); } ARB_INLINE void arb_mul_2exp_fmpz(arb_t y, const arb_t x, const fmpz_t e) { arf_mul_2exp_fmpz(arb_midref(y), arb_midref(x), e); mag_mul_2exp_fmpz(arb_radref(y), arb_radref(x), e); } ARB_INLINE int arb_is_int(const arb_t x) { return mag_is_zero(arb_radref(x)) && arf_is_int(arb_midref(x)); } ARB_INLINE int arb_contains_zero(const arb_t x) { return arf_cmpabs_mag(arb_midref(x), arb_radref(x)) <= 0; } ARB_INLINE int arb_is_nonzero(const arb_t x) { return !arb_contains_zero(x); } ARB_INLINE int arb_is_positive(const arb_t x) { return (arf_sgn(arb_midref(x)) > 0) && (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) < 0) && !arf_is_nan(arb_midref(x)); } ARB_INLINE int arb_is_nonnegative(const arb_t x) { return (arf_sgn(arb_midref(x)) >= 0) && (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) <= 0) && !arf_is_nan(arb_midref(x)); } ARB_INLINE int arb_is_negative(const arb_t x) { return (arf_sgn(arb_midref(x)) < 0) && (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) < 0) && !arf_is_nan(arb_midref(x)); } ARB_INLINE int arb_is_nonpositive(const arb_t x) { return (arf_sgn(arb_midref(x)) <= 0) && (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) <= 0) && !arf_is_nan(arb_midref(x)); } ARB_INLINE int arb_contains_negative(const arb_t x) { return (arf_sgn(arb_midref(x)) < 0) || (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) > 0) || arf_is_nan(arb_midref(x)); } ARB_INLINE int arb_contains_nonpositive(const arb_t x) { return (arf_sgn(arb_midref(x)) <= 0) || (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) >= 0) || arf_is_nan(arb_midref(x)); } ARB_INLINE int arb_contains_positive(const arb_t x) { return (arf_sgn(arb_midref(x)) > 0) || (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) > 0) || arf_is_nan(arb_midref(x)); } ARB_INLINE int arb_contains_nonnegative(const arb_t x) { return (arf_sgn(arb_midref(x)) >= 0) || (arf_mag_cmpabs(arb_radref(x), arb_midref(x)) >= 0) || arf_is_nan(arb_midref(x)); } void arb_get_mag_lower(mag_t z, const arb_t x); void arb_get_mag_lower_nonnegative(mag_t z, const arb_t x); ARB_INLINE void arb_get_mag(mag_t z, const arb_t x) { mag_t t; mag_init_set_arf(t, arb_midref(x)); mag_add(z, t, arb_radref(x)); mag_clear(t); } ARB_INLINE void arb_get_mid_arb(arb_t z, const arb_t x) { arf_set(arb_midref(z), arb_midref(x)); mag_zero(arb_radref(z)); } ARB_INLINE void arb_get_rad_arb(arb_t z, const arb_t x) { arf_set_mag(arb_midref(z), arb_radref(x)); mag_zero(arb_radref(z)); } ARB_INLINE void arb_get_abs_ubound_arf(arf_t u, const arb_t x, slong prec) { arf_t t; arf_init_set_mag_shallow(t, arb_radref(x)); if (arf_sgn(arb_midref(x)) < 0) arf_sub(u, arb_midref(x), t, prec, ARF_RND_UP); else arf_add(u, arb_midref(x), t, prec, ARF_RND_UP); arf_abs(u, u); } ARB_INLINE void arb_get_abs_lbound_arf(arf_t u, const arb_t x, slong prec) { arf_t t; arf_init_set_mag_shallow(t, arb_radref(x)); if (arf_sgn(arb_midref(x)) > 0) { arf_sub(u, arb_midref(x), t, prec, ARF_RND_UP); } else { arf_add(u, arb_midref(x), t, prec, ARF_RND_UP); arf_neg(u, u); } if (arf_sgn(u) < 0) arf_zero(u); } slong arb_rel_error_bits(const arb_t x); ARB_INLINE slong arb_rel_accuracy_bits(const arb_t x) { return -arb_rel_error_bits(x); } ARB_INLINE slong arb_bits(const arb_t x) { return arf_bits(arb_midref(x)); } void arb_randtest_exact(arb_t x, flint_rand_t state, slong prec, slong mag_bits); void arb_randtest_wide(arb_t x, flint_rand_t state, slong prec, slong mag_bits); void arb_randtest_precise(arb_t x, flint_rand_t state, slong prec, slong mag_bits); void arb_randtest(arb_t x, flint_rand_t state, slong prec, slong mag_bits); void arb_randtest_special(arb_t x, flint_rand_t state, slong prec, slong mag_bits); void arb_add_error_arf(arb_t x, const arf_t err); void arb_add_error_2exp_si(arb_t x, slong err); void arb_add_error_2exp_fmpz(arb_t x, const fmpz_t err); void arb_add_error(arb_t x, const arb_t error); ARB_INLINE void arb_add_error_mag(arb_t x, const mag_t err) { mag_add(arb_radref(x), arb_radref(x), err); } int arb_contains_arf(const arb_t x, const arf_t y); int arb_contains_fmpq(const arb_t x, const fmpq_t y); int arb_contains_fmpz(const arb_t x, const fmpz_t y); int arb_contains_si(const arb_t x, slong y); int arb_contains_mpfr(const arb_t x, const mpfr_t y); int arb_overlaps(const arb_t x, const arb_t y); int arb_contains(const arb_t x, const arb_t y); int arb_contains_int(const arb_t x); void arb_get_interval_fmpz_2exp(fmpz_t a, fmpz_t b, fmpz_t exp, const arb_t x); int arb_get_unique_fmpz(fmpz_t z, const arb_t x); void arb_get_fmpz_mid_rad_10exp(fmpz_t mid, fmpz_t rad, fmpz_t exp, const arb_t x, slong n); void arb_floor(arb_t z, const arb_t x, slong prec); void arb_ceil(arb_t z, const arb_t x, slong prec); void arb_set_interval_arf(arb_t x, const arf_t a, const arf_t b, slong prec); void arb_set_interval_mpfr(arb_t x, const mpfr_t a, const mpfr_t b, slong prec); void arb_get_interval_arf(arf_t a, arf_t b, const arb_t x, slong prec); void arb_get_interval_mpfr(mpfr_t a, mpfr_t b, const arb_t x); void arb_union(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const arb_t x, slong bits); void arb_add(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_add_arf(arb_t z, const arb_t x, const arf_t y, slong prec); void arb_add_ui(arb_t z, const arb_t x, ulong y, slong prec); void arb_add_si(arb_t z, const arb_t x, slong y, slong prec); void arb_add_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec); void arb_add_fmpz_2exp(arb_t z, const arb_t x, const fmpz_t man, const fmpz_t exp, slong prec); void arb_sub(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_sub_arf(arb_t z, const arb_t x, const arf_t y, slong prec); void arb_sub_ui(arb_t z, const arb_t x, ulong y, slong prec); void arb_sub_si(arb_t z, const arb_t x, slong y, slong prec); void arb_sub_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec); void arb_mul(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_mul_arf(arb_t z, const arb_t x, const arf_t y, slong prec); void arb_mul_si(arb_t z, const arb_t x, slong y, slong prec); void arb_mul_ui(arb_t z, const arb_t x, ulong y, slong prec); void arb_mul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec); void arb_addmul(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_addmul_arf(arb_t z, const arb_t x, const arf_t y, slong prec); void arb_addmul_si(arb_t z, const arb_t x, slong y, slong prec); void arb_addmul_ui(arb_t z, const arb_t x, ulong y, slong prec); void arb_addmul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec); void arb_submul(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_submul_arf(arb_t z, const arb_t x, const arf_t y, slong prec); void arb_submul_si(arb_t z, const arb_t x, slong y, slong prec); void arb_submul_ui(arb_t z, const arb_t x, ulong y, slong prec); void arb_submul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec); void arb_div(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_div_arf(arb_t z, const arb_t x, const arf_t y, slong prec); void arb_div_si(arb_t z, const arb_t x, slong y, slong prec); void arb_div_ui(arb_t z, const arb_t x, ulong y, slong prec); void arb_div_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec); void arb_fmpz_div_fmpz(arb_t z, const fmpz_t x, const fmpz_t y, slong prec); void arb_ui_div(arb_t z, ulong x, const arb_t y, slong prec); ARB_INLINE void arb_inv(arb_t y, const arb_t x, slong prec) { arb_ui_div(y, 1, x, prec); } ARB_INLINE void arb_set_fmpq(arb_t y, const fmpq_t x, slong prec) { arb_fmpz_div_fmpz(y, fmpq_numref(x), fmpq_denref(x), prec); } void arb_sqrt(arb_t z, const arb_t x, slong prec); void arb_sqrt_arf(arb_t z, const arf_t x, slong prec); void arb_sqrt_fmpz(arb_t z, const fmpz_t x, slong prec); void arb_sqrt_ui(arb_t z, ulong x, slong prec); void arb_sqrtpos(arb_t z, const arb_t x, slong prec); void arb_hypot(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_rsqrt(arb_t z, const arb_t x, slong prec); void arb_rsqrt_ui(arb_t z, ulong x, slong prec); void arb_sqrt1pm1(arb_t r, const arb_t z, slong prec); void arb_pow_fmpz_binexp(arb_t y, const arb_t b, const fmpz_t e, slong prec); void arb_pow_fmpz(arb_t y, const arb_t b, const fmpz_t e, slong prec); void arb_pow_ui(arb_t y, const arb_t b, ulong e, slong prec); void arb_ui_pow_ui(arb_t y, ulong b, ulong e, slong prec); void arb_si_pow_ui(arb_t y, slong b, ulong e, slong prec); void arb_pow_fmpq(arb_t y, const arb_t x, const fmpq_t a, slong prec); void arb_div_2expm1_ui(arb_t z, const arb_t x, ulong n, slong prec); void arb_pow(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_root_ui(arb_t z, const arb_t x, ulong k, slong prec); void arb_root(arb_t z, const arb_t x, ulong k, slong prec); /* back compat */ void arb_log(arb_t z, const arb_t x, slong prec); void arb_log_arf(arb_t z, const arf_t x, slong prec); void arb_log_ui(arb_t z, ulong x, slong prec); void arb_log_fmpz(arb_t z, const fmpz_t x, slong prec); void arb_log1p(arb_t r, const arb_t z, slong prec); void arb_exp(arb_t z, const arb_t x, slong prec); void arb_expm1(arb_t z, const arb_t x, slong prec); void arb_exp_invexp(arb_t z, arb_t w, const arb_t x, slong prec); void arb_sin(arb_t s, const arb_t x, slong prec); void arb_cos(arb_t c, const arb_t x, slong prec); void arb_sin_cos(arb_t s, arb_t c, const arb_t x, slong prec); void arb_sin_pi(arb_t s, const arb_t x, slong prec); void arb_cos_pi(arb_t c, const arb_t x, slong prec); void arb_sin_cos_pi(arb_t s, arb_t c, const arb_t x, slong prec); void arb_tan(arb_t y, const arb_t x, slong prec); void arb_cot(arb_t y, const arb_t x, slong prec); void arb_tan_pi(arb_t y, const arb_t x, slong prec); void arb_cot_pi(arb_t y, const arb_t x, slong prec); void _arb_sin_pi_fmpq_algebraic(arb_t s, ulong p, ulong q, slong prec); void _arb_cos_pi_fmpq_algebraic(arb_t c, ulong p, ulong q, slong prec); void _arb_sin_cos_pi_fmpq_algebraic(arb_t s, arb_t c, ulong p, ulong q, slong prec); void arb_sin_cos_pi_fmpq(arb_t s, arb_t c, const fmpq_t x, slong prec); void arb_sin_pi_fmpq(arb_t s, const fmpq_t x, slong prec); void arb_cos_pi_fmpq(arb_t c, const fmpq_t x, slong prec); void arb_sinc(arb_t z, const arb_t x, slong prec); void arb_sinh(arb_t z, const arb_t x, slong prec); void arb_cosh(arb_t z, const arb_t x, slong prec); void arb_sinh_cosh(arb_t s, arb_t c, const arb_t x, slong prec); void arb_tanh(arb_t y, const arb_t x, slong prec); void arb_coth(arb_t y, const arb_t x, slong prec); void arb_atan_arf(arb_t z, const arf_t x, slong prec); void arb_atan(arb_t z, const arb_t x, slong prec); void arb_atan2(arb_t z, const arb_t b, const arb_t a, slong prec); void arb_asin(arb_t z, const arb_t x, slong prec); void arb_acos(arb_t z, const arb_t x, slong prec); void arb_atanh(arb_t z, const arb_t x, slong prec); void arb_asinh(arb_t z, const arb_t x, slong prec); void arb_acosh(arb_t z, const arb_t x, slong prec); void arb_fac_ui(arb_t z, ulong n, slong prec); void arb_doublefac_ui(arb_t z, ulong n, slong prec); void arb_bin_ui(arb_t z, const arb_t n, ulong k, slong prec); void arb_bin_uiui(arb_t z, ulong n, ulong k, slong prec); void arb_fib_fmpz(arb_t z, const fmpz_t n, slong prec); void arb_fib_ui(arb_t z, ulong n, slong prec); void arb_const_pi(arb_t z, slong prec); void arb_const_sqrt_pi(arb_t z, slong prec); void arb_const_log_sqrt2pi(arb_t z, slong prec); void arb_const_log2(arb_t z, slong prec); void arb_const_log10(arb_t z, slong prec); void arb_const_euler(arb_t z, slong prec); void arb_const_catalan(arb_t z, slong prec); void arb_const_e(arb_t z, slong prec); void arb_const_khinchin(arb_t z, slong prec); void arb_const_glaisher(arb_t z, slong prec); void arb_agm(arb_t z, const arb_t x, const arb_t y, slong prec); void arb_lgamma(arb_t z, const arb_t x, slong prec); void arb_rgamma(arb_t z, const arb_t x, slong prec); void arb_gamma(arb_t z, const arb_t x, slong prec); void arb_gamma_fmpq(arb_t z, const fmpq_t x, slong prec); void arb_gamma_fmpz(arb_t z, const fmpz_t x, slong prec); void arb_digamma(arb_t y, const arb_t x, slong prec); void arb_zeta(arb_t z, const arb_t s, slong prec); void arb_hurwitz_zeta(arb_t z, const arb_t s, const arb_t a, slong prec); void arb_rising_ui_bs(arb_t y, const arb_t x, ulong n, slong prec); void arb_rising_ui_rs(arb_t y, const arb_t x, ulong n, ulong m, slong prec); void arb_rising_ui_rec(arb_t y, const arb_t x, ulong n, slong prec); void arb_rising_ui(arb_t z, const arb_t x, ulong n, slong prec); void arb_rising_fmpq_ui(arb_t y, const fmpq_t x, ulong n, slong prec); void arb_rising(arb_t z, const arb_t x, const arb_t n, slong prec); void arb_rising2_ui_rs(arb_t u, arb_t v, const arb_t x, ulong n, ulong m, slong prec); void arb_rising2_ui_bs(arb_t u, arb_t v, const arb_t x, ulong n, slong prec); void arb_rising2_ui(arb_t u, arb_t v, const arb_t x, ulong n, slong prec); void arb_log_ui_from_prev(arb_t s, ulong k, arb_t log_prev, ulong prev, slong prec); void arb_const_apery(arb_t s, slong prec); void arb_zeta_ui_asymp(arb_t x, ulong s, slong prec); void arb_zeta_ui_borwein_bsplit(arb_t x, ulong s, slong prec); void arb_zeta_ui_euler_product(arb_t z, ulong s, slong prec); void arb_zeta_ui_bernoulli(arb_t x, ulong n, slong prec); void arb_zeta_ui_vec_borwein(arb_ptr z, ulong start, slong num, ulong step, slong prec); void arb_zeta_ui(arb_t x, ulong n, slong prec); void arb_zeta_ui_vec_even(arb_ptr x, ulong start, slong num, slong prec); void arb_zeta_ui_vec_odd(arb_ptr x, ulong start, slong num, slong prec); void arb_zeta_ui_vec(arb_ptr x, ulong start, slong num, slong prec); void arb_bernoulli_ui(arb_t b, ulong n, slong prec); void arb_bernoulli_ui_zeta(arb_t b, ulong n, slong prec); void arb_polylog(arb_t w, const arb_t s, const arb_t z, slong prec); void arb_polylog_si(arb_t w, slong s, const arb_t z, slong prec); void arb_chebyshev_t_ui(arb_t a, ulong n, const arb_t x, slong prec); void arb_chebyshev_t2_ui(arb_t a, arb_t b, ulong n, const arb_t x, slong prec); void arb_chebyshev_u_ui(arb_t a, ulong n, const arb_t x, slong prec); void arb_chebyshev_u2_ui(arb_t a, arb_t b, ulong n, const arb_t x, slong prec); void arb_power_sum_vec(arb_ptr res, const arb_t a, const arb_t b, slong len, slong prec); void arb_bell_sum_taylor(arb_t res, const fmpz_t n, const fmpz_t a, const fmpz_t b, const fmpz_t mmag, slong prec); void arb_bell_sum_bsplit(arb_t res, const fmpz_t n, const fmpz_t a, const fmpz_t b, const fmpz_t mmag, slong prec); void arb_bell_fmpz(arb_t res, const fmpz_t n, slong prec); #define ARB_DEF_CACHED_CONSTANT(name, comp_func) \ TLS_PREFIX slong name ## _cached_prec = 0; \ TLS_PREFIX arb_t name ## _cached_value; \ void name ## _cleanup(void) \ { \ arb_clear(name ## _cached_value); \ name ## _cached_prec = 0; \ } \ void name(arb_t x, slong prec) \ { \ if (name ## _cached_prec < prec) \ { \ if (name ## _cached_prec == 0) \ { \ arb_init(name ## _cached_value); \ flint_register_cleanup_function(name ## _cleanup); \ } \ comp_func(name ## _cached_value, prec + 32); \ name ## _cached_prec = prec; \ } \ arb_set_round(x, name ## _cached_value, prec); \ } /* vector functions */ ARB_INLINE arb_ptr _arb_vec_entry_ptr(arb_ptr vec, slong i) { return vec + i; } ARB_INLINE void _arb_vec_zero(arb_ptr A, slong n) { slong i; for (i = 0; i < n; i++) arb_zero(A + i); } ARB_INLINE int _arb_vec_is_zero(arb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) if (!arb_is_zero(vec + i)) return 0; return 1; } ARB_INLINE int _arb_vec_is_finite(arb_srcptr x, slong len) { slong i; for (i = 0; i < len; i++) if (!arb_is_finite(x + i)) return 0; return 1; } ARB_INLINE void _arb_vec_set(arb_ptr res, arb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) arb_set(res + i, vec + i); } ARB_INLINE void _arb_vec_set_round(arb_ptr res, arb_srcptr vec, slong len, slong prec) { slong i; for (i = 0; i < len; i++) arb_set_round(res + i, vec + i, prec); } ARB_INLINE void _arb_vec_swap(arb_ptr res, arb_ptr vec, slong len) { slong i; for (i = 0; i < len; i++) arb_swap(res + i, vec + i); } ARB_INLINE void _arb_vec_neg(arb_ptr B, arb_srcptr A, slong n) { slong i; for (i = 0; i < n; i++) arb_neg(B + i, A + i); } ARB_INLINE void _arb_vec_sub(arb_ptr C, arb_srcptr A, arb_srcptr B, slong n, slong prec) { slong i; for (i = 0; i < n; i++) arb_sub(C + i, A + i, B + i, prec); } ARB_INLINE void _arb_vec_add(arb_ptr C, arb_srcptr A, arb_srcptr B, slong n, slong prec) { slong i; for (i = 0; i < n; i++) arb_add(C + i, A + i, B + i, prec); } ARB_INLINE void _arb_vec_scalar_mul(arb_ptr res, arb_srcptr vec, slong len, const arb_t c, slong prec) { slong i; for (i = 0; i < len; i++) arb_mul(res + i, vec + i, c, prec); } ARB_INLINE void _arb_vec_scalar_div(arb_ptr res, arb_srcptr vec, slong len, const arb_t c, slong prec) { slong i; for (i = 0; i < len; i++) arb_div(res + i, vec + i, c, prec); } ARB_INLINE void _arb_vec_scalar_mul_fmpz(arb_ptr res, arb_srcptr vec, slong len, const fmpz_t c, slong prec) { slong i; arf_t t; arf_init(t); arf_set_fmpz(t, c); for (i = 0; i < len; i++) arb_mul_arf(res + i, vec + i, t, prec); arf_clear(t); } ARB_INLINE void _arb_vec_scalar_mul_2exp_si(arb_ptr res, arb_srcptr src, slong len, slong c) { slong i; for (i = 0; i < len; i++) arb_mul_2exp_si(res + i, src + i, c); } ARB_INLINE void _arb_vec_scalar_addmul(arb_ptr res, arb_srcptr vec, slong len, const arb_t c, slong prec) { slong i; for (i = 0; i < len; i++) arb_addmul(res + i, vec + i, c, prec); } ARB_INLINE void _arb_vec_dot(arb_t res, arb_srcptr vec1, arb_srcptr vec2, slong len2, slong prec) { slong i; arb_zero(res); for (i = 0; i < len2; i++) arb_addmul(res, vec1 + i, vec2 + i, prec); } ARB_INLINE void _arb_vec_norm(arb_t res, arb_srcptr vec, slong len, slong prec) { slong i; arb_zero(res); for (i = 0; i < len; i++) arb_addmul(res, vec + i, vec + i, prec); } ARB_INLINE void _arb_vec_get_mag(mag_t bound, arb_srcptr vec, slong len) { if (len < 1) { mag_zero(bound); } else { mag_t t; slong i; arb_get_mag(bound, vec); mag_init(t); for (i = 1; i < len; i++) { arb_get_mag(t, vec + i); mag_max(bound, bound, t); } mag_clear(t); } } ARB_INLINE slong _arb_vec_bits(arb_srcptr x, slong len) { slong i, b, c; b = 0; for (i = 0; i < len; i++) { c = arb_bits(x + i); b = FLINT_MAX(b, c); } return b; } ARB_INLINE void _arb_vec_set_powers(arb_ptr xs, const arb_t x, slong len, slong prec) { slong i; for (i = 0; i < len; i++) { if (i == 0) arb_one(xs + i); else if (i == 1) arb_set_round(xs + i, x, prec); else if (i % 2 == 0) arb_mul(xs + i, xs + i / 2, xs + i / 2, prec); else arb_mul(xs + i, xs + i - 1, x, prec); } } ARB_INLINE void _arb_vec_add_error_arf_vec(arb_ptr res, arf_srcptr err, slong len) { slong i; for (i = 0; i < len; i++) arb_add_error_arf(res + i, err + i); } ARB_INLINE void _arb_vec_add_error_mag_vec(arb_ptr res, mag_srcptr err, slong len) { slong i; for (i = 0; i < len; i++) mag_add(arb_radref(res + i), arb_radref(res + i), err + i); } ARB_INLINE void _arb_vec_indeterminate(arb_ptr vec, slong len) { slong i; for (i = 0; i < len; i++) arb_indeterminate(vec + i); } ARB_INLINE void _arb_vec_trim(arb_ptr res, arb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) arb_trim(res + i, vec + i); } ARB_INLINE int _arb_vec_get_unique_fmpz_vec(fmpz * res, arb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) if (!arb_get_unique_fmpz(res + i, vec + i)) return 0; return 1; } /* arctangent implementation */ #define ARB_ATAN_TAB1_BITS 8 #define ARB_ATAN_TAB1_PREC 512 #define ARB_ATAN_TAB1_LIMBS (ARB_ATAN_TAB1_PREC / FLINT_BITS) #define ARB_ATAN_TAB21_BITS 5 #define ARB_ATAN_TAB22_BITS 5 #define ARB_ATAN_TAB2_PREC 4608 #define ARB_ATAN_TAB2_LIMBS (ARB_ATAN_TAB2_PREC / FLINT_BITS) extern const mp_limb_t arb_atan_tab1[1 << ARB_ATAN_TAB1_BITS][ARB_ATAN_TAB1_LIMBS]; extern const mp_limb_t arb_atan_tab21[1 << ARB_ATAN_TAB21_BITS][ARB_ATAN_TAB2_LIMBS]; extern const mp_limb_t arb_atan_tab22[1 << ARB_ATAN_TAB22_BITS][ARB_ATAN_TAB2_LIMBS]; extern const mp_limb_t arb_atan_pi2_minus_one[ARB_ATAN_TAB2_LIMBS]; void _arb_atan_taylor_naive(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int alternating); void _arb_atan_taylor_rs(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int alternating); /* logarithm implementation */ #define ARB_LOG_TAB11_BITS 7 #define ARB_LOG_TAB12_BITS 7 #define ARB_LOG_TAB1_PREC 512 #define ARB_LOG_TAB1_LIMBS (ARB_LOG_TAB1_PREC / FLINT_BITS) #define ARB_LOG_TAB21_BITS 5 #define ARB_LOG_TAB22_BITS 5 #define ARB_LOG_TAB2_PREC 4608 #define ARB_LOG_TAB2_LIMBS (ARB_LOG_TAB2_PREC / FLINT_BITS) extern const mp_limb_t arb_log_tab11[1 << ARB_LOG_TAB11_BITS][ARB_LOG_TAB1_LIMBS]; extern const mp_limb_t arb_log_tab12[1 << ARB_LOG_TAB12_BITS][ARB_LOG_TAB1_LIMBS]; extern const mp_limb_t arb_log_tab21[1 << ARB_LOG_TAB21_BITS][ARB_LOG_TAB2_LIMBS]; extern const mp_limb_t arb_log_tab22[1 << ARB_LOG_TAB22_BITS][ARB_LOG_TAB2_LIMBS]; extern const mp_limb_t arb_log_log2_tab[ARB_LOG_TAB2_LIMBS]; /* exponential implementation */ /* only goes up to log(2) * 256 */ #define ARB_EXP_TAB1_NUM 178 #define ARB_EXP_TAB1_BITS 8 #define ARB_EXP_TAB1_PREC 512 #define ARB_EXP_TAB1_LIMBS (ARB_EXP_TAB1_PREC / FLINT_BITS) /* only goes up to log(2) * 32 */ #define ARB_EXP_TAB21_NUM 23 #define ARB_EXP_TAB21_BITS 5 #define ARB_EXP_TAB22_NUM (1 << ARB_EXP_TAB22_BITS) #define ARB_EXP_TAB22_BITS 5 #define ARB_EXP_TAB2_PREC 4608 #define ARB_EXP_TAB2_LIMBS (ARB_EXP_TAB2_PREC / FLINT_BITS) extern const mp_limb_t arb_exp_tab1[ARB_EXP_TAB1_NUM][ARB_EXP_TAB1_LIMBS]; extern const mp_limb_t arb_exp_tab21[ARB_EXP_TAB21_NUM][ARB_EXP_TAB2_LIMBS]; extern const mp_limb_t arb_exp_tab22[ARB_EXP_TAB22_NUM][ARB_EXP_TAB2_LIMBS]; void _arb_exp_taylor_naive(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N); void _arb_exp_taylor_rs(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N); void arb_exp_arf_bb(arb_t z, const arf_t x, slong prec, int minus_one); int _arb_get_mpn_fixed_mod_log2(mp_ptr w, fmpz_t q, mp_limb_t * error, const arf_t x, mp_size_t wn); slong _arb_exp_taylor_bound(slong mag, slong prec); void _arb_exp_sum_bs_powtab(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N); void _arb_exp_sum_bs_simple(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N); /* sin/cos implementation */ /* only goes up to (pi/4) * 256 */ #define ARB_SIN_COS_TAB1_NUM 203 #define ARB_SIN_COS_TAB1_BITS 8 #define ARB_SIN_COS_TAB1_PREC 512 #define ARB_SIN_COS_TAB1_LIMBS (ARB_SIN_COS_TAB1_PREC / FLINT_BITS) /* only goes up to (pi/4) * 32 */ #define ARB_SIN_COS_TAB21_NUM 26 #define ARB_SIN_COS_TAB21_BITS 5 #define ARB_SIN_COS_TAB22_NUM (1 << ARB_SIN_COS_TAB22_BITS) #define ARB_SIN_COS_TAB22_BITS 5 #define ARB_SIN_COS_TAB2_PREC 4608 #define ARB_SIN_COS_TAB2_LIMBS (ARB_SIN_COS_TAB2_PREC / FLINT_BITS) extern const mp_limb_t arb_sin_cos_tab1[2 * ARB_SIN_COS_TAB1_NUM][ARB_SIN_COS_TAB1_LIMBS]; extern const mp_limb_t arb_sin_cos_tab21[2 * ARB_SIN_COS_TAB21_NUM][ARB_SIN_COS_TAB2_LIMBS]; extern const mp_limb_t arb_sin_cos_tab22[2 * ARB_SIN_COS_TAB22_NUM][ARB_SIN_COS_TAB2_LIMBS]; #define ARB_PI4_TAB_LIMBS (4608 / FLINT_BITS) extern const mp_limb_t arb_pi4_tab[ARB_PI4_TAB_LIMBS]; void _arb_sin_cos_taylor_naive(mp_ptr ysin, mp_ptr ycos, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N); void _arb_sin_cos_taylor_rs(mp_ptr ysin, mp_ptr ycos, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int sinonly, int alternating); int _arb_get_mpn_fixed_mod_pi4(mp_ptr w, fmpz_t q, int * octant, mp_limb_t * error, const arf_t x, mp_size_t wn); ARB_INLINE mp_bitcnt_t _arb_mpn_leading_zeros(mp_srcptr d, mp_size_t n) { mp_limb_t t; mp_size_t zero_limbs; mp_bitcnt_t bits; zero_limbs = 0; while (1) { t = d[n - zero_limbs - 1]; if (t != 0) { count_leading_zeros(bits, t); return bits + FLINT_BITS * zero_limbs; } zero_limbs++; if (zero_limbs == n) return FLINT_BITS * zero_limbs; } } void _arb_atan_sum_bs_simple(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N); void _arb_atan_sum_bs_powtab(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N); void arb_atan_arf_bb(arb_t z, const arf_t x, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/arb/000077500000000000000000000000001264125401100130265ustar00rootroot00000000000000arb-2.8.1/arb/abs.c000066400000000000000000000023211264125401100137350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_abs(arb_t y, const arb_t x) { arf_abs(arb_midref(y), arb_midref(x)); mag_set(arb_radref(y), arb_radref(x)); } arb-2.8.1/arb/acos.c000066400000000000000000000037721264125401100141300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_acos(arb_t z, const arb_t x, slong prec) { arb_t t, u; if (arb_is_exact(x)) { int side; if (arf_is_zero(arb_midref(x))) { arb_const_pi(z, prec); arb_mul_2exp_si(z, z, -1); return; } side = arf_cmpabs_2exp_si(arb_midref(x), 0); /* +/- 1 */ if (side == 0) { if (arf_is_one(arb_midref(x))) arb_zero(z); else arb_const_pi(z, prec); return; } else if (side > 0) { arb_indeterminate(z); return; } } arb_init(t); arb_init(u); arb_one(t); arb_submul(t, x, x, prec); arb_rsqrt(t, t, prec); arb_mul(t, x, t, prec); arb_atan(t, t, prec); arb_const_pi(u, prec); arb_mul_2exp_si(u, u, -1); arb_sub(z, u, t, prec); arb_clear(t); arb_clear(u); } arb-2.8.1/arb/acosh.c000066400000000000000000000027031264125401100142710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_acosh(arb_t z, const arb_t x, slong prec) { if (arb_is_one(x)) { arb_zero(z); } else { arb_t t; arb_init(t); arb_mul(t, x, x, prec + 4); arb_sub_ui(t, t, 1, prec + 4); arb_sqrt(t, t, prec + 4); arb_add(t, t, x, prec + 4); arb_log(z, t, prec); arb_clear(t); } } arb-2.8.1/arb/add.c000066400000000000000000000057221264125401100137300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_add(arb_t z, const arb_t x, const arb_t y, slong prec) { int inexact; inexact = arf_add(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND); mag_add(arb_radref(z), arb_radref(x), arb_radref(y)); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); } void arb_add_arf(arb_t z, const arb_t x, const arf_t y, slong prec) { int inexact; inexact = arf_add(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } void arb_add_ui(arb_t z, const arb_t x, ulong y, slong prec) { int inexact; inexact = arf_add_ui(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } void arb_add_si(arb_t z, const arb_t x, slong y, slong prec) { int inexact; inexact = arf_add_si(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } void arb_add_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) { int inexact; inexact = arf_add_fmpz(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } void arb_add_fmpz_2exp(arb_t z, const arb_t x, const fmpz_t man, const fmpz_t exp, slong prec) { int inexact; inexact = arf_add_fmpz_2exp(arb_midref(z), arb_midref(x), man, exp, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } arb-2.8.1/arb/add_error.c000066400000000000000000000045051264125401100151370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_add_error_arf(arb_t x, const arf_t err) { mag_t t; if (arf_is_zero(err)) return; if (mag_is_zero(arb_radref(x))) { arf_get_mag(arb_radref(x), err); return; } mag_init(t); arf_get_mag(t, err); mag_add(arb_radref(x), arb_radref(x), t); mag_clear(t); } void arb_add_error_2exp_si(arb_t x, slong err) { fmpz_t t; if (mag_is_zero(arb_radref(x))) { mag_one(arb_radref(x)); mag_mul_2exp_si(arb_radref(x), arb_radref(x), err); return; } fmpz_init(t); fmpz_set_si(t, err); mag_add_2exp_fmpz(arb_radref(x), arb_radref(x), t); fmpz_clear(t); } void arb_add_error_2exp_fmpz(arb_t x, const fmpz_t err) { if (mag_is_zero(arb_radref(x))) { mag_one(arb_radref(x)); mag_mul_2exp_fmpz(arb_radref(x), arb_radref(x), err); return; } mag_add_2exp_fmpz(arb_radref(x), arb_radref(x), err); } void arb_add_error(arb_t x, const arb_t err) { mag_t u; if (arb_is_zero(err)) return; if (mag_is_zero(arb_radref(x))) { arb_get_mag(arb_radref(x), err); return; } mag_init(u); arb_get_mag(u, err); mag_add(arb_radref(x), arb_radref(x), u); mag_clear(u); } arb-2.8.1/arb/addmul.c000066400000000000000000000103211264125401100144350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_addmul_arf(arb_t z, const arb_t x, const arf_t y, slong prec) { mag_t ym; int inexact; if (arb_is_exact(x)) { inexact = arf_addmul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); } else if (ARB_IS_LAGOM(x) && ARF_IS_LAGOM(y) && ARB_IS_LAGOM(z)) { mag_fast_init_set_arf(ym, y); mag_fast_addmul(arb_radref(z), ym, arb_radref(x)); inexact = arf_addmul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_fast_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); } else { mag_init_set_arf(ym, y); mag_addmul(arb_radref(z), ym, arb_radref(x)); inexact = arf_addmul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); mag_clear(ym); } } void arb_addmul(arb_t z, const arb_t x, const arb_t y, slong prec) { mag_t zr, xm, ym; int inexact; if (arb_is_exact(y)) { arb_addmul_arf(z, x, arb_midref(y), prec); } else if (arb_is_exact(x)) { arb_addmul_arf(z, y, arb_midref(x), prec); } else if (ARB_IS_LAGOM(x) && ARB_IS_LAGOM(y) && ARB_IS_LAGOM(z)) { mag_fast_init_set_arf(xm, arb_midref(x)); mag_fast_init_set_arf(ym, arb_midref(y)); mag_fast_init_set(zr, arb_radref(z)); mag_fast_addmul(zr, xm, arb_radref(y)); mag_fast_addmul(zr, ym, arb_radref(x)); mag_fast_addmul(zr, arb_radref(x), arb_radref(y)); inexact = arf_addmul(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARF_RND_DOWN); if (inexact) arf_mag_fast_add_ulp(zr, zr, arb_midref(z), prec); *arb_radref(z) = *zr; } else { mag_init_set_arf(xm, arb_midref(x)); mag_init_set_arf(ym, arb_midref(y)); mag_init_set(zr, arb_radref(z)); mag_addmul(zr, xm, arb_radref(y)); mag_addmul(zr, ym, arb_radref(x)); mag_addmul(zr, arb_radref(x), arb_radref(y)); inexact = arf_addmul(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARF_RND_DOWN); if (inexact) arf_mag_add_ulp(arb_radref(z), zr, arb_midref(z), prec); else mag_set(arb_radref(z), zr); mag_clear(zr); mag_clear(xm); mag_clear(ym); } } void arb_addmul_si(arb_t z, const arb_t x, slong y, slong prec) { arf_t t; arf_init_set_si(t, y); /* no need to free */ arb_addmul_arf(z, x, t, prec); } void arb_addmul_ui(arb_t z, const arb_t x, ulong y, slong prec) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ arb_addmul_arf(z, x, t, prec); } void arb_addmul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) { arf_t t; if (!COEFF_IS_MPZ(*y)) { arf_init_set_si(t, *y); /* no need to free */ arb_addmul_arf(z, x, t, prec); } else { arf_init(t); arf_set_fmpz(t, y); arb_addmul_arf(z, x, t, prec); arf_clear(t); } } arb-2.8.1/arb/agm.c000066400000000000000000000040011264125401100137310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_agm(arb_t z, const arb_t x, const arb_t y, slong prec) { arb_t t, u, v, w; if (arb_contains_negative(x) || arb_contains_negative(y)) { arb_indeterminate(z); return; } if (arb_is_zero(x) || arb_is_zero(y)) { arb_zero(z); return; } arb_init(t); arb_init(u); arb_init(v); arb_init(w); arb_set(t, x); arb_set(u, y); while (!arb_overlaps(t, u) && !arb_contains_nonpositive(t) && !arb_contains_nonpositive(u)) { arb_add(v, t, u, prec); arb_mul_2exp_si(v, v, -1); arb_mul(w, t, u, prec); arb_sqrt(w, w, prec); arb_swap(v, t); arb_swap(w, u); } if (!arb_is_finite(t) || !arb_is_finite(u)) { arb_indeterminate(z); } else { arb_union(z, t, u, prec); } arb_clear(t); arb_clear(u); arb_clear(v); arb_clear(w); } arb-2.8.1/arb/asin.c000066400000000000000000000037261264125401100141340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_asin(arb_t z, const arb_t x, slong prec) { arb_t t; if (arb_is_exact(x)) { int side; if (arf_is_zero(arb_midref(x))) { arb_zero(z); return; } side = arf_cmpabs_2exp_si(arb_midref(x), 0); /* +/- 1 */ if (side == 0) { if (arf_is_one(arb_midref(x))) { arb_const_pi(z, prec); } else { arb_const_pi(z, prec); arb_neg(z, z); } arb_mul_2exp_si(z, z, -1); return; } else if (side > 0) { arb_indeterminate(z); return; } } arb_init(t); arb_one(t); arb_submul(t, x, x, prec); arb_rsqrt(t, t, prec); arb_mul(t, x, t, prec); arb_atan(z, t, prec); arb_clear(t); } arb-2.8.1/arb/asinh.c000066400000000000000000000031601264125401100142740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_asinh(arb_t z, const arb_t x, slong prec) { if (arb_is_zero(x)) { arb_zero(z); } else { arb_t t; arb_init(t); arb_mul(t, x, x, prec + 4); arb_sqrt1pm1(t, t, prec + 4); if (arf_sgn(arb_midref(x)) >= 0) { arb_add(t, t, x, prec + 4); arb_log1p(z, t, prec); } else { arb_sub(t, t, x, prec + 4); arb_log1p(z, t, prec); arb_neg(z, z); } arb_clear(t); } } arb-2.8.1/arb/atan.c000066400000000000000000000241161264125401100141210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define TMP_ALLOC_LIMBS(size) TMP_ALLOC((size) * sizeof(mp_limb_t)) /* atan(x) = x + eps, |eps| < x^3*/ void arb_atan_eps(arb_t z, const arf_t x, slong prec) { fmpz_t mag; fmpz_init(mag); fmpz_mul_ui(mag, ARF_EXPREF(x), 3); arb_set_arf(z, x); arb_set_round(z, z, prec); arb_add_error_2exp_fmpz(z, mag); fmpz_clear(mag); } /* atan(x) = pi/2 - eps, eps < 1/x <= 2^(1-mag) */ void arb_atan_inf_eps(arb_t z, const arf_t x, slong prec) { fmpz_t mag; fmpz_init(mag); fmpz_neg(mag, ARF_EXPREF(x)); fmpz_add_ui(mag, mag, 1); if (arf_sgn(x) > 0) { arb_const_pi(z, prec); } else { arb_const_pi(z, prec); arb_neg(z, z); } arb_mul_2exp_si(z, z, -1); arb_add_error_2exp_fmpz(z, mag); fmpz_clear(mag); } int _arf_get_integer_mpn(mp_ptr y, mp_srcptr x, mp_size_t xn, slong exp); int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec) { slong exp, exp_shift; int inexact; exp = (slong)(xn - fixn) * FLINT_BITS; while (xn > 0 && xp[xn-1] == 0) { xn--; exp -= FLINT_BITS; } if (xn == 0) { arf_zero(z); return 0; } else { inexact = _arf_set_round_mpn(z, &exp_shift, xp, xn, negative, prec, ARB_RND); fmpz_set_si(ARF_EXPREF(z), exp + exp_shift); return inexact; } } /* TODO: move out */ void mag_add_ui_2exp_si(mag_t z, const mag_t x, ulong y, slong e) { mag_t t; mag_init(t); mag_set_ui_2exp_si(t, y, e); mag_add(z, x, t); mag_clear(t); } void arb_atan_arf(arb_t z, const arf_t x, slong prec) { if (arf_is_special(x)) { if (arf_is_zero(x)) { arb_zero(z); } else if (arf_is_pos_inf(x)) { arb_const_pi(z, prec); arb_mul_2exp_si(z, z, -1); } else if (arf_is_neg_inf(x)) { arb_const_pi(z, prec); arb_mul_2exp_si(z, z, -1); arb_neg(z, z); } else { arb_indeterminate(z); } } else if (COEFF_IS_MPZ(*ARF_EXPREF(x))) { if (fmpz_sgn(ARF_EXPREF(x)) < 0) arb_atan_eps(z, x, prec); else arb_atan_inf_eps(z, x, prec); } else { slong exp, wp, wn, N, r; mp_srcptr xp; mp_size_t xn, tn; mp_ptr tmp, w, t, u; mp_limb_t p1, q1bits, p2, q2bits, error, error2; int negative, inexact, reciprocal; TMP_INIT; exp = ARF_EXP(x); negative = ARF_SGNBIT(x); if (exp < -(prec/2) - 2 || exp > prec + 2) { if (exp < 0) arb_atan_eps(z, x, prec); else arb_atan_inf_eps(z, x, prec); return; } ARF_GET_MPN_READONLY(xp, xn, x); /* Special case: +/- 1 (we require |x| != 1 later on) */ if (exp == 1 && xn == 1 && xp[xn-1] == LIMB_TOP) { arb_const_pi(z, prec); arb_mul_2exp_si(z, z, -2); if (negative) arb_neg(z, z); return; } /* Absolute working precision (NOT rounded to a limb multiple) */ wp = prec - FLINT_MIN(0, exp) + 4; /* Too high precision to use table */ if (wp > ARB_ATAN_TAB2_PREC) { arb_atan_arf_bb(z, x, prec); return; } /* Working precision in limbs */ wn = (wp + FLINT_BITS - 1) / FLINT_BITS; TMP_START; tmp = TMP_ALLOC_LIMBS(4 * wn + 3); w = tmp; /* requires wn+1 limbs */ t = w + wn + 1; /* requires wn+1 limbs */ u = t + wn + 1; /* requires 2wn+1 limbs */ /* ----------------------------------------------------------------- */ /* Convert x or 1/x to a fixed-point number |w| < 1 */ /* ----------------------------------------------------------------- */ if (exp <= 0) /* |x| < 1 */ { reciprocal = 0; /* todo: just zero top */ flint_mpn_zero(w, wn); /* w = x as a fixed-point number */ error = _arf_get_integer_mpn(w, xp, xn, exp + wn * FLINT_BITS); } else /* |x| > 1 */ { slong one_exp, one_limbs, one_bits; mp_ptr one; reciprocal = 1; one_exp = xn * FLINT_BITS + wn * FLINT_BITS - exp; flint_mpn_zero(w, wn); /* 1/x becomes zero */ if (one_exp >= FLINT_BITS - 1) { /* w = 1/x */ one_limbs = one_exp / FLINT_BITS; one_bits = one_exp % FLINT_BITS; if (one_limbs + 1 >= xn) { one = TMP_ALLOC_LIMBS(one_limbs + 1); flint_mpn_zero(one, one_limbs); one[one_limbs] = UWORD(1) << one_bits; /* todo: only zero necessary part */ flint_mpn_zero(w, wn); mpn_tdiv_q(w, one, one_limbs + 1, xp, xn); /* Now w must be < 1 since x > 1 and we rounded down; thus w[wn] must be zero */ } } /* todo: moderate powers of two would be exact... */ error = 1; } /* ----------------------------------------------------------------- */ /* Table-based argument reduction */ /* ----------------------------------------------------------------- */ /* choose p such that p/q <= x < (p+1)/q */ if (wp <= ARB_ATAN_TAB1_PREC) q1bits = ARB_ATAN_TAB1_BITS; else q1bits = ARB_ATAN_TAB21_BITS; p1 = w[wn-1] >> (FLINT_BITS - q1bits); /* atan(w) = atan(p/q) + atan(w2) */ /* where w2 = (q*w-p)/(q+p*w) */ if (p1 != 0) { t[wn] = (UWORD(1) << q1bits) + mpn_mul_1(t, w, wn, p1); flint_mpn_zero(u, wn); u[2 * wn] = mpn_lshift(u + wn, w, wn, q1bits) - p1; mpn_tdiv_q(w, u, 2 * wn + 1, t, wn + 1); error++; /* w2 is computed with 1 ulp error */ } /* Do a second round of argument reduction */ if (wp <= ARB_ATAN_TAB1_PREC) { p2 = 0; } else { q2bits = ARB_ATAN_TAB21_BITS + ARB_ATAN_TAB22_BITS; p2 = w[wn-1] >> (FLINT_BITS - q2bits); if (p2 != 0) { t[wn] = (UWORD(1) << q2bits) + mpn_mul_1(t, w, wn, p2); flint_mpn_zero(u, wn); u[2 * wn] = mpn_lshift(u + wn, w, wn, q2bits) - p2; mpn_tdiv_q(w, u, 2 * wn + 1, t, wn + 1); error++; } } /* |w| <= 2^-r */ r = _arb_mpn_leading_zeros(w, wn); /* N >= (wp-r)/(2r) */ N = (wp - r + (2*r-1)) / (2*r); /* Evaluate Taylor series */ _arb_atan_taylor_rs(t, &error2, w, wn, N, 1); /* Taylor series evaluation error */ error += error2; /* Size of output number */ tn = wn; /* First table lookup */ if (p1 != 0) { if (wp <= ARB_ATAN_TAB1_PREC) mpn_add_n(t, t, arb_atan_tab1[p1] + ARB_ATAN_TAB1_LIMBS - tn, tn); else mpn_add_n(t, t, arb_atan_tab21[p1] + ARB_ATAN_TAB2_LIMBS - tn, tn); error++; } /* Second table lookup */ if (p2 != 0) { mpn_add_n(t, t, arb_atan_tab22[p2] + ARB_ATAN_TAB2_LIMBS - tn, tn); error++; } /* pi/2 - atan(1/x) */ if (reciprocal) { t[tn] = LIMB_ONE - mpn_sub_n(t, arb_atan_pi2_minus_one + ARB_ATAN_TAB2_LIMBS - tn, t, tn); /* result can be >= 1 */ tn += (t[tn] != 0); /* error of pi/2 */ error++; } /* The accumulated arithmetic error */ mag_set_ui_2exp_si(arb_radref(z), error, -wn * FLINT_BITS); /* Truncation error from the Taylor series */ mag_add_ui_2exp_si(arb_radref(z), arb_radref(z), 1, -r*(2*N+1)); /* Set the midpoint */ inexact = _arf_set_mpn_fixed(arb_midref(z), t, tn, wn, negative, prec); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); TMP_END; } } void arb_atan(arb_t z, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_atan_arf(z, arb_midref(x), prec); } else { mag_t t, u; mag_init(t); mag_init(u); arb_get_mag_lower(t, x); if (mag_is_zero(t)) { mag_set(t, arb_radref(x)); } else { mag_mul_lower(t, t, t); mag_one(u); mag_add_lower(t, t, u); mag_div(t, arb_radref(x), t); } arb_atan_arf(z, arb_midref(x), prec); mag_add(arb_radref(z), arb_radref(z), t); mag_clear(t); mag_clear(u); } } arb-2.8.1/arb/atan2.c000066400000000000000000000100601264125401100141740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_atan2(arb_t r, const arb_t b, const arb_t a, slong prec) { #define am arb_midref(a) #define ar arb_radref(a) #define bm arb_midref(b) #define br arb_radref(b) /* a + bi is a real number */ if (arb_is_zero(b)) { /* exactly zero */ if (arb_is_zero(a)) { /* define arg(0) = 0 by convention */ arb_zero(r); } /* interval contains only nonnegative numbers */ else if (arf_sgn(am) > 0 && arf_cmpabs_mag(am, ar) >= 0) { arb_zero(r); } /* interval contains only negative numbers */ else if (arf_sgn(am) < 0 && arf_cmpabs_mag(am, ar) > 0) { arb_const_pi(r, prec); } else { /* both positive and negative -- argument will be in [0, pi] */ arb_t t; arb_init(t); arb_const_pi(t, prec); arb_mul_2exp_si(t, t, -1); arb_set(r, t); arb_add_error(r, t); arb_clear(t); } } /* an imaginary number */ else if (arb_is_zero(a)) { /* interval contains only positive numbers */ if (arf_sgn(bm) > 0 && arf_cmpabs_mag(bm, br) > 0) { arb_const_pi(r, prec); arb_mul_2exp_si(r, r, -1); } /* interval contains only negative numbers */ else if (arf_sgn(bm) < 0 && arf_cmpabs_mag(bm, br) > 0) { arb_const_pi(r, prec); arb_neg(r, r); arb_mul_2exp_si(r, r, -1); } else { /* both positive and negative -- argument will be in 0 +/- pi/2 */ arb_t t; arb_init(t); arb_const_pi(t, MAG_BITS); arb_mul_2exp_si(t, t, -1); arb_zero(r); arb_add_error(r, t); arb_clear(t); } } /* strictly in the right half-plane -- atan(b/a) */ else if (arf_sgn(am) > 0 && arf_cmpabs_mag(am, ar) > 0) { arb_div(r, b, a, prec); arb_atan(r, r, prec); } /* strictly in the upper half-plane -- pi/2 - atan(a/b) */ else if (arf_sgn(bm) > 0 && arf_cmpabs_mag(bm, br) > 0) { arb_t t; arb_init(t); arb_div(r, a, b, prec); arb_atan(r, r, prec); arb_const_pi(t, prec); arb_mul_2exp_si(t, t, -1); arb_sub(r, t, r, prec); arb_clear(t); } /* strictly in the lower half-plane -- -pi/2 - atan(a/b) */ else if (arf_sgn(bm) < 0 && arf_cmpabs_mag(bm, br) > 0) { arb_t t; arb_init(t); arb_div(r, a, b, prec); arb_atan(r, r, prec); arb_const_pi(t, prec); arb_mul_2exp_si(t, t, -1); arb_add(r, t, r, prec); arb_neg(r, r); arb_clear(t); } /* overlaps the nonpositive half-axis -- [-pi, pi] */ else { arb_t t; arb_init(t); arb_const_pi(t, MAG_BITS); arb_zero(r); arb_add_error(r, t); arb_clear(t); } } arb-2.8.1/arb/atan_arf_bb.c000066400000000000000000000217761264125401100154250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void mag_add_ui_2exp_si(mag_t, const mag_t, ulong, slong); /* Determine N such that the error is bounded by 2^-prec. We choose an N with many trailing zeros to improve efficiency of the binary splitting. With N = 0, 1, 2, ... the highest included term is x, x^3, x^5, ... so the error is bounded by x^3, x^5, x^7, ... = x^(2N+3) */ static slong bs_num_terms(slong mag, slong prec) { slong N; if (mag >= 0) abort(); N = 0; while (mag * (2 * N + 3) > -prec) N++; if (N > 10000) while (N % 128 != 0) N++; if (N > 1000) while (N % 16 != 0) N++; if (N > 100) while (N % 2 != 0) N++; return N; } /* Argument reduction: apply atan(x) = 2 atan(x/(1+sqrt(1+x^2))) a total of r times, and convert result to a fixed-point number res together with absolute error err. With an initial inversion if xmag > 0. */ void arb_atan_bb_reduce(fmpz_t res, mag_t err, const arf_t x, slong xmag, slong r, slong prec) { int inexact; if (r == 0) { if (xmag <= 0) { inexact = arf_get_fmpz_fixed_si(res, x, -prec); mag_set_ui_2exp_si(err, inexact, -prec); } else { slong wp; arb_t t; wp = FLINT_MAX(8, prec - xmag); arb_init(t); arb_set_arf(t, x); arb_set_round(t, t, wp); arb_ui_div(t, 1, t, wp); mag_set(err, arb_radref(t)); inexact = arf_get_fmpz_fixed_si(res, arb_midref(t), -prec); mag_add_ui_2exp_si(err, err, inexact, -prec); arb_clear(t); } } else { slong k; arb_t p, p2, q, q2; arb_init(p); arb_init(p2); arb_init(q); arb_init(q2); if (xmag <= 0) { arb_set_arf(p, x); arb_set_round(p, p, prec); arb_mul(p2, p, p, prec); arb_add_ui(q, p2, 1, prec); arb_sqrt(q, q, prec); arb_add_ui(q, q, 1, prec); for (k = 1; k < r; k++) { if (k == 1) { arb_mul_2exp_si(q2, q, 1); arb_add(q2, q2, p2, prec); } else { arb_mul(q2, q, q, prec); } arb_add(q2, p2, q2, prec); arb_sqrt(q2, q2, prec); arb_add(q, q, q2, prec); } } else { arb_one(p); arb_one(p2); arb_set_arf(q, x); arb_set_round(q, q, prec); for (k = 0; k < r; k++) { arb_mul(q2, q, q, prec); arb_add(q2, p2, q2, prec); arb_sqrt(q2, q2, prec); arb_add(q, q, q2, prec); } } arb_div(p, p, q, prec); mag_set(err, arb_radref(p)); inexact = arf_get_fmpz_fixed_si(res, arb_midref(p), -prec); mag_add_ui_2exp_si(err, err, inexact, -prec); arb_clear(p); arb_clear(p2); arb_clear(q); arb_clear(q2); } } void arb_atan_arf_bb(arb_t z, const arf_t x, slong prec) { slong iter, bits, r, mag, q, wp, N; slong argred_bits, start_bits; mp_bitcnt_t Qexp[1]; int inverse; mag_t inp_err; fmpz_t s, t, u, P, Q, err; if (arf_is_zero(x)) { arb_zero(z); return; } if (arf_is_special(x)) { abort(); } if (ARF_SGNBIT(x)) { arf_t y; arf_init_neg_shallow(y, x); arb_atan_arf_bb(z, y, prec); arb_neg(z, z); return; } mag = arf_abs_bound_lt_2exp_si(x); /* We assume that this function only gets called with something reasonable as input (huge/tiny input will be handled by the main atan wrapper). */ if (FLINT_ABS(mag) > 2 * prec + 100) { flint_printf("arb_atan_arf_bb: unexpectedly large/small input\n"); abort(); } /* approximate by x - x^3 / 3 or pi/2 - 1/x + (1/3)/x^3 */ if (mag < -prec / 4 - 2 || (mag-1) > prec / 5 + 3) { arb_t t; arb_init(t); arb_set_arf(t, x); if (mag < 0) { arb_mul(t, t, t, prec); arb_mul_arf(t, t, x, prec); arb_div_ui(t, t, 3, prec); arb_sub_arf(t, t, x, prec); arb_neg(z, t); /* error is bounded by x^5 */ mag_add_ui_2exp_si(arb_radref(z), arb_radref(z), 1, 5 * mag); } else { arb_ui_div(t, 1, t, prec); arb_mul(z, t, t, prec); arb_mul(z, z, t, prec); arb_div_ui(z, z, 3, prec); arb_sub(z, t, z, prec); arb_const_pi(t, prec + 2); arb_mul_2exp_si(t, t, -1); arb_sub(z, t, z, prec); /* error is bounded by 1/x^5, and 1/x <= 2^(1-mag) */ mag_add_ui_2exp_si(arb_radref(z), arb_radref(z), 1, 5 * (1-mag)); } arb_clear(t); return; } argred_bits = 8; start_bits = 16; /* Argument reduction q times. */ q = FLINT_MAX(0, mag + argred_bits); /* Determine working precision. */ wp = prec + 10 + 2 * q + 2 * FLINT_BIT_COUNT(prec); if (mag < 0) wp += (-mag); fmpz_init(s); fmpz_init(t); fmpz_init(u); fmpz_init(Q); fmpz_init(P); fmpz_init(err); /* in fixed-point ulp */ mag_init(inp_err); /* absolute error */ arb_atan_bb_reduce(t, inp_err, x, mag, q, wp); inverse = mag > 0; /* todo: compute in function, or pass to it */ /* s = 0, t = x */ for (iter = 0, bits = start_bits; !fmpz_is_zero(t); iter++, bits *= 2) { /* Extract bits. */ r = FLINT_MIN(bits, wp); fmpz_tdiv_q_2exp(u, t, wp - r); if (!fmpz_is_zero(u)) { /* Binary splitting (+1 fixed-point ulp truncation error). */ mag = fmpz_bits(u) - r; N = bs_num_terms(mag, wp); if (N != 0) { _arb_atan_sum_bs_powtab(P, Q, Qexp, u, r, N); /* multiply by u/2^r */ fmpz_mul(P, P, u); *Qexp += r; /* T = T / Q (+1 fixed-point ulp error). */ if (*Qexp >= wp) { fmpz_tdiv_q_2exp(P, P, *Qexp - wp); fmpz_tdiv_q(P, P, Q); } else { fmpz_mul_2exp(P, P, wp - *Qexp); fmpz_tdiv_q(P, P, Q); } fmpz_add(s, s, P); } /* add u/2^r */ fmpz_mul_2exp(Q, u, wp - r); fmpz_add(s, s, Q); /* 1 ulp from the division, 1 ulp from truncating the Taylor series */ fmpz_add_ui(err, err, 2); } /* atan(t) = atan(u/2^r) + atan((t 2^r - u)/(2^r + u t)) */ fmpz_mul_2exp(P, t, r); fmpz_mul_2exp(Q, u, wp); fmpz_sub(P, P, Q); fmpz_one(Q); fmpz_mul_2exp(Q, Q, r + wp); fmpz_addmul(Q, t, u); fmpz_mul_2exp(P, P, wp); fmpz_tdiv_q(t, P, Q); /* 1 ulp error from the division */ fmpz_add_ui(err, err, 1); } /* add both err and inp_err */ arf_set_fmpz(arb_midref(z), s); mag_set_fmpz(arb_radref(z), err); arb_mul_2exp_si(z, z, -wp); mag_add(arb_radref(z), arb_radref(z), inp_err); /* argument reduction: atan(x) = 2^q atan(x') */ arb_mul_2exp_si(z, z, q); /* outmost argument reduction: atan(x) = +/-pi/2 - atan(1/x) */ if (inverse) { arb_t pi2; arb_init(pi2); arb_const_pi(pi2, wp); arb_mul_2exp_si(pi2, pi2, -1); arb_sub(z, pi2, z, wp); arb_clear(pi2); } arb_set_round(z, z, prec); fmpz_clear(s); fmpz_clear(t); fmpz_clear(u); fmpz_clear(Q); fmpz_clear(P); fmpz_clear(err); mag_clear(inp_err); } arb-2.8.1/arb/atan_sum_bs_powtab.c000066400000000000000000000073651264125401100170540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" slong _arb_compute_bs_exponents(slong * tab, slong n); slong _arb_get_exp_pos(const slong * tab, slong step); static void bsplit(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const slong * xexp, const fmpz * xpow, mp_bitcnt_t r, slong a, slong b) { if (b - a == 1) { fmpz_set(T, xpow); if (a % 2 == 0) fmpz_neg_ui(Q, 2 * a + 3); else fmpz_set_ui(Q, 2 * a + 3); *Qexp = 2 * r; } else if (b - a == 2) { fmpz_mul_ui(T, xpow, 2 * a + 5); fmpz_mul_2exp(T, T, 2 * r); fmpz_submul_ui(T, xpow + 1, 2 * a + 3); if (a % 2 == 1) fmpz_neg(T, T); fmpz_neg_ui(Q, 2 * a + 3); fmpz_mul_ui(Q, Q, 2 * a + 5); *Qexp = 4 * r; } else { slong step, m, i; mp_bitcnt_t Q2exp[1]; fmpz_t Q2, T2; step = (b - a) / 2; m = a + step; fmpz_init(Q2); fmpz_init(T2); bsplit(T, Q, Qexp, xexp, xpow, r, a, m); bsplit(T2, Q2, Q2exp, xexp, xpow, r, m, b); fmpz_mul(T, T, Q2); fmpz_mul_2exp(T, T, *Q2exp); /* find x^step in table */ i = _arb_get_exp_pos(xexp, step); fmpz_mul(T2, T2, Q); fmpz_addmul(T, xpow + i, T2); fmpz_clear(T2); fmpz_mul(Q, Q, Q2); *Qexp = *Qexp + *Q2exp; fmpz_clear(Q2); } } void _arb_atan_sum_bs_powtab(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) { slong * xexp; slong length, i; fmpz * xpow; /* compute the powers of x^2 that will appear (at least x^2) */ xexp = flint_calloc(2 * FLINT_BITS, sizeof(slong)); length = _arb_compute_bs_exponents(xexp, N); xpow = _fmpz_vec_init(length); fmpz_mul(xpow, x, x); /* build x^i table */ for (i = 1; i < length; i++) { if (xexp[i] == 2 * xexp[i-1]) { fmpz_mul(xpow + i, xpow + i - 1, xpow + i - 1); } else if (xexp[i] == 2 * xexp[i-2]) /* prefer squaring if possible */ { fmpz_mul(xpow + i, xpow + i - 2, xpow + i - 2); } else if (xexp[i] == 2 * xexp[i-1] + 1) { fmpz_mul(xpow + i, xpow + i - 1, xpow + i - 1); fmpz_mul(xpow + i, xpow + i, xpow); } else if (xexp[i] == 2 * xexp[i-2] + 1) { fmpz_mul(xpow + i, xpow + i - 2, xpow + i - 2); fmpz_mul(xpow + i, xpow + i, xpow); } else { flint_printf("power table has the wrong structure!\n"); abort(); } } bsplit(T, Q, Qexp, xexp, xpow, r, 0, N); _fmpz_vec_clear(xpow, length); flint_free(xexp); } arb-2.8.1/arb/atan_sum_bs_simple.c000066400000000000000000000043331264125401100170410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void bsplit(fmpz_t P, fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong a, slong b) { if (b - a == 1) { fmpz_mul(P, x, x); fmpz_set(T, P); if (a % 2 == 0) fmpz_neg_ui(Q, 2 * a + 3); else fmpz_set_ui(Q, 2 * a + 3); *Qexp = 2 * r; } else { slong step, m; mp_bitcnt_t Q2exp[1]; fmpz_t P2, Q2, T2; step = (b - a) / 2; m = a + step; fmpz_init(P2); fmpz_init(Q2); fmpz_init(T2); bsplit(P, T, Q, Qexp, x, r, a, m); bsplit(P2, T2, Q2, Q2exp, x, r, m, b); fmpz_mul(T, T, Q2); fmpz_mul_2exp(T, T, *Q2exp); fmpz_mul(T2, T2, Q); fmpz_addmul(T, P, T2); fmpz_mul(P, P, P2); fmpz_mul(Q, Q, Q2); *Qexp = *Qexp + *Q2exp; fmpz_clear(P2); fmpz_clear(Q2); fmpz_clear(T2); } } void _arb_atan_sum_bs_simple(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) { fmpz_t P; fmpz_init(P); bsplit(P, T, Q, Qexp, x, r, 0, N); fmpz_clear(P); } arb-2.8.1/arb/atan_tab.c000066400000000000000000004057041264125401100147550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #if FLINT_BITS == 64 #define Z2(a,b) UWORD(0x ## b ## a) #else #define Z2(a,b) UWORD(0x ## a), UWORD(0x ## b) #endif #define Z8(a,b,c,d,e,f,g,h) Z2(a,b), Z2(c,d), Z2(e,f), Z2(g,h), const mp_limb_t arb_atan_pi2_minus_one[ARB_ATAN_TAB2_LIMBS] = { Z8(cd984a96,b6fe288f,9da97637,899cd975,9f3629da,b47db7d7,0cb51231,2f2e4f61) Z8(204fb062,60d4a7db,8260035d,cbb6705e,5b3ca61d,f1ff280d,7b746f7b,92ea3cec) Z8(c04c8dbd,83a9b964,a4f8e04d,6d87f569,68050924,9be86b92,214d811e,0dff6fb9) Z8(1b1fbb83,2769d531,ab60b553,a00d224f,42e09039,7037baec,9dc5af5f,3ec252e1) Z8(a2b7cfda,4677430c,41218744,33652c9f,9cd780bb,50f8b28e,3f7d954c,5d1df828) Z8(09bd1df2,b77785b6,55a899d1,4b07d394,6c2a17b4,3528d069,d5e9c478,33864e30) Z8(7b74b64d,10e33421,4f0fcdaf,34e47825,52421002,9705a241,c1fa211c,87b6b7f9) Z8(e9cb5662,11c49f40,75b28dc4,ee131181,f4c2bad8,77c22eae,2ef64019,a43e5630) Z8(7d90d4c8,b0ec04e6,b31410c9,e25ff40d,35a5dcd7,9dc7a44c,944ac33b,3d1929c0) Z8(b61267ae,57eb5d19,4dc3c98f,672e1f0b,ba0c18fb,15d4e2ae,b1b7de15,d9f70a08) Z8(be3974c9,50aa4357,08a0f467,5a662e1a,1555885b,2ae51cb5,31f40a20,2ba44c31) Z8(d52ad5ca,732a92f9,2ab02e30,bc5797ed,de98a593,6b8abbe0,d80f451f,364f0745) Z8(301d0c07,c73cee58,5c6d9c77,6520bc8c,943042f8,e2e8d811,95793009,ce186a9c) Z8(e12d2cda,3daa520e,410aa577,38c5e6ac,b9475b2c,06caba47,fa499ebf,d22c7f51) Z8(38aba734,31b4906c,42c77e0b,8400f971,d9c8b67b,9250cca3,f8963fcc,5d3e4822) Z8(b5133f4b,dc70d7f6,e80d6fdb,17feb96d,4c6fdad6,e89885d3,c4bcfd8d,c90b6aec) Z8(daa3848b,9fc26ada,e4be286e,605614db,9a748636,df2a3367,1c6809bb,a29410f3) Z8(76273644,04177d4c,14cf98e8,52049c11,01b839a2,898cc517,42d18469,921fb544) }; const mp_limb_t arb_atan_tab1[1 << ARB_ATAN_TAB1_BITS][ARB_ATAN_TAB1_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(800f56c0,471a535c,67be3ae1,d89ebbe4,6126f5a9,d62450d6,f625cdfb,6d688680) Z8(2682bef6,892248ad,eb9bc957,167c18ba,6b6d4f7e,4bb12afb,aaddddb9,00ffffaa) },{ Z8(d79ae2a7,570f29f8,9717e1e5,cc7790ed,ac4a4e52,6f9cb7c5,28bc8f59,2111d081) Z8(cfdd9ca1,3507a2ae,2e345e00,8ed0ad40,f77cc15e,d00c46a3,5bbba972,01fffd55) },{ Z8(61e8f518,1b37431d,e4186302,46af6bbf,91294bed,9e608b5c,ebea3e47,dc4ab848) Z8(ac4d1fad,14db0e87,1beddd8e,6f3b42e4,ee5a5b71,6d7f457b,30986134,02fff700) },{ Z8(4df9c218,85a1b8fb,797ad494,bcabe016,286e9ba4,68d09936,858d1e57,a36a1de9) Z8(c9d5872e,81a57e00,0437bbd1,2083bd97,0057dd81,ef9e3159,776e5356,03ffeaab) },{ Z8(a5a0cb92,6b52a899,206a0785,3293c311,165a6a5a,734d22a1,c5de3191,38d13644) Z8(a3132784,56335a58,5200eb10,fd306b02,04d3fd27,ec153c93,c629bfed,04ffd657) },{ Z8(a08edf4a,83a73639,cba0219c,a9c8faab,c0bef870,36a7ad69,89a224cf,6e211e53) Z8(4ac30913,c49cd215,6aaedaa2,8dd4fb81,cab5251b,ce7603f5,12970d6b,05ffb806) },{ Z8(c468bf81,d7aa9735,a501ca08,8750f3a2,175e84fc,c64cbc9c,549887da,63253408) Z8(02ffdb3c,9aaafeff,6171a4ba,cb479a5c,f7f8cafc,f209c454,ca45c470,06ff8db7) },{ Z8(6f362901,1358c95c,c276afc4,13c86927,f7a43e2d,0f282ff5,897e5f9d,3b2a91f5) Z8(a26b0830,b2380bed,a606dc40,9c036814,6ed46310,13bcebbb,ea5d892a,07ff556e) },{ Z8(879c8a25,fc7e1c8c,29974e6b,237c9daf,a9dcd26e,74fc920d,75f96824,d1bc0156) Z8(379ee4be,381d3599,1bc682b8,a4ff745e,89968a2a,0c123d1f,17624bb1,08ff0d2e) },{ Z8(59d2161b,993c1e86,eee6b8d2,aef449a6,a2c015f4,32971e8b,7d6fac19,0a0e82e9) Z8(7fd2da02,0729939d,220db88c,184ecc9b,30da72f6,918538b2,b4e4ec8b,09feb2f8) },{ Z8(b02c5942,89362e3f,c991b205,0adf3417,fcaf53f6,ec4b00d9,5f2e123c,9b020587) Z8(7c28c6a2,b6bd8276,525a72aa,3c64d55b,ff317148,76e77e9c,fd1d96a5,0afe44d2) },{ Z8(162c790b,257b0e0e,d755b36e,9b14ed68,6717017d,ed0894b8,439bbf1e,a5989626) Z8(17de7976,a7731202,f807f208,71dddd64,61df56ec,f220e10d,186d14fc,0bfdc0c2) },{ Z8(e376bcfd,068a96f1,dfbb2b41,2d70daca,1f0d1878,02748cfd,1e707ffe,8fe00659) Z8(e6d80f3a,b29c65b4,6fddb3ed,5847020d,578395ba,4520f5e1,34c26fa6,0cfd24cc) },{ Z8(8610cb40,ef5ac7c0,74a3fd6e,2ef90dd0,d44f2ce7,be000539,57af8bc6,b5ffc5d0) Z8(a8994635,0d1b3e5c,95a4be50,9a51f29e,00b0ebac,c03969ab,9ce221ce,0dfc6ef8) },{ Z8(d1766d52,3c9d4d00,98dcfd4f,d19de2a9,544ce10a,84887d3c,4a1a6eb6,00c86503) Z8(a07bc5f6,a582d3ae,c0fda8e7,6f59d19e,d0d2fcff,6b928efb,cf8c40fb,0efb9d4f) },{ Z8(4ef2a858,42521de9,625a4c0a,b1404b3e,6ac74803,493fe292,473e9b7d,d0249009) 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Z8(494a1322,eb3fe5fa,d87a36a4,21b81774,2d74e019,67b7d66f,b7602294,a746f2dd) },{ Z8(cf362c29,6ac8c4f7,83cbe1ad,41da709b,12d4e3b8,c43078b5,dcbda61d,e9c2ff7d) Z8(f0d11959,566e7e8b,e235aaba,b0d212ca,4b4d1412,13f3e7c2,ee8bf1d5,a7e809db) },{ Z8(e2c7df9c,9c76be14,05d79a4b,dd835439,247e47ff,9ede3d4c,448c4b55,eca1ba5d) Z8(f257d01e,878211b1,af4bc660,e17ab4a5,63de1ee8,dcd6832a,2f6c0923,a888856e) },{ Z8(f9834a8e,d1ea5a0e,1e72816d,d998cbba,bec24271,28bfc71a,f528f87f,a88d2a6d) Z8(b62709d6,bdbab4d9,527462b0,73ca99a3,de41b9df,19217375,8f4fd7ab,a92865f7) },{ Z8(06151b1b,85c67da6,f8431ede,72eb259f,0562adec,ff7ad99b,36a1ca19,45931d74) Z8(7dbf5c4d,094f003a,e427bf1c,f9971655,be7933f5,916a84b5,4830f5c8,a9c7abdc) },{ Z8(2ee6065e,d84d5aeb,79d2847e,d4607a6b,cfa4716d,abc4e90a,102e3539,ec29e77a) Z8(f769d388,91bd6827,77ef508b,72cde548,782acc51,648ff1e8,b1647b14,aa665781) },{ Z8(632e0106,cab1b0aa,88b7fd78,9a2542b2,0e2c0151,286ac91b,e2ec9b6d,7fa5fb8a) Z8(5bca3585,9f321fca,8e69e270,fa1db9e7,11000fd4,739e1bd0,3861a332,ab04694e) },{ Z8(c13b6108,400185f2,618b50ba,cf855bad,ba485390,b40008b7,e73fb9c1,14ff539c) Z8(2a4d08e4,56a20620,e0d2c55b,03728b70,2b469fb6,fe5966f0,599dcc2b,aba1e1a9) },{ Z8(fd8a3574,d3fdb776,c3bde77f,4a195daf,6f325ae3,9b9aabd1,1ca234ff,3cc6eb35) Z8(a7edf055,b854b5cf,6c42068c,183db540,6afa8ef4,a36273a5,997dd6a1,ac3ec0fb) },{ Z8(36a498ee,4614067c,ffed0b20,f90a8bfd,39a2b99f,b278542a,9defb54c,64815216) Z8(c4e2513f,f4309a24,130dd772,1951bb83,8769f24d,f677dfb2,7d5cedc9,acdb07ae) },{ Z8(6fbacf1d,53a309f4,593da3a9,7bb25f2e,c109498e,8d0d947a,64684b8f,20410073) Z8(327860b8,361bd73d,5ac7f639,529f4f43,86cdb591,25ee2952,84a8bae6,ad76b62c) },{ Z8(42dc23e5,4c5681e8,10ced33d,c068fdf7,9c89b025,813b0f95,a482e425,1b7384af) Z8(c5f182b7,01e2dca4,c42ac104,c1476866,995154ab,8562c352,2213059c,ae11cce1) },{ Z8(c53c2cdf,5307ed4b,3b746c2d,3fd6f785,dd439af3,c6586fe1,eef1f3d7,95ee0fd1) Z8(c44fdd30,04407947,43effe26,03742b46,3e52070a,14725e2f,b4d8c080,aeac4c38) },{ Z8(19c27a4b,069518ef,608d99e1,778f23a9,43d8a1f6,3843bdcb,b6b5a68c,77bd59a9) Z8(4e3a097c,6dd5e77f,bfbb5c68,4736fc44,1904f916,08a41bae,821e7ef4,af4634a0) },{ Z8(0e621cec,cbf0d745,ef9a241a,b16df078,24d12ebd,f7f68473,916f0675,2a7b1f70) Z8(72810af7,922e6f31,f25347b4,7e411319,3aa0ae62,cc0bffd2,ae624f92,afdf8686) },{ Z8(ec62b0f9,ee29a6a0,3fcf63df,c74448b5,74cf6262,a5f8fbc4,e64810a7,1ddf854d) Z8(13d626cd,04696a5f,1149f517,a5b0f42a,cd9cdaf2,8f2ccd75,3702f448,b078425a) },{ Z8(21fb6e4b,3a0ebf2d,119ac76f,314716be,bdfca441,790bb09a,042594fc,205110bd) Z8(cce6db2b,5d3ed56b,4df9e1c7,09e2828d,b9f6a7b5,43d65788,ebdc6f6a,b110688a) },{ Z8(ea5ad26f,499d0c17,b70a6d35,52abf343,d2824dd1,06202b00,2db1af63,2e434885) Z8(d5f02eee,66a635d2,716ea56a,3ae3c1f6,b2f9e94a,5e62be56,68f9db3a,b1a7f989) },{ Z8(50442247,1a366759,6c3402d3,ead0314f,5fe4e0c5,39cb4dbb,84ef7278,25329c79) Z8(c0f40bad,3c3177a2,53734cea,b2a3bdca,b8c33242,d7eff716,105c7f84,b23ef5c7) },{ Z8(4d7b2d36,7763ad68,fc564739,c63c589b,c7c3f6c2,bdfba59e,63e3ba8f,dfe5b792) Z8(8a0944ed,ea469bc3,9071ce0e,a2d0847e,c6b9dc4b,63262866,03d81743,b2d55db6) },{ Z8(d039ae93,4785f476,9e977afb,0cfdc69c,fca71d8c,70c045a9,ef498a57,43ac8c5f) Z8(409dcd1e,751e5dec,0783f6fe,e469ff28,4462f939,59014174,1f043691,b36b31c9) },{ Z8(c06e926e,2238c933,a073dcc1,3d2abd15,7dd4e84f,75f0e008,8c44cea3,a6e1ef9d) Z8(ea37fc5f,43c06970,2ffd0ff7,69a53095,bc3f1576,56579305,f142bf9c,b4007273) },{ Z8(c024ee45,d3fdabd0,89caa556,3c2d9478,cc470fe0,0c2b1434,4359fdcf,7486ae52) Z8(551c4356,0a83bf69,8e5b3e75,7426f3bb,5971ca78,972b51d4,b7db53b2,b495202a) },{ Z8(b6b7c2b7,a308e1fb,c5632729,9a25eeaa,89f6a700,f453dc7b,ff66eee0,61ae10f0) Z8(01bbffe2,7c6c5a10,fab778f9,c0998af1,2c3f989b,934c772b,582bac12,b5293b62) },{ Z8(26ed1cad,ae8d5530,1792d5ca,ee8b0c5c,eeee6cf7,ba2ca0ef,6fa8d575,e58350f3) Z8(8cea9535,8cddaac1,b3891e07,75216f47,5e3907d5,f8f3cee7,59ecc4af,b5bcc490) },{ Z8(ac4d031e,6a18bd61,6e12b2a6,5318b2be,84d20003,7231de7d,7667216b,32f340bf) Z8(d59cf075,dc78e6d2,567914a6,ee7e3ade,80c8a0b6,9de29bd2,e18cc1c0,b64fbc2a) },{ Z8(bd39b09b,76e88d40,f851e99c,7851427f,c4551044,235a7456,37ad0b6c,e30321a9) Z8(622e4065,f25b5517,73b3fd15,0ad7a1ec,f5c86498,1de72a31,aa9d7790,b6e222a8) },{ Z8(13c3d8bd,f13b3aac,2b00266f,3d93f8ad,95595742,83f97104,eebef105,67a20c15) Z8(e0e3d97d,9bfbd896,0d67f497,f91a4955,4e3ef828,5dd460cc,02577ad2,b773f881) },{ Z8(945e8cf3,38257e41,4380781c,e8c53e21,2668272c,49c49ec7,cec98182,4655f065) Z8(64cae530,a012155f,14c79a80,3d7aecc1,10a4443d,cb2da552,c2319e73,b8053e2b) },{ Z8(47d04f2f,b7e0289b,564de9df,38d73bdc,c7501845,b772d374,edafdea6,dc6367da) Z8(fa8544aa,2801763c,aa36f135,5a4d5a41,102f7717,b2066fb1,4a8cc2b9,b895f421) },{ Z8(a91c42b1,0c4ccbf5,1fc7fb02,6a57f0ec,5ce1e224,59fc20bb,dadbb900,85a0e5c8) Z8(31debfaa,279fbde2,f28bcf2a,05fde833,266bc460,22ccb6cd,7d73d865,b9261ada) },{ Z8(4269812b,9f568d99,8d284245,929e144a,0cdd73d1,36ddd27f,7f14ee9c,fe9e8c16) Z8(ac1e21d1,2e44e671,d5d0f7a0,f01f06d4,2d100e70,5fd06a89,b96ff977,b9b5b2d0) },{ Z8(ee5469aa,c24f5187,62ea50d2,cbe25d89,37c5c425,ed6648f6,0d634fec,41a41f8d) Z8(51eece27,0672fcfd,d454a343,23228454,0942e386,654c2cb1,d470782f,ba44bc7d) },{ Z8(773d151b,a0ce4d29,31a19866,e98e80f5,f0fbf88e,cda43312,c372d285,f8603fba) Z8(989256d6,d8ae8b68,0a8c7b1e,48cca731,10da150b,95898e52,16c6c3dc,bad3385c) },{ Z8(d8317a9d,b58a00b1,5ae2bca9,3fed4473,86ae2a0f,892edee9,6927dd63,902eb955) Z8(05b79464,e2c7194d,6f8d6c65,1342deff,07915ae6,a4aa35b9,36360232,bb6126e6) },{ Z8(7ac67c19,ca1d2723,96ee2335,888ad40d,ff8f33bd,b1618881,94867be0,43eb5053) Z8(20d4c84d,877735b9,a599e7d2,740e9aaf,a7ae3e62,4c11f821,51163ae6,bbee8897) },{ Z8(c4c3c40d,994e9987,5d58da8a,920ba34f,d050067c,d4140c7b,569845f3,010c85fc) Z8(5514a995,231796bb,5ba4ab8a,13fab81f,e80fb290,d4113006,e98af280,bc7b5dea) },{ Z8(078d591c,2fc841ff,55ab5af7,75a8ca78,11f4d92f,afabb0ad,f3ec992a,04259565) Z8(c71fed79,be81bf84,8a497168,15d7d6a5,fabb5d74,e33e6c0a,e0cd1089,bd07a75c) },{ Z8(af58dc87,2b300fb3,924473f2,ce65df39,1202cd89,9f3a1bfe,5ca4f7fb,384a4671) Z8(56e4bb84,a593af0f,c726f312,89fb1e26,c09b1791,fe419f7d,7287ec62,bd936569) },{ Z8(db99522b,1495ad10,570f1ff0,64640bd9,c33c7379,a3c88dfd,639ea69e,7e4bb855) Z8(664ccbbe,9c2bf459,7fa58b32,6bbb76d2,5109b743,7965a606,30495b76,be1e988d) },{ Z8(eb3af07c,c26f2caa,16036500,14b1de73,edc0ee63,94f33cd5,014699b1,4130f65d) Z8(655bf345,74fdaef1,f13d5c3a,01438341,55282e7d,1043c5e7,fd049aac,bea94144) },{ Z8(948cdeea,3b85c8bc,189c9cdd,624975d4,49182faa,9801fe64,7bfd7059,ec13bb8d) Z8(e7738e7a,1511e852,a2606cd8,6f6bfd26,8e50ada6,a8ee913e,08a7ec6f,bf33600e) },{ Z8(91c017b8,905b317a,a99fba77,1a3acefd,f6180765,21db31c0,0de6e856,6093845c) Z8(64b3656a,6ab1d623,53934558,ce2085df,441a24b5,b9501d5a,cbc4c3fa,bfbcf565) },{ Z8(aebd0b6a,2234ea74,e80b5754,1856411b,4880f10e,215fd084,a87870f0,86e41e4e) Z8(b9a23642,548e902e,a46a50a5,59538bab,2b630d4d,19b11d41,034a55fe,c04601ca) },{ Z8(990563e3,dfe86b83,ac95ccb6,3ad03636,485bc5c2,a34ac5cf,51a62f57,44ffa53c) Z8(a10b2d25,37081467,aef436f6,d58ee867,6e92fa24,89dd62c4,ac526640,c0ce85b8) },{ Z8(f2ab784f,7d87e16d,d5ce0fad,74459366,e7517870,f29f8b05,83833ee6,8d6fdbad) Z8(d1575070,0987beec,703e16c4,695bf27c,d2425ea8,92fce924,00002945,c15681b0) },{ Z8(2de4649e,69584910,e337a1a4,4574b346,ead7180d,0458efab,16023b26,75af9aa6) Z8(815709d1,6653bbab,e3b003f2,1812b904,361448e7,838827fe,6f711098,c1ddf62e) },{ Z8(3ccfa487,5a07a42e,6570fc40,6ed05d32,b4e62c8d,c1a7586f,12dc125d,5b06891e) Z8(ce882276,fc8ce728,1847c57b,8039a8ec,c1713e2f,c9ee01f5,9fbf57e7,c264e3b2) },{ Z8(9f6c1e9a,5c930791,e8cb14e3,41f3a7c6,49d272f4,16f02476,00e8f7ef,ca811d6a) Z8(a9724511,a4a42eff,0e4baa66,e970ec0e,c61bb9fa,b373fe45,661628b5,c2eb4abb) },{ Z8(629652b2,5c2a2311,5ede1189,e88a3fcb,1159f52c,0df7a13e,df6f5268,c38e91ba) Z8(218c6d64,aa12aec8,d04b7f6a,93a72f30,c678fde0,5626eb9f,c3d72a04,c3712bc7) },{ Z8(6c572099,e2a717f3,dfd54159,31d1e173,9a81f5fb,c86286b1,826637a2,ca40809d) Z8(3061f2f3,57b7468f,cab62fb5,ce4aa623,4bc61565,f5ad957f,e2d1510a,c3f68756) },{ Z8(88c93f33,c2db39af,5903eb22,3a4558bd,438ff50d,0a313650,cb63ad19,1ccc9b7c) Z8(f32b4f93,91d85ec0,63cb83ea,97192bb8,667e2502,4b8b6951,1188c7b3,c47b5de8) },{ Z8(d28d2f5a,098b6ca9,0006bc9a,24ed1b16,f8463c22,a068eb0c,45c51352,b0fd5694) Z8(4f97d1fa,fe669d99,0039834e,4da621b6,bc9e0221,8cb43d10,bf8fbd54,c4ffaffa) },{ Z8(65f31f3b,388e1c1e,b8b30016,a8c80473,83abad85,3498d020,c61fe6c9,9ba8c506) Z8(b4ab95c9,f66d6033,14b2bfbe,6837d6da,9263d1d4,99db3524,79eff5e0,c5837e0e) },{ Z8(892289f0,149126ae,59c15a7b,1893fef7,5ce6c6be,449d5230,47a14fa2,f2db2abb) Z8(79a3ff17,442531f3,8a15c194,6f74b5da,66516455,480edb88,e7a4eb7d,c606c8a2) },{ Z8(4dd071bf,8c241234,57a88b57,cd4c845e,d58b13d2,69f86fc8,4647ee8f,6f575b7c) Z8(1422a61b,a723e05b,e3af549f,dd13c472,574ca266,e7345576,c626564f,c6899037) },{ Z8(7cd74955,f6c32fc7,4175eb9d,724d1c66,de8162ac,bb9c9bcf,b5848c7e,bd069fab) Z8(48417fda,adfde929,af9b702a,0e9c986e,09f2be38,e7d54fbd,e602ee13,c70bd54c) },{ Z8(6b4b1aa2,4d3fb729,fc0fe1f4,e0b01556,21b73f1e,b2be5028,5bb954e9,97285197) Z8(9d7e8a06,d41681b3,e8b4d30a,3c9c7639,9fe946b2,8e55c9c9,278b38ee,c78d9862) },{ Z8(e94d85d3,1eca4460,75c0f295,6f6ffd22,393e3682,9a21e260,119a5614,5c540c8c) Z8(7298a4a4,8402ae01,c708214c,3b7d29be,91ef71d4,ccbcac07,778c3ad0,c80ed9f7) },{ Z8(03e2135d,a0d8504a,644636cd,e0a59182,73ceabab,b0e884ab,01e3f55f,a5917ced) Z8(7ea0180b,d9884aae,e7b9333e,167b4c95,a90d530c,745076df,cc19d89d,c88f9a8c) }}; const mp_limb_t arb_atan_tab21[1 << ARB_ATAN_TAB21_BITS][ARB_ATAN_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(b05b5f26,0e71e093,0e01723a,81e8b531,5b7039bf,5077ba19,d2c215ef,f8683492) Z8(db5e2e25,083b4901,184e277e,48487df1,4489185c,db600462,9f50bd14,302e7051) Z8(e0ee0aa7,9a4b316c,89582fe4,32916544,dc172ba5,69a141a4,84ba4a5c,380f1768) Z8(b77501e0,9ebb1272,440d80cf,63fff32a,c8ffcd77,07e2a4dc,4e20aad8,c9bfa51b) Z8(0bdd5f0d,503f8851,1da324e4,77b05217,496d0a20,6c86a4e7,fc3f074c,1cc4f214) Z8(6fbf44e6,95583c13,d84f80dc,12dc69b0,228ce8b6,3480beea,554f25d4,3ebc36f7) Z8(62b425fb,f2bc846f,d3021773,836e1db1,1f7b3dbf,05d87ee7,bb74aa0f,407fb1b6) Z8(fe3e623f,a3d13d38,596a7b7f,dcd9e7cd,faaa0890,cece21bb,b868f38b,3aa5fd19) Z8(79ec81b3,c24479cd,157d9fd9,b1276330,aab2fb48,ef0d9133,feb17148,68ee429c) Z8(d9022ab5,8c9ed5ad,bf33872c,837e9ccd,c85eeb48,1fb2cd92,a7d87ae8,84d12671) Z8(c83e269b,8fddbe4c,53d59835,c38b6b3f,9ec9c439,27d81b23,b70c54d9,107f1ba3) Z8(f7c5f629,11fed0e8,c24d389b,535c7f97,79b53203,a94d5b55,f2204a83,e07290bf) Z8(7de781f3,1edadbe4,eb0d0d2d,2aa2c686,45a41873,2542bcea,ab381617,a96f6f0b) Z8(86bda292,90024115,9a021aa8,007cd63d,c63aee74,6b06eb7e,cb7ef091,d48c02b4) Z8(62e872f9,e79f94d2,b58df3bb,7a05eb9d,b400d0a2,4d6e16de,385e8484,d0aaa133) Z8(737b4914,e5bbc8bd,197ca05c,aac8a1ba,fb5cb3d5,a628e2f5,89d759fc,a9d14ab5) Z8(6f362901,1358c95c,c276afc4,13c86927,f7a43e2d,0f282ff5,897e5f9d,3b2a91f5) Z8(a26b0830,b2380bed,a606dc40,9c036814,6ed46310,13bcebbb,ea5d892a,07ff556e) },{ Z8(a04a314b,aee9953e,ede190bc,3d5577f9,9df5f7eb,b374863f,ddbbf656,89ae6707) Z8(bf218df6,493cd567,cd6fd15f,8d63640e,6ce8a993,fe4329a2,663f987b,0ddd0edb) Z8(6fe63d6d,1877d90e,1db23199,2e3e9d2b,497fb0f9,01a357df,788a5888,34c89866) 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Z8(84857775,7f50b381,a690cae8,3ce32547,8dbd3fd4,48a17fa7,d6569a4f,0200153c) Z8(c6289c74,6ef14fd7,ed96088a,1509884c,804e33b4,29ebbb8f,27d37352,07eb95e0) Z8(2dd460a0,5b6b1b96,a8d35f9f,eb9c3f18,0107dc6d,31e63e04,0e2d33be,99d94270) Z8(f356ab87,0a219e0b,cc0383a4,4c5c1cdb,cbbaa179,5bcae903,7c9c6fd7,f52a7a4f) Z8(a5597967,922f0c49,5f4676d7,9cabf63b,943f8efd,92583a04,1c7b8bec,483c3161) Z8(c4c3c40d,994e9987,5d58da8a,920ba34f,d050067c,d4140c7b,569845f3,010c85fc) Z8(5514a995,231796bb,5ba4ab8a,13fab81f,e80fb290,d4113006,e98af280,bc7b5dea) },{ Z8(81de9d80,03b223de,d039c61d,7e1350a3,b41e3854,03b24867,53bd5c8f,fb52b21d) Z8(d0352a8e,6840e2ca,fa0842ae,5aec252b,c481027d,cc6e5e2c,081494ce,df91ecce) Z8(6f14423e,3d41b0e0,21675e1c,9858334a,b27653c3,6ac4c295,7a237820,af22dfbc) Z8(d4f409c0,4f5b0586,a5df172b,b2265cdb,f0489f92,158b5a06,243d98b2,4cc4b98f) Z8(74d35428,2e7ca208,af3560e8,3a876c71,1906e550,f27dbb63,f29cc6f7,29d810a0) Z8(1d789cc5,100a91f2,ca8da484,752caa9e,f3bcfb8d,e0595b00,5dff6ba8,8a0a2f02) Z8(cc782240,6f32870a,69b3ffad,a5a0ba2a,83b5cac7,57bf2cd5,e92290f7,c9152cc4) Z8(2935b365,eff21108,1247bfc8,8c077778,cb031e91,a68f9b3c,1869a20f,4f453917) Z8(aa4ab122,8b4e7dbc,8d412247,d033efbd,c10198af,ed731db8,ea108367,7a5ec9f2) Z8(72955ae5,fe2bb72b,af465492,d52c0a2f,35715140,552085c6,57dbb962,4a151a44) Z8(f341c314,87d3e68a,0bc84da5,3d9a69b8,9edaf68f,e366fd35,5cd6f003,8312631b) Z8(5f7d4df9,2b6a2964,38d67dd8,6c52004c,fc3ec8a9,1ad0721b,b501bcfe,da3a9b2e) Z8(e6234172,6ac6cf92,9043c38d,4f79b74a,bd49a944,da866c15,80b9acc1,8d70fc6b) Z8(ee113e6e,823eca41,d001e26e,c8957830,896bb351,6ada4790,e7a9eedd,a7cde098) Z8(03e0aa20,c09c3cec,c458a36c,c05d176f,952dd883,89da2be4,3a7a01f3,154423cf) Z8(69689b35,16e76528,1cd1ca1d,7398e294,a3ea8816,ff22073b,d98c6dc4,b3824d04) Z8(990563e3,dfe86b83,ac95ccb6,3ad03636,485bc5c2,a34ac5cf,51a62f57,44ffa53c) Z8(a10b2d25,37081467,aef436f6,d58ee867,6e92fa24,89dd62c4,ac526640,c0ce85b8) },{ Z8(bbeb1a29,4328117c,71cafe1f,018db6f2,92f225fb,c63681ef,15fb04e8,190e1926) Z8(a1c167c9,ea706133,8f8cd082,9e1ee94d,5a757c2d,7363dd22,e52d76b0,d3689e8a) Z8(48da8ace,b17bc881,6a589d4f,18cb5df7,75e2bce0,21cdbd1e,145d4827,1582e3c4) Z8(b401684e,9b6c077d,938ef323,29f687b9,5992d78c,bd85681d,086382e0,8a42abfb) Z8(31cba5c6,932f0f49,1424a207,1686df35,6000be26,3e246d4c,951ead5c,cc5453a3) Z8(080f85e0,be042309,78646572,dd51462c,8c6bee70,345e8209,4b896e0a,8c271488) Z8(422b194d,8dda6cfa,4a55ba5d,349af5a2,3d52055d,72acdb4a,adea6229,9ae13f52) Z8(2768f61c,06b3b391,4fb50b78,a62e0fc7,4d648251,4b8f850c,77b35dda,56286bbd) Z8(5be2596c,1061a783,4108d8e9,6ea5ef1f,1586930c,cf230192,b7b74435,fd232313) Z8(74a5434d,b8e58b49,4bcfe2f1,f6a831ab,1c8ae45b,0a4d1589,4de3471d,50097313) Z8(db216163,c3fd9a75,bc33fada,36e724b5,a50c86a3,68e3b607,e3c507d1,9df08637) Z8(17dd6bff,c4ccafdf,60e232ce,d9f546bc,79be3645,73135e62,a934eacb,59b99cb4) Z8(050c17ba,45e804e0,c304867d,ed957369,2d101f73,261bbf2d,bff69efd,b89bf286) Z8(b80109d4,bfc84e09,0b27532c,2adb86cc,d9e7ca85,2bd3c648,677c770c,860a284c) Z8(b444f7c2,192de355,84bd6d21,47db6fe3,0f64a8a2,94b53592,e4a4ac8a,9ead20cc) Z8(317ce959,951dcb80,6781f28f,ff54b364,c29c132a,974f5c21,5162ea6a,a7f99074) Z8(d28d2f5a,098b6ca9,0006bc9a,24ed1b16,f8463c22,a068eb0c,45c51352,b0fd5694) Z8(4f97d1fa,fe669d99,0039834e,4da621b6,bc9e0221,8cb43d10,bf8fbd54,c4ffaffa) }}; const mp_limb_t arb_atan_tab22[1 << ARB_ATAN_TAB22_BITS][ARB_ATAN_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(4c3ac38b,589e430c,2e6f7f91,c289fc70,145bf0df,0c3692f7,d6d8b040,44316380) Z8(97514b37,acaf17b3,e68a3c04,aea607e9,0af2544d,a32eeb07,b2b1aef0,946e52b4) Z8(da8596e6,053e0c45,8d91efb1,5144f76b,fa04c6a8,f3e43dc7,b0f0210e,7cdcd4e4) Z8(61ad9354,e72b4529,ef37577b,0cb3aafd,9c58b4c3,47084c92,be5e5c3a,ee4aa6e2) Z8(4b611117,7e1d9b3d,32f71430,25bc6bce,2393e8fe,002712a0,2aa40e92,945a21f0) Z8(cb630373,523772df,11736138,a787e495,23ecb6b9,ac043bec,1f2271d3,1edf1f3d) Z8(aeea9d29,68d4bb7f,8422da7c,43fbcbe0,e0a4e899,f619a8c7,fe226c86,b5a79402) Z8(9c10cd25,934e6a41,32343fbd,d045f200,ee64bebd,d7c5c12f,1d92696c,f1e08b1c) Z8(bb5d5de5,ab349bf0,a981dd9e,b0a71162,e70e4b44,4fc25e00,c44aee66,ac2167fa) Z8(a2782a18,65ccf04b,cc496f57,e7cbaf79,60590c07,bf2a9ed6,00a2d3c2,3bbbb56e) Z8(5a0931fa,1e84a88b,bf2fff8d,701fc319,72d9426c,7938c11f,3c4ae4c8,c84a5619) Z8(d39a5056,091885e3,935ee0b3,81274c2e,305ee653,acfde487,aaaeb9e8,41b1b0e3) Z8(df2eb4bc,f561157c,bef75039,c749b113,9b48b9f1,1b23e5bc,8a9432db,c4908409) Z8(179a1615,951f23f8,e072d33a,92994444,27c90056,5ab92363,0cd49ba5,0a457c22) Z8(239a43d0,bd6ac569,76e5ec3c,69f53efc,a7ebb12e,0caf2808,c0833015,e7a6cf90) Z8(2e7623fa,fe89590f,b553a459,50993e96,761acc15,5f6fe436,817c1b8a,f9aad29d) Z8(b8be4cc8,9468017e,67ffc46a,de2b462e,19a9e4ad,3a2371fa,7f3e659f,c0779364) Z8(5d60ee69,3ce83591,aaca1311,5f34dbc3,019fbcea,76e52e5a,aaaab777,003ffffe) },{ Z8(9bedac36,43075603,4bb8bf7f,1ea43d28,154f9e79,c51923d0,a5a00164,8d686a29) Z8(649d74e8,5d5cc7d9,6e986087,90389910,daa6a9a2,37da4ec8,d6351b74,ab869941) Z8(96516bdf,a8a2b71d,09f324e6,0dfc688d,7dc2b99f,8176b932,d5d53190,5ca44af3) Z8(06931603,e65496e9,8d269b5f,de7baf5b,b8c330ac,87a6ffa7,628d559e,916374b4) Z8(9a3ac382,f44dfeb1,febf70cf,401fdd32,66dc98a5,85757b7e,45a915a1,a4eb4b42) Z8(3fd4fc68,ef18a159,f975996d,158185b5,b8bc74e3,645e9bac,944515c3,76a76402) Z8(87dc6843,39cab1ee,297d2d77,4694b2d9,9aa8b29b,0bb2f763,405b73d6,642a741c) Z8(f2ee1d87,8a6d93e4,1b2e9ae3,06409eef,e63dbbee,a1b6db59,ae8fc52d,99203cc2) Z8(56a8437a,4604d946,5f8340bb,3f01e677,da2cc547,fbeb7bc7,5e54d5c5,64227064) Z8(f709e2f7,c79d77a5,d5cacaea,4df0d3c7,13e9f587,84b7dc60,81258b44,dd551780) Z8(e57682ea,5ac9e292,3e1d5210,25193aea,2bf9cc03,0a4a1daf,a7e38aac,a6890ea3) Z8(af9d01f3,944cb339,cc4a248d,2e2bf769,fbff8a90,2fa2e20a,9e2a2a72,3bfee575) Z8(ec6dbbc5,31f1fecf,813ced72,65709531,72d05b30,d4d4506f,cdd85c10,0d03883b) Z8(0562becc,a57ffeb5,897d5508,ed6fc4c6,ecd9f279,f73020e7,97dd9372,1338279e) Z8(07b0cbb1,4712c611,84c13ae1,67a9377c,fd9b98ec,a19e148d,f0406b86,5b9a202b) Z8(39aaef44,4d58fbf1,c4aa0ac1,4ee6d3d1,0fe0de91,230b2353,c47d28b1,7c68126f) Z8(a99a8d6d,ea07c22b,7ea6d959,e21904e9,35b13873,3c7b60c1,3dd3db79,891139d5) Z8(2d83ee26,ec67783a,ee23880b,e8f2409f,ab02251c,a5ca6ade,5556eeee,007ffff5) },{ Z8(4ba337dd,2c84cf1e,10eb2839,c33dd7c4,ebc43e3b,53e53828,cde9d09c,190654af) Z8(978ceca8,3ee0f584,c4e567ff,96dbf230,e5096eff,c19cb26d,b0f8d900,ceb877c8) Z8(2deb188a,359d6340,40d651e9,87f79203,4993d399,e170b48f,28ae712f,eae4743c) Z8(82f4e87c,e180b305,bfb449d4,d0b80a68,19a9b1ad,d6a333a3,ffe6f933,a601497e) Z8(51044de6,d028e9e5,12329400,da647a36,e34520a3,789c9d86,4ded2f71,333c1b25) Z8(40fd461b,9d57015c,8cc55d88,d9b25dcd,a4517127,2d0a24bb,df317366,58e42916) Z8(e8059189,9abf7e95,7a548854,34e8c574,437ddff2,d15b1dcd,90cd22fd,5613bb20) Z8(c495962a,23e7136d,90a61ccd,4397b6ac,039dd1d8,a79ca9da,86407e47,05dd44e4) Z8(9c0b0539,34c6d856,392f05cb,c61a881e,1d77ea22,90bd6222,bc065656,61f3b1a5) Z8(9c80c546,422affb2,e9bf8115,7105555b,347bd856,e28870bf,d775a863,b6d27de7) Z8(6b8078c4,9425acd4,9713191a,f59cc5c9,7eef1c39,b96712d5,9d3d3138,6600aeab) Z8(9013cdf3,da8ba674,1f3926f0,04096d05,a51a892f,2ca79b29,31161fb1,df6fc111) Z8(57d002c8,443264c8,d39ff304,9adb5c8c,16ec2085,6ca3ba0b,1f4cac86,f0536d3f) Z8(6bed9b5c,609c7a5a,ae25519f,aec4da62,627a7277,feb6de1c,fc1dae44,a80bfef4) Z8(0c09028d,57b3dba4,3aafff35,317c6588,469f17bf,f92cb860,21b7659b,d7b76314) Z8(029d5f04,df5b5676,39d6a99f,a80ca45e,4d42e4ae,00794eaa,d4aec58e,3e86e62b) Z8(00cc16e9,13ea12ff,30aeee8c,0e650304,02c3837b,90537f6e,dc05eaab,11f9f434) Z8(13a47a91,1cbb4c1a,a60ce5c4,8de69489,b3ea592d,84b1adb7,000c2661,00bfffdc) },{ Z8(597cfe73,379da73b,7161b809,3a1ff32e,e0ad98c5,81edea8d,261fbdd3,0babf3b7) Z8(18bda01a,4a06c9b0,821cb75c,1c5fe7c0,cee30ac5,e4608bee,304a7202,6a9c2057) Z8(8c18e53b,1a526cd1,6bc9dd0c,9a576c17,e106a689,7f4b6e46,203d8270,55926b22) Z8(3184a312,b7e286f2,de6f380d,e8e62ba0,86a3a22b,5711d770,12f1e361,01320723) Z8(9e96bccc,e83db15e,1d8edd1c,3b58402a,ad2a9828,a333325b,40d9261c,a27169a3) Z8(3b4b20e2,d9c2829f,1c5d63fb,c86869cf,2b028aaf,7bfb9efa,3da1e364,0856adf9) Z8(0743fcea,2a294770,94fde202,4bdd8012,615c2eed,6cf3ce5c,47596024,ca0119af) Z8(0a327790,211106ce,5018c972,263b2d2e,d9e5b140,35372f36,fba6dba9,0a3c54e6) Z8(5a9ef78e,eb194e74,fae531d6,bb6d6e0b,1af8cc3e,07e2cf6d,9487ea80,65a53ff2) Z8(21fc3fc3,0f0dd7c1,81583f10,b0f0cd49,cc9d442d,ac5a5c34,632bdc8b,4c18f2e8) Z8(6d32d099,b8775468,f04bccfe,21089cba,5f926a97,88d187b9,cd63c70d,8422b529) Z8(7b30cc41,223ce80e,9e17a8ba,04efb441,5712e797,be91d30c,2bd45592,bbe7680b) Z8(85473f30,f5ee39d0,2113fa09,4d949394,cc27dff4,68231593,e1eea31c,1dbc2268) Z8(54558210,39fb69f4,7ae4394e,410db23b,5770748e,0d8d2ec4,7e81c1b2,4ea62293) Z8(3af5c0b4,9a115f45,ec11d7b4,2d6732a5,5ed283bc,d6e151bb,39ce0b47,f92cf817) Z8(cd97455b,5b5bc45c,81eea5ec,0c132116,1e51bd83,4346f7fe,d429a60f,1191d908) Z8(800f56c0,471a535c,67be3ae1,d89ebbe4,6126f5a9,d62450d6,f625cdfb,6d688680) Z8(2682bef6,892248ad,eb9bc957,167c18ba,6b6d4f7e,4bb12afb,aaddddb9,00ffffaa) },{ Z8(fbb161b1,b0d88060,50cb27fc,5ae76d53,34d9cdb9,e1ae7dc7,dd7263f0,b43684d6) Z8(a0cc7fd2,319fd4a6,ca8511e6,deb9dad5,71f93e35,bc65973b,cc988c26,13794bd9) Z8(f4bef158,06b5bf8a,4be5aeff,ffc2a83b,1c1bc001,1ddd065c,59700d73,afbe1c8a) Z8(b6d8a5e8,483fff54,1f1ae1fc,84d4de8f,59c38a2c,d0c4ae5f,005ad885,5ceed779) Z8(70e5491b,64baeff9,df2076dd,f8e27954,8479a34e,bfca5a94,9a8a53bf,f591c7f7) Z8(59be928c,f446cd15,a10df36c,1634c942,004243c6,c937b8ec,9b50888a,58ba94a9) Z8(32360941,78a576b2,28cc9148,fd3cc2fa,5dbc8c69,ec3aefab,30c720be,36cd5192) Z8(ded1dde7,1a083b32,1efc5044,c2ac7d7f,11409098,e5a2be84,e648f509,82169dae) Z8(711193dd,d2fc15fd,cb664dc6,145be7b5,7e0b5455,400ff96f,8ac04539,d0ead211) Z8(e1bf3403,2dcebb29,6100902c,e88dd068,59e1eec5,28c7f787,4e134ca9,1ea743e5) Z8(d4fc04d5,b1a61bb4,30eec069,de9b1f33,977721dd,619b6b8d,6aed6049,6c3074dd) Z8(988b5b2d,0f495cd9,c883dda1,0baaafb2,03e88aab,d0f5c4e7,d29b5a7e,7be81e16) Z8(1f9fbac7,cbe3a562,cd046c9c,3abbdac1,4327855d,65928de4,73739a86,e45a53cd) Z8(63f0e93d,c69a9bed,a977cc16,77a131dc,076676ff,3dd80a59,ea9d8fbe,26528b0b) Z8(dc29c5ae,f99599a4,bb355c76,2682e045,4745e126,5c9f1839,a0e75bbb,284e400d) Z8(59ee623b,4d501f3a,819aecc9,fb53b338,b1fe043d,157e0c67,6d2bb5b0,586f9859) Z8(ec6453f4,80cf258f,904dc9eb,706af9d2,a67e846f,2eb0dad9,6dd89d52,0b0bfd53) Z8(37af3ca8,05728e6c,73bb5b5d,23a27b81,70ba3778,f34dd408,55f194a6,013fff59) },{ Z8(fd10d3e8,38481fc6,511cf624,873c413f,d182aaac,95c8ef13,88afab4f,94671d5b) Z8(f0f2fdc9,c8f2705d,a4bd4f9a,7baa8f29,ea8edd6c,a45879f5,94e28846,5686c6cf) Z8(7587b9ad,557255c9,8c8486c4,95938901,49ba4a9c,61622fc5,836ef927,f28b7918) Z8(2472be05,a653a100,6063b2db,a2ca6bd3,d49d21cd,6cf700b0,dca9400f,31be1c3b) Z8(3e9516b1,32eb3e21,bb096877,a17db57a,475f4a56,92b2d8e0,9573179d,740dea57) Z8(83e7b98e,d5f9ffec,83f1e256,c6399eea,31ede81b,3a7fed5f,068c1e15,caddaced) Z8(9ce3b566,02dabfab,c6a21c8b,d2a18f66,2f04ab39,184c6f50,b1c5cc66,6fbfc0f9) Z8(5e693776,df42bd4f,399bf17a,41d745c0,f605656d,a61de96a,f7db0137,7e4b597a) Z8(48e36a01,0a35d984,47e7e4cd,647b9219,6a51e59a,484a71f2,3f6a4f3f,eb58c969) Z8(f8d1d9ee,3e2fab62,c66a2ed2,231878cf,9adcbf3e,9f205f84,f6bddf45,0ff184af) Z8(d37aa099,9c5e6b26,992735ba,280cb451,d2c50437,49775b41,6d6f710e,6c157c6c) Z8(97f35aed,9ea98724,6e07ae2c,005cedd5,ee3f607e,70cd801a,67731644,b3db2bb8) Z8(65619d3f,33dc763a,371c01ea,db4f972d,9431546b,01992e40,8a754610,7bda23d6) Z8(5c2259ba,93b27323,050bfbb4,84a37025,27158537,7f81d867,4c58b5c7,5c6d38dc) Z8(df9180a4,2a756324,c5bb8cf1,2ede8624,9d72ea85,79f21f43,d7850047,65326389) Z8(9079f6a5,febc831f,19898b99,f4aa7989,9d954b47,0b60183f,08ef2aa6,4390605f) Z8(4d558e16,6d4934de,67e6cc80,6b11e270,6880033c,39898cad,14990381,390de9a0) 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ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void _arb_atan_taylor_naive(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int alternating) { ulong k; mp_ptr s, t, x1, x2, u; mp_size_t nn = xn + 1; if (N == 0) { flint_mpn_zero(y, xn); error[0] = 0; return; } if (N == 1) { flint_mpn_copyi(y, x, xn); error[0] = 0; } s = flint_malloc(sizeof(mp_limb_t) * nn); t = flint_malloc(sizeof(mp_limb_t) * nn); u = flint_malloc(sizeof(mp_limb_t) * 2 * nn); x1 = flint_malloc(sizeof(mp_limb_t) * nn); x2 = flint_malloc(sizeof(mp_limb_t) * nn); flint_mpn_zero(s, nn); flint_mpn_zero(t, nn); flint_mpn_zero(u, 2 * nn); flint_mpn_zero(x1, nn); flint_mpn_zero(x2, nn); /* x1 = x */ flint_mpn_copyi(x1 + 1, x, xn); /* x2 = x * x */ mpn_mul_n(u, x1, x1, nn); flint_mpn_copyi(x2, u + nn, nn); /* s = t = x */ flint_mpn_copyi(s, x1, nn); flint_mpn_copyi(t, x1, nn); for (k = 1; k < N; k++) { /* t = t * x2 */ mpn_mul_n(u, t, x2, nn); flint_mpn_copyi(t, u + nn, nn); /* u = t / (2k+1) */ mpn_divrem_1(u, 0, t, nn, 2 * k + 1); if (alternating & k) mpn_sub_n(s, s, u, nn); else mpn_add_n(s, s, u, nn); } flint_mpn_copyi(y, s + 1, xn); error[0] = 2; flint_free(s); flint_free(t); flint_free(u); flint_free(x1); flint_free(x2); } arb-2.8.1/arb/atan_taylor_rs.c000066400000000000000000000730731264125401100162250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* See verify_taylor.py for code to generate tables and proof of correctness */ int _arf_get_integer_mpn(mp_ptr y, mp_srcptr x, mp_size_t xn, slong exp); #define TMP_ALLOC_LIMBS(size) TMP_ALLOC((size) * sizeof(mp_limb_t)) #define ODD_RECIPROCAL_TAB_SIZE 256 #if FLINT_BITS == 64 const mp_limb_t odd_reciprocal_tab_numer[ODD_RECIPROCAL_TAB_SIZE] = { UWORD(13835020108241056725), UWORD(4611673369413685575), UWORD(2767004021648211345), UWORD(1976431444034436675), UWORD(1537224456471228525), UWORD(1257729100749186975), UWORD(1064232316018542825), UWORD(922334673882737115), UWORD(813824712249473925), UWORD(728158953065318775), UWORD(658810481344812225), UWORD(601522613401785075), UWORD(553400804329642269), UWORD(512408152157076175), UWORD(477069658904864025), UWORD(446290971233582475), UWORD(419243033583062325), UWORD(395286288806887335), UWORD(373919462384893425), UWORD(354744105339514275), UWORD(337439514835147725), UWORD(321744653680024575), UWORD(307444891294245705), UWORD(294362129962575675), UWORD(43378025254434585), UWORD(41676926224848915), UWORD(40104212027684805), UWORD(38645877044859903), UWORD(37289881359075345), UWORD(36025817584191435), UWORD(34844643237168765), UWORD(33738464086782455), UWORD(32700357499496841), UWORD(31724227424884995), UWORD(30804684600975285), UWORD(29936947006581615), UWORD(18078521432946975), UWORD(17596427528068389), UWORD(17139377462404275), UWORD(16705469172216825), UWORD(16292988451915175), UWORD(15900386320543725), UWORD(15526259583589755), UWORD(15169334075921025), UWORD(14828450164102575), UWORD(14502550160495925), UWORD(14190667361345475), UWORD(34099971069969189), UWORD(33396878882959515), UWORD(32722194461081545), UWORD(32074230214327455), UWORD(31451429627641485), UWORD(30852354777591171), UWORD(30275675249038065), UWORD(29720158271991495), UWORD(29184659924748405), UWORD(28668117271213035), UWORD(70414222249896525), UWORD(69210560331094875), UWORD(68047357636454625), UWORD(66922607923455375), UWORD(65834435436895125), UWORD(64781084469904803), UWORD(63760909911323625), UWORD(62772368672388375), UWORD(61814011898764125), UWORD(60884477885248875), UWORD(59982485620282225), UWORD(22849011931010265), UWORD(22520249169412995), UWORD(22200813010981605), UWORD(21890312129709135), UWORD(21588376789989009), UWORD(21294657377880315), UWORD(21008823050660445), UWORD(20730560493698055), UWORD(20459572774826185), UWORD(11592603279646389), UWORD(11444926804746435), UWORD(11300965461290505), UWORD(11160580797175095), UWORD(11023641155491965), UWORD(10890021262698123), UWORD(10759601846378385), UWORD(10632269280149055), UWORD(10507915253480645), UWORD(3812050066792275), UWORD(3768483780314649), UWORD(3725902042683975), UWORD(3684271852262925), UWORD(3643561666050075), UWORD(3603741319973025), UWORD(3564781954351695), UWORD(3526655944144725), UWORD(3489336833624675), UWORD(56769492397408245), UWORD(56181207502098315), UWORD(55604989989256281), UWORD(55040472324390735), UWORD(54487301748266205), UWORD(53945139541815795), UWORD(53413660334507265), UWORD(52892551453194999), UWORD(52381512308719685), UWORD(7543627748528235), UWORD(7472124167973465), UWORD(7401963377663855), UWORD(7333107904383261), UWORD(7265521656416595), UWORD(7199169860467585), UWORD(7134019002001815), UWORD(7070036768800005), UWORD(827619730851221), UWORD(820327927055175), UWORD(813163491011025), UWORD(806123114465475), UWORD(799203602753325), UWORD(792401869963935), UWORD(785714934352425), UWORD(779139913981275), UWORD(1317621181161285), UWORD(1306776562386295), UWORD(1296108998611713), UWORD(1285614188906355), UWORD(1275287970521565), UWORD(1265126313385935), UWORD(1255125314861145), UWORD(1245281194744587), UWORD(30567046059275355), UWORD(30331007093566665), UWORD(30098585583271135), UWORD(29869699000888845), UWORD(29644267310316099), UWORD(29422212873534705), UWORD(29203460361463815), UWORD(28987936668759285), UWORD(438859621842675), UWORD(435667915502001), UWORD(432522298783575), UWORD(429421780512725), UWORD(426365397733275), UWORD(423352214710425), UWORD(420381321975615), UWORD(417451835411325), UWORD(22634811266652585), UWORD(22479245553479715), UWORD(22325803604309205), UWORD(22174442223941007), UWORD(22025119380682145), UWORD(21877794167433435), UWORD(21732426764327565), UWORD(21588978402846855), UWORD(19609694213279247), UWORD(19481943762378405), UWORD(19355847038997315), UWORD(19231372138424985), UWORD(19108487971406295), UWORD(18987164238254509), UWORD(18867371403943755), UWORD(18749080674138465), UWORD(9266890993958325), UWORD(9209510863964775), UWORD(9152836950955761), UWORD(9096856296821475), UWORD(9041556258542925), UWORD(8986924498672575), UWORD(8932948976158025), UWORD(8879617937494395), UWORD(552205768818165), UWORD(548947917674695), UWORD(545728281793905), UWORD(542546192687235), UWORD(539400997367309), UWORD(536292057901215), UWORD(533218750979145), UWORD(17071036886667995), UWORD(16974317130936165), UWORD(16878687175268919), UWORD(16784128703698785), UWORD(16690623808413555), UWORD(16598154978450045), UWORD(16506705088761615), UWORD(16416257389645113), UWORD(912010168967625), UWORD(907067024420375), UWORD(902177175232125), UWORD(897339764104875), UWORD(892553952029649), UWORD(887818917801375), UWORD(883133857549125), UWORD(29941527972993945), UWORD(29785175346503115), UWORD(29630447162884917), UWORD(29477318236978535), UWORD(29325763901569905), UWORD(29175759994144995), UWORD(29027282844047565), UWORD(28880309260027071), UWORD(1449018065980485), UWORD(1441754817529455), UWORD(1434564020434545), UWORD(1427444596015515), UWORD(1420395486899389), UWORD(1413415656496935), UWORD(1406504088494505), UWORD(592554335551395), UWORD(589684823030565), UWORD(586842968461743), UWORD(584028373888785), UWORD(581240648953755), UWORD(578479410716445), UWORD(575744283479015), UWORD(433241218467057), UWORD(431211985593675), UWORD(429201673306525), UWORD(427210018209975), UWORD(425236761774825), UWORD(423281650226435), UWORD(421344434435925), UWORD(2623079648743785), UWORD(2611183595915015), UWORD(2599394956655805), UWORD(2587712282693307), UWORD(2576134151674545), UWORD(2564659166589135), UWORD(2553285955207365), UWORD(210505107582315), UWORD(209579810406129), UWORD(208662612111135), UWORD(207753406829605), UWORD(206852090530995), UWORD(205958560982265), UWORD(205072717709223), UWORD(3779907202434825), UWORD(3763788195174975), UWORD(3747806079696525), UWORD(3731959119528675), UWORD(3716245607446449), UWORD(3700663864857575), UWORD(3685212241204725), UWORD(4501257379467765), UWORD(4482618632554855), UWORD(4464133607265969), UWORD(4445800409700195), UWORD(4427617176940685), UWORD(4409582076423615), UWORD(4391693305322505), UWORD(355589942551207), UWORD(354158997108345), UWORD(352739522170035), UWORD(351331380364965), UWORD(349934436506655), UWORD(348548557550193), UWORD(347173612549995), UWORD(6291002587483845), UWORD(6266380268159055), }; const mp_limb_t odd_reciprocal_tab_denom[ODD_RECIPROCAL_TAB_SIZE] = { UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(13835020108241056725), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(2125523237467294665), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(1319732064605129175), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(3239497251647072955), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(8097635558738100375), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(3130314634548406305), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(1796853508345190295), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(659484661555063575), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(10842973047904974795), UWORD(1576618199442401115), UWORD(1576618199442401115), UWORD(1576618199442401115), UWORD(1576618199442401115), UWORD(1576618199442401115), UWORD(1576618199442401115), UWORD(1576618199442401115), UWORD(1576618199442401115), UWORD(186214439441524725), UWORD(186214439441524725), UWORD(186214439441524725), UWORD(186214439441524725), UWORD(186214439441524725), UWORD(186214439441524725), UWORD(186214439441524725), UWORD(186214439441524725), UWORD(317546704659869685), UWORD(317546704659869685), UWORD(317546704659869685), UWORD(317546704659869685), UWORD(317546704659869685), UWORD(317546704659869685), UWORD(317546704659869685), UWORD(317546704659869685), UWORD(7855730837233766235), UWORD(7855730837233766235), UWORD(7855730837233766235), UWORD(7855730837233766235), UWORD(7855730837233766235), UWORD(7855730837233766235), UWORD(7855730837233766235), UWORD(7855730837233766235), UWORD(119808676763050275), UWORD(119808676763050275), UWORD(119808676763050275), UWORD(119808676763050275), UWORD(119808676763050275), UWORD(119808676763050275), UWORD(119808676763050275), UWORD(119808676763050275), UWORD(6541460456062597065), UWORD(6541460456062597065), UWORD(6541460456062597065), UWORD(6541460456062597065), UWORD(6541460456062597065), UWORD(6541460456062597065), UWORD(6541460456062597065), UWORD(6541460456062597065), UWORD(5980956735050170335), UWORD(5980956735050170335), UWORD(5980956735050170335), UWORD(5980956735050170335), UWORD(5980956735050170335), UWORD(5980956735050170335), UWORD(5980956735050170335), UWORD(5980956735050170335), UWORD(2974672009060622325), UWORD(2974672009060622325), UWORD(2974672009060622325), UWORD(2974672009060622325), UWORD(2974672009060622325), UWORD(2974672009060622325), UWORD(2974672009060622325), UWORD(2974672009060622325), UWORD(186093344091721605), UWORD(186093344091721605), UWORD(186093344091721605), UWORD(186093344091721605), UWORD(186093344091721605), UWORD(186093344091721605), UWORD(186093344091721605), UWORD(5991933947220466245), UWORD(5991933947220466245), UWORD(5991933947220466245), UWORD(5991933947220466245), UWORD(5991933947220466245), UWORD(5991933947220466245), UWORD(5991933947220466245), UWORD(5991933947220466245), UWORD(334707732011118375), UWORD(334707732011118375), UWORD(334707732011118375), UWORD(334707732011118375), UWORD(334707732011118375), UWORD(334707732011118375), UWORD(334707732011118375), UWORD(11407722157710693045), UWORD(11407722157710693045), UWORD(11407722157710693045), UWORD(11407722157710693045), UWORD(11407722157710693045), UWORD(11407722157710693045), UWORD(11407722157710693045), UWORD(11407722157710693045), UWORD(575260172194252545), UWORD(575260172194252545), UWORD(575260172194252545), UWORD(575260172194252545), UWORD(575260172194252545), UWORD(575260172194252545), UWORD(575260172194252545), UWORD(243539831911623345), UWORD(243539831911623345), UWORD(243539831911623345), UWORD(243539831911623345), UWORD(243539831911623345), UWORD(243539831911623345), UWORD(243539831911623345), UWORD(184127517848499225), UWORD(184127517848499225), UWORD(184127517848499225), UWORD(184127517848499225), UWORD(184127517848499225), UWORD(184127517848499225), UWORD(184127517848499225), UWORD(1151531965798521615), UWORD(1151531965798521615), UWORD(1151531965798521615), UWORD(1151531965798521615), UWORD(1151531965798521615), UWORD(1151531965798521615), UWORD(1151531965798521615), UWORD(95358813734788695), UWORD(95358813734788695), UWORD(95358813734788695), UWORD(95358813734788695), UWORD(95358813734788695), UWORD(95358813734788695), UWORD(95358813734788695), UWORD(1765216663537063275), UWORD(1765216663537063275), UWORD(1765216663537063275), UWORD(1765216663537063275), UWORD(1765216663537063275), UWORD(1765216663537063275), UWORD(1765216663537063275), UWORD(2165104799523994965), UWORD(2165104799523994965), UWORD(2165104799523994965), UWORD(2165104799523994965), UWORD(2165104799523994965), UWORD(2165104799523994965), UWORD(2165104799523994965), UWORD(176017021562847465), UWORD(176017021562847465), UWORD(176017021562847465), UWORD(176017021562847465), UWORD(176017021562847465), UWORD(176017021562847465), UWORD(176017021562847465), UWORD(3202120317029277105), UWORD(3202120317029277105), }; #else const mp_limb_t odd_reciprocal_tab_numer[ODD_RECIPROCAL_TAB_SIZE] = { UWORD(1673196525), UWORD(557732175), UWORD(334639305), UWORD(239028075), UWORD(185910725), UWORD(152108775), UWORD(128707425), UWORD(111546435), UWORD(98423325), UWORD(88062975), UWORD(79676025), UWORD(72747675), UWORD(66927861), UWORD(12806255), UWORD(11923065), UWORD(11153835), UWORD(10477845), UWORD(9879111), UWORD(9345105), UWORD(60902835), UWORD(57931965), UWORD(55237455), UWORD(52782457), UWORD(50536395), UWORD(48473685), UWORD(3267715), UWORD(3144405), UWORD(3030063), UWORD(2923745), UWORD(2824635), UWORD(6310395), UWORD(6110065), UWORD(5922063), UWORD(5745285), UWORD(5578755), UWORD(33304425), UWORD(32391975), UWORD(31528189), UWORD(30709275), UWORD(29931825), UWORD(18208955), UWORD(17770185), UWORD(17352063), UWORD(16953165), UWORD(16572195), UWORD(28280835), UWORD(27672645), UWORD(27090063), UWORD(26531505), UWORD(25995515), UWORD(1157205), UWORD(1134735), UWORD(1113121), UWORD(1092315), UWORD(1442445), UWORD(1416455), UWORD(1391385), UWORD(1367187), UWORD(590359), UWORD(580437), UWORD(570843), UWORD(561561), UWORD(2146173), UWORD(2112375), UWORD(2079625), UWORD(2047875), UWORD(2570805), UWORD(2532719), UWORD(2495745), UWORD(2459835), UWORD(1016015), UWORD(1001805), UWORD(987987), UWORD(974545), UWORD(3580965), UWORD(3533535), UWORD(3487345), UWORD(3442347), UWORD(4172637), UWORD(4120151), UWORD(4068969), UWORD(4019043), UWORD(1608711), UWORD(1589445), UWORD(1570635), UWORD(1552265), UWORD(5544525), UWORD(5481159), UWORD(5419225), UWORD(5358675), UWORD(6330885), UWORD(6261695), UWORD(6194001), UWORD(6127755), UWORD(2396095), UWORD(2371005), UWORD(2346435), UWORD(2322369), UWORD(8119797), UWORD(8038191), UWORD(7958209), UWORD(7879803), UWORD(9128493), UWORD(9040295), UWORD(8953785), UWORD(8868915), UWORD(3405815), UWORD(3374133), UWORD(3343035), UWORD(3312505), UWORD(11389725), UWORD(11287575), UWORD(11187241), UWORD(11088675), UWORD(12648405), UWORD(12538895), UWORD(12431265), UWORD(12325467), UWORD(4665519), UWORD(4626477), UWORD(4588083), UWORD(4550321), UWORD(15437253), UWORD(15312255), UWORD(15189265), UWORD(15068235), UWORD(16973565), UWORD(16840439), UWORD(16709385), UWORD(16580355), UWORD(6202855), UWORD(6155685), UWORD(6109227), UWORD(6063465), UWORD(73983), UWORD(73437), UWORD(72899), UWORD(77283), UWORD(76725), UWORD(76175), UWORD(80655), UWORD(80085), UWORD(79523), UWORD(84099), UWORD(83517), UWORD(82943), UWORD(87615), UWORD(87021), UWORD(86435), UWORD(91203), UWORD(90597), UWORD(89999), UWORD(94863), UWORD(94245), UWORD(93635), UWORD(98595), UWORD(97965), UWORD(97343), UWORD(102399), UWORD(101757), UWORD(101123), UWORD(106275), UWORD(105621), UWORD(104975), UWORD(110223), UWORD(109557), UWORD(108899), UWORD(114243), UWORD(113565), UWORD(112895), UWORD(118335), UWORD(117645), UWORD(116963), UWORD(122499), UWORD(121797), UWORD(121103), UWORD(126735), UWORD(126021), UWORD(125315), UWORD(131043), UWORD(130317), UWORD(129599), UWORD(135423), UWORD(134685), UWORD(133955), UWORD(139875), UWORD(139125), UWORD(138383), UWORD(144399), UWORD(143637), UWORD(142883), UWORD(148995), UWORD(148221), UWORD(147455), UWORD(153663), UWORD(152877), UWORD(152099), UWORD(158403), UWORD(157605), UWORD(156815), UWORD(163215), UWORD(162405), UWORD(161603), UWORD(168099), UWORD(167277), UWORD(166463), UWORD(173055), UWORD(172221), UWORD(171395), UWORD(178083), UWORD(177237), UWORD(176399), UWORD(183183), UWORD(182325), UWORD(181475), UWORD(188355), UWORD(187485), UWORD(186623), UWORD(193599), UWORD(192717), UWORD(191843), UWORD(198915), UWORD(198021), UWORD(197135), UWORD(204303), UWORD(203397), UWORD(202499), UWORD(209763), UWORD(208845), UWORD(207935), UWORD(215295), UWORD(214365), UWORD(213443), UWORD(220899), UWORD(219957), UWORD(219023), UWORD(226575), UWORD(225621), UWORD(224675), UWORD(232323), UWORD(231357), UWORD(230399), UWORD(238143), UWORD(237165), UWORD(236195), UWORD(244035), UWORD(243045), UWORD(242063), UWORD(249999), UWORD(248997), UWORD(248003), UWORD(256035), UWORD(255021), UWORD(254015), UWORD(262143), UWORD(261117), }; const mp_limb_t odd_reciprocal_tab_denom[ODD_RECIPROCAL_TAB_SIZE] = { UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(1673196525), UWORD(345768885), UWORD(345768885), UWORD(345768885), UWORD(345768885), UWORD(345768885), UWORD(345768885), UWORD(2375210565), UWORD(2375210565), UWORD(2375210565), UWORD(2375210565), UWORD(2375210565), UWORD(2375210565), UWORD(166653465), UWORD(166653465), UWORD(166653465), UWORD(166653465), UWORD(166653465), UWORD(384934095), UWORD(384934095), UWORD(384934095), UWORD(384934095), UWORD(384934095), UWORD(2364614175), UWORD(2364614175), UWORD(2364614175), UWORD(2364614175), UWORD(2364614175), UWORD(1474925355), UWORD(1474925355), UWORD(1474925355), UWORD(1474925355), UWORD(1474925355), UWORD(2573555985), UWORD(2573555985), UWORD(2573555985), UWORD(2573555985), UWORD(2573555985), UWORD(116877705), UWORD(116877705), UWORD(116877705), UWORD(116877705), UWORD(157226505), UWORD(157226505), UWORD(157226505), UWORD(157226505), UWORD(69072003), UWORD(69072003), UWORD(69072003), UWORD(69072003), UWORD(268271625), UWORD(268271625), UWORD(268271625), UWORD(268271625), UWORD(341917065), UWORD(341917065), UWORD(341917065), UWORD(341917065), UWORD(143258115), UWORD(143258115), UWORD(143258115), UWORD(143258115), UWORD(533563785), UWORD(533563785), UWORD(533563785), UWORD(533563785), UWORD(655104009), UWORD(655104009), UWORD(655104009), UWORD(655104009), UWORD(265437315), UWORD(265437315), UWORD(265437315), UWORD(265437315), UWORD(959202825), UWORD(959202825), UWORD(959202825), UWORD(959202825), UWORD(1145890185), UWORD(1145890185), UWORD(1145890185), UWORD(1145890185), UWORD(452861955), UWORD(452861955), UWORD(452861955), UWORD(452861955), UWORD(1599600009), UWORD(1599600009), UWORD(1599600009), UWORD(1599600009), UWORD(1871341065), UWORD(1871341065), UWORD(1871341065), UWORD(1871341065), UWORD(725438595), UWORD(725438595), UWORD(725438595), UWORD(725438595), UWORD(2517129225), UWORD(2517129225), UWORD(2517129225), UWORD(2517129225), UWORD(2896484745), UWORD(2896484745), UWORD(2896484745), UWORD(2896484745), UWORD(1105728003), UWORD(1105728003), UWORD(1105728003), UWORD(1105728003), UWORD(3782126985), UWORD(3782126985), UWORD(3782126985), UWORD(3782126985), UWORD(4294311945), UWORD(4294311945), UWORD(4294311945), UWORD(4294311945), UWORD(1618945155), UWORD(1618945155), UWORD(1618945155), UWORD(1618945155), UWORD(19901427), UWORD(19901427), UWORD(19901427), UWORD(21252825), UWORD(21252825), UWORD(21252825), UWORD(22664055), UWORD(22664055), UWORD(22664055), UWORD(24136413), UWORD(24136413), UWORD(24136413), UWORD(25671195), UWORD(25671195), UWORD(25671195), UWORD(27269697), UWORD(27269697), UWORD(27269697), UWORD(28933215), UWORD(28933215), UWORD(28933215), UWORD(30663045), UWORD(30663045), UWORD(30663045), UWORD(32460483), UWORD(32460483), UWORD(32460483), UWORD(34326825), UWORD(34326825), UWORD(34326825), UWORD(36263367), UWORD(36263367), UWORD(36263367), UWORD(38271405), UWORD(38271405), UWORD(38271405), UWORD(40352235), UWORD(40352235), UWORD(40352235), UWORD(42507153), UWORD(42507153), UWORD(42507153), UWORD(44737455), UWORD(44737455), UWORD(44737455), UWORD(47044437), UWORD(47044437), UWORD(47044437), UWORD(49429395), UWORD(49429395), UWORD(49429395), UWORD(51893625), UWORD(51893625), UWORD(51893625), UWORD(54438423), UWORD(54438423), UWORD(54438423), UWORD(57065085), UWORD(57065085), UWORD(57065085), UWORD(59774907), UWORD(59774907), UWORD(59774907), UWORD(62569185), UWORD(62569185), UWORD(62569185), UWORD(65449215), UWORD(65449215), UWORD(65449215), UWORD(68416293), UWORD(68416293), UWORD(68416293), UWORD(71471715), UWORD(71471715), UWORD(71471715), UWORD(74616777), UWORD(74616777), UWORD(74616777), UWORD(77852775), UWORD(77852775), UWORD(77852775), UWORD(81181005), UWORD(81181005), UWORD(81181005), UWORD(84602763), UWORD(84602763), UWORD(84602763), UWORD(88119345), UWORD(88119345), UWORD(88119345), UWORD(91732047), UWORD(91732047), UWORD(91732047), UWORD(95442165), UWORD(95442165), UWORD(95442165), UWORD(99250995), UWORD(99250995), UWORD(99250995), UWORD(103159833), UWORD(103159833), UWORD(103159833), UWORD(107169975), UWORD(107169975), UWORD(107169975), UWORD(111282717), UWORD(111282717), UWORD(111282717), UWORD(115499355), UWORD(115499355), UWORD(115499355), UWORD(119821185), UWORD(119821185), UWORD(119821185), UWORD(124249503), UWORD(124249503), UWORD(124249503), UWORD(128785605), UWORD(128785605), UWORD(128785605), UWORD(133430787), UWORD(133430787), }; #endif void _arb_atan_taylor_rs(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int alternating) { mp_ptr s, t, xpow; mp_limb_t new_denom, old_denom, c; slong power, k, m; TMP_INIT; TMP_START; if (N >= ODD_RECIPROCAL_TAB_SIZE) { flint_printf("_arb_atan_taylor_rs: N too large!\n"); abort(); } if (N <= 2) { if (N == 0) { flint_mpn_zero(y, xn); error[0] = 0; } else if (N == 1) { flint_mpn_copyi(y, x, xn); error[0] = 0; } else { t = TMP_ALLOC_LIMBS(3 * xn); /* x * (1 - x^2 / 3) */ /* higher index ---> */ /* t = | | x^2 (lo) | x^2 (hi) | */ mpn_sqr(t + xn, x, xn); /* t = | x^3 (lo) | x^3 (hi) | x^2 (hi) | */ mpn_mul_n(t, t + 2 * xn, x, xn); /* y = x - x^3 / 3 */ mpn_divrem_1(t, 0, t + xn, xn, 3); if (alternating) mpn_sub_n(y, x, t, xn); else mpn_add_n(y, x, t, xn); error[0] = 3; } } else { /* Choose m ~= sqrt(num_terms) (m must be even, >= 2) */ m = 2; while (m * m < N) m += 2; /* todo: merge allocations */ xpow = TMP_ALLOC_LIMBS((m + 1) * xn); s = TMP_ALLOC_LIMBS(xn + 2); t = TMP_ALLOC_LIMBS(2 * xn + 2); /* todo: 1 limb too much? */ /* higher index ---> */ /* | ---xn--- | */ /* xpow = | | (x^2)^m | (x^2)^(m-1) | ... | (x^2)^2 | x^2 | */ #define XPOW_WRITE(__k) (xpow + (m - (__k)) * xn) #define XPOW_READ(__k) (xpow + (m - (__k) + 1) * xn) mpn_sqr(XPOW_WRITE(1), x, xn); mpn_sqr(XPOW_WRITE(2), XPOW_READ(1), xn); for (k = 4; k <= m; k += 2) { mpn_mul_n(XPOW_WRITE(k - 1), XPOW_READ(k / 2), XPOW_READ(k / 2 - 1), xn); mpn_sqr(XPOW_WRITE(k), XPOW_READ(k / 2), xn); } flint_mpn_zero(s, xn + 1); /* todo: skip one nonscalar multiplication (use x^m) when starting on x^0 */ power = (N - 1) % m; for (k = N - 1; k >= 0; k--) { c = odd_reciprocal_tab_numer[k]; new_denom = odd_reciprocal_tab_denom[k]; old_denom = odd_reciprocal_tab_denom[k+1]; /* change denominators */ if (new_denom != old_denom && k < N - 1) { /* hack when s is negative: add 1 to get a positive number */ if (alternating && (k % 2 == 0)) s[xn] += old_denom; /* multiply by new denominator */ s[xn + 1] = mpn_mul_1(s, s, xn + 1, new_denom); /* divide by old denominator */ mpn_divrem_1(s, 0, s, xn + 2, old_denom); if (s[xn + 1] != 0) { flint_printf("bad division!\n"); abort(); } /* subtract 1 */ if (alternating && (k % 2 == 0)) s[xn] -= new_denom; } if (power == 0) { /* sub/add c * x^0 -- only top limb is affected */ if (alternating & k) s[xn] -= c; else s[xn] += c; /* Outer polynomial evaluation: multiply by (x^2)^m */ if (k != 0) { mpn_mul(t, s, xn + 1, XPOW_READ(m), xn); flint_mpn_copyi(s, t + xn, xn + 1); } power = m - 1; } else { if (alternating & k) s[xn] -= mpn_submul_1(s, XPOW_READ(power), xn, c); else s[xn] += mpn_addmul_1(s, XPOW_READ(power), xn, c); power--; } } /* finally divide by denominator and multiply by x */ mpn_divrem_1(s, 0, s, xn + 1, odd_reciprocal_tab_denom[0]); mpn_mul(t, s, xn + 1, x, xn); flint_mpn_copyi(y, t + xn, xn); /* error bound (ulp) */ error[0] = 2; } TMP_END; } arb-2.8.1/arb/atanh.c000066400000000000000000000027341264125401100142730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_atanh(arb_t z, const arb_t x, slong prec) { if (arb_is_zero(x)) { arb_zero(z); } else { arb_t t; arb_init(t); arb_sub_ui(t, x, 1, prec + 4); arb_div(t, x, t, prec + 4); arb_mul_2exp_si(t, t, 1); arb_neg(t, t); arb_log1p(z, t, prec); arb_mul_2exp_si(z, z, -1); arb_clear(t); } } arb-2.8.1/arb/bell_fmpz.c000066400000000000000000000210541264125401100151460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "arith.h" #include "double_extras.h" /* \sum_{k=0}^{a-1} \frac{k^n}{k!} */ /* b = a * \frac{(a-1)^n}{(a-1)!} */ /* assumes n > 0, a >= 0 */ static void lower_bound(mag_t bound, const fmpz_t a, const fmpz_t n) { arb_t t, u; slong wp; if (fmpz_is_zero(a)) { mag_zero(bound); return; } wp = 10 + fmpz_bits(n); arb_init(t); arb_init(u); /* decreasing condition: a * (a-1)^n < a^n */ arb_set_fmpz(t, a); arb_pow_fmpz(t, t, n, wp); arb_set_fmpz(u, a); arb_sub_ui(u, u, 1, wp); arb_pow_fmpz(u, u, n, wp); arb_mul_fmpz(u, u, a, wp); if (arb_lt(u, t)) { arb_gamma_fmpz(t, a, wp); arb_div(t, u, t, wp); arb_get_mag(bound, t); } else { mag_inf(bound); } arb_clear(t); arb_clear(u); } /* b^n [ ((b+1)/b)^n ((b+2)/b)^n ] --- [ 1 + ----------- + ----------- + .... ] b! [ (b+1) (b+1)(b+2) ] */ static void upper_bound(mag_t bound, const fmpz_t b, const fmpz_t n) { arb_t t, u; slong wp; wp = 10 + 2 * fmpz_bits(n); arb_init(t); arb_init(u); /* decreasing condition: (1+1/b)^n / (b+1) < 1 */ /* geometric series factor: 1 + t^2 + t^3 + ... = 1/(1-t) */ arb_one(t); arb_div_fmpz(t, t, b, wp); arb_add_ui(t, t, 1, wp); arb_pow_fmpz(t, t, n, wp); arb_set_fmpz(u, b); arb_add_ui(u, u, 1, wp); arb_div(t, t, u, wp); arb_one(u); arb_sub(u, u, t, wp); if (arb_is_positive(u)) { arb_set_fmpz(t, b); arb_pow_fmpz(t, t, n, wp); arb_div(t, t, u, wp); arb_set_fmpz(u, b); arb_add_ui(u, u, 1, wp); arb_gamma(u, u, wp); arb_div(t, t, u, wp); arb_get_mag(bound, t); } else { mag_inf(bound); } arb_clear(t); arb_clear(u); } /* approximate; need not give a correct bound, but should be accurate so that we find near-optimal cutoffs (we compute correct bounds elsewhere) */ static void _arb_bell_mag(fmpz_t mmag, const fmpz_t n, const fmpz_t k) { if (fmpz_cmp_ui(k, 1) <= 0) { fmpz_set(mmag, k); } else if (fmpz_bits(n) < 50) { double dn, dk, z, u, lg; dn = fmpz_get_d(n); dk = fmpz_get_d(k); z = dk + 1.0; u = 1.0 / z; lg = 0.91893853320467274178 + (z-0.5)*log(z) - z; lg = lg + u * (0.08333333333333333 - 0.00277777777777777778 * (u * u) + 0.00079365079365079365079 * ((u * u) * (u * u))); u = (dn * log(dk) - lg) * 1.4426950408889634074 + 1.0; fmpz_set_d(mmag, u); } else { arb_t t, u; arf_t bound; slong prec; arb_init(t); arb_init(u); arf_init(bound); prec = 10 + 1.1 * fmpz_bits(n); arb_log_fmpz(t, k, prec); arb_mul_fmpz(t, t, n, prec); arb_set_fmpz(u, k); arb_add_ui(u, u, 1, prec); arb_lgamma(u, u, prec); arb_sub(t, t, u, prec); arb_const_log2(u, prec); arb_div(t, t, u, prec); arf_set_mag(bound, arb_radref(t)); arf_add(bound, arb_midref(t), bound, prec, ARF_RND_CEIL); arf_get_fmpz(mmag, bound, ARF_RND_CEIL); arb_clear(t); arb_clear(u); arf_clear(bound); } } void arb_bell_find_cutoffs(fmpz_t A, fmpz_t B, fmpz_t M, fmpz_t Mmag, const fmpz_t n, slong prec) { fmpz_t a, amag, b, bmag, m, mmag, w, wmag, Amag, Bmag; fmpz_init(a); fmpz_init(amag); fmpz_init(b); fmpz_init(bmag); fmpz_init(m); fmpz_init(mmag); fmpz_init(w); fmpz_init(wmag); fmpz_init(Amag); fmpz_init(Bmag); if (fmpz_bits(n) < 53 && 0) { double dn = fmpz_get_d(n); fmpz_set_d(M, dn / d_lambertw(dn)); _arb_bell_mag(Mmag, n, M); } else { /* do ternary search for M */ fmpz_zero(a); fmpz_mul_ui(b, n, 2); fmpz_zero(amag); fmpz_zero(bmag); while (_fmpz_sub_small(b, a) > 4) { fmpz_sub(m, b, a); fmpz_tdiv_q_ui(m, m, 3); fmpz_mul_2exp(w, m, 1); fmpz_add(m, a, m); fmpz_add(w, a, w); _arb_bell_mag(mmag, n, m); _arb_bell_mag(wmag, n, w); if (fmpz_cmp(mmag, wmag) < 0) { fmpz_swap(a, m); fmpz_swap(amag, mmag); } else { fmpz_swap(b, w); fmpz_swap(bmag, wmag); } } fmpz_set(M, a); fmpz_set(Mmag, amag); } /* bisect for A */ fmpz_zero(a); fmpz_zero(amag); fmpz_set(b, M); fmpz_set(bmag, Mmag); while (_fmpz_sub_small(b, a) > 4) { fmpz_sub(m, b, a); fmpz_tdiv_q_2exp(m, m, 1); fmpz_add(m, a, m); _arb_bell_mag(mmag, n, m); /* mmag < Mmag - p */ if (_fmpz_sub_small(mmag, Mmag) < -prec) { fmpz_swap(a, m); fmpz_swap(amag, mmag); } else { fmpz_swap(b, m); fmpz_swap(bmag, mmag); } } fmpz_set(A, a); fmpz_set(Amag, amag); /* bisect for B */ fmpz_set(a, M); fmpz_set(amag, Mmag); fmpz_mul_ui(b, n, 2); fmpz_zero(bmag); while (_fmpz_sub_small(b, a) > 4) { fmpz_sub(m, b, a); fmpz_tdiv_q_2exp(m, m, 1); fmpz_add(m, a, m); _arb_bell_mag(mmag, n, m); /* mmag < Mmag - p */ if (_fmpz_sub_small(mmag, Mmag) < -prec || fmpz_sgn(mmag) <= 0) { fmpz_swap(b, m); fmpz_swap(bmag, mmag); } else { fmpz_swap(a, m); fmpz_swap(amag, mmag); } } fmpz_set(B, a); fmpz_set(Bmag, amag); fmpz_clear(a); fmpz_clear(amag); fmpz_clear(b); fmpz_clear(bmag); fmpz_clear(m); fmpz_clear(mmag); fmpz_clear(w); fmpz_clear(wmag); fmpz_clear(Amag); fmpz_clear(Bmag); } void arb_bell_fmpz(arb_t res, const fmpz_t n, slong prec) { fmpz_t a, b, m, mmag, c; arb_t t; mag_t bound; if (fmpz_sgn(n) < 0) { arb_zero(res); return; } if (fmpz_fits_si(n)) { slong nn = fmpz_get_si(n); /* compute exactly if we would be computing at least half the bits of the exact number */ if (nn < 50 || prec > 0.5 * nn * log(0.7*nn / log(nn)) * 1.442695041) { fmpz_init(a); arith_bell_number(a, nn); arb_set_round_fmpz(res, a, prec); fmpz_clear(a); return; } } fmpz_init(a); fmpz_init(b); fmpz_init(m); fmpz_init(mmag); fmpz_init(c); arb_init(t); mag_init(bound); arb_bell_find_cutoffs(a, b, m, mmag, n, 1.03 * prec + fmpz_bits(n) + 2); /* cutoff: n > 2^12 * prec^2 */ fmpz_set_ui(c, prec); fmpz_mul_ui(c, c, prec); fmpz_mul_2exp(c, c, 12); if (fmpz_cmp(n, c) > 0) arb_bell_sum_taylor(res, n, a, b, mmag, prec + 2); else arb_bell_sum_bsplit(res, n, a, b, mmag, prec + 2); lower_bound(bound, a, n); arb_add_error_mag(res, bound); upper_bound(bound, b, n); arb_add_error_mag(res, bound); arb_const_e(t, prec + 2); arb_div(res, res, t, prec); fmpz_clear(a); fmpz_clear(b); fmpz_clear(m); fmpz_clear(mmag); fmpz_clear(c); arb_clear(t); mag_clear(bound); } void arb_bell_ui(arb_t res, ulong n, slong prec) { fmpz_t t; fmpz_init(t); fmpz_set_ui(t, n); arb_bell_fmpz(res, t, prec); fmpz_clear(t); } arb-2.8.1/arb/bell_sum_bsplit.c000066400000000000000000000056541264125401100163630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void bsplit(arb_t P, arb_t Q, const fmpz_t n, const fmpz_t a, const fmpz_t b, slong prec) { fmpz_t t; fmpz_init(t); fmpz_sub(t, b, a); if (fmpz_sgn(t) <= 0) { arb_zero(P); arb_one(Q); } else if (fmpz_cmp_ui(t, 20) < 0) { slong steps, k; arb_t u; arb_init(u); arb_zero(P); arb_one(Q); steps = fmpz_get_si(t); for (k = steps - 1; k >= 0; k--) { fmpz_add_ui(t, a, k); arb_set_round_fmpz(u, t, prec); arb_pow_fmpz(u, u, n, prec); arb_addmul(P, Q, u, prec); if (!fmpz_is_zero(t)) arb_mul_fmpz(Q, Q, t, prec); } arb_clear(u); } else { fmpz_t m; arb_t P1, Q2; fmpz_init(m); arb_init(P1); arb_init(Q2); fmpz_add(m, a, b); fmpz_tdiv_q_2exp(m, m, 1); bsplit(P1, Q, n, a, m, prec); bsplit(P, Q2, n, m, b, prec); arb_mul(Q, Q, Q2, prec); arb_addmul(P, P1, Q2, prec); fmpz_clear(m); arb_clear(P1); arb_clear(Q2); } fmpz_clear(t); } void arb_bell_sum_bsplit(arb_t res, const fmpz_t n, const fmpz_t a, const fmpz_t b, const fmpz_t mmag, slong prec) { if (fmpz_cmp(a, b) >= 0) { arb_zero(res); } else { slong wp; arb_t P, Q; wp = _fmpz_sub_small(b, a); wp = FLINT_BIT_COUNT(FLINT_ABS(wp)); wp = prec + fmpz_bits(n) + fmpz_bits(a) + wp; arb_init(P); arb_init(Q); bsplit(P, Q, n, a, b, wp); arb_div(res, P, Q, wp); if (!fmpz_is_zero(a)) { arb_gamma_fmpz(P, a, wp); arb_div(res, res, P, wp); } arb_set_round(res, res, prec); arb_clear(P); arb_clear(Q); } } arb-2.8.1/arb/bell_sum_taylor.c000066400000000000000000000143641264125401100163760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "arb_poly.h" /* tuning parameter */ #define RADIUS_BITS 3 void _arb_bell_sum_taylor(arb_t res, const fmpz_t n, const fmpz_t a, const fmpz_t b, const fmpz_t mmag, slong tol) { fmpz_t m, r, R, tmp; mag_t B, C, D, bound; arb_t t, u; slong wp, k, N; if (_fmpz_sub_small(b, a) < 5) { arb_bell_sum_bsplit(res, n, a, b, mmag, tol); return; } fmpz_init(m); fmpz_init(r); fmpz_init(R); fmpz_init(tmp); /* r = max(m - a, b - m) */ /* m = a + (b - a) / 2 */ fmpz_sub(r, b, a); fmpz_cdiv_q_2exp(r, r, 1); fmpz_add(m, a, r); fmpz_mul_2exp(R, r, RADIUS_BITS); mag_init(B); mag_init(C); mag_init(D); mag_init(bound); arb_init(t); arb_init(u); if (fmpz_cmp(R, m) >= 0) { mag_inf(C); mag_inf(D); } else { /* C = exp(R * |F'(m)| + (1/2) R^2 * (n/(m-R)^2 + 1/(m-R))) */ /* C = exp(R * (|F'(m)| + (1/2) R * (n/(m-R) + 1)/(m-R))) */ /* D = (1/2) R * (n/(m-R) + 1)/(m-R) */ fmpz_sub(tmp, m, R); mag_set_fmpz(D, n); mag_div_fmpz(D, D, tmp); mag_one(C); mag_add(D, D, C); mag_div_fmpz(D, D, tmp); mag_mul_fmpz(D, D, R); mag_mul_2exp_si(D, D, -1); /* C = |F'(m)| */ wp = 20 + 1.05 * fmpz_bits(n); arb_set_fmpz(t, n); arb_div_fmpz(t, t, m, wp); fmpz_add_ui(tmp, m, 1); arb_set_fmpz(u, tmp); arb_digamma(u, u, wp); arb_sub(t, t, u, wp); arb_get_mag(C, t); /* C = exp(R * (C + D)) */ mag_add(C, C, D); mag_mul_fmpz(C, C, R); mag_exp(C, C); } if (mag_cmp_2exp_si(C, tol / 4 + 2) > 0) { _arb_bell_sum_taylor(res, n, a, m, mmag, tol); _arb_bell_sum_taylor(t, n, m, b, mmag, tol); arb_add(res, res, t, 2 * tol); } else { arb_ptr mx, ser1, ser2, ser3; /* D = T(m) */ wp = 20 + 1.05 * fmpz_bits(n); arb_set_fmpz(t, m); arb_pow_fmpz(t, t, n, wp); fmpz_add_ui(tmp, m, 1); arb_gamma_fmpz(u, tmp, wp); arb_div(t, t, u, wp); arb_get_mag(D, t); /* error bound: (b-a) * C * D * B^N / (1 - B), B = r/R */ /* ((b-a) * C * D * 2) * 2^(-N*RADIUS_BITS) */ /* ((b-a) * C * D * 2) */ mag_mul(bound, C, D); mag_mul_2exp_si(bound, bound, 1); fmpz_sub(tmp, b, a); mag_mul_fmpz(bound, bound, tmp); /* N = (tol + log2((b-a)*C*D*2) - mmag) / RADIUS_BITS */ if (mmag == NULL) { /* estimate D ~= 2^mmag */ fmpz_add_ui(tmp, MAG_EXPREF(C), tol); fmpz_cdiv_q_ui(tmp, tmp, RADIUS_BITS); } else { fmpz_sub(tmp, MAG_EXPREF(bound), mmag); fmpz_add_ui(tmp, tmp, tol); fmpz_cdiv_q_ui(tmp, tmp, RADIUS_BITS); } if (fmpz_cmp_ui(tmp, 5 * tol / 4) > 0) N = 5 * tol / 4; else if (fmpz_cmp_ui(tmp, 2) < 0) N = 2; else N = fmpz_get_ui(tmp); /* multiply by 2^(-N*RADIUS_BITS) */ mag_mul_2exp_si(bound, bound, -N * RADIUS_BITS); mx = _arb_vec_init(2); ser1 = _arb_vec_init(N); ser2 = _arb_vec_init(N); ser3 = _arb_vec_init(N); /* estimate (this should work for moderate n and tol) */ wp = 1.1 * tol + 1.05 * fmpz_bits(n) + 5; /* increase precision until convergence */ while (1) { /* (m+x)^n / gamma(m+1+x) */ arb_set_fmpz(mx, m); arb_one(mx + 1); _arb_poly_log_series(ser1, mx, 2, N, wp); for (k = 0; k < N; k++) arb_mul_fmpz(ser1 + k, ser1 + k, n, wp); arb_add_ui(mx, mx, 1, wp); _arb_poly_lgamma_series(ser2, mx, 2, N, wp); _arb_vec_sub(ser1, ser1, ser2, N, wp); _arb_poly_exp_series(ser3, ser1, N, N, wp); /* t = a - m, u = b - m */ arb_set_fmpz(t, a); arb_sub_fmpz(t, t, m, wp); arb_set_fmpz(u, b); arb_sub_fmpz(u, u, m, wp); arb_power_sum_vec(ser1, t, u, N, wp); arb_zero(res); for (k = 0; k < N; k++) arb_addmul(res, ser3 + k, ser1 + k, wp); if (mmag != NULL) { if (_fmpz_sub_small(MAG_EXPREF(arb_radref(res)), mmag) <= -tol) break; } else { if (arb_rel_accuracy_bits(res) >= tol) break; } wp = 2 * wp; } /* add the series truncation bound */ arb_add_error_mag(res, bound); _arb_vec_clear(mx, 2); _arb_vec_clear(ser1, N); _arb_vec_clear(ser2, N); _arb_vec_clear(ser3, N); } mag_clear(B); mag_clear(C); mag_clear(D); mag_clear(bound); arb_clear(t); arb_clear(u); fmpz_clear(m); fmpz_clear(r); fmpz_clear(R); fmpz_clear(tmp); } void arb_bell_sum_taylor(arb_t res, const fmpz_t n, const fmpz_t a, const fmpz_t b, const fmpz_t mmag, slong prec) { _arb_bell_sum_taylor(res, n, a, b, mmag, prec + 5); } arb-2.8.1/arb/bernoulli_ui.c000066400000000000000000000033571264125401100156720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "bernoulli.h" void arb_bernoulli_ui(arb_t b, ulong n, slong prec) { if (n < bernoulli_cache_num) { arb_set_fmpq(b, bernoulli_cache + n, prec); } else { int use_frac; use_frac = (n < BERNOULLI_SMALL_NUMER_LIMIT) || (n % 2 != 0); if (!use_frac && n < UWORD_MAX / 1000) use_frac = (prec > bernoulli_global_prec(n)); if (use_frac) { fmpq_t t; fmpq_init(t); bernoulli_fmpq_ui(t, n); arb_set_fmpq(b, t, prec); fmpq_clear(t); } else { arb_bernoulli_ui_zeta(b, n, prec); } } } arb-2.8.1/arb/bernoulli_ui_zeta.c000066400000000000000000000035761264125401100167200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_zeta_inv_ui_euler_product(arb_t z, ulong s, slong prec); void arb_bernoulli_ui_zeta(arb_t b, ulong n, slong prec) { slong wp, piwp; arb_t t, u; if (n < 10 || n % 2 != 0) abort(); wp = prec + 8; piwp = wp + 2*FLINT_BIT_COUNT(n); arb_init(t); arb_init(u); /* |B_n| = 2 * n! / (2*pi)^n * zeta(n) */ arb_fac_ui(b, n, piwp); arb_const_pi(t, piwp); arb_mul_2exp_si(t, t, 1); arb_pow_ui(t, t, n, piwp); if (n > 0.7 * wp) { arb_zeta_ui_asymp(u, n, wp); arb_mul(b, b, u, wp); } else { arb_zeta_inv_ui_euler_product(u, n, wp); arb_mul(t, t, u, wp); } arb_div(b, b, t, prec); arb_mul_2exp_si(b, b, 1); if (n % 4 == 0) arb_neg(b, b); arb_clear(t); arb_clear(u); } arb-2.8.1/arb/bin.c000066400000000000000000000032721264125401100137460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_bin_ui(arb_t x, const arb_t n, ulong k, slong prec) { if (k == 0) { arb_one(x); } else if (k == 1) { arb_set_round(x, n, prec); } else { arb_t t, u; arb_init(t); arb_init(u); arb_sub_ui(t, n, k - 1, prec); arb_rising_ui(t, t, k, prec); arb_fac_ui(u, k, prec); arb_div(x, t, u, prec); arb_clear(t); arb_clear(u); } } void arb_bin_uiui(arb_t x, ulong n, ulong k, slong prec) { arb_t t; arb_init(t); arb_set_ui(t, n); arb_bin_ui(x, t, k, prec); arb_clear(t); } arb-2.8.1/arb/ceil.c000066400000000000000000000031671264125401100141150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_ceil(arb_t z, const arb_t x, slong prec) { if (!arb_is_finite(x)) { arb_indeterminate(z); } else if (arb_is_exact(x)) { arf_ceil(arb_midref(z), arb_midref(x)); mag_zero(arb_radref(z)); arb_set_round(z, z, prec); } else { arf_t a, b; arf_init(a); arf_init(b); arb_get_interval_arf(a, b, x, prec); arf_ceil(a, a); arf_ceil(b, b); arb_set_interval_arf(z, a, b, prec); arf_clear(a); arf_clear(b); } } arb-2.8.1/arb/chebyshev_t2_ui.c000066400000000000000000000036241264125401100162610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_chebyshev_t2_ui(arb_t a, arb_t b, ulong n, const arb_t x, slong prec) { int i; arb_set_round(a, x, prec); arb_one(b); if (n <= 1) { if (n == 0) arb_swap(a, b); return; } for (i = FLINT_BIT_COUNT(n - 1) - 1; i >= 0; i--) { if (((n - 1) >> i) & 1) { arb_mul(b, b, a, prec); arb_mul_2exp_si(b, b, 1); arb_sub(b, b, x, prec); arb_mul(a, a, a, prec); arb_mul_2exp_si(a, a, 1); arb_sub_ui(a, a, 1, prec); } else { arb_mul(a, a, b, prec); arb_mul_2exp_si(a, a, 1); arb_sub(a, a, x, prec); arb_mul(b, b, b, prec); arb_mul_2exp_si(b, b, 1); arb_sub_ui(b, b, 1, prec); } } } arb-2.8.1/arb/chebyshev_t_ui.c000066400000000000000000000037431264125401100162010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_chebyshev_t_ui(arb_t y, ulong n, const arb_t x, slong prec) { int i, r; if (n <= 1) { if (n == 0) arb_one(y); else arb_set_round(y, x, prec); return; } count_trailing_zeros(r, n); if ((n >> r) == 1) { arb_mul(y, x, x, prec); arb_mul_2exp_si(y, y, 1); arb_sub_ui(y, y, 1, prec); r -= 1; } else { /* we only need one value, so break out final iteration */ arb_t t, u; arb_init(t); arb_init(u); arb_chebyshev_t2_ui(t, u, (n >> (r + 1)) + 1, x, prec); arb_mul(t, t, u, prec); arb_mul_2exp_si(t, t, 1); arb_sub(y, t, x, prec); arb_clear(t); arb_clear(u); } for (i = 0; i < r; i++) { arb_mul(y, y, y, prec); arb_mul_2exp_si(y, y, 1); arb_sub_ui(y, y, 1, prec); } } arb-2.8.1/arb/chebyshev_u2_ui.c000066400000000000000000000037421264125401100162630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_chebyshev_u2_ui(arb_t a, arb_t b, ulong n, const arb_t x, slong prec) { int i; arb_t t, u; if (n == 0) { arb_one(a); arb_zero(b); return; } arb_set_round(a, x, prec); arb_mul_2exp_si(a, a, 1); arb_one(b); if (n == 1) return; arb_init(t); arb_init(u); for (i = FLINT_BIT_COUNT(n) - 2; i >= 0; i--) { arb_add(t, a, b, prec); arb_sub(u, a, b, prec); if ((n >> i) & 1) { arb_submul(b, x, a, prec); arb_mul(a, a, b, prec); arb_neg(a, a); arb_mul_2exp_si(a, a, 1); arb_mul(b, t, u, prec); } else { arb_submul(a, x, b, prec); arb_mul(b, a, b, prec); arb_mul_2exp_si(b, b, 1); arb_mul(a, t, u, prec); } } arb_clear(t); arb_clear(u); } arb-2.8.1/arb/chebyshev_u_ui.c000066400000000000000000000034211264125401100161730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_chebyshev_u_ui(arb_t y, ulong n, const arb_t x, slong prec) { arb_t a, b; if (n <= 1) { if (n == 0) { arb_one(y); } else { arb_set_round(y, x, prec); arb_mul_2exp_si(y, y, 1); } return; } arb_init(a); arb_init(b); arb_chebyshev_u2_ui(a, b, n / 2, x, prec); if (n % 2 == 0) { arb_add(y, a, b, prec); arb_sub(b, a, b, prec); arb_mul(y, y, b, prec); } else { arb_submul(b, a, x, prec); arb_mul(y, a, b, prec); arb_mul_2exp_si(y, y, 1); arb_neg(y, y); } arb_clear(a); arb_clear(b); } arb-2.8.1/arb/const_apery.c000066400000000000000000000032771264125401100155310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "hypgeom.h" void arb_const_apery_eval(arb_t s, slong prec) { hypgeom_t series; arb_t t; arb_init(t); hypgeom_init(series); fmpz_poly_set_str(series->A, "3 77 250 205"); fmpz_poly_set_str(series->B, "1 1"); fmpz_poly_set_str(series->P, "6 0 0 0 0 0 -1"); fmpz_poly_set_str(series->Q, "6 32 320 1280 2560 2560 1024"); prec += 4 + FLINT_CLOG2(prec); arb_hypgeom_infsum(s, t, series, prec, prec); arb_mul_ui(t ,t, 64, prec); arb_div(s, s, t, prec); hypgeom_clear(series); arb_clear(t); } ARB_DEF_CACHED_CONSTANT(arb_const_apery, arb_const_apery_eval) arb-2.8.1/arb/const_catalan.c000066400000000000000000000032661264125401100160120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "hypgeom.h" void arb_const_catalan_eval(arb_t s, slong prec) { hypgeom_t series; arb_t t; arb_init(t); hypgeom_init(series); fmpz_poly_set_str(series->A, "3 19 56 40"); fmpz_poly_set_str(series->B, "1 1"); fmpz_poly_set_str(series->P, "5 0 0 0 32 -64"); fmpz_poly_set_str(series->Q, "5 9 96 352 512 256"); prec += FLINT_CLOG2(prec); arb_hypgeom_infsum(s, t, series, prec, prec); arb_mul_ui(t, t, 18, prec); arb_div(s, s, t, prec); hypgeom_clear(series); arb_clear(t); } ARB_DEF_CACHED_CONSTANT(arb_const_catalan, arb_const_catalan_eval) arb-2.8.1/arb/const_e.c000066400000000000000000000031451264125401100146270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "hypgeom.h" void arb_const_e_eval(arb_t s, slong prec) { hypgeom_t series; arb_t t; arb_init(t); hypgeom_init(series); fmpz_poly_set_str(series->A, "1 1"); fmpz_poly_set_str(series->B, "1 1"); fmpz_poly_set_str(series->P, "1 1"); fmpz_poly_set_str(series->Q, "2 0 1"); prec += FLINT_CLOG2(prec); arb_hypgeom_infsum(s, t, series, prec, prec); arb_div(s, s, t, prec); hypgeom_clear(series); arb_clear(t); } ARB_DEF_CACHED_CONSTANT(arb_const_e, arb_const_e_eval) arb-2.8.1/arb/const_euler.c000066400000000000000000000176431264125401100155270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "hypgeom.h" typedef struct { arb_t P; arb_t Q; arb_t T; arb_t C; arb_t D; arb_t V; } euler_bsplit_struct; typedef euler_bsplit_struct euler_bsplit_t[1]; static void euler_bsplit_init(euler_bsplit_t s) { arb_init(s->P); arb_init(s->Q); arb_init(s->T); arb_init(s->C); arb_init(s->D); arb_init(s->V); } static void euler_bsplit_clear(euler_bsplit_t s) { arb_clear(s->P); arb_clear(s->Q); arb_clear(s->T); arb_clear(s->C); arb_clear(s->D); arb_clear(s->V); } static void euler_bsplit_1_merge(euler_bsplit_t s, euler_bsplit_t L, euler_bsplit_t R, slong wp, int cont) { arb_t t, u, v; arb_init(t); arb_init(u); arb_init(v); if (cont) arb_mul(s->P, L->P, R->P, wp); arb_mul(s->Q, L->Q, R->Q, wp); arb_mul(s->D, L->D, R->D, wp); /* T = LP RT + RQ LT*/ arb_mul(t, L->P, R->T, wp); arb_mul(v, R->Q, L->T, wp); arb_add(s->T, t, v, wp); /* C = LC RD + RC LD */ if (cont) { arb_mul(s->C, L->C, R->D, wp); arb_addmul(s->C, R->C, L->D, wp); } /* V = RD (RQ LV + LC LP RT) + LD LP RV */ arb_mul(u, L->P, R->V, wp); arb_mul(u, u, L->D, wp); arb_mul(v, R->Q, L->V, wp); arb_addmul(v, t, L->C, wp); arb_mul(v, v, R->D, wp); arb_add(s->V, u, v, wp); arb_clear(t); arb_clear(u); arb_clear(v); } static void euler_bsplit_1(euler_bsplit_t s, slong n1, slong n2, slong N, slong wp, int cont) { if (n2 - n1 == 1) { arb_set_si(s->P, N); /* p = N^2 */ arb_mul(s->P, s->P, s->P, wp); arb_set_si(s->Q, n1 + 1); /* q = (k + 1)^2 */ arb_mul(s->Q, s->Q, s->Q, wp); arb_set_si(s->C, 1); arb_set_si(s->D, n1 + 1); arb_set(s->T, s->P); arb_set(s->V, s->P); } else { euler_bsplit_t L, R; slong m = (n1 + n2) / 2; euler_bsplit_init(L); euler_bsplit_init(R); euler_bsplit_1(L, n1, m, N, wp, 1); euler_bsplit_1(R, m, n2, N, wp, 1); euler_bsplit_1_merge(s, L, R, wp, cont); euler_bsplit_clear(L); euler_bsplit_clear(R); } } static void euler_bsplit_2(arb_t P, arb_t Q, arb_t T, slong n1, slong n2, slong N, slong wp, int cont) { if (n2 - n1 == 1) { if (n1 == 0) { arb_set_si(P, 1); arb_set_si(Q, 4 * N); arb_set_si(T, 1); } else { arb_si_pow_ui(P, 1 - 2*n1, 3, wp); arb_neg(P, P); arb_set_si(Q, 32 * n1); arb_mul_ui(Q, Q, N, wp); arb_mul_ui(Q, Q, N, wp); } arb_set(T, P); } else { arb_t P2, Q2, T2; slong m = (n1 + n2) / 2; arb_init(P2); arb_init(Q2); arb_init(T2); euler_bsplit_2(P, Q, T, n1, m, N, wp, 1); euler_bsplit_2(P2, Q2, T2, m, n2, N, wp, 1); arb_mul(T, T, Q2, wp); arb_mul(T2, T2, P, wp); arb_add(T, T, T2, wp); if (cont) arb_mul(P, P, P2, wp); arb_mul(Q, Q, Q2, wp); arb_clear(P2); arb_clear(Q2); arb_clear(T2); } } static void atanh_bsplit(arb_t s, ulong c, slong a, slong prec) { arb_t t; hypgeom_t series; hypgeom_init(series); arb_init(t); fmpz_poly_set_ui(series->A, 1); fmpz_poly_set_coeff_ui(series->B, 0, 1); fmpz_poly_set_coeff_ui(series->B, 1, 2); fmpz_poly_set_ui(series->P, 1); fmpz_poly_set_ui(series->Q, c * c); arb_hypgeom_infsum(s, t, series, prec, prec); arb_mul_si(s, s, a, prec); arb_mul_ui(t, t, c, prec); arb_div(s, s, t, prec); arb_clear(t); hypgeom_clear(series); } static ulong next_smooth(ulong n) { ulong t, k; for (k = n; ; k++) { t = k; while (t % 2 == 0) t /= 2; while (t % 3 == 0) t /= 3; while (t % 5 == 0) t /= 5; if (t == 1) return k; } } static void arb_log_ui_smooth(arb_t s, ulong n, slong prec) { ulong m, i, j, k; arb_t t; m = n; i = j = k = 0; while (m % 2 == 0) { m /= 2; i++; } while (m % 3 == 0) { m /= 3; j++; } while (m % 5 == 0) { m /= 5; k++; } if (m != 1) abort(); arb_init(t); prec += FLINT_CLOG2(prec); atanh_bsplit(s, 31, 14*i + 22*j + 32*k, prec); atanh_bsplit(t, 49, 10*i + 16*j + 24*k, prec); arb_add(s, s, t, prec); atanh_bsplit(t, 161, 6*i + 10*j + 14*k, prec); arb_add(s, s, t, prec); arb_clear(t); } void arb_const_euler_eval(arb_t res, slong prec) { euler_bsplit_t sum; arb_t t, u, v, P2, T2, Q2; slong bits, wp, wp2, n, N, M; bits = prec + 10; n = 0.086643397569993163677 * bits + 1; /* log(2) / 8 */ /* round n to have many trailing zeros, speeding up arithmetic, and make it smooth to allow computing the logarithm cheaply */ if (n > 256) { int b = FLINT_BIT_COUNT(n); n = next_smooth((n >> (b-4)) + 1) << (b-4); } else { n = next_smooth(n); } /* As shown in the paper, it is sufficient to take N >= alpha n + 1 where alpha = 3/W(3/e) = 4.970625759544... */ { fmpz_t a; fmpz_init(a); fmpz_set_ui(a, n); fmpz_mul_ui(a, a, 4970626); fmpz_cdiv_q_ui(a, a, 1000000); fmpz_add_ui(a, a, 1); N = fmpz_get_ui(a); fmpz_clear(a); } M = 2 * n; wp = bits + 2 * FLINT_BIT_COUNT(n); wp2 = bits/2 + 2 * FLINT_BIT_COUNT(n); euler_bsplit_init(sum); arb_init(P2); arb_init(T2); arb_init(Q2); arb_init(t); arb_init(u); arb_init(v); /* Compute S0 = V / (Q D), I0 = 1 + T / Q */ euler_bsplit_1(sum, 0, N, n, wp, 0); /* I0 = T / Q */ arb_add(sum->T, sum->T, sum->Q, wp); /* Compute S0 / I0 = V / (D T) */ arb_mul(t, sum->T, sum->D, wp); arb_div(res, sum->V, t, wp); /* Compute K0 (actually I_0(2n) K_0(2n)) = T2 / Q2 */ euler_bsplit_2(P2, Q2, T2, 0, M, n, wp2, 0); /* Compute K0 / I^2 = Q^2 * T2 / (Q2 * T^2) */ arb_set_round(t, sum->Q, wp2); arb_mul(t, t, t, wp2); arb_mul(t, t, T2, wp2); arb_set_round(u, sum->T, wp2); arb_mul(u, u, u, wp2); arb_mul(u, u, Q2, wp2); arb_div(t, t, u, wp2); arb_sub(res, res, t, wp); /* subtract log(n) */ arb_log_ui_smooth(u, n, wp); arb_sub(res, res, u, wp); /* add error bound 24 exp(-8n) */ { mag_t b; mag_init(b); /* exp(-8) < 737690121 * 2^-41 */ mag_set_ui_2exp_si(b, 737690121, -41); mag_pow_ui(b, b, n); mag_mul_ui(b, b, 24); mag_add(arb_radref(res), arb_radref(res), b); mag_clear(b); } arb_clear(P2); arb_clear(T2); arb_clear(Q2); arb_clear(t); arb_clear(u); arb_clear(v); euler_bsplit_clear(sum); } ARB_DEF_CACHED_CONSTANT(arb_const_euler, arb_const_euler_eval) arb-2.8.1/arb/const_glaisher.c000066400000000000000000000033611264125401100162010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "acb_poly.h" void arb_const_glaisher_eval(arb_t y, slong prec) { acb_struct z[2]; acb_t s, a; slong wp; acb_init(z + 0); acb_init(z + 1); acb_init(s); acb_init(a); wp = prec + 20; /* directly evaluating at s = -1 is slightly faster than evaluating at s = 2 */ acb_set_si(s, -1); acb_one(a); _acb_poly_zeta_cpx_series(z, s, a, 0, 2, wp); arb_one(y); arb_div_ui(y, y, 12, wp); arb_sub(y, y, acb_realref(z + 1), wp); arb_exp(y, y, wp); acb_clear(z + 0); acb_clear(z + 1); acb_clear(s); acb_clear(a); } ARB_DEF_CACHED_CONSTANT(arb_const_glaisher, arb_const_glaisher_eval) arb-2.8.1/arb/const_khinchin.c000066400000000000000000000060671264125401100162040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" void arb_const_khinchin_eval_param(arb_t s, ulong N, ulong M, slong prec) { arb_t t, u, h; arb_ptr pows; slong k, n; arb_init(t); arb_init(u); arb_init(h); if (N < 2) abort(); /* if (M < 0) abort(); */ pows = _arb_vec_init(N - 2); /* sum of logarithms */ arb_zero(s); for (k = 2; k < N; k++) { arb_set_ui(t, k - 1); arb_div_ui(t, t, k, prec); arb_log(t, t, prec); arb_set_ui(u, k + 1); arb_div_ui(u, u, k, prec); arb_log(u, u, prec); arb_mul(t, t, u, prec); arb_sub(s, s, t, prec); } /* alternating harmonic numbers */ arb_one(h); /* powers */ for (k = 0; k < N - 2; k++) arb_one(pows + k); /* sum of zetas */ for (n = 1; n <= M; n++) { /* zeta(2n,N) / n */ arb_zeta_ui(t, 2 * n, prec); arb_sub_ui(t, t, 1, prec); for (k = 0; k < N - 2; k++) { arb_div_ui(pows + k, pows + k, (k + 2) * (k + 2), prec); arb_sub(t, t, pows + k, prec); } arb_div_ui(t, t, n, prec); arb_mul(t, t, h, prec); arb_add(s, s, t, prec); /* forward h by two */ arb_set_ui(u, 2 * n); arb_mul_ui(u, u, 2 * n + 1, prec); arb_inv(u, u, prec); arb_sub(h, h, u, prec); } /* error bound 1/N^(2M) */ arb_set_ui(t, N); arb_pow_ui(t, t, 2 * M, MAG_BITS); arb_inv(t, t, MAG_BITS); arb_add_error(s, t); arb_log_ui(t, 2, prec); arb_div(s, s, t, prec); arb_exp(s, s, prec); _arb_vec_clear(pows, N - 2); arb_clear(t); arb_clear(u); arb_clear(h); } void arb_const_khinchin_eval(arb_t K, slong prec) { ulong N, M; prec += 10 + 2 * FLINT_BIT_COUNT(prec); /* heuristic */ N = pow(prec, 0.35); M = (prec * 0.69314718055994530942) / (2 * log(N)); arb_const_khinchin_eval_param(K, N, M, prec); } ARB_DEF_CACHED_CONSTANT(arb_const_khinchin, arb_const_khinchin_eval) arb-2.8.1/arb/const_log10.c000066400000000000000000000037501264125401100153270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "hypgeom.h" static void atanh_bsplit(arb_t s, ulong c, slong a, slong prec) { arb_t t; hypgeom_t series; hypgeom_init(series); arb_init(t); fmpz_poly_set_ui(series->A, 1); fmpz_poly_set_coeff_ui(series->B, 0, 1); fmpz_poly_set_coeff_ui(series->B, 1, 2); fmpz_poly_set_ui(series->P, 1); fmpz_poly_set_ui(series->Q, c * c); arb_hypgeom_infsum(s, t, series, prec, prec); arb_mul_si(s, s, a, prec); arb_mul_ui(t, t, c, prec); arb_div(s, s, t, prec); arb_clear(t); hypgeom_clear(series); } void arb_const_log10_eval(arb_t s, slong prec) { arb_t t; arb_init(t); prec += FLINT_CLOG2(prec); atanh_bsplit(s, 31, 46, prec); atanh_bsplit(t, 49, 34, prec); arb_add(s, s, t, prec); atanh_bsplit(t, 161, 20, prec); arb_add(s, s, t, prec); arb_clear(t); } ARB_DEF_CACHED_CONSTANT(arb_const_log10, arb_const_log10_eval) arb-2.8.1/arb/const_log2.c000066400000000000000000000032561264125401100152510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "hypgeom.h" void arb_const_log2_eval(arb_t s, slong prec) { hypgeom_t series; arb_t t; arb_init(t); hypgeom_init(series); fmpz_poly_set_str(series->A, "1 1"); fmpz_poly_set_str(series->B, "1 1"); fmpz_poly_set_str(series->P, "2 0 -1"); fmpz_poly_set_str(series->Q, "2 4 8"); prec += FLINT_CLOG2(prec); arb_hypgeom_infsum(s, t, series, prec, prec); arb_mul_ui(s, s, 3, prec); arb_mul_2exp_si(t, t, 2); arb_div(s, s, t, prec); hypgeom_clear(series); arb_clear(t); } ARB_DEF_CACHED_CONSTANT(arb_const_log2, arb_const_log2_eval) arb-2.8.1/arb/const_log_sqrt2pi.c000066400000000000000000000025041264125401100166460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" void _arb_const_log_sqrt2pi(arb_t t, slong prec) { arb_const_pi(t, prec + 2); arb_mul_2exp_si(t, t, 1); arb_log(t, t, prec); arb_mul_2exp_si(t, t, -1); } ARB_DEF_CACHED_CONSTANT(arb_const_log_sqrt2pi, _arb_const_log_sqrt2pi) arb-2.8.1/arb/const_pi.c000066400000000000000000000034541264125401100150160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "hypgeom.h" void arb_const_pi_eval(arb_t s, slong prec) { hypgeom_t series; arb_t t, u; arb_init(t); arb_init(u); hypgeom_init(series); fmpz_poly_set_str(series->A, "2 13591409 545140134"); fmpz_poly_set_str(series->B, "1 1"); fmpz_poly_set_str(series->P, "4 5 -46 108 -72"); fmpz_poly_set_str(series->Q, "4 0 0 0 10939058860032000"); prec += FLINT_CLOG2(prec) + 5; arb_hypgeom_infsum(s, t, series, prec, prec); arb_rsqrt_ui(u, 640320, prec); arb_mul(s, s, u, prec); arb_mul_ui(t, t, 640320 / 12, prec); arb_div(s, t, s, prec); hypgeom_clear(series); arb_clear(t); arb_clear(u); } ARB_DEF_CACHED_CONSTANT(arb_const_pi, arb_const_pi_eval) arb-2.8.1/arb/const_sqrt_pi.c000066400000000000000000000023751264125401100160700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void _arb_const_sqrt_pi(arb_t t, slong prec) { arb_const_pi(t, prec + 2); arb_sqrt(t, t, prec); } ARB_DEF_CACHED_CONSTANT(arb_const_sqrt_pi, _arb_const_sqrt_pi) arb-2.8.1/arb/contains.c000066400000000000000000000051521264125401100150130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_contains(const arb_t x, const arb_t y) { arf_t t; arf_t u; arf_t xr, yr; arf_struct tmp[4]; int left_ok, right_ok; if (arb_is_exact(y)) return arb_contains_arf(x, arb_midref(y)); if (arf_is_nan(arb_midref(y))) return arf_is_nan(arb_midref(x)); arf_init(t); arf_init(u); arf_init_set_mag_shallow(xr, arb_radref(x)); arf_init_set_mag_shallow(yr, arb_radref(y)); /* fast check */ arf_sub(t, arb_midref(x), xr, 30, ARF_RND_CEIL); arf_sub(u, arb_midref(y), yr, 30, ARF_RND_FLOOR); left_ok = arf_cmp(t, u) <= 0; /* exact check */ if (!left_ok) { arf_init_set_shallow(tmp + 0, arb_midref(x)); arf_init_neg_mag_shallow(tmp + 1, arb_radref(x)); arf_init_neg_shallow(tmp + 2, arb_midref(y)); arf_init_set_mag_shallow(tmp + 3, arb_radref(y)); arf_sum(t, tmp, 4, 30, ARF_RND_DOWN); left_ok = arf_sgn(t) <= 0; } /* fast check */ arf_add(t, arb_midref(x), xr, 30, ARF_RND_FLOOR); arf_add(u, arb_midref(y), yr, 30, ARF_RND_CEIL); right_ok = (arf_cmp(t, u) >= 0); /* exact check */ if (!right_ok) { arf_init_set_shallow(tmp + 0, arb_midref(x)); arf_init_set_mag_shallow(tmp + 1, arb_radref(x)); arf_init_neg_shallow(tmp + 2, arb_midref(y)); arf_init_neg_mag_shallow(tmp + 3, arb_radref(y)); arf_sum(t, tmp, 4, 30, ARF_RND_DOWN); right_ok = arf_sgn(t) >= 0; } arf_clear(t); arf_clear(u); return left_ok && right_ok; } arb-2.8.1/arb/contains_arf.c000066400000000000000000000040461264125401100156440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_contains_arf(const arb_t x, const arf_t y) { if (arf_is_nan(y)) { return arf_is_nan(arb_midref(x)); } else if (arf_is_nan(arb_midref(x))) { return 1; } else if (arb_is_exact(x)) { return arf_equal(arb_midref(x), y); } else { arf_t t; arf_struct tmp[3]; int result; arf_init(t); /* y >= xm - xr <=> 0 >= xm - xr - y */ arf_init_set_shallow(tmp + 0, arb_midref(x)); arf_init_neg_mag_shallow(tmp + 1, arb_radref(x)); arf_init_neg_shallow(tmp + 2, y); arf_sum(t, tmp, 3, 30, ARF_RND_DOWN); result = (arf_sgn(t) <= 0); if (result) { /* y <= xm + xr <=> 0 <= xm + xr - y */ arf_init_set_mag_shallow(tmp + 1, arb_radref(x)); arf_sum(t, tmp, 3, 30, ARF_RND_DOWN); result = (arf_sgn(t) >= 0); } arf_clear(t); return result; } } arb-2.8.1/arb/contains_fmpq.c000066400000000000000000000024531264125401100160370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_contains_fmpq(const arb_t x, const fmpq_t y) { fmprb_t t; int result; fmprb_init(t); arb_get_fmprb(t, x); result = fmprb_contains_fmpq(t, y); fmprb_clear(t); return result; } arb-2.8.1/arb/contains_fmpz.c000066400000000000000000000024231264125401100160450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_contains_fmpz(const arb_t x, const fmpz_t y) { int ans; arf_t t; arf_init(t); arf_set_fmpz(t, y); ans = arb_contains_arf(x, t); arf_clear(t); return ans; } arb-2.8.1/arb/contains_int.c000066400000000000000000000035301264125401100156630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_contains_int(const arb_t x) { if (arf_is_int(arb_midref(x))) { return 1; } else if (!arb_is_finite(x)) { return arb_contains_zero(x); } else if (arb_is_exact(x)) { return 0; } else if (mag_cmp_2exp_si(arb_radref(x), -1) >= 0) /* radius >= 1/2 */ { return 1; } else { /* radius is < 1/2, so it's enough to test the two integers bracketing the midpoint */ arf_t t; int res; arf_init(t); arf_floor(t, arb_midref(x)); res = arb_contains_arf(x, t); if (!res) { arf_ceil(t, arb_midref(x)); res = arb_contains_arf(x, t); } arf_clear(t); return res; } } arb-2.8.1/arb/contains_mpfr.c000066400000000000000000000024221264125401100160340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_contains_mpfr(const arb_t x, const mpfr_t y) { int ans; arf_t t; arf_init(t); arf_set_mpfr(t, y); ans = arb_contains_arf(x, t); arf_clear(t); return ans; } arb-2.8.1/arb/contains_si.c000066400000000000000000000024101264125401100155000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_contains_si(const arb_t x, slong y) { int ans; arf_t t; arf_init(t); arf_set_si(t, y); ans = arb_contains_arf(x, t); arf_clear(t); return ans; } arb-2.8.1/arb/cot.c000066400000000000000000000023701264125401100137610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_cot(arb_t y, const arb_t x, slong prec) { arb_t u; arb_init(u); arb_sin_cos(y, u, x, prec + 4); arb_div(y, u, y, prec); arb_clear(u); } arb-2.8.1/arb/cot_pi.c000066400000000000000000000023761264125401100144570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_cot_pi(arb_t y, const arb_t x, slong prec) { arb_t u; arb_init(u); arb_sin_cos_pi(y, u, x, prec + 4); arb_div(y, u, y, prec); arb_clear(u); } arb-2.8.1/arb/coth.c000066400000000000000000000035251264125401100141340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_coth(arb_t y, const arb_t x, slong prec) { arb_t t, u; int sign = arf_sgn(arb_midref(x)) < 0; arb_init(t); arb_init(u); arb_mul_2exp_si(t, x, 1); if (!sign) arb_neg(t, t); if (arf_cmpabs_2exp_si(arb_midref(x), 1) > 0) { /* coth(x) = 1 + 2 exp(-2x) / (1 - exp(-2x)) */ arb_exp(t, t, prec + 4); arb_sub_ui(u, t, 1, prec + 4); arb_div(y, t, u, prec + 4); arb_mul_2exp_si(y, y, 1); arb_sub_ui(y, y, 1, prec); } else { /* coth(x) = (exp(2x) + 1) / (exp(2x) - 1) */ arb_expm1(t, t, prec + 4); arb_add_ui(y, t, 2, prec + 4); arb_div(y, y, t, prec); } if (!sign) arb_neg(y, y); arb_clear(t); arb_clear(u); } arb-2.8.1/arb/digamma.c000066400000000000000000000062671264125401100146040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "arith.h" void arb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const arb_t x, int use_reflect, int digamma, slong prec); void arb_gamma_stirling_eval(arb_t s, const arb_t z, slong nterms, int digamma, slong prec); void arb_digamma(arb_t y, const arb_t x, slong prec) { int reflect; slong r, n, wp; arb_t t, u, v; if (arb_is_exact(x)) { const arf_struct * mid = arb_midref(x); if (arf_is_special(mid)) { arb_indeterminate(y); return; } else if (arf_is_int(mid)) { if (arf_sgn(mid) < 0) { arb_indeterminate(y); return; } else if (arf_cmpabs_ui(mid, 30 + prec / 2) < 0) { fmpq_t h; arb_init(t); fmpq_init(h); /* should change to fmpq_harmonic_ui when flint upgrades */ arith_harmonic_number(h, arf_get_si(mid, ARF_RND_DOWN) - 1); arb_set_fmpq(y, h, prec + 2); arb_const_euler(t, prec + 2); arb_sub(y, y, t, prec); arb_clear(t); fmpq_clear(h); return; } } } wp = prec + FLINT_BIT_COUNT(prec); arb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 1, wp); arb_init(t); arb_init(u); arb_init(v); /* psi(x) = psi((1-x)+r) - h(1-x,r) - pi*cot(pi*x) */ if (reflect) { arb_sub_ui(t, x, 1, wp); arb_neg(t, t); arb_cot_pi(v, x, wp); arb_const_pi(u, wp); arb_mul(v, v, u, wp); arb_rising2_ui(y, u, t, r, wp); arb_div(u, u, y, wp); arb_add(v, v, u, wp); arb_add_ui(t, t, r, wp); arb_gamma_stirling_eval(u, t, n, 1, wp); arb_sub(y, u, v, wp); } else { arb_add_ui(t, x, r, wp); arb_gamma_stirling_eval(u, t, n, 1, wp); arb_rising2_ui(y, t, x, r, wp); arb_div(t, t, y, wp); arb_sub(y, u, t, prec); } arb_clear(t); arb_clear(u); arb_clear(v); } arb-2.8.1/arb/div.c000066400000000000000000000106231264125401100137560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_div_arf(arb_t z, const arb_t x, const arf_t y, slong prec) { mag_t zr, ym; int inexact; if (arf_is_zero(y)) { if (arf_is_nan(arb_midref(x))) arb_indeterminate(z); else arb_zero_pm_inf(z); } else if (arb_is_exact(x)) { inexact = arf_div(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); else mag_zero(arb_radref(z)); } else if (mag_is_inf(arb_radref(x))) { arf_div(arb_midref(z), arb_midref(x), y, prec, ARB_RND); mag_inf(arb_radref(z)); } else { mag_init(ym); mag_init(zr); arf_get_mag_lower(ym, y); mag_div(zr, arb_radref(x), ym); inexact = arf_div(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), zr, arb_midref(z), prec); else mag_swap(arb_radref(z), zr); mag_clear(ym); mag_clear(zr); } } void arb_div(arb_t z, const arb_t x, const arb_t y, slong prec) { mag_t zr, xm, ym, yl, yw; int inexact; if (arb_is_exact(y)) { arb_div_arf(z, x, arb_midref(y), prec); } else if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) { arf_div(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND); mag_inf(arb_radref(z)); } else { mag_init_set_arf(xm, arb_midref(x)); mag_init_set_arf(ym, arb_midref(y)); mag_init(zr); mag_init(yl); mag_init(yw); /* (|x|*yrad + |y|*xrad)/(y*(|y|-yrad)) */ mag_mul(zr, xm, arb_radref(y)); mag_addmul(zr, ym, arb_radref(x)); arb_get_mag_lower(yw, y); arf_get_mag_lower(yl, arb_midref(y)); mag_mul_lower(yl, yl, yw); mag_div(zr, zr, yl); inexact = arf_div(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), zr, arb_midref(z), prec); else mag_swap(arb_radref(z), zr); mag_clear(xm); mag_clear(ym); mag_clear(zr); mag_clear(yl); mag_clear(yw); } } void arb_div_si(arb_t z, const arb_t x, slong y, slong prec) { arf_t t; arf_init_set_si(t, y); /* no need to free */ arb_div_arf(z, x, t, prec); } void arb_div_ui(arb_t z, const arb_t x, ulong y, slong prec) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ arb_div_arf(z, x, t, prec); } void arb_div_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) { arf_t t; if (!COEFF_IS_MPZ(*y)) { arf_init_set_si(t, *y); /* no need to free */ arb_div_arf(z, x, t, prec); } else { arf_init(t); arf_set_fmpz(t, y); arb_div_arf(z, x, t, prec); arf_clear(t); } } void arb_fmpz_div_fmpz(arb_t z, const fmpz_t x, const fmpz_t y, slong prec) { int inexact; inexact = arf_fmpz_div_fmpz(arb_midref(z), x, y, prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); else mag_zero(arb_radref(z)); } void arb_ui_div(arb_t z, ulong x, const arb_t y, slong prec) { arb_t t; arb_init(t); arb_set_ui(t, x); arb_div(z, t, y, prec); arb_clear(t); } arb-2.8.1/arb/div_2expm1_ui.c000066400000000000000000000042611264125401100156500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_div_2expm1_ui(arb_t y, const arb_t x, ulong n, slong prec) { if (n < FLINT_BITS) { arb_div_ui(y, x, (UWORD(1) << n) - 1, prec); } else if (n < 1024 + prec / 32 || n > WORD_MAX / 4) { arb_t t; fmpz_t e; arb_init(t); fmpz_init_set_ui(e, n); arb_one(t); arb_mul_2exp_fmpz(t, t, e); arb_sub_ui(t, t, 1, prec); arb_div(y, x, t, prec); arb_clear(t); fmpz_clear(e); } else { arb_t s, t; slong i, b; arb_init(s); arb_init(t); /* x / (2^n - 1) = sum_{k>=1} x * 2^(-k*n)*/ arb_mul_2exp_si(s, x, -n); arb_set(t, s); b = 1; for (i = 2; i <= prec / n + 1; i++) { arb_mul_2exp_si(t, t, -n); arb_add(s, s, t, prec); b = i; } /* error bound: sum_{k>b} x * 2^(-k*n) <= x * 2^(-b*n - (n-1)) */ arb_mul_2exp_si(t, x, -b*n - (n-1)); arb_abs(t, t); arb_add_error(s, t); arb_set(y, s); arb_clear(s); arb_clear(t); } } arb-2.8.1/arb/doublefac_ui.c000066400000000000000000000027061264125401100156200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_doublefac_ui(arb_t res, ulong n, slong prec) { if (n % 2 == 0) { arb_fac_ui(res, n / 2, prec); arb_mul_2exp_si(res, res, n / 2); } else { arb_t t; arb_init(t); arb_doublefac_ui(t, n - 1, prec + 5); arb_fac_ui(res, n, prec + 5); arb_div(res, res, t, prec); arb_clear(t); } } arb-2.8.1/arb/exp.c000066400000000000000000000340761264125401100140000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define TMP_ALLOC_LIMBS(__n) TMP_ALLOC((__n) * sizeof(mp_limb_t)) int _arf_get_integer_mpn(mp_ptr y, mp_srcptr x, mp_size_t xn, slong exp); int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec); void arb_exp_arf_huge(arb_t z, const arf_t x, slong mag, slong prec, int minus_one) { arb_t ln2, t, u; fmpz_t q; slong wp; arb_init(ln2); arb_init(t); arb_init(u); fmpz_init(q); wp = prec + mag + 10; arb_const_log2(ln2, wp); arb_set_arf(t, x); arb_div(u, t, ln2, wp); arf_get_fmpz(q, arb_midref(u), ARF_RND_DOWN); arb_submul_fmpz(t, ln2, q, wp); arb_exp(z, t, prec); arb_mul_2exp_fmpz(z, z, q); if (minus_one) arb_sub_ui(z, z, 1, prec); arb_clear(ln2); arb_clear(t); arb_clear(u); fmpz_clear(q); } /* |x| >= 2^expbound */ static void arb_exp_arf_overflow(arb_t z, slong expbound, int negative, int minus_one, slong prec) { if (!negative) { arf_zero(arb_midref(z)); mag_inf(arb_radref(z)); } else { /* x <= -2^expbound ==> 0 < exp(x) <= 2^(-2^expbound) */ fmpz_t t; fmpz_init(t); fmpz_set_si(t, -1); fmpz_mul_2exp(t, t, expbound); arf_one(arb_midref(z)); mag_one(arb_radref(z)); arb_mul_2exp_fmpz(z, z, t); if (minus_one) arb_sub_ui(z, z, 1, prec); fmpz_clear(t); } } static void arb_exp_arf_fallback(arb_t z, const arf_t x, slong mag, slong prec, int minus_one) { if (mag > 64) arb_exp_arf_huge(z, x, mag, prec, minus_one); else arb_exp_arf_bb(z, x, prec, minus_one); } static void arb_exp_arf(arb_t z, const arf_t x, slong prec, int minus_one) { slong maglim = FLINT_MAX(128, 2 * prec); if (arf_is_special(x)) { if (minus_one) { if (arf_is_zero(x)) arb_zero(z); else if (arf_is_pos_inf(x)) arb_pos_inf(z); else if (arf_is_neg_inf(x)) arb_set_si(z, -1); else arb_indeterminate(z); } else { if (arf_is_zero(x)) arb_one(z); else if (arf_is_pos_inf(x)) arb_pos_inf(z); else if (arf_is_neg_inf(x)) arb_zero(z); else arb_indeterminate(z); } } else if (COEFF_IS_MPZ(ARF_EXP(x))) { if (fmpz_sgn(ARF_EXPREF(x)) > 0) { /* huge input */ arb_exp_arf_overflow(z, maglim, ARF_SGNBIT(x), minus_one, prec); } else { /* |exp(x) - (1 + x)| <= |x^2| */ fmpz_t t; int inexact; fmpz_init(t); fmpz_mul_2exp(t, ARF_EXPREF(x), 1); inexact = arf_add_ui(arb_midref(z), x, minus_one ? 0 : 1, prec, ARB_RND); mag_one(arb_radref(z)); mag_mul_2exp_fmpz(arb_radref(z), arb_radref(z), t); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); fmpz_clear(t); } } else { slong exp, wp, wn, N, r, wprounded, finaln; fmpz_t n; mp_ptr tmp, w, t, u, finalvalue; mp_limb_t p1, q1bits, p2, q2bits, error, error2; int negative, inexact; TMP_INIT; exp = ARF_EXP(x); negative = ARF_SGNBIT(x); /* handle tiny input */ /* |exp(x) - 1| <= 2|x| */ if (!minus_one && exp < -prec - 4) { arf_one(arb_midref(z)); mag_set_ui_2exp_si(arb_radref(z), 1, exp + 1); return; } /* |exp(x) - (1 + x)| <= |x^2| */ else if (exp < (minus_one ? -prec - 4 : -(prec / 2) - 4)) { inexact = arf_add_ui(arb_midref(z), x, minus_one ? 0 : 1, prec, ARB_RND); mag_set_ui_2exp_si(arb_radref(z), 1, 2 * exp); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); return; } /* handle huge input */ if (exp > maglim) { arb_exp_arf_overflow(z, maglim, negative, minus_one, prec); return; } /* Absolute working precision (NOT rounded to a limb multiple) */ wp = prec + 8; if (minus_one && exp <= 0) wp += (-exp); /* Number of limbs */ wn = (wp + FLINT_BITS - 1) / FLINT_BITS; /* Precision rounded to a number of bits */ wprounded = FLINT_BITS * wn; /* Don't be close to the boundary (to allow adding adding the Taylor series truncation error without overflow) */ wp = FLINT_MAX(wp, wprounded - (FLINT_BITS - 4)); /* Too high precision to use table -- use generic algorithm */ if (wp > ARB_EXP_TAB2_PREC) { arb_exp_arf_fallback(z, x, exp, prec, minus_one); return; } TMP_START; tmp = TMP_ALLOC_LIMBS(4 * wn + 3); w = tmp; /* requires wn+1 limbs */ t = w + wn + 1; /* requires wn+1 limbs */ u = t + wn + 1; /* requires 2wn+1 limbs */ /* reduce modulo log(2) */ fmpz_init(n); if (_arb_get_mpn_fixed_mod_log2(w, n, &error, x, wn) == 0) { /* may run out of precision for log(2) */ arb_exp_arf_fallback(z, x, exp, prec, minus_one); fmpz_clear(n); TMP_END; return; } /* err(w) translates to a propagated error bounded by err(w) * exp'(x) < err(w) * exp(1) < err(w) * 3 */ error *= 3; /* Table-based argument reduction (1 or 2 steps) */ if (wp <= ARB_EXP_TAB1_PREC) { q1bits = ARB_EXP_TAB1_BITS; q2bits = 0; p1 = w[wn-1] >> (FLINT_BITS - q1bits); w[wn-1] -= (p1 << (FLINT_BITS - q1bits)); p2 = 0; } else { q1bits = ARB_EXP_TAB21_BITS; q2bits = ARB_EXP_TAB21_BITS + ARB_EXP_TAB22_BITS; p1 = w[wn-1] >> (FLINT_BITS - q1bits); w[wn-1] -= (p1 << (FLINT_BITS - q1bits)); p2 = w[wn-1] >> (FLINT_BITS - q2bits); w[wn-1] -= (p2 << (FLINT_BITS - q2bits)); } /* |w| <= 2^-r */ r = _arb_mpn_leading_zeros(w, wn); /* Choose number of terms N such that Taylor series truncation error is <= 2^-wp */ N = _arb_exp_taylor_bound(-r, wp); if (N < 60) { /* Evaluate Taylor series */ _arb_exp_taylor_rs(t, &error2, w, wn, N); /* Taylor series evaluation error */ error += error2; /* Taylor series truncation error */ error += UWORD(1) << (wprounded-wp); } else /* Compute cosh(a) from sinh(a) using a square root. */ { /* the summation for sinh is actually done to (2N-1)! */ N = (N + 1) / 2; /* Evaluate Taylor series for sinh */ _arb_sin_cos_taylor_rs(t, u, &error2, w, wn, N, 1, 0); error += error2; error += UWORD(1) << (wprounded-wp); /* 1 + sinh^2, with wn + 1 limbs */ mpn_sqr(u, t, wn); u[2 * wn] = 1; /* cosh, with wn + 1 limbs */ mpn_sqrtrem(w, u, u, 2 * wn + 1); /* exp = sinh + cosh */ t[wn] = w[wn] + mpn_add_n(t, t, w, wn); /* Error for cosh */ /* When converting sinh to cosh, the error for cosh must be smaller than the error for sinh; but we also get 1 ulp extra error from the square root. */ error2 = error + 1; /* Error for sinh + cosh */ error += error2; } if (wp <= ARB_EXP_TAB1_PREC) { if (p1 == 0) { finalvalue = t; finaln = wn + 1; } else { /* Divide by 2 to get |t| <= 1 (todo: check this?) */ mpn_rshift(t, t, wn + 1, 1); error = (error >> 1) + 2; mpn_mul_n(u, t, arb_exp_tab1[p1] + ARB_EXP_TAB1_LIMBS - wn, wn); /* (t + err1 * ulp) * (u + err2 * ulp) + 1ulp = t*u + (err1*u + err2*t + t*u*ulp + 1) * ulp note |u| <= 1, |t| <= 1 */ error += 4; finalvalue = u + wn; finaln = wn; /* we have effectively divided by 2^2 -- todo use inline function */ fmpz_add_ui(n, n, 2); } } else { if (p1 == 0 && p2 == 0) { finalvalue = t; finaln = wn + 1; } else { /* Divide by 2 to get |t| <= 1 (todo: check this?) */ mpn_rshift(t, t, wn + 1, 1); error = (error >> 1) + 2; mpn_mul_n(u, arb_exp_tab21[p1] + ARB_EXP_TAB2_LIMBS - wn, arb_exp_tab22[p2] + ARB_EXP_TAB2_LIMBS - wn, wn); /* error of w <= 4 ulp */ flint_mpn_copyi(w, u + wn, wn); /* todo: avoid with better alloc */ mpn_mul_n(u, t, w, wn); /* (t + err1 * ulp) * (w + 4 * ulp) + 1ulp = t*u + (err1*w + 4*t + t*w*ulp + 1) * ulp note |w| <= 1, |t| <= 1 */ error += 6; finalvalue = u + wn; finaln = wn; /* we have effectively divided by 2^3 -- todo use inline function */ fmpz_add_ui(n, n, 3); } } /* The accumulated arithmetic error */ mag_set_ui_2exp_si(arb_radref(z), error, -wprounded); /* Set the midpoint */ if (!minus_one) { inexact = _arf_set_mpn_fixed(arb_midref(z), finalvalue, finaln, wn, 0, prec); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); } else { _arf_set_mpn_fixed(arb_midref(z), finalvalue, finaln, wn, 0, finaln * FLINT_BITS); } arb_mul_2exp_fmpz(z, z, n); if (minus_one) arb_sub_ui(z, z, 1, prec); TMP_END; fmpz_clear(n); } } void arb_exp(arb_t z, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_exp_arf(z, arb_midref(x), prec, 0); } else { /* exp(a+b) - exp(a) = exp(a) * (exp(b)-1) */ if (mag_cmp_2exp_si(arb_radref(x), 20) < 0 || !arb_is_finite(x)) { mag_t t, u; mag_init_set(t, arb_radref(x)); mag_init(u); arb_exp_arf(z, arb_midref(x), prec, 0); mag_expm1(t, t); arb_get_mag(u, z); mag_addmul(arb_radref(z), t, u); mag_clear(t); mag_clear(u); } else { /* [+/- exp(a+b)], allowing extended exponent range */ arf_t t; arf_init(t); arf_set_mag(t, arb_radref(x)); arf_add(t, arb_midref(x), t, MAG_BITS, ARF_RND_CEIL); arb_exp_arf(z, t, prec, 0); arb_get_mag(arb_radref(z), z); arf_zero(arb_midref(z)); arf_clear(t); } } } void arb_expm1(arb_t z, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_exp_arf(z, arb_midref(x), prec, 1); } else { if (mag_cmp_2exp_si(arb_radref(x), 20) < 0) { /* [exp(a+b) - 1] - [exp(a) - 1] = exp(a) * (exp(b)-1) */ mag_t t, u, one; mag_init_set(t, arb_radref(x)); mag_init(u); mag_init(one); mag_one(one); arb_exp_arf(z, arb_midref(x), prec, 1); mag_expm1(t, t); arb_get_mag(u, z); mag_add(u, u, one); mag_addmul(arb_radref(z), t, u); mag_clear(t); mag_clear(u); mag_clear(one); } else { arb_exp(z, x, prec); arb_sub_ui(z, z, 1, prec); } } } void arb_exp_invexp(arb_t z, arb_t w, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_exp_arf(z, arb_midref(x), prec, 0); arb_inv(w, z, prec); } else { /* exp(a+b) - exp(a) = exp(a) * (exp(b)-1) */ if (mag_cmp_2exp_si(arb_radref(x), 20) < 0 || !arb_is_finite(x)) { mag_t t, u; mag_init_set(t, arb_radref(x)); mag_init(u); arb_exp_arf(z, arb_midref(x), prec, 0); arb_inv(w, z, prec); mag_expm1(t, t); arb_get_mag(u, z); mag_addmul(arb_radref(z), t, u); arb_get_mag(u, w); mag_addmul(arb_radref(w), t, u); mag_clear(t); mag_clear(u); } else { arb_t v; arb_init(v); arb_neg(v, x); arb_exp(z, x, prec); arb_exp(w, v, prec); arb_clear(v); } } } arb-2.8.1/arb/exp_arf_bb.c000066400000000000000000000114431264125401100152640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* Determine N such that the error is bounded by 2^-prec when summing the Taylor series of exp(x) up to term x^N inclusive. We choose an N with many trailing zeros to improve efficiency of the binary splitting. */ static slong bs_num_terms(slong mag, slong prec) { slong N; N = _arb_exp_taylor_bound(mag, prec); /* Convert from N exclusive to N inclusive. */ N--; if (N > 10000) while (N % 128 != 0) N++; if (N > 1000) while (N % 16 != 0) N++; if (N > 100) while (N % 2 != 0) N++; return N; } void arb_exp_arf_bb(arb_t z, const arf_t x, slong prec, int minus_one) { slong k, iter, bits, r, mag, q, wp, N; slong argred_bits, start_bits; mp_bitcnt_t Qexp[1]; int inexact; fmpz_t t, u, T, Q; arb_t w; if (arf_is_zero(x)) { if (minus_one) arb_zero(z); else arb_one(z); return; } if (arf_is_special(x)) { abort(); } mag = arf_abs_bound_lt_2exp_si(x); /* We assume that this function only gets called with something reasonable as input (huge/tiny input will be handled by the main exp wrapper). */ if (mag > 200 || mag < -2 * prec - 100) { flint_printf("arb_exp_arf_bb: unexpectedly large/small input\n"); abort(); } if (prec < 100000000) { argred_bits = 16; start_bits = 32; } else { argred_bits = 32; start_bits = 64; } /* Argument reduction: exp(x) -> exp(x/2^q). This improves efficiency of the first iteration in the bit-burst algorithm. */ q = FLINT_MAX(0, mag + argred_bits); /* Determine working precision. */ wp = prec + 10 + 2 * q + 2 * FLINT_BIT_COUNT(prec); if (minus_one && mag < 0) wp += (-mag); fmpz_init(t); fmpz_init(u); fmpz_init(Q); fmpz_init(T); arb_init(w); /* Convert x/2^q to a fixed-point number. */ inexact = arf_get_fmpz_fixed_si(t, x, -wp + q); /* Aliasing of z and x is safe now that only use t. */ /* Start with z = 1. */ arb_one(z); /* Bit-burst loop. */ for (iter = 0, bits = start_bits; !fmpz_is_zero(t); iter++, bits *= 2) { /* Extract bits. */ r = FLINT_MIN(bits, wp); fmpz_tdiv_q_2exp(u, t, wp - r); /* Binary splitting (+1 fixed-point ulp truncation error). */ mag = fmpz_bits(u) - r; N = bs_num_terms(mag, wp); _arb_exp_sum_bs_powtab(T, Q, Qexp, u, r, N); /* T = T / Q (+1 fixed-point ulp error). */ if (*Qexp >= wp) { fmpz_tdiv_q_2exp(T, T, *Qexp - wp); fmpz_tdiv_q(T, T, Q); } else { fmpz_mul_2exp(T, T, wp - *Qexp); fmpz_tdiv_q(T, T, Q); } /* T = 1 + T */ fmpz_one(Q); fmpz_mul_2exp(Q, Q, wp); fmpz_add(T, T, Q); /* Now T = exp(u) with at most 2 fixed-point ulp error. */ /* Set z = z * T. */ arf_set_fmpz(arb_midref(w), T); arf_mul_2exp_si(arb_midref(w), arb_midref(w), -wp); mag_set_ui_2exp_si(arb_radref(w), 2, -wp); arb_mul(z, z, w, wp); /* Remove used bits. */ fmpz_mul_2exp(u, u, wp - r); fmpz_sub(t, t, u); } /* We have exp(x + eps) - exp(x) < 2*eps (by assumption that the argument reduction is large enough). */ if (inexact) arb_add_error_2exp_si(z, -wp + 1); fmpz_clear(t); fmpz_clear(u); fmpz_clear(Q); fmpz_clear(T); arb_clear(w); /* exp(x) = exp(x/2^q)^(2^q) */ for (k = 0; k < q; k++) arb_mul(z, z, z, wp); if (minus_one) arb_sub_ui(z, z, 1, wp); arb_set_round(z, z, prec); } arb-2.8.1/arb/exp_sum_bs_powtab.c000066400000000000000000000140251264125401100167140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* When splitting [a,b) into [a,m), [m,b), we need the power x^(m-a). This function computes all the exponents (m-a) that can appear when doing binary splitting with the top-level interval [0,n), assuming that we always choose m = a + floor((b-a)/2), and that the case b-a = 2 is inlined. */ slong _arb_compute_bs_exponents(slong * tab, slong n) { slong a, b, aa, /* ab, */ ba, bb, length; if (n == 1) { tab[0] = 1; return 1; } if (n == 2 || n == 3 || n == 4) { tab[0] = 1; tab[1] = 2; return 2; } if (n == 6) { tab[0] = 1; tab[1] = 2; tab[2] = 3; return 3; } /* first binary splitting call */ a = n >> 1; b = n - (n >> 1); tab[0] = a; length = 1; for (;;) { /* split a -> aa, ab and b -> ba, bb */ aa = a >> 1; /* ab = a - aa; */ ba = b >> 1; bb = b - ba; tab[length] = ba; length++; /* at length 3, we split into 2, 1 (and maybe also 2, 2) */ if (ba == 3) { tab[length] = 2; tab[length + 1] = 1; length += 2; break; } /* stop if we have reached 1, or if at 2 and the length is a power of 2 (in which case we never reach 1) */ if (ba == 1 || (ba == 2 && (n & (n-1)) == 0)) break; /* if left and right lengths are different, also add the right length */ if (aa != ba && aa != 1) { tab[length] = aa; length++; } a = aa; b = bb; } /* we always include x^1 in the table, even if the binary splitting terminates at step length 2 */ if (tab[length-1] != 1) { tab[length] = 1; length++; } /* reverse table */ for (a = 0; a < length / 2; a++) { b = tab[a]; tab[a] = tab[length - a - 1]; tab[length - a - 1] = b; } return length; } /* just do a linear search */ slong _arb_get_exp_pos(const slong * tab, slong step) { slong i; for (i = 0; ; i++) { if (tab[i] == step) return i; if (tab[i] == 0) { flint_printf("ERROR: exponent %wd not in table!\n", step); abort(); } } } static void bsplit(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const slong * xexp, const fmpz * xpow, mp_bitcnt_t r, slong a, slong b) { int cc; if (b - a == 1) { count_trailing_zeros(cc, (a + 1)); fmpz_set_ui(Q, (a + 1) >> cc); *Qexp = r + cc; fmpz_set(T, xpow); } else if (b - a == 2) { fmpz_mul_ui(T, xpow, a + 2); fmpz_mul_2exp(T, T, r); fmpz_add(T, T, xpow + 1); count_trailing_zeros(cc, (a + 2)); fmpz_set_ui(Q, (a + 2) >> cc); *Qexp = r + cc; count_trailing_zeros(cc, (a + 1)); fmpz_mul_ui(Q, Q, (a + 1) >> cc); *Qexp += r + cc; } else { slong step, m, i; mp_bitcnt_t Q2exp[1]; fmpz_t Q2, T2; step = (b - a) / 2; m = a + step; fmpz_init(Q2); fmpz_init(T2); bsplit(T, Q, Qexp, xexp, xpow, r, a, m); bsplit(T2, Q2, Q2exp, xexp, xpow, r, m, b); fmpz_mul(T, T, Q2); fmpz_mul_2exp(T, T, *Q2exp); /* find x^step in table */ i = _arb_get_exp_pos(xexp, step); fmpz_addmul(T, xpow + i, T2); fmpz_clear(T2); fmpz_mul(Q, Q, Q2); *Qexp = *Qexp + *Q2exp; fmpz_clear(Q2); } } void _arb_exp_sum_bs_powtab(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) { slong * xexp; slong length, i; fmpz * xpow; /* compute the powers of x that will appear (at least x^1) */ xexp = flint_calloc(2 * FLINT_BITS, sizeof(slong)); length = _arb_compute_bs_exponents(xexp, N); xpow = _fmpz_vec_init(length); xpow[0] = *x; /* create shallow copy of x */ /* build x^i table */ for (i = 1; i < length; i++) { if (xexp[i] == 2 * xexp[i-1]) { fmpz_mul(xpow + i, xpow + i - 1, xpow + i - 1); } else if (xexp[i] == 2 * xexp[i-2]) /* prefer squaring if possible */ { fmpz_mul(xpow + i, xpow + i - 2, xpow + i - 2); } else if (xexp[i] == 2 * xexp[i-1] + 1) { fmpz_mul(xpow + i, xpow + i - 1, xpow + i - 1); fmpz_mul(xpow + i, xpow + i, xpow); } else if (xexp[i] == 2 * xexp[i-2] + 1) { fmpz_mul(xpow + i, xpow + i - 2, xpow + i - 2); fmpz_mul(xpow + i, xpow + i, xpow); } else { flint_printf("power table has the wrong structure!\n"); abort(); } } bsplit(T, Q, Qexp, xexp, xpow, r, 0, N); fmpz_init(xpow + 0); /* don't free the shallow copy of x */ _fmpz_vec_clear(xpow, length); flint_free(xexp); } arb-2.8.1/arb/exp_sum_bs_simple.c000066400000000000000000000041531264125401100167120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void bsplit(fmpz_t P, fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, slong r, slong a, slong b, int cont) { if (b - a == 1) { fmpz_set(P, x); fmpz_set_ui(Q, a + 1); *Qexp = r; fmpz_set(T, P); } else { slong m; mp_bitcnt_t Q2exp[1]; fmpz_t P2, Q2, T2; m = a + (b - a) / 2; fmpz_init(P2); fmpz_init(Q2); fmpz_init(T2); bsplit(P, T, Q, Qexp, x, r, a, m, 1); bsplit(P2, T2, Q2, Q2exp, x, r, m, b, 1); fmpz_mul(T, T, Q2); fmpz_mul_2exp(T, T, *Q2exp); fmpz_addmul(T, P, T2); fmpz_mul(Q, Q, Q2); *Qexp = *Qexp + *Q2exp; if (cont) fmpz_mul(P, P, P2); fmpz_clear(P2); fmpz_clear(Q2); fmpz_clear(T2); } } void _arb_exp_sum_bs_simple(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) { fmpz_t P; fmpz_init(P); bsplit(P, T, Q, Qexp, x, r, 0, N, 0); fmpz_clear(P); } arb-2.8.1/arb/exp_tab.c000066400000000000000000003216501264125401100146230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #if FLINT_BITS == 64 #define Z2(a,b) UWORD(0x ## b ## a) #else #define Z2(a,b) UWORD(0x ## a), UWORD(0x ## b) #endif #define Z8(a,b,c,d,e,f,g,h) Z2(a,b), Z2(c,d), Z2(e,f), Z2(g,h), const mp_limb_t arb_exp_tab1[ARB_EXP_TAB1_NUM][ARB_EXP_TAB1_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,80000000) },{ Z8(ff554e0d,eaf5c2fa,5c67ff57,abee91b9,020d348f,e82f3725,fafa1201,575bd293) Z8(d0372a42,1eb90105,8676076f,de780649,3554f733,45152169,5aabbbe9,80804015) },{ Z8(7539dd57,e5a39b83,5319c8f5,32a6326f,421fa89a,c54f1230,b416c333,da17fb32) Z8(c0482614,80ab44b0,ed70fa46,37b1c91e,39b44e99,1931c15e,00222d86,810100ab) },{ Z8(e184c3b3,c58f8dbc,34da4bae,bbc6f344,767a5698,39c05a2d,27d75440,28927bad) Z8(2c5d5be9,a747371f,0ac8a0c5,b2d88edc,773b6516,6ca08d0e,b103b504,81824241) },{ Z8(c5f3a3dc,73f545e0,3415b128,87330d08,9ab33afe,5993a7fc,8b7f018c,67380747) Z8(5ec2eb5c,835210e4,a313b765,b790820f,822735a2,5c3259f4,aef1c8bd,8204055a) },{ Z8(2aff18d3,8a31a8cd,bcf94f83,66a19fd1,42d9b6fe,41da9652,16a3dd96,1a75fc21) Z8(12a99dec,c67acf4e,181af4d3,277b532d,6f1fc743,6d0fbdc3,bd1036e1,82864a77) },{ Z8(31ae8d90,71b06712,3048b19c,41ae308a,8b915b5a,6e3f14ae,271261f8,88ab6a8b) Z8(c8bf2dd3,173a4446,46104e0a,42bd2733,4adbb70d,2b2cebaf,2086e8a7,8309121b) },{ Z8(b08d6622,76f0ab8c,58614061,045cf4ca,0746e9f4,dab69d5e,fa9674f0,8a9a605e) Z8(0ba1fc43,a77c428f,30830a66,3f64c60c,cf3484c2,ed9945c8,a104277d,838c5cc7) },{ Z8(fa5e04c3,15a1b025,58c8cf5e,600ffa90,36da5eed,ab7e698e,f9e9a1cc,5c7720f2) Z8(fb0c3076,89fef98b,92234035,55280bc2,d4064bd3,05e841d5,893f64c7,84102b00) },{ Z8(314b6b0b,17b00bf5,348c1c57,d271ab7d,078067ed,fa493689,52d00e27,e9f872a7) Z8(762265a9,3720d66e,93c2ba38,5d17bac3,d6fbe6b7,2277b709,a77c8498,84947d49) },{ Z8(a6eee1fe,4f2e618a,0226a8f9,f2486800,eff57f8e,e7c949d8,a10f6f11,4bbc4e57) Z8(c20d2769,76b3175a,ca7bc0b3,9fafcc07,cd8d8884,2e60e7ca,4e0fac0a,85195427) },{ Z8(16a47ce9,2eca70dd,e5764424,ff05f601,635e0cc2,23c7725c,f8f02447,1a1a8833) Z8(910f86ab,3c5dbada,098d739d,fc17f52c,90afe905,7d6e234f,53e19398,859eb01e) },{ Z8(65f03ae8,26407119,96d943f0,58531dfb,6e386d7b,b69f8894,731f1fee,ea9a7502) Z8(369fd391,b283022a,043be481,ed3ac5a3,2594af50,967f31eb,14f45e14,862491b4) },{ Z8(b4f0d23e,e311637b,bcd99b4e,a18be517,5e3be3ee,6a86a3c1,c8a332d5,ca7a8250) Z8(c230356f,e1e4cf30,c1f52eda,622fd1b2,54712710,735b6853,72e8f4b3,86aaf96e) },{ Z8(09376634,f971d411,543de67f,26853de0,f9928040,c4230144,d85cd08a,4db3ffb7) Z8(4e94081c,7fe48459,68805db6,7d8b029e,1a0e0eae,9209beb6,d584e8b9,8731e7d3) },{ Z8(1ae82c51,3b513f8f,b8290d66,5c8bc828,44537ddb,34c177b5,a4a9bef4,c9cf2a83) Z8(0f8c48ac,a744e4ad,011547f0,ef77ad79,168701d1,b966251a,2b38db4b,87b95d6b) },{ Z8(c3ec7771,94d3ccf6,c5428436,44a1b430,410caf75,56f32f75,25d7aa18,d2f4ee1c) Z8(ef3fcf23,624bec06,c3e1237c,dd14aaba,12e4d4a8,d8d00cf1,e9a76bea,88415abb) },{ Z8(ad201cba,c49b7467,b12d3cff,78069023,19b293f5,4db3c62e,5f44189a,67cd64ec) Z8(fc907294,01e1487f,bc51f747,435c4a97,d9bcd368,f1794615,0e2cae21,88c9e04e) },{ Z8(6f450efa,c116b6e5,74dd3a44,cca4c182,091da1a2,82551654,3e65c65a,ad53eca0) Z8(74774a1b,fe2d70f4,ff6a7549,0d22651b,1e4256f6,7f0e6253,1e6626ed,8952eeaa) },{ Z8(9d4df7d7,4e574c75,6ace1e5e,f042a379,87e05013,a19ff4aa,0f7388c7,97a469e8) Z8(fea4349a,e01bcb46,31b11be1,ab7a48af,296927f1,5d2b5d3a,28bb5264,89dc8659) },{ Z8(45827151,eb233b9f,eae73603,eb8227f1,2e4df3ca,ff06158c,1283deec,a0867b97) Z8(8c3d07ab,c4c607fb,252590b5,3204d2b5,13ce2f05,af50ce37,c4e6b22a,8a66a7e4) },{ Z8(7b6f9498,a77871cb,c7852dba,944762a9,a8660859,e16afa51,0e7d6158,d5cc78d5) Z8(01f1c868,59c88bc8,15d3244e,4630d03b,089acf68,d9d7f8b7,147f6537,8af153d7) },{ Z8(bcff94a1,ecce7623,4ad6897f,17b55cd9,e25e4701,3bf5f538,c3d5aece,096ae22d) Z8(7d2ef735,13e29881,a01809dc,f6e2ba5f,82cae079,23b72aa5,c3834979,8b7c8aba) },{ Z8(f6ee0cee,17a6b464,9439ddb4,c1e11367,99080f5f,9736e366,27094655,03a51f82) Z8(628f06e9,6956229c,4767396f,1a3777e4,d3079a98,22c48dd2,08e1a7db,8c084d1b) },{ Z8(754c3938,74e5fa46,a3e485cd,73e7aae1,ca779092,27bd225f,2e1dfd17,f7da756c) Z8(f503d876,04261d08,ea6c3274,f3da3da8,40755e14,9e8c66dd,a7066b44,8c949b83) },{ Z8(3e4aefad,273c6da4,faa8f661,ae7879f5,1fd1563f,00f3c053,2f1c87bd,165e8af7) Z8(cf420806,78113051,ea50abec,90b2581c,a3ee97c2,20c13e5d,ec65e30e,8d217680) },{ Z8(0a32b41d,4539d082,52aca6e8,8099986f,71474f4f,e9ec3d99,a5004eb6,1ca3fda5) Z8(ced96c90,1a6ec938,d9e848ce,956773bc,00eedaab,f5c92a52,b4091181,8daede9f) },{ Z8(55c90bc5,41896020,fc1c67ef,7959583b,a49ae8a4,b4dd8211,59b34efb,3a95d5dd) Z8(1d84535d,c29e27c5,b1707447,5c5e1c92,1ebff081,ebf3e989,661a86f0,8e3cd46d) },{ Z8(e1ce068b,eb9216a2,ac1983f1,ad8bffb6,441648fe,f480be00,7bfe9766,705792c8) Z8(c4a424c8,f0946cb9,6a39122f,7629b2da,06c3015f,ac7a4d32,f873c9e8,8ecb5877) },{ Z8(0e9e3fa5,1a51d8f4,4c56a1f9,9d172707,b0dbab91,f76bd471,c90d28e9,884d09ab) Z8(e52992c8,68922f7d,25f11282,9701baa4,6808fb4e,1689123e,ef2b4d19,8f5a6b4d) },{ Z8(4b3208f7,b04edb2a,93ec95f7,3168b6e9,dcd7c570,000aab51,20b212a2,b4da6405) Z8(48a7a6d6,83b4124f,8eb396a0,c57d8298,e625fbf5,92485a20,5d22f376,8fea0d7e) },{ Z8(827a03ef,c230bac2,2c4330b7,3025da31,65c99270,7fabbc3a,a1605373,9ff86ee1) Z8(b3009532,21637b8e,330b7a67,6b488058,62ec47c2,e00df647,e4972327,907a3f98) },{ Z8(12b5ae61,0a584fe3,ef3e2399,178072e9,2ce1e182,4ef19144,3a8af5bb,bc3b803a) Z8(8118966c,bbb5b0f2,54ab82be,3c5f8642,7035c6a1,76b441c2,b7ae67ce,910b022d) },{ Z8(7afef92e,647f369d,7f9733ad,0cced069,6823001d,9c5901b3,83ed1e44,e2a422ac) Z8(50bbe330,83e9c1c6,c38f6f71,7f068e1b,dc0e7861,1369dfa1,9909a4b9,919c55cd) },{ Z8(16306395,56ad1e1c,b994ac18,18a8ef2d,c1d2a98b,a4794333,7f783bf5,b286404a) Z8(46779a79,be9e8a03,8c6d328f,bbebe950,5d77d732,ad38f205,dc54d790,922e3b09) },{ Z8(a4e8f4ce,71ebfa13,298ff3dc,e974b9d0,3de2fc9c,e0a935be,e51fa743,4eb040f3) Z8(3127f9b0,02421d87,dfae293a,0a70cd55,1411f170,8efecda2,66d86c10,92c0b274) },{ Z8(804c447e,d3ba6d91,0539ddb4,735d22d7,a7e1c9d0,14c5c9eb,1238e6a3,daba3c05) Z8(6f959d26,77d59047,6356c038,6763c7e8,4d070592,eb986004,b00b215a,9353bc9f) },{ Z8(c77449f0,38db74d5,a5f626bd,a5e257df,4cd4abcc,0183ea35,cf30482f,2251c46d) Z8(eb8d48c3,bfda9858,1fa50b25,d8069a7a,123ea059,d1a4052c,c224817b,93e75a1e) },{ Z8(169e5bb7,491ab6f9,fbf113a9,0af845a0,a903e47f,097985c0,0bfadb52,bd2a6016) Z8(b3113bb9,2a497a4a,fac69782,8a84bd5b,0097199a,f667f4e7,3aafebac,947b8b85) },{ Z8(a1517ce4,da86c052,47a67561,127cfaa5,97acb08f,f0a615e4,b0bd87e1,7fd15f21) Z8(64c595de,523cc7ad,d839cdfc,7f38f6e0,36a250bc,622d53a9,4b2031ed,95105167) },{ Z8(06557e3f,751a929f,8482b781,38f8d82d,5dbb18d1,fae289c7,0dba2b34,5ed19617) Z8(9bcb9778,d23a6bec,30f5450e,32a17622,cebec9a5,9bb3e062,b963ca80,95a5ac59) },{ Z8(54bc32de,dca7cbd1,fa03b236,5742f008,3db0b97e,1139e905,34b639ff,1a3ecb2f) Z8(52322710,c73ea90f,a4c2e759,8fff291b,3f6365b2,8449c43b,e07995e9,963b9cf1) },{ Z8(e1836a48,4916fbf3,407b6cd6,bd3577d4,06021fe6,9bc4fd30,b8d6f8c6,129d3a7e) Z8(f5557d0f,a2e2151a,801f08da,c3cd4cba,c2d11ea9,aa8ec61f,b10639f5,96d223c5) },{ Z8(9f929cb0,6dcac6ad,8e9f7724,12a2ab4b,908a440d,873d4b3f,3095135d,fc8afd92) Z8(f9d0e418,f1fe1c91,0381d908,ba2d8fc6,557ecedf,6efaa729,b1ea126e,9769416b) },{ Z8(16d41b76,5c56ee07,28a91c78,043e61f8,db2401d3,1d97ef3c,deb5ff7e,b6576877) Z8(35d5059d,d53a4794,764049f1,7458999f,7ffaabe3,eae44b1a,00d7b805,9800f67b) },{ Z8(be072c3c,ac83c46d,959ce10f,43441db1,aa0c6342,ba62c3b0,18b5bd1a,876f4af1) Z8(6eddc485,16620f72,f2e0ce50,90cf4044,e85fca95,21031f3a,52eb1e16,9899438b) },{ Z8(817cb6c9,000d8da1,3cd8ceda,19c9d6ec,db5aafbf,5e9350cd,facf6daf,f14adb6e) Z8(ca068ef0,7c50e649,8eb31936,1138b433,6c669095,953687e2,f54147c9,99322934) },{ Z8(7f8681bd,a190226b,ab4cd129,f7ea201c,4e5c013b,f7875ad0,99180921,1037c2d5) Z8(ac49b2cd,e784b424,f946e585,09873a27,aa22abbf,00c890e9,cd909545,99cba810) },{ Z8(87dd346f,ca85cf4b,24f1a452,34a88b53,1f7f1004,106e57b6,b021cf84,c73b9006) Z8(f1746808,230db4ad,8982478c,84735853,e33249a2,7062465b,5ac1a96a,9a65c0b8) },{ Z8(7c356e5b,69f8fa96,61870a99,0218d591,c193a385,1f1178c0,72e52501,1838941b) 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Z8(93034bfe,6fb21abd,7f40ff4d,45422ccf,13425149,f435b5cb,710af5fd,bf66d175) },{ Z8(19c092f5,20a81315,8711865a,92f265e5,cf26b468,a2fa5bf5,34812af1,4e2c2982) Z8(a9e20ce6,90ca9c65,e1347404,65aa4053,44a5ecea,65cddb8c,3daa2e5d,c026981a) },{ Z8(83977506,9c00bc7d,ebc08671,dee69b9a,de44e88f,ca6c1ea3,672ec0db,1260dc86) Z8(272afe61,f2e1a444,44b59fdb,f63c0079,ead13e0a,2ee3bdea,b266dc47,c0e71ee5) },{ Z8(25028178,12037413,9ccb1c5b,63f490eb,5e9dd556,07573da0,c5837f50,1e1938dc) Z8(16dc603b,f98ed4cb,6d1ae251,093817ad,c6f57226,255944c2,561c7fb4,c1a86698) },{ Z8(03209717,f54802d2,aecbd04d,590e7f5b,fc2d0809,2c7df221,b2d2bb18,7a70191f) Z8(7c006bc0,91414899,ce7fed4a,a6ed6ae3,7ed294cc,5906c6b5,708dd7a9,c26a6ff3) },{ Z8(ea842a56,c052e96e,5fd77ccd,e87b8c0a,40ad1bc5,8c9037cf,a54d79b3,c870f8ad) Z8(ae299105,ef42b65a,3b6732a5,973c231f,52ad1394,ee10dd0a,0b262a0a,c32d3bb9) },{ Z8(423989dc,5d433de4,29d10404,655dfd06,bd089ac0,6bb5a8dc,b784184a,9aeaa364) Z8(e4a7f061,a56401d4,0c2ba283,c85f615a,635cf646,8e40acf6,f1bb4d17,c3f0caab) },{ Z8(a88dbe14,3925e22d,4c08737e,01c27c77,54e39070,27fccb82,50fbc815,90255f7d) Z8(0ebce480,5ba28aa2,237f4260,c3921216,4fd72211,7aea431b,b350734e,c4b51d8f) },{ Z8(9e450251,61d15c1c,dc0d05d5,ff20755a,f755fdbe,9c9bce2f,e1699c41,70ba4947) Z8(14d71b3d,6c746eae,383f2aa8,8141ffcb,91b2c2a2,0b574ecb,a2d9ba83,c57a3528) },{ Z8(437c3383,9fe16284,87de5042,dca079a4,03810d69,72c15684,c963000a,568ecb75) Z8(76b0c25c,3b076185,85527ef9,89bf1067,298885f7,26da076c,d8007ee1,c640123b) },{ Z8(151d2ddf,0a8e114c,cc3c2a74,b13cb635,d3ccef25,7ae5552d,8f55ce41,1321420e) Z8(6c72fdcc,2dfb9c08,0455c310,05155289,6baaabd4,0d9d1247,2fe872a7,c706b58f) },{ Z8(d5a7b8e8,3bbd8b4b,2214cd3a,43680dbf,557b21fb,3a339f99,17becf72,1b970557) Z8(d972e9d4,9838fb2a,67d26a4c,dc7cadf3,2fec566b,87fa9e46,4df57b59,c7ce1fe9) },{ Z8(f5435eee,fde1152c,e5596792,319a3ade,e329f528,f3fc39d7,792c15e3,5e12a3b0) Z8(6582ecf2,bc54ce32,67c1b712,c6c05fbf,bb81f492,599f6200,9c925538,c8965211) },{ Z8(e913bbd9,f54fe18c,cb7e4ad4,a807353e,4d5452b6,f2f6fe4b,993fe5a7,f9fefdef) Z8(e44ba29f,b393e307,eab2bd1f,8c19dc51,f9e4fa85,9bfe7ce9,4df7fdb9,c95f4cd0) },{ Z8(5667fb6c,6d21a0d6,c54c352c,c5260037,547abbfe,232e0da3,32576260,fb3baf37) Z8(92db93c5,6e9b22ab,bd9f7b87,6f0f2e74,65e90818,6aa2343e,5cf5e5d3,ca2910ee) },{ Z8(c57bef96,54de87bb,2052188b,7a330b85,3bc84734,9ab35c73,6d59fed7,dca7c99f) Z8(606a12ca,a8bf2b0a,b22a658b,ced25507,6754c87e,13b3e6e3,8dbaecdc,caf39f35) },{ Z8(5c7c1499,f2175128,b346a805,f9062eea,2fee8a52,df560f89,9993625f,2bb5dc26) Z8(d3a18680,a6301f3d,aed07ede,a504e461,567f34e6,c7ac2852,6e9f24c9,cbbef870) },{ Z8(5966214d,8a064fcd,f110f4ea,9fad9313,9b3b39b1,9323c576,2124bce1,46bc0986) Z8(a95d0bfe,e6ff9d1a,a996a9b9,54110fd9,74501497,8c7b829a,58ee609b,cc8b1d6a) },{ Z8(07a18560,c3ef438c,37565596,1c58ae4d,8fd3518e,a80aec8e,f238fa41,285141af) Z8(2ef8594b,cf0e9eb2,814e8f01,10974eb3,9248af3d,02a5b3d6,71b38db6,cd580eef) },{ Z8(2a8c2876,45019444,2adbebf2,53ba4954,ff8cd094,48f8284f,c5b98d99,2d30379f) Z8(1894f13c,4d189b4b,acc0a03b,ad33b8eb,4911dd65,55bd1e4f,aa84d8ff,ce25cdcc) },{ Z8(5bc36a9f,a874ce15,3a2c3bfd,02df602a,3d883ed1,b2e00161,7fa54fb2,563dc448) Z8(fef27101,0d5e303f,906a6f06,40c5d596,683cc396,7d6b5edd,c250a086,cef45acf) },{ Z8(711bea89,8404537b,1915acda,85fa2772,eb0f9700,76b4e01d,b19cc4de,3114031b) Z8(a1a512b4,0ffc163e,78c9882c,ee329dc2,0cc0f4e8,c0bf5eb9,462b3282,cfc3b6c7) },{ Z8(b0e2dcec,331084dd,1a094645,4eda5811,bad48876,bd2934dc,3ee5134f,6994dd65) Z8(a40efc98,06f83937,8809cb09,4b966d51,f7f1dbb5,3ad18943,921d5a79,d093e282) },{ Z8(622ab504,8708889e,9fe8f468,f393e2b2,2bf84aac,06f7b439,fdd4fcb3,0e443d49) Z8(3e8ea209,f911e058,8ba8f1c1,313b9041,baa4f7c3,edf4e0e1,d1f3bd56,d164ded1) },{ Z8(8e469c5f,b7b55c63,f4034825,b093d0f9,33c1b323,9625d23f,c09b8904,75d96488) Z8(a29020e5,42809947,9e14fbe2,b479f315,33c49361,c1a04dbc,020f054e,d236ac86) },{ Z8(15b12f49,ae19ba80,7b30f91d,a4f6acc6,cb8acc8b,9f376dfb,d4891710,177ab93c) Z8(31b3f966,e225fe48,0985a3ac,fb28f8b6,6f99fcd8,96ff7d5b,f034de4b,d3094c70) },{ Z8(4c856c5b,c45abd1b,3e4cc7b3,9f296296,827726a4,e7f0620e,29cfed99,570d38f2) Z8(586d2d29,a2d24860,9b15bb7e,4ab78332,330ffbb1,70aed201,3c61c3c7,d3dcbf65) },{ Z8(a14f9d6a,40af76b3,515a0721,3ff55e30,759d6670,d619ffb6,67792471,afecebe6) Z8(6df80c69,b7f73291,7632f559,fc19a230,a5750dbe,7b8b0556,599ba0d9,d4b10636) },{ Z8(7072207b,d5c66a4d,3f2d55f5,e8d9a37e,e43bfe85,196dc33e,fcb13687,f08ab0bc) Z8(7adacc42,5d4fc5e1,9fa9ac90,127b6b1e,d1ee3708,98b41492,8ec5434d,d58621b8) },{ Z8(a0b8389b,e3207f39,c24cb421,281ff827,7ac3d886,572605d0,4546c334,7b11f3dc) Z8(08669b56,87ffa2a7,87d1bd8b,2cd600ba,23f3b4e3,dbec9f0a,f772a298,d65c12c0) },{ Z8(445257e5,76d9efd9,dffaef61,d8f2f8b5,8fc0be5d,ced4f11c,6c5f3e88,56c3922a) Z8(8dd82973,59b92b63,f65578d4,ca749d1e,34383c6f,455be61b,84bdfb7f,d732da25) },{ Z8(835536d5,7fd2073b,17e535c4,4ef89b06,d68462e7,c2fb173e,65dff318,a2e069e3) Z8(bf6a39ef,c330c68d,fc9aab78,b9fbe8a3,4ced89db,d269ea89,fe1dc13f,d80a78bc) },{ Z8(c8116b07,39ca0c02,f7c5b7af,67d64641,52b0ff0f,ba977b87,3e7a148a,0c762a19) Z8(a928b9d5,8a36598b,b3f54253,1296e7a0,5c4b6c12,d6f38c3a,023b651c,d8e2ef5f) },{ Z8(56f34986,2fd5634e,8cfd88fb,1a084931,047b3ef1,887ca7cc,13914ed8,39b591b4) Z8(edf5bf0a,e2a71844,e704fea6,f615c6cd,1541ab5f,6670eb83,07caf517,d9bc3ee4) },{ Z8(fe0506a0,b3067371,cf018213,72f6bb3d,6262875e,a2831ae7,34757798,89f5fab6) Z8(a1e4145a,282b6931,17422c96,9e98652b,2c633a72,6bdb6d0d,5e6392b5,da966825) },{ Z8(bfcb8b97,eb2bf6f3,6a46367e,ad7a57f4,2134ae0d,f4ebbd12,8ac88ec8,ea7034b9) Z8(361b8b87,06ec1807,2a4d9a0b,6a186b0f,26322c0d,e72b8224,2f58c2aa,db716bfd) },{ Z8(ed51cca0,530b7d9c,2572b460,9a5dd026,fbe79755,592d97f4,7e666ebe,bce614e8) Z8(0c1e853a,d9488fb3,059b1481,bea17eeb,dec15a0d,a0298edf,7e94963f,dc4d4b46) },{ Z8(8e3f8906,e4640745,fd385368,2d8ea59f,7e9bdc35,f1dbab2d,9ef3d999,f88abaa1) Z8(c4808eee,d320c45a,381a9084,aa3a07c9,1ae0267b,7809cf1c,2b72af4b,dd2a06dd) },{ Z8(a6680edb,d1d16fc1,d75e8251,3d141627,69e6208d,77c35997,3cf79993,f2559850) Z8(1c201ba4,06ac6190,c4ee08d7,5ea8023c,aa5379a5,5de1cc2e,f19c1fa4,de079f9d) },{ Z8(75a0f478,68892404,1bc1112c,7818cd8e,cd8924ee,bfdc1acf,3f7c0f4c,392264f1) Z8(29c1d42c,f5a6e5bb,090d1f26,2067d94b,ac3689ee,c577aa70,69e424d9,dee61666) },{ Z8(b71e5c8c,9110d3ee,a97299c0,a22bb82c,c3f668c9,cde4401e,5cd7debc,ca0b27a4) Z8(b7cabf62,9e19db65,33aa2029,531313a2,29ea9705,5c392a65,0b25c11a,dfc56c15) },{ Z8(ba3c0b7b,c3ada609,5e23b131,8a058f3a,e3d34978,e671ef70,b8baf4c3,028a03d9) Z8(e4b48c89,92a2a7af,f3f4f547,ba617fe1,211002f5,955289dd,2b223221,e0a5a189) },{ Z8(dde01da1,004700f5,c8cc79fb,729892df,88c5c57d,5c237235,08d06681,18ac2663) Z8(0b862160,d3753405,2fa6c011,278ae0a7,9ce12dfa,83e55b19,ff60470b,e186b7a2) },{ Z8(617e0c5c,a2932f56,0e918760,6df7d9c0,65bb64e3,ae2bb304,3b1be63a,e7182eb4) Z8(d49dced0,1ccf1070,591cbf2a,ddbf01b5,a7115f8c,5945c89f,9e0c95ee,e268af43) },{ Z8(00a6dd83,e2fbbaef,c91ddb68,94372e22,522ab689,066dbfdb,dd326c06,7ea73811) Z8(f3b36886,33c03b67,382c3c69,fd90856c,134e32db,bcea731e,feda9219,e34b894c) },{ Z8(4b7067f0,e72f5e86,2c5f93ca,c69a0c3c,6b455326,dc6e8131,5f6c1d72,4e2bd082) Z8(ded6f346,6e7007ca,3d97c538,8fafb8d8,40027983,14610330,fbe683dd,e42f46a1) },{ Z8(23ebb2cb,6a0c4c6d,5e0ee797,5cb61333,d55639ac,d91f066b,879dffca,84aab7d2) Z8(09ed5c25,30c7327a,7746098d,d1ceeadd,da21eba3,b3208b98,529862b6,e513e826) },{ Z8(0bb5eb72,38e0aff6,47d6f8ef,8a0b23f8,9baf3bd7,2e6c4c75,58d9c85c,5c88230d) Z8(bff85dd1,7f7f2762,792b8628,f82a1033,96307c24,cc7bd34b,a48792ce,e5f96ebe) },{ Z8(9a542785,bfbe8dec,114166c1,ff42e769,4b368972,2beee4db,8c2ec9a3,35eae14a) Z8(2791c9b2,252c5298,f75d74e1,29134679,b400bd2a,e54173ad,785f86a1,e6dfdb50) },{ Z8(db658566,aa327d20,00a4d724,d588e59a,29e4861d,9bfd1668,512e501a,069b2197) Z8(cd31d2dd,7f2f51cd,6f678cca,583cd3bb,eccc4bb2,66c74a26,3ac545bf,e7c72ec2) },{ Z8(a190daf4,67d57aa6,6310798b,e2ca630c,2ae050b8,47ce4920,f9c612e8,4830d47d) Z8(350d0125,e8d606e1,38ba9955,ca63d36b,c2057bdc,da32f09e,3f3dd981,e8af69fb) },{ Z8(44ef9bfb,aa8a5cb4,c716215a,0f05d516,55c4c08c,e574ecd1,f62179a6,ed3c15f7) Z8(b2ea1871,23ddfc67,e54bd2eb,ca67acd8,4e2bd4f7,38caabe9,c115a0a7,e9988de3) },{ Z8(94a550a9,81186b21,73c4fd9b,fb717032,47f11980,4a01d815,94fa9b64,d558324d) Z8(1efa0239,2110bcae,5e35a24c,99ccbbf1,8696a5eb,a4fa676c,e4488ab0,ea829b64) },{ Z8(eb269c97,a19fd787,94f01cd4,545bcbf3,68d55890,df4c30f8,2c57784f,d94633d6) Z8(15239b43,5af32341,427b591d,4b0053d1,89153eb8,c77fd14b,b66b3bf1,eb6d9368) },{ Z8(dfe791e5,3d83d656,8b2d5eab,54e27e3a,6aaaf7b5,4b013a86,9838a4c1,526665e9) Z8(8cf2cacd,f994bfb7,62fb38ab,200c0692,a9c876d7,f4e061f0,2f951b38,ec5976da) },{ Z8(efdfd5b7,bea7aa27,d8c27f3e,ff9487a9,aeab4d1f,53b5d9b3,8d82d4b0,1e0e261a) Z8(385b54b9,7e395189,a20fd7f7,113f105c,47a42e7f,28e4f590,334b49fa,ed4646a5) },{ Z8(8a333813,1230ba36,70f1847f,2391a770,ae9af36f,fe997902,82b91346,1e07350a) Z8(aa17224a,9e8da19f,e9a45daa,d96fdcd1,e7d22466,d05987ce,916c87e7,ee3403b6) },{ Z8(62c86a25,66a2f427,2f60a29b,e80b2fdf,272e61fc,d8363b33,cfe1effc,51acdd2d) Z8(2c2a932d,a14067fc,050387f0,ca170f74,b6d52de2,44bd8397,071e02e5,ef22aefc) },{ Z8(602a9113,7a19eb5c,cb948e42,da909450,80c29fa2,8d28fb42,b8ba990e,56eb6cd1) Z8(2022a7e4,654f064b,85d0692e,64bdddb7,474db8f4,c9eaded3,3fb9143f,f0124964) },{ Z8(dfa0b15e,5453c30e,5fb79ce9,d394ba5a,88a8cf05,c67f83c4,42e76677,d78ae111) Z8(8c4f102e,65fcf44b,466bbe3a,c48418b3,12f35e84,cb00cf6b,d5b9ec1b,f102d3de) },{ Z8(fc5da659,e2c3f169,788963ee,861838cc,66d38d7b,549c574d,7c677430,2df90375) Z8(a0eaf3e7,37720269,7a93e758,944e1508,8c3dbdbc,02133a23,53af2c05,f1f44f5c) },{ Z8(2d5651d6,60fd715f,5cb2cb47,474f34ae,4ba4ff34,dba6d630,569c069f,d3957af6) Z8(517eb975,60edfbfd,182a7ae3,412646d9,dd47dc64,2542fa88,352a7191,f2e6bcce) },{ Z8(2e48c039,7f2369d2,af5b0a59,2982d668,5ba9f2b5,f31a1ab1,c3804243,47303c7d) Z8(ff996f4f,a28a2e1a,e4a41c5c,e3883793,d554bf61,a3f5bc94,e7b1d205,f3da1d26) },{ Z8(43c830a9,a6f5e7bb,b5816fcd,621f9b8f,b3f452ba,c0a32cba,f8169db9,5e768a9e) Z8(42a3cc44,47c4dcd9,4adde0a0,0a71d023,af6dcc17,efe744e9,cbb247f1,f4ce7159) },{ Z8(e5576823,543c4d65,abb50a5c,58f1b00b,5add5a29,7a7930dc,2a2e8894,01086ac1) Z8(055677e5,26f9b9a9,391809ca,2c4aa001,822689a6,bfc2a480,357313b0,f5c3ba5b) },{ Z8(d9d78745,2834630b,29c68f56,24644130,1c59be74,cb1a9027,0ab6e51c,9956a0e3) Z8(e0372057,d8960c5c,36404c21,5c03bf58,fed26645,abd8e26f,6e0a0fc3,f6b9f920) },{ Z8(99cbe8af,7f6fff2c,df34ce76,34b7685c,5e881ac5,c64bc3a1,9d4f1392,49155312) Z8(20ee71e3,66e5e571,6eb5ce24,40fbff04,cf6bfb78,796514df,b450f9fd,f7b12e9f) },{ Z8(861e6582,cd574dd5,14cd6868,6de97581,5b1f5d5c,265ed135,1535c340,01badaad) Z8(a2b0b4fc,3a7353f2,0c46c5f5,18755d2e,e0d3c9d5,5d9ca530,3ddbb270,f8a95bd0) },{ Z8(fa7189c6,3e60f494,5744dd78,b9d57c90,2a825301,14879d63,c399f431,ea42f6f8) Z8(214345a5,301cae1e,ebb86660,4b4ce3b2,1241192b,778e87aa,37ef7116,f9a281aa) },{ Z8(57c184cb,fd04a089,b207417a,8702866c,814b82b9,a510ed0f,3183b9ec,e48fe6cc) Z8(66066779,a0249dd4,3841bbd3,48f4753e,3b84c167,b68e7a57,c87af32b,fa9ca126) },{ Z8(16046cbc,50469526,81ef72aa,ff2e5326,e9295725,0204a6a1,5e43bd18,de07a97b) Z8(1985f4ba,94bc8820,fc38d27b,4bbd74ca,a2011b23,5a9adff8,0f0fa131,fb97bb40) },{ Z8(77c1c18b,795349da,8ec50e53,3e6d7856,f2258d3b,06fe377a,fda373ea,6d802008) Z8(59bb9bcd,3e7a7c1e,34a0f83b,60a464ae,5dd07b84,34d57a94,25dbae94,fc93d0f1) },{ Z8(031ca474,5026dbeb,7ce0bd44,f1f05b66,8c7b4b71,bca71107,488da9fd,a4ee473e) Z8(4c035694,e706cad6,eb3df6e9,71da10dd,a0e8a6a4,c7ca1e1b,22a533ef,fd90e336) },{ Z8(8e8e7f80,6a93691c,9db6f5a0,f3fb6332,c0c7dee3,1cd658c8,e1e5ce66,b6cd35dd) Z8(4749b4fd,d2a0a1dd,ad8263b1,12708a7a,32cb9121,61db6846,17c644e9,fe8ef30c) },{ Z8(56c08660,8943b13c,712a870c,b5d43da7,f9593285,b23ada82,7d7c915c,9ecde802) Z8(408864d5,d5780f49,ebee8587,e45235ee,ce1767a0,47c599e3,152a029f,ff8e0171) }}; const mp_limb_t arb_exp_tab21[ARB_EXP_TAB21_NUM][ARB_EXP_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,80000000) },{ Z8(4472c0f8,ace594d6,d38928a3,84790964,d113c005,f40c26ae,e6ddfd26,266822bf) Z8(ec3f47eb,2a8046fd,5fa366ab,686490a3,2d01a1d7,ef5202db,6190ef2b,bf300bde) Z8(29265764,53b7e301,8e705924,17a70134,8bde9ebb,6d71a7f3,294c4962,223416ec) Z8(f1e37dc1,7e973faa,ea015a21,cf66072e,bc0b2f32,0acf95a1,1f0d8b39,a713c29a) Z8(0a60ad4e,6e75a6b8,1eaafd6d,4340c7a1,34ad65b0,be61ef54,1ba5d160,e86c0152) Z8(947de038,971cdb56,6d6e060d,dd8f81d9,ffe742c3,41b4b7e6,342b3c29,76773d80) Z8(128d01f7,a26bd8b4,8c9cac7c,41caf690,ddab72e7,0236b793,c45295af,03bf738a) Z8(831a9c0d,05e1fe7f,15aa0d83,1877fa3d,5ae8db63,53c56952,49fc922e,0696cab8) Z8(583bba53,0c9efe9f,dc50cc91,046244a4,fde437d4,82fad707,f07f57b8,221fa97b) Z8(d4111811,fa7701dd,e292844e,d9c759f4,65bbeddb,eb0302f6,71f59074,6a05f80c) Z8(78bcb929,f58f419f,fbe25010,04e7ccfc,3ea91626,0cf5286c,d0bafad2,db353db4) Z8(4e0732af,e5b2867a,e76e3108,b248a16f,96528658,e05d25b6,274beb73,e7de0309) Z8(5e6ed9c6,a69d6d23,3a96cd53,d03c7a63,c5058bf2,22a3bfb7,718d90be,6ab2a3f8) Z8(ff164d22,d354c736,c36a9c62,d25988ae,2688ed67,79fa4a09,c2443036,2c6f96d6) Z8(f4bf2315,51b4eee8,a769bdd8,22e6a4f4,9e083efa,5d23675f,50864a14,e957d4f1) Z8(035d4369,afe73add,9080cf85,3ae83f20,8d50af3d,1da61115,1330bbcb,491de178) Z8(fa5e04c3,15a1b025,58c8cf5e,600ffa90,36da5eed,ab7e698e,f9e9a1cc,5c7720f2) Z8(fb0c3076,89fef98b,92234035,55280bc2,d4064bd3,05e841d5,893f64c7,84102b00) },{ Z8(663190da,ec073363,c3078b85,be25dd09,468d4ae3,14a8e07f,b304a9eb,de679fb7) Z8(4df4ae3e,119af2b1,87144778,dcf515b8,582b6aa2,517a2265,1176c096,7065504e) Z8(3d5fb6eb,bfa73cc7,a6b2ecc1,88a77afa,36280d05,a313360e,829f0ad5,c04233bf) Z8(cec1eca7,a097712b,226d9f48,d8c1857e,2714fb65,872e1b7f,df6201dc,bd114bfd) Z8(d64c72f5,f022f720,17efdab6,817cc779,1d2a0fc6,da54a3ed,db3f4e4b,bcab01a1) Z8(80620f05,bb2a4a0f,fa590326,f99d2179,1c8e0f0d,6fecaa60,4eb31827,4faa1f6d) Z8(ba890381,01a5e678,6c78c1aa,c287c738,57170015,61df12d6,6dfc9df4,5e47c53b) Z8(b43fbde3,4f3cbb04,ac900d46,7078a04b,b394a032,7e475caf,345e7a8c,b303df64) Z8(30db834b,1223c104,b9b489b9,2d25413d,402617a3,f0b6eb7c,e376fbf1,aaf5acd4) Z8(fe2babfa,ea8dca4d,a2c45b39,de03b6b2,316aec27,62d8eed9,15c4fd2b,4a4d27bb) Z8(41185619,45dc863a,f4633175,04cbbeed,e6884f97,d255e81a,5bc64cfd,58a2b00a) Z8(d755be8b,7112ba07,087b8447,3c58d622,cc5d00d6,910512f7,1540051d,f742087a) Z8(ed61440f,7d090cbb,75f6498b,ff9fd1b7,2ce07430,12418e67,a5381697,a76d34ba) Z8(9aa28205,4a072607,0a4ffad4,33a2b1ac,7aebec0b,36401fad,d2804c04,da9d9f61) Z8(8f5f8ae2,868e17be,d23d522e,de0fd4c0,b4bfe3ab,6979ba38,733f0a61,bf9407bf) Z8(5603de1a,f907a318,1273996a,02aaf44f,c38ccd92,f8300a73,c363e9a8,7a3bad21) Z8(c3ec7771,94d3ccf6,c5428436,44a1b430,410caf75,56f32f75,25d7aa18,d2f4ee1c) Z8(ef3fcf23,624bec06,c3e1237c,dd14aaba,12e4d4a8,d8d00cf1,e9a76bea,88415abb) },{ Z8(68c67282,f96bc683,edda9c98,6544adbe,be69e504,200459bd,238b11ad,7a4edca8) Z8(da99f3e2,c8d1b034,4b4e8cbb,520693eb,b1a98c20,e5fae2f9,6e67dcfb,9cb77549) Z8(a26114da,85780704,0a481621,35ebda27,27febffe,f7572d9d,cedcfad0,318f5174) Z8(ce074442,9d2f705a,64584661,cda21342,16e918af,d5a3cc14,104b15c6,3cf2ea83) Z8(c852b2c8,78699c02,ad8a5369,a3d5fa3c,09afd1a5,e706fda5,fbbbf834,648ff2d1) Z8(71b88079,a8f8eaf6,1a4004d0,50d68062,8c5e3814,ead64902,3ba8f8e1,bda1a3fc) Z8(10caf856,01919667,b6365de4,3c2c6888,121f461e,c6808726,d31b9259,e3ce6dbf) Z8(fc1e6b7b,e1d97687,f009cc7f,2e0e5211,0f9c046e,d9667624,f759ceed,78831f71) Z8(639b614d,7bfd43c4,9eec0516,f7d64f58,fea38871,f36b6110,62b0772c,f6d6a6ca) Z8(522c01b8,9fe913d5,f63bae53,f01d3bc2,bd109add,42e23021,711a64e1,c31adf80) Z8(234fc039,f2ba9071,d8549781,03047762,d3c77555,50951ec3,17eb37f9,fa20784a) Z8(f54f05a3,7524922b,09291e7f,3666f742,478f27e9,c6edfb2b,4d556278,6cefcad4) Z8(eded82a3,c9af04e8,50ef9f0b,06853a72,c4ad2a5e,c6342bfe,eff2d99a,861fb104) Z8(5f7891b5,ac9105f8,83a1fbd0,a839466d,35d23e04,26f74405,0725886c,e33b7a65) Z8(c7d4d902,cb987c53,424f268d,27bf1365,e7a26f92,ba5e9359,c130deea,02f4ac98) Z8(ab82e878,98e8a0e2,6ea0ac35,a8b532bc,3fe97008,fea35eca,da991560,f4979020) Z8(754c3938,74e5fa46,a3e485cd,73e7aae1,ca779092,27bd225f,2e1dfd17,f7da756c) Z8(f503d876,04261d08,ea6c3274,f3da3da8,40755e14,9e8c66dd,a7066b44,8c949b83) },{ Z8(ad250250,b2b19bcc,d9a7ab01,027dc694,2b2b4565,1c90126a,99696df2,20b11da7) Z8(45574cc3,823ba074,d51b00e3,35bd43c3,5650494f,804ced10,84e29133,a5edb1b7) Z8(cd59d5b7,3be8972a,cab67074,f21c925e,2ac75f56,970b15eb,37d9d833,3a902a26) Z8(2265a024,1a548db7,48b7dc78,8594921f,cfd11b44,5ad2f3c1,cfb2c1a5,757a20f3) Z8(76626895,c732f9ee,e0954098,25694b1d,bc1ab3ad,702f50e0,c7533e91,3a6e7181) Z8(a1d596f0,c7378638,3e20bb16,22f1cc82,134e1641,df9a324d,1538e1b8,1512023c) Z8(31df0feb,4ceee8d2,42b5f394,1d1cca2d,16fd9fcf,24590bcd,e50cdc3a,647c72c6) Z8(a322e9ab,67ee8abe,9851c48b,ea26f1a8,25f95443,cbf050fb,64280c6d,00cef364) Z8(93aee173,a743f1a5,8fd71bfd,9bfaf183,a6904146,90751199,26f3eca7,27302dff) Z8(a022d18e,0baa833a,ea46f860,fb4d570f,2fb14f7a,f140557b,f5674789,dce13872) Z8(3dcaadb1,e602af16,822b265a,85906b98,45e53547,4d294592,6b3c804a,42bb1493) Z8(dda641dd,221553ab,b97c6bdc,346c48fa,6ec00e6d,2a29949d,0c4cf137,a37c1fa5) Z8(578454aa,aa502868,74e6da75,a404b34d,a0e328d4,20618ccf,4dfa5b0e,a2242795) Z8(cd72b010,673e8eab,08bc7029,c032cff9,bf81b9e1,6b6de0d0,683d80c4,64fdbeee) Z8(fca37ef6,6b910290,f941c428,e725e5cf,492ae8ec,9bb7089d,7f8d4e68,a87b83f2) Z8(43d3e4f4,e0fca75c,53588b0c,ea6f9d21,f88e5662,3d723db7,15b27cdd,73ae406c) Z8(12b5ae61,0a584fe3,ef3e2399,178072e9,2ce1e182,4ef19144,3a8af5bb,bc3b803a) Z8(8118966c,bbb5b0f2,54ab82be,3c5f8642,7035c6a1,76b441c2,b7ae67ce,910b022d) },{ Z8(5cabe6fa,d179ab66,515b5f8f,572b9a31,90ef1f02,ec806ab5,db964747,ede41227) Z8(231f9219,ed090e66,595b04a8,29b11881,ca88eacc,f3a1f938,a6060f5e,430a6294) Z8(00bf388a,6f09b6e9,b5c1aa40,1448fb78,7b0af18a,80ae580a,2e540e4f,211a5104) Z8(9ec0791d,428bf47d,ffd3ce2b,84597174,af222380,3df1d306,0c3e20f4,372fd639) Z8(f1ae630d,80fa1315,579ebebb,55709b21,f5bb2c16,97e38a49,834694b1,377d32d6) Z8(31f46924,d0fc002e,cc51fc44,24a390eb,413ca80b,9f14c78b,14ae98cf,f37f7d81) Z8(818d0a3c,623d6c32,577b7671,cc441196,65bba68b,eedded17,a4638368,e63b818b) Z8(84068640,57acb3b0,abca19ae,444c11e9,4ffd32bd,9634df59,66f1e083,99a37a02) Z8(3ca2812a,ef36dbbd,604f5295,069b804e,66475ad2,4720f755,d7672c96,488247b8) Z8(f35192b7,4d13b8b6,3fc161f1,efd82a73,0d1dc805,5cb9d24f,7cba6dc1,80239192) Z8(258d3964,87da5dde,4f20af74,b795651b,3941d2cf,dfe12607,a334494d,97930939) Z8(05b58dda,ae01caee,fcfbca51,3eeedd34,065185d5,2769cb9e,ce04ef35,c90f0711) Z8(e3fbc9c1,b5522ed3,02ac1fd3,114642f1,ec8da0ad,03790ccc,e29b6b69,12fd74fb) Z8(3bc19829,b70e2461,44883b8b,9e0adb76,47bb9f9b,003378e4,cd435926,85b1f94b) Z8(827f8d06,46af0dde,eeac3f95,72937d7d,9a81fd57,075bdb50,1ce7bbcc,486cab49) Z8(83caf092,8bd21cb7,99ebc909,b4a66dbb,3082ca7c,bea710ca,dc44f8b4,fde78c8a) Z8(06557e3f,751a929f,8482b781,38f8d82d,5dbb18d1,fae289c7,0dba2b34,5ed19617) Z8(9bcb9778,d23a6bec,30f5450e,32a17622,cebec9a5,9bb3e062,b963ca80,95a5ac59) },{ Z8(a7747307,b263d7bf,f3bbc444,7d4dafad,6448214e,95325cae,376ee95c,6781c13a) Z8(2302b794,f39751a7,64b4f8e2,b9059243,2b32f391,b23943e0,efa7d4ef,6c965f30) Z8(a24f7390,3d06da7b,3c4811cd,e62626ce,122907ce,ae9ad95a,a7fbfb98,a87d8c47) Z8(989b4afb,988f60bf,b9c4c827,625b4b00,b1a977c1,4bda3b4a,fea563e7,ccece089) Z8(dee28cbf,2c155fcb,4aeca5ba,30d9a97f,9658e5e0,8624e00b,0ced991c,e0c2f0e9) Z8(a406a085,d35b1d45,ece36f6c,ff68d8bc,aa5192e5,b5896d80,5b332c6b,f7008f70) Z8(b250ccc4,a5202613,8aeddc9e,970cc1c1,4d9e01f2,2504b4f1,474f2c08,90b46ca2) Z8(049941eb,7bc557bf,a5272ac6,f965d7a0,25876a8d,c91e267f,faffefc2,69f0f737) Z8(18021930,54737195,98a94f67,9e73cff9,ccd69b30,06dbb997,b9f58e33,2b4fb23a) Z8(ad6f797d,4d800fe6,74b76750,02e31c52,162a7cac,9fb0b597,d04fc79c,ccf697c4) Z8(7c1b9f7d,010c1c56,d5962de7,49f3473f,4a30db25,db6c82a3,3b5d3f80,484327fd) Z8(0ad2ea9f,10f7b15a,26748eff,59b7d126,881a9fb2,c3b05b02,8b47b139,12c9bd77) Z8(461a3119,00e643ba,e5fd4f20,90533b85,579c7b44,8da537da,40bc7123,d787fbe8) Z8(7602b554,b3a42a9e,0e72c101,2d78f585,d4714450,a1b0faf5,7faa00d5,636f1626) Z8(50ed39d0,8a041948,5b21cced,4089dc6f,3ac6acae,c3e820f5,d1d7bc89,51f95440) Z8(7c3c9db1,54cdfb44,d6549541,305c4433,53c202cc,cbe54b73,d6e5985d,0a6fe368) Z8(87dd346f,ca85cf4b,24f1a452,34a88b53,1f7f1004,106e57b6,b021cf84,c73b9006) Z8(f1746808,230db4ad,8982478c,84735853,e33249a2,7062465b,5ac1a96a,9a65c0b8) },{ Z8(6e0137c6,7e9ec2dd,40876348,aff4a4e6,d4d74ef3,a8e84f52,a24e5464,95bc503d) Z8(9c5820e6,533ddb67,b2072ec7,96375acc,6ac8febc,973f4a46,60d20630,037e5dae) Z8(ecd84645,da68605e,6b7d54c4,4add14c4,31bd6547,48554320,10453b5f,648fb89d) Z8(c623bb02,cf74ea28,d5c3eeb6,e4021b88,43e4f9df,7d838e47,739da2fd,b1a3ef19) Z8(279e226c,62fce404,3d2bbc23,cd633e8d,31e97787,2558a943,a8b8baac,4bfa3798) Z8(6fc0d47d,d10f1501,1b14636f,db76d741,61e13ae5,ee29deab,eb765bc2,2b6d4968) Z8(76982060,6509ab31,5fd2cff1,1eb6b4f9,bd798b5a,c6ca6b20,7490bd6f,ede574a3) Z8(17df092d,2d0a0263,ea489c01,113d9c34,0f1586db,66eac017,c7400e7f,1f0a0e08) Z8(4d71957c,491cbc27,8717de76,15b9f5d9,13483331,1bf88ca0,554a2ec8,11fc9915) Z8(fb46903d,ef5ab40b,5a1d36f3,b5793cfd,96b2b718,0f732eaa,21bb88b5,f3b66917) Z8(d9c9f788,413d743e,92c24a92,f988382e,af1b1ae7,172f46d7,0eae6361,7e6dfe3a) Z8(63ae03d6,1386760f,45415014,7b694f56,5ba5be11,ea5ff8e4,e723bb41,d6296f14) Z8(f60eb550,ea165b7b,c34de712,85639ab1,1ac4b161,d155eba0,ffd05f23,5043cf23) Z8(bf2a9513,dafcef28,5928410c,7bc38168,1d25c9c2,691e581f,576e5e1e,338cf4b7) Z8(3e30966f,167a3620,a907cd8a,beb23729,26cccbef,53dfb869,cca84510,19f36644) Z8(c9d86da4,48649402,b45bcb24,606f4232,dc65b97a,f40934e1,a79d84aa,a4a01bab) Z8(c19b29c7,6cfcc965,dd49750a,b76abdf7,0e8b6bdf,24273cf6,9a601d51,3db9cdea) Z8(bcef8461,23cf2474,10a259ca,abbb03b0,6028ab6b,bbdee020,08ee5d51,9f4c6f55) },{ Z8(838671aa,1f05d0e3,ad4ea3dc,9bf8077b,58989b32,52cfcaae,8af24eb8,0c878390) Z8(44035afc,6c1408ab,3726813a,e76cfa8e,b6a0aad4,8d53a88b,c2812d6a,0e00db83) Z8(3e698770,b7fd3be7,5dc7e479,6dc6c98c,ed34df17,455d961e,9155c658,e1c8698e) Z8(4bf286ac,24269055,695a602b,e865d36b,09e93f24,1315633b,1c288d2d,f6bb157c) Z8(3a2957c0,97bcadbd,6cadd3ce,ad2b4cbe,16fb89aa,d4c7d3f1,6e72c1c7,af8633ba) Z8(1a197df4,a1b06662,fdf8d498,452c01ed,d945d3d1,28495196,864fef00,fbc9289c) 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Z8(9835e0ce,2bf4dd82,f7681dd4,470f9998,9c7b4fab,d1f9c56a,49bfefb8,1ff2254a) Z8(c8a86731,921fd0cc,f8b4b5ff,ff51b106,01a963d9,742a8eb1,c9cad826,cbbe90d2) Z8(05f53be7,b2daa55c,9872fa6d,483280d2,d2b6b00f,399c5be3,91cf8fb6,a93c6b60) Z8(8dd877d6,af0d48d2,4b4d04a4,19167770,6286e71c,fe56f3e4,c6c4faa5,c69db1ae) Z8(859f80bf,70a13ded,f24f18cd,84514e38,f77aa802,ab2030c7,ff97ecf1,3b2f575d) Z8(d100b799,587cdfec,4f867f2d,7fdea26c,e6c5dcd5,31507573,9e65c54c,631d04de) Z8(847c31c8,3f65c927,9e3954b8,092eafbc,cfd90fc0,630a8c0e,bdc7bfdb,87b6ee33) Z8(e149bd2a,45e52513,b918055d,df0b9079,c5f8fa19,7e568a0e,73c6cebe,2fcca9ad) Z8(9a5a4cae,0ff31493,f79356f4,556f85af,f9327526,0e72064c,cc0ca4e9,d3890053) Z8(b256d2aa,8e0bea85,19363ff2,63321e2c,9cc676ac,2ff05f80,6f42273a,0b99819f) Z8(d9d78745,2834630b,29c68f56,24644130,1c59be74,cb1a9027,0ab6e51c,9956a0e3) Z8(e0372057,d8960c5c,36404c21,5c03bf58,fed26645,abd8e26f,6e0a0fc3,f6b9f920) },{ Z8(08501603,683caee5,742696cd,05d080b8,8e0078e9,8f30358e,8783ae7d,be2ac4c7) Z8(787b52d7,100d9b64,8c009439,0e7ae058,7035c9b4,94647330,bfbea8dd,06de228c) Z8(0d9b2256,f7759b21,510b5176,cb126e78,5d597b62,e48f7347,bc4b8c8d,21256cdb) Z8(733f08c6,5da01e31,5226aadf,44d5c2d1,94eba949,d3de45f5,33b247f4,5ec369d7) Z8(80e03828,c3805408,6cd2cae9,e0d56b47,2dc4ccc9,3e1890c1,f1db4994,86ecd96e) Z8(e43b0a87,3501b90b,6fd9de40,2e542da8,77d07733,d3235c22,e978e17b,6a6023b5) Z8(9f6e4736,651b28b5,94025a03,d1f0ba06,c77a627f,750a036a,6a4cd2cc,bbbb30b9) Z8(255fe91c,dc9b2962,9733ff0d,2c36d720,df47d512,ecac88e6,36f754e3,058dc86b) Z8(722d5007,908a9be7,0e618051,f9c40ffe,30cc5362,f7cb9de2,7454b97b,7332ff02) Z8(6b808f4d,f8aa64e5,d4f3b5a5,97ad4a64,df36e995,86aacd70,e54d5679,c3bb4d1c) Z8(24459835,912e8b4c,4ff40fd2,dd5136b6,d5e2e7dd,4b8900b5,74cb6d49,53bbe7c9) Z8(8e4f9cf0,e6971b76,c838b45d,ec21b17c,c78988a5,1d36f9a2,981c0c39,3f1f3ce1) Z8(1ef3b30b,512ed7a4,b68885df,59957a80,c1ff7f98,6f685d1b,e7632f69,04088e1d) Z8(4d49eb70,69fb4f22,84060732,de88d2ea,e7a8865c,b3664e87,79c635ee,3d6618e9) Z8(4af3b029,3e49bc7f,2036566b,44f0f5e5,27138b02,06132e38,d5c63bb6,6ac69456) Z8(ba01e911,27bc2083,4d6b3332,475f36c9,32083e4e,01d7c09d,8bd1891e,cbc7b1d9) Z8(8e8e7f80,6a93691c,9db6f5a0,f3fb6332,c0c7dee3,1cd658c8,e1e5ce66,b6cd35dd) Z8(4749b4fd,d2a0a1dd,ad8263b1,12708a7a,32cb9121,61db6846,17c644e9,fe8ef30c) }}; const mp_limb_t arb_exp_tab22[ARB_EXP_TAB22_NUM][ARB_EXP_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,80000000) },{ Z8(03b8b0fb,acc1e74f,d3401986,545cd9de,d54ae904,d6e786bd,ffe88931,52d43454) Z8(df46d3da,c07b2995,19f6f3fa,ffdf5aaa,0531dac6,8ed0aac1,e4c26f9e,aaa7016f) Z8(7eb44608,fef9bd87,09b26d00,16480a1e,9445a7bb,ddadd016,b31ae70c,59b6d5a2) Z8(7ba583e0,34361d34,bc8207d0,a1866c76,d32ca01f,fa81adad,b6819ef6,28042fdc) Z8(ea00267f,6451a464,2e8f1318,bc3aa440,765278c5,6f64c3ae,947ba912,63d54b04) Z8(6e60845d,b88376ff,eba6fd41,1db0d07f,db881ee2,d219f2c4,25f7340c,343c60ac) Z8(56f37f93,dcfeed59,82ece08e,46eec10c,bb758db3,e8c0fac7,ecd6ceec,005d849d) Z8(56e70113,ac3d06ed,7d145cda,67a7c824,27b378ac,8737e92f,01a44cab,5f14bc43) Z8(f1cb53c0,abdcec42,db59fbf2,7a29199b,2a333c5a,5420f425,c92d28cb,a470ff3e) Z8(76d83042,0b85cdd9,a1e8f5d8,9749698a,91592982,d84a78bb,4e33ed6f,550eff7e) Z8(b6abab11,5cc94f7e,4d2b7e8e,243b1703,4eb45f36,eeec3817,16c7e29a,4f971829) Z8(bbcc3012,a0ad1d3d,203fd476,4401471b,b9efb83c,d305d47e,197192e0,3e35f637) Z8(0ffcad45,41c2e455,44228877,56f2ed4c,d4e2f9fc,d513cbdc,462b44c0,7790f00e) Z8(0dd744dc,0796aa70,638f0f03,ff6036a9,00fb04b3,942c3e42,6f1c5388,537bdfab) Z8(12324781,8d21cc97,9c6ffd76,f4589007,0bc1b3fc,6fb370a5,3bea4f42,24d1b86b) Z8(b14d4e1c,07836c20,9cac0191,aa0ed669,670949a1,3806abc5,d84e903b,6ebc201b) Z8(c24c77cf,47f7c7bf,a452e423,d8e0ac63,f87cb252,86dec92d,851cc1a9,d0e18717) Z8(927372a0,2c6f8635,a2d3aa12,2a408ea8,37493bd5,f1c73674,555aaaee,80200400) },{ Z8(79777d59,324ee7e4,c1f44d16,8b34cd9f,93f10143,3d7fa0bb,207e9f96,4eb09eb5) Z8(48a27810,fa30f046,a73e0198,48e18ac4,28a8cee1,d784c3bf,294e0a9e,50ab3912) Z8(b21065c5,6d4cc4b2,074642ad,bacb1ec0,aeaab3f7,fa98fd22,e8ab030f,c1f49749) Z8(df519b31,8f1c0721,2efed010,65396edd,987bb849,36cfb318,8239d916,40bcf1a2) Z8(465188b0,3720f304,0b522bc3,283bea2c,0537f7c6,e2e24da4,3c78808e,e19afda9) Z8(9253dfde,a5b09543,8134b17d,51ce9636,f09b366b,d3aca3c0,5e908566,22e69369) Z8(7edb6bb4,eb30c804,598a9843,4d3c8b19,9769062b,68373103,173dce18,c1b322a5) Z8(47230b6d,8ba117dd,df088141,420f9e4e,d0e989bc,330e8c04,fd956672,57202737) Z8(a826393e,54b55414,66ebc0d1,dd44292a,63c6da41,dc1b9aee,b72b443b,c63599af) Z8(e749f0c3,e601e3ee,3ea0e3ae,e2299adf,80923f15,bfbf7faa,ad3f0f50,3b6f7d14) Z8(fed4cad9,72621213,141d166a,47ae7cd8,fd30674d,602ed8ce,45a0a2d2,38657f1b) Z8(cf3a85b7,ce49f688,b054e223,66396d44,4e245cca,b40a4f0d,89101048,3262b09a) Z8(edcb136c,2934446f,7d93a205,6f8e8424,8fafb37e,b45546c7,f4b07cc4,f890f91f) Z8(c7864953,1d1527d5,5ca0fb6d,4c0c50ab,d7cfe8a0,182e7ff0,601488a1,1def11e9) Z8(1b981f50,8ef3e807,09eba861,ab7b0576,7b75d98a,a333d8fd,3ce9ffaf,aca016a6) Z8(b915d148,b8db52f5,17ffd9e0,72df3a87,79e5a00c,3bc3ee67,51a377d1,9a670745) Z8(3f06f65d,04eb1d5c,ffafd365,049b2d7e,abf3b2ab,3fd7dc72,ffdcdd75,51f84a84) Z8(75d2909c,a202d35f,0abf4e86,cdd724d1,b97a6479,3ea0eade,ab000889,80401002) },{ Z8(96ba8909,0a0201da,6ed13830,26d70be1,87c7d74c,fdcc1a5a,5d6c1ae3,d576b23f) Z8(333b2ecd,31f713e3,5ee91c12,33d3b703,ad02e4a3,fc4344a9,bad77f34,40c468b2) Z8(a0b6f069,530a4eaf,a548d6db,6aeccbd4,53756048,d3e8b488,fe236b24,bb00951d) Z8(391b5fe4,7ea88ebf,10da122a,5602e9b2,30578cd8,a3569a69,e33ba09a,5067833c) Z8(3554d397,5ec36aa5,2b62b6de,a6a480ec,b85acb7c,5083b319,881ee588,7c5d6130) Z8(652e7695,8b95687d,f28b5482,037bbe66,ce9d701d,8913b8fe,897a6907,1a93d7f3) Z8(04bbe10a,71994759,9ac66383,a96afa3b,b9007797,ebfd954d,e06e88b6,59ed00d5) Z8(8eb679de,1a713099,6a55f947,0ecfe69c,443c1f30,9518b45c,3b275771,c5d04dfe) Z8(d3b1bea8,5daf81b8,8a15cd9c,a3014e82,f8d75f6f,d9cc25b9,424bd20c,05d84e59) Z8(5c4aaac9,fa70dfd6,8e770b4b,456fdc7d,1389e418,c721ed84,16cac398,af7d57a7) Z8(09e626b5,eba1e359,752f5f2f,5581a201,81362ddf,5821752e,fd92fe29,41c3748b) Z8(0abfd98a,f5a282f6,1aa40602,f354ebb5,66d9ea67,8cfc4b6d,5b5ebcf4,a6de9de5) Z8(8e3c8af0,e114a7f6,4c890bea,175a5a91,b2a853dd,709be027,27dedfc7,f86c485d) Z8(3eba10f2,8e401074,9aab0272,05a23bf2,c0f792a4,92d98eda,993f8c6d,adfee4ea) Z8(d0287f28,b6166d0c,107a6442,30f735b1,4871dd86,571a0d3c,6ae61f4b,2c8c8e89) Z8(f6ac196c,d81dafcf,4a3e7b5e,d898b6fc,f12ca26e,e57ebc9c,559d824f,64a80fb6) Z8(950fc9d0,3a554359,ced464f4,20889b29,096b7204,74f41faf,2ba5710f,a2283a1d) Z8(8c205922,9076afe4,65854e0f,0295b6a4,fe4d3866,e744a71e,01b040d4,80602409) },{ Z8(7dcb51e0,afe482ff,beefc606,1727322b,3e7b8164,760019d7,bbeb20ac,cc3e8676) Z8(6b8e430b,6ea24846,ab34686e,c6cf51b9,4bcae1d2,dcc70373,b8a2dc3a,e8e83af0) Z8(16bc987d,c58ed487,883868a7,4cf8cf36,d455dbbc,bcd3d67b,f0f70284,861d86c9) Z8(da0d9c7e,fe3bef24,c611ec14,f29b8087,b375e50a,695e5b19,ab1a7127,9b14d5cc) Z8(b5d0c1af,560079fb,8a72bd06,5aab4d29,3be6cc65,a1d5034d,1c8899d9,6cb4d5ac) Z8(c1eb02f2,078231d0,24447b99,9f851217,78a2b54e,1f74581e,32de2c25,254076b6) Z8(7b44413c,264694bf,4a441c3c,831e8276,2dde6ddb,56b0a084,d411a8a2,3842b59f) Z8(3afb6bf8,c004a0bf,dd425c46,a0705ace,0cbb5961,0b434b89,ca901fa3,633bb34e) Z8(3c232ed5,3e125cb8,2dff1684,66cd4af9,64cb8957,0c08696f,cbc025e1,20489d4f) Z8(90965566,084d2e55,8ec6511c,014a3737,411de64c,48b5440b,ce857dc2,6798da7e) Z8(c9f79aac,5c4347fe,11bda442,07d6aec7,3a9f0fce,81d2a25b,4a830e45,a82f082a) Z8(b4e946ef,840e7dc4,f577a676,2163a215,47dec8d1,0bef4d19,d9cb6ed3,b41876a2) Z8(eba0499a,f9db521b,6d007e01,425c65b0,e039bca1,0d8fe45e,f6c1ec9e,56db3f34) Z8(78873748,bfd44117,63ea747f,730ad69e,78773929,102c4e83,a7dadc36,3203e971) Z8(4aadf7ae,54067aaf,edadcbca,1a6765cd,afe9f0f9,e9b19b90,607bce29,302fd653) Z8(7e9a3473,9f1da49a,3c7ac797,db39e59d,40a811bc,56a00d37,57bda725,f96e18cc) Z8(ff554e0d,eaf5c2fa,5c67ff57,abee91b9,020d348f,e82f3725,fafa1201,575bd293) Z8(d0372a42,1eb90105,8676076f,de780649,3554f733,45152169,5aabbbe9,80804015) },{ Z8(b98d7006,b5b3fbb6,165a494d,79d6bc5d,29cfac64,92feec94,97e5370f,6d1ca01e) Z8(5c522f84,d210c6b9,8cee0836,9eda3628,27088025,d21c28da,0ba2b06e,04723d37) Z8(335a65af,9c618969,d0feae89,450ee3ed,a771d4f9,b06a52cd,d816f0f4,1d2d0604) Z8(86e1465c,1f6d9be4,070b89c6,0dfb88ea,8436ef7b,9281ad38,010bb79b,2384dbdb) Z8(14dd2291,6721df7a,1c499979,fc3665ef,42a57710,7d1d8a06,95790c22,1cc2328f) Z8(22be2038,8a0fb0cd,ab58c444,c76d32c7,07eff20a,8cd98047,80e2679a,c80df062) Z8(a11c935a,720750bc,7b1b1610,29128604,cce1b2b2,d97f58c9,1fc0c68e,7be8f196) Z8(c80c2a1b,8abf3276,7df23c87,bd87b4ee,ec440f3a,e60abb69,4fd0f901,46c8ed21) Z8(e9486783,02cd26ad,bf97459c,201a0ec7,5f34c72e,29c68c6f,bb13d0f8,a7bde7ba) Z8(739bfb7e,e289e191,792fdee1,047fad5f,8a77bdf1,68981ca8,53085631,ba579ae2) Z8(6b95c253,7b18951e,311870d8,e57d8f45,a92e2515,8213e7b0,1b65ce52,a312ef01) Z8(ed23063a,daaa0ba3,3fcbd91e,852b188a,656a480f,59cac7d7,cef1a6a2,5e442d15) Z8(16b0a205,a994d0b5,822195ee,0a933ebc,43d3b558,103198b8,89547d21,b83f64ef) Z8(4621214e,f0151b40,6737186d,aebdc6f0,6303391a,545005bb,74f57df6,48797ab2) Z8(58d785ff,a4382f53,d4236916,f1c815cc,9315fffc,e1a88ec7,82d4f891,f7d5195f) Z8(11f95baa,02756770,3d520122,5d4887e0,2a36f587,b0e56390,1266f519,b6dce1f2) Z8(323bbc7e,f5a060e2,c08f5456,17afdf77,9e1a904a,b2d81cf7,6d090151,2086d001) Z8(6675accc,5a6653bd,bb3124d1,005dce48,8a236bc9,10cc773a,b7b34203,80a06429) },{ Z8(876449d4,d160da90,5421bd7d,75fd8893,df1deda8,0341607a,693f4fb9,145c68e7) Z8(822b563e,cd1b4db0,a7f6df89,4e23e157,da783068,4fa1773b,d05cad09,5cc1f398) Z8(d070f00c,d5ac1209,a779fb81,77c9a42f,abb859d1,8442e79c,09ed46af,bb00315c) Z8(62ef4dad,dc2b30d2,58da2832,7e1d08f8,b88ad558,bfe88a71,fc9b7af8,dd4b9e1b) Z8(2a281f3a,c4b33f96,03a47424,8791f75b,bbe20701,1ba2b6c8,d34305c4,8fc42106) Z8(963ebff7,dc0d20ea,fe63c1f9,0dfcd3c6,66aaf8bc,a0cb48ec,5baca9b2,c3f5dab7) Z8(c94fca3c,87dda06b,19ea53f9,ea2d14c2,7c152da6,eb07491b,5bba393b,0072f2d6) Z8(c1974a90,fdbf4ce3,f7078ed0,fcabb990,9c43a4c9,6e89e546,ed9f5e83,f03cca77) Z8(dfc078fb,fcaca9bc,9f8e6e81,873c470e,7a2b803f,5aa34b9a,1accce33,fc68c38c) Z8(11f98354,88faed69,0fe0b7cb,7a36f41c,ca43c732,80707aca,2d16bb98,6785623d) Z8(12bd7a0f,701d93e2,efff4a35,11c43ee3,7e24eca0,14511eb3,e037b4dc,776fa1c8) Z8(27b1e111,aff342f2,e4724dcc,d5d3e43b,e2d7b859,6bc4df58,5849f2a2,11ac6b0f) Z8(870cb740,4f259c37,c76d4124,f163ba54,22e246e3,ba1578f9,0a45343f,f457859a) Z8(2645b431,07d2a7bd,89037290,139fc90c,7b181e29,5a380c43,838096db,5640bfab) Z8(79306d2d,03c45a17,f9876699,8c8b05d8,d3cdee15,971e09c4,f25d48e3,0b68d496) Z8(e1fab982,1787d098,f188e595,995fefa1,584689db,35c7fd88,f23d2ea5,824255ec) Z8(c166e477,29edd062,c32c5dd0,da211698,317fb710,ad10b872,d60190ed,39ff5341) Z8(9d17e8cf,617ada6e,e72f240b,3e5babe1,8cb02cd4,6f2ac8f5,1b081ba0,80c09048) },{ Z8(a3dfa477,c368c35d,d93f73fb,756097fd,fe57f5d2,35be3fb3,78a495f6,a312dea7) Z8(3bb5baa7,0d8c9e3c,6f201a87,91e0bd0d,13fd5b7c,d80423ef,bd1c637b,f2499b83) Z8(becc8dac,70c67401,83b79255,153c94e8,5dba29b2,13156b4d,30254812,e0ff64f8) Z8(852eaace,3446bd94,7d548730,16ccdd80,096a20e1,c0d6e945,e902a956,2f76ec70) Z8(e02f9897,6308fe2f,0dd10bcd,ac2e9091,587742d4,bf8f8ae0,5c603f15,d2aaa214) Z8(fe0fe206,76b2186e,e12a7a24,dd2b5436,8d94c75d,a709743f,ee4a81cc,96661b18) Z8(0a15823f,481b77b3,bd9b5384,6c3f0452,b692cbf9,66b3ce69,b1a75866,05dde90e) Z8(70df257e,9ef089ce,9afa121c,349e69ec,7e08e525,75980dd4,02a689dc,9dbc0f0c) Z8(eae1bef0,15e6cb71,214e45c1,878bb12f,65543f98,443ee3fd,6bebb3d2,b3eaaded) Z8(239df50b,ecd712ab,62bc26a9,602a70dd,2a3ec602,490f62c8,b6fb7278,c0941599) Z8(bb4eb9e5,15e60885,c5915803,bc94f8de,442e36c7,99ed9ed5,606ad26d,d51960ce) Z8(28fabcce,31d140fb,497dd53f,2a9e2f10,85a40ab3,875b51c8,299dc08c,bd3a461e) 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Z8(001bf582,01c3d0a5,a163750d,259d7c59,32f3629c,2e48b09d,4610b706,cc2ad7c5) Z8(bc19d6d0,a8f8bf96,30ec3190,9bbc4bda,98576ff0,c630dc4b,128f36c8,0cb87b4a) Z8(81b78882,119850ab,33d3ae36,4e85426e,8a84d83d,063d0e81,f4a8357f,a01196df) Z8(7b0bba13,09ae65c6,986ad834,fd0535e5,8d108d10,bc9c5cc0,103ecbff,fbe03879) Z8(41643aa5,d2eb49c4,661cce39,bcf3134f,4131119e,57c0ea21,9b8fac86,1cc07da2) Z8(3229416d,ec45cad3,121f4b23,386b4f13,5c1236be,8d8e84d5,ceaa823a,f87d396a) Z8(3b8f3b04,b98d2785,6b39013d,414a26e1,6e4708c0,1582cd67,680379f4,c750387f) Z8(3ff6a04e,fac0f617,19c31758,9c3d1729,51d3f338,bc414a7f,2a31b689,90223629) Z8(0d371e0d,232759e7,95cc9009,6f7c685d,8bc8b40e,27bc7157,f26fd248,83ef2b15) }}; arb-2.8.1/arb/exp_taylor_bound.c000066400000000000000000000067011264125401100165530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013, 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define TABSIZE 256 /* bounds for log2(1/n!) */ static const int rec_fac_bound_2exp_si_tab[TABSIZE] = { 0, 0, -1, -2, -4, -6, -9, -12, -15, -18, -21, -25, -28, -32, -36, -40, -44, -48, -52, -56, -61, -65, -69, -74, -79, -83, -88, -93, -97, -102, -107, -112, -117, -122, -127, -132, -138, -143, -148, -153, -159, -164, -169, -175, -180, -186, -191, -197, -202, -208, -214, -219, -225, -231, -237, -242, -248, -254, -260, -266, -272, -278, -284, -289, -295, -302, -308, -314, -320, -326, -332, -338, -344, -350, -357, -363, -369, -375, -382, -388, -394, -401, -407, -413, -420, -426, -433, -439, -446, -452, -458, -465, -472, -478, -485, -491, -498, -504, -511, -518, -524, -531, -538, -544, -551, -558, -564, -571, -578, -585, -591, -598, -605, -612, -619, -626, -632, -639, -646, -653, -660, -667, -674, -681, -688, -695, -702, -709, -716, -723, -730, -737, -744, -751, -758, -765, -772, -779, -786, -793, -801, -808, -815, -822, -829, -836, -844, -851, -858, -865, -872, -880, -887, -894, -901, -909, -916, -923, -931, -938, -945, -952, -960, -967, -975, -982, -989, -997, -1004, -1011, -1019, -1026, -1034, -1041, -1049, -1056, -1064, -1071, -1078, -1086, -1093, -1101, -1108, -1116, -1123, -1131, -1139, -1146, -1154, -1161, -1169, -1176, -1184, -1192, -1199, -1207, -1214, -1222, -1230, -1237, -1245, -1253, -1260, -1268, -1276, -1283, -1291, -1299, -1306, -1314, -1322, -1329, -1337, -1345, -1353, -1360, -1368, -1376, -1384, -1391, -1399, -1407, -1415, -1423, -1430, -1438, -1446, -1454, -1462, -1470, -1477, -1485, -1493, -1501, -1509, -1517, -1525, -1532, -1540, -1548, -1556, -1564, -1572, -1580, -1588, -1596, -1604, -1612, -1620, -1628, -1636, -1644, -1652, -1660, -1668, -1675 }; static __inline__ long rec_fac_bound_2exp_si(slong n) { if (n < TABSIZE) { return rec_fac_bound_2exp_si_tab[n]; } else { mag_t t; mag_init(t); mag_rfac_ui(t, n); /* todo: check for overflow */ return MAG_EXP(t); } } slong _arb_exp_taylor_bound(slong mag, slong prec) { slong i; /* assume x <= 1/4 */ if (mag > -2) { flint_printf("_arb_exp_taylor_bound: too large input %wd\n", mag); abort(); } for (i = 1; ; i++) { if (mag * i + rec_fac_bound_2exp_si(i) < -prec - 1) return i; } } arb-2.8.1/arb/exp_taylor_naive.c000066400000000000000000000040721264125401100165450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void _arb_exp_taylor_naive(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N) { ulong k; mp_ptr s, t, u, v; mp_size_t nn = xn + 1; if (N == 0) { flint_mpn_zero(y, xn + 1); error[0] = 0; return; } s = flint_malloc(sizeof(mp_limb_t) * (nn + 1)); t = flint_malloc(sizeof(mp_limb_t) * nn); v = flint_malloc(sizeof(mp_limb_t) * nn); u = flint_malloc(sizeof(mp_limb_t) * 2 * nn); /* s = 1 */ flint_mpn_zero(s, nn); s[nn] = 1; /* t = v = x */ flint_mpn_zero(t, nn); flint_mpn_copyi(t + 1, x, xn); flint_mpn_copyi(v, t, nn); for (k = 1; k < N; k++) { s[nn] += mpn_add_n(s, s, t, nn); /* t = t * x / (k + 1) */ mpn_mul_n(u, t, v, nn); flint_mpn_copyi(t, u + nn, nn); mpn_divrem_1(t, 0, t, nn, k + 1); } flint_mpn_copyi(y, s + 1, xn + 1); error[0] = 2; flint_free(s); flint_free(t); flint_free(u); flint_free(v); } arb-2.8.1/arb/exp_taylor_rs.c000066400000000000000000000754621264125401100161020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* See verify_taylor.py for code to generate tables and proof of correctness */ #define TMP_ALLOC_LIMBS(size) TMP_ALLOC((size) * sizeof(mp_limb_t)) #define FACTORIAL_TAB_SIZE 288 #if FLINT_BITS == 64 const mp_limb_t factorial_tab_numer[FACTORIAL_TAB_SIZE] = { UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(1216451004088320000), UWORD(405483668029440000), UWORD(101370917007360000), UWORD(20274183401472000), UWORD(3379030566912000), UWORD(482718652416000), UWORD(60339831552000), UWORD(6704425728000), UWORD(670442572800), UWORD(60949324800), UWORD(5079110400), UWORD(390700800), UWORD(27907200), UWORD(1860480), UWORD(116280), UWORD(6840), UWORD(380), UWORD(20), UWORD(1), UWORD(169958063987712000), UWORD(7725366544896000), UWORD(335885501952000), UWORD(13995229248000), UWORD(559809169920), UWORD(21531121920), UWORD(797448960), UWORD(28480320), UWORD(982080), UWORD(32736), UWORD(1056), UWORD(33), UWORD(1), UWORD(405179306820288000), UWORD(11576551623436800), UWORD(321570878428800), UWORD(8691104822400), UWORD(228713284800), UWORD(5864443200), UWORD(146611080), UWORD(3575880), UWORD(85140), UWORD(1980), UWORD(45), UWORD(1), UWORD(129210868410624000), UWORD(2749167412992000), UWORD(57274321104000), UWORD(1168863696000), UWORD(23377273920), UWORD(458377920), UWORD(8814960), UWORD(166320), UWORD(3080), UWORD(56), UWORD(1), UWORD(13431688016947200), UWORD(231580827878400), UWORD(3925098777600), UWORD(65418312960), UWORD(1072431360), UWORD(17297280), UWORD(274560), UWORD(4290), UWORD(66), UWORD(1), UWORD(51698307350592000), UWORD(760269225744000), UWORD(11018394576000), UWORD(157405636800), UWORD(2216980800), UWORD(30791400), UWORD(421800), UWORD(5700), UWORD(76), UWORD(1), UWORD(166872705665702400), UWORD(2139393662380800), UWORD(27080932435200), UWORD(338511655440), UWORD(4179156240), UWORD(50965320), UWORD(614040), UWORD(7310), UWORD(86), UWORD(1), UWORD(4900933563926400), UWORD(55692426862800), UWORD(625757605200), UWORD(6952862280), UWORD(76405080), UWORD(830490), UWORD(8930), UWORD(95), UWORD(1), UWORD(10385445095625600), UWORD(107066444284800), UWORD(1092514737600), UWORD(11035502400), UWORD(110355024), UWORD(1092624), UWORD(10712), UWORD(104), UWORD(1), UWORD(20632508204394240), UWORD(194646303815040), UWORD(1819124334720), UWORD(16843743840), UWORD(154529760), UWORD(1404816), UWORD(12656), UWORD(113), UWORD(1), UWORD(38823716505974400), UWORD(337597534834560), UWORD(2910323576160), UWORD(24874560480), UWORD(210801360), UWORD(1771440), UWORD(14762), UWORD(122), UWORD(1), UWORD(69746158460160000), UWORD(562469019840000), UWORD(4499752158720), UWORD(35712318720), UWORD(281199360), UWORD(2196870), UWORD(17030), UWORD(131), UWORD(1), UWORD(120384786168259200), UWORD(905148768182400), UWORD(6754841553600), UWORD(50035863360), UWORD(367910760), UWORD(2685480), UWORD(19460), UWORD(140), UWORD(1), UWORD(1346749373249280), UWORD(9484150515840), UWORD(66322730880), UWORD(460574520), UWORD(3176376), UWORD(21756), UWORD(148), UWORD(1), UWORD(1961463552048000), UWORD(13076423680320), UWORD(86598832320), UWORD(569729160), UWORD(3723720), UWORD(24180), UWORD(156), UWORD(1), UWORD(2802505908948480), UWORD(17737379170560), UWORD(111555843840), UWORD(697224024), UWORD(4330584), UWORD(26732), UWORD(164), UWORD(1), UWORD(3935446603320960), UWORD(23707509658560), UWORD(141961135680), UWORD(845006760), UWORD(5000040), UWORD(29412), UWORD(172), UWORD(1), UWORD(5440248896544000), UWORD(31265798256000), UWORD(178661704320), UWORD(1015123320), UWORD(5735160), UWORD(32220), UWORD(180), UWORD(1), UWORD(7413519413139840), UWORD(40733623149120), UWORD(222588104640), UWORD(1209717960), UWORD(6539016), UWORD(35156), UWORD(188), UWORD(1), UWORD(9970981685683200), UWORD(52478850977280), UWORD(274758382080), UWORD(1431033240), UWORD(7414680), UWORD(38220), UWORD(196), UWORD(1), UWORD(13250183553129600), UWORD(66920118955200), UWORD(336282004800), UWORD(1681410024), UWORD(8365224), UWORD(41412), UWORD(204), UWORD(1), UWORD(17413448982209280), UWORD(84531305738880), UWORD(408363795840), UWORD(1963287480), UWORD(9393720), UWORD(44732), UWORD(212), UWORD(1), UWORD(22651084881532800), UWORD(105846191035200), UWORD(492307865280), UWORD(2279203080), UWORD(10503240), UWORD(48180), UWORD(220), UWORD(1), UWORD(29184853478054400), UWORD(131463303955200), UWORD(589521542400), UWORD(2631792600), UWORD(11696856), UWORD(51756), UWORD(228), UWORD(1), UWORD(37271720825539200), UWORD(162050960111040), UWORD(701519307840), UWORD(3023790120), UWORD(12977640), UWORD(55460), UWORD(236), UWORD(1), UWORD(47207892014680320), UWORD(198352487456640), UWORD(829926725760), UWORD(3458028024), UWORD(14348664), UWORD(59292), UWORD(244), UWORD(1), UWORD(59333143654512000), UWORD(241191640872000), UWORD(976484376000), UWORD(3937437000), UWORD(15813000), UWORD(63252), UWORD(252), UWORD(1), UWORD(284751785364480), UWORD(1121070021120), UWORD(4396353024), UWORD(17173254), UWORD(66822), UWORD(259), UWORD(1), UWORD(334679402201760), UWORD(1282296560160), UWORD(4894261680), UWORD(18609360), UWORD(70490), UWORD(266), UWORD(1), UWORD(391698294099840), UWORD(1461560798880), UWORD(5433311520), UWORD(20123376), UWORD(74256), UWORD(273), UWORD(1), UWORD(456592291848000), UWORD(1660335606720), UWORD(6015708720), UWORD(21717360), UWORD(78120), UWORD(280), UWORD(1), UWORD(530208485286480), UWORD(1880171933640), UWORD(6643717080), UWORD(23393370), UWORD(82082), UWORD(287), UWORD(1), }; const mp_limb_t factorial_tab_denom[FACTORIAL_TAB_SIZE] = { UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(2432902008176640000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(3569119343741952000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(13776096431889792000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(5943699946888704000), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(765606216965990400), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(3463786592489664000), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(12849198336259084800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(426381220061596800), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(997002729180057600), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(2166413361461395200), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(4425903681681081600), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(8578777490599680000), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(15890791774210214400), UWORD(189891661628148480), UWORD(189891661628148480), UWORD(189891661628148480), UWORD(189891661628148480), UWORD(189891661628148480), UWORD(189891661628148480), UWORD(189891661628148480), UWORD(189891661628148480), UWORD(292258069255152000), UWORD(292258069255152000), UWORD(292258069255152000), UWORD(292258069255152000), UWORD(292258069255152000), UWORD(292258069255152000), UWORD(292258069255152000), UWORD(292258069255152000), UWORD(439993427704911360), UWORD(439993427704911360), UWORD(439993427704911360), UWORD(439993427704911360), UWORD(439993427704911360), UWORD(439993427704911360), UWORD(439993427704911360), UWORD(439993427704911360), UWORD(649348689547958400), UWORD(649348689547958400), UWORD(649348689547958400), UWORD(649348689547958400), UWORD(649348689547958400), UWORD(649348689547958400), UWORD(649348689547958400), UWORD(649348689547958400), UWORD(941163059102112000), UWORD(941163059102112000), UWORD(941163059102112000), UWORD(941163059102112000), UWORD(941163059102112000), UWORD(941163059102112000), UWORD(941163059102112000), UWORD(941163059102112000), UWORD(1341847013778311040), UWORD(1341847013778311040), UWORD(1341847013778311040), UWORD(1341847013778311040), UWORD(1341847013778311040), UWORD(1341847013778311040), UWORD(1341847013778311040), UWORD(1341847013778311040), UWORD(1884515538594124800), UWORD(1884515538594124800), UWORD(1884515538594124800), UWORD(1884515538594124800), UWORD(1884515538594124800), UWORD(1884515538594124800), UWORD(1884515538594124800), UWORD(1884515538594124800), UWORD(2610286159966531200), UWORD(2610286159966531200), UWORD(2610286159966531200), UWORD(2610286159966531200), UWORD(2610286159966531200), UWORD(2610286159966531200), UWORD(2610286159966531200), UWORD(2610286159966531200), UWORD(3569757041352902400), UWORD(3569757041352902400), UWORD(3569757041352902400), UWORD(3569757041352902400), UWORD(3569757041352902400), UWORD(3569757041352902400), UWORD(3569757041352902400), UWORD(3569757041352902400), UWORD(4824681079766486400), UWORD(4824681079766486400), UWORD(4824681079766486400), UWORD(4824681079766486400), UWORD(4824681079766486400), UWORD(4824681079766486400), UWORD(4824681079766486400), UWORD(4824681079766486400), UWORD(6449852618650022400), UWORD(6449852618650022400), UWORD(6449852618650022400), UWORD(6449852618650022400), UWORD(6449852618650022400), UWORD(6449852618650022400), UWORD(6449852618650022400), UWORD(6449852618650022400), UWORD(8535224069048476800), UWORD(8535224069048476800), UWORD(8535224069048476800), UWORD(8535224069048476800), UWORD(8535224069048476800), UWORD(8535224069048476800), UWORD(8535224069048476800), UWORD(8535224069048476800), UWORD(11188270407479235840), UWORD(11188270407479235840), UWORD(11188270407479235840), UWORD(11188270407479235840), UWORD(11188270407479235840), UWORD(11188270407479235840), UWORD(11188270407479235840), UWORD(11188270407479235840), UWORD(14536620195355440000), UWORD(14536620195355440000), UWORD(14536620195355440000), UWORD(14536620195355440000), UWORD(14536620195355440000), UWORD(14536620195355440000), UWORD(14536620195355440000), UWORD(14536620195355440000), UWORD(72042201697213440), UWORD(72042201697213440), UWORD(72042201697213440), UWORD(72042201697213440), UWORD(72042201697213440), UWORD(72042201697213440), UWORD(72042201697213440), UWORD(87016644572457600), UWORD(87016644572457600), UWORD(87016644572457600), UWORD(87016644572457600), UWORD(87016644572457600), UWORD(87016644572457600), UWORD(87016644572457600), UWORD(104583444524657280), UWORD(104583444524657280), UWORD(104583444524657280), UWORD(104583444524657280), UWORD(104583444524657280), UWORD(104583444524657280), UWORD(104583444524657280), UWORD(125106287966352000), UWORD(125106287966352000), UWORD(125106287966352000), UWORD(125106287966352000), UWORD(125106287966352000), UWORD(125106287966352000), UWORD(125106287966352000), UWORD(148988584365500880), UWORD(148988584365500880), UWORD(148988584365500880), UWORD(148988584365500880), UWORD(148988584365500880), UWORD(148988584365500880), UWORD(148988584365500880), }; #else const mp_limb_t factorial_tab_numer[FACTORIAL_TAB_SIZE] = { UWORD(479001600), UWORD(479001600), UWORD(239500800), UWORD(79833600), UWORD(19958400), UWORD(3991680), UWORD(665280), UWORD(95040), UWORD(11880), UWORD(1320), UWORD(132), UWORD(12), UWORD(1), UWORD(19535040), UWORD(1395360), UWORD(93024), UWORD(5814), UWORD(342), UWORD(19), UWORD(1), UWORD(165765600), UWORD(7893600), UWORD(358800), UWORD(15600), UWORD(650), UWORD(26), UWORD(1), UWORD(24165120), UWORD(863040), UWORD(29760), UWORD(992), UWORD(32), UWORD(1), UWORD(60233040), UWORD(1771560), UWORD(50616), UWORD(1406), UWORD(38), UWORD(1), UWORD(2961840), UWORD(74046), UWORD(1806), UWORD(43), UWORD(1), UWORD(4669920), UWORD(103776), UWORD(2256), UWORD(48), UWORD(1), UWORD(7027800), UWORD(140556), UWORD(2756), UWORD(53), UWORD(1), UWORD(10182480), UWORD(185136), UWORD(3306), UWORD(58), UWORD(1), UWORD(14295960), UWORD(238266), UWORD(3906), UWORD(63), UWORD(1), UWORD(19545240), UWORD(300696), UWORD(4556), UWORD(68), UWORD(1), UWORD(26122320), UWORD(373176), UWORD(5256), UWORD(73), UWORD(1), UWORD(34234200), UWORD(456456), UWORD(6006), UWORD(78), UWORD(1), UWORD(44102880), UWORD(551286), UWORD(6806), UWORD(83), UWORD(1), UWORD(635970), UWORD(7482), UWORD(87), UWORD(1), UWORD(728910), UWORD(8190), UWORD(91), UWORD(1), UWORD(830490), UWORD(8930), UWORD(95), UWORD(1), UWORD(941094), UWORD(9702), UWORD(99), UWORD(1), UWORD(1061106), UWORD(10506), UWORD(103), UWORD(1), UWORD(1190910), UWORD(11342), UWORD(107), UWORD(1), UWORD(1330890), UWORD(12210), UWORD(111), UWORD(1), UWORD(1481430), UWORD(13110), UWORD(115), UWORD(1), UWORD(1642914), UWORD(14042), UWORD(119), UWORD(1), UWORD(1815726), UWORD(15006), UWORD(123), UWORD(1), UWORD(2000250), UWORD(16002), UWORD(127), UWORD(1), UWORD(2196870), UWORD(17030), UWORD(131), UWORD(1), UWORD(2405970), UWORD(18090), UWORD(135), UWORD(1), UWORD(2627934), UWORD(19182), UWORD(139), UWORD(1), UWORD(2863146), UWORD(20306), UWORD(143), UWORD(1), UWORD(3111990), UWORD(21462), UWORD(147), UWORD(1), UWORD(3374850), UWORD(22650), UWORD(151), UWORD(1), UWORD(3652110), UWORD(23870), UWORD(155), UWORD(1), UWORD(3944154), UWORD(25122), UWORD(159), UWORD(1), UWORD(4251366), UWORD(26406), UWORD(163), UWORD(1), UWORD(4574130), UWORD(27722), UWORD(167), UWORD(1), UWORD(4912830), UWORD(29070), UWORD(171), UWORD(1), UWORD(5267850), UWORD(30450), UWORD(175), UWORD(1), UWORD(5639574), UWORD(31862), UWORD(179), UWORD(1), UWORD(6028386), UWORD(33306), UWORD(183), UWORD(1), UWORD(6434670), UWORD(34782), UWORD(187), UWORD(1), UWORD(6858810), UWORD(36290), UWORD(191), UWORD(1), UWORD(7301190), UWORD(37830), UWORD(195), UWORD(1), UWORD(7762194), UWORD(39402), UWORD(199), UWORD(1), UWORD(8242206), UWORD(41006), UWORD(203), UWORD(1), UWORD(8741610), UWORD(42642), UWORD(207), UWORD(1), UWORD(9260790), UWORD(44310), UWORD(211), UWORD(1), UWORD(9800130), UWORD(46010), UWORD(215), UWORD(1), UWORD(10360014), UWORD(47742), UWORD(219), UWORD(1), UWORD(10940826), UWORD(49506), UWORD(223), UWORD(1), UWORD(11542950), UWORD(51302), UWORD(227), UWORD(1), UWORD(12166770), UWORD(53130), UWORD(231), UWORD(1), UWORD(12812670), UWORD(54990), UWORD(235), UWORD(1), UWORD(13481034), UWORD(56882), UWORD(239), UWORD(1), UWORD(14172246), UWORD(58806), UWORD(243), UWORD(1), UWORD(14886690), UWORD(60762), UWORD(247), UWORD(1), UWORD(15624750), UWORD(62750), UWORD(251), UWORD(1), UWORD(16386810), UWORD(64770), UWORD(255), UWORD(1), UWORD(66306), UWORD(258), UWORD(1), UWORD(67860), UWORD(261), UWORD(1), UWORD(69432), UWORD(264), UWORD(1), UWORD(71022), UWORD(267), UWORD(1), UWORD(72630), UWORD(270), UWORD(1), UWORD(74256), UWORD(273), UWORD(1), UWORD(75900), UWORD(276), UWORD(1), UWORD(77562), UWORD(279), UWORD(1), UWORD(79242), UWORD(282), UWORD(1), UWORD(80940), UWORD(285), UWORD(1), UWORD(82656), UWORD(288), }; const mp_limb_t factorial_tab_denom[FACTORIAL_TAB_SIZE] = { UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(479001600), UWORD(253955520), UWORD(253955520), UWORD(253955520), UWORD(253955520), UWORD(253955520), UWORD(253955520), UWORD(253955520), UWORD(3315312000), UWORD(3315312000), UWORD(3315312000), UWORD(3315312000), UWORD(3315312000), UWORD(3315312000), UWORD(3315312000), UWORD(652458240), UWORD(652458240), UWORD(652458240), UWORD(652458240), UWORD(652458240), UWORD(652458240), UWORD(1987690320), UWORD(1987690320), UWORD(1987690320), UWORD(1987690320), UWORD(1987690320), UWORD(1987690320), UWORD(115511760), UWORD(115511760), UWORD(115511760), UWORD(115511760), UWORD(115511760), UWORD(205476480), UWORD(205476480), UWORD(205476480), UWORD(205476480), UWORD(205476480), UWORD(344362200), UWORD(344362200), UWORD(344362200), UWORD(344362200), UWORD(344362200), UWORD(549853920), UWORD(549853920), UWORD(549853920), UWORD(549853920), UWORD(549853920), UWORD(843461640), UWORD(843461640), UWORD(843461640), UWORD(843461640), UWORD(843461640), UWORD(1250895360), UWORD(1250895360), UWORD(1250895360), UWORD(1250895360), UWORD(1250895360), UWORD(1802440080), UWORD(1802440080), UWORD(1802440080), UWORD(1802440080), UWORD(1802440080), UWORD(2533330800), UWORD(2533330800), UWORD(2533330800), UWORD(2533330800), UWORD(2533330800), UWORD(3484127520), UWORD(3484127520), UWORD(3484127520), UWORD(3484127520), UWORD(3484127520), UWORD(53421480), UWORD(53421480), UWORD(53421480), UWORD(53421480), UWORD(64144080), UWORD(64144080), UWORD(64144080), UWORD(64144080), UWORD(76405080), UWORD(76405080), UWORD(76405080), UWORD(76405080), UWORD(90345024), UWORD(90345024), UWORD(90345024), UWORD(90345024), UWORD(106110600), UWORD(106110600), UWORD(106110600), UWORD(106110600), UWORD(123854640), UWORD(123854640), UWORD(123854640), UWORD(123854640), UWORD(143736120), UWORD(143736120), UWORD(143736120), UWORD(143736120), UWORD(165920160), UWORD(165920160), UWORD(165920160), UWORD(165920160), UWORD(190578024), UWORD(190578024), UWORD(190578024), UWORD(190578024), UWORD(217887120), UWORD(217887120), UWORD(217887120), UWORD(217887120), UWORD(248031000), UWORD(248031000), UWORD(248031000), UWORD(248031000), UWORD(281199360), UWORD(281199360), UWORD(281199360), UWORD(281199360), UWORD(317588040), UWORD(317588040), UWORD(317588040), UWORD(317588040), UWORD(357399024), UWORD(357399024), UWORD(357399024), UWORD(357399024), UWORD(400840440), UWORD(400840440), UWORD(400840440), UWORD(400840440), UWORD(448126560), UWORD(448126560), UWORD(448126560), UWORD(448126560), UWORD(499477800), UWORD(499477800), UWORD(499477800), UWORD(499477800), UWORD(555120720), UWORD(555120720), UWORD(555120720), UWORD(555120720), UWORD(615288024), UWORD(615288024), UWORD(615288024), UWORD(615288024), UWORD(680218560), UWORD(680218560), UWORD(680218560), UWORD(680218560), UWORD(750157320), UWORD(750157320), UWORD(750157320), UWORD(750157320), UWORD(825355440), UWORD(825355440), UWORD(825355440), UWORD(825355440), UWORD(906070200), UWORD(906070200), UWORD(906070200), UWORD(906070200), UWORD(992565024), UWORD(992565024), UWORD(992565024), UWORD(992565024), UWORD(1085109480), UWORD(1085109480), UWORD(1085109480), UWORD(1085109480), UWORD(1183979280), UWORD(1183979280), UWORD(1183979280), UWORD(1183979280), UWORD(1289456280), UWORD(1289456280), UWORD(1289456280), UWORD(1289456280), UWORD(1401828480), UWORD(1401828480), UWORD(1401828480), UWORD(1401828480), UWORD(1521390024), UWORD(1521390024), UWORD(1521390024), UWORD(1521390024), UWORD(1648441200), UWORD(1648441200), UWORD(1648441200), UWORD(1648441200), UWORD(1783288440), UWORD(1783288440), UWORD(1783288440), UWORD(1783288440), UWORD(1926244320), UWORD(1926244320), UWORD(1926244320), UWORD(1926244320), UWORD(2077627560), UWORD(2077627560), UWORD(2077627560), UWORD(2077627560), UWORD(2237763024), UWORD(2237763024), UWORD(2237763024), UWORD(2237763024), UWORD(2406981720), UWORD(2406981720), UWORD(2406981720), UWORD(2406981720), UWORD(2585620800), UWORD(2585620800), UWORD(2585620800), UWORD(2585620800), UWORD(2774023560), UWORD(2774023560), UWORD(2774023560), UWORD(2774023560), UWORD(2972539440), UWORD(2972539440), UWORD(2972539440), UWORD(2972539440), UWORD(3181524024), UWORD(3181524024), UWORD(3181524024), UWORD(3181524024), UWORD(3401339040), UWORD(3401339040), UWORD(3401339040), UWORD(3401339040), UWORD(3632352360), UWORD(3632352360), UWORD(3632352360), UWORD(3632352360), UWORD(3874938000), UWORD(3874938000), UWORD(3874938000), UWORD(3874938000), UWORD(4129476120), UWORD(4129476120), UWORD(4129476120), UWORD(4129476120), UWORD(16974336), UWORD(16974336), UWORD(16974336), UWORD(17575740), UWORD(17575740), UWORD(17575740), UWORD(18191184), UWORD(18191184), UWORD(18191184), UWORD(18820830), UWORD(18820830), UWORD(18820830), UWORD(19464840), UWORD(19464840), UWORD(19464840), UWORD(20123376), UWORD(20123376), UWORD(20123376), UWORD(20796600), UWORD(20796600), UWORD(20796600), UWORD(21484674), UWORD(21484674), UWORD(21484674), UWORD(22187760), UWORD(22187760), UWORD(22187760), UWORD(22906020), UWORD(22906020), UWORD(22906020), UWORD(23639616), UWORD(23639616), }; #endif void _arb_exp_taylor_rs(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N) { mp_ptr s, t, xpow; mp_limb_t new_denom, old_denom, c; slong power, k, m; TMP_INIT; TMP_START; if (N >= FACTORIAL_TAB_SIZE - 1) { flint_printf("_arb_exp_taylor_rs: N too large!\n"); abort(); } if (N <= 3) { if (N <= 1) { flint_mpn_zero(y, xn); y[xn] = N; error[0] = 0; } else if (N == 2) { flint_mpn_copyi(y, x, xn); y[xn] = 1; error[0] = 0; } else { /* 1 + x + x^2 / 2 */ t = TMP_ALLOC_LIMBS(2 * xn); mpn_sqr(t, x, xn); mpn_rshift(t + xn, t + xn, xn, 1); y[xn] = mpn_add_n(y, x, t + xn, xn) + 1; error[0] = 2; } } else { /* Choose m ~= sqrt(num_terms) (m must be even, >= 2) */ /* TODO: drop evenness assumption since we don't have sign issues here? */ /* TODO: then just need to fix power construction below... */ m = 2; while (m * m < N) m += 2; /* todo: merge allocations */ xpow = TMP_ALLOC_LIMBS((m + 1) * xn); s = TMP_ALLOC_LIMBS(xn + 2); t = TMP_ALLOC_LIMBS(2 * xn + 2); /* todo: 1 limb too much? */ /* higher index ---> */ /* | ---xn--- | */ /* xpow = | | x^m | x^(m-1) | ... | x^2 | x | */ #define XPOW_WRITE(__k) (xpow + (m - (__k)) * xn) #define XPOW_READ(__k) (xpow + (m - (__k) + 1) * xn) flint_mpn_copyi(XPOW_READ(1), x, xn); mpn_sqr(XPOW_WRITE(2), XPOW_READ(1), xn); for (k = 4; k <= m; k += 2) { mpn_mul_n(XPOW_WRITE(k - 1), XPOW_READ(k / 2), XPOW_READ(k / 2 - 1), xn); mpn_sqr(XPOW_WRITE(k), XPOW_READ(k / 2), xn); } flint_mpn_zero(s, xn + 1); /* todo: skip one nonscalar multiplication (use x^m) when starting on x^0 */ power = (N - 1) % m; for (k = N - 1; k >= 0; k--) { c = factorial_tab_numer[k]; new_denom = factorial_tab_denom[k]; old_denom = factorial_tab_denom[k+1]; /* change denominators */ if (new_denom != old_denom && k < N - 1) { mpn_divrem_1(s, 0, s, xn + 1, old_denom); } if (power == 0) { /* add c * x^0 -- only top limb is affected */ s[xn] += c; /* Outer polynomial evaluation: multiply by x^m */ if (k != 0) { mpn_mul(t, s, xn + 1, XPOW_READ(m), xn); flint_mpn_copyi(s, t + xn, xn + 1); } power = m - 1; } else { s[xn] += mpn_addmul_1(s, XPOW_READ(power), xn, c); power--; } } /* finally divide by denominator */ mpn_divrem_1(y, 0, s, xn + 1, factorial_tab_denom[0]); /* error bound (ulp) */ error[0] = 2; } TMP_END; } arb-2.8.1/arb/fac.c000066400000000000000000000024111264125401100137210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_fac_ui(arb_t x, ulong n, slong prec) { fmpz_t t; fmpz_init(t); fmpz_set_ui(t, n); fmpz_add_ui(t, t, 1); arb_gamma_fmpz(x, t, prec); fmpz_clear(t); } arb-2.8.1/arb/fib.c000066400000000000000000000055751264125401100137460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* Fibonacci numbers using binary powering. D. Takahashi, "A fast algorithm for computing large Fibonacci numbers", Information Processing Letters 75 (2000) 243–246 */ void arb_fib_fmpz(arb_t f, const fmpz_t n, slong prec) { arb_t t, u; slong wp, sign, i; if (fmpz_sgn(n) < 0) { fmpz_t m; fmpz_init(m); fmpz_neg(m, n); arb_fib_fmpz(f, m, prec); if (fmpz_is_even(m)) arb_neg(f, f); fmpz_clear(m); return; } if (fmpz_cmp_ui(n, 4) <= 0) { ulong x = fmpz_get_ui(n); arb_set_ui(f, x - (x > 1)); return; } wp = ARF_PREC_ADD(prec, 3 * fmpz_bits(n)); arb_init(u); arb_init(t); arb_set_ui(f, UWORD(1)); arb_set_ui(u, UWORD(1)); sign = -1; for (i = fmpz_flog_ui(n, UWORD(2)) - 1; i > 0; i--) { arb_mul(t, f, f, wp); arb_add(f, f, u, wp); arb_mul_2exp_si(f, f, -1); arb_mul(f, f, f, wp); arb_mul_2exp_si(f, f, 1); arb_submul_ui(f, t, 3, wp); arb_sub_si(f, f, 2 * sign, wp); arb_mul_ui(u, t, 5, wp); arb_add_si(u, u, 2 * sign, wp); sign = 1; if (fmpz_tstbit(n, i)) { arb_set(t, f); arb_add(f, f, u, wp); arb_mul_2exp_si(f, f, -1); arb_mul_2exp_si(t, t, 1); arb_add(u, f, t, wp); sign = -1; } } if (fmpz_tstbit(n, 0)) { arb_add(f, f, u, wp); arb_mul_2exp_si(f, f, -1); arb_mul(f, f, u, wp); arb_sub_si(f, f, sign, prec); } else { arb_mul(f, f, u, prec); } arb_clear(u); arb_clear(t); } void arb_fib_ui(arb_t f, ulong n, slong prec) { fmpz_t t; fmpz_init_set_ui(t, n); arb_fib_fmpz(f, t, prec); fmpz_clear(t); } arb-2.8.1/arb/floor.c000066400000000000000000000031731264125401100143170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_floor(arb_t z, const arb_t x, slong prec) { if (!arb_is_finite(x)) { arb_indeterminate(z); } else if (arb_is_exact(x)) { arf_floor(arb_midref(z), arb_midref(x)); mag_zero(arb_radref(z)); arb_set_round(z, z, prec); } else { arf_t a, b; arf_init(a); arf_init(b); arb_get_interval_arf(a, b, x, prec); arf_floor(a, a); arf_floor(b, b); arb_set_interval_arf(z, a, b, prec); arf_clear(a); arf_clear(b); } } arb-2.8.1/arb/gamma.c000066400000000000000000000515471264125401100142700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "acb.h" #include "bernoulli.h" #include "hypgeom.h" /* tuning factor */ #define GAMMA_STIRLING_BETA 0.27 #define PI 3.1415926535897932385 static slong choose_n(double log2z, double argz, int digamma, slong prec) { double argf, boundn; slong n; argf = 1.0 / cos(0.5 * argz); argf = log(argf) * (1. / log(2)); for (n = 1; ; n++) { if (digamma) boundn = bernoulli_bound_2exp_si(2*n) - (2*n)*log2z + (2*n+1)*argf; else boundn = bernoulli_bound_2exp_si(2*n) - (2*n-1)*log2z + (2*n)*argf; /* success */ if (boundn <= -prec) return n; /* if the term magnitude does not decrease, r is too small */ if (boundn > 1) { flint_printf("exception: gamma_stirling_choose_param failed to converge\n"); abort(); } } } static void choose_small(int * reflect, slong * r, slong * n, double x, double y, int use_reflect, int digamma, slong prec) { double w, argz, log2z; slong rr; /* use reflection formula if very negative */ if (x < -5.0 && use_reflect) { *reflect = 1; x = 1.0 - x; } else { *reflect = 0; } /* argument reduction until |z| >= w */ w = FLINT_MAX(1.0, GAMMA_STIRLING_BETA * prec); rr = 0; while (x < 1.0 || x*x + y*y < w*w) { x++; rr++; } log2z = 0.5 * log(x*x + y*y) * 1.44269504088896341; argz = atan2(y, x); *r = rr; *n = choose_n(log2z, argz, digamma, prec); } static void choose_large(int * reflect, slong * r, slong * n, const arf_t a, const arf_t b, int use_reflect, int digamma, slong prec) { if (use_reflect && arf_sgn(a) < 0) *reflect = 1; else *reflect = 0; *r = 0; /* so big that we will certainly have n = 0 */ if (arf_cmpabs_2exp_si(a, WORD_MAX / 8) >= 0 || arf_cmpabs_2exp_si(b, WORD_MAX / 8) >= 0) { *n = 0; } else { slong ab, bb; double log2z, argz; ab = arf_abs_bound_lt_2exp_si(a); bb = arf_abs_bound_lt_2exp_si(b); log2z = FLINT_MAX(ab, bb); /* piecewise approximation of the argument */ if (arf_is_zero(b)) { if ((arf_sgn(a) < 0) && !(*reflect)) argz = PI; else argz = 0.0; } else { if ((arf_sgn(a) < 0) && !(*reflect)) if (arf_cmpabs(a, b) <= 0) argz = PI * 0.75; else argz = PI; else if (arf_cmpabs(a, b) <= 0) argz = PI * 0.25; else argz = PI * 0.5; } if (argz == PI) *n = 0; else *n = choose_n(log2z, argz, digamma, prec); } } void acb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const acb_t z, int use_reflect, int digamma, slong prec) { const arf_struct * a = arb_midref(acb_realref(z)); const arf_struct * b = arb_midref(acb_imagref(z)); if (!arf_is_finite(a) || !arf_is_finite(b)) { *reflect = *r = *n = 0; } else if (arf_cmpabs_2exp_si(a, 40) > 0 || arf_cmpabs_2exp_si(b, 40) > 0) { choose_large(reflect, r, n, a, b, use_reflect, digamma, prec); } else { choose_small(reflect, r, n, arf_get_d(a, ARF_RND_UP), arf_get_d(b, ARF_RND_UP), use_reflect, digamma, prec); } } void arb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const arb_t x, int use_reflect, int digamma, slong prec) { const arf_struct * a = arb_midref(x); if (arf_is_inf(a) || arf_is_nan(a)) { *reflect = *r = *n = 0; } else if (arf_cmpabs_2exp_si(a, 40) > 0) { arf_t b; arf_init(b); choose_large(reflect, r, n, a, b, use_reflect, digamma, prec); arf_clear(b); } else { choose_small(reflect, r, n, arf_get_d(a, ARF_RND_UP), 0.0, use_reflect, digamma, prec); } } void acb_gamma_bound_phase(mag_t bound, const acb_t z) { arf_t x, y, t, u; int xsign; slong prec; arf_init(x); arf_init(y); arf_init(t); arf_init(u); prec = MAG_BITS; /* first compute x, y such that |arg(z)| <= arg(x+yi) */ /* argument increases with smaller real parts */ arf_set_mag(x, arb_radref(acb_realref(z))); arf_sub(x, arb_midref(acb_realref(z)), x, prec, ARF_RND_FLOOR); xsign = arf_sgn(x); if (xsign >= 0) /* argument increases away from the real axis */ arb_get_abs_ubound_arf(y, acb_imagref(z), prec); else /* argument increases closer to the real axis */ arb_get_abs_lbound_arf(y, acb_imagref(z), prec); if (arf_is_zero(y)) { if (xsign > 0) mag_one(bound); else mag_inf(bound); } else { if (xsign >= 0) { /* compute upper bound for t = y / (sqrt(x^2 + y^2) + x) */ arf_mul(t, x, x, prec, ARF_RND_DOWN); arf_mul(u, y, y, prec, ARF_RND_DOWN); arf_add(t, t, u, prec, ARF_RND_DOWN); arf_sqrt(t, t, prec, ARF_RND_DOWN); arf_add(t, t, x, prec, ARF_RND_DOWN); arf_div(t, y, t, prec, ARF_RND_UP); } else { /* compute upper bound for t = (sqrt(x^2 + y^2) - x) / y */ arf_mul(t, x, x, prec, ARF_RND_UP); arf_mul(u, y, y, prec, ARF_RND_UP); arf_add(t, t, u, prec, ARF_RND_UP); arf_sqrt(t, t, prec, ARF_RND_UP); arf_sub(t, t, x, prec, ARF_RND_UP); arf_div(t, t, y, prec, ARF_RND_UP); } /* compute upper bound for sqrt(1 + t^2) */ arf_mul(t, t, t, prec, ARF_RND_UP); arf_add_ui(t, t, 1, prec, ARF_RND_UP); arf_sqrt(t, t, prec, ARF_RND_UP); arf_get_mag(bound, t); } arf_clear(x); arf_clear(y); arf_clear(t); arf_clear(u); } /* 2 |B_{2n}| G(2n+k-1) / (G(k+1) G(2n+1)) |z| (T |z|^{-1})^(2n+k) TODO: CHECK n >= 1 ? */ void acb_gamma_stirling_bound(mag_ptr err, const acb_t z, slong k0, slong knum, slong n) { mag_t c, t, u, v; slong i, k; if (arb_contains_zero(acb_imagref(z)) && arb_contains_nonpositive(acb_realref(z))) { for (i = 0; i < knum; i++) mag_inf(err + i); return; } mag_init(c); mag_init(t); mag_init(u); mag_init(v); /* t = lower bound for |z| */ acb_get_mag_lower(t, z); /* v = upper bound for |z| */ acb_get_mag(v, z); /* c = upper bound for 1/(cos(arg(z)/2) |z|) */ acb_gamma_bound_phase(c, z); mag_div(c, c, t); /* numerator: 2 B_{2n} gamma(2n+k-1) |z| */ mag_bernoulli_div_fac_ui(err, 2 * n); mag_mul_2exp_si(err, err, 1); mag_fac_ui(u, 2 * n + k0 - 2); mag_mul(err, err, u); mag_mul(err, err, v); /* denominator gamma(k+1) gamma(2n+1) */ mag_rfac_ui(t, k0); mag_mul(err, err, t); /* multiply by c^(2n+k) */ mag_pow_ui(t, c, 2 * n + k0); mag_mul(err, err, t); for (i = 1; i < knum; i++) { /* recurrence factor: c * (2n+k-2) / k */ k = k0 + i; mag_mul(err + i, err + i - 1, c); mag_mul_ui(err + i, err + i, 2 * n + k - 2); mag_div_ui(err + i, err + i, k); } mag_clear(c); mag_clear(t); mag_clear(u); mag_clear(v); } void arb_gamma_stirling_bound(mag_ptr err, const arb_t x, slong k0, slong knum, slong n) { acb_t z; acb_init(z); acb_set_arb(z, x); acb_gamma_stirling_bound(err, z, k0, knum, n); acb_clear(z); } void arb_gamma_stirling_coeff(arb_t b, ulong k, int digamma, slong prec) { fmpz_t d; fmpz_init(d); BERNOULLI_ENSURE_CACHED(2 * k); arb_set_round_fmpz(b, fmpq_numref(bernoulli_cache + 2 * k), prec); if (digamma) fmpz_mul_ui(d, fmpq_denref(bernoulli_cache + 2 * k), 2 * k); else fmpz_mul2_uiui(d, fmpq_denref(bernoulli_cache + 2 * k), 2 * k, 2 * k - 1); arb_div_fmpz(b, b, d, prec); fmpz_clear(d); } void arb_gamma_stirling_eval(arb_t s, const arb_t z, slong nterms, int digamma, slong prec) { arb_t b, t, logz, zinv, zinv2; mag_t err; slong k, term_prec; double z_mag, term_mag; arb_init(b); arb_init(t); arb_init(logz); arb_init(zinv); arb_init(zinv2); arb_log(logz, z, prec); arb_inv(zinv, z, prec); nterms = FLINT_MAX(nterms, 1); arb_zero(s); if (nterms > 1) { arb_mul(zinv2, zinv, zinv, prec); z_mag = arf_get_d(arb_midref(logz), ARF_RND_UP) * 1.44269504088896; for (k = nterms - 1; k >= 1; k--) { term_mag = bernoulli_bound_2exp_si(2 * k); term_mag -= (2 * k - 1) * z_mag; term_prec = prec + term_mag; term_prec = FLINT_MIN(term_prec, prec); term_prec = FLINT_MAX(term_prec, 10); if (prec > 2000) { arb_set_round(t, zinv2, term_prec); arb_mul(s, s, t, term_prec); } else arb_mul(s, s, zinv2, term_prec); arb_gamma_stirling_coeff(b, k, digamma, term_prec); arb_add(s, s, b, term_prec); } if (digamma) arb_mul(s, s, zinv2, prec); else arb_mul(s, s, zinv, prec); } /* remainder bound */ mag_init(err); arb_gamma_stirling_bound(err, z, digamma ? 1 : 0, 1, nterms); mag_add(arb_radref(s), arb_radref(s), err); mag_clear(err); if (digamma) { arb_neg(s, s); arb_mul_2exp_si(zinv, zinv, -1); arb_sub(s, s, zinv, prec); arb_add(s, s, logz, prec); } else { /* (z-0.5)*log(z) - z + log(2*pi)/2 */ arb_one(t); arb_mul_2exp_si(t, t, -1); arb_sub(t, z, t, prec); arb_mul(t, logz, t, prec); arb_add(s, s, t, prec); arb_sub(s, s, z, prec); arb_const_log_sqrt2pi(t, prec); arb_add(s, s, t, prec); } arb_clear(t); arb_clear(b); arb_clear(zinv); arb_clear(zinv2); arb_clear(logz); } void arb_gamma_fmpq_stirling(arb_t y, const fmpq_t a, slong prec) { int reflect; slong r, n, wp; arb_t x, t, u, v; wp = prec + FLINT_BIT_COUNT(prec); arb_init(x); arb_init(t); arb_init(u); arb_init(v); arb_set_fmpq(x, a, wp); arb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 0, wp); if (reflect) { /* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */ fmpq_t b; fmpq_init(b); fmpz_sub(fmpq_numref(b), fmpq_denref(a), fmpq_numref(a)); fmpz_set(fmpq_denref(b), fmpq_denref(a)); arb_rising_fmpq_ui(u, b, r, wp); fmpq_clear(b); arb_const_pi(v, wp); arb_mul(u, u, v, wp); arb_sub_ui(t, x, 1, wp); arb_neg(t, t); arb_add_ui(t, t, r, wp); arb_gamma_stirling_eval(v, t, n, 0, wp); arb_exp(v, v, wp); arb_sin_pi_fmpq(t, a, wp); arb_mul(v, v, t, wp); } else { /* gamma(x) = gamma(x+r) / rf(x,r) */ arb_add_ui(t, x, r, wp); arb_gamma_stirling_eval(u, t, n, 0, wp); arb_exp(u, u, prec); arb_rising_fmpq_ui(v, a, r, wp); } arb_div(y, u, v, prec); arb_clear(t); arb_clear(u); arb_clear(v); arb_clear(x); } void arb_gamma_const_1_3_eval(arb_t s, slong prec) { hypgeom_t series; arb_t t, u; slong wp = prec + 4 + 2 * FLINT_BIT_COUNT(prec); arb_init(t); arb_init(u); hypgeom_init(series); fmpz_poly_set_str(series->A, "1 1"); fmpz_poly_set_str(series->B, "1 1"); fmpz_poly_set_str(series->P, "4 5 -46 108 -72"); fmpz_poly_set_str(series->Q, "4 0 0 0 512000"); prec += FLINT_CLOG2(prec); arb_hypgeom_infsum(s, t, series, wp, wp); arb_sqrt_ui(u, 10, wp); arb_mul(t, t, u, wp); arb_const_pi(u, wp); arb_pow_ui(u, u, 4, wp); arb_mul_ui(u, u, 12, wp); arb_mul(s, s, u, wp); arb_div(s, s, t, wp); arb_root_ui(s, s, 2, wp); arb_root_ui(s, s, 3, prec); hypgeom_clear(series); arb_clear(t); arb_clear(u); } ARB_DEF_CACHED_CONSTANT(arb_gamma_const_1_3, arb_gamma_const_1_3_eval) void arb_gamma_const_1_4_eval(arb_t x, slong prec) { arb_t t, u; slong wp = prec + 4 + 2 * FLINT_BIT_COUNT(prec); arb_init(t); arb_init(u); arb_one(t); arb_sqrt_ui(u, 2, wp); arb_agm(x, t, u, wp); arb_const_pi(t, wp); arb_mul_2exp_si(t, t, 1); arb_sqrt(u, t, wp); arb_mul(u, u, t, wp); arb_div(x, u, x, wp); arb_sqrt(x, x, wp); arb_clear(t); arb_clear(u); } ARB_DEF_CACHED_CONSTANT(arb_gamma_const_1_4, arb_gamma_const_1_4_eval) void arb_gamma_small_frac(arb_t y, unsigned int p, unsigned int q, slong prec) { slong wp = prec + 4; if (q == 1) { arb_one(y); } else if (q == 2) /* p = 1 */ { arb_const_sqrt_pi(y, prec); } else if (q == 3) { if (p == 1) { arb_gamma_const_1_3(y, prec); } else /* p = 2 */ { arb_t t; arb_init(t); arb_gamma_const_1_3(y, wp); arb_sqrt_ui(t, 3, wp); arb_mul(y, y, t, wp); arb_const_pi(t, wp); arb_div(y, t, y, prec); arb_mul_2exp_si(y, y, 1); arb_clear(t); } } else if (q == 4) { if (p == 1) { arb_gamma_const_1_4(y, prec); } else /* p = 3 */ { arb_t t; arb_init(t); arb_sqrt_ui(y, 2, wp); arb_const_pi(t, wp); arb_mul(y, y, t, wp); arb_gamma_const_1_4(t, wp); arb_div(y, y, t, prec); arb_clear(t); } } else if (q == 6) { arb_t t; arb_init(t); arb_const_pi(t, wp); arb_div_ui(t, t, 3, wp); arb_sqrt(t, t, wp); arb_set_ui(y, 2); arb_root_ui(y, y, 3, wp); arb_mul(t, t, y, wp); arb_gamma_const_1_3(y, wp); arb_mul(y, y, y, prec); if (p == 1) { arb_div(y, y, t, prec); } else /* p = 5 */ { arb_div(y, t, y, wp); arb_const_pi(t, wp); arb_mul(y, y, t, prec); arb_mul_2exp_si(y, y, 1); } arb_clear(t); } else { flint_printf("small fraction not implemented!\n"); abort(); } } void arb_gamma_fmpq_outward(arb_t y, const fmpq_t x, slong prec) { fmpq_t a; fmpz_t n; fmpz p, q; slong m; arb_t t, u; fmpq_init(a); fmpz_init(n); arb_init(t); arb_init(u); /* write x = a + n with 0 < a <= 1 */ if (fmpz_is_one(fmpq_denref(x))) { fmpq_one(a); fmpz_sub_ui(n, fmpq_numref(x), 1); } else { fmpz_fdiv_qr(n, fmpq_numref(a), fmpq_numref(x), fmpq_denref(x)); fmpz_set(fmpq_denref(a), fmpq_denref(x)); } if (!fmpz_fits_si(n)) { flint_printf("gamma: too large fmpq to reduce to 0!\n"); abort(); } m = fmpz_get_si(n); /* evaluate gamma(a) */ p = *fmpq_numref(a); q = *fmpq_denref(a); if (q == 1 || q == 2 || q == 3 || q == 4 || q == 6) { arb_gamma_small_frac(t, p, q, prec); } else { flint_printf("arb_gamma_fmpq: invalid fraction\n"); abort(); } /* argument reduction */ if (m >= 0) { arb_rising_fmpq_ui(u, a, m, prec); arb_mul(y, t, u, prec); } else { arb_rising_fmpq_ui(u, x, -m, prec); arb_div(y, t, u, prec); } fmpq_clear(a); fmpz_clear(n); arb_clear(t); arb_clear(u); } void arb_gamma_fmpq(arb_t y, const fmpq_t x, slong prec) { fmpz p, q; p = *fmpq_numref(x); q = *fmpq_denref(x); if ((q == 1 || q == 2 || q == 3 || q == 4 || q == 6) && !COEFF_IS_MPZ(p)) { if (q == 1) { if (p <= 0) { arb_indeterminate(y); return; } if (p < 1200 || 1.44265 * (p*log(p) - p) < 15.0 * prec) { fmpz_t t; fmpz_init(t); fmpz_fac_ui(t, p - 1); arb_set_round_fmpz(y, t, prec); fmpz_clear(t); return; } } p = FLINT_ABS(p); if (p < q * 500.0 || p < q * (500.0 + 0.1 * prec * sqrt(prec))) { arb_gamma_fmpq_outward(y, x, prec); return; } } arb_gamma_fmpq_stirling(y, x, prec); } void arb_gamma_fmpz(arb_t y, const fmpz_t x, slong prec) { fmpq_t t; *fmpq_numref(t) = *x; *fmpq_denref(t) = WORD(1); arb_gamma_fmpq(y, t, prec); } static void _arb_gamma(arb_t y, const arb_t x, slong prec, int inverse) { int reflect; slong r, n, wp; arb_t t, u, v; if (arb_is_exact(x)) { const arf_struct * mid = arb_midref(x); if (arf_is_special(mid)) { if (!inverse && arf_is_pos_inf(mid)) arb_set(y, x); else if (arf_is_nan(mid) || arf_is_neg_inf(mid) || !inverse) arb_indeterminate(y); else arb_zero(y); return; } else if (inverse && arf_is_int(mid) && arf_sgn(mid) < 0) { arb_zero(y); } else { /* fast gamma(n), gamma(n/2) or gamma(n/4) */ if (arf_cmpabs_2exp_si(mid, prec) < 0 && arf_is_int_2exp_si(mid, -2)) { fmpq_t a; fmpq_init(a); arf_get_fmpq(a, mid); arb_gamma_fmpq(y, a, prec + 2 * inverse); if (inverse) arb_inv(y, y, prec); fmpq_clear(a); return; } } } wp = prec + FLINT_BIT_COUNT(prec); arb_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 0, wp); arb_init(t); arb_init(u); arb_init(v); if (reflect) { /* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */ arb_sub_ui(t, x, 1, wp); arb_neg(t, t); arb_rising_ui_rec(u, t, r, wp); arb_const_pi(v, wp); arb_mul(u, u, v, wp); arb_add_ui(t, t, r, wp); arb_gamma_stirling_eval(v, t, n, 0, wp); arb_exp(v, v, wp); arb_sin_pi(t, x, wp); arb_mul(v, v, t, wp); } else { /* gamma(x) = gamma(x+r) / rf(x,r) */ arb_add_ui(t, x, r, wp); arb_gamma_stirling_eval(u, t, n, 0, wp); arb_exp(u, u, prec); arb_rising_ui_rec(v, x, r, wp); } if (inverse) arb_div(y, v, u, prec); else arb_div(y, u, v, prec); arb_clear(t); arb_clear(u); arb_clear(v); } void arb_gamma(arb_t y, const arb_t x, slong prec) { _arb_gamma(y, x, prec, 0); } void arb_rgamma(arb_t y, const arb_t x, slong prec) { _arb_gamma(y, x, prec, 1); } void arb_lgamma(arb_t y, const arb_t x, slong prec) { int reflect; slong r, n, wp; arb_t t, u; if (!arb_is_positive(x)) { arb_indeterminate(y); return; } /* fast gamma(n), gamma(n/2) or gamma(n/4) */ if (arb_is_exact(x) && arf_is_int_2exp_si(arb_midref(x), -2) && arf_cmpabs_2exp_si(arb_midref(x), prec) < 0) { fmpq_t a; fmpq_init(a); arf_get_fmpq(a, arb_midref(x)); arb_gamma_fmpq(y, a, prec); arb_log(y, y, prec); fmpq_clear(a); return; } wp = prec + FLINT_BIT_COUNT(prec); arb_gamma_stirling_choose_param(&reflect, &r, &n, x, 0, 0, wp); /* log(gamma(x)) = log(gamma(x+r)) - log(rf(x,r)) */ arb_init(t); arb_init(u); arb_add_ui(t, x, r, wp); arb_gamma_stirling_eval(u, t, n, 0, wp); arb_rising_ui_rec(t, x, r, wp); arb_log(t, t, wp); arb_sub(y, u, t, prec); arb_clear(t); arb_clear(u); } arb-2.8.1/arb/get_fmpz_mid_rad_10exp.c000066400000000000000000000052331264125401100175040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_get_fmpz_mid_rad_10exp(fmpz_t mid, fmpz_t rad, fmpz_t exp, const arb_t x, slong n) { fmpz_t e, m; arb_t t, u; arf_t r; slong prec; int roundmid, roundrad; if (!arb_is_finite(x) || arb_is_zero(x)) { fmpz_zero(mid); fmpz_zero(rad); fmpz_zero(exp); return; } /* We compute m such that x * 10^m ~= 10^(n+5). If x = 2^e then m = (n+5) - e*log(2)/log(10). */ fmpz_init(e); fmpz_init(m); arb_init(t); arb_init(u); arf_init(r); if (arf_cmpabs_mag(arb_midref(x), arb_radref(x)) > 0) fmpz_set(e, ARF_EXPREF(arb_midref(x))); else fmpz_set(e, ARF_EXPREF(arb_radref(x))); prec = fmpz_bits(e) + 15; arb_const_log2(t, prec); arb_const_log10(u, prec); arb_div(t, t, u, prec); arb_mul_fmpz(t, t, e, prec); arb_neg(t, t); arb_add_ui(t, t, n + 5, prec); arf_get_fmpz(m, arb_midref(t), ARF_RND_FLOOR); arb_set_ui(t, 10); fmpz_neg(exp, m); prec = n * 3.32192809488736 + 30; if (fmpz_sgn(m) >= 0) { arb_pow_fmpz_binexp(t, t, m, prec + 2 * fmpz_bits(m)); arb_mul(t, x, t, prec); } else { fmpz_neg(m, m); arb_pow_fmpz_binexp(t, t, m, prec + 2 * fmpz_bits(m)); arb_div(t, x, t, prec); } roundmid = arf_get_fmpz_fixed_si(mid, arb_midref(t), 0); arf_set_mag(r, arb_radref(t)); roundrad = arf_get_fmpz_fixed_si(rad, r, 0); fmpz_add_ui(rad, rad, roundmid + roundrad); fmpz_clear(e); fmpz_clear(m); arb_clear(t); arb_clear(u); arf_clear(r); } arb-2.8.1/arb/get_interval_arf.c000066400000000000000000000025101264125401100165030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_get_interval_arf(arf_t a, arf_t b, const arb_t x, slong prec) { arf_t r; arf_init_set_mag_shallow(r, arb_radref(x)); arf_sub(a, arb_midref(x), r, prec, ARF_RND_FLOOR); arf_add(b, arb_midref(x), r, prec, ARF_RND_CEIL); } arb-2.8.1/arb/get_interval_fmpz_2exp.c000066400000000000000000000024441264125401100176530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_get_interval_fmpz_2exp(fmpz_t a, fmpz_t b, fmpz_t exp, const arb_t x) { fmprb_t t; fmprb_init(t); arb_get_fmprb(t, x); fmprb_get_interval_fmpz_2exp(a, b, exp, t); fmprb_clear(t); } arb-2.8.1/arb/get_interval_mpfr.c000066400000000000000000000027031264125401100167030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_get_interval_mpfr(mpfr_t a, mpfr_t b, const arb_t x) { arf_t r, t; arf_init(t); arf_init_set_mag_shallow(r, arb_radref(x)); arf_sub(t, arb_midref(x), r, mpfr_get_prec(a), ARF_RND_FLOOR); arf_get_mpfr(a, t, MPFR_RNDD); arf_add(t, arb_midref(x), r, mpfr_get_prec(b), ARF_RND_CEIL); arf_get_mpfr(b, t, MPFR_RNDU); arf_clear(t); } arb-2.8.1/arb/get_mag_lower.c000066400000000000000000000052551264125401100160140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" static __inline__ void _arb_get_mag_lower(mag_t z, const arf_t mid, const mag_t rad) { if (mag_is_inf(rad) || arf_is_zero(mid)) { mag_zero(z); } else if (mag_is_zero(rad)) { arf_get_mag_lower(z, mid); } else if (!arf_is_finite(mid)) { mag_inf(z); } else { slong shift, fix; shift = _fmpz_sub_small(MAG_EXPREF(mid), MAG_EXPREF(rad)); /* mid < rad */ if (shift < 0) { mag_zero(z); } else if (shift <= 1) /* can be cancellation */ { arf_t t; arf_init(t); arf_set_mag(t, rad); if (arf_sgn(mid) > 0) { arf_sub(t, mid, t, MAG_BITS, ARF_RND_DOWN); } else { arf_add(t, mid, t, MAG_BITS, ARF_RND_DOWN); arf_neg(t, t); } if (arf_sgn(t) <= 0) mag_zero(z); else arf_get_mag_lower(z, t); arf_clear(t); } else { mp_limb_t m; ARF_GET_TOP_LIMB(m, mid); m = m >> (FLINT_BITS - MAG_BITS); if (shift <= MAG_BITS) m = m - (MAG_MAN(rad) >> shift) - 1; else m = m - 1; fix = !(m >> (MAG_BITS - 1)); m <<= fix; MAG_MAN(z) = m; _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(mid), -fix); } } } void arb_get_mag_lower(mag_t z, const arb_t x) { _arb_get_mag_lower(z, arb_midref(x), arb_radref(x)); } arb-2.8.1/arb/get_mag_lower_nonnegative.c000066400000000000000000000047341264125401100204120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" static __inline__ void _arb_get_mag_lower_nonnegative(mag_t z, const arf_t mid, const mag_t rad) { if (mag_is_inf(rad) || arf_is_special(mid) || arf_sgn(mid) < 0) { mag_zero(z); } else if (mag_is_zero(rad)) { arf_get_mag_lower(z, mid); } else { slong shift, fix; shift = _fmpz_sub_small(MAG_EXPREF(mid), MAG_EXPREF(rad)); /* mid < rad */ if (shift < 0) { mag_zero(z); } else if (shift <= 1) /* can be cancellation */ { arf_t t; arf_init(t); arf_set_mag(t, rad); arf_sub(t, mid, t, MAG_BITS, ARF_RND_DOWN); if (arf_sgn(t) <= 0) mag_zero(z); else arf_get_mag_lower(z, t); arf_clear(t); } else { mp_limb_t m; ARF_GET_TOP_LIMB(m, mid); m = m >> (FLINT_BITS - MAG_BITS); if (shift <= MAG_BITS) m = m - (MAG_MAN(rad) >> shift) - 1; else m = m - 1; fix = !(m >> (MAG_BITS - 1)); m <<= fix; MAG_MAN(z) = m; _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(mid), -fix); } } } void arb_get_mag_lower_nonnegative(mag_t z, const arb_t x) { _arb_get_mag_lower_nonnegative(z, arb_midref(x), arb_radref(x)); } arb-2.8.1/arb/get_mpn_fixed_mod_log2.c000066400000000000000000000124301264125401100175640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define TMP_ALLOC_LIMBS(__n) TMP_ALLOC((__n) * sizeof(mp_limb_t)) /* Compute wn-limb fixed-point number w, a number of ulps error, and an exponent q such that x = (w + xi * error) - q * log(2) where 0 <= w < log(2) and |xi| <= 1. Returns 0 if unsuccessful (high enough precision for log(2) to be available) and 1 if successful. Assumes nonspecial x; its exponent must not be an mpz. Error analysis: We first set n = |x| - e1 d = log(2) - e2 where 0 <= e1, e2 <= 1 ulp are the errors resulting from truncating to fixed-point numbers (note that the value of log(2) is correctly rounded). Next, we compute q, r such that 0 <= r < d and q*d + r = n (this is just integer division with remainder, done exactly). The real number we want to approximate is r_exact = |x| - q * log(2). The approximation r satisfies |r_exact - r| = |(|x| - q * log(2)) - (n - q * d)| = ||x| - q * log(2) - (|x| - e1) + q * (log(2) - e2)| = |e1 - q * e2| <= (q + 1) ulp. We select the working precision so that (q + 1) ulp is at most 1 ulp in the target precision. It is sufficient to use tn extra limbs where (q + 1) <= 2^(FLINT_BITS * tn). Note that q + 1 <= n / d + 1 <= |x| * 1.5 + 1 < 2^(exp+2). So it is sufficient to choose tn = ceil((exp+2)/FLINT_BITS). Now we round the result to the final precision: w = r - e3. This can add 1 more ulp of error, so the error may be 2 ulp. Finally, if x < 0, we correct the sign by setting,x = log(2) - x, q = -(q+1). This adds 1 more ulp (from the approximation of log(2)), for a total of 3 ulp. */ int _arf_get_integer_mpn(mp_ptr y, mp_srcptr x, mp_size_t xn, slong exp); int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec); int _arb_get_mpn_fixed_mod_log2(mp_ptr w, fmpz_t q, mp_limb_t * error, const arf_t x, mp_size_t wn) { mp_srcptr xp; mp_size_t xn; int negative; slong exp; ARF_GET_MPN_READONLY(xp, xn, x); exp = ARF_EXP(x); negative = ARF_SGNBIT(x); if (exp <= -1) { /* todo: just zero top */ flint_mpn_zero(w, wn); *error = _arf_get_integer_mpn(w, xp, xn, exp + wn * FLINT_BITS); if (!negative) { fmpz_zero(q); } else { if (wn > ARB_LOG_TAB2_LIMBS) return 0; mpn_sub_n(w, arb_log_log2_tab + ARB_LOG_TAB2_LIMBS - wn, w, wn); *error += 1; /* log(2) has 1 ulp error */ fmpz_set_si(q, -1); } return 1; /* success */ } else { mp_ptr qp, rp, np; mp_srcptr dp; mp_size_t qn, rn, nn, dn, tn, alloc; TMP_INIT; tn = ((exp + 2) + FLINT_BITS - 1) / FLINT_BITS; dn = wn + tn; /* denominator */ nn = wn + 2 * tn; /* numerator */ qn = nn - dn + 1; /* quotient */ rn = dn; /* remainder */ if (dn > ARB_LOG_TAB2_LIMBS) return 0; TMP_START; alloc = qn + rn + nn; qp = TMP_ALLOC_LIMBS(alloc); rp = qp + qn; np = rp + rn; dp = arb_log_log2_tab + ARB_LOG_TAB2_LIMBS - dn; /* todo: prove that zeroing is unnecessary */ flint_mpn_zero(np, nn); _arf_get_integer_mpn(np, xp, xn, exp + dn * FLINT_BITS); mpn_tdiv_qr(qp, rp, 0, np, nn, dp, dn); if (!negative) { flint_mpn_copyi(w, rp + tn, wn); *error = 2; } else { if (mpn_add_1(qp, qp, qn, 1)) { /* I believe this cannot happen (should prove it) */ flint_printf("mod log(2): unexpected carry\n"); abort(); } mpn_sub_n(w, dp + tn, rp + tn, wn); *error = 3; } /* read the exponent */ while (qn > 1 && qp[qn-1] == 0) qn--; if (qn == 1) { if (!negative) fmpz_set_ui(q, qp[0]); else fmpz_neg_ui(q, qp[0]); } else { fmpz_set_mpn_large(q, qp, qn, negative); } TMP_END; return 1; } } arb-2.8.1/arb/get_mpn_fixed_mod_pi4.c000066400000000000000000000073251264125401100174240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define TMP_ALLOC_LIMBS(__n) TMP_ALLOC((__n) * sizeof(mp_limb_t)) int _arf_get_integer_mpn(mp_ptr y, mp_srcptr x, mp_size_t xn, slong exp); int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec); int _arb_get_mpn_fixed_mod_pi4(mp_ptr w, fmpz_t q, int * octant, mp_limb_t * error, const arf_t x, mp_size_t wn) { mp_srcptr xp; mp_size_t xn; slong exp; ARF_GET_MPN_READONLY(xp, xn, x); exp = ARF_EXP(x); if (exp <= -1) { flint_mpn_zero(w, wn); *error = _arf_get_integer_mpn(w, xp, xn, exp + wn * FLINT_BITS); *octant = 0; if (q != NULL) fmpz_zero(q); return 1; } else if (exp == 0) { mp_srcptr dp; if (wn > ARB_PI4_TAB_LIMBS) return 0; flint_mpn_zero(w, wn); *error = _arf_get_integer_mpn(w, xp, xn, exp + wn * FLINT_BITS); dp = arb_pi4_tab + ARB_PI4_TAB_LIMBS - wn; if (mpn_cmp(w, dp, wn) < 0) { *octant = 0; if (q != NULL) fmpz_zero(q); } else { *octant = 1; if (q != NULL) fmpz_one(q); mpn_sub_n(w, w, dp, wn); mpn_sub_n(w, dp, w, wn); *error += 2; } return 1; } else { mp_ptr qp, rp, np; mp_srcptr dp; mp_size_t qn, rn, nn, dn, tn, alloc; TMP_INIT; tn = ((exp + 2) + FLINT_BITS - 1) / FLINT_BITS; dn = wn + tn; /* denominator */ nn = wn + 2 * tn; /* numerator */ qn = nn - dn + 1; /* quotient */ rn = dn; /* remainder */ if (dn > ARB_PI4_TAB_LIMBS) return 0; TMP_START; alloc = qn + rn + nn; qp = TMP_ALLOC_LIMBS(alloc); rp = qp + qn; np = rp + rn; dp = arb_pi4_tab + ARB_PI4_TAB_LIMBS - dn; flint_mpn_zero(np, nn); _arf_get_integer_mpn(np, xp, xn, exp + dn * FLINT_BITS); mpn_tdiv_qr(qp, rp, 0, np, nn, dp, dn); *octant = qp[0] % 8; if (*octant % 2 == 0) { flint_mpn_copyi(w, rp + tn, wn); *error = 2; } else { mpn_sub_n(w, dp + tn, rp + tn, wn); *error = 3; } if (q != NULL) { /* read the exponent */ while (qn > 1 && qp[qn-1] == 0) qn--; if (qn == 1) fmpz_set_ui(q, qp[0]); else fmpz_set_mpn_large(q, qp, qn, 0); } TMP_END; return 1; } } arb-2.8.1/arb/get_rand_fmpq.c000066400000000000000000000024421264125401100160020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const arb_t x, slong bits) { fmprb_t t; fmprb_init(t); arb_get_fmprb(t, x); fmprb_get_rand_fmpq(q, state, t, bits); fmprb_clear(t); } arb-2.8.1/arb/get_str.c000066400000000000000000000303611264125401100146440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include #include #include "arb.h" #define RADIUS_DIGITS 3 char * _arb_condense_digits(char * s, slong n) { slong i, j, run, out; char * res; res = flint_malloc(strlen(s) + 128); /* space for some growth */ out = 0; for (i = 0; s[i] != '\0'; ) { if (isdigit(s[i])) { run = 0; for (j = 0; isdigit(s[i + j]); j++) run++; if (run > 3 * n) { for (j = 0; j < n; j++) { res[out] = s[i + j]; out++; } out += flint_sprintf(res + out, "{...%wd digits...}", run - 2 * n); for (j = run - n; j < run; j++) { res[out] = s[i + j]; out++; } } else { for (j = 0; j < run; j++) { res[out] = s[i + j]; out++; } } i += run; } else { res[out] = s[i]; i++; out++; } } res[out] = '\0'; res = flint_realloc(res, strlen(res) + 1); flint_free(s); return res; } /* Format (digits=d, exponent=e) as floating-point or fixed-point. Reallocates the input and mutates the exponent. */ void _arb_digits_as_float_str(char ** d, fmpz_t e, slong minfix, slong maxfix) { slong i, n, alloc, dotpos; /* do nothing with 0 or something non-numerical */ if (!((*d)[0] >= '1' && (*d)[0] <= '9')) return; n = strlen(*d); fmpz_add_ui(e, e, n - 1); /* fixed-point or integer format */ /* we require e < n - 1; otherwise we would have to insert trailing zeros [todo: could allow e < n, if printing integers without radix point] */ if (fmpz_cmp_si(e, minfix) >= 0 && fmpz_cmp_si(e, maxfix) <= 0 && fmpz_cmp_si(e, n - 1) < 0) { slong exp = *e; /* 0.000xxx */ if (exp < 0) { /* 0. + (-1-exp) zeros + digits + null terminator */ alloc = 2 + (-1-exp) + n + 1; *d = flint_realloc(*d, alloc); /* copy in reverse order, including null terminator */ for (i = n; i >= 0; i--) (*d)[2 + (-1-exp) + i] = (*d)[i]; for (i = 0; i < 2 + (-1-exp); i++) (*d)[i] = (i == 1) ? '.' : '0'; } else /* xxx.yyy --- must have dotpos < n - 1 */ { dotpos = exp + 1; alloc = n + 2; /* space for . and null terminator */ (*d) = flint_realloc(*d, alloc); /* copy fractional part in reverse order, including null */ for (i = n; i >= dotpos; i--) (*d)[i + 1] = (*d)[i]; (*d)[dotpos] = '.'; } } else { /* format as xe+zzz or x.yyye+zzz */ alloc = n + 1 + 2 + fmpz_sizeinbase(e, 10) + 1; *d = flint_realloc(*d, alloc); /* insert . */ if (n > 1) { /* copy fractional part in reverse order */ for (i = n; i >= 1; i--) (*d)[i + 1] = (*d)[i]; (*d)[1] = '.'; } (*d)[n + (n > 1)] = 'e'; if (fmpz_sgn(e) >= 0) { (*d)[n + (n > 1) + 1] = '+'; } else { (*d)[n + (n > 1) + 1] = '-'; fmpz_neg(e, e); } fmpz_get_str((*d) + n + (n > 1) + 2, 10, e); /* writes null byte */ } } /* Rounds a string of decimal digits (null-terminated). to length at most n. The rounding mode can be ARF_RND_DOWN, ARF_RND_UP or ARF_RND_NEAR. The string is overwritten in-place, truncating it as necessary. The input should not have a leading sign or leading zero digits, but can have trailing zero digits. Computes shift and error such that int(input) = int(output) * 10^shift + error exactly. */ void _arb_digits_round_inplace(char * s, mp_bitcnt_t * shift, fmpz_t error, slong n, arf_rnd_t rnd) { slong i, m; int up; if (n < 1) { flint_printf("_arb_digits_round_inplace: require n >= 1\n"); abort(); } m = strlen(s); if (m <= n) { *shift = 0; fmpz_zero(error); return; } /* always round down */ if (rnd == ARF_RND_DOWN) { up = 0; } else if (rnd == ARF_RND_UP) /* round up if tail is nonzero */ { up = 0; for (i = n; i < m; i++) { if (s[i] != '0') { up = 1; break; } } } else /* round to nearest (up on tie -- todo: round-to-even?) */ { up = (s[n] >= '5' && s[n] <= '9'); } if (!up) { /* simply truncate */ fmpz_set_str(error, s + n, 10); s[n] = '\0'; *shift = m - n; } else { int digit, borrow, carry; /* error = 10^(m-n) - s[n:], where s[n:] is nonzero */ /* i.e. 10s complement the truncated digits */ borrow = 0; for (i = m - 1; i >= n; i--) { digit = 10 - (s[i] - '0') - borrow; if (digit == 10) { digit = 0; borrow = 0; } else { borrow = 1; } s[i] = digit + '0'; } if (!borrow) { flint_printf("expected borrow!\n"); abort(); } fmpz_set_str(error, s + n, 10); fmpz_neg(error, error); /* add 1 ulp to the leading digits */ carry = 1; for (i = n - 1; i >= 0; i--) { digit = (s[i] - '0') + carry; if (digit > 9) { digit = 0; carry = 1; } else { carry = 0; } s[i] = digit + '0'; } /* carry-out -- only possible if we started with all 9s, so now the rest will be 0s which we don't have to shift explicitly */ if (carry) { s[0] = '1'; *shift = m - n + 1; } else { *shift = m - n; } s[n] = '\0'; /* truncate */ } } void arb_get_str_parts(int * negative, char **mid_digits, fmpz_t mid_exp, char **rad_digits, fmpz_t rad_exp, const arb_t x, slong n, int more) { fmpz_t mid, rad, exp, err; slong good; mp_bitcnt_t shift; if (!arb_is_finite(x)) { *negative = 0; fmpz_zero(mid_exp); *mid_digits = flint_malloc(4); if (arf_is_nan(arb_midref(x))) strcpy(*mid_digits, "nan"); else strcpy(*mid_digits, "0"); fmpz_zero(rad_exp); *rad_digits = flint_malloc(4); strcpy(*rad_digits, "inf"); return; } fmpz_init(mid); fmpz_init(rad); fmpz_init(exp); fmpz_init(err); /* heuristic part */ if (!more) { good = arb_rel_accuracy_bits(x) * 0.30102999566398119521 + 2; n = FLINT_MIN(n, good); } arb_get_fmpz_mid_rad_10exp(mid, rad, exp, x, FLINT_MAX(n, 1)); *negative = arf_sgn(arb_midref(x)) < 0; fmpz_abs(mid, mid); *mid_digits = fmpz_get_str(NULL, 10, mid); *rad_digits = NULL; /* Truncate further so that 1 ulp error can be guaranteed (rigorous part) Note: mid cannot be zero here if n >= 1 and rad != 0. */ if (n >= 1 && !(more || fmpz_is_zero(rad))) { slong lenmid, lenrad, rem; *rad_digits = fmpz_get_str(NULL, 10, rad); lenmid = strlen(*mid_digits); lenrad = strlen(*rad_digits); if (lenmid > lenrad) { /* we will truncate at n or n-1 */ good = lenmid - lenrad; /* rounding to nearest can add at most 0.5 ulp */ /* look at first omitted digit */ rem = ((*mid_digits)[good]) - '0'; if (rem < 5) rem = rem + 1; else rem = 10 - rem; /* and include the leading digit of the radius */ rem = rem + ((*rad_digits)[0] - '0') + 1; /* if error is <= 1.0 ulp, we get to keep the extra digit */ if (rem > 10) good -= 1; n = FLINT_MIN(n, good); } else { n = 0; } /* todo: avoid recomputing? */ flint_free(*rad_digits); } /* no accurate digits -- output 0 +/- rad */ if (n < 1) { fmpz_add(rad, rad, mid); fmpz_zero(mid); strcpy(*mid_digits, "0"); /* must have space already! */ } else { _arb_digits_round_inplace(*mid_digits, &shift, err, n, ARF_RND_NEAR); fmpz_add_ui(mid_exp, exp, shift); fmpz_abs(err, err); fmpz_add(rad, rad, err); } /* write radius */ if (fmpz_is_zero(rad)) { *rad_digits = fmpz_get_str(NULL, 10, rad); fmpz_zero(rad_exp); } else { *rad_digits = fmpz_get_str(NULL, 10, rad); _arb_digits_round_inplace(*rad_digits, &shift, err, RADIUS_DIGITS, ARF_RND_UP); fmpz_add_ui(rad_exp, exp, shift); } fmpz_clear(mid); fmpz_clear(rad); fmpz_clear(exp); fmpz_clear(err); } char * arb_get_str(const arb_t x, slong n, ulong flags) { char * res; char * mid_digits; char * rad_digits; int negative, more, skip_rad, skip_mid; fmpz_t mid_exp; fmpz_t rad_exp; slong condense; if (arb_is_zero(x)) { res = flint_malloc(2); strcpy(res, "0"); return res; } more = flags & ARB_STR_MORE; condense = flags / ARB_STR_CONDENSE; if (!arb_is_finite(x)) { res = flint_malloc(10); if (arf_is_nan(arb_midref(x))) strcpy(res, "nan"); else strcpy(res, "[+/- inf]"); return res; } fmpz_init(mid_exp); fmpz_init(rad_exp); arb_get_str_parts(&negative, &mid_digits, mid_exp, &rad_digits, rad_exp, x, n, more); skip_mid = mid_digits[0] == '0'; skip_rad = (rad_digits[0] == '0') || ((flags & ARB_STR_NO_RADIUS) && !skip_mid); _arb_digits_as_float_str(&mid_digits, mid_exp, -4, FLINT_MAX(6, n - 1)); _arb_digits_as_float_str(&rad_digits, rad_exp, -2, 2); if (skip_rad) { res = flint_malloc(strlen(mid_digits) + 2); if (negative) strcpy(res, "-"); else strcpy(res, ""); strcat(res, mid_digits); } else if (skip_mid) { res = flint_malloc(strlen(rad_digits) + 7); strcpy(res, "[+/- "); strcat(res, rad_digits); strcat(res, "]"); } else { res = flint_malloc(strlen(mid_digits) + strlen(rad_digits) + 9); strcpy(res, "["); if (negative) strcat(res, "-"); strcat(res, mid_digits); strcat(res, " +/- "); strcat(res, rad_digits); strcat(res, "]"); } if (condense) res = _arb_condense_digits(res, condense); flint_free(mid_digits); flint_free(rad_digits); fmpz_clear(mid_exp); fmpz_clear(rad_exp); return res; } arb-2.8.1/arb/get_unique_fmpz.c000066400000000000000000000024361264125401100164000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_get_unique_fmpz(fmpz_t z, const arb_t x) { fmprb_t t; int ans; fmprb_init(t); arb_get_fmprb(t, x); ans = fmprb_get_unique_fmpz(z, t); fmprb_clear(t); return ans; } arb-2.8.1/arb/hurwitz_zeta.c000066400000000000000000000032351264125401100157340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "acb.h" void arb_hurwitz_zeta(arb_t res, const arb_t s, const arb_t z, slong prec) { if (!arb_contains_si(s, 1) && (arb_is_positive(z) || (arb_is_int(z) && arb_is_int(s) && arb_is_nonpositive(s)))) { acb_t a, b, c; acb_init(a); acb_init(b); acb_init(c); acb_set_arb(a, s); acb_set_arb(b, z); acb_hurwitz_zeta(c, a, b, prec); arb_set(res, acb_realref(c)); acb_clear(a); acb_clear(b); acb_clear(c); } else { arb_indeterminate(res); } } arb-2.8.1/arb/hypot.c000066400000000000000000000030231264125401100143330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_hypot(arb_t z, const arb_t x, const arb_t y, slong prec) { if (arb_is_zero(y)) { arb_abs(z, x); } else if (arb_is_zero(x)) { arb_abs(z, y); } else { arb_t t; arb_init(t); /* TODO: use arb_fmma */ arb_mul(t, x, x, prec + 4); arb_mul(z, y, y, prec + 4); arb_add(t, t, z, prec + 4); arb_sqrtpos(z, t, prec); arb_clear(t); } } arb-2.8.1/arb/inlines.c000066400000000000000000000021501264125401100146310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define ARB_INLINES_C #include "arb.h" arb-2.8.1/arb/log.c000066400000000000000000000273071264125401100137640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define TMP_ALLOC_LIMBS(size) TMP_ALLOC((size) * sizeof(mp_limb_t)) /* requires x != 1 */ static void arf_log_via_mpfr(arf_t z, const arf_t x, slong prec, arf_rnd_t rnd) { mpfr_t xf, zf; mp_ptr zptr, tmp; mp_srcptr xptr; mp_size_t xn, zn, val; TMP_INIT; TMP_START; zn = (prec + FLINT_BITS - 1) / FLINT_BITS; tmp = TMP_ALLOC(zn * sizeof(mp_limb_t)); ARF_GET_MPN_READONLY(xptr, xn, x); xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = ARF_SGNBIT(x) ? -1 : 1; xf->_mpfr_exp = ARF_EXP(x); zf->_mpfr_d = tmp; zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); mpfr_log(zf, xf, arf_rnd_to_mpfr(rnd)); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); if (zf->_mpfr_sign < 0) ARF_NEG(z); fmpz_set_si(ARF_EXPREF(z), zf->_mpfr_exp); TMP_END; } int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec); void mag_add_ui_2exp_si(mag_t z, const mag_t x, ulong y, slong e); void arb_log_arf_huge(arb_t z, const arf_t x, slong prec) { arf_t t; arb_t c; fmpz_t exp; slong wp; arf_init(t); arb_init(c); fmpz_init(exp); fmpz_neg(exp, ARF_EXPREF(x)); arf_mul_2exp_fmpz(t, x, exp); wp = prec + 4 - fmpz_bits(exp); wp = FLINT_MAX(wp, 4); arb_log_arf(z, t, wp); arb_const_log2(c, prec + 4); arb_submul_fmpz(z, c, exp, prec); arf_clear(t); arb_clear(c); fmpz_clear(exp); } void arb_log_arf(arb_t z, const arf_t x, slong prec) { if (arf_is_special(x)) { if (arf_is_pos_inf(x)) arb_pos_inf(z); else arb_indeterminate(z); } else if (ARF_SGNBIT(x)) { arb_indeterminate(z); } else if (ARF_IS_POW2(x)) { if (fmpz_is_one(ARF_EXPREF(x))) { arb_zero(z); } else { fmpz_t exp; fmpz_init(exp); _fmpz_add_fast(exp, ARF_EXPREF(x), -1); arb_const_log2(z, prec + 2); arb_mul_fmpz(z, z, exp, prec); fmpz_clear(exp); } } else if (COEFF_IS_MPZ(*ARF_EXPREF(x))) { arb_log_arf_huge(z, x, prec); } else { slong exp, wp, wn, N, r, closeness_to_one; mp_srcptr xp; mp_size_t xn, tn; mp_ptr tmp, w, t, u; mp_limb_t p1, q1bits, p2, q2bits, error, error2, cy; int negative, inexact, used_taylor_series; TMP_INIT; exp = ARF_EXP(x); negative = 0; ARF_GET_MPN_READONLY(xp, xn, x); /* compute a c >= 0 such that |x-1| <= 2^(-c) if c > 0 */ closeness_to_one = 0; if (exp == 0) { slong i; closeness_to_one = FLINT_BITS - FLINT_BIT_COUNT(~xp[xn - 1]); if (closeness_to_one == FLINT_BITS) { for (i = xn - 2; i > 0 && xp[i] == LIMB_ONES; i--) closeness_to_one += FLINT_BITS; closeness_to_one += (FLINT_BITS - FLINT_BIT_COUNT(~xp[i])); } } else if (exp == 1) { closeness_to_one = FLINT_BITS - FLINT_BIT_COUNT(xp[xn - 1] & (~LIMB_TOP)); if (closeness_to_one == FLINT_BITS) { slong i; for (i = xn - 2; xp[i] == 0; i--) closeness_to_one += FLINT_BITS; closeness_to_one += (FLINT_BITS - FLINT_BIT_COUNT(xp[i])); } closeness_to_one--; } /* if |t-1| <= 0.5 */ /* |log(1+t) - t| <= t^2 */ /* |log(1+t) - (t-t^2/2)| <= t^3 */ if (closeness_to_one > prec + 1) { inexact = arf_sub_ui(arb_midref(z), x, 1, prec, ARB_RND); mag_set_ui_2exp_si(arb_radref(z), 1, -2 * closeness_to_one); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); return; } else if (2 * closeness_to_one > prec + 1) { arf_t t, u; arf_init(t); arf_init(u); arf_sub_ui(t, x, 1, ARF_PREC_EXACT, ARF_RND_DOWN); arf_mul(u, t, t, ARF_PREC_EXACT, ARF_RND_DOWN); arf_mul_2exp_si(u, u, -1); inexact = arf_sub(arb_midref(z), t, u, prec, ARB_RND); mag_set_ui_2exp_si(arb_radref(z), 1, -3 * closeness_to_one); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); arf_clear(t); arf_clear(u); return; } /* Absolute working precision (NOT rounded to a limb multiple) */ wp = prec + closeness_to_one + 5; /* Too high precision to use table */ if (wp > ARB_LOG_TAB2_PREC) { arf_log_via_mpfr(arb_midref(z), x, prec, ARB_RND); arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); return; } /* Working precision in limbs */ wn = (wp + FLINT_BITS - 1) / FLINT_BITS; TMP_START; tmp = TMP_ALLOC_LIMBS(4 * wn + 3); w = tmp; /* requires wn+1 limbs */ t = w + wn + 1; /* requires wn+1 limbs */ u = t + wn + 1; /* requires 2wn+1 limbs */ /* read x-1 */ if (xn <= wn) { flint_mpn_zero(w, wn - xn); mpn_lshift(w + wn - xn, xp, xn, 1); error = 0; } else { mpn_lshift(w, xp + xn - wn, wn, 1); error = 1; } /* First table-based argument reduction */ if (wp <= ARB_LOG_TAB1_PREC) q1bits = ARB_LOG_TAB11_BITS; else q1bits = ARB_LOG_TAB21_BITS; p1 = w[wn-1] >> (FLINT_BITS - q1bits); /* Special case: covers logarithms of small integers */ if (xn == 1 && (w[wn-1] == (p1 << (FLINT_BITS - q1bits)))) { p2 = 0; flint_mpn_zero(t, wn); used_taylor_series = 0; N = r = 0; /* silence compiler warning */ } else { /* log(1+w) = log(1+p/q) + log(1 + (qw-p)/(p+q)) */ w[wn] = mpn_mul_1(w, w, wn, UWORD(1) << q1bits) - p1; mpn_divrem_1(w, 0, w, wn + 1, p1 + (UWORD(1) << q1bits)); error += 1; /* Second table-based argument reduction (fused with log->atanh conversion) */ if (wp <= ARB_LOG_TAB1_PREC) q2bits = ARB_LOG_TAB11_BITS + ARB_LOG_TAB12_BITS; else q2bits = ARB_LOG_TAB21_BITS + ARB_LOG_TAB22_BITS; p2 = w[wn-1] >> (FLINT_BITS - q2bits); u[2 * wn] = mpn_lshift(u + wn, w, wn, q2bits); flint_mpn_zero(u, wn); flint_mpn_copyi(t, u + wn, wn + 1); t[wn] += p2 + (UWORD(1) << (q2bits + 1)); u[2 * wn] -= p2; mpn_tdiv_q(w, u, 2 * wn + 1, t, wn + 1); /* propagated error from 1 ulp error: 2 atanh'(1/3) = 2.25 */ error += 3; /* |w| <= 2^-r */ r = _arb_mpn_leading_zeros(w, wn); /* N >= (wp-r)/(2r) */ N = (wp - r + (2*r-1)) / (2*r); N = FLINT_MAX(N, 0); /* Evaluate Taylor series */ _arb_atan_taylor_rs(t, &error2, w, wn, N, 0); /* Multiply by 2 */ mpn_lshift(t, t, wn, 1); /* Taylor series evaluation error (multiply by 2) */ error += error2 * 2; used_taylor_series = 1; } /* Size of output number */ tn = wn; /* First table lookup */ if (p1 != 0) { if (wp <= ARB_LOG_TAB1_PREC) mpn_add_n(t, t, arb_log_tab11[p1] + ARB_LOG_TAB1_LIMBS - tn, tn); else mpn_add_n(t, t, arb_log_tab21[p1] + ARB_LOG_TAB2_LIMBS - tn, tn); error++; } /* Second table lookup */ if (p2 != 0) { if (wp <= ARB_LOG_TAB1_PREC) mpn_add_n(t, t, arb_log_tab12[p2] + ARB_LOG_TAB1_LIMBS - tn, tn); else mpn_add_n(t, t, arb_log_tab22[p2] + ARB_LOG_TAB2_LIMBS - tn, tn); error++; } /* add exp * log(2) */ exp--; if (exp > 0) { cy = mpn_addmul_1(t, arb_log_log2_tab + ARB_LOG_TAB2_LIMBS - tn, tn, exp); t[tn] = cy; tn += (cy != 0); error += exp; } else if (exp < 0) { t[tn] = 0; u[tn] = mpn_mul_1(u, arb_log_log2_tab + ARB_LOG_TAB2_LIMBS - tn, tn, -exp); if (mpn_cmp(t, u, tn + 1) >= 0) { mpn_sub_n(t, t, u, tn + 1); } else { mpn_sub_n(t, u, t, tn + 1); negative = 1; } error += (-exp); tn += (t[tn] != 0); } /* The accumulated arithmetic error */ mag_set_ui_2exp_si(arb_radref(z), error, -wn * FLINT_BITS); /* Truncation error from the Taylor series */ if (used_taylor_series) mag_add_ui_2exp_si(arb_radref(z), arb_radref(z), 1, -r*(2*N+1) + 1); /* Set the midpoint */ inexact = _arf_set_mpn_fixed(arb_midref(z), t, tn, wn, negative, prec); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); TMP_END; } } void arb_log(arb_t y, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_log_arf(y, arb_midref(x), prec); } else { /* Let the input be [a-b, a+b]. We require a > b >= 0 (otherwise the interval contains zero or a negative number and the logarithm is not defined). The error is largest at a-b, and we have log(a) - log(a-b) = log(1 + b/(a-b)). */ mag_t err; mag_init(err); arb_get_mag_lower_nonnegative(err, x); if (mag_is_zero(err)) { mag_inf(err); } else { mag_div(err, arb_radref(x), err); mag_log1p(err, err); } arb_log_arf(y, arb_midref(x), prec); mag_add(arb_radref(y), arb_radref(y), err); mag_clear(err); } } void arb_log_ui(arb_t z, ulong x, slong prec) { arf_t t; arf_init(t); arf_set_ui(t, x); arb_log_arf(z, t, prec); arf_clear(t); } void arb_log_fmpz(arb_t z, const fmpz_t x, slong prec) { arf_t t; arf_init(t); arf_set_fmpz(t, x); arb_log_arf(z, t, prec); arf_clear(t); } arb-2.8.1/arb/log1p.c000066400000000000000000000041251264125401100142160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void arb_log1p_tiny(arb_t r, const arb_t z, slong prec) { mag_t b, c; arb_t t; mag_init(b); mag_init(c); arb_init(t); /* if |z| < 1, then |log(1+z) - [z - z^2/2]| <= |z|^3/(1-|z|) */ arb_get_mag(b, z); mag_one(c); mag_sub_lower(c, c, b); mag_pow_ui(b, b, 3); mag_div(b, b, c); arb_mul(t, z, z, prec); arb_mul_2exp_si(t, t, -1); arb_sub(r, z, t, prec); if (mag_is_finite(b)) arb_add_error_mag(r, b); else arb_indeterminate(r); mag_clear(b); mag_clear(c); arb_clear(t); } void arb_log1p(arb_t r, const arb_t z, slong prec) { slong magz; if (arb_is_zero(z)) { arb_zero(r); return; } magz = arf_abs_bound_lt_2exp_si(arb_midref(z)); if (magz < -prec) { arb_log1p_tiny(r, z, prec); } else { if (magz < 0) arb_add_ui(r, z, 1, prec + (-magz) + 4); else arb_add_ui(r, z, 1, prec + 4); arb_log(r, r, prec); } } arb-2.8.1/arb/log_tab.c000066400000000000000000004060111264125401100146030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #if FLINT_BITS == 64 #define Z2(a,b) UWORD(0x ## b ## a) #else #define Z2(a,b) UWORD(0x ## a), UWORD(0x ## b) #endif #define Z8(a,b,c,d,e,f,g,h) Z2(a,b), Z2(c,d), Z2(e,f), Z2(g,h), const mp_limb_t arb_log_log2_tab[ARB_LOG_TAB2_LIMBS] = { Z8(78b63c9f,897a39ce,1e238438,52ab3316,a6c4c60c,062b1a63,e8f70edd,3ea8449f) Z8(26fac51c,6425a415,f95884e0,c5e5767d,8a0e23fa,c0b1b31d,3a49bd0d,85db6ab0) Z8(c8daadd8,175eb4af,a892374e,f07afff3,0dea891e,8f682625,9c38339d,cecb72f1) Z8(ac9f45ae,5f6f7ceb,e76115c0,6c472096,fbbd9d42,972cd18b,bd67c724,0ab111bb) Z8(a0c238b9,473826fd,d24aaebd,61c1696d,2413d5e3,156e0c29,dc4e7487,95184460) Z8(901e646a,d7622658,d7373958,ef2f0ce2,c4e9207c,2ac5b61c,beba7d05,57339ba2) Z8(08391a0c,0060e499,6af50302,62136319,3d0bd2f9,05c128d5,cee886b9,36e02b20) Z8(f3d949f2,0bbb16fa,c9942109,422183ed,8c66d3c5,5e9222b8,6b1ca3cf,61affd44) Z8(9538b982,268a5c1f,fbcf0755,8d6f5177,228a4ef9,a17293d1,731cdc8e,44a02554) Z8(30af889b,96d4e6d3,8f969834,5570b6c6,1ae273ee,7598a195,b365853d,4d162db3) Z8(5064c18b,5f50b518,1b2db31b,078f735d,6c606cb1,ae313cdb,b1e17b9d,955d5179) Z8(17350d2c,0c480a54,5cfe7aa3,074db601,5e148e82,6a9c7f8a,3564a337,25669b33) Z8(d1d6095d,4c1a1e0b,9393514c,cccc4e65,b479cd33,c943e732,db8990e5,17460775) Z8(1400b396,7d2e23de,fc1efa15,ee569d6d,8fe551a2,610d30f8,fb5bfb90,07f4ca11) Z8(0f3fd5c6,da2d97c5,2f20e3a2,655fa187,38303248,f5dfa6bd,9d6548ca,72ce87b1) Z8(7657f74b,256fa0ec,b136603b,b9ea9bc3,317c387e,1acbda11,224ae8c5,3e96ca16) Z8(1169b825,27573b29,c1382144,ed2eae35,4afa1b10,559552fb,6debac98,e7b87620) Z8(8baafa2b,8a0d175b,7298b62d,40f34326,03f2f6af,c9e3b398,d1cf79ab,b17217f7) }; const mp_limb_t arb_log_tab11[1 << ARB_LOG_TAB11_BITS][ARB_LOG_TAB1_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(90d465bf,d4520ee2,9bb0f82e,d99e1b46,facf68d7,e4c4a44a,51bc9855,d122f7ff) Z8(6b5788c3,76702788,f9a073a8,b3db2c3e,1dc282d2,c3769039,b106788f,01fe02a6) },{ Z8(1ef3a140,e808e153,3b4ede62,ba7510a9,8f9f71cc,7841aece,758dcd0b,7a59b490) Z8(77122f83,d140fe05,3ddc5335,eb03be90,6f57aadb,f3db4e9a,1f807c79,03f81516) },{ Z8(31e125ae,9bb5ffe0,140b9e2f,086d1607,45ddab78,67ded6c5,0efcad2b,d0f00eba) Z8(3a835116,96efb673,87466226,53c40a94,5af00773,49fd531c,f56c46aa,05ee46c1) },{ Z8(7cb29271,02127ef4,0f6e3a39,9ce34431,e0a5d2e3,55d9a7ba,ec979e9d,8a38a3ff) Z8(e3673dcd,df6c758f,ddf35ad1,aefae14c,ef229fae,3e3f04f1,9e0cc013,07e0a6c3) },{ Z8(12db1d0e,d5872e70,d45e4a00,5c3e9eb0,48f34c0f,28b7bf29,3fa03b71,747318fe) Z8(a91dfcd4,d0eb0381,f4c603a3,5eb87846,5c8a7235,80ad9015,ff5eafd4,09cf43dc) },{ Z8(5d61ffe8,c6e2905e,afeeec68,457ce7cd,97a6304c,f5c2a876,9f71bf4e,e9b91ebf) Z8(a3a2b779,7d674deb,a89d8cb0,9bf701b2,252c163c,1a7950f7,196e7e23,0bba2c7b) },{ Z8(b0b4ed5d,212b939a,5665b730,6f275dc8,647b0999,766e7cbf,7d96a5a1,1abee2d1) Z8(9e448511,77778bea,fc53dc9e,bce26340,fb66e94a,468a63ec,8cb8df61,0da16eb8) },{ Z8(77e6bc16,9bc35789,e7a9459e,99f0cc1d,85badcca,908722d9,de861006,6172da6b) Z8(96f69849,71851f0a,75b52596,d3474d33,75997898,be64b8b7,08b15330,0f851860) },{ Z8(fe8e2388,8e4540e2,7a5a64e0,8b8cbbc7,7b015b41,0d7918c7,2c6a3b15,8b8cbcb1) Z8(264acee4,37e6cb88,685a6aad,a42905a6,d325e46d,625c173d,a37ae0e8,116536ee) },{ Z8(9e866ba2,9fec8cce,3429d182,68413893,0bbafb1c,69e2cdb8,7bb59c4a,2b83c452) Z8(5d37b037,e6103880,78467950,1a0eca5b,4d137502,99837610,1bd1d092,1341d796) },{ Z8(9de15b17,ed9027ae,f8ee1435,bb355b22,f457addf,3e6b4fb0,e7a295c0,84d7db82) Z8(7aa339ed,96961165,c3e10deb,c9c7e09b,2f91584b,278e686a,06183f69,151b073f) },{ Z8(eed4c843,a047161c,dc5afe2a,fa8c6dd6,644009ed,c1e6a872,ba4a6521,284ac3fe) Z8(34b59afd,812f38a0,087fdf23,50c1ef65,19b640ce,e499b9ed,e56b4b9b,16f0d28a) },{ Z8(c69d37d7,d1080d7c,1025284d,ff89c5d4,5de8d145,cecb8c1d,5115bbde,0ae26ff9) Z8(00e87966,799d33d0,d7c4c4b4,02603e40,edab4357,acb42a65,319b20f5,18c345d6) },{ Z8(427b81cc,48646831,a02b9473,7748a795,ab52ff3b,f726f31b,7818f6b5,ef3f32ca) Z8(2911a622,eab11fa4,d398d01d,9f67e22e,3aa4c79a,0bd22a9c,4ad56365,1a926d3a) },{ Z8(d6fdaaad,f159cd13,edfe76e2,e55d167e,3211078e,f7d0cf3e,b458f0de,87d91901) Z8(bbc664d5,163e7f6c,3772cac1,966af8dc,61b1769d,d617ef81,5bc74315,1c5e548f) },{ Z8(ec0c6459,286a0066,f9a71577,fd2c1f6c,2646cc77,a023f574,cfca2ad7,9e05a342) 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Z8(a905792e,92f74d1e,233b3294,2c1be100,f06b25b5,1874deae,9c6defde,6fad3676) },{ Z8(94468a54,d7b83c67,98048347,0c272ece,a2533c60,82649140,682717c8,9e8a6c59) Z8(f0a1b552,d2bd6d07,4099fe79,18e57d81,69b60bb5,cf052dea,36b535ce,70f75e9f) },{ Z8(aeae65d4,f0706129,810e4f3e,d3f90b7f,a11bc8db,62066c1d,f9ba7754,432551fa) Z8(c97f8e8d,e1e267ea,235b8362,8ecbd4e8,fee6892b,97607bcb,6a6886b0,723fdf1e) },{ Z8(5c1d0e27,6ec32e26,0d5e87c6,baaa4e9f,5046a410,f09f4cae,3e4cab06,ac982b71) Z8(6940f2da,30f2257a,ede56473,19180165,26749c43,f4af2ab4,17cfaded,7386bc2e) },{ Z8(efccd9a7,17c86357,90b72371,2651580b,0abb7696,e57cd327,6915d53c,e48da163) Z8(025705ed,1279aed9,d6e583ff,b4dff5ef,a36fd18a,7b232faf,03af5587,74cbf9f8) },{ Z8(2a826c1a,0333ac1d,ea7efd86,55e66b44,e62627e5,188320b4,24b62912,5a74aeb9) Z8(3363c7fc,50800d47,77ebd803,94cc1824,5110ea50,456e8bb2,28bcf941,760f9c96) },{ Z8(76a1ca55,43a3f551,4518e0fc,0f1e32ef,3e5b508f,8b63c711,7d60fbbe,2451e71d) Z8(5c94d3aa,250ff699,bafcfd59,50684ce6,76e1fe9f,989a9274,071282fb,7751a813) },{ Z8(c257dfed,dbddcce8,03e16c65,af8088bb,d9a1ee03,f819a863,e2671dcb,8b5ae70c) Z8(cdd6a4f1,8750a8ca,c3da432c,07be2ec9,2918d8a8,f63d1655,f1b09872,78922069) },{ Z8(d0dde8c5,a9caba57,0f3da399,19386ee6,ee0ef38a,b9a877bb,946cb64f,b2114303) Z8(1899206a,a956c38f,ee015120,a18e2aa5,ed1bb404,f68dbcf2,5a1e1f8d,79d10987) },{ Z8(9d4179e1,47cd2a96,91996ce0,dd6e9f64,c45b6ee0,64bf71ef,1a908802,ee62d104) Z8(22d5eb97,999b100f,bd8e5113,972fca0e,4e5bfb08,73b94fcd,1a33005d,7b0e6749) },{ Z8(5906267b,9727ebe7,3bffd807,bda7391f,0a0ba86f,9cd3cbbb,669c3df9,c07f81b3) Z8(9dfd6268,ea5ce16b,9ec747b1,64911742,73d75cf5,720ec44c,bc1bb2cd,7c4a3d7e) },{ Z8(8abec40d,2f01653d,2bc13395,6093422f,2840a0bf,4866a344,bddb7177,9ccd0b6b) Z8(829c25b6,769bb433,09381f6e,48299816,34148654,15b0f2db,c0a2b185,7d848fe9) },{ Z8(ed8fd682,4827b3e4,39ca9988,6fb9d4a8,1ce07db2,bcc34caa,592550d9,eb29d0b0) Z8(fa53d65d,34ba102e,4dc7b6e6,cde2ef18,1afec6d4,becf93aa,e3cc7b66,7ebd623d) },{ Z8(9d15cc1e,12704f76,383503a1,8a334b0f,1fc312eb,f921e345,73b2b50d,eee7b8f9) Z8(1790e838,3b38ae3b,8e29866b,379d3ea6,1af246e3,5f40d932,5fd26156,7ff4b821) },{ Z8(67a46987,94062760,e89d878e,3a732eb6,0c759abe,e2af09cf,3605037f,0ba66448) Z8(d7258b51,a25591cf,34ebb89e,4b8b8c4c,3ffe346e,e34aebf7,2e87f634,812a952d) },{ Z8(4136900c,f04505f9,fd9b2fd0,ec760e66,63f372ff,f2039753,16f3e26d,b21e3f7c) Z8(eeafe183,9e3bf732,18e0a7e0,1c88e1e2,3bed4da1,e6080459,4936932f,825efced) },{ Z8(53b65adc,76def4c8,e81a013e,690afdf2,184fb062,23989734,20e6ea98,297156dc) Z8(aa7c2a28,80a11439,210f75ce,a5d75211,b755b2b7,bcb1c488,e6fa0272,8391f2e0) },{ Z8(7ada428f,cc00dcd8,c000a5b4,3b9be86a,5db6f492,7080891d,9daa94e0,978f0a6b) Z8(96240ed5,bde39b4a,389f13c4,3f135a26,1fe03811,fed4a7fa,b9a905c8,84c37a7a) },{ Z8(eac77298,d04a9e2e,5716b0d4,7259863e,dee7403c,9b0099ab,6ea5168f,60e4aff4) Z8(c52fb7f6,90936f50,5d3ed11a,366fbbf3,ffe69b64,c4bdd99e,295415b4,85f39721) },{ Z8(d95cf419,b28d415b,f24b352a,cc6ff342,809d44d5,9401a2c5,7ba5461a,50cba9e1) Z8(f9cabf0a,b3c6badd,430bd090,59ee145b,b1f1a3f7,572ef4b4,8e645fb7,87224c2e) },{ Z8(0eb07925,e5b1269d,ed9b187a,d1d2fd21,3b889e3b,f02ede9f,9f62ab2c,2e64de1d) Z8(945a0a58,a2072c7e,7e4ae138,63e6f990,c8c5f241,1f64d85b,6a64b7ef,884f9cf1) },{ Z8(46e32681,abcee122,2922d148,7967d053,e1370c8f,cf0146bd,779f7757,d9f2a988) Z8(51b63a9a,3451ee15,48cde6bb,c9d5fd40,86a5a24e,0918ce3e,9f7de298,897b8cac) },{ Z8(66b86f42,f9c14cea,33bde7be,fee11155,438d5e9d,e1958c8d,38859b27,50a4b66c) Z8(0e33c3df,26dfe952,1cf1faee,3a330f34,f14054ed,799d1cb2,a6af4d4c,8aa61e97) },{ Z8(d0ece291,32eb4370,23a91da6,5798053d,8fc6853a,2d5aee94,45224e00,21f25c1f) Z8(34f3fab2,5be20076,147c6d48,37d86476,e970d58e,30737d03,c4cd05fe,8bcf55de) },{ Z8(c2eb376c,ef9a8ef1,d7aac1ac,e29dd595,ef6da3e9,de764d2d,66f272b7,80ce3afe) Z8(a3ef0ea2,e98ec9b5,c371d36f,78ea06c2,ef3d5710,e5eebbc0,3e4b7662,8cf735a3) },{ Z8(a482791d,13c9d868,6dfa8df5,b660ecca,7dbcefc9,4eccce8c,02e8f0cc,411af4cc) Z8(8a493f54,81559525,ef8dce37,4c2379b2,e2efc77f,a7c766fd,89e125e4,8e1dc0fb) },{ Z8(28e74d7e,4f6620b1,dd0bf7cf,fdbe964c,deac4090,e678c55e,ab58d60f,6e709121) Z8(5ba0cde2,9a4b1c06,696ad39f,ca4f4817,1e35f2e7,62cd2f9f,820681ef,8f42faf3) },{ Z8(9abaca2d,18da6190,7ab564b6,d1252aec,c7629553,022a6191,c984a22c,e12af53d) Z8(c9110b22,beeaffac,3b527cba,481a9128,fd849e89,81e87bad,955b6c9a,9066e68c) },{ Z8(44f5ae8c,46563067,d9225675,228fec0c,20b70553,37e3a916,53349bf8,f29881dc) Z8(8150f4a5,5a9f0930,5b0c6c60,bcdfcc1f,5240a471,f1b43916,f5fa1416,918986bd) },{ Z8(0075384d,9003f45b,8607f720,d3e059e8,1c66423a,3a28cb9e,ac221819,72804429) Z8(3894e474,feca10f4,01ae8308,50a06eb3,1e710847,21d6d688,c7be59e0,92aade74) },{ Z8(fa1895f4,5558e6af,15fa0ed3,c0dc1d6b,6de19a53,92b0f0fd,a10dfdb1,b09a0aae) Z8(9ec6647e,7437d665,433bbdf4,527d7309,438ffc03,c1f9edcb,4d88d75b,93caf094) },{ Z8(c23e9c20,fa880bc2,44803285,36d6e47d,b25cde63,0c7b750c,e0814130,53a0d1b8) Z8(1d0d3dfd,33a48e4f,6a10aa67,fc1f5596,67db5d0c,e6b65d2e,15845642,94e9bff6) },{ Z8(888c4872,979b5ac4,58797f08,ca3f05b7,6ea286d6,f59eb28a,c7a398d4,f1efd6be) Z8(88043648,2d83ac42,b745196d,a546f842,4f312a40,d4e18dd1,24745dcb,96074f6a) },{ Z8(a599dff0,51789fa5,ec7a3208,9aa1da7d,bf521374,3c526d19,97f074ad,f8a93521) Z8(3f080baf,79b79196,475e2e71,794a2964,0d589296,a10c3491,20134202,9723a1b7) },{ Z8(1304d6c1,db24c695,ceab26fa,4556832d,52740265,879fae51,e748ff9a,d3bc93b7) Z8(636df445,4042089c,8119ba91,0b701333,36cdee18,ac850fab,7885f0fd,983eb99a) },{ Z8(a5640a3c,8297bef5,57cb315a,0dc0b96c,bc7ef3d3,a6b569fe,246215d1,d14142a8) Z8(56157af9,6b3a547a,ddf94bde,ba133462,16b06715,2ab5b3d9,90eb8990,995899c8) },{ Z8(45128ad4,bf91ec4e,35a6ed7e,bad3588c,305274e7,3cf7c12f,366668d1,5e8524f6) Z8(9d8edefe,c765792d,b6be4109,1ddfd382,72757253,5c96c42e,e70e98b7,9a7144ec) },{ Z8(b0a314a7,c8b6db72,3474d5d3,618792f8,c0d05d00,5a8770ef,9d03b869,d14e8265) Z8(2bb4ff77,c110a792,16c364d0,8d986c28,efc8f895,e8124226,3a3dae2e,9b88bdaa) },{ Z8(48fe0250,829512bd,61955f50,2df8d830,3dc6a386,a87f09fa,b57fe9db,bc176f0a) Z8(2170e2c2,41e7a845,00413260,1717c9e7,f8c38f62,221301b6,b150cd4e,9c9f069a) },{ Z8(7bd85e3d,e34b5769,ca04f4bb,2a5f91d4,39c54415,b42d4279,4c9cf538,880cc792) Z8(c90a2c44,29adc2b4,1a54790d,e6d9b959,9b341d6d,76f60c2c,ffe1157c,9db4224f) },{ Z8(a0ce0994,eb29783a,c4b53d6d,97af626a,64671d5b,76ffe838,89dee616,cfe36b8d) Z8(f297662b,0bd03b10,df1ff936,9d96954a,93cf6b80,2131e856,8ab7d520,9ec81353) },{ Z8(6fa22492,9d4d0b6b,045b8bbc,2e916e2d,c5cd1a0d,ed2d7b5a,4f170359,d8c6dbf6) Z8(bba84ce8,71168dc1,4b72b4f9,ecf33acb,5dde6c84,74ea82e5,8b7a12da,9fdadc26) },{ Z8(d6124129,2018ce5c,1df6c2fd,5f29ec91,892e5832,2bdfda46,1bb82762,6471b5af) Z8(2a5e02a7,247c0b84,56f59974,4486ea27,00bbca9c,25e617a3,33957323,a0ec7f42) },{ Z8(82f9c9e0,48f0123e,eafb93f5,4995554c,a3bb3481,72e33343,751d317a,0a091231) Z8(76d75442,e23ae16a,7ce6611a,b774c2fe,70cb6c1b,93dcdb07,ce733bd3,a1fcff17) },{ Z8(1ec278af,031238ab,e66d803f,29c9172a,e5fef460,6124acfc,7750befb,5e241add) Z8(52e7f931,6bdd6ab9,16887279,e59a4980,e39a20ae,5bd9bd99,e2f613e8,a30c5e10) },{ Z8(d6d3d6f1,f8b49e95,50bdc64b,6f85a5ab,052e0cb4,3b248f20,3e6f4167,feea5337) Z8(c4c1348b,6d9c0712,7535ca72,efbe7833,fe84b0c1,af45d980,5446fb9e,a41a9e8f) },{ Z8(369cb411,5c9fdf23,a883d1a7,d83cab84,445c1b43,322aec8e,db555408,23bd3235) Z8(84ebc206,5bf1a66c,af47e744,6f7191d8,61b6316e,3dfa3d37,81f5d811,a527c2ed) },{ Z8(17bc15c2,efad36ce,b966f5f9,f84b0423,42ec4a7e,a85f6dd1,65a33b31,96bb5520) Z8(905668df,1b7a54a6,71eab2c3,1b11377c,37ec33b6,4766e98c,6771cd8b,a633cd7e) },{ Z8(e9bbbb42,0b863a1b,a0c9e024,3ab169cc,c1b47d5a,c1f3168c,0464cdd9,aca74ac1) Z8(2eb5190b,c9ea4c64,f774593d,bd794408,2aee1a18,84c2b22c,badd84e5,a73ec08d) },{ Z8(5463ae30,44a034cf,f48a4b7d,0955efb8,bf4cceff,34a81880,68cf4ff3,ae3a7fb0) Z8(77258b86,ab09e042,9cbb2de3,39ed8a98,b61ed2f2,59d2d85a,0b435a5e,a8489e60) },{ Z8(c1df5ebf,8a7e5bd3,d6775e9f,bbe00b2b,eceb1f55,031e3061,3e381ca3,ca138ee0) Z8(29d4eb53,a388b633,4c39b31e,d0920f6a,97aea7be,be4578ad,de2d5773,a9516932) },{ Z8(b44ebf27,07bdebd9,ba72c6bb,37b0af6e,74fac90f,cc6b9908,e041db14,d82bb3ba) Z8(3fd0d75b,916e796b,4ebab5f9,5d56af71,c1796894,aa145a1e,cca4bd48,aa59233c) },{ Z8(860598be,68a891be,419576de,bdf5913f,71a9ad49,9309a22c,7697b2fe,e4b7faf8) Z8(2e3f55d3,52d39be0,35094514,5631bf5c,fe59cdc1,e310b9b1,9f9cca08,ab5fcead) },{ Z8(12c4fabd,800743a3,a2cbcafc,9f7e13a3,3754421a,dbe424b0,90272b07,cbf0d848) Z8(6848f351,cefc72f5,c446c7b7,601ab2b5,4585513c,9792ec98,6bcc4984,ac656dae) },{ Z8(14f3b1d7,77d02118,d6b30d46,faeab5b9,04f30d08,869cbad3,7b2300e7,0c763464) Z8(5b324a78,7753b3c8,8161ccf7,839e0457,1cd40845,4d552f81,acf967d9,ad6a0261) },{ Z8(409651e0,a0ec4685,0b291788,f5270b8d,11141c98,752dd2fa,066ebca8,ff6f3b30) Z8(ccb86b9a,72812da9,b0db90f8,50ae328e,418af602,b71e2eb8,60bb2467,ae6d8ee3) },{ Z8(6e5357ef,6502ee16,4e559a75,486c32a2,2036cccd,46a4f082,c523dc46,5f3cbd97) Z8(51d2f00f,e6688102,e7a29309,29f04ae4,103ef4c6,b04afe92,20b3ab86,af701549) },{ Z8(4df8fd3f,bbdc25e6,05a0089b,f91ab8af,0ee934fc,bc66fd20,fa3e3768,c5e4901a) Z8(c1549af0,96012a8e,ccaabf0a,17ce375a,76554335,e44ad05a,3c46c653,b07197a2) }}; const mp_limb_t arb_log_tab12[1 << ARB_LOG_TAB12_BITS][ARB_LOG_TAB1_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(0c7e47ed,4b04b13f,e5e46287,7785988e,adc4b604,455be77f,db837e0c,9876d250) Z8(3228bbda,f7b8170b,08a27c47,0dcf437a,809be9c1,56221f77,00155515,0003fff8) },{ Z8(5d3950db,eb8cb58a,5bc2ca6a,2f9fd6b9,795b75ca,f576ffd9,c36eede8,f2added6) Z8(c4b26860,46c08a95,de4647be,6a90d794,2bc2bf0f,c443999e,00aaa6aa,0007ffe0) },{ Z8(df684222,3331882a,5bbccd32,ed548b07,37bf2957,dd4f60be,63e70f62,0c11e6c9) Z8(e4fe2376,1761433d,33f47284,631e94d2,7ea01f6c,c25eceb4,023febc0,000bffb8) },{ Z8(e976cdd1,bd5c2e9e,116cb84f,f6577335,de7bf63a,add50321,e5b794e8,83c3767c) Z8(8222f25f,c9b2e919,8002d083,49c8cd0b,e271ee05,885de026,05551558,000fff80) },{ Z8(8ffd6108,b5f4be26,13bf8e54,580566be,3e42853f,73edc4f2,385d2695,26f78ace) Z8(7c2eb67c,624afcb5,b1195c2e,ead9fd07,6f07f956,6e07f2e5,0a6a0e74,0013ff38) },{ Z8(8397d72e,9cb25d77,08872f77,6259b85d,79f21fa0,fe7e018f,94cff6d6,a6ba5f7e) Z8(6496860f,112126f4,fce97760,ec66a6b4,4fcc8cbf,4ae6f3d7,11febc18,0017fee0) },{ Z8(dd783371,6ebe5d38,e52d4841,07891503,a142f477,c716cde1,a8180ccf,f533be7a) Z8(86f4eca4,a36b3c59,41bf2ab6,05302d4d,867db3af,d625df1d,1c92fd49,001bfe78) },{ Z8(71564207,2e395e6a,648d0b5c,d4954a65,10a5afda,2369cbdd,a5e80ec2,7dcd939c) Z8(5c09d7ac,4e588a36,e5e0fc9e,545eb8e9,b318cb38,06678ad8,2aa6ab11,001ffe00) },{ Z8(a74c1f7b,c8174f2c,4cc3b548,280cd516,fc13a506,be31314c,9f59c45d,72151c08) Z8(9ada2548,b3fa3abb,cee967f2,6704965e,74d6486d,7195f625,3cb99878,0023fd78) },{ Z8(0a8bc7fd,5940caeb,5946eabe,3329656e,197b2784,204f6b19,e73d96eb,e2ce3906) Z8(f3403917,958fda30,07f8f64e,4dd54982,e472577d,acaa1d02,534b928d,0027fce0) },{ Z8(ba15b9c1,9d400eff,63997eef,1f52bf03,b96cd7b8,4e6f8931,72908d79,9584befb) Z8(0731c1c5,a523ed83,746ceba4,481e5b33,9460290d,ab6c51d6,6edc6061,002bfc38) },{ Z8(865897d0,e4422d88,804121a1,f719dc94,0b06bab2,564bce4a,77837236,a2ac2a15) Z8(4b0345d4,0ddb364e,f20ddf24,c18ae3fd,6fe9680e,202d1d41,8febc309,002ffb80) },{ Z8(c67f8e67,c756b402,e95530fa,d96a8508,8b260572,d27384a1,ed01736c,aa92f585) Z8(142fe815,681298a2,2666f5a6,84fdf71e,bea16a3c,db76a4f8,b6f9759c,0033fab8) },{ Z8(96ee51c7,2b4aae3a,37445efc,3528f10b,2447a3a2,262fd12e,8aea37ae,ee8fa41d) Z8(25bfe902,6aa3cc1f,44187b24,fc0ffe45,7dfc3806,2bb69a56,e4852d3a,0037f9e0) },{ Z8(01761986,7a9639e1,83ebcae9,a207aeaf,93202e05,e12a8362,f7ed7dc7,9b5cfe21) Z8(5907d500,08937816,b236f63b,0a6da4ba,2f4485b6,3ce0b154,190e9903,003bf8f9) },{ Z8(88455ab2,2cbec254,033072c1,ac4e6045,5f35b760,d3878b77,f158acdd,453519e9) Z8(a6eb720c,6e34c564,62ef4eb0,8e30d617,2499268e,7809a0a3,5515621f,003ff801) },{ Z8(d6aba998,7285ccad,cb6da537,24bbd3dd,1faaf79f,dde40d3a,a21dbeca,002ff1cb) Z8(dc6eb7a7,da5b99de,a85e4861,d7bec86c,440a6381,e2faab95,99192bbb,0043f6f9) },{ Z8(d575a542,48cdff42,994b5242,fbff851d,e7243654,915506af,2f36d303,5936d46d) Z8(10692284,4e70a24f,51898a1e,9fec675c,2461f0fe,7fbdb689,e599930b,0047f5e1) },{ Z8(af26aa96,52ad5bde,e081969a,48cd173c,ce824ace,d0826b70,62e17050,20a86cd9) Z8(daf119ce,ff749b05,a14a8966,4b07e3b0,5395028d,ac21e68c,3b162f47,004bf4ba) },{ 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Z8(d203908e,02ca62d3,4f34347e,e2aa8e94,4c7af8fd,e5a7ad41,9d52858e,a2d55b1d) Z8(63d691aa,c506387e,8d073984,9768cf4f,882c3c80,17be100b,76b05097,01275563) },{ Z8(056e4b9d,cb547362,85d30619,0774c3cc,7b76e77d,62feab55,548d2205,c2f25a83) Z8(af1e55b3,c94991fd,965a9e22,bbbb20f2,5b064949,1d84d28b,dbfdad89,012b50c0) },{ Z8(43c0bf69,99519342,d5fa1e25,88a414fc,c298ab06,437c8525,e6ba0238,87d5c579) Z8(0f34341c,9630b883,20673da0,9c847e0c,87a84e42,97b89292,66898566,012f4c0e) },{ Z8(d416551e,e6cef8a5,af4390de,0ca7a65d,bb045932,a09689d9,e7aad825,54bfb4ec) Z8(33815654,ae5ec783,7f40727b,1f120f44,872a5f20,37191316,16d21754,0133474c) },{ Z8(343c1335,c30433ec,9700948f,2e37bb15,5b7d91ff,c57703c4,77ed2379,97f3c2c3) Z8(73ff4d94,a8611edc,eeec0c6f,cf20cd6c,41abf980,d89033cc,ed559c92,01374279) },{ Z8(09091dd8,42208d0e,2ff745c0,900fcd07,a4ad11d9,af23eb6c,7de4f9b6,4b9989aa) Z8(90a20265,2defe197,08c9080e,18f6394d,afe104d1,e2fc2485,ea92487f,013b3d97) },{ Z8(4533ce4b,200d4e60,b0eb1eff,a6dd1f16,73b6e444,ad86fb62,5722681e,57075db5) Z8(357fb684,e444e58f,29be3018,19350e86,50117ab0,a4f24dd2,0f064895,013f38a6) },{ Z8(f3a83285,fef1d22e,3f469677,e72ea369,1038de7d,18e5003d,c99664c8,cacf87fe) Z8(a27038e6,3c826b1b,13003313,6c225df5,953b429a,b27aef90,5b2fc46b,014333a4) },{ Z8(7d0c6591,d8332a29,b302dadc,cb9be321,410944d7,2bcfc6e4,dfe028f9,265b03bd) Z8(3b590bc2,c72671de,687bfb68,759bab55,6411b343,42c5761e,cf8cddb7,01472e92) },{ Z8(e73a7b96,da4c756c,df5ff9c8,117a037f,a5f765ff,dbe54cc2,fc107cd5,b4474cf0) Z8(c499edb6,5ad22684,f01e84a9,cc1fc4ed,9ea46f21,8dd586d6,6c9bb04b,014b2971) },{ Z8(26332e90,fba231d8,08d3adb4,e9a84341,a0b1e214,49b2fd3e,ce035f1d,f5842953) Z8(901e6a3a,63ccf79c,727a81b6,5521fdc1,ac87eff4,2a28c489,32da521a,014f2440) },{ Z8(71e6a2a3,e976e893,168d772e,8f55352a,6125ba6b,77e347bb,0c95d6d1,ae102c35) Z8(a04a112f,660461a5,52edfe67,d5aa24f6,da6d0e16,6a554c9e,22c6d333,01531eff) },{ Z8(d5e7e949,56743794,3db16793,5a355b17,5ddd09cc,53041652,eb004d11,56c39ee6) Z8(97854ceb,495c1afb,39030db5,eb60b1f3,592a2409,baa0ed8c,3cdf3dc6,015719ae) },{ Z8(e16e1f3d,025f9fcb,1929bfa2,9d8bec12,ab8dbab8,1ac7047c,531aab4e,ee875b6e) Z8(33737d75,7bb1028a,82d1dc36,480f5056,91501c47,fe911753,81a19622,015b144d) },{ Z8(4416a069,fc31f39d,ad9e9a29,cf707c8d,b2cce68f,29314e71,f17649b8,db435061) Z8(00d4a03c,a0e610e5,e219d481,69e4b23b,6d7fbf03,ee7386af,f18bdab6,015f0edc) },{ Z8(d87c55fc,65885a99,241478cc,078f0771,2e5d38d8,5e29e3b5,f02e7126,8bc74965) Z8(41089ae5,cd34fd1f,bc0d52f3,b818ca49,2acff685,74dfaba2,8d1c0411,0163095c) },{ Z8(575a3b04,6d8341c5,be54b372,4ef7a209,9d661c04,46ae6e72,acc0f8a7,1b8d1725) Z8(e769cb62,c31f7727,c63b3e1b,c5a28c43,2bb47af2,0c30cc10,54d004e2,016703cc) },{ Z8(012c7add,9a9acd1d,68ebabdc,17fa0b44,19745604,1aef3cc3,5d8b8345,d65ae94a) Z8(785c0766,636cd4c7,89ee9874,6f5ae2f0,36f5696e,1bf8e315,4925c9f9,016afe2c) },{ Z8(d1f287d9,7933958e,5b32f32a,a9591ae6,eb12cd3d,4032326d,6656effc,d5fb7469) Z8(0fdc295f,d3b37d89,6fe06366,920acf95,796bb608,566c3dc1,6a9b3a48,016ef87c) },{ Z8(ccabebb6,d760c7b1,1ab86a22,21073e23,a56ebd93,72024eea,b0b8805c,82e0477b) Z8(6ca3fca0,3a9e6470,13fa14fd,366bdb39,8e5c2ba3,15c5d5eb,b9ae36e3,0172f2bc) },{ Z8(e92b7468,f91fbb7c,b5ec76a4,a150c369,d4073501,0f790d1a,ac10c6f5,7783092b) Z8(983b004b,bcc0b6e5,b08d164f,610d389b,bf72c898,b9a46bc4,36dc9afe,0176eced) },{ Z8(a8aac846,2f645b37,349ad849,8b4ec729,9208251e,16159412,90ab2734,b7e5eb7c) Z8(caacc5c2,54b1db46,bb561c2e,5361e455,9a8aba04,04605edc,e2a43bf3,017ae70d) },{ Z8(96cb638a,faabafc3,0e8ca9f4,16064670,73a2bce7,95165acf,a35e4561,6beb75e0) Z8(f1aded85,903ae028,8d165ca4,2800d1f3,e89c01eb,785a4740,bd82e93a,017ee11e) },{ Z8(53083785,2f7d6353,6717bc37,23d6413e,e25020f7,e7c074ba,fe2117de,d3ac8cb2) Z8(7faafde2,b24fdc38,067c90d5,896910a8,fe56f5a2,b5424f66,c7f66c72,0182db1f) },{ Z8(35b40305,ab118f51,8f80ab48,92ffa364,0e609295,62206c08,35eae090,aea7f360) Z8(46acd659,bd4482f4,2d792fc0,187d0295,4c2739a6,d5584f8b,027c895c,0186d511) },{ Z8(e4586812,8267f186,b664f802,9903520b,324fc988,7180dffd,d2e2b8e7,c724f4f2) Z8(055fdbce,c814fa3e,12b05de7,43763ab0,008badf3,caa4ab34,6d92fddd,018acef2) },{ Z8(c3cc6dd6,78a51015,586a5595,c46c3051,4a14d3ee,97527cf8,4f886a54,f5b8b4e0) Z8(f983e17b,5846fd06,4728876c,3162cbfa,7ce6e1e4,bc29f183,09b781fe,018ec8c4) },{ Z8(91ac9328,3f24c2ff,80665588,901d1d86,15598dfa,3eefcbb9,bfce012c,a3ba4988) Z8(31706441,449fa385,40ebc439,705c8708,4a241fed,630f4107,d767c7ed,0192c285) },{ Z8(f5f17f0c,e417372a,b09692a5,b0f7c682,0ec096e3,8cb94c7d,443f2d9d,7b3122b3) Z8(473030df,e0abfed8,ec606f07,c1a49f5e,27c7f04b,67c36fb0,d7217bfc,0196bc37) },{ Z8(b5a017c6,67e1505d,398efcd9,401068d1,8da15e2d,a8ac79c0,738e3b3a,d23494a1) Z8(3e5b020d,a26fdf99,063009b2,37a4216f,bd401543,bf18f79f,096244a3,019ab5da) },{ Z8(9ce14854,fb9ad100,7cef26b8,46d455b4,8da98fca,570a1785,425fbf6f,09edfedb) Z8(90f3c067,86a00eb5,0f6eed91,747aceb0,62867bbb,075aa978,6ea7c281,019eaf6c) },{ Z8(e2c19157,9434f3ec,e1f9e66b,8032d462,faa4d041,b0872bc5,2a616571,62bda43a) Z8(580bfe3f,75aec43b,f0a26462,d72d1652,626c6772,e55924db,076f9057,01a2a8ef) },{ Z8(55e779aa,d51a3aa5,3e2c93bb,1dda62eb,893f3070,9ba945ba,9b7040b3,dbd4122b) Z8(e640ba32,4bc3e23f,8b567604,7982e2a7,06274260,617117c2,d4374312,01a6a261) },{ Z8(fcbed80f,15e25d10,774d3bfb,a9a3f88a,868dfa18,017af617,5ce0f30c,1c922a28) Z8(8d3502f4,cd19aee6,5120781c,c60ec200,a6feead7,448a455d,d57c69c1,01aa9bc4) },{ Z8(c350c3a9,38ae4f1a,e99d875c,2aeffba6,eae45054,d6409c8f,0fecab7b,56ce31be) Z8(4747edfc,ea66a259,ce670094,ee57448a,f0462344,750f552a,0bbc8d9c,01ae9518) },{ Z8(5871e10a,4808a045,b2bad39d,1ada7eeb,eabb563e,9329dc9d,f878bf3d,f2b07d64) Z8(6593c333,ac5cd41d,ca2d5319,7b5d8bc5,6910e094,53de6ae4,77753203,01b28e5b) },{ Z8(f6efedab,88013657,01f0718b,0e1eba94,2d91f351,47667de4,6a68c633,0dd1e97c) Z8(176e511a,56f7f603,bceedd0b,7a46a98d,4a69a136,19328800,1923d47d,01b6878f) },{ Z8(dc428b95,bef79abf,182edfb8,122b110c,23123d4d,8b3bef01,aa1eda86,fe9452ab) Z8(f2a0c323,68563aeb,8e635f8b,543266ab,9416b5dc,3185b765,f145ecb9,01ba80b2) },{ Z8(d2f30446,a066ddcc,39b9e717,15e9f367,405db65e,2b4f58fd,0525be43,32b68b50) Z8(20ecce05,4a9e0f8f,d51f7739,309e2f1e,3f52763c,9a6c0404,0058ec8f,01be79c7) },{ Z8(fa460a86,6942bea1,8493f488,cd2e702a,43412b1c,b62dfa51,19907817,81af1ecf) Z8(12cc5e38,b6f595a2,1bea4f90,df4cce9d,5c2dbefa,3f673afc,46da4001,01c272cb) },{ Z8(7bb40ea9,22ed3898,e39d6b1c,399ba758,fe53830d,b672f8a0,be0d7aff,21f3a892) Z8(81bdf9b4,5159085b,ebf9c52b,c8a18685,d3aaca0a,56b379ff,c5474d38,01c66bbf) },{ Z8(8f529643,64ea9670,e9cbfb1b,552bc14e,e269a902,77ef4c52,ef2bf716,e0b5a3aa) Z8(903cb0f8,0d8eef1e,a5dd757e,6da264e5,75f77800,be0c8a9a,7c1d7488,01ca64a4) },{ Z8(f14e730b,4363d589,8fcb8fd3,6daa273a,0755651c,934df6ec,f543a503,873828d7) Z8(85fb9975,a832fa14,a063e9b8,c4395d82,e98976c0,576c0b0b,6bda1070,01ce5d79) },{ Z8(77667c69,61052bf8,e5f22c61,4403a1c2,ae9aa9cf,ac609e23,3819a51e,5d96c7f1) Z8(5c2f57be,4b4e13f3,142be1fa,76753283,fd3c5830,65c0655e,94fa7597,01d2563e) },{ Z8(5748ea25,342c8e69,26fd9300,36a2ad59,699004de,dcd12487,5d14cb33,1751acf8) Z8(dcef186a,2d4c6ff0,fb1f13b7,06f93d9b,ccf1a1da,e99c9569,f7fbf2d0,01d64ef3) },{ Z8(538cbbbb,628c87b2,30868ffc,ee809ce2,3a204807,cb3c1dd8,558a2e3b,3b87d7d8) Z8(07b71510,0e752d45,1cc16136,70d0c31c,15952489,fde0be62,955bd11a,01da4799) },{ Z8(c4b271ea,cdef4ed7,8ca00d36,b5f7a740,6c919cb5,5aa90462,4ded25e3,0cfa2376) Z8(30c94590,8392a755,baa9fb98,699d2ddf,02cc804b,345b90b1,6d97539f,01de402f) },{ Z8(2243d44e,bb5a11a4,194c2b5c,98651b98,bd6b9d38,9b405ae3,4cd5b301,7b3f709a) Z8(7f40419f,7ec4adca,7b140cef,6b8c28b3,adff9dc2,f26480b1,812bb7b2,01e238b5) },{ Z8(356b1f60,ec2ee5cf,29868a31,16291d8b,ffd69d70,98e63e9c,1c34017a,f5adccfe) Z8(0a0aa162,843652e0,960f78f0,966ecbc5,73d11909,cd6ecf05,d09634d7,01e6312b) },{ Z8(c33f9f65,e4fac114,15927c6b,3afcfbaf,8798e474,0cbf09f4,4ae7f878,d91d7bdf) Z8(4f9bcbf7,68830083,588d3104,d73dab8f,32891c12,e7956329,5c53fcbb,01ea2992) },{ Z8(2cdbf61c,89ec95d9,339e0db4,b744434d,708140bd,606ce0c7,8e9e5c21,0260a55a) Z8(d9cd3411,3e1d81e3,01ce9e9b,32a7d697,7162f640,4c1f78f6,24e23b3a,01ee21e9) },{ Z8(8c8d9511,04878ca0,8fcfc9ef,2f7f2907,33514767,0ee8e7f0,80be14b0,77d91940) Z8(da35fb25,eededab8,8812028f,2e1d8afb,5e1ddc95,4bfe21bb,2abe165b,01f21a30) },{ Z8(7bdd410a,25b49440,c86c5794,15b29515,64dc2389,69514c55,ccc5fcb9,f1ddfc07) Z8(3d3a2566,2d9c67ac,b2e63012,d400c64e,7ba3a8f2,da429994,6e64ae54,01f61267) },{ Z8(f6725be6,4314e3b5,d71e6baf,2896befc,5e6b55ff,ac21ee8a,fdb1ce5f,7a42502b) Z8(fa5d1c6e,62b187fd,6bac0a8b,70ef0e95,ca0d270c,e88d71b2,f0531d8a,01fa0a8e) }}; const mp_limb_t arb_log_tab21[1 << ARB_LOG_TAB21_BITS][ARB_LOG_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(62755d69,e496938f,05daf00f,5baf03de,e7d47be0,876a8079,f673a2de,42c7eaa7) Z8(7c0dedcf,b951ad59,fb7be050,cdb6b676,c61b4b9a,5c71d0a4,e70de3e1,b2478447) Z8(c7c58559,1947ba58,ed644c21,3a4a3445,45cb0fe7,28872ee9,2b52267a,c6888f9c) Z8(ab77734d,4f53d356,57f7b519,1eec2e2f,486fc6bd,1678ec26,eecd9969,c88799c9) Z8(f6b13852,e1f836bd,79cac542,79ca2220,3edc6351,17e1d8b3,d27618a9,c2141a5f) Z8(323af80c,5d01cc32,3d4c10e1,410d860d,0c975e1e,ed109f87,9495b1ac,6483bfe1) Z8(67c3706b,8b72920a,b906f4ed,463788a7,3af1b218,0f14f335,de1bef77,8540a3f4) Z8(caee6903,f0bfd950,c7661262,a8d061ff,ccdd8781,948d50d9,0c5fc975,d573845b) Z8(d564ebbb,e3d444d4,56901629,6bbdb38c,422a728a,00872128,d70f97be,ecdd781c) Z8(77077723,c7b39aa9,8dd25814,64b3d053,bdc530c5,cac1d2bb,b4bee981,4bcc2822) Z8(638db165,034e5ceb,5911a433,775b6575,6721f58a,1740d6c6,660c9f0c,0afd3039) Z8(2ad6ab1a,8400cdeb,0182f7f2,4eda72ef,278b39ed,9c07347d,e853cd50,29bdf766) Z8(6c5511c1,415cd4cc,3dbea7a3,7fa5d3aa,e1a5772e,e8b45e05,0a4e2e28,1c0e0822) Z8(4785a221,f6b2b036,6bd6a362,c035aad5,2ee8293e,626c2ef2,1bc4d08a,ce921467) Z8(ea801ae8,1cc99aa5,403dd582,93e18189,8bd310a6,750b0863,532b6b9b,5faea913) Z8(8fd1d5f6,48625f86,c1bb60f6,c6ee8bcf,8d212c6b,f6cf9703,38eed29c,ff7bd74c) Z8(7cb29271,02127ef4,0f6e3a39,9ce34431,e0a5d2e3,55d9a7ba,ec979e9d,8a38a3ff) Z8(e3673dcd,df6c758f,ddf35ad1,aefae14c,ef229fae,3e3f04f1,9e0cc013,07e0a6c3) },{ Z8(cdfb11b8,fe5201f7,f83a048c,5ff73ba7,2e3dc08b,0c37df21,a532ebf3,60eafe86) Z8(d274008a,edfe0e06,e2846224,ce94dd65,dbd5db88,fc2a05af,0e14f1c4,acc9fcdf) Z8(136d75e3,db83a653,3209b121,d53c774d,a61d5746,d6d53036,fec4a7d6,7575a44b) Z8(b0dc11c7,33af26db,5b61b49e,119ec434,f811504b,61b2f223,3f704e8a,955d39e7) Z8(64e6504b,3312496e,3312631c,10b84ee5,a70ecef1,e4d50c14,8c65bd71,84016a52) Z8(929c44fb,e842912b,2b44d39d,df8712b5,c81476a3,83cab0ec,a9362560,8ae27c16) Z8(b94a7a5f,3e7e4715,f6324a76,ebfc64cb,2297a345,bdbe51e4,5ddaadec,51b0ed53) Z8(786ab619,2745d1a4,852d3853,354223c2,d12f0e36,ce6586e6,b126e954,355f3293) Z8(72b38100,d61a9908,1eda05b7,2a134f90,6a6eec21,4883f333,7753257d,bfcb2222) Z8(36fa4365,4df3bf39,e3704572,866603a5,321515af,d39a56e3,faa48510,befda077) Z8(5c3586c6,cea9eb88,d5f32769,2ebe437e,550b5ddd,d27eea99,e47e74d9,67cd3330) Z8(eb97c7c8,b48eb540,734ec246,f139c8bb,8e6239d2,c2ec2f61,fc43d0cb,f2a711e3) Z8(6e339208,2f14b1da,18a07a32,86d0d6f3,9fb7dd8e,9da47afc,c2d0065c,8963312b) Z8(89ac698c,c14e8a75,06e51059,c27b07cf,bfd7f245,c3f710ac,9362f430,6596620c) Z8(a5d9c7d8,f85fcf25,b857a365,0fea5d7b,99f1c7fc,3c5c1d2c,980ce36e,8f93e053) 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Z8(2cc49ff4,0b5a9641,3745eee8,82824bb8,538089ec,ae68605b,255d053d,61aa7e12) Z8(b52125ce,54d00b90,a0087f7b,b018bbe6,13935138,b5f485c5,d8607716,c3980058) Z8(47e34849,863d86b9,594f47bf,a786818b,9bb8d65c,9b4edbf9,6c818496,02982ed5) Z8(b552b6d3,74ed572c,b898270d,520afb7c,b28a390d,2e3fd36d,1e715463,1e8137b7) Z8(a7cd3b3e,98fe10d8,391807b6,7fa8fab2,4a76e622,7c68fa37,d0312505,4361ac7e) Z8(44c57247,eb91267e,0993defb,7fac0d00,badcfd7a,cce8877c,6cc847ac,4295b4ae) Z8(4963a9de,c5fb10c7,c1ade436,b4e2b8d8,32912d69,e9e0738e,d97d4406,bcf86386) Z8(2e918be6,00a48ef6,4fbe79b5,e542b336,49e21124,e8160d82,27b07cfc,faa91fbb) Z8(e390d654,5ad1d164,77ba8c2c,a898ed7a,9dfb8a63,25905df3,8554ce25,45fc5808) Z8(5da25d23,1b7f6cb7,f5705199,96870e23,3638b665,a8577261,48ea60b9,a98889ef) Z8(e5087839,1688b24f,6295523f,ef59d2cc,9757fd4e,027aab15,52e00e87,e15b4f43) Z8(c1df5ebf,8a7e5bd3,d6775e9f,bbe00b2b,eceb1f55,031e3061,3e381ca3,ca138ee0) Z8(29d4eb53,a388b633,4c39b31e,d0920f6a,97aea7be,be4578ad,de2d5773,a9516932) },{ Z8(153cb58d,9d1f3b57,75530e68,f08e872a,a184c327,af2fe70d,06f64b38,a5440619) Z8(3831eb50,5f738423,be87fdda,06be990d,7c63344b,51edd5b8,d2725e8f,512bbe25) Z8(2e62b328,6e4d892f,24fd156f,b5bf400f,ff26c676,b3987dc0,3953a3a7,8d61146d) Z8(dd206e6d,10ea88dc,684c9812,a160a9e8,547dd5dc,7f61f9c3,2716985f,ab3b272d) Z8(4c07eb13,cb821d1f,8ce5b245,0d09bbe6,96971363,9f8542c7,0bbce0b8,bd4229c7) Z8(496e87e1,2518b9ee,ba6fd008,7fc537dd,1c71268a,03859467,f95b8212,ba3c30cb) Z8(960f5d47,076dcd45,825f3677,3ba0f0e2,e3cad1ac,559cf693,461d7a9e,171d1e06) Z8(19267d02,1f86b8d2,e7b1b333,bf28270e,a0e0a7b7,aaaeb90e,db418488,77793fdf) Z8(f14cd468,d0f2df53,76e1e65a,c6508ec1,2f9e49b4,f5637638,ddd41982,dacfd3dd) Z8(abc5ced5,258af8cd,84816543,e5daeeed,a162f3d0,f3a852c5,485be88b,01730602) Z8(859bd7de,15b7cab2,4ce7f96f,f9ba8f0e,f6d58700,9478f9cc,723551bd,00db20eb) Z8(ffa47cb0,5cc63fdc,bfd0b5df,4bb12429,555ae671,c1c3a260,7487ebb0,1585033c) Z8(b4176022,ed76404c,b0f6d2db,6a119e93,d5e9d3a3,da919a24,e74aff7b,5b8b86df) Z8(e6cfd8b8,4db00763,2ec17c58,39b33119,9d970103,b8c85166,fe40c52f,315885df) Z8(5f9b9466,cf9b5c80,63d5d87c,ca827530,959e83df,43d087a5,72c94eb9,897a6a48) Z8(ace1d88b,bb5cb1da,fab389ef,567cafe4,08b45e3c,0b672174,1e3ee20a,df6cf0db) Z8(14f3b1d7,77d02118,d6b30d46,faeab5b9,04f30d08,869cbad3,7b2300e7,0c763464) Z8(5b324a78,7753b3c8,8161ccf7,839e0457,1cd40845,4d552f81,acf967d9,ad6a0261) }}; const mp_limb_t arb_log_tab22[1 << ARB_LOG_TAB22_BITS][ARB_LOG_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(8b9c1b7b,ba0ac6ef,1a7045fb,4fc1d240,49754d0c,0ee63f28,92ace9ec,61286fdf) Z8(94505634,73d96965,a62f60e0,055c524f,0f70b0a8,971925e7,4dba6d41,1d0343c1) Z8(15184612,1c93c13a,339710c3,7d998d9c,bbdb40ab,b6953722,a7f3cdda,9043605e) Z8(e2baecec,bb52b604,b0cf3c1d,e53a8b19,3c664ac4,309a02e2,37d88a1b,40123301) Z8(3fe22798,db932747,6e1f2190,1539e8aa,1ba538bc,4ce6ebd4,a8e1d420,4c534451) Z8(cae3482a,d5da9d6d,f84d4875,d43ff73b,5be57b4b,2c369b63,30fd2a8c,9a7f805e) Z8(1d148440,23dc7790,d23bd975,b5e01fa9,5a441e62,ecb5474d,1301a31f,b13942a0) Z8(93410acb,a122639e,e9f6f560,a2e52c2a,aa6e8e71,30824fe9,c39edfc8,bfd9acdc) Z8(4c404a85,66a1eeb2,af4c12e3,d317e9d2,ee056799,80e78b52,d0cfec3c,f815825f) Z8(6c410527,9d07dda1,dee67101,2f38e5ce,92c7b4c4,f5bf18b7,0b57d454,2f6457da) Z8(6bde9b31,f2e4d6ea,da57c458,223b7241,1a1ccbb9,54227606,bf840fbd,733b38d9) Z8(b73e7e2c,6030da8b,9a0cdfba,2545acb3,349cfc81,2144dce2,f80ee38a,2e8d392c) Z8(b4be72fe,5aed89a3,a8bd4890,a60c002c,d2d4e3c5,03b09d89,f1da3961,46519661) Z8(22042320,3ef4aab1,04d8021a,49b8e564,460b00ea,a29a7413,7a6aae61,65cfc75e) Z8(86a9a132,e6798564,43affb63,5ae185a4,d8c15808,e44f4657,909380ff,0e08c996) Z8(38603bf8,1685f930,739145b4,8a85d6da,d1f3a988,5634cb94,fcd59644,a77480cf) Z8(88455ab2,2cbec254,033072c1,ac4e6045,5f35b760,d3878b77,f158acdd,453519e9) Z8(a6eb720c,6e34c564,62ef4eb0,8e30d617,2499268e,7809a0a3,5515621f,003ff801) },{ Z8(1820e771,3ec50815,4d4d2810,167213ee,c5cba55b,1a2e2146,4b671030,50a75899) Z8(7f7673b6,b67c591b,cc52f381,090db620,c3a9950f,3907c163,b3c1252f,d37e177b) Z8(570c696c,36d9e7df,6543f7b8,8046e6f9,883b8e6a,f8d8ae4c,e951b6da,16958281) Z8(260ce86d,dd738efb,d169984d,133ac712,460a77ce,063c65f4,6e377198,4b093da1) Z8(7074326f,09c467db,c475f0ee,07a6cde1,048c0ec6,1f4bcf35,4c252858,c0f9fc7d) Z8(967ff841,aa6be419,03c9c381,2f749a85,da7edb91,27b211e0,4da0fcd5,fdafbdbb) Z8(d342c332,38863499,03365b1b,83341d06,3a34c495,5193488e,60347866,4be607f2) Z8(239e8009,bb9acee2,d5c48b5a,d1329eb4,27081c5a,b633247c,32efe299,039b2543) Z8(e23507a2,524d4c4d,17a38fc9,a86222f6,f154207c,da8d25f4,067c135e,3cf9ce0f) Z8(9920a33b,0c29fe68,d50a22e1,623a73fc,7d546db8,920f1c5b,d033bf48,d552bcc9) Z8(98456d70,e245eb3c,fe19736c,4aef3e49,5254e891,7436f3a4,5c0234b9,c2652db3) Z8(a171693c,e5a8d090,4b98cec5,86824650,bc7498e3,7bb06abd,b7e7100b,646687a2) Z8(9f372aaa,aab2bf43,da7f38c0,7c137902,83a15d37,5a707dab,9057134a,3ebc5c52) Z8(0cb55bce,4e7f263d,57c7a3d3,466c9b42,3b7796f8,c43b2902,f125f292,bc58191f) Z8(d718b11c,ffa8b50c,50a4a8e4,b6908ce7,a57f428b,70f430d8,27d5b7aa,495a2bac) Z8(47a4461c,d9327644,5d80eb3a,40cec96c,c5592007,84a8727d,d534ba9b,afa9c34b) Z8(d4bb4228,566babed,4e690306,d0d98ea2,492e4bba,dd3f9376,02ec7bf0,66e737d1) Z8(12ace6e8,c73356cc,e89a011e,cad8ec22,3e3b1ab1,e29e3a15,a6ac4399,007fe00a) },{ Z8(7bd45892,87ef1432,93549182,4e728fff,a17c9125,da83839d,a6de1efb,1d4a0b1f) Z8(1e586971,ece7bad2,0fd32d12,9f11b41b,3657dd9c,b33685d5,7bc0c31d,e8bcac58) Z8(80b3eebf,fab0f545,539ecd49,ee6beb53,30f670e9,d454f238,dbc65ab6,d0af3118) Z8(45a79682,a847a930,938dbc27,bc78ee6c,843f9f24,63431555,a8ba07a4,faa828c9) Z8(33959f27,cb625266,f07a9c49,5ae75939,279a7691,27b5a542,55dc3d88,a05ddb9c) Z8(0f4d7c27,70678ab5,477b4b67,9a89a333,6b725bd3,4291c99b,8b2095fc,268ec52f) Z8(62dac762,7547581f,aaa6ba30,c628bc03,0afff1d9,db3df166,2c75639f,a7b1a6df) Z8(96ae84ad,643a671e,8af38941,c0670dd4,ceb649a7,26523995,e7622e82,37f66b02) Z8(3572e1c0,083ee489,f6b9e6ba,46492d42,3762c6d1,442e03a9,0d4716e6,d684c7f3) Z8(bbc8c4ab,d2e80ad4,78bb6f2a,f4ccb747,e6efad6a,853af45c,98068b82,f9a00236) Z8(093fb52a,551d5ccc,0630c57b,2c74921c,b2b6e3fc,585291c4,8a609eb2,4b1a2568) Z8(944c1d45,1363d727,3937a37e,4c23ba0d,50818dbf,23688c83,8ed17760,1078bd24) Z8(ebe8d2bb,51a8fcbf,08be40b1,e83ffe1b,a6855626,15c0cb36,5dd54d65,a7660cd9) Z8(e6611264,18716941,7f00d1bd,9cb2f10d,9a6ea927,e16e59e0,059da5d3,4f589431) Z8(bdacdedf,7a79a587,3934d586,d54fd545,9c7a1a87,29e3fc75,50e1ce1a,f6a61f85) Z8(98212551,f82a20a4,7ef1937e,38645e42,8689e34d,bbd64d47,a3a3f54c,8d40afbb) Z8(c4b9be54,ab3b6a5f,e75d1021,85aab5ec,40365daf,008f1701,a6729ae2,9df4c673) Z8(15be5920,d672b536,013b32ce,8d568dc2,09cffdad,44eb4324,ebcc1ed3,00bfb823) },{ Z8(159dfc29,0420113d,f0e9b3e6,b7936a46,60530cb1,f5cd5799,d8a0c647,da1edbd5) Z8(1fd5c6c7,989a5d1f,1c1bfb1c,03db7723,88285f8e,c11b6f9d,fb78539b,685d0a7e) Z8(7aee5a5f,9280afe4,cd6de643,3373848f,fa3e66b3,9c96bea8,58aea360,8af4141e) Z8(2e993e91,c92da4df,3621c5f7,2dc22291,bcac49cc,eec45274,a35ff6b7,2f803695) Z8(21deeaec,1edaa6e5,c14426a6,977a092b,3509370a,8b74c1be,b241a9c4,d7c03a18) Z8(dd303505,b20fb3e9,aedb3496,f8ba7565,11d343b9,effc119a,fa42f81c,563f7da4) Z8(cf33ca5b,519232b1,1028b9f1,62b9516c,7e216a4a,359c3a23,f1865ed8,d15cb138) Z8(cf8e12aa,23a2797d,e867994f,e397895a,b54a3b53,70dd7510,6713f112,27ce9645) Z8(65e81ed6,8248dab8,7809567f,591b205e,a19551ba,349e37cf,64252869,45689adf) Z8(09c7e224,c8c909b3,287ab29e,4453ea2d,5195f48f,9751eb89,43905827,71644fac) Z8(e1d514a0,fa29f816,fbbb0296,7da66aff,0fb28fab,a96edf95,39d54a86,fb85b2fa) Z8(2233dba2,4b86566c,e395110e,ea7f2a23,b18e035d,2165e381,52423ede,e85275f1) Z8(5261af84,a1582928,55dd750b,5d0932d4,00bc47c3,ff02871b,db020f7d,7356e4f5) Z8(98e0e51b,0094d420,99eb61d1,afb8deac,90122dc4,b2855ff8,41112acf,3f8c2665) Z8(78983289,ff71220b,0282b5cd,55a3a8c2,da1a5e4c,7813a608,2c5278bd,30120813) Z8(edf7e201,07b4996d,0f632916,d438bb96,430ecb69,82b09d3b,ac79813d,89db3dfe) Z8(f0697e38,b4baf715,3a53ec28,699b4749,cc95af15,d137bfbc,4192b38f,7ed64a06) Z8(5a1a3322,91ba6e33,6d725824,8ccd29dd,da6a5bb4,50435ab4,15885e02,00ff8055) },{ Z8(163a181d,4f6d4e62,917d8eea,77bc891c,1064df82,0c3a465b,ea8fc220,a32f4ca1) Z8(2d0de89f,6582a9ea,59535a94,964628d7,f58350a8,6b1ef5d7,e5d287ed,7e0f3ed4) Z8(e6a9cd8d,16f35a5f,2465edeb,302b9513,0e364757,72c9d4b2,e848099f,6943e817) Z8(13eed651,302bf46c,9aad1e32,5f4b348c,a633111c,003a6c4c,bb2943ab,5761801e) Z8(fcdf642c,a0a1dc2c,9fcb3b43,e8c95255,d1593e22,28775bd5,774dd809,386f3302) Z8(df0ec0bb,6ac0a21f,41e0f6d0,2ef627b7,b7428421,37accab4,b1cf6123,0b69b432) Z8(b7f4ee2e,aaa79e1a,9bc6556e,27af121b,d30dc35b,b0f6c930,84f33ea1,0260d988) Z8(ac8474f2,f616d2d1,b6309807,a8647e3f,483af5c8,6db19849,ef0dd35c,b3853143) Z8(b8dbd4db,d02f15ae,3ea5c588,03447b7e,a3a59810,a655da6a,ae5b2481,331db353) Z8(5cc0976a,37aef47d,d76d23c0,027df6dd,c5672c45,29bb2452,2c43b0e2,44688e57) Z8(8aaa3e93,9b11e25b,51f476a2,4b7d4a20,5e50e8ea,42259149,954dd970,2a2fd89f) Z8(0c4ea5e1,e5e4ca0c,3632ac57,216b8010,ef8929cf,6e81651b,f5e09ae7,089b83e2) Z8(ac9df9c4,52cdcc4e,a28bd8f8,50541114,0b225dc1,0378c3fa,5009627a,98ef6b8d) Z8(cf32a022,f9743e40,8d5dbc36,038cbf8c,e1f6560b,2d51b5ab,5ee8d28a,c29a8350) Z8(3fd2b1e1,c0dfe8b1,02d3005d,94499fd6,7e992b8c,1e00171a,09a45d9d,c77ea17b) Z8(d1256823,1dbd11a0,cba07a73,09d32ece,22b2eab7,40d37dd8,6deb1ebd,3525dc95) Z8(4533ce4b,200d4e60,b0eb1eff,a6dd1f16,73b6e444,ad86fb62,5722681e,57075db5) Z8(357fb684,e444e58f,29be3018,19350e86,50117ab0,a4f24dd2,0f064895,013f38a6) },{ Z8(b6d927ef,2dadc888,915de342,2b4f6ab8,8c0ab401,a89beec6,4d35a509,f1879dbb) Z8(c15674f8,6147567d,81977456,712f397a,10d85abb,e5114af3,c37a9f23,4ff380a7) Z8(0b968932,723778dc,ee888c13,b8923376,eee291f0,79bf0802,6fd1f78d,219ee90d) Z8(b456aadc,f93259cd,e4526f25,68c1f275,7654332b,d667a1bd,a0de82a0,e3c73b24) Z8(86a1cc6e,2b44ac9c,ef0753f4,0a1e1547,b87bb88b,0ab81f39,0a422432,dcd030fe) Z8(bb3435c1,a60fd723,f320ccff,806caec6,15ac24a9,aafedd83,c00972c3,389f689c) Z8(33c6f737,ceb7a640,cbde462d,8520a153,cb8a23cf,d872bcc7,ce23f62a,a5391b84) Z8(47283289,764df5e5,528d20fc,c5dcb614,43c16e02,1d9188db,7f7ebe30,fad8a6b9) Z8(95de8bb5,7ba69284,86b5fca1,485a7070,9404a9b1,ac1aef31,a34a7ada,57e47774) Z8(5c146598,0606f86c,acd4e9e2,4150bcfb,93c99f83,719d0376,bece1034,9bba59a4) Z8(dc51a41f,4e4ea224,b18e5608,66b1ec80,2be01ca1,215340da,797d53e7,3ad0a97e) Z8(6bea07d5,3fb637bc,30a6e3de,66dc519d,2134d5d6,d58d048b,ff690887,616f321a) Z8(4d3f1203,7b69e111,4123d8e6,636baa17,92fc4fb2,e1189a7b,dbb29855,8634c60d) Z8(19ddc4eb,c84544d4,dd160b19,240f1c39,db986bd7,74d1cdc9,5fe65ca8,5daaa81c) Z8(e0cb53c9,6a8f6671,03c41668,2cd38aeb,bc9346ea,73b640e7,b0542801,001d58fd) Z8(c6388d39,48b06b91,373f9fde,d61bb167,705e24db,440d4f96,b197b8ee,6a24d5eb) Z8(96cb638a,faabafc3,0e8ca9f4,16064670,73a2bce7,95165acf,a35e4561,6beb75e0) Z8(f1aded85,903ae028,8d165ca4,2800d1f3,e89c01eb,785a4740,bd82e93a,017ee11e) },{ Z8(cf3a1be4,63afd436,9b560d1d,ab80e16f,7f3ffcef,46e47c32,c1bf0472,f5a9f01a) Z8(0aa50d58,694510a8,ac140b11,b7a0de0b,d773812d,b63e717b,3aa487ec,17d75929) Z8(33f38e01,d03d7d23,7b78605b,9dbd5945,2deca3ef,dacc0972,b66d1fab,5478b89f) Z8(6c8d604e,8ccb6228,56402f4f,6928d694,364ba4dc,b2e31d10,e7b09ed8,fafd3006) Z8(5664e5b5,818130b4,f02a5932,8fcdf74c,878a7fdc,2124693f,4b625ac8,8760d4cc) Z8(fbc3f0a8,d1fdf130,ee3b4bc8,45eb702c,5e2c16d2,87cf864f,22f7526f,7095fddc) Z8(33a6afe4,e3880a59,ed7defd6,ad38cb99,5740ebfc,f9fb8b41,091292ce,670ba3e7) Z8(a4b0fcd0,171ec2ab,da497e07,cab51d6a,06e053c2,113ea9eb,f120900c,a718dd95) Z8(a1cb5819,32258f47,17786fda,0f7d2d89,85c9e03b,0f862316,a4e15b37,41b090c9) Z8(ed376256,2a2d735c,05d62d79,cd168e50,a6104590,8b8b0c50,06390c6f,0ed79ca9) Z8(d1182bca,62af2ec5,9e8841e5,710ba75a,e6242703,1b18c13d,bcf7abd8,e2ed4bec) 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Z8(d575075b,b1bf895e,78fd94fb,79b4fc43,f4276543,e89c3e0b,104bdfaa,aa3519d2) Z8(834fbf89,a0ffd6ec,1c6b1d2f,606b52ab,45c52ecf,0d71e150,e432fbe5,428e1272) Z8(39b66eb9,b664efe3,71468977,b5b17fe6,d3c4ee69,eccd6884,90ee479f,4560fcc4) Z8(439d8e86,c3b30470,77d8871d,420bf9ee,3f5f203d,e3be9629,29ba0aab,3426c7cc) Z8(2dce18f3,0a027547,e193c5e6,f40f54b1,9f531ac4,52a68166,84d2c1d4,8af92b9e) Z8(2f428085,1c3b0114,8b53892d,72da518a,56abe013,076d5b2b,0fd8ad99,95595e86) Z8(66328621,92ed6e0d,2b45c6ef,3a01bd99,f91f2185,6df1aed3,67529e4a,de68c28b) Z8(cc74b470,a1c84162,14e85f09,9aa72160,e08110cd,0b224027,b28bca1c,d6476424) Z8(92cd7e50,247d9415,dba32570,eeaef994,fa6ed634,d55132cf,22a79d51,99ac3485) Z8(ae17f608,501ce93e,8cf1b4f4,b09e4791,61a987e3,da6aaf85,177024d8,b5491f43) Z8(50963782,5aea5cee,c459534a,a6dadd21,a387eea6,f136353a,9f6540e8,15059665) Z8(1dc6647a,6e41bbb4,d7fe2bda,9ececb92,62ded8ba,42302365,a05c719b,8a38da37) Z8(caef1492,e39f22c4,d4cba29a,9f473bc3,3520217f,bc76a14c,0ef6f273,6cc64971) Z8(593c8c4b,9ef237fc,8280a270,7cbd57db,cdee2b06,887a3da7,1d5bc6c5,a39df003) Z8(f43c4f35,39b1a417,7ea7115c,4111ca18,97fa4c19,eed3e8d0,4391fb5c,c64de291) Z8(5d9a5446,c3823d20,25310f76,0254bce6,89a0a329,c8a42948,8fcbd7ee,0bc27e8a) Z8(285c62b1,feea7834,fce882f9,68a22913,27abe10f,3e100040,aed28011,43cdf32b) Z8(35208971,8b00bde2,4f562287,62e61977,095529a8,b2c67dcd,150f30f8,0764699b) },{ Z8(62efed4a,55d9387e,8c14c622,8c591b98,21463246,d317fffb,8f7446d6,60a2476f) Z8(3f121620,6a0714c6,aa6efd2b,ef804980,226aa06b,6e670d15,85ed5130,24387392) Z8(f07e8607,c53088ef,2d173656,ac9137b0,bac63b66,537145d5,1122fd72,3c77d04c) Z8(b8f79cb0,7fa04398,ae00a8bc,3e9cea5d,78557d53,77742a8e,583acdc8,c3831771) Z8(c0186f48,d9e720cd,8187d24b,6e98d06b,f2b79f98,7b259256,6c3a8dfb,a9d5c488) Z8(587d5097,b8f34624,db93947b,b704b541,b105084e,4fd6257d,5f8d20c0,27b21e5f) Z8(c2a50d89,72efb36f,86f04428,2d787c2f,f4a8efa3,cf507845,747a7d69,029a22f9) Z8(d25a9931,8a785631,4c9ed692,aa7dc6e1,08cef331,1bb51ece,ed8aa4ba,2794a522) Z8(b67bff11,c515eb2e,afae91ac,a9b4c4dd,7798b9bc,fd09a602,9ceb2b26,de469963) Z8(bcedbceb,d908c4c5,5d01d3ad,5ce60c54,e4fb5689,4f07e9b1,72ca5e44,895eeaaa) Z8(8a5c7f50,0e370696,dccb0b50,4ae1431f,583d8943,8747770e,cf945c43,3e8770a4) Z8(6a05d1cf,6ee574c1,5cba0c6b,806ecba7,25c682f6,cc4da9e3,238b71f4,477c1c6d) Z8(a9c6160a,4c35ad28,0192c602,c0453095,9aa9efe2,45f82774,5acfc755,be1a90a3) Z8(fac4999f,840947cf,eef0e341,8e48c91d,82b60837,1cdf2664,80cf22ff,ab5874db) Z8(ab845e92,508f74a5,07f63095,4b573425,9a7a2074,bd351766,a8f73d53,0c41f64f) Z8(99facf27,e3de9df4,22b8d3ec,e2a022cd,5ea2d09c,26edce1c,494feb0d,d629cd56) Z8(630346e3,635144e2,378409fc,87012299,a556dc48,d48fc658,82a4441f,a8c1ebd6) Z8(f0a5b553,221ccad4,2d3e91ef,be0fe5f4,167294c9,e10d6380,c3372b02,07a28fb8) }}; arb-2.8.1/arb/log_ui_from_prev.c000066400000000000000000000073661264125401100165430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void bsplit(fmpz_t p1, fmpz_t q1, fmpz_t r1, const fmpz_t p, const fmpz_t q, slong a, slong b, int cont) { if (b - a == 1) { if (a == 0) { fmpz_set(p1, p); fmpz_mul_ui(q1, q, 2*a+1); fmpz_mul_ui(r1, p, 2*a+1); } else { fmpz_mul(p1, p, p); fmpz_mul(q1, q, q); fmpz_mul_ui(q1, q1, 2*a+1); fmpz_mul_ui(r1, p1, 2*a+1); } } else { fmpz_t p2, q2, r2; slong m; m = (a + b) / 2; fmpz_init(p2); fmpz_init(q2); fmpz_init(r2); bsplit(p1, q1, r1, p, q, a, m, 1); bsplit(p2, q2, r2, p, q, m, b, 1); fmpz_mul(p1, p1, q2); fmpz_addmul(p1, r1, p2); fmpz_mul(q1, q1, q2); if (cont) fmpz_mul(r1, r1, r2); fmpz_clear(p2); fmpz_clear(q2); fmpz_clear(r2); } } #define LOG2 0.69314718055994530942 /* Assumption: p/q <= 2 */ static void atanh_bs(arb_t s, ulong p, ulong q, slong prec) { fmpz_t pp, qq, P, Q, R; double logqp; slong N; if (p == 0) { arb_zero(s); return; } fmpz_init(pp); fmpz_init(qq); fmpz_init(P); fmpz_init(Q); fmpz_init(R); /* If N >= 1 and p/q <= 1/2, the error is bounded by (p/q)^(2N+1). For error <= 2^-prec, it is sufficient to pick N >= (1/2) * (prec * log(2) / log(q/p) - 1). */ logqp = mag_d_log_lower_bound(q / (double) p) * (1.0 - 1e-12); N = ceil((prec * (0.5 * LOG2) / logqp) * (1.0 + 1e-12)); N = FLINT_MAX(N, 1); fmpz_set_ui(pp, p); fmpz_set_ui(qq, q); bsplit(P, Q, R, pp, qq, 0, N, 0); arb_fmpz_div_fmpz(s, P, Q, prec); arb_add_error_2exp_si(s, -prec); fmpz_clear(pp); fmpz_clear(qq); fmpz_clear(P); fmpz_clear(Q); fmpz_clear(R); } static int n_width(ulong k) { int a, b; count_leading_zeros(a, k); count_trailing_zeros(b, k); return FLINT_BITS - a - b; } void arb_log_ui_from_prev(arb_t s, ulong k, arb_t log_prev, ulong prev, slong prec) { if (prev < 2 || prec < 600 || (prec < ARB_LOG_TAB2_PREC - 64 && n_width(k) <= ARB_LOG_TAB21_BITS + 1) || k < prev || (k + prev) < prev || (k - prev) >= 0.25 * (k + prev)) { arb_log_ui(s, k, prec); } else { arb_t t; ulong p, q; arb_init(t); p = k - prev; q = k + prev; if ((p % 2 == 0) && (q % 2 == 0)) { p >>= 1; q >>= 1; } atanh_bs(t, p, q, prec); arb_mul_2exp_si(t, t, 1); arb_add(s, log_prev, t, prec); arb_clear(t); } } arb-2.8.1/arb/mul.c000066400000000000000000000103271264125401100137720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_mul_arf(arb_t z, const arb_t x, const arf_t y, slong prec) { mag_t zr, ym; int inexact; if (arb_is_exact(x)) { inexact = arf_mul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); else mag_zero(arb_radref(z)); } else if (ARB_IS_LAGOM(x) && ARF_IS_LAGOM(y) && ARB_IS_LAGOM(z)) { mag_fast_init_set_arf(ym, y); mag_init(zr); mag_fast_mul(zr, ym, arb_radref(x)); inexact = arf_mul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_fast_add_ulp(zr, zr, arb_midref(z), prec); *arb_radref(z) = *zr; } else { mag_init_set_arf(ym, y); mag_init(zr); mag_mul(zr, ym, arb_radref(x)); inexact = arf_mul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), zr, arb_midref(z), prec); else mag_swap(arb_radref(z), zr); mag_clear(ym); mag_clear(zr); } } void arb_mul(arb_t z, const arb_t x, const arb_t y, slong prec) { mag_t zr, xm, ym; int inexact; if (arb_is_exact(x)) { arb_mul_arf(z, y, arb_midref(x), prec); } else if (arb_is_exact(y)) { arb_mul_arf(z, x, arb_midref(y), prec); } else if (ARB_IS_LAGOM(x) && ARB_IS_LAGOM(y) && ARB_IS_LAGOM(z)) { mag_fast_init_set_arf(xm, arb_midref(x)); mag_fast_init_set_arf(ym, arb_midref(y)); mag_init(zr); mag_fast_mul(zr, xm, arb_radref(y)); mag_fast_addmul(zr, ym, arb_radref(x)); mag_fast_addmul(zr, arb_radref(x), arb_radref(y)); inexact = arf_mul(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND); if (inexact) arf_mag_fast_add_ulp(zr, zr, arb_midref(z), prec); *arb_radref(z) = *zr; } else { mag_init_set_arf(xm, arb_midref(x)); mag_init_set_arf(ym, arb_midref(y)); mag_init(zr); mag_mul(zr, xm, arb_radref(y)); mag_addmul(zr, ym, arb_radref(x)); mag_addmul(zr, arb_radref(x), arb_radref(y)); inexact = arf_mul(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), zr, arb_midref(z), prec); else mag_swap(arb_radref(z), zr); mag_clear(xm); mag_clear(ym); mag_clear(zr); } } void arb_mul_si(arb_t z, const arb_t x, slong y, slong prec) { arf_t t; arf_init_set_si(t, y); /* no need to free */ arb_mul_arf(z, x, t, prec); } void arb_mul_ui(arb_t z, const arb_t x, ulong y, slong prec) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ arb_mul_arf(z, x, t, prec); } void arb_mul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) { arf_t t; if (!COEFF_IS_MPZ(*y)) { arf_init_set_si(t, *y); /* no need to free */ arb_mul_arf(z, x, t, prec); } else { arf_init(t); arf_set_fmpz(t, y); arb_mul_arf(z, x, t, prec); arf_clear(t); } } arb-2.8.1/arb/neg.c000066400000000000000000000023211264125401100137410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_neg(arb_t y, const arb_t x) { arf_neg(arb_midref(y), arb_midref(x)); mag_set(arb_radref(y), arb_radref(x)); } arb-2.8.1/arb/neg_round.c000066400000000000000000000023001264125401100151450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_neg_round(arb_t x, const arb_t y, slong prec) { arb_set_round(x, y, prec); arb_neg(x, x); } arb-2.8.1/arb/overlaps.c000066400000000000000000000035761264125401100150400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_overlaps(const arb_t x, const arb_t y) { arf_t t; arf_struct u[4]; int result; if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) return 1; if (arf_equal(arb_midref(x), arb_midref(y))) return 1; arf_init(t); /* |xm - ym| <= xr + yr */ if (arf_cmp(arb_midref(x), arb_midref(y)) >= 0) { arf_init_set_shallow(u + 0, arb_midref(x)); arf_init_neg_shallow(u + 1, arb_midref(y)); } else { arf_init_neg_shallow(u + 0, arb_midref(x)); arf_init_set_shallow(u + 1, arb_midref(y)); } arf_init_neg_mag_shallow(u + 2, arb_radref(x)); arf_init_neg_mag_shallow(u + 3, arb_radref(y)); arf_sum(t, u, 4, 30, ARF_RND_DOWN); result = arf_sgn(t) <= 0; arf_clear(t); return result; } arb-2.8.1/arb/polylog.c000066400000000000000000000033031264125401100146560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "acb.h" int polylog_is_real(const acb_t s, const acb_t z); void arb_polylog(arb_t w, const arb_t s, const arb_t z, slong prec) { acb_t ss, zz; acb_init(ss); acb_init(zz); acb_set_arb(ss, s); acb_set_arb(zz, z); if (polylog_is_real(ss, zz)) { acb_polylog(zz, ss, zz, prec); arb_set(w, acb_realref(zz)); } else { arb_indeterminate(w); } acb_clear(ss); acb_clear(zz); } void arb_polylog_si(arb_t w, slong s, const arb_t z, slong prec) { arb_t t; arb_init(t); arb_set_si(t, s); arb_polylog(w, t, z, prec); arb_clear(t); } arb-2.8.1/arb/pow.c000066400000000000000000000055211264125401100140020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define BINEXP_LIMIT 64 void _arb_pow_exp(arb_t z, const arb_t x, int negx, const arb_t y, slong prec) { arb_t t; arb_init(t); if (negx) { arb_neg(t, x); arb_log(t, t, prec); } else arb_log(t, x, prec); arb_mul(t, t, y, prec); arb_exp(z, t, prec); arb_clear(t); } void arb_pow(arb_t z, const arb_t x, const arb_t y, slong prec) { if (arb_is_zero(y)) { arb_one(z); return; } if (arb_is_zero(x)) { if (arb_is_positive(y)) arb_zero(z); else arb_indeterminate(z); return; } if (arb_is_exact(y) && !arf_is_special(arb_midref(x))) { const arf_struct * ymid = arb_midref(y); /* small half-integer or integer */ if (arf_cmpabs_2exp_si(ymid, BINEXP_LIMIT) < 0 && arf_is_int_2exp_si(ymid, -1)) { fmpz_t e; fmpz_init(e); if (arf_is_int(ymid)) { arf_get_fmpz_fixed_si(e, ymid, 0); arb_pow_fmpz_binexp(z, x, e, prec); } else { arf_get_fmpz_fixed_si(e, ymid, -1); arb_sqrt(z, x, prec + fmpz_bits(e)); arb_pow_fmpz_binexp(z, z, e, prec); } fmpz_clear(e); return; } else if (arf_is_int(ymid) && arf_sgn(arb_midref(x)) < 0) { /* use (-x)^n = (-1)^n * x^n to avoid NaNs at least at high enough precision */ int odd = !arf_is_int_2exp_si(ymid, 1); _arb_pow_exp(z, x, 1, y, prec); if (odd) arb_neg(z, z); return; } } _arb_pow_exp(z, x, 0, y, prec); } arb-2.8.1/arb/pow_fmpq.c000066400000000000000000000035621264125401100150300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_pow_fmpq(arb_t y, const arb_t x, const fmpq_t a, slong prec) { if (fmpz_is_one(fmpq_denref(a))) { arb_pow_fmpz(y, x, fmpq_numref(a), prec); } else { int use_exp; slong k = *fmpq_denref(a); if (k == 2 || k == 4) use_exp = 0; else if (k > 1 && k < 50) use_exp = prec < (WORD(1) << ((k / 8) + 8)); else use_exp = 1; if (use_exp) { arb_log(y, x, prec + 10); arb_mul_fmpz(y, y, fmpq_numref(a), prec + 10); arb_div_fmpz(y, y, fmpq_denref(a), prec + 10); arb_exp(y, y, prec); } else { arb_root_ui(y, x, k, prec); arb_pow_fmpz(y, y, fmpq_numref(a), prec); } } } arb-2.8.1/arb/pow_fmpz.c000066400000000000000000000032631264125401100150370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_pow_fmpz(arb_t y, const arb_t b, const fmpz_t e, slong prec) { arb_pow_fmpz_binexp(y, b, e, prec); } void arb_pow_ui(arb_t y, const arb_t b, ulong e, slong prec) { fmpz_t f; fmpz_init_set_ui(f, e); arb_pow_fmpz(y, b, f, prec); fmpz_clear(f); } void arb_ui_pow_ui(arb_t y, ulong b, ulong e, slong prec) { arb_t t; arb_init(t); arb_set_ui(t, b); arb_pow_ui(y, t, e, prec); arb_clear(t); } void arb_si_pow_ui(arb_t y, slong b, ulong e, slong prec) { arb_t t; arb_init(t); arb_set_si(t, b); arb_pow_ui(y, t, e, prec); arb_clear(t); } arb-2.8.1/arb/pow_fmpz_binexp.c000066400000000000000000000043241264125401100164030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_pow_fmpz_binexp(arb_t y, const arb_t b, const fmpz_t e, slong prec) { slong i, wp, bits; if (-WORD(2) <= *e && *e <= WORD(2)) { if (*e == WORD(0)) arb_one(y); else if (*e == WORD(1)) arb_set_round(y, b, prec); else if (*e == -WORD(1)) arb_inv(y, b, prec); else if (*e == WORD(2)) arb_mul(y, b, b, prec); else { arb_inv(y, b, prec); arb_mul(y, y, y, prec); } return; } if (fmpz_sgn(e) < 0) { fmpz_t f; fmpz_init(f); fmpz_neg(f, e); arb_pow_fmpz_binexp(y, b, f, prec + 2); arb_inv(y, y, prec); fmpz_clear(f); return; } if (y == b) { arb_t t; arb_init(t); arb_set(t, b); arb_pow_fmpz_binexp(y, t, e, prec); arb_clear(t); return; } arb_set(y, b); bits = fmpz_bits(e); wp = ARF_PREC_ADD(prec, bits); for (i = bits - 2; i >= 0; i--) { arb_mul(y, y, y, wp); if (fmpz_tstbit(e, i)) arb_mul(y, y, b, wp); } } arb-2.8.1/arb/power_sum_vec.c000066400000000000000000000043031264125401100160470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "bernoulli.h" #include "arb_poly.h" /* todo: don't use exact bernoulli numbers for large len */ /* todo: output exact integers when precise enough */ void arb_power_sum_vec(arb_ptr res, const arb_t a, const arb_t b, slong len, slong prec) { arb_ptr t, u, v; slong k; if (len < 1) return; t = _arb_vec_init(len + 1); u = _arb_vec_init(len + 1); v = _arb_vec_init(len + 1); /* exp(ax), exp(bx) */ arb_set(t + 1, a); arb_set(u + 1, b); _arb_poly_exp_series(t, t, 2, len + 1, prec); _arb_poly_exp_series(u, u, 2, len + 1, prec); _arb_vec_sub(t, u, t, len + 1, prec); /* x/(exp(x)-1) */ BERNOULLI_ENSURE_CACHED(len + 1); for (k = 0; k <= len; k++) arb_set_fmpq(u + k, bernoulli_cache + k, prec); _arb_poly_borel_transform(u, u, len + 1, prec); _arb_poly_mullow(v, t, len + 1, u, len + 1, len + 1, prec); _arb_poly_inv_borel_transform(v, v, len + 1, prec); for (k = 0; k < len; k++) arb_div_ui(res + k, v + k + 1, k + 1, prec); _arb_vec_clear(t, len + 1); _arb_vec_clear(u, len + 1); _arb_vec_clear(v, len + 1); } arb-2.8.1/arb/print.c000066400000000000000000000030131264125401100143230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_print(const arb_t x) { arf_print(arb_midref(x)); flint_printf(" +/- "); mag_print(arb_radref(x)); } void arb_printd(const arb_t x, slong digits) { arf_printd(arb_midref(x), FLINT_MAX(digits, 1)); flint_printf(" +/- "); mag_printd(arb_radref(x), 5); } void arb_printn(const arb_t x, slong digits, ulong flags) { char * s = arb_get_str(x, digits, flags); flint_printf("%s", s); flint_free(s); } arb-2.8.1/arb/randtest.c000066400000000000000000000055551264125401100150300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_randtest_exact(arb_t x, flint_rand_t state, slong prec, slong mag_bits) { arf_randtest(arb_midref(x), state, prec, mag_bits); mag_zero(arb_radref(x)); } void arb_randtest_wide(arb_t x, flint_rand_t state, slong prec, slong mag_bits) { arf_randtest(arb_midref(x), state, prec, mag_bits); mag_randtest(arb_radref(x), state, mag_bits); } void arb_randtest_precise(arb_t x, flint_rand_t state, slong prec, slong mag_bits) { arf_randtest(arb_midref(x), state, prec, mag_bits); if (arf_is_zero(arb_midref(x)) || (n_randint(state, 8) == 0)) { mag_zero(arb_radref(x)); } else { mag_randtest(arb_radref(x), state, 0); if (!mag_is_zero(arb_radref(x))) { fmpz_add_si(MAG_EXPREF(arb_radref(x)), ARF_EXPREF(arb_midref(x)), -prec + 2 - n_randint(state, 8)); } } } void arb_randtest(arb_t x, flint_rand_t state, slong prec, slong mag_bits) { switch (n_randint(state, 8)) { case 0: arb_randtest_exact(x, state, prec, mag_bits); break; case 1: arb_randtest_wide(x, state, prec, mag_bits); break; default: arb_randtest_precise(x, state, prec, mag_bits); } } void arb_randtest_special(arb_t x, flint_rand_t state, slong prec, slong mag_bits) { arb_randtest(x, state, prec, mag_bits); if (n_randint(state, 10) == 0) mag_inf(arb_radref(x)); switch (n_randint(state, 10)) { case 0: arf_pos_inf(arb_midref(x)); break; case 1: arf_neg_inf(arb_midref(x)); break; case 2: arf_nan(arb_midref(x)); mag_inf(arb_radref(x)); break; default: break; } } arb-2.8.1/arb/rel_error_bits.c000066400000000000000000000031271264125401100162110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" slong arb_rel_error_bits(const arb_t x) { fmpz_t t; slong result; if (mag_is_zero(arb_radref(x))) { if (arf_is_nan(arb_midref(x))) return ARF_PREC_EXACT; else return -ARF_PREC_EXACT; } if (arf_is_special(arb_midref(x)) || mag_is_inf(arb_radref(x))) return ARF_PREC_EXACT; fmpz_init(t); fmpz_add_ui(t, MAG_EXPREF(arb_radref(x)), 1); result = _fmpz_sub_small(t, ARF_EXPREF(arb_midref(x))); fmpz_clear(t); return result; } arb-2.8.1/arb/richcmp.c000066400000000000000000000127011264125401100146200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" int arb_eq(const arb_t x, const arb_t y) { if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y))) return 0; if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) return 0; if (arf_is_inf(arb_midref(x)) || arf_is_inf(arb_midref(y)) || (mag_is_zero(arb_radref(x)) && mag_is_zero(arb_radref(y)))) return arf_equal(arb_midref(x), arb_midref(y)); return 0; } int arb_ne(const arb_t x, const arb_t y) { if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y))) return 0; if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) return 0; if (arf_is_inf(arb_midref(x)) || arf_is_inf(arb_midref(y)) || (mag_is_zero(arb_radref(x)) && mag_is_zero(arb_radref(y)))) return !arf_equal(arb_midref(x), arb_midref(y)); return !arb_overlaps(x, y); } int arb_lt(const arb_t x, const arb_t y) { arf_struct u[4]; arf_t t; int res; if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y))) return 0; if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) return 0; if (arf_is_inf(arb_midref(x)) || arf_is_inf(arb_midref(y)) || (mag_is_zero(arb_radref(x)) && mag_is_zero(arb_radref(y)))) return arf_cmp(arb_midref(x), arb_midref(y)) < 0; /* xm + xr < ym - yr <=> xm + xr - ym + yr < 0 */ arf_init_set_shallow(u + 0, arb_midref(x)); arf_init_neg_shallow(u + 1, arb_midref(y)); arf_init_set_mag_shallow(u + 2, arb_radref(x)); arf_init_set_mag_shallow(u + 3, arb_radref(y)); arf_init(t); arf_sum(t, u, 4, 30, ARF_RND_DOWN); res = (arf_sgn(t) < 0); arf_clear(t); return res; } int arb_le(const arb_t x, const arb_t y) { arf_struct u[4]; arf_t t; int res; if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y))) return 0; if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) return (arf_is_neg_inf(arb_midref(x)) && mag_is_finite(arb_radref(x))) || (arf_is_pos_inf(arb_midref(y)) && mag_is_finite(arb_radref(y))); if (arf_is_inf(arb_midref(x)) || arf_is_inf(arb_midref(y)) || (mag_is_zero(arb_radref(x)) && mag_is_zero(arb_radref(y)))) return arf_cmp(arb_midref(x), arb_midref(y)) <= 0; /* xm + xr <= ym - yr <=> xm + xr - ym + yr <= 0 */ arf_init_set_shallow(u + 0, arb_midref(x)); arf_init_neg_shallow(u + 1, arb_midref(y)); arf_init_set_mag_shallow(u + 2, arb_radref(x)); arf_init_set_mag_shallow(u + 3, arb_radref(y)); arf_init(t); arf_sum(t, u, 4, 30, ARF_RND_DOWN); res = (arf_sgn(t) <= 0); arf_clear(t); return res; } int arb_gt(const arb_t x, const arb_t y) { arf_struct u[4]; arf_t t; int res; if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y))) return 0; if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) return 0; if (arf_is_inf(arb_midref(x)) || arf_is_inf(arb_midref(y)) || (mag_is_zero(arb_radref(x)) && mag_is_zero(arb_radref(y)))) return arf_cmp(arb_midref(x), arb_midref(y)) > 0; /* xm - xr > ym + yr <=> xm - xr - ym - yr > 0 */ arf_init_set_shallow(u + 0, arb_midref(x)); arf_init_neg_shallow(u + 1, arb_midref(y)); arf_init_neg_mag_shallow(u + 2, arb_radref(x)); arf_init_neg_mag_shallow(u + 3, arb_radref(y)); arf_init(t); arf_sum(t, u, 4, 30, ARF_RND_DOWN); res = (arf_sgn(t) > 0); arf_clear(t); return res; } int arb_ge(const arb_t x, const arb_t y) { arf_struct u[4]; arf_t t; int res; if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y))) return 0; if (mag_is_inf(arb_radref(x)) || mag_is_inf(arb_radref(y))) return (arf_is_pos_inf(arb_midref(x)) && mag_is_finite(arb_radref(x))) || (arf_is_neg_inf(arb_midref(y)) && mag_is_finite(arb_radref(y))); if (arf_is_inf(arb_midref(x)) || arf_is_inf(arb_midref(y)) || (mag_is_zero(arb_radref(x)) && mag_is_zero(arb_radref(y)))) return arf_cmp(arb_midref(x), arb_midref(y)) >= 0; /* xm - xr >= ym + yr <=> xm - xr - ym - yr >= 0 */ arf_init_set_shallow(u + 0, arb_midref(x)); arf_init_neg_shallow(u + 1, arb_midref(y)); arf_init_neg_mag_shallow(u + 2, arb_radref(x)); arf_init_neg_mag_shallow(u + 3, arb_radref(y)); arf_init(t); arf_sum(t, u, 4, 30, ARF_RND_DOWN); res = (arf_sgn(t) >= 0); arf_clear(t); return res; } arb-2.8.1/arb/rising2_ui.c000066400000000000000000000024761264125401100152550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_rising2_ui(arb_t u, arb_t v, const arb_t x, ulong n, slong prec) { if (prec < 512 || n < 8 || arb_bits(x) < prec / 8) arb_rising2_ui_bs(u, v, x, n, prec); else arb_rising2_ui_rs(u, v, x, n, 0, prec); } arb-2.8.1/arb/rising2_ui_bs.c000066400000000000000000000045301264125401100157320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void bsplit(arb_t p, arb_t q, const arb_t x, ulong a, ulong b, slong prec) { if (b - a < 8) { ulong k; arb_t t; arb_one(p); arb_add_ui(q, x, a, prec); arb_init(t); for (k = a + 1; k < b; k++) { arb_add_ui(t, x, k, prec); arb_mul(p, p, t, prec); arb_add(p, p, q, prec); arb_mul(q, q, t, prec); } arb_clear(t); } else { arb_t r, s; ulong m; arb_init(r); arb_init(s); m = a + (b - a) / 2; bsplit(p, q, x, a, m, prec); bsplit(r, s, x, m, b, prec); arb_mul(p, p, s, prec); arb_mul(r, r, q, prec); arb_add(p, p, r, prec); arb_mul(q, q, s, prec); arb_clear(r); arb_clear(s); } } void arb_rising2_ui_bs(arb_t u, arb_t v, const arb_t x, ulong n, slong prec) { if (n == 0) { arb_zero(v); arb_one(u); } else if (n == 1) { arb_set(u, x); arb_one(v); } else { arb_t t; slong wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); arb_init(t); /* support aliasing */ arb_set(t, x); bsplit(v, u, t, 0, n, wp); arb_clear(t); } } arb-2.8.1/arb/rising2_ui_rs.c000066400000000000000000000076601264125401100157610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void _gamma_rf_bsplit(fmpz * A, ulong a, ulong b) { ulong n = b - a; if (n == 0) { fmpz_one(A); } else if (n < 8) { ulong j, k; fmpz_set_ui(A, a); fmpz_one(A + 1); for (j = 1; j < n; j++) { fmpz_one(A + j + 1); for (k = j; k > 0; k--) { fmpz_mul_ui(A + k, A + k, a + j); fmpz_add(A + k, A + k, A + k - 1); } fmpz_mul_ui(A, A, a + j); } } else { ulong m = a + (b - a) / 2; ulong w = m - a; ulong v = b - m; fmpz *t, *A1, *A2; t = _fmpz_vec_init(w + v + 2); A1 = t; A2 = A1 + w + 1; _gamma_rf_bsplit(A1, a, m); _gamma_rf_bsplit(A2, m, b); _fmpz_poly_mul(A, A2, v + 1, A1, w + 1); _fmpz_vec_clear(t, w + v + 2); } } void arb_rising2_ui_rs(arb_t u, arb_t v, const arb_t x, ulong n, ulong m, slong prec) { if (n == 0) { arb_zero(v); arb_one(u); } else if (n == 1) { arb_set(u, x); arb_one(v); } else { slong wp; ulong i, j, a, b; arb_ptr xs; arb_t S, T, U, V; fmpz *A, *B; wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); if (m == 0) { ulong m1, m2; m1 = 0.6 * pow(wp, 0.4); m2 = n_sqrt(n); m = FLINT_MIN(m1, m2); } m = FLINT_MAX(m, 1); xs = _arb_vec_init(m + 1); A = _fmpz_vec_init(2 * m + 1); B = A + (m + 1); arb_init(S); arb_init(T); arb_init(U); arb_init(V); _arb_vec_set_powers(xs, x, m + 1, wp); for (i = 0; i < n; i += m) { a = i; b = FLINT_MIN(n, a + m); if (a == 0 || b != a + m) { _gamma_rf_bsplit(A, a, b); } else { fmpz tt = m; _fmpz_poly_taylor_shift(A, &tt, m + 1); } _fmpz_poly_derivative(B, A, b - a + 1); arb_set_fmpz(S, A); for (j = 1; j <= b - a; j++) arb_addmul_fmpz(S, xs + j, A + j, wp); arb_set_fmpz(T, B); for (j = 1; j < b - a; j++) arb_addmul_fmpz(T, xs + j, B + j, wp); if (i == 0) { arb_set(U, S); arb_set(V, T); } else { arb_mul(V, V, S, wp); arb_addmul(V, U, T, wp); arb_mul(U, U, S, wp); } } arb_set(u, U); arb_set(v, V); _arb_vec_clear(xs, m + 1); _fmpz_vec_clear(A, 2 * m + 1); arb_clear(S); arb_clear(T); arb_clear(U); arb_clear(V); } } arb-2.8.1/arb/rising_fmpq_ui.c000066400000000000000000000047021264125401100162100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void bsplit(arb_t y, const fmpz_t p, const fmpz_t q, ulong a, ulong b, slong prec) { if (b - a <= 8) { fmpz_t t, u; ulong c; fmpz_init(t); fmpz_init(u); fmpz_mul_ui(t, q, a); fmpz_add(t, t, p); fmpz_set(u, t); for (c = a + 1; c < b; c++) { fmpz_add(u, u, q); fmpz_mul(t, t, u); } arb_set_round_fmpz(y, t, prec); fmpz_clear(t); fmpz_clear(u); } else { arb_t w; ulong m = a + (b - a) / 2; arb_init(w); bsplit(y, p, q, a, m, prec); bsplit(w, p, q, m, b, prec); arb_mul(y, y, w, prec); arb_clear(w); } } void arb_rising_fmpq_ui(arb_t y, const fmpq_t x, ulong n, slong prec) { if (n == 0) { arb_one(y); } else if (n == 1) { arb_set_fmpq(y, x, prec); } else { slong wp; wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); bsplit(y, fmpq_numref(x), fmpq_denref(x), 0, n, wp); if (fmpz_is_one(fmpq_denref(x))) { arb_set_round(y, y, prec); } else { arb_t t; arb_init(t); arb_set_fmpz(t, fmpq_denref(x)); arb_pow_ui(t, t, n, wp); arb_div(y, y, t, prec); arb_clear(t); } } } arb-2.8.1/arb/rising_ui.c000066400000000000000000000036721264125401100151720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_rising_ui(arb_t y, const arb_t x, ulong n, slong prec) { if (n < FLINT_MAX(prec, 100)) { arb_rising_ui_rec(y, x, n, prec); } else { arb_t t; arb_init(t); arb_add_ui(t, x, n, prec); arb_gamma(t, t, prec); arb_rgamma(y, x, prec); arb_mul(y, y, t, prec); arb_clear(t); } } void arb_rising(arb_t y, const arb_t x, const arb_t n, slong prec) { if (arb_is_int(n) && arf_sgn(arb_midref(n)) >= 0 && arf_cmpabs_ui(arb_midref(n), FLINT_MAX(prec, 100)) < 0) { arb_rising_ui_rec(y, x, arf_get_si(arb_midref(n), ARF_RND_DOWN), prec); } else { arb_t t; arb_init(t); arb_add(t, x, n, prec); arb_gamma(t, t, prec); arb_rgamma(y, x, prec); arb_mul(y, y, t, prec); arb_clear(t); } } arb-2.8.1/arb/rising_ui_bs.c000066400000000000000000000044021264125401100156460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* assumes y and x are not aliased */ static void bsplit(arb_t y, const arb_t x, ulong a, ulong b, slong prec) { if (b - a == 1) { arb_set_round(y, x, prec); } else if (b - a <= 10) { slong i; arb_t t; arb_init(t); arb_add_ui(t, x, a, prec); arb_add_ui(y, x, a + 1, prec); arb_mul(y, y, t, prec); for (i = a + 2; i < b; i++) { arb_add_ui(t, x, i, prec); arb_mul(y, y, t, prec); } arb_clear(t); } else { arb_t t, u; ulong m = a + (b - a) / 2; arb_init(t); arb_init(u); bsplit(t, x, a, m, prec); bsplit(u, x, m, b, prec); arb_mul(y, t, u, prec); arb_clear(t); arb_clear(u); } } void arb_rising_ui_bs(arb_t y, const arb_t x, ulong n, slong prec) { if (n == 0) { arb_one(y); } else if (n == 1) { arb_set_round(y, x, prec); } else { arb_t t; slong wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); arb_init(t); bsplit(t, x, 0, n, wp); arb_set_round(y, t, prec); arb_clear(t); } } arb-2.8.1/arb/rising_ui_rec.c000066400000000000000000000024601264125401100160150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_rising_ui_rec(arb_t y, const arb_t x, ulong n, slong prec) { if (prec < 512 || n < 8 || arb_bits(x) < prec / 8) arb_rising_ui_bs(y, x, n, prec); else arb_rising_ui_rs(y, x, n, 0, prec); } arb-2.8.1/arb/rising_ui_rs.c000066400000000000000000000075661264125401100157040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "arb.h" void rising_difference_polynomial(fmpz * s, fmpz * c, ulong m) { slong i, j, v; fmpz_t t; fmpz_init(t); arith_stirling_number_1u_vec(s, m, m + 1); /* Compute the first row */ for (i = 0; i < m; i++) { fmpz_set_ui(t, m); fmpz_mul_ui(t, t, (i + 1)); fmpz_mul(c + i, s + (i + 1), t); for (j = i + 2; j < m + 1; j++) { fmpz_mul_ui(t, t, m * j); fmpz_divexact_ui(t, t, j - i); fmpz_addmul(c + i, s + j, t); } } /* Extend using recurrence and symmetry */ for (v = 1; v < m; v++) { for (i = v; i < m - v; i++) { fmpz_mul_ui(t, c + (v - 1) * m + (i + 1), i + 1); fmpz_divexact_ui(c + v * m + i, t, v); } for (i = 0; i < v; i++) fmpz_set(c + v * m + i, c + i * m + v); } fmpz_clear(t); } void arb_rising_ui_rs(arb_t y, const arb_t x, ulong n, ulong m, slong prec) { arb_ptr xs; arb_t t, u, v; ulong i, k, rem; fmpz_t c, h; fmpz *s, *d; slong wp; if (n == 0) { arb_one(y); return; } if (n == 1) { arb_set_round(y, x, prec); return; } wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n)); arb_init(t); arb_init(u); arb_init(v); fmpz_init(c); fmpz_init(h); if (m == 0) { ulong m1, m2; m1 = 0.2 * pow(wp, 0.4); m2 = n_sqrt(n); m = FLINT_MIN(m1, m2); } m = FLINT_MIN(m, n); m = FLINT_MAX(m, 1); xs = _arb_vec_init(m + 1); d = _fmpz_vec_init(m * m); s = _fmpz_vec_init(m + 1); _arb_vec_set_powers(xs, x, m + 1, wp); rising_difference_polynomial(s, d, m); /* tail */ rem = m; while (rem + m <= n) rem += m; arb_one(y); for (k = rem; k < n; k++) { arb_add_ui(t, xs + 1, k, wp); arb_mul(y, y, t, wp); } /* initial rising factorial */ arb_zero(t); for (i = 1; i <= m; i++) arb_addmul_fmpz(t, xs + i, s + i, wp); arb_mul(y, y, t, wp); /* the leading coefficient is always the same */ arb_mul_fmpz(xs + m - 1, xs + m - 1, d + m - 1 + 0, wp); for (k = 0; k + 2 * m <= n; k += m) { for (i = 0; i < m - 1; i++) { fmpz_set_ui(h, k); _fmpz_poly_evaluate_horner_fmpz(c, d + i * m, m - i, h); if (i == 0) arb_add_fmpz(t, t, c, wp); else arb_addmul_fmpz(t, xs + i, c, wp); } arb_add(t, t, xs + m - 1, wp); arb_mul(y, y, t, wp); } arb_set_round(y, y, prec); arb_clear(t); arb_clear(u); arb_clear(v); _arb_vec_clear(xs, m + 1); _fmpz_vec_clear(d, m * m); _fmpz_vec_clear(s, m + 1); fmpz_clear(c); fmpz_clear(h); } arb-2.8.1/arb/root_ui.c000066400000000000000000000061501264125401100146540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void arb_root_arf(arb_t z, const arf_t x, ulong k, slong prec) { int inexact = arf_root(arb_midref(z), x, k, prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); else mag_zero(arb_radref(z)); } void arb_root_ui_algebraic(arb_t res, const arb_t x, ulong k, slong prec) { mag_t r, msubr, m1k, t; if (arb_is_exact(x)) { arb_root_arf(res, arb_midref(x), k, prec); return; } if (!arb_is_nonnegative(x)) { arb_indeterminate(res); return; } mag_init(r); mag_init(msubr); mag_init(m1k); mag_init(t); /* x = [m-r, m+r] */ mag_set(r, arb_radref(x)); /* m - r */ arb_get_mag_lower(msubr, x); /* m^(1/k) */ arb_root_arf(res, arb_midref(x), k, prec); /* bound for m^(1/k) */ arb_get_mag(m1k, res); /* C = min(1, log(1+r/(m-r))/k) */ mag_div(t, r, msubr); mag_log1p(t, t); mag_div_ui(t, t, k); if (mag_cmp_2exp_si(t, 0) > 0) mag_one(t); /* C m^(1/k) */ mag_mul(t, m1k, t); mag_add(arb_radref(res), arb_radref(res), t); mag_clear(r); mag_clear(msubr); mag_clear(m1k); mag_clear(t); } void arb_root_ui_exp(arb_t res, const arb_t x, ulong k, slong prec) { arb_log(res, x, prec + 4); arb_div_ui(res, res, k, prec + 4); arb_exp(res, res, prec); } void arb_root_ui(arb_t res, const arb_t x, ulong k, slong prec) { if (k == 0) { arb_indeterminate(res); } else if (k == 1) { arb_set_round(res, x, prec); } else if (k == 2) { arb_sqrt(res, x, prec); } else if (k == 4) { arb_sqrt(res, x, prec + 2); arb_sqrt(res, res, prec); } else { if (k > 50 || prec < (WORD(1) << ((k / 8) + 8))) arb_root_ui_exp(res, x, k, prec); else arb_root_ui_algebraic(res, x, k, prec); } } /* backwards compatible alias */ void arb_root(arb_t res, const arb_t x, ulong k, slong prec) { arb_root_ui(res, x, k, prec); } arb-2.8.1/arb/rsqrt.c000066400000000000000000000056351264125401100143560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" void mag_pow_minus_three_half(mag_t z, const mag_t x) { double t; if (mag_is_zero(x)) { mag_inf(z); } else if (mag_is_inf(x)) { mag_zero(z); } else { if (fmpz_is_even(MAG_EXPREF(x))) { fmpz_mul_si(MAG_EXPREF(z), MAG_EXPREF(x), -3); t = MAG_MAN(x) * (1.0 / (LIMB_ONE << MAG_BITS)); } else { fmpz_add_ui(MAG_EXPREF(z), MAG_EXPREF(x), 1); fmpz_mul_si(MAG_EXPREF(z), MAG_EXPREF(z), -3); t = MAG_MAN(x) * (0.5 / (LIMB_ONE << MAG_BITS)); } fmpz_tdiv_q_2exp(MAG_EXPREF(z), MAG_EXPREF(z), 1); t = 1.0 / (t * sqrt(t)); t = t * (1.0 + 1e-10); mag_set_d_2exp_fmpz(z, t, MAG_EXPREF(z)); } } void arb_rsqrt(arb_t z, const arb_t x, slong prec) { int inexact; if (arb_contains_nonpositive(x)) { arb_indeterminate(z); return; } if (arb_is_exact(x)) { inexact = arf_rsqrt(arb_midref(z), arb_midref(x), prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); else mag_zero(arb_radref(z)); } else { mag_t t; mag_init(t); /* error bound: (1/2) (x-r)^(-3/2) * r */ arb_get_mag_lower(t, x); mag_pow_minus_three_half(t, t); mag_mul(t, t, arb_radref(x)); mag_mul_2exp_si(t, t, -1); inexact = arf_rsqrt(arb_midref(z), arb_midref(x), prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), t, arb_midref(z), prec); else mag_swap(arb_radref(z), t); mag_clear(t); } } void arb_rsqrt_ui(arb_t z, ulong x, slong prec) { arb_t t; arb_init(t); arb_set_ui(t, x); arb_rsqrt(z, t, prec); arb_clear(t); } arb-2.8.1/arb/set.c000066400000000000000000000023221264125401100137640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_set(arb_t x, const arb_t y) { arf_set(arb_midref(x), arb_midref(y)); mag_set(arb_radref(x), arb_radref(y)); } arb-2.8.1/arb/set_interval_arf.c000066400000000000000000000035171264125401100165270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* [(a + b) +/- (b - a)] / 2 */ void arb_set_interval_arf(arb_t x, const arf_t a, const arf_t b, slong prec) { arf_t t; int inexact; if (arf_is_inf(a) && arf_equal(a, b)) { /* [-inf, -inf] or [+inf, +inf] */ arf_set(arb_midref(x), a); mag_zero(arb_radref(x)); return; } arf_init(t); arf_sub(t, b, a, MAG_BITS, ARF_RND_UP); if (arf_sgn(t) < 0) { flint_printf("exception: arb_set_interval_arf: endpoints not ordered\n"); abort(); } arf_get_mag(arb_radref(x), t); inexact = arf_add(arb_midref(x), a, b, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(x), arb_radref(x), arb_midref(x), prec); arb_mul_2exp_si(x, x, -1); arf_clear(t); } arb-2.8.1/arb/set_interval_mpfr.c000066400000000000000000000025441264125401100167220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_set_interval_mpfr(arb_t x, const mpfr_t a, const mpfr_t b, slong prec) { arf_t aa, bb; arf_init(aa); arf_init(bb); arf_set_mpfr(aa, a); arf_set_mpfr(bb, b); arb_set_interval_arf(x, aa, bb, prec); arf_clear(aa); arf_clear(bb); } arb-2.8.1/arb/set_round.c000066400000000000000000000026051264125401100151770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_set_round(arb_t z, const arb_t x, slong prec) { int inexact; inexact = arf_set_round(arb_midref(z), arb_midref(x), prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } arb-2.8.1/arb/set_round_fmpz.c000066400000000000000000000025411264125401100162320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_set_round_fmpz(arb_t y, const fmpz_t x, slong prec) { int inexact; inexact = arf_set_round_fmpz(arb_midref(y), x, prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(y), arb_midref(y), prec); else mag_zero(arb_radref(y)); } arb-2.8.1/arb/set_round_fmpz_2exp.c000066400000000000000000000026021264125401100171660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_set_round_fmpz_2exp(arb_t y, const fmpz_t x, const fmpz_t exp, slong prec) { int inexact; inexact = arf_set_round_fmpz_2exp(arb_midref(y), x, exp, prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(y), arb_midref(y), prec); else mag_zero(arb_radref(y)); } arb-2.8.1/arb/set_str.c000066400000000000000000000133271264125401100146630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include #include #include "arb.h" static int arb_set_float_str(arb_t res, const char * inp, slong prec) { char * emarker; char * buf; int error; slong i; fmpz_t exp; fmpz_t man; slong num_int, num_frac; int after_radix; if (inp[0] == '+') { return arb_set_float_str(res, inp + 1, prec); } if (inp[0] == '-') { error = arb_set_float_str(res, inp + 1, prec); arb_neg(res, res); return error; } if (strcmp(inp, "inf") == 0) { arb_pos_inf(res); return 0; } if (strcmp(inp, "nan") == 0) { arb_indeterminate(res); return 0; } error = 0; fmpz_init(exp); fmpz_init(man); buf = flint_malloc(strlen(inp) + 1); emarker = strchr(inp, 'e'); /* parse exponent (0 by default) */ if (emarker != NULL) { /* allow e+42 as well as e42 */ if (emarker[1] == '+') { if (!(emarker[2] >= '0' && emarker[2] <= '9')) error = 1; else error = fmpz_set_str(exp, emarker + 2, 10); } else error = fmpz_set_str(exp, emarker + 1, 10); if (error) goto cleanup; } /* parse floating-point part */ { num_int = 0; num_frac = 0; after_radix = 0; for (i = 0; inp + i != emarker && inp[i] != '\0'; i++) { if (inp[i] == '.' && !after_radix) { after_radix = 1; } else if (inp[i] >= '0' && inp[i] <= '9') { buf[num_int + num_frac] = inp[i]; num_frac += after_radix; num_int += !after_radix; } else { error = 1; goto cleanup; } } buf[num_int + num_frac] = '\0'; /* put trailing zeros into the exponent */ while (num_int + num_frac > 1 && buf[num_int + num_frac - 1] == '0') { buf[num_int + num_frac - 1] = '\0'; num_frac--; } fmpz_sub_si(exp, exp, num_frac); error = fmpz_set_str(man, buf, 10); if (error) goto cleanup; } if (fmpz_is_zero(man)) { arb_zero(res); } else if (fmpz_is_zero(exp)) { arb_set_round_fmpz(res, man, prec); } else { arb_t t; arb_init(t); arb_set_ui(t, 10); arb_set_fmpz(res, man); if (fmpz_sgn(exp) > 0) { arb_pow_fmpz_binexp(t, t, exp, prec + 4); arb_mul(res, res, t, prec); } else { fmpz_neg(exp, exp); arb_pow_fmpz_binexp(t, t, exp, prec + 4); arb_div(res, res, t, prec); } arb_clear(t); } cleanup: fmpz_clear(exp); fmpz_clear(man); flint_free(buf); if (error) arb_indeterminate(res); return error; } int arb_set_str(arb_t res, const char * inp, slong prec) { char * buf; char * split; char * first; char * last; slong i, len; int error; error = 0; len = strlen(inp); buf = flint_malloc(len + 1); for (i = 0; i <= len; i++) buf[i] = tolower(inp[i]); split = strstr(buf, "+/-"); if (split == NULL) { /* strip whitespace and brackets */ first = buf; while (isspace(first[0]) || first[0] == '[') first++; last = buf + len; while (last - first > 0 && (isspace(last[-1]) || last[-1] == ']')) last--; last[0] = '\0'; error = arb_set_float_str(res, first, prec); } else { arb_t rad; arb_init(rad); /* strip whitespace and brackets */ first = buf; while (isspace(first[0]) || first[0] == '[') first++; last = split; while (last - first > 0 && (isspace(last[-1]) || last[-1] == ']')) last--; last[0] = '\0'; if (first == last) arb_zero(res); else error = arb_set_float_str(res, first, prec); if (!error) { /* strip whitespace and brackets */ first = split + 3; while (isspace(first[0]) || first[0] == '[') first++; last = buf + len; while (last - first > 0 && (isspace(last[-1]) || last[-1] == ']')) last--; last[0] = '\0'; error = arb_set_float_str(rad, first, prec); arb_abs(rad, rad); arb_add_error(res, rad); } arb_clear(rad); } flint_free(buf); return error; } arb-2.8.1/arb/sin_cos.c000066400000000000000000000447771264125401100146520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "mpn_extras.h" #define TMP_ALLOC_LIMBS(__n) TMP_ALLOC((__n) * sizeof(mp_limb_t)) int _arf_get_integer_mpn(mp_ptr y, mp_srcptr x, mp_size_t xn, slong exp); int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec); #define MAGLIM(prec) FLINT_MAX(65536, (4*prec)) static void _arf_sin(arf_t z, const arf_t x, slong prec, arf_rnd_t rnd) { mpfr_t xf, zf; mp_ptr zptr, tmp; mp_srcptr xptr; mp_size_t xn, zn, val; TMP_INIT; TMP_START; zn = (prec + FLINT_BITS - 1) / FLINT_BITS; tmp = TMP_ALLOC(zn * sizeof(mp_limb_t)); ARF_GET_MPN_READONLY(xptr, xn, x); xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = ARF_SGNBIT(x) ? -1 : 1; xf->_mpfr_exp = ARF_EXP(x); zf->_mpfr_d = tmp; zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); mpfr_sin(zf, xf, arf_rnd_to_mpfr(rnd)); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); if (zf->_mpfr_sign < 0) ARF_NEG(z); fmpz_set_si(ARF_EXPREF(z), zf->_mpfr_exp); TMP_END; } static void _arf_cos(arf_t z, const arf_t x, slong prec, arf_rnd_t rnd) { mpfr_t xf, zf; mp_ptr zptr, tmp; mp_srcptr xptr; mp_size_t xn, zn, val; TMP_INIT; TMP_START; zn = (prec + FLINT_BITS - 1) / FLINT_BITS; tmp = TMP_ALLOC(zn * sizeof(mp_limb_t)); ARF_GET_MPN_READONLY(xptr, xn, x); xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = ARF_SGNBIT(x) ? -1 : 1; xf->_mpfr_exp = ARF_EXP(x); zf->_mpfr_d = tmp; zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); mpfr_cos(zf, xf, arf_rnd_to_mpfr(rnd)); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); if (zf->_mpfr_sign < 0) ARF_NEG(z); fmpz_set_si(ARF_EXPREF(z), zf->_mpfr_exp); TMP_END; } static void _arf_sin_cos(arf_t z, arf_t w, const arf_t x, slong prec, arf_rnd_t rnd) { mpfr_t xf, zf, wf; mp_ptr zptr, wptr, tmp, tmp2; mp_srcptr xptr; mp_size_t xn, zn, wn, val; TMP_INIT; TMP_START; zn = wn = (prec + FLINT_BITS - 1) / FLINT_BITS; tmp = TMP_ALLOC(2 * zn * sizeof(mp_limb_t)); tmp2 = tmp + zn; ARF_GET_MPN_READONLY(xptr, xn, x); xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = ARF_SGNBIT(x) ? -1 : 1; xf->_mpfr_exp = ARF_EXP(x); zf->_mpfr_d = tmp; zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; wf->_mpfr_d = tmp2; wf->_mpfr_prec = prec; wf->_mpfr_sign = 1; wf->_mpfr_exp = 0; mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); mpfr_sin_cos(zf, wf, xf, arf_rnd_to_mpfr(rnd)); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); if (zf->_mpfr_sign < 0) ARF_NEG(z); fmpz_set_si(ARF_EXPREF(z), zf->_mpfr_exp); val = 0; while (tmp2[val] == 0) val++; ARF_GET_MPN_WRITE(wptr, wn - val, w); flint_mpn_copyi(wptr, tmp2 + val, wn - val); if (wf->_mpfr_sign < 0) ARF_NEG(w); fmpz_set_si(ARF_EXPREF(w), wf->_mpfr_exp); TMP_END; } void arb_sin_cos_arf_new(arb_t zsin, arb_t zcos, const arf_t x, slong prec) { int want_sin, want_cos; slong exp, wp, wn, N, r, wprounded; mp_ptr tmp, w, sina, cosa, sinb, cosb, ta, tb; mp_ptr sinptr, cosptr; mp_limb_t p1, q1bits, p2, q2bits, error, error2; int negative, inexact, octant; int sinnegative, cosnegative, swapsincos; TMP_INIT; want_sin = (zsin != NULL); want_cos = (zcos != NULL); exp = ARF_EXP(x); negative = ARF_SGNBIT(x); /* Absolute working precision (NOT rounded to a limb multiple) */ wp = prec + 8; if (want_sin && exp <= 0) wp += (-exp); /* Number of limbs */ wn = (wp + FLINT_BITS - 1) / FLINT_BITS; /* Precision rounded to a number of bits */ wprounded = FLINT_BITS * wn; /* Don't be close to the boundary (to allow adding adding the Taylor series truncation error without overflow) */ wp = FLINT_MAX(wp, wprounded - (FLINT_BITS - 4)); /* Too high precision to use table -- use generic algorithm */ if (wp > ARB_SIN_COS_TAB2_PREC) { if (want_sin && want_cos) { _arf_sin_cos(arb_midref(zsin), arb_midref(zcos), x, prec, ARB_RND); arf_mag_set_ulp(arb_radref(zsin), arb_midref(zsin), prec); arf_mag_set_ulp(arb_radref(zcos), arb_midref(zcos), prec); } else if (want_sin) { _arf_sin(arb_midref(zsin), x, prec, ARB_RND); arf_mag_set_ulp(arb_radref(zsin), arb_midref(zsin), prec); } else { _arf_cos(arb_midref(zcos), x, prec, ARB_RND); arf_mag_set_ulp(arb_radref(zcos), arb_midref(zcos), prec); } return; } TMP_START; tmp = TMP_ALLOC_LIMBS(9 * wn); w = tmp; /* requires wn limbs */ sina = w + wn; /* requires wn limbs */ cosa = sina + wn; /* requires wn limbs */ sinb = cosa + wn; /* requires wn limbs */ cosb = sinb + wn; /* requires wn limbs */ ta = cosb + wn; /* requires 2*wn limbs */ tb = ta + 2*wn; /* requires 2*wn limbs */ /* reduce modulo pi/4 */ if (_arb_get_mpn_fixed_mod_pi4(w, NULL, &octant, &error, x, wn) == 0) { /* may run out of precision for pi/4 */ if (want_sin && want_cos) { _arf_sin_cos(arb_midref(zsin), arb_midref(zcos), x, prec, ARB_RND); arf_mag_set_ulp(arb_radref(zsin), arb_midref(zsin), prec); arf_mag_set_ulp(arb_radref(zcos), arb_midref(zcos), prec); } else if (want_sin) { _arf_sin(arb_midref(zsin), x, prec, ARB_RND); arf_mag_set_ulp(arb_radref(zsin), arb_midref(zsin), prec); } else { _arf_cos(arb_midref(zcos), x, prec, ARB_RND); arf_mag_set_ulp(arb_radref(zcos), arb_midref(zcos), prec); } TMP_END; return; } sinnegative = (octant >= 4) ^ negative; cosnegative = (octant >= 2 && octant <= 5); swapsincos = (octant == 1 || octant == 2 || octant == 5 || octant == 6); /* Table-based argument reduction (1 or 2 steps) */ if (wp <= ARB_SIN_COS_TAB1_PREC) { q1bits = ARB_SIN_COS_TAB1_BITS; q2bits = 0; p1 = w[wn-1] >> (FLINT_BITS - q1bits); w[wn-1] -= (p1 << (FLINT_BITS - q1bits)); p2 = 0; } else { q1bits = ARB_SIN_COS_TAB21_BITS; q2bits = ARB_SIN_COS_TAB21_BITS + ARB_SIN_COS_TAB22_BITS; p1 = w[wn-1] >> (FLINT_BITS - q1bits); w[wn-1] -= (p1 << (FLINT_BITS - q1bits)); p2 = w[wn-1] >> (FLINT_BITS - q2bits); w[wn-1] -= (p2 << (FLINT_BITS - q2bits)); } /* |w| <= 2^-r */ r = _arb_mpn_leading_zeros(w, wn); /* Choose number of terms N such that Taylor series truncation error is <= 2^-wp */ N = _arb_exp_taylor_bound(-r, wp); /* the summation for sin/cos is actually done to (2N-1)! */ N = (N + 1) / 2; if (N < 14) { /* Evaluate Taylor series */ _arb_sin_cos_taylor_rs(sina, cosa, &error2, w, wn, N, 0, 1); /* Taylor series evaluation error */ error += error2; /* Taylor series truncation error */ error += UWORD(1) << (wprounded-wp); } else /* Compute cos(a) from sin(a) using a square root. */ { /* Evaluate Taylor series */ _arb_sin_cos_taylor_rs(sina, cosa, &error2, w, wn, N, 1, 1); error += error2; error += UWORD(1) << (wprounded-wp); if (flint_mpn_zero_p(sina, wn)) { flint_mpn_store(cosa, wn, LIMB_ONES); error = FLINT_MAX(error, 1); } else { mpn_sqr(ta, sina, wn); /* 1 - s^2 (negation guaranteed to have borrow) */ mpn_neg(ta, ta, 2 * wn); /* top limb of ta must be nonzero, so no need to normalize before calling mpn_sqrtrem */ mpn_sqrtrem(cosa, ta, ta, 2 * wn); /* When converting sin to cos, the error for cos must be smaller than the error for sin; but we also get 1 ulp extra error from the square root. */ error += 1; } } /* sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b) cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b) [F1+e1]*[F2+e2] + [F3+e3]*[F4+e4] - F1 F2 + F3 F4 = e1 e2 + e3 e4 + e2 F1 + e1 F2 + e4 F3 + e3 F4 <= (e1 + e2 + e3 + e4) + 1 (ulp) <= 2*left_err + 2*right_err + 1 (ulp) Truncating both terms before adding adds another 2 ulp, so the error is bounded by <= 2*left_err + 2*right_err + 3 (ulp) */ if (p1 == 0 && p2 == 0) /* no table lookups */ { sinptr = sina; cosptr = cosa; } else if (p1 == 0 || p2 == 0) /* only one table lookup */ { mp_srcptr sinc, cosc; if (wp <= ARB_SIN_COS_TAB1_PREC) /* must be in table 1 */ { sinc = arb_sin_cos_tab1[2 * p1] + ARB_SIN_COS_TAB1_LIMBS - wn; cosc = arb_sin_cos_tab1[2 * p1 + 1] + ARB_SIN_COS_TAB1_LIMBS - wn; } else if (p1 != 0) { sinc = arb_sin_cos_tab21[2 * p1] + ARB_SIN_COS_TAB2_LIMBS - wn; cosc = arb_sin_cos_tab21[2 * p1 + 1] + ARB_SIN_COS_TAB2_LIMBS - wn; } else { sinc = arb_sin_cos_tab22[2 * p2] + ARB_SIN_COS_TAB2_LIMBS - wn; cosc = arb_sin_cos_tab22[2 * p2 + 1] + ARB_SIN_COS_TAB2_LIMBS - wn; } if ((want_sin && !swapsincos) || (want_cos && swapsincos)) { mpn_mul_n(ta, sina, cosc, wn); mpn_mul_n(tb, cosa, sinc, wn); mpn_add_n(w, ta + wn, tb + wn, wn); } if ((want_cos && !swapsincos) || (want_sin && swapsincos)) { mpn_mul_n(ta, cosa, cosc, wn); mpn_mul_n(tb, sina, sinc, wn); mpn_sub_n(ta, ta + wn, tb + wn, wn); } sinptr = w; cosptr = ta; error = 2 * error + 2 * 1 + 3; } else /* two table lookups, must be in table 2 */ { mp_srcptr sinc, cosc, sind, cosd; sinc = arb_sin_cos_tab21[2 * p1] + ARB_SIN_COS_TAB2_LIMBS - wn; cosc = arb_sin_cos_tab21[2 * p1 + 1] + ARB_SIN_COS_TAB2_LIMBS - wn; sind = arb_sin_cos_tab22[2 * p2] + ARB_SIN_COS_TAB2_LIMBS - wn; cosd = arb_sin_cos_tab22[2 * p2 + 1] + ARB_SIN_COS_TAB2_LIMBS - wn; mpn_mul_n(ta, sinc, cosd, wn); mpn_mul_n(tb, cosc, sind, wn); mpn_add_n(sinb, ta + wn, tb + wn, wn); mpn_mul_n(ta, cosc, cosd, wn); mpn_mul_n(tb, sinc, sind, wn); mpn_sub_n(cosb, ta + wn, tb + wn, wn); error2 = 2 * 1 + 2 * 1 + 3; if ((want_sin && !swapsincos) || (want_cos && swapsincos)) { mpn_mul_n(ta, sina, cosb, wn); mpn_mul_n(tb, cosa, sinb, wn); mpn_add_n(w, ta + wn, tb + wn, wn); } if ((want_cos && !swapsincos) || (want_sin && swapsincos)) { mpn_mul_n(ta, cosa, cosb, wn); mpn_mul_n(tb, sina, sinb, wn); mpn_sub_n(ta, ta + wn, tb + wn, wn); } error = 2 * error + 2 * error2 + 3; sinptr = w; cosptr = ta; } if (swapsincos) { mp_ptr tmptr = sinptr; sinptr = cosptr; cosptr = tmptr; } /* The accumulated error */ if (want_sin) { mag_set_ui_2exp_si(arb_radref(zsin), error, -wprounded); if (want_cos) mag_set(arb_radref(zcos), arb_radref(zsin)); } else { mag_set_ui_2exp_si(arb_radref(zcos), error, -wprounded); } /* Set the midpoint */ if (want_sin) { inexact = _arf_set_mpn_fixed(arb_midref(zsin), sinptr, wn, wn, sinnegative, prec); if (inexact) arf_mag_add_ulp(arb_radref(zsin), arb_radref(zsin), arb_midref(zsin), prec); } if (want_cos) { inexact = _arf_set_mpn_fixed(arb_midref(zcos), cosptr, wn, wn, cosnegative, prec); if (inexact) arf_mag_add_ulp(arb_radref(zcos), arb_radref(zcos), arb_midref(zcos), prec); } TMP_END; } void arb_sin_arf(arb_t s, const arf_t x, slong prec, slong maglim) { if (arf_is_special(x)) { if (arf_is_zero(x)) { arb_zero(s); } else if (arf_is_nan(x)) { arb_indeterminate(s); } else { arf_zero(arb_midref(s)); mag_one(arb_radref(s)); } } else { slong xmag; /* 2^(xmag-1) <= |x| < 2^xmag */ xmag = ARF_EXP(x); if (xmag >= -(prec/3) - 2 && xmag <= maglim) { arb_sin_cos_arf_new(s, NULL, x, prec); } /* sin x = x + eps, |eps| < x^3 */ else if (fmpz_sgn(ARF_EXPREF(x)) < 0) { fmpz_t t; fmpz_init(t); fmpz_mul_ui(t, ARF_EXPREF(x), 3); arb_set_arf(s, x); arb_set_round(s, s, prec); arb_add_error_2exp_fmpz(s, t); fmpz_clear(t); } /* huge */ else { arf_zero(arb_midref(s)); mag_one(arb_radref(s)); } } } void arb_cos_arf(arb_t c, const arf_t x, slong prec, slong maglim) { if (arf_is_special(x)) { if (arf_is_zero(x)) { arb_one(c); } else if (arf_is_nan(x)) { arb_indeterminate(c); } else { arf_zero(arb_midref(c)); mag_one(arb_radref(c)); } } else { slong xmag; /* 2^(xmag-1) <= |x| < 2^xmag */ xmag = ARF_EXP(x); if (xmag >= -(prec/2) - 2 && xmag <= maglim) { arb_sin_cos_arf_new(NULL, c, x, prec); } /* cos x = 1 - eps, |eps| < x^2 */ else if (fmpz_sgn(ARF_EXPREF(x)) < 0) { fmpz_t t; fmpz_init(t); fmpz_mul_ui(t, ARF_EXPREF(x), 2); arb_one(c); arb_add_error_2exp_fmpz(c, t); fmpz_clear(t); } /* huge */ else { arf_zero(arb_midref(c)); mag_one(arb_radref(c)); } } } void arb_sin_cos_arf(arb_t s, arb_t c, const arf_t x, slong prec, slong maglim) { if (arf_is_special(x)) { if (arf_is_zero(x)) { arb_zero(s); arb_one(c); } else if (arf_is_nan(x)) { arb_indeterminate(s); arb_set(c, s); } else { arf_zero(arb_midref(s)); mag_one(arb_radref(s)); arb_set(c, s); } } else { slong xmag; /* 2^(xmag-1) <= |x| < 2^xmag */ xmag = ARF_EXP(x); if (xmag >= -(prec/2) - 2 && xmag <= maglim) { arb_sin_cos_arf_new(s, c, x, prec); } /* sin x = x + eps, |eps| < x^3 */ /* cos x = 1 - eps, |eps| < x^2 */ else if (fmpz_sgn(ARF_EXPREF(x)) < 0) { fmpz_t t; fmpz_init(t); fmpz_mul_ui(t, ARF_EXPREF(x), 3); arb_set_arf(s, x); arb_set_round(s, s, prec); arb_add_error_2exp_fmpz(s, t); fmpz_divexact_ui(t, t, 3); fmpz_mul_ui(t, t, 2); arb_one(c); arb_add_error_2exp_fmpz(c, t); fmpz_clear(t); } /* huge */ else { arf_zero(arb_midref(s)); mag_one(arb_radref(s)); arb_set(c, s); } } } void arb_sin(arb_t s, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_sin_arf(s, arb_midref(x), prec, MAGLIM(prec)); } else { mag_t t; mag_init(t); if (mag_cmp_2exp_si(arb_radref(x), 1) > 0) mag_set_ui_2exp_si(t, 1, 1); else mag_set(t, arb_radref(x)); arb_sin_arf(s, arb_midref(x), prec, MAGLIM(prec)); mag_add(arb_radref(s), arb_radref(s), t); mag_clear(t); } } void arb_cos(arb_t s, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_cos_arf(s, arb_midref(x), prec, MAGLIM(prec)); } else { mag_t t; mag_init(t); if (mag_cmp_2exp_si(arb_radref(x), 1) > 0) mag_set_ui_2exp_si(t, 1, 1); else mag_set(t, arb_radref(x)); arb_cos_arf(s, arb_midref(x), prec, MAGLIM(prec)); mag_add(arb_radref(s), arb_radref(s), t); mag_clear(t); } } void arb_sin_cos(arb_t s, arb_t c, const arb_t x, slong prec) { if (arb_is_exact(x)) { arb_sin_cos_arf(s, c, arb_midref(x), prec, MAGLIM(prec)); } else { mag_t t; mag_init(t); if (mag_cmp_2exp_si(arb_radref(x), 1) > 0) mag_set_ui_2exp_si(t, 1, 1); else mag_set(t, arb_radref(x)); arb_sin_cos_arf(s, c, arb_midref(x), prec, MAGLIM(prec)); mag_add(arb_radref(s), arb_radref(s), t); mag_add(arb_radref(c), arb_radref(c), t); mag_clear(t); } } arb-2.8.1/arb/sin_cos_pi.c000066400000000000000000000104561264125401100153250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_sin_pi(arb_t y, const arb_t x, slong prec) { arb_t t; arb_t u; fmpz_t v; if (!arb_is_finite(x)) { arb_indeterminate(y); return; } if (arf_cmpabs_2exp_si(arb_midref(x), FLINT_MAX(65536, (4*prec))) > 0) { arf_zero(arb_midref(y)); mag_one(arb_radref(y)); return; } arb_init(t); arb_init(u); fmpz_init(v); arb_mul_2exp_si(t, x, 1); arf_get_fmpz(v, arb_midref(t), ARF_RND_NEAR); arb_sub_fmpz(t, t, v, prec); arb_const_pi(u, prec); arb_mul(t, t, u, prec); arb_mul_2exp_si(t, t, -1); switch (fmpz_fdiv_ui(v, 4)) { case 0: arb_sin(y, t, prec); break; case 1: arb_cos(y, t, prec); break; case 2: arb_sin(y, t, prec); arb_neg(y, y); break; default: arb_cos(y, t, prec); arb_neg(y, y); break; } fmpz_clear(v); arb_clear(t); arb_clear(u); } void arb_cos_pi(arb_t y, const arb_t x, slong prec) { arb_t t; arb_t u; fmpz_t v; if (!arb_is_finite(x)) { arb_indeterminate(y); return; } if (arf_cmpabs_2exp_si(arb_midref(x), FLINT_MAX(65536, (4*prec))) > 0) { arf_zero(arb_midref(y)); mag_one(arb_radref(y)); return; } arb_init(t); arb_init(u); fmpz_init(v); arb_mul_2exp_si(t, x, 1); arf_get_fmpz(v, arb_midref(t), ARF_RND_NEAR); arb_sub_fmpz(t, t, v, prec); arb_const_pi(u, prec); arb_mul(t, t, u, prec); arb_mul_2exp_si(t, t, -1); switch (fmpz_fdiv_ui(v, 4)) { case 0: arb_cos(y, t, prec); break; case 1: arb_sin(y, t, prec); arb_neg(y, y); break; case 2: arb_cos(y, t, prec); arb_neg(y, y); break; default: arb_sin(y, t, prec); break; } fmpz_clear(v); arb_clear(t); arb_clear(u); } void arb_sin_cos_pi(arb_t s, arb_t c, const arb_t x, slong prec) { arb_t t; arb_t u; fmpz_t v; if (!arb_is_finite(x)) { arb_indeterminate(s); arb_indeterminate(c); return; } if (arf_cmpabs_2exp_si(arb_midref(x), FLINT_MAX(65536, (4*prec))) > 0) { arf_zero(arb_midref(s)); mag_one(arb_radref(s)); arf_zero(arb_midref(c)); mag_one(arb_radref(c)); return; } arb_init(t); arb_init(u); fmpz_init(v); arb_mul_2exp_si(t, x, 1); arf_get_fmpz(v, arb_midref(t), ARF_RND_NEAR); arb_sub_fmpz(t, t, v, prec); arb_const_pi(u, prec); arb_mul(t, t, u, prec); arb_mul_2exp_si(t, t, -1); switch (fmpz_fdiv_ui(v, 4)) { case 0: arb_sin_cos(s, c, t, prec); break; case 1: arb_sin_cos(c, s, t, prec); arb_neg(c, c); break; case 2: arb_sin_cos(s, c, t, prec); arb_neg(s, s); arb_neg(c, c); break; default: arb_sin_cos(c, s, t, prec); arb_neg(s, s); break; } fmpz_clear(v); arb_clear(t); arb_clear(u); } arb-2.8.1/arb/sin_cos_pi_fmpq.c000066400000000000000000000122431264125401100163440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" static int use_algebraic(const fmpz_t v, const fmpz_t w, slong prec) { fmpz q = *w; int r; if (COEFF_IS_MPZ(q)) return 0; if (q <= 6) return 1; count_trailing_zeros(r, q); q >>= r; if (r >= 4 && prec < (r - 3) * 300) return 0; if (q > 1000) return 0; if (prec < 1500 + 150 * q) return 0; return 1; } void _arb_sin_cos_pi_fmpq_oct(arb_t s, arb_t c, const fmpz_t v, const fmpz_t w, slong prec) { if (use_algebraic(v, w, prec)) { _arb_sin_cos_pi_fmpq_algebraic(s, c, *v, *w, prec); } else { arb_const_pi(s, prec); arb_mul_fmpz(s, s, v, prec); arb_div_fmpz(s, s, w, prec); arb_sin_cos(s, c, s, prec); } } void _arb_sin_pi_fmpq_oct(arb_t s, const fmpz_t v, const fmpz_t w, slong prec) { if (use_algebraic(v, w, prec)) { _arb_sin_pi_fmpq_algebraic(s, *v, *w, prec); } else { arb_const_pi(s, prec); arb_mul_fmpz(s, s, v, prec); arb_div_fmpz(s, s, w, prec); arb_sin(s, s, prec); } } void _arb_cos_pi_fmpq_oct(arb_t c, const fmpz_t v, const fmpz_t w, slong prec) { if (use_algebraic(v, w, prec)) { _arb_cos_pi_fmpq_algebraic(c, *v, *w, prec); } else { arb_const_pi(c, prec); arb_mul_fmpz(c, c, v, prec); arb_div_fmpz(c, c, w, prec); arb_cos(c, c, prec); } } static unsigned int reduce_octant(fmpz_t v, fmpz_t w, const fmpq_t x) { const fmpz * p = fmpq_numref(x); const fmpz * q = fmpq_denref(x); unsigned int octant; mp_bitcnt_t vval, wval; if (*p > COEFF_MIN / 8 && *p < COEFF_MAX / 8 && *q > 0 && *q < COEFF_MAX / 4) { slong pp, qq, ww, vv, tt; pp = *p; qq = *q; tt = pp * 4; ww = tt / qq; vv = tt - qq * ww; /* compute correct (floor) quotient and remainder */ if (vv < 0) { ww--; vv += qq; } octant = ((ulong) ww) % 8; ww = qq * 4; if (octant % 2 != 0) vv = qq - vv; if (vv != 0) { count_trailing_zeros(vval, vv); count_trailing_zeros(wval, ww); vval = FLINT_MIN(vval, wval); vv >>= vval; ww >>= vval; } fmpz_set_si(v, vv); fmpz_set_si(w, ww); } else { fmpz_mul_2exp(w, p, 2); fmpz_fdiv_qr(w, v, w, q); octant = fmpz_fdiv_ui(w, 8); fmpz_mul_2exp(w, q, 2); if (octant % 2 != 0) fmpz_sub(v, q, v); vval = fmpz_val2(v); wval = fmpz_val2(w); vval = FLINT_MIN(vval, wval); if (vval != 0) { fmpz_tdiv_q_2exp(v, v, vval); fmpz_tdiv_q_2exp(w, w, vval); } } return octant; } void arb_sin_cos_pi_fmpq(arb_t s, arb_t c, const fmpq_t x, slong prec) { fmpz_t v, w; unsigned int octant; fmpz_init(v); fmpz_init(w); octant = reduce_octant(v, w, x); if ((octant + 1) % 4 < 2) _arb_sin_cos_pi_fmpq_oct(s, c, v, w, prec); else _arb_sin_cos_pi_fmpq_oct(c, s, v, w, prec); if ((octant + 6) % 8 < 4) arb_neg(c, c); if (octant >= 4) arb_neg(s, s); fmpz_clear(v); fmpz_clear(w); } void arb_sin_pi_fmpq(arb_t s, const fmpq_t x, slong prec) { fmpz_t v, w; unsigned int octant; fmpz_init(v); fmpz_init(w); octant = reduce_octant(v, w, x); if ((octant + 1) % 4 < 2) _arb_sin_pi_fmpq_oct(s, v, w, prec); else _arb_cos_pi_fmpq_oct(s, v, w, prec); if (octant >= 4) arb_neg(s, s); fmpz_clear(v); fmpz_clear(w); } void arb_cos_pi_fmpq(arb_t c, const fmpq_t x, slong prec) { fmpz_t v, w; unsigned int octant; fmpz_init(v); fmpz_init(w); octant = reduce_octant(v, w, x); if ((octant + 1) % 4 < 2) _arb_cos_pi_fmpq_oct(c, v, w, prec); else _arb_sin_pi_fmpq_oct(c, v, w, prec); if ((octant + 6) % 8 < 4) arb_neg(c, c); fmpz_clear(v); fmpz_clear(w); } arb-2.8.1/arb/sin_cos_pi_fmpq_algebraic.c000066400000000000000000000312571264125401100203430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "arb_poly.h" /* include minpoly code here until it appears in a flint release */ #include "fmpz_poly.h" #include "ulong_extras.h" /* Use a lookup table for small n. We skip 53, 59 and 61, as the coefficients do not fit in 16 bits. */ #define MINPOLY_TAB_NUM 65 #define MINPOLY_TAB_MAX_LEN 24 static const char minpoly_len_tab[MINPOLY_TAB_NUM] = { 1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 3, 6, 3, 7, 4, 5, 5, 9, 4, 10, 5, 7, 6, 12, 5, 11, 7, 10, 7, 15, 5, 16, 9, 11, 9, 13, 7, 19, 10, 13, 9, 21, 7, 22, 11, 13, 12, 24, 9, 22, 11, 17, 13, 27, 10, 21, 13, 19, 15, 30, 9, 31, 16, 19, 17 }; static const short minpoly_tab[MINPOLY_TAB_NUM][MINPOLY_TAB_MAX_LEN] = { {1}, {-2, 1}, {2, 1}, {1, 1}, {0, 1}, {-1, 1, 1}, {-1, 1}, {-1, -2, 1, 1}, {-2, 0, 1}, {1, -3, 0, 1}, {-1, -1, 1}, {1, 3, -3, -4, 1, 1}, {-3, 0, 1}, {-1, 3, 6, -4, -5, 1, 1}, {1, -2, -1, 1}, {1, 4, -4, -1, 1}, {2, 0, -4, 0, 1}, {1, -4, -10, 10, 15, -6, -7, 1, 1}, {-1, -3, 0, 1}, {1, 5, -10, -20, 15, 21, -7, -8, 1, 1}, {5, 0, -5, 0, 1}, {1, -8, 8, 6, -6, -1, 1}, {-1, 3, 3, -4, -1, 1}, {-1, -6, 15, 35, -35, -56, 28, 36, -9, -10, 1, 1}, {1, 0, -4, 0, 1}, {-1, 5, 25, -5, -50, 1, 35, 0, -10, 0, 1}, {-1, -3, 6, 4, -5, -1, 1}, {1, 9, 0, -30, 0, 27, 0, -9, 0, 1}, {-7, 0, 14, 0, -7, 0, 1}, {-1, 7, 28, -56, -126, 126, 210, -120, -165, 55, 66, -12, -13, 1, 1}, {1, -4, -4, 1, 1}, {-1, -8, 28, 84, -126, -252, 210, 330, -165, -220, 66, 78, -13, -14, 1, 1}, {2, 0, -16, 0, 20, 0, -8, 0, 1}, {1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1}, {1, 4, -10, -10, 15, 6, -7, -1, 1}, {1, 8, -40, -46, 110, 71, -113, -43, 54, 11, -12, -1, 1}, {-3, 0, 9, 0, -6, 0, 1}, {-1, 9, 45, -120, -330, 462, 924, -792, -1287, 715, 1001, -364, -455, 105, 120, -16, -17, 1, 1}, {-1, 5, 10, -20, -15, 21, 7, -8, -1, 1}, {1, 12, -12, -79, 79, 103, -103, -53, 53, 12, -12, -1, 1}, {1, 0, -12, 0, 19, 0, -8, 0, 1}, {1, -10, -55, 165, 495, -792, -1716, 1716, 3003, -2002, -3003, 1365, 1820, -560, -680, 136, 153, -18, -19, 1, 1}, {1, 8, 8, -6, -6, 1, 1}, {1, 11, -55, -220, 495, 1287, -1716, -3432, 3003, 5005, -3003, -4368, 1820, 2380, -680, -816, 153, 171, -19, -20, 1, 1}, {-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1}, {1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1}, {1, -6, -15, 35, 35, -56, -28, 36, 9, -10, -1, 1}, {-1, -12, 66, 286, -715, -2002, 3003, 6435, -6435, -11440, 8008, 12376, -6188, -8568, 3060, 3876, -969, -1140, 190, 210, -21, -22, 1, 1}, {1, 0, -16, 0, 20, 0, -8, 0, 1}, {-1, 14, 49, -371, -196, 2072, 294, -5147, -210, 7007, 77, -5733, -14, 2940, 1, -952, 0, 189, 0, -21, 0, 1}, {-1, -5, 25, 5, -50, -1, 35, 0, -10, 0, 1}, {1, 16, -16, -188, 188, 526, -526, -596, 596, 339, -339, -103, 103, 16, -16, -1, 1}, {13, 0, -91, 0, 182, 0, -156, 0, 65, 0, -13, 0, 1}, {0}, {-1, 9, 0, -30, 0, 27, 0, -9, 0, 1}, {1, 12, -108, -151, 951, 877, -2891, -2058, 4489, 2442, -4080, -1639, 2289, 650, -801, -151, 170, 19, -20, -1, 1}, {1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1}, {1, -20, 20, 265, -265, -989, 989, 1519, -1519, -1198, 1198, 531, -531, -134, 134, 18, -18, -1, 1}, {-1, -7, 28, 56, -126, -126, 210, 120, -165, -55, 66, 12, -13, -1, 1}, {0}, {1, 0, -8, 0, 14, 0, -7, 0, 1}, {0}, {1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1}, {1, 24, 72, -170, -534, 405, 1385, -459, -1782, 276, 1287, -90, -546, 15, 135, -1, -18, 0, 1}, {2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1}, }; /* Recurrence for coefficients in rescaled Chebyshev polynomials */ #define CHEB_NEXT(y, x, m, k) \ fmpz_mul2_uiui(y, x, m - 2*k + 1, m - 2*k + 2); \ fmpz_divexact2_uiui(y, y, k, m - k); \ fmpz_neg(y, y); \ /* Computes the monic integer polynomial n odd: 2 (T(s+1,x/2) - T(s,x/2)), s = (n - 1) / 2 n even: 2 (T(s+1,x/2) - T(s-1,x/2)), s = n / 2 */ static void chebyshev_sum(fmpz * a, ulong n) { ulong s, k, m; if (n == 1) { fmpz_set_si(a, -2); fmpz_one(a + 1); return; } if (n == 2) { fmpz_set_si(a, -4); fmpz_zero(a + 1); fmpz_one(a + 2); return; } s = n / 2; m = s + 1; fmpz_one(a + m); for (k = 1; k <= m / 2; k++) { CHEB_NEXT(a + m - 2 * k, a + m - 2 * k + 2, m, k); } if (n % 2 == 1) { m = s; fmpz_set_si(a + m, -1); for (k = 1; k <= m / 2; k++) { CHEB_NEXT(a + m - 2 * k, a + m - 2 * k + 2, m, k); } } else { m = s - 1; /* Use the top coefficient as scratch space. */ for (k = 1; k <= m / 2; k++) { CHEB_NEXT(a + m + 2, a + m + 2, m, k); fmpz_sub(a + m - 2*k, a + m - 2*k, a + m + 2); } for (k = 1 - (m % 2); k < m + 2; k += 2) fmpz_zero(a + k); fmpz_sub_ui(a + m, a + m, 1); /* Set the top coefficient again. */ fmpz_one(a + m + 2); } } #define MUL_TMP(P, Plen, T, Tlen) \ fmpz * swap; \ if (Plen >= Tlen) \ _fmpz_poly_mul(U, P, Plen, T, Tlen); \ else \ _fmpz_poly_mul(U, T, Tlen, P, Plen); \ Plen = Plen + Tlen - 1; \ swap = P; P = U; U = swap; \ void _arb_fmpz_poly_cos_minpoly(fmpz * f, ulong n) { fmpz *P, *Q, *T, *U; int *mu; ulong Pdeg, Qdeg; ulong Plen, Qlen, Tlen; ulong d; if (n < MINPOLY_TAB_NUM && minpoly_len_tab[n] <= MINPOLY_TAB_MAX_LEN) { for (d = 0; d < minpoly_len_tab[n]; d++) fmpz_set_si(f + d, minpoly_tab[n][d]); return; } /* Compute values of the Moebius function. We do this as a precomputation as it allows us to bound in advance the degrees of the numerator and denominator. */ mu = flint_calloc(n + 1, sizeof(int)); Pdeg = Qdeg = 0; for (d = 1; d <= n; d++) { if (n % d == 0) { mu[d] = n_moebius_mu(n / d); if (mu[d] == 1) Pdeg += (d / 2 + 1); else if (mu[d] == -1) Qdeg += (d / 2 + 1); } } /* We use two extra arrays as scratch space (note that Qdeg < Pdeg). */ P = _fmpz_vec_init(Pdeg + 1); Q = _fmpz_vec_init(Pdeg + 1); T = _fmpz_vec_init(Pdeg + 1); U = _fmpz_vec_init(Pdeg + 1); Plen = Qlen = 1; fmpz_one(P); fmpz_one(Q); for (d = 1; d <= n; d++) { if (n % d == 0 && mu[d] != 0) { chebyshev_sum(T, d); Tlen = d / 2 + 2; if (mu[d] > 0) { MUL_TMP(P, Plen, T, Tlen); } else { MUL_TMP(Q, Qlen, T, Tlen); } } } _fmpz_poly_div(f, P, Plen, Q, Qlen); _fmpz_vec_clear(P, Pdeg + 1); _fmpz_vec_clear(Q, Pdeg + 1); _fmpz_vec_clear(T, Pdeg + 1); _fmpz_vec_clear(U, Pdeg + 1); flint_free(mu); } void arb_fmpz_poly_cos_minpoly(fmpz_poly_t f, ulong n) { slong len = (n < MINPOLY_TAB_NUM) ? minpoly_len_tab[n] : n_euler_phi(n) / 2 + 1; fmpz_poly_fit_length(f, len); _arb_fmpz_poly_cos_minpoly(f->coeffs, n); _fmpz_poly_set_length(f, len); } void _arb_cos_pi_fmpq_algebraic(arb_t c, ulong p, ulong q, slong prec) { /* handle simple angles using exact formulas */ if (q <= 6) { if (p == 0) { arb_one(c); } else if (q == 2) /* p/q must be 1/2 */ { arb_zero(c); } else if (q == 3) /* p/q must be 1/3 */ { arb_set_ui(c, 1); arb_mul_2exp_si(c, c, -1); } else if (q == 4) /* p/q must be 1/4 */ { arb_sqrt_ui(c, 2, prec); arb_mul_2exp_si(c, c, -1); } else if (q == 5) /* p/q must be 1/5 or 2/5 */ { arb_sqrt_ui(c, 5, prec + 3); arb_add_si(c, c, (p == 1) ? 1 : -1, prec); arb_mul_2exp_si(c, c, -2); } else if (q == 6) /* p/q must be 1/6 */ { arb_sqrt_ui(c, 3, prec); arb_mul_2exp_si(c, c, -1); } } /* reduce even denominator */ else if (q % 2 == 0) { slong extra = 2 * FLINT_BIT_COUNT(q) + 2; if (4 * p <= q) { _arb_cos_pi_fmpq_algebraic(c, p, q / 2, prec + extra); arb_add_ui(c, c, 1, prec + extra); } else { _arb_cos_pi_fmpq_algebraic(c, q / 2 - p, q / 2, prec + extra); arb_sub_ui(c, c, 1, prec + extra); arb_neg(c, c); } arb_mul_2exp_si(c, c, -1); arb_sqrt(c, c, prec); } else { /* compute root of the minimal polynomial */ slong start_prec, eval_extra_prec; fmpz_poly_t poly; arb_poly_t fpoly; arf_t interval_bound; arb_t interval; arf_init(interval_bound); arb_init(interval); fmpz_poly_init(poly); arb_poly_init(fpoly); if (p % 2 == 0) arb_fmpz_poly_cos_minpoly(poly, q); else arb_fmpz_poly_cos_minpoly(poly, 2 * q); eval_extra_prec = fmpz_poly_max_bits(poly) * 2; /* heuristic */ eval_extra_prec = FLINT_ABS(eval_extra_prec); arb_poly_set_fmpz_poly(fpoly, poly, ARF_PREC_EXACT); /* todo: smallify for accuracy */ start_prec = 100 + eval_extra_prec; arb_const_pi(c, start_prec); arb_mul_ui(c, c, p, start_prec); arb_div_ui(c, c, q, start_prec); arb_cos(c, c, start_prec); arb_mul_2exp_si(c, c, 1); /* poly is for 2*cos */ if (100 + eval_extra_prec - 10 < prec) { arb_set(interval, c); mag_mul_2exp_si(arb_radref(interval), arb_radref(interval), 1); _arb_poly_newton_convergence_factor(interval_bound, fpoly->coeffs, fpoly->length, interval, start_prec); _arb_poly_newton_refine_root(c, fpoly->coeffs, fpoly->length, c, interval, interval_bound, eval_extra_prec, prec); } arb_mul_2exp_si(c, c, -1); fmpz_poly_clear(poly); arb_poly_clear(fpoly); arf_clear(interval_bound); arb_clear(interval); } } void _arb_sin_pi_fmpq_algebraic(arb_t s, ulong p, ulong q, slong prec) { if (q % 2 == 0) { p = q / 2 - p; while ((p % 2 == 0) && (q % 2 == 0)) { p /= 2; q /= 2; } _arb_cos_pi_fmpq_algebraic(s, p, q, prec); } else { _arb_cos_pi_fmpq_algebraic(s, q - 2 * p, 2 * q, prec); } } void _arb_sin_cos_pi_fmpq_algebraic(arb_t s, arb_t c, ulong p, ulong q, slong prec) { slong wp; if (q <= 6) { if (p == 0) { arb_one(c); arb_zero(s); return; } else if (q == 2) /* p/q must be 1/2 */ { arb_zero(c); arb_one(s); return; } else if (q == 4) /* p/q must be 1/4 */ { arb_sqrt_ui(c, 2, prec); arb_mul_2exp_si(c, c, -1); arb_set(s, c); return; } } wp = prec + 3; /* prefer the formula with less cancellation */ if (p <= q / 4) { _arb_sin_pi_fmpq_algebraic(s, p, q, wp); arb_mul(c, s, s, wp); arb_sub_ui(c, c, 1, wp); arb_neg(c, c); arb_sqrt(c, c, prec); } else { _arb_cos_pi_fmpq_algebraic(c, p, q, wp); arb_mul(s, c, c, wp); arb_sub_ui(s, s, 1, wp); arb_neg(s, s); arb_sqrt(s, s, prec); } } arb-2.8.1/arb/sin_cos_tab.c000066400000000000000000007036131264125401100154670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #if FLINT_BITS == 64 #define Z2(a,b) UWORD(0x ## b ## a) #else #define Z2(a,b) UWORD(0x ## a), UWORD(0x ## b) #endif #define Z8(a,b,c,d,e,f,g,h) Z2(a,b), Z2(c,d), Z2(e,f), Z2(g,h), const mp_limb_t arb_pi4_tab[ARB_PI4_TAB_LIMBS] = { Z8(e6cc254b,db7f1447,ced4bb1b,44ce6cba,cf9b14ed,da3edbeb,865a8918,179727b0) Z8(9027d831,b06a53ed,413001ae,e5db382f,ad9e530e,f8ff9406,3dba37bd,c9751e76) Z8(602646de,c1d4dcb2,d27c7026,36c3fab4,34028492,4df435c9,90a6c08f,86ffb7dc) Z8(8d8fddc1,93b4ea98,d5b05aa9,d0069127,2170481c,b81bdd76,cee2d7af,1f612970) Z8(515be7ed,233ba186,a090c3a2,99b2964f,4e6bc05d,287c5947,1fbecaa6,2e8efc14) Z8(04de8ef9,dbbbc2db,2ad44ce8,2583e9ca,b6150bda,1a946834,6af4e23c,99c32718) Z8(bdba5b26,88719a10,a787e6d7,1a723c12,a9210801,4b82d120,e0fd108e,43db5bfc) Z8(74e5ab31,08e24fa0,bad946e2,770988c0,7a615d6c,bbe11757,177b200c,521f2b18) Z8(3ec86a64,d8760273,d98a0864,f12ffa06,1ad2ee6b,cee3d226,4a25619d,1e8c94e0) Z8(db0933d7,abf5ae8c,a6e1e4c7,b3970f85,5d060c7d,8aea7157,58dbef0a,ecfb8504) Z8(df1cba64,a85521ab,04507a33,ad33170d,8aaac42d,15728e5a,98fa0510,15d22618) Z8(ea956ae5,3995497c,95581718,de2bcbf6,6f4c52c9,b5c55df0,ec07a28f,9b2783a2) Z8(180e8603,e39e772c,2e36ce3b,32905e46,ca18217c,f1746c08,4abc9804,670c354e) Z8(7096966d,9ed52907,208552bb,1c62f356,dca3ad96,83655d23,fd24cf5f,69163fa8) Z8(1c55d39a,98da4836,a163bf05,c2007cb8,ece45b3d,49286651,7c4b1fe6,ae9f2411) Z8(5a899fa5,ee386bfb,f406b7ed,0bff5cb6,a637ed6b,f44c42e9,625e7ec6,e485b576) Z8(6d51c245,4fe1356d,f25f1437,302b0a6d,cd3a431b,ef9519b3,8e3404dd,514a0879) Z8(3b139b22,020bbea6,8a67cc74,29024e08,80dc1cd1,c4c6628b,2168c234,c90fdaa2) }; const mp_limb_t arb_sin_cos_tab1[2 * ARB_SIN_COS_TAB1_NUM][ARB_SIN_COS_TAB1_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) },{ Z8(c584231f,42c62544,77e886cc,aa20f9f8,fe4f25a3,210a5354,2c1d4109,1721956d) Z8(e9e36b4d,c4405259,25cbf0c7,20e25319,b26e498b,6a76a798,55577777,00ffffd5) },{ Z8(0370b3ba,94cd273e,2b207969,23a42900,14c6dcb3,23a6dbba,dbd88646,159e76d5) Z8(c276c47f,596a5b46,b54082cd,09039032,f7502b17,a4fbefbe,0aaaaa4f,ffff8000) },{ Z8(caec7acc,0d534b7e,4ae2e1bb,d3da4dc1,c8be6a05,16fa88a2,4353efc3,20596653) Z8(cd9c4aa4,943448d9,32d90612,ca4a3d86,1221010c,6e8744e6,aaeeeee8,01fffeaa) },{ Z8(e7c976ee,c55d8730,f47670bb,d4ba6011,ffc81fb4,d9fe3873,c6c9dd2e,f9b9ba8e) Z8(4c4ab792,64b0f827,585b1e5f,283c5951,b5b41832,4034032d,aaaa93e9,fffe0000) },{ Z8(8fdee34a,3fc81c11,4ce297c3,b59ee6f6,fb0e8d78,082af7b6,821e7854,3584d0b3) Z8(11de693e,b5ab634a,85d81bd2,cef9d52c,7e126af1,5082ea0d,020665f7,02fffb80) },{ Z8(a40379e7,ad1cfcf5,b7ac5136,6de072e9,f4ad5f6b,18c2a1eb,3c74e210,4a1df9d1) Z8(d94391b8,36bc82aa,f68391c5,18efb2d1,090fa8bf,f6750326,5ffefccc,fffb8003) },{ Z8(fdaf9747,8e9b8e30,566197ee,72435801,c62e2cf7,eb4498fb,5ea2034d,a1bd4211) Z8(985b1d56,077ec1bd,f5624024,62c181f7,1f113dca,aa938cac,5dddda9d,03fff555) },{ Z8(b77519c6,3a897fe0,6eb671be,01e286c4,edc98229,4942277e,e7d32643,9b3ed7ad) Z8(6ac7f294,121a3235,8d241e94,104dd21b,de6ace45,4514074b,aaa4fa51,fff8000a) },{ Z8(e3463014,cf3d5b67,78186dc9,3801a36e,ce2161f8,0373d0bf,6276fde2,4cf23b8a) Z8(f0bfed96,50fae5a7,7c6e0e96,4a14e87a,cccea63e,19b3218a,c4b545d5,04ffeb2a) },{ Z8(0aa8cc75,71ebe6b5,3da0bebf,2c3d56ff,aeedaac3,0b0e9804,0840625f,1e268993) Z8(1f19c22d,8bbdf397,c116c793,644d7b15,9a68ae63,21ed0e0d,0a94f726,fff3801a) },{ Z8(5bacb364,5423d214,a7f1a284,d474869f,89626be2,c4224296,a2fb6ce6,8fda35a7) Z8(4ec65078,057e5d7c,5e37ac6b,848a2e8e,27336737,efe2b515,40cc9541,05ffdc00) },{ Z8(555152bc,0b70a74a,ba9a9f17,8d823963,f1545bab,8a7f9869,ae2388f8,29fa7dd4) Z8(24020b86,f3a5aeed,50c100b1,135c2400,f79e495c,db5d0d2e,ffbf335c,ffee0035) },{ Z8(2e956a62,54707381,b634a0df,4304d14f,986f637c,02c0513f,a293758b,51d78b0e) Z8(a7332c80,bcb27f61,d2358820,03e277d3,4f02b7c5,f20c232a,e163a0dd,06ffc6d5) },{ Z8(b2849471,f41b4606,fa909aed,3958ae98,d8b099fd,0463c8a9,5a06813c,e1bc72de) Z8(9bd85d30,80c5648e,373fe8f1,4ab4504c,5a0fbdb7,382f503a,0a074478,ffe78064) },{ Z8(d76c7aa2,144d32b9,855bd545,58df22c8,b8e9f930,cc5797fe,df450ee3,b1e32374) 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Z8(4ccb161e,21387ac8,ea8c1eff,dc77d77c,dbe8ceeb,0f90645a,1f6ab0b7,9b67aa6c) },{ Z8(37cfb87e,ac681235,d19bb1ab,a8b18fb6,1d77b6ad,3f7f55f5,5fa19ed7,54f55757) Z8(9ed300d0,6f8db35e,360e9dd0,fff2f2a6,32111fdd,44bb91cd,68be7395,cb6f0c48) },{ Z8(307cd9e6,d6d14ec2,8d9242b0,952e6f6a,24f1dd6b,8f14cad5,d045cab1,648a462b) Z8(bd7b9183,8e62a282,ceb1ac8a,6a547cd7,857991ca,05256c4f,b14156ef,9c32cba2) },{ Z8(d1df7c8f,fb375501,21d4b453,b25c3ad9,b0493a9c,0acc4600,787a6268,ca0e0e62) Z8(b3db1448,43d7be83,87a780b2,a773f879,3a66a0e6,204bbc0f,658fe5e8,cad33f00) },{ Z8(1b0e64ff,cb7db449,24615176,82029b38,8cbcc658,c3028a81,46bab7ef,673ad504) Z8(abefa250,7280b4f5,e3300699,90435c79,b7ecdef6,74da3b98,84798719,9cfd50a6) },{ Z8(1f462ccd,70f4445e,adcbf9ea,fa92a9b1,f53f9ae5,6b99fbc2,d437c2a4,43b373f9) Z8(cf7174e9,42037586,4bb9abe2,726e60a8,e3a45bd1,8de52f15,3447e205,ca36a6e5) },{ Z8(e97c1e35,46ea126e,379e0dac,786c6e86,11796b5f,44cf8f64,5254e08c,424dc9d3) Z8(b8488d55,2e08cf2b,886cfefe,0feece34,f8582659,9ac582d0,14204e68,9dc738ad) },{ Z8(5fe59211,a24c5d20,2c4e8bf5,e6df49fe,268b4389,989e0803,7b914ad9,bc3bc9cf) Z8(44878c62,203577de,daf6aae1,981e414b,64b3ddb7,11ff93fe,6cf48c89,c9994493) },{ Z8(27fa60ab,ddc6b473,4dfaa2b1,38b94eb6,48526969,dbae43ba,708ba13f,ed213d83) Z8(6e7fb1e1,870aac84,dc636c6c,069417ce,9e9e2d58,015216a5,783ff08b,9e9082ec) },{ Z8(60df74d1,c54a55ab,c83ecaed,27a66fcb,284c6390,a14b5b0d,4e999059,7a255737) Z8(041b5ee0,4f75f241,6ad7f15a,84891349,068fb449,a1660261,71da8f3f,c8fb18a8) },{ Z8(13b4bb64,54ab6869,0f005d79,c66d69cb,e5e0de6a,0afae163,dbfeaf35,5f266059) Z8(8101780c,59731103,c3f0a747,9040c45e,c1019984,6a3c7aa3,66a9cf90,9f592e9b) },{ Z8(f268261d,f7deea62,7ec4adcd,2ab491c7,34643dd5,412b54db,74f5aa51,6e32cd41) Z8(7d820c74,aff3c424,bf157de0,122876bf,47929682,14ef546c,6ed7b6f0,c85c23c2) },{ Z8(f28301ed,0d175c6b,e51ca4c9,fa8d59cf,e601f617,cde40777,2be41884,26cceee7) Z8(43f85dd0,9e38d91f,afc59c70,383f369d,02e31f6e,a6552176,33bfb607,a0213af1) },{ Z8(a045d1a2,12b3aeaa,3fab41be,27cf56e5,9ece4c11,4db25c3c,0e7c06db,25af3495) Z8(4679640b,cde9ce0b,4cfc0dff,99fd0fb8,08b49c99,8b09594f,58c4c78a,c7bc6680) },{ Z8(62c7faa4,000a21a6,d5c577d8,084c77e2,e4fa0d9d,388f4620,7dc82b30,42b1e8c6) Z8(68656948,076b9b0f,3e534358,ecfad43f,9e9a15ff,11fa50fd,d33c828c,a0e8a725) },{ Z8(cf4f372d,509e6f8a,a7533ca6,62e30d91,388d1e0e,10e96fe7,6ee476c8,59ccddd0) Z8(56437f1a,c40a4f00,dfb0a1d6,7d9adcb9,a03cca20,e2da5615,ecd6875c,c71be181) },{ Z8(d0eaca40,52441e30,7da798fb,3c501091,c3c7eb97,3f796a65,df7f6935,6320cbec) Z8(1094e8cf,ea4ec71f,c82b9b58,0ad3ae83,aca5adad,0acce6c2,d8fc33fa,a1af7271) },{ Z8(0982c705,4018a644,29b10c97,45d445f7,e561e9a3,e3d5ee51,02fef304,e28f1559) Z8(42b30f7d,bd6965c7,4333b6c2,066c35b9,cc55b98a,45b71ac7,affe01eb,c67a9567) },{ Z8(d517276e,b70ff3ad,973634be,ef29ee5f,93f211d4,6ca11f40,914f1901,7bda4332) Z8(4ad66f31,bb0b7cdf,cb1d9eb7,82c66160,5f5405c1,527c32b5,79c35582,a2759c0e) },{ Z8(d1b06f8b,122b6b60,8dbe2d11,02336e0f,29d5350a,e9896341,5da0dddd,4676a1cc) Z8(16de6ad4,365389b7,f93655d2,4f82ed4c,981e3480,7c07d28e,ee48030c,c5d882d2) },{ Z8(e6ad2e98,28730c2f,be4161b8,a4aff1fe,6ee08661,da71bdf6,4834c677,0496f5fb) Z8(cb558558,e7849d9e,8b2579da,ab28cb60,bd34862d,f2a623ca,8c05c9d4,a33b2335) },{ Z8(9fc86c65,bb040495,66c6dc11,3e69ea0f,dca2de26,0462a339,86a5b775,2e71debb) Z8(8b024b74,bb0e0230,aae8b1fa,623f1eda,86f32a1f,9271d995,ba3bcaea,c535aa65) },{ Z8(6ba387bb,62a14d7d,df192ccb,33f91922,6f7e7f0e,711adcf9,ed8758ba,06e3e927) Z8(455e21e5,cc364cea,1afe642b,f105e130,5e038346,d6b17382,88acf49c,a4000721) },{ Z8(a5764264,41b7e613,44f2d217,569a58c3,99d81f84,0f57cf7f,515ed81a,b093ee31) Z8(bcfd3bb7,885b981b,c2052ca8,66371ac4,b08884fc,1b38827d,ec38fb89,c4920cc2) },{ Z8(c2f0dc57,1dd2cd8b,e5d4a44f,f770bd16,358ae087,827c7ff2,b77857fa,7c3b618b) Z8(525b3f19,ecb08b0b,a6a090d6,9bc62f2f,691bfd87,f236b9ef,8bdd4185,a4c4470d) },{ Z8(d3b977c0,97790ae0,12bf54fd,0cb86957,7ccf7016,31335dec,942639c5,1d0b40ac) Z8(ef8179bf,0f24d3cb,c086722d,621f8db2,566629d8,1e410878,21d4c073,c3edaa8e) },{ Z8(b59e76d8,ebcbbcb3,8135b970,ca67bcb8,1112d213,3b933649,b9eee978,bdb97a99) Z8(810cce73,634a21b1,08d93793,16c3e9bd,62cdd293,6d02b9c6,55bb0808,a587e235) },{ Z8(5d951b21,af0ddcf7,f210dd4b,155ae8da,896dbd42,24b3c22f,aa953d08,c4542be0) Z8(1bf5caac,fe376bad,c51b4c13,35b4e9c0,9dd1381a,8ffe2bfe,bd363133,c348846b) },{ Z8(65621b65,c5bd01fa,d4acaafe,2a53dbec,5dc52f57,f4e0a47e,8e450c7c,33ce3c5c) Z8(fc6435e1,a41f60e4,64de18d4,a47220c4,dedd6862,f0f720bd,4b2ecb33,a64ad7d5) },{ Z8(40cab1ea,de676c83,f39fef84,483c80e1,d33a2acd,9fb0c4f4,bdfbddec,644cbd64) Z8(5453898a,50b7417b,9b834dd2,589e0206,4fac0bbc,ecbd60c5,e471ef3b,c2a29b00) },{ Z8(ce32a23f,99865f07,caf12b08,a9f717aa,006142fd,7d0d50ea,30372f5c,ed0e2843) Z8(6e58ead4,f3db7eea,c3079246,96dabf88,12bb748b,da0ec907,76a8d4b6,a70d272a) },{ Z8(ebfdca6f,f9d19c3f,824996aa,4ed7d4a9,e622f071,72f6910a,69f13e45,a7b77d3d) Z8(24fdc9f2,b5496272,343e53ad,fe814ec2,722f643f,5a613ec8,80e4ffdd,c1fbeef3) },{ Z8(1d531087,dfc6382a,2378f667,484bb783,b518e14a,eee14b02,b7c8256a,69ce99ef) Z8(755165aa,26a49b0b,dc708c02,84394ea1,bee3c202,ad8e98c4,88e42a5d,a7cecf72) },{ Z8(691e5e6a,266aeda1,dd19990d,0bf9c1b4,fc54adb5,42438571,012ad137,cae4d306) Z8(21d398b7,486d9ff4,dcf71e73,42542cbd,83b0fe27,76825189,3e8ee2f9,c15480ea) },{ Z8(215eddce,6525549f,55430115,ff9d7a6e,72ac7226,1a0fe34d,a9975ce8,4214f8cf) Z8(c6f12a2d,c985491e,e735f8bc,20f7e7fb,f9e24399,e2f3c76e,d9a8dd47,a88fcfeb) },{ Z8(6db6a625,4148ab97,27ed8b40,9e2eb1dd,e2f2afa8,fb6290b1,4361b8cc,9660116b) Z8(7de9aa6d,7a48a6e9,4356fb50,ebcb8bed,b90cb15a,ba37a3ee,8b6ae710,c0ac518c) },{ Z8(ac56ec04,890c3730,d422d132,ff83b0db,c29b765c,1e13a30a,8f606b95,01038993) Z8(cca5cff1,a3d8a26d,b88ee895,fceac47a,73819370,af7af179,688db20f,a95027d5) },{ Z8(1e6fbc6c,60d1c2dc,e7c30f32,9619cb3e,2b62c8de,4bca8792,51b3819d,e9b6ce2a) Z8(e43a043f,ce6e660a,1bdb7eed,ebcc6e6e,b2a73066,1f6ac151,96c8bb55,c0036182) },{ Z8(48a44a6d,a44af301,b6066288,e6ab77f2,bd9c04a5,f1f67e10,3f16aac5,9294d3a7) Z8(d5bb8102,ac216fbc,187f1471,3193b47f,3911b8a0,2c28520d,ddb92123,aa0fd66e) },{ Z8(0ca836a7,3320e22c,a88c1652,37c0d3c6,0e2fe16a,0a605af0,292cfca7,3da58f49) Z8(5fad5a6c,11c6cae8,1877c028,b4e48306,567cf3e3,75969296,50a44068,bf59b175) },{ Z8(f9f9b33e,7248794f,88ec1dfc,0529d89d,0df30a43,c1441a52,a41619d3,32912522) Z8(14f9e381,71e34834,8ad5534f,35b862cb,faf9f80b,d6081229,8aa1ae8d,aacedaf8) },{ Z8(54b9549b,9827b85d,fd615c97,79d8c10e,60f8ed0e,02c23a19,497cc6ca,9d776ab3) Z8(1e4ff94f,2be7f6e0,fbdfad15,e9da1856,4624c532,9524be9b,68fc986e,beaf420e) },{ Z8(cb130e48,de9a0465,19d3aa6e,13da5dd7,65686c06,38664d38,9ec7f704,d2cc1f1b) Z8(f55b9e01,c8d57dfd,fce43d55,dc2e7109,c65d7e3a,10ed343e,6acd9872,ab8d34b3) },{ Z8(3d0097bb,acb3f967,18b3a28f,e3981a86,aab2a1f9,bcf88c51,8b3002ee,8a52d51d) Z8(ea4a4846,283fefa0,243de8f2,d75a5560,8cbf4da1,614946a8,4f2a771c,be0413f8) },{ Z8(c71baf37,feee7693,1def3e87,c00d7342,d3b5f168,8905b801,a932296e,3052e595) Z8(5a4227e6,24607c29,10bc61d4,c3a65366,89d0d9f9,fe4592af,2491db72,ac4ae2e1) },{ Z8(f45194f7,62c09480,62754be0,fb383dfd,ba10a2c1,f696a48f,044f2aaf,f2eff911) Z8(a91c3918,d119698e,e35b4c83,c7a88750,a1373c37,483f3902,3135b26d,bd5827de) },{ Z8(0c02f411,1ff32882,cef2f697,a350cff6,7b2c8614,44556858,97ab55d4,e2546438) Z8(07cbd9f5,d6b23197,6f51e09b,636e74e7,b0ac24b8,a3a9057b,09d08c4f,ad07e4c4) },{ Z8(2b506e3a,80a59c78,ab1cad5d,23020c5f,346397fe,87a14359,25dc1e2b,3ac99c0f) Z8(21761101,1b34047e,c64a4e73,8ab14808,a376bec9,b122c574,fb2a14a9,bcab7e6b) },{ Z8(f7569076,70c9d4ad,80dc17ca,ac32e85e,f6ff8689,29267ea8,65ee7ef9,71e3bee3) Z8(9badf8c4,d5daf23e,b7a7d9fd,837f508a,15d858e3,07986543,18b685f1,adc4399f) },{ Z8(c3c551b0,9026ae27,199070fa,1d0a39d8,09f2b280,824d3570,5aa9da99,37c47c53) Z8(0e553a43,d3883121,79c768aa,b3cf8cf9,6d948663,85540223,566b7069,bbfe184e) },{ Z8(f5459f68,b53cadf4,06f81956,e7c8e051,27e858ee,ef13e9a8,a6a40f98,0a971a49) Z8(cd044cb1,7533f532,646425fc,476747c2,f140a488,966e1d6a,fc786b2d,ae7fe0b5) },{ Z8(8c9582b2,94980cc7,5304c25d,1fa13c55,d8e7df66,cc891f2d,d069f9b5,106dbe6f) Z8(e35575c3,e4aee845,0e7e44e6,e0bfb8f2,b9d993b4,c151839c,a908f73e,bb4ff632) },{ Z8(c677e41b,9143c42d,c266f052,b509c11e,7ab985bc,619d8270,62b33d6f,072b8bc7) Z8(38ade61b,d1c17663,23d57fe2,15606dd8,4519dcaf,cdcca897,0e0efb84,af3ad94d) },{ Z8(4da93476,ef62efbe,a51d4c60,cec5f580,6e1e1ff7,d45aa122,c42ed5cf,468b46b4) Z8(424db0af,ae64c22d,722801a1,2f94f99f,77159480,b651d3d6,150fd3b4,baa118c7) },{ Z8(14aa239b,5ca19494,f01dd6c9,bf408993,bd88ab79,4f0ff52a,1dddf51d,17a7b385) Z8(27ff6e25,bc4d5213,6c228e0a,9a5dfd5a,16e33f5e,d9defdc4,54f2ba16,aff522a9) },{ Z8(bdc5bd4f,12332859,5fc193fd,c3d84b49,1d084321,d228c5af,360e0103,56d55b53) Z8(d122de5b,4c3f8862,becacdd1,12230f14,95082990,628e135a,77dd0751,b9f180ba) },{ Z8(40bceafa,32bea5dd,d2ef9124,3326d7f1,b6e13602,abd4e97c,43831456,96047e2a) Z8(6d1d1abe,d0586057,3e912af0,ca6cb5fc,ceb0f64f,7d82f3fc,87d6e61c,b0aebc10) },{ Z8(479b3a66,997ffb26,67eed7d6,c8eb495f,6f5aa8c8,d4a72b22,ee097db0,682e9672) Z8(c908f94c,65aa441a,bd6d47ff,37a95ec6,eae2bc42,022de97f,696e8d47,b9412ebc) },{ Z8(bb6195f7,f25f9130,1b9549c0,e65999ff,92b101df,0963f8c7,0e6b7a1f,537a1a26) Z8(b926281f,53d6d400,078baa0c,c3c1225e,7cc23bd3,4cf5493b,0d63c424,b167a4c9) },{ Z8(86802969,6b056974,8fcdb467,2276059c,81be199f,b036479c,371dd16e,dda15e63) Z8(e58884d3,95e185f8,df940fa8,053730bb,9016bfa1,b614a053,3bb3c284,b890237d) },{ Z8(6b25eded,6c355392,d60a2c0d,cd4c4f37,bc7bc645,e4c0a8cc,4db2ce0e,d8038e83) Z8(ffa4d664,f6ed4a1c,231d611e,acbd3dc9,e999db8d,f1d197dd,fcf0375a,b21fdc19) },{ Z8(8f63fe0d,b442ef46,3cbe3801,2adc91be,47820e40,356b6c1c,cb456399,96399059) Z8(3645ae2a,ede1d3cb,faeace7b,86e6fe7f,6ba0965b,d8702367,f9dd13d5,b7de5fad) },{ Z8(a4ba456e,337f8452,91cfce6b,280080ed,d4011d71,42e8bd78,674d79fd,adc9eb89) Z8(3324815f,b026e673,3e29c1bc,e6d838c0,a77e1ca3,df2d6e20,1f3aaa24,b2d7614b) },{ Z8(8c842515,2adf15a5,b1c84bf3,79d6bf35,2646465b,94570eeb,b3b7ab27,fd5c5984) Z8(8e92b508,fe55d6ec,f0224a4a,f203f6b3,14c3d7d4,50dbdb7a,67aaf2c0,b72be400) },{ Z8(aeaf3f7e,dbc46936,4825ea3d,70d3a1ac,6c5d41f1,68bbf9f9,33a43ffa,7645763d) Z8(c2e66b84,768e7579,41f16117,ff47c12e,04145dc1,8d443c3c,ef214550,b38e33a4) },{ Z8(f9d28424,773bd205,da771ce0,71968fb0,627d099b,800a19de,1577763d,8a95419f) Z8(d0d646ec,d9f91389,acde57f6,f1a81925,2e79c13f,f32a51e8,00bc11d2,b678b127) },{ Z8(efb95d69,6f114a27,eb08228f,b5536120,2b4ae134,539ad8d9,5b30f6ab,111ddc38) Z8(2aeb4aae,d103207e,b2b133f7,11f0433e,434a59d1,05913765,9a597529,b4445270) },{ Z8(72c91199,73399f6c,2c4ab755,4da5f5b0,4e622c2f,62ec3d35,3e185eac,81bddfc3) Z8(6d6b90e8,9d9c53ee,e74fe751,3e73b6e5,4b1a498d,ac786ccf,f7dae915,b5c4c7d4) },{ Z8(4006f8a9,d5713745,2be2d16b,721dc592,34a02103,ade26dcf,99e2b9c0,e002efe7) Z8(f06a5b98,76efbf2e,da395601,3bbc9894,9f0d41d6,3a53f0b0,0226bbb1,b4f9bcf8) },{ Z8(a8140fbb,4ae92cf8,c2be9804,8c19f8b9,fd595376,694150c3,2cd0280f,5b1a4e4d) Z8(6c2d0fbf,6a1bbeb8,db5c1c7f,8406fdde,4974fe3f,fa0b372e,364a834d,b51028be) },{ Z8(f641a4ee,ba070aa1,7c9828e2,76e9d345,5b14a748,b3db3b6d,5d804b74,e8ad23b6) Z8(80f7b8b0,35098806,29d77010,e0a580d9,8f8b7a30,5753847e,bc10cf51,b5ae7285) },{ Z8(2a0c4b42,3726790d,f61b2a70,8b698cc6,4e1e4fa2,d7160eff,140ca7b3,5215df18) Z8(85e8e950,37e63acb,5835239a,8cd14b17,ec8f22a6,dca4cf40,5b1294ca,b45ad497) }}; const mp_limb_t arb_sin_cos_tab21[2 * ARB_SIN_COS_TAB21_NUM][ARB_SIN_COS_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) 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Z8(9f2a8018,61770423,3f4f8063,f5136161,dda87ae5,1c93b4cf,20980571,ed54ff71) Z8(395760ef,21a27ad4,ae85347f,b10b210f,df345326,b354754e,1576c5a5,d7b91567) Z8(8696d86d,07c16269,e61cd462,0c9747a1,a7e0f9f8,d8f7ac1b,8c698bc2,75ada6c3) Z8(ab912147,4bdc7922,69f16066,4c3ee0f1,945c03ea,e2c2253b,a36256c7,07972402) Z8(476c4263,20a2e7f8,6390abe6,611d379d,5ac779a8,f6e2efb8,9cfc47ac,b0502507) Z8(eb3f410c,00e83e70,01989b9f,d1ab1d06,2874e6ff,a6f64f9a,0d55dc43,94ffbeb7) Z8(1b2cc713,52891210,7ef259a1,f9cd7e0a,9489f286,90a7b3df,707073b8,67eb7d50) Z8(6af0edc1,e3d7ff4c,c0aab52e,9e1a05c6,fab4bdfb,b75e84b9,8debe52d,ec150670) Z8(75e2a407,ad4094c5,a73d4f2b,bae254a0,960dcafd,09a88275,e0fe9c25,e3b0e3f1) Z8(5f545f16,5b74e740,1f33c07a,1a80077f,9437fb62,5329e655,5df6de9a,d3150c03) Z8(9ea77159,75d9ce75,3f4ba064,e1ae5385,5bfd83ff,8bded550,27fd19c5,d22dfdc5) Z8(de4b45d6,8f58de60,e18c3aa1,b498d248,04e57a1b,acbc896c,d6c388f1,5439bea4) Z8(bebe8e59,f1467c91,1cbb2c01,bde418ed,19e2e127,bb2fcc2b,5d2603eb,8e28b193) Z8(95bc6bec,2b99c9a3,0a290389,cfb2759f,67fa0196,cccfcf16,af6b4d46,eb2c5f58) Z8(b1ae7846,d02b97e8,84c1e0f4,96ee711f,4a0e45f7,41602038,fb825705,86f62731) Z8(a4b2a421,ccd95f9d,8283e803,a116e80b,db02969c,383c3ab7,342fe205,b609267a) Z8(c3e646d1,fff062e6,5a2928bd,f80466e8,4de215b8,070f7328,4fa69a65,ff800aaa) },{ Z8(7e3d1af6,306e1398,1f737361,e0edd53e,c3b2c911,6eb951b7,82593dce,77339be5) Z8(dedc46b3,fe78a065,29a1f9f4,19182e34,a575361b,0cc235e3,c63b29ee,37172d63) Z8(ecc25c5d,90edabbb,2a1ad5d6,9f8688e5,324ac1cb,9938fb49,d683a12e,39b31ae6) Z8(1f6894c8,a79baafc,670f5399,47760acd,b8711b88,d966d630,fb7a21cb,2f3b9786) Z8(7aae678f,dcfd3d4b,5389393c,8f65e3f1,439f7fc9,b2a716c2,c2937690,0644349a) Z8(814a9296,b437ee90,5d97aab6,11cf9373,15bb199c,11c6387e,f7ecad17,fd9c1287) Z8(fdd5c3f7,78efaa15,f4b43663,6d370f11,513cc759,35522296,67ea06cf,619bda6b) Z8(e88c58c4,8eb31996,7aa3df00,8bbf1ba0,ac316236,9e74b423,f49310fd,fac7d829) Z8(abd1884c,834814e3,8d305e8b,d2e1ad20,f00a35f9,aa4e003a,fd4e3808,c6e3e2ad) Z8(687d53e3,473d7d3b,cdb504a0,9c554870,29045ed7,8eecfe5b,9c5054cc,a7aeabe9) Z8(5f98af21,639ff111,0c74eb09,f5e082be,d4d04a2d,596380c4,1687fe49,31587c86) Z8(b3a0cf25,d9d29464,b07c1169,3defaa77,63965af6,9149a497,08487555,171c586a) Z8(c431c150,2d3c3440,8b7e1f3d,bc9d8a89,3749f89a,b3f0f6d2,6b67ecb2,69df13a4) Z8(7a8f745f,dc6230f8,9f242116,61ddd376,44b8e911,8ddd0266,b5799624,4a4e3552) Z8(c4b699ef,c646f1d7,979d9cf2,38a5ab15,836bcdf0,a4c2fbba,32bff9ce,1f92ef97) Z8(1146a05b,ac6c29a4,aaf430c3,c5f5c19a,28ed8b5c,6ba19947,bda60cad,fc9fb9d6) Z8(0566391d,9e5c45f0,77b2a1c0,669ee14c,a4e4c850,27c6f292,1adeb42c,0a60fc19) Z8(db21f7ef,cdeae791,c393f5aa,e59085f4,501a1007,fc2d1800,2550e41a,17f70103) },{ Z8(717e2dee,8181dd09,4fbe442d,9f7710c4,25197ff7,6b5cb80f,495a19b3,8fb336eb) Z8(ad5fa360,b03f488d,e0350c6c,67389da2,feba6bb4,dc469f07,8bc497ba,ad8209a7) Z8(fd7f504f,93c5c665,4c35b590,d8db2f2b,8ecad7b1,51d59c53,cb60d901,e192f6c9) Z8(46440e95,58a04ebb,5820b109,dbe6f75b,f45d4003,e754dbe0,44194525,172b408f) 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Z8(00b8d279,ee14a39e,89b1244f,569956c9,1abbd0e7,f97ede86,b8bf597b,2d190e11) Z8(37044f29,24cc70ab,d0877263,c56fe8d5,46bdca3e,55483dc1,c4c574f8,91327289) Z8(0398e235,fdb10941,48325ebc,acc692c6,e7d6b6ab,79665e7a,52180adb,75a82d01) Z8(216d7d42,21562010,8b8ecf97,792a17c2,d272a21c,8034269d,e4bbc453,096ca489) Z8(3819c31d,4f420c50,3aaa3746,2af2716e,158760df,872038a3,2e1d98fc,193ef418) Z8(cf9c07e0,8a14d35a,e139c061,0522a6cc,758f3119,d45d8ebf,6ca92c66,2216f6e7) Z8(b1e16b7f,6840b21c,3e1087d3,b8f0d3f6,08670457,f0bd9650,423b6b67,62f8e2b5) Z8(8f320c80,23c9209e,6629b88b,c9ae21f6,2e61613d,e36a6cfb,222e7c37,ab8cde4a) Z8(ad7a1947,c5a6d2b4,e384e189,8774f2e8,46f048d9,c1978c6e,f394f878,9c9d8ed3) Z8(63e9be95,462762ee,76983983,d085c22b,02f99be8,b80fc4c7,d4ac8a7e,c503f211) Z8(df0d343d,58c1b818,f0a0409d,8557f2ce,60a3205f,9623e31c,0827bcb0,9cc4a821) Z8(b2bbfee2,40efc916,b29e78e8,52f47075,9364d504,056260c7,a05d11e3,1a84141b) Z8(6df825d0,092efa4e,1e6eee31,cbcd918b,22a317fd,4a51cc83,ab477ae2,9998c8fa) Z8(31f892f2,d478a67c,2ceda66f,7ddeecc9,3042a8fc,6b4c4b1a,5054eeb6,928c5bda) Z8(044f8786,5a23b635,1cc391d3,8f7cb21d,6967127d,b7e285f1,88305cc1,5953d866) Z8(d517276e,b70ff3ad,973634be,ef29ee5f,93f211d4,6ca11f40,914f1901,7bda4332) Z8(4ad66f31,bb0b7cdf,cb1d9eb7,82c66160,5f5405c1,527c32b5,79c35582,a2759c0e) },{ Z8(72aa41c8,9fb203cf,7298571b,58bd4295,52dbfac0,962c0f81,4075fb9a,80fe6803) Z8(48dcd218,49732822,9156640e,22f61d42,c3409dd6,7191d056,bc1bd3f1,e718a5ef) Z8(625ac2ec,e01263b6,59ac32a6,228c0ee2,748cb89c,ed296aab,8786f98f,210f655e) Z8(bab1b39c,c3c6c160,f4ff7481,c95b27ec,3a17d185,49d839c3,be472402,64314abf) Z8(2e35ecc3,3704b188,27be2bc0,54068d4d,e2e60be9,6bc735fa,faa8c0c1,638b4bc4) Z8(e9eadc25,4bc7c705,a0172e0a,62475449,9736efcc,684c0f88,a1a55bb9,1310cafa) Z8(f6bfb3d2,6f2b86dc,2f9b0c1c,dd1f93c4,32e888e4,69c11bdd,2d09c6b0,335685dd) Z8(fb01afad,e171f05f,c89f543c,139d89f7,8f0b8822,21861ef5,c07cda47,f3614101) Z8(3ff70794,702d995d,7d723fb4,0770831b,52749355,b4bdcb43,1cc21619,c7474526) Z8(f9470fc1,18c59c2c,5fa775aa,5466d2b8,4b0daa10,80aa5f60,6269bfb1,d6dffb6c) Z8(576f7700,6ab267d8,e8aaad8c,9bf2299e,953caa46,3e95db5b,e04690cd,e678b61e) Z8(6890f398,93ee0c2b,70ee01ae,cfa1715b,03e22d67,76942d1f,7d69b519,ed39dd27) Z8(4b49b807,bdfd9a4b,b26a67c8,019f2c2a,5e312275,4f413b69,abf7586a,03ae445d) Z8(9fd9c44c,8c232192,9be7611e,e34b07ad,570940e6,592317b3,176a22db,c6678387) Z8(1316bc5c,3936d6e6,a01fd034,174bcc0c,0246b9f0,1eb4a9cb,28aba4bc,fc90b2a3) Z8(1f4707f7,8dd119a9,ddc90133,2376174e,ad789019,1ad326f1,499cf19d,2b7190a6) Z8(d1b06f8b,122b6b60,8dbe2d11,02336e0f,29d5350a,e9896341,5da0dddd,4676a1cc) Z8(16de6ad4,365389b7,f93655d2,4f82ed4c,981e3480,7c07d28e,ee48030c,c5d882d2) },{ Z8(f7584d16,c902f221,79441dfc,1549088a,d62f96c4,c94c04c3,9c706888,aa6dbea4) Z8(219cb083,75184036,62755020,09229c82,241b0570,c88c813c,377a8bdc,076bbfbb) Z8(14b7b42b,093bc633,5396af98,9fd5847c,37cfc00c,72cc073a,e55ccfd8,051263d4) Z8(6656b24e,4f8021a0,f9360152,530c44d9,e5293e7d,3ae9033f,f27dc100,09f9dd34) Z8(042a2a9a,093075fb,6b86357c,4f357641,33e5edf3,e2e12f08,b38904ea,64d23074) Z8(bef69d49,cbd474c6,0a75d7e7,de712688,55b1bcbb,57991c7c,8e01507b,8feef664) Z8(f111e8a3,759dc600,f0620105,f711c6df,7aeed988,de4134e7,364f50ad,6422c14e) Z8(cdfc1ee0,f55865d0,a9c8e599,4c00da19,3092a183,5bd28923,fe14fd9e,f29a4c86) Z8(ea5bcfd6,2dc5e461,66a1e991,d5ef515b,8b293454,c1efadf1,df97088e,d8dc1c89) Z8(10c06d93,9dc38e9f,1ccf9a7f,cbccf897,0cf65b84,8e5f1281,0e78fac1,ead6a85b) Z8(937f349a,b3583913,4e3edd6a,1d41cafa,a4cd41fa,deb460a3,d9ae0ed0,3a008302) Z8(17aa26de,107b36c8,d50e638c,d7589b70,127b6f53,1aa09e34,b936cf34,f4ccd990) Z8(af43e24f,55673787,a3955ab5,562cbf5f,d7052875,99a69d00,6d8b6197,2206e66a) Z8(58eff311,6d2e172f,ab69ef04,acc07956,d0d13a69,9cbb57f0,dae4cb3b,487eb980) Z8(305fe6c9,5cc9110f,d8a26db0,d20dad38,2419c5b8,886c0911,20474b35,26988b3d) Z8(520d3776,e7a8e1a4,731500a7,4679930c,291c2bba,f1eed1c0,efa4a395,e1664007) Z8(215eddce,6525549f,55430115,ff9d7a6e,72ac7226,1a0fe34d,a9975ce8,4214f8cf) Z8(c6f12a2d,c985491e,e735f8bc,20f7e7fb,f9e24399,e2f3c76e,d9a8dd47,a88fcfeb) },{ Z8(eaaa1bc9,de763a75,13c798a6,cfa29156,2ea80de2,20b6f242,a3ec9d9e,7284b3cc) Z8(09f62682,a7fb5284,851df16c,5145bec7,f6d39dbe,0e2e33ca,c741fcff,4e9863db) Z8(4e4f85ee,5fe3ba1f,93b98c3b,a2eb9d63,5ce31e54,004ac3e0,5079a14c,84cf855e) Z8(0104ec51,7cc3e197,7a693862,5f1f55ab,b50deae6,d8264515,a9b8c109,7260179f) Z8(30ab6920,5b4078c6,5f102123,a6967ce1,1fe4927c,b1bc8977,3c5c5720,f03e07b6) Z8(c65cb58c,49f36308,f04b07e5,57f0f36f,af8d3dee,a857c4ae,09f586b7,d8208c2b) Z8(8f0ba46b,5d2a3875,11345820,5deecccf,d65ea79d,2da5ca60,e01416df,1223a4b5) Z8(047859d6,6fc50ced,3eb0fddc,3656a9f2,41650d0c,2b3b3647,17c5cdb7,daa2832a) Z8(839def48,5e075cb8,a91dd93d,97db7162,23eae84b,a5adc77e,ced34a63,940e7c4b) Z8(91582da7,2a909a07,f4cfdae0,b5554ea9,c21d97fe,14e3e2d7,f7e8d1a7,b4a4e017) Z8(92d41587,cabbc49e,c785e823,157b0273,f3e9b93c,8c32e17c,f67e464e,c374cdc9) Z8(4a81efe2,955278e7,64635805,aa0a5d71,346c9bc4,1084f03a,de4eabb0,8f792bed) Z8(dd1b163a,1d92c613,5d57b0c9,73908bae,73c86030,33206ea2,72e6343c,ea4438e5) Z8(5e5b27fd,14eae6c7,d6b05a55,bd0caf33,0522a926,ccbada42,5696dcf0,4a5cd73d) Z8(84f7ff86,0eaa3926,e5d9f74a,7805fa5d,87131de0,9e4384a4,2311ed73,54a416b7) Z8(8c3b7fe8,b3d03a08,5ddb2b2d,53093eec,61521ba8,85079f3c,dae799cc,55fc77f7) Z8(6db6a625,4148ab97,27ed8b40,9e2eb1dd,e2f2afa8,fb6290b1,4361b8cc,9660116b) Z8(7de9aa6d,7a48a6e9,4356fb50,ebcb8bed,b90cb15a,ba37a3ee,8b6ae710,c0ac518c) },{ Z8(8146ef86,1e21b0dc,94c239d9,623028c9,ac786783,be3796c8,440729c5,d45214a1) Z8(1081f102,88d48b28,3fa8beb4,fbed0e70,9950a057,44a6512b,53fd0174,41b9a64d) Z8(c015231a,718bcf5a,6a02369f,d6282f4c,c62db523,34350b99,fad983af,8a0cdc41) Z8(8dc6c5c6,de938b26,28814d70,83f9f67b,ef2657d0,6f0634fd,69e5ce84,c92c78fa) Z8(a4050f2a,96922b50,b6cc64aa,07c3c387,60fce5eb,03bfc115,7248092e,4421b282) Z8(db44a9d6,5101b96a,856a916d,7ce2d831,276a2e3d,9319571f,2cd6b8a8,3f559bc1) Z8(95a29215,22e5433e,5b4a21f3,25fc5a3b,f657f56a,43fc92f8,bf62a7a1,50b6d44f) Z8(47c37a9d,0372faf6,aa6181be,dc7c451d,10acbb5a,4efb18e6,5b572710,da1eed73) Z8(8cda5bde,3eb68632,e9000f08,b03b2b7a,b376b138,2e9915d0,6b13fed7,8e2ac220) Z8(579c696e,758d0bd1,3490dc1c,0dfd46de,82784e52,aff26b40,a42d0fdb,a8b1cde2) Z8(72b4ab24,7589b939,7b6f83b2,a4848d27,73c6f602,d0f83096,72fed717,e49d90a9) Z8(01b29481,802c4c4e,4211755b,28421097,4f3f9b27,afc857ff,1a6997cc,2643b076) Z8(bab6556c,cc49be09,f0d6011b,c5a2b785,346b867c,002920f1,96eead01,c7e4e3ee) Z8(15b65fbe,6ef9c4d4,9459d0ce,635b6f39,0e987bc6,af4964ea,93a037c6,80148dbd) Z8(2aaaa784,5c8f6855,2b7bd8b9,2d7fa7d7,cf257516,2d946de2,4e6beb47,d3042a20) Z8(8b6899b8,cfc6e9e0,e76d4989,ffc3c398,e64d7717,af419799,baa33593,988fd59e) Z8(f5459f68,b53cadf4,06f81956,e7c8e051,27e858ee,ef13e9a8,a6a40f98,0a971a49) Z8(cd044cb1,7533f532,646425fc,476747c2,f140a488,966e1d6a,fc786b2d,ae7fe0b5) },{ Z8(0a4d46f3,053a6f92,63f7193b,c8fc3cf7,ec20c825,ba9b6b4a,83a0e662,c7a8a3bd) Z8(ed9f5064,5c84708c,6141681d,9391c70b,98265a57,7fb2563e,13952c30,155299bc) Z8(2042f165,0abd82d4,527cff24,c3a77dea,8fa224d7,9fcfbbd9,8884e95b,9627d11a) Z8(140fac51,d4a637ab,e7b34121,29959997,77757122,9a05d2bc,4ab5cc04,4988b9cb) Z8(bec6b81d,d0f88e68,6c1fb45a,2d0ffd4a,773ca5d3,aba196ea,f184954a,4223581a) Z8(d53fc8aa,320b2554,7a0b722b,8db9e36d,7f507b2b,7ec19166,14e221c2,f82ac027) Z8(4e1713ac,bc45ba04,2a0e32d8,ad6414c3,53d3e2ce,0c7116cd,3ed8700f,e5b64cd2) Z8(4b76aa52,803182c7,75d8eee1,cb0320a3,3b735c99,638ac7a2,a1576b36,a769f620) Z8(a8ab7d9b,06756c7b,49d48083,3eda1e85,09efccc4,2d84e559,c191c446,f9edb8fc) Z8(8dd703b4,9c537e22,6e64fcce,4819e217,b676a260,b43d6216,4b028e6d,0fa0280c) Z8(434cb844,09e535ab,273f87bf,a1a1bca4,d7adb95b,68075b88,54d5f6a7,47824569) Z8(ce76d5ad,6f306378,0a8c5a46,fcf01054,24783339,b396bfab,416e64cb,5e1cfab8) Z8(d11590c9,ee2a2ac8,4bc91bfc,38b91773,98c4b344,30891746,ff67184b,9a7bb115) Z8(b25f8b0e,582006c5,ce2b0da4,dbe46dd5,01dafb04,6509c104,107c00cf,44f065e5) Z8(e25903ed,560d0916,21f76bb4,ea5c6808,c92bd72c,b7c6323b,610fc749,c98b64d0) Z8(1587b4ff,61fb608e,4a1b4868,ebc25092,75e04249,420d95f0,37c8d3ad,03bbc7be) Z8(8c9582b2,94980cc7,5304c25d,1fa13c55,d8e7df66,cc891f2d,d069f9b5,106dbe6f) Z8(e35575c3,e4aee845,0e7e44e6,e0bfb8f2,b9d993b4,c151839c,a908f73e,bb4ff632) },{ Z8(fced3a0f,73677216,f37a50a9,e6695f15,4624fae8,5b5dbe47,1fcb5803,1b618f2a) Z8(44748b8b,4e422175,d610c7f3,481937c8,aa2fc15e,f2a754f7,b335eb6d,94d0bcec) Z8(42853eec,96281e02,bc1a8adb,0e126ae4,7b45363c,86241398,6cfd0947,bb064960) Z8(e8cb845a,ba927717,cdc91aab,450bdfe9,ca254e12,24fb7ebb,2f51dd96,a527b371) Z8(d6e80d1c,e4c150e9,56e6c8be,0634ba41,9a21e798,6412cdd2,8c11784f,20a647f6) Z8(765396ef,7fa6f231,35121b53,81df0464,1db74c5e,aaeafceb,d39812d8,68e4b744) Z8(863ffe20,8ec917ea,c7b8096e,d5ab3930,8ae89c08,2e60d986,de336329,1f59adef) Z8(ee0d65b5,0fe00c04,209acbe8,7ca1179d,9a922749,c5850c77,242a80f8,2915180c) Z8(a632ebeb,110bfc7b,9b7b9e2c,f5b6c47b,44286c2b,5bdc8b25,506931c5,a28824d3) Z8(bb9dc8d0,2c67480c,c36e94e8,1cc3f53c,54e523b4,8c3d033b,cbde12b8,65c9087a) Z8(bf65b70b,cf607731,5b4059ae,56e00b0c,fd3d2993,797cc00a,8663963d,f4b6d78e) Z8(afcb1316,b5d50883,2dd1f440,28e01507,caacaefd,84afec08,d3d9266e,f9a4e2ab) Z8(3cee5f18,107f795d,cd38e678,6a0006a8,a79954b1,86693808,d42f67d3,c50addf2) Z8(7c54858d,e006a1b0,c4ac0e7a,af271db5,40213653,e7bd897e,e5a3d995,c2cc42b9) Z8(140314d0,2ba9e707,6186e48b,619e024e,caabb84e,c1557feb,e302502a,12d40ff5) Z8(a45c539a,86433a5b,fcbe505b,560cc7ca,abad4678,2824f2d8,089039d5,7373ca7c) Z8(efb95d69,6f114a27,eb08228f,b5536120,2b4ae134,539ad8d9,5b30f6ab,111ddc38) Z8(2aeb4aae,d103207e,b2b133f7,11f0433e,434a59d1,05913765,9a597529,b4445270) },{ Z8(55c52d9b,2079293f,266bccbd,995de7ad,49ccdbfa,1a909571,c7c27258,2b7c55b6) Z8(68e6e000,35cefd5f,42673e65,b37174b6,61fc186f,2073140c,86ebc13a,cf9ec9b2) Z8(2a242841,eded5651,78cdb97e,cb2c4a14,1f58f98a,51bb3bff,3e06b766,f63baa4b) Z8(b5a04397,c1db6437,ef4463c5,a9cea0cc,90aeac4f,2c49133b,aa41a566,e6666420) Z8(0c993034,8c6fe4b8,2949592e,133ffd5c,5e9d1767,9b370b6b,a895ff88,00bf9512) Z8(a43d36be,ef0954d7,4b9cc316,ce3dded0,dd05e790,6830b134,1c3264af,e45f8e45) Z8(61c06257,894d833b,7efd7967,503148da,cbe786b7,6f2204af,479fa7bd,325294e6) Z8(c847cf24,952d8577,8caf3a8b,6087ef81,589b3077,af032009,a2563029,31570933) Z8(fc2c2331,836a09de,4286198a,c91079f4,8b48ca43,45f05078,9c669b00,be0cabb9) Z8(339ea3d5,f44277fa,2c58e1b2,cc7db996,4f763bb5,aeff479b,e05d6d65,737d3847) Z8(08907b9b,488bed29,7607d91d,0a66b840,48718e94,9c642786,94d49441,de7f33e1) Z8(602dd604,f66a5a2e,fcc461b2,644f3463,32ade9d7,ca4983dd,6d4b1494,07f139b9) Z8(6901d476,0b073c68,643749df,a4c5b89e,db6a49c3,c5a04680,799585f9,fba170a5) Z8(ff58729e,a7a24cc2,4f2af059,4281c9bc,a9f6f666,d22d4e06,87314c18,9b2269e1) Z8(c8dcd584,0eadb51a,90ee9223,bc139a86,366cea4a,01f4e5c0,ad20f6e4,ab016631) Z8(b1571fa9,023600ee,6f3cc5b1,9e0793d8,05f49514,49244449,e7dc3024,dbe3c930) Z8(72c91199,73399f6c,2c4ab755,4da5f5b0,4e622c2f,62ec3d35,3e185eac,81bddfc3) Z8(6d6b90e8,9d9c53ee,e74fe751,3e73b6e5,4b1a498d,ac786ccf,f7dae915,b5c4c7d4) }}; const mp_limb_t arb_sin_cos_tab22[2 * ARB_SIN_COS_TAB22_NUM][ARB_SIN_COS_TAB2_LIMBS] = {{ Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) Z8(00000000,00000000,00000000,00000000,00000000,00000000,00000000,00000000) },{ Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) Z8(ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff,ffffffff) },{ Z8(370d0dbb,d133d2af,293f7660,41e6d1e0,3fd9988f,ef7a65da,bb5ab0cc,58f10d37) Z8(196aca8b,c62227a0,9b63185b,00a7cd98,19c8d7f0,35b3b678,8ebe6c24,fddcaaf9) Z8(87ed9056,cadfcac7,27b89df2,5ee474a5,e23fef08,cc39d58f,9afef193,715ca371) Z8(a6ea982c,ab6c35bb,1dc09422,50e88862,60d5c943,a70a47fc,c40034c0,e9e27117) Z8(ecd40cd3,f4fc351e,e054beea,0b4e7847,cef43bb3,b0a54a59,b02e604f,b3ddbc1f) Z8(204ce260,9efaadc1,25ddcf5e,b0836434,fc104e98,cdb73d54,06ead7d6,9cd83f53) Z8(eb156721,6abde0e6,06a4e3d6,43b5daae,441d8598,1dad0bb4,3791885a,ef90f16c) Z8(7bc256b8,deb9ac6d,b865b6dc,1939d5ca,c82a5a16,71fa50f1,4ad21c2a,bba8b41c) Z8(4cc06a44,2dff89d8,1578d90e,cd0833ea,efd9e91f,99a92841,2465bb99,7fc15d08) Z8(bb14e72f,f8b556db,b768057c,6eb27835,6552d95e,efe9a77e,42629efe,24d4c293) Z8(df89adfd,1726b1d9,e26ac62d,f7064fa9,0351da06,a820f727,a38b2408,b2c53a09) Z8(c9db9024,1e42f4bc,b723cf34,2e734481,d6f1e198,c97f9d1c,d9a5784b,9f51a9b2) Z8(9b578483,2153ad4a,47c08884,bf3cfdcf,1f397f2d,d0167a11,6b9c78ba,5065084e) Z8(cf8445f1,e90dd1ff,b3442520,8a5a4eab,a172dfa3,970d3618,352d2816,282cf9df) Z8(30e3d8c6,40af04b0,80fd8a20,9df6ec49,05453097,2b56558d,545de355,95609223) Z8(0018c1d0,4195be37,94e6d7e8,b9fb06bc,56cc89b6,1980f945,a033e3c8,cc347db6) Z8(78f33770,541a5b9b,cf786c4c,5fc14621,6abe2f10,90736720,4c533f8a,247a7949) Z8(8b0b60ae,da38f350,4f4348a9,7ad79ced,9db5698f,dddda9da,555555dd,003fffff) },{ Z8(7e01d160,8c2baa1b,ea2e971a,924d8012,b0fd9af6,24a61dc5,2e93fae5,91b6e434) Z8(7174e535,a9a51a76,d7a55dba,d8753355,00c2a6b8,482cef0c,5c4f508f,94e15efa) Z8(4e8d03d6,adb5ddf9,7839b1da,d1d52495,924e52bc,bda48b7b,a1fd8e80,0605265d) Z8(6dcdfd10,796eee9f,30a2c491,0b7a2616,4a01e13a,856b8b77,ca5c61e5,77fe5ce1) Z8(333a7443,569753bc,f16b29f9,0bafb325,a7516313,302b0d10,88aaf76d,f1a74f0a) Z8(7501a20f,c477cb51,b3f36f5b,553198fe,d4077777,53e1fdc0,9d98742d,74b2598f) Z8(0b017caf,3bb28410,e23e29d0,a75eac1f,68d0f715,9aab33cc,8f6af827,b3830188) Z8(1a283d2a,8fc68f6f,5c5c9daa,476c9e26,80ea38ed,0e2e52dc,1d5709b4,a3307a04) Z8(0ccebd55,e5fd575a,eb2af906,e60c3325,e1261516,6ff9d168,48e43c7a,218b8cec) Z8(8bad869e,773d8e88,c4784a1f,fbebbc6f,805b8591,46c9383f,2e79b290,56981513) Z8(1f880e0b,3cef1bf7,ffd45881,1bad0c36,00cc2276,fb9adbfe,44e18d5c,846c8dde) Z8(d4671611,6ae5cad4,f22ac6e9,25a110e7,8c15b58a,66a64e77,8ae8c517,863026ad) Z8(12d2fe3d,ef0538a1,e85366a4,c13496f5,5f38c369,46f2416e,eee8efa8,3b1f4639) Z8(61a00174,4cf4d454,731cf33c,19e4151c,12a5ba52,62b5c14c,8652ce6e,613ca3d0) Z8(b7a89315,cf78da75,672013cd,04bb6006,d6014f31,774dc4a4,cc1858c5,01b31089) Z8(f556eba4,6f881f68,5bebf492,2cdff950,6e353b24,52e5d955,5aacf241,f3683b91) Z8(a43b3321,786d5656,2638f6f6,ce32b63d,f29d77c3,3ce4ca6b,f1606a99,249478c7) Z8(218ac62a,3b56be83,959fd08b,7067c57e,9a69a650,a4fa4fa6,000aaaaa,fffff800) },{ Z8(b8403cf9,59492746,a3fc925c,98a2d108,3393d104,33ca9ea1,3916d291,cd7592dc) Z8(15400b44,8127c82d,d604db6e,f31de919,3c6010a3,c4606cf3,f2b4905b,b2fcd8cc) Z8(94b2efa1,7db51491,b6c05e21,e08ff0a9,f87a4dd8,630d587d,99a06095,e5d92ab6) Z8(0eb7f022,bb701754,cbe96eb6,742b8337,2665e2e3,ff8bfbca,4934ffef,1b5864ea) Z8(dc40e984,6655281b,05ab8352,26fc716b,ea584194,02b24b4d,79ededd2,d2755fb7) Z8(64b8eb7c,5ac77d2d,6f4dba8d,bb544f07,df4ddce3,e0790fcd,af2a7725,0bca5906) Z8(d981e911,7751548b,bdd32701,a29a875f,56b97f40,97b53a5b,24a2b0c1,f86588bb) Z8(dff807ea,1e001421,b49d2d0a,21591d79,1916dd50,c039759d,26ae3c9a,6d3ea427) Z8(eea05437,0f6b6e06,8a82e4e5,8c2943f5,7211aa7b,f9a61a45,acb9dcc8,b3bba369) Z8(069ad198,47410694,d710a819,691381b4,10f0da94,728411a2,7572776f,d37da6b7) Z8(73f7abc7,4cd10511,162118c7,5f6643e6,fca179a4,180aa255,dda681f2,11ce00ae) Z8(7267e588,01d01117,419899ee,dddeda31,cbb86aab,b923bc22,e2926b11,1e9ca5cf) Z8(8a442cb7,a1fdd976,18cae98f,06e7098a,37e76e75,89f23f0a,5876010c,ddc0259c) Z8(a86094cd,8c547a5e,d68056b8,a75f5c4e,8c5870b4,1daed039,096d40c7,2fd1f89c) Z8(073559bc,06427156,b6429d2a,41051985,b7126c57,691a4111,bfa3bb13,0477f492) Z8(e2fc83b4,a3856fee,c7f8f950,b4e1dc3d,cf5cabbd,73a2004d,cc5f04ee,8c603843) Z8(d586e1e8,36f73cf2,8ce764d3,bed5a942,e5a1f7a0,7a2b9bfc,76ad2efb,f813d949) Z8(8f5d3f78,521a69e0,b574f652,9dc026d3,b8d7ff39,bba1ba1b,aaaabbbb,007ffffa) },{ Z8(7748a6f3,54ae9cd1,9fc02d0e,5b252e65,43ad733c,4d3e1ec2,f0f1df98,aea5a2fe) Z8(f90eea6a,87ab92c7,06143123,cb33e447,ccc229d3,1af3afe2,3a762420,0bf6e2c1) Z8(e6326408,4f51875f,7b99bde3,43f7486e,e4d1b2d9,90e2855f,5e9469c5,fbd9eb10) Z8(825372db,66cc8790,8f50d40a,8fb44d25,898db129,7d2d8bf5,40f4b5a0,0c24e8a7) Z8(c32580ed,9dbea8d0,99057e43,af54a33a,8a049ad7,76ab19b5,a2439c63,f0b2f899) Z8(468cbe03,35af469e,41f8335c,8c164cfd,00e95f73,d3072c9e,b22f8a37,a2b745be) Z8(87846e40,10a79463,f9e4190d,02d196d3,feb3c960,847d82e5,c5019dc2,8d43e048) Z8(78de10ad,dc83fd38,43ec9c28,30170e16,0c539e65,dd793965,985d2375,0f58b6f0) Z8(f07c121c,1dd341d3,8baaf5a7,464bc351,7a4cdf97,9cba4e88,38d19f47,95c5b900) Z8(1a06bf4c,bad2a45e,35bde4ac,8e6941ca,c5499d8a,d47b0227,194d6579,39b6ea2c) Z8(9ba75f17,b2c0fa1b,17cb6891,e21f76a7,9c4d65d8,f8a427e4,9ba94020,93ebb975) Z8(17e2d921,41f6a291,75855735,5f172c57,27d4d614,42a0971b,0297fb8e,5b315551) Z8(d2862c2d,24e4c0a8,e575e389,2690ec07,95cb4f57,c6a3576f,ce6a51f0,d384c264) Z8(fab24def,7c4a7aa9,e9d3529b,de91c0ca,24e75625,5659d422,34f2001c,808b6d93) Z8(0d73c947,72ab9e48,83c0e9f3,de7b2ee4,aa7a61ec,4df3d374,e62428c0,a03795f4) Z8(f5c8525d,0f8e5a53,c1ace188,2a7633ee,474bbe68,d1e9e3a4,d9c9454a,dc506239) Z8(267301f4,58e7d5bc,64f6761b,420f2eec,4d7a6842,69678391,5c7fd885,72c23b20) Z8(f3ed34bc,77280380,64d2d641,eff69abc,ade9b6c8,3e93eade,00aaaaa9,ffffe000) },{ Z8(e8bc7449,34367665,ebda10af,96191907,9875c971,ef2a7d2b,351acf73,b6fd5957) Z8(19b803b8,4e9a9870,a20f171e,1169a751,9b1e71fe,d0d3bef0,6f13c4bc,89eea4c7) Z8(15642ea5,3006b1ba,b6208140,9a9ded53,f7707705,8a0239e3,274b1eca,144c5e4d) Z8(b9e7a938,dc62d5f6,1a2bd09e,d921ecd8,6aae1e27,8395b24c,702556f3,0c6ab967) Z8(02f78234,2a4ee510,ba43a9e9,87f35503,ff74887b,f9b47659,970b9c49,13934c77) Z8(5da154f0,f77cf547,fd728bc4,f17fb420,7e0d8454,9742d987,dee7e723,589a9502) Z8(daf3747e,f6baf4df,a22ff49c,2d18a868,c47ba0a3,0f8161c9,1cc1c763,28ddaf72) Z8(be93ec20,affb8983,e36c6d3f,432edef6,25b8e98f,94fae5af,b4762b7f,a1d9056c) Z8(0bce268f,3c3f55b5,bf638fb8,0bc79005,d24de3b6,bff33254,3f35ae1c,054132a9) Z8(e7c28112,f26a27b7,8bad5c45,6301bbfb,31300d05,be99abb8,cb844e6b,69cd2eb4) Z8(4c1f8ec4,48a6a8b1,a01c89a0,1c0596c4,78fabea0,fb1896f2,77fbe917,c28b4d79) Z8(da4deae0,f7a3a396,a9b6b7bb,f2120c7a,5210f19b,01f8fd5b,15350496,07a9cab5) Z8(56c219fc,0dffd9b3,5fdfe98a,9e9b1194,5e0fc10b,0d322877,f8792962,a5a8eeb8) Z8(5da52fa7,30192382,ece5fd02,203e7e65,d81a02e2,552ce3f8,2f50f2a9,5e80751c) Z8(d50126c7,063b8f01,3877db14,2b55b49d,f527a81c,7aae9902,acedf552,345f51e6) Z8(bae60ae9,af5c5c27,575d6bcd,3da8b2df,f66d310e,bf076ad4,9e1a0ee2,4264bfde) Z8(7506a5b5,3d438ab1,df9414bc,a27ac426,a558d4b5,b0522a7f,7edffaf3,86ef829a) Z8(4620ec5e,013de67f,54a8e0b4,92916d53,95f15a8a,97dd41d7,00008199,00bfffee) },{ Z8(0bc5789c,5a1c70a6,66ba25d1,904daae1,7f1af3a2,a6824c94,d2afc156,8ae0cd0f) Z8(aac25b86,99086514,251ff782,2b7e1c57,61c49cbe,4d221c93,b4e6654f,a38b68f0) Z8(40b0c40c,0c05714a,798d9ec9,da087e15,5fcb9076,36a6399c,83bab7ee,ef5a4a32) Z8(957473d8,9cd0c502,11b47c1c,6d9e130d,fdeacee1,49fd9107,930f3f9b,e88bbafb) Z8(a2b24e3b,35070a52,fe03b7f8,512ce54e,fee4e660,b857f05e,c5af1154,7ab958a5) Z8(f0b49864,10c2212c,1eb1d1bf,2edb32af,6c8e5eaf,d1cf2704,ac24b38c,3e36f38f) Z8(c1d7d826,a605af57,0923d3c2,4a63c25b,ac10735a,9cb1f4a7,d2367645,af9e81b5) Z8(7b7f9131,8f8c5083,1f384078,089fd245,5ee98bc7,7b7dacf9,d86f676e,7430ce5c) Z8(9e1b171a,4d87ad0c,f98c307d,f39ca5bc,646585f5,d5b62884,6878dc7e,0f2eaf89) Z8(631c8edf,87aba042,478d2633,42d2642d,fd54fce8,30bbe038,c3002e8d,80c390d7) Z8(678caf32,8c22e158,87780ba5,50220857,fcd87257,ccc4fd92,fda08a8a,8a2fb609) Z8(fe89755f,793938b1,040907bc,6e9c30fd,807d1412,3921c98c,afe37b21,c7025973) Z8(f27cea7b,8eeebaae,e07c2630,22bdfd0a,e883bb00,be0b324d,15065158,b5e54cc1) Z8(1669f01f,8a845674,16acdf97,d9876386,ee1948e4,9df1e68e,7d282342,92296d85) Z8(98b8bc07,1a7f19da,1f0a145b,0826e888,393468c0,09a6b316,70725193,c90eb4c9) Z8(99167b4c,c3e0d245,4b4df671,c1672008,b8175879,641b799a,6617b259,9d5dacda) Z8(b90824eb,0648d5e1,1c9a4ac9,58d7f79b,fd106c29,143f347b,667c4285,95152607) Z8(28d7483f,d9065bf8,8852eb83,9350fcfb,070dce43,ccccf675,035fffef,ffffb800) },{ Z8(d379d4f2,7d6ee2c3,60eba55f,3104dc97,a6f4f97d,b0479229,f4891e01,10afb56c) Z8(e84d11a6,e698b668,535042c2,d18db85f,e76557d2,9e3decb0,d507eae3,a9b06d81) Z8(fe4dbafb,18e4f25e,c9043d08,b08e918f,1874524b,fec3ff9b,743213b5,c0795288) Z8(d4edf2c6,29d573da,ec07d2a3,74503f45,f04e93cd,08ef672b,8afa93ef,469593df) Z8(1a3242b4,0caf6168,8993eb7a,afcfca79,cc207ad4,a0a623ee,66a718b5,0ac873c2) Z8(fc6d7172,f114bc29,c8fd84d2,129bdae2,84ecb14d,3c18b93f,a5847540,a92ae8b0) Z8(0ecc4391,33182948,aaab5a3d,e5a0f29c,4eeb0521,97cd2992,b5e4222c,01ce4397) Z8(f9fd5e02,84f2ab17,53a1d200,cd925400,ef81a2e7,665a1e61,0e944094,542b913b) Z8(ee90787f,e374acb7,556c4c8a,f5ff29a2,8cfb22c9,f93e7f02,c785ea9f,af0f6021) Z8(aa213678,d149325d,4bb225ee,fdfaedfa,80b09588,61b10d62,68a060a6,b16acee6) Z8(1523d2dd,9cfd9c2e,4e270948,bdf6a68b,6c64d15b,7a8f75fc,4ff8d59a,d16bb654) Z8(c339250a,e691ec0b,5b926a68,1836f3d6,502a3b12,7db020ca,87eac12f,ef1454a9) Z8(4f3b93f3,83d3f535,3a5a9abb,ef63b1e5,8156ab65,f02388cc,b6391642,d5024d2b) Z8(4357dd3a,c2726045,d4605fca,2482a424,6ae33f28,077c1143,b760a707,a48f16f6) Z8(aa4c4ff1,e6db3644,9a0d2450,8f3c8c64,4e330b9f,af5db8d3,f58638a7,70153c77) Z8(48927f69,4f111940,c1e8c4db,c18685a6,6f763f7b,49147aaf,887096d1,d2500397) Z8(c584231f,42c62544,77e886cc,aa20f9f8,fe4f25a3,210a5354,2c1d4109,1721956d) Z8(e9e36b4d,c4405259,25cbf0c7,20e25319,b26e498b,6a76a798,55577777,00ffffd5) },{ Z8(a525ce04,08dbedaf,7b19cb49,027b64f5,4ad6470e,10ad730e,10b1460b,3d79d8db) Z8(1ca3ded9,a32ab1b9,c1dd7af0,7c0095db,26957436,ad400174,3993ca07,9ac315c1) Z8(5d2ffde4,2c145796,adfec139,257e5769,2a1452ab,fbc877d5,4e6f985c,ecb350a1) Z8(a7753d8a,ba6004d1,41674415,d71a4d69,d2c7f624,39dcd12c,4cf5d32c,04e1c1a3) Z8(48e3bc31,365bf995,d92713a1,4d7a66cd,91c76350,d64d9c8c,e973a90b,cee0a81c) Z8(13f93c89,2806c058,753bf848,6ccd274b,f70d0f09,bfedeb00,1a5378ea,eee68cb5) 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ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void _arb_sin_cos_taylor_naive(mp_ptr ysin, mp_ptr ycos, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N) { ulong k; mp_ptr s, s2, t, u, v; mp_size_t nn = xn + 1; if (N == 0) { flint_mpn_zero(ysin, xn); flint_mpn_zero(ycos, xn); error[0] = 0; return; } s = flint_malloc(sizeof(mp_limb_t) * (nn + 1)); s2 = flint_malloc(sizeof(mp_limb_t) * (nn + 1)); t = flint_malloc(sizeof(mp_limb_t) * nn); v = flint_malloc(sizeof(mp_limb_t) * nn); u = flint_malloc(sizeof(mp_limb_t) * 2 * nn); /* s = 1 */ flint_mpn_zero(s, nn); s[nn] = 1; /* s2 = 0 */ flint_mpn_zero(s2, nn + 1); /* t = v = x */ flint_mpn_zero(t, nn); flint_mpn_copyi(t + 1, x, xn); flint_mpn_copyi(v, t, nn); for (k = 1; k < 2 * N; k++) { if (k % 4 == 0) s[nn] += mpn_add_n(s, s, t, nn); else if (k % 4 == 1) s2[nn] += mpn_add_n(s2, s2, t, nn); else if (k % 4 == 2) s[nn] -= mpn_sub_n(s, s, t, nn); else s2[nn] -= mpn_sub_n(s2, s2, t, nn); /* t = t * x / (k + 1) */ mpn_mul_n(u, t, v, nn); flint_mpn_copyi(t, u + nn, nn); mpn_divrem_1(t, 0, t, nn, k + 1); } if (s[nn] != 0) { flint_mpn_store(ycos, xn, LIMB_ONES); flint_mpn_copyi(ysin, s2 + 1, xn); } else { flint_mpn_copyi(ycos, s + 1, xn); flint_mpn_copyi(ysin, s2 + 1, xn); } error[0] = 2; flint_free(s); flint_free(s2); flint_free(t); flint_free(u); flint_free(v); } arb-2.8.1/arb/sin_cos_taylor_rs.c000066400000000000000000000131261264125401100167300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* See verify_taylor.py for code to generate tables and proof of correctness */ #define TMP_ALLOC_LIMBS(size) TMP_ALLOC((size) * sizeof(mp_limb_t)) #define FACTORIAL_TAB_SIZE 288 extern const mp_limb_t factorial_tab_numer[FACTORIAL_TAB_SIZE]; extern const mp_limb_t factorial_tab_denom[FACTORIAL_TAB_SIZE]; void _arb_sin_cos_taylor_rs(mp_ptr ysin, mp_ptr ycos, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int sinonly, int alternating) { mp_ptr s, t, xpow; mp_limb_t new_denom, old_denom, c; slong power, k, m; int cosorsin; TMP_INIT; TMP_START; if (2 * N >= FACTORIAL_TAB_SIZE - 1) { flint_printf("_arb_sin_cos_taylor_rs: N too large!\n"); abort(); } if (N <= 1) { if (N == 0) { flint_mpn_zero(ysin, xn); if (!sinonly) flint_mpn_zero(ycos, xn); error[0] = 0; } else if (N == 1) { flint_mpn_copyi(ysin, x, xn); if (!sinonly) flint_mpn_store(ycos, xn, LIMB_ONES); error[0] = 1; } } else { /* Choose m ~= sqrt(num_terms) (m must be even, >= 2) */ m = 2; while (m * m < N) m += 2; /* todo: merge allocations */ xpow = TMP_ALLOC_LIMBS((m + 1) * xn); s = TMP_ALLOC_LIMBS(xn + 2); t = TMP_ALLOC_LIMBS(2 * xn + 2); /* todo: 1 limb too much? */ /* higher index ---> */ /* | ---xn--- | */ /* xpow = | | x^m | x^(m-1) | ... | x^2 | x | */ #define XPOW_WRITE(__k) (xpow + (m - (__k)) * xn) #define XPOW_READ(__k) (xpow + (m - (__k) + 1) * xn) mpn_sqr(XPOW_WRITE(1), x, xn); mpn_sqr(XPOW_WRITE(2), XPOW_READ(1), xn); for (k = 4; k <= m; k += 2) { mpn_mul_n(XPOW_WRITE(k - 1), XPOW_READ(k / 2), XPOW_READ(k / 2 - 1), xn); mpn_sqr(XPOW_WRITE(k), XPOW_READ(k / 2), xn); } for (cosorsin = sinonly; cosorsin < 2; cosorsin++) { flint_mpn_zero(s, xn + 1); /* todo: skip one nonscalar multiplication (use x^m) when starting on x^0 */ power = (N - 1) % m; for (k = N - 1; k >= 0; k--) { c = factorial_tab_numer[2 * k + cosorsin]; new_denom = factorial_tab_denom[2 * k + cosorsin]; old_denom = factorial_tab_denom[2 * k + cosorsin + 2]; /* change denominators */ if (new_denom != old_denom && k < N - 1) { if (alternating && (k % 2 == 0)) s[xn] += old_denom; mpn_divrem_1(s, 0, s, xn + 1, old_denom); if (alternating && (k % 2 == 0)) s[xn] -= 1; } if (power == 0) { /* add c * x^0 -- only top limb is affected */ if (alternating & k) s[xn] -= c; else s[xn] += c; /* Outer polynomial evaluation: multiply by x^m */ if (k != 0) { mpn_mul(t, s, xn + 1, XPOW_READ(m), xn); flint_mpn_copyi(s, t + xn, xn + 1); } power = m - 1; } else { if (alternating & k) s[xn] -= mpn_submul_1(s, XPOW_READ(power), xn, c); else s[xn] += mpn_addmul_1(s, XPOW_READ(power), xn, c); power--; } } /* finally divide by denominator */ if (cosorsin == 0) { mpn_divrem_1(t, 0, s, xn + 1, factorial_tab_denom[0]); /* perturb down to a number < 1 if necessary. note that this does not invalidate the error bound: 1 - ulp is either 1 ulp too small or must be closer to the exact value */ if (t[xn] == 0) flint_mpn_copyi(ycos, t, xn); else flint_mpn_store(ycos, xn, LIMB_ONES); } else { mpn_divrem_1(s, 0, s, xn + 1, factorial_tab_denom[0]); mpn_mul(t, s, xn + 1, x, xn); flint_mpn_copyi(ysin, t + xn, xn); } } /* error bound (ulp) */ error[0] = 2; } TMP_END; } arb-2.8.1/arb/sinc.c000066400000000000000000000052661264125401100141370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "arb.h" void _arb_sinc_derivative_bound(mag_t d, const arb_t x) { /* |f'(x)| < min(arb_get_mag(x), 1) / 2 */ mag_t r, one; mag_init(r); mag_init(one); arb_get_mag(r, x); mag_one(one); mag_min(d, r, one); mag_mul_2exp_si(d, d, -1); mag_clear(r); mag_clear(one); } void _arb_sinc_direct(arb_t z, const arb_t x, slong prec) { /* z = sin(x) / x */ slong wp; arb_t y; wp = prec + 2; arb_init(y); arb_sin(y, x, wp); arb_div(z, y, x, prec); arb_clear(y); } void arb_sinc(arb_t z, const arb_t x, slong prec) { mag_t c, r; mag_init(c); mag_init(r); mag_set_ui_2exp_si(c, 5, -1); arb_get_mag_lower(r, x); if (mag_cmp(c, r) < 0) { /* x is not near the origin */ _arb_sinc_direct(z, x, prec); } else if (mag_cmp_2exp_si(arb_radref(x), 1) < 0) { /* determine error magnitude using the derivative bound */ if (arb_is_exact(x)) { mag_zero(c); } else { _arb_sinc_derivative_bound(r, x); mag_mul(c, arb_radref(x), r); } /* evaluate sinc at the midpoint of x */ if (arf_is_zero(arb_midref(x))) { arb_one(z); } else { arb_get_mid_arb(z, x); _arb_sinc_direct(z, z, prec); } /* add the error */ mag_add(arb_radref(z), arb_radref(z), c); } else { /* x has a large radius and includes points near the origin */ arf_zero(arb_midref(z)); mag_one(arb_radref(z)); } mag_clear(c); mag_clear(r); } arb-2.8.1/arb/sinh_cosh.c000066400000000000000000000052731264125401100151560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_sinh(arb_t s, const arb_t x, slong prec) { if (arb_is_zero(x)) { arb_zero(s); } else { arb_t t; slong wp = prec + 4; arb_init(t); if (arf_cmpabs_2exp_si(arb_midref(x), -1) <= 0) { arb_expm1(s, x, wp); arb_add_ui(t, s, 1, wp); arb_div(t, s, t, wp); arb_add(s, s, t, prec); } else { arb_exp_invexp(s, t, x, wp); arb_sub(s, s, t, prec); } arb_mul_2exp_si(s, s, -1); arb_clear(t); } } void arb_cosh(arb_t c, const arb_t x, slong prec) { if (arb_is_zero(x)) { arb_one(c); } else { arb_t t; slong wp = prec + 4; arb_init(t); arb_exp_invexp(c, t, x, wp); arb_add(c, c, t, prec); arb_mul_2exp_si(c, c, -1); arb_clear(t); } } void arb_sinh_cosh(arb_t s, arb_t c, const arb_t x, slong prec) { if (arb_is_zero(x)) { arb_zero(s); arb_one(c); } else { slong wp = prec + 4; arb_t t; arb_init(t); if (arf_cmpabs_2exp_si(arb_midref(x), -1) <= 0) { arb_expm1(s, x, wp); arb_add_ui(t, s, 1, wp); arb_inv(c, t, wp); arb_addmul(s, s, c, prec); arb_add(c, c, t, prec); } else { arb_exp_invexp(c, t, x, wp); arb_sub(s, c, t, prec); arb_add(c, c, t, prec); } arb_mul_2exp_si(s, s, -1); arb_mul_2exp_si(c, c, -1); arb_clear(t); } } arb-2.8.1/arb/sqrt.c000066400000000000000000000056271264125401100141750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_sqrt_ui(arb_t z, ulong x, slong prec) { arf_t t; arf_init_set_ui(t, x); /* no need to free */ arb_sqrt_arf(z, t, prec); } void arb_sqrt_fmpz(arb_t z, const fmpz_t x, slong prec) { arf_t t; arf_init(t); arf_set_fmpz(t, x); arb_sqrt_arf(z, t, prec); arf_clear(t); } void arb_sqrt_arf(arb_t z, const arf_t x, slong prec) { if (arf_sgn(x) < 0) { arb_indeterminate(z); } else { int inexact; inexact = arf_sqrt(arb_midref(z), x, prec, ARB_RND); if (inexact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); else mag_zero(arb_radref(z)); } } void arb_sqrt(arb_t z, const arb_t x, slong prec) { mag_t rx, zr; int inexact; if (arb_is_exact(x)) { arb_sqrt_arf(z, arb_midref(x), prec); } else if (arb_contains_negative(x)) { arb_indeterminate(z); } else { mag_init(zr); mag_init(rx); /* rx = upper bound for r / x */ arf_get_mag_lower(rx, arb_midref(x)); mag_div(rx, arb_radref(x), rx); inexact = arf_sqrt(arb_midref(z), arb_midref(x), prec, ARB_RND); /* zr = upper bound for sqrt(x) */ arf_get_mag(zr, arb_midref(z)); if (inexact) arf_mag_add_ulp(zr, zr, arb_midref(z), prec); /* propagated error: sqrt(x) - sqrt(x-r) = sqrt(x) * [1 - sqrt(1 - r/x)] <= sqrt(x) * 0.5 * (rx + rx^2) */ mag_addmul(rx, rx, rx); mag_mul(zr, zr, rx); mag_mul_2exp_si(zr, zr, -1); /* add the rounding error */ if (inexact) arf_mag_add_ulp(arb_radref(z), zr, arb_midref(z), prec); else mag_swap(arb_radref(z), zr); mag_clear(zr); mag_clear(rx); } } arb-2.8.1/arb/sqrt1pm1.c000066400000000000000000000043111264125401100146610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void arb_sqrt1pm1_tiny(arb_t r, const arb_t z, slong prec) { mag_t b, c; arb_t t; mag_init(b); mag_init(c); arb_init(t); /* if |z| < 1, then |(sqrt(1+z)-1) - (z/2-z^2/8)| <= |z|^3/(1-|z|)/16 */ arb_get_mag(b, z); mag_one(c); mag_sub_lower(c, c, b); mag_pow_ui(b, b, 3); mag_div(b, b, c); mag_mul_2exp_si(b, b, -4); arb_mul(t, z, z, prec); arb_mul_2exp_si(t, t, -2); arb_sub(r, z, t, prec); arb_mul_2exp_si(r, r, -1); if (mag_is_finite(b)) arb_add_error_mag(r, b); else arb_indeterminate(r); mag_clear(b); mag_clear(c); arb_clear(t); } void arb_sqrt1pm1(arb_t r, const arb_t z, slong prec) { slong magz, wp; if (arb_is_zero(z)) { arb_zero(r); return; } magz = arf_abs_bound_lt_2exp_si(arb_midref(z)); if (magz < -prec) { arb_sqrt1pm1_tiny(r, z, prec); } else { if (magz < 0) wp = prec + (-magz) + 4; else wp = prec + 4; arb_add_ui(r, z, 1, wp); arb_sqrt(r, r, wp); arb_sub_ui(r, r, 1, wp); } } arb-2.8.1/arb/sqrtpos.c000066400000000000000000000051351264125401100147110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" static __inline__ void arb_nonnegative_part(arb_t z, const arb_t x, slong prec) { if (arb_contains_negative(x)) { arf_t t; arf_init(t); arf_set_mag(t, arb_radref(x)); arf_add(arb_midref(z), arb_midref(x), t, MAG_BITS, ARF_RND_CEIL); if (arf_sgn(arb_midref(z)) <= 0) { mag_zero(arb_radref(z)); } else { arf_mul_2exp_si(arb_midref(z), arb_midref(z), -1); arf_get_mag(arb_radref(z), arb_midref(z)); /* XXX: needed since arf_get_mag is inexact */ arf_set_mag(arb_midref(z), arb_radref(z)); } arf_clear(t); } else { arb_set(z, x); } } void arb_sqrtpos(arb_t z, const arb_t x, slong prec) { if (!arb_is_finite(x)) { if (mag_is_zero(arb_radref(x)) && arf_is_pos_inf(arb_midref(x))) arb_pos_inf(z); else arb_zero_pm_inf(z); } else if (arb_contains_nonpositive(x)) { arf_t t; arf_init(t); arf_set_mag(t, arb_radref(x)); arf_add(t, arb_midref(x), t, MAG_BITS, ARF_RND_CEIL); if (arf_sgn(t) <= 0) { arb_zero(z); } else { arf_sqrt(t, t, MAG_BITS, ARF_RND_CEIL); arf_mul_2exp_si(t, t, -1); arf_set(arb_midref(z), t); arf_get_mag(arb_radref(z), t); } arf_clear(t); } else { arb_sqrt(z, x, prec); } arb_nonnegative_part(z, z, prec); } arb-2.8.1/arb/sub.c000066400000000000000000000051601264125401100137650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_sub(arb_t z, const arb_t x, const arb_t y, slong prec) { int inexact; inexact = arf_sub(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND); mag_add(arb_radref(z), arb_radref(x), arb_radref(y)); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); } void arb_sub_arf(arb_t z, const arb_t x, const arf_t y, slong prec) { int inexact; inexact = arf_sub(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } void arb_sub_ui(arb_t z, const arb_t x, ulong y, slong prec) { int inexact; inexact = arf_sub_ui(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } void arb_sub_si(arb_t z, const arb_t x, slong y, slong prec) { int inexact; inexact = arf_sub_si(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } void arb_sub_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) { int inexact; inexact = arf_sub_fmpz(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(x), arb_midref(z), prec); else mag_set(arb_radref(z), arb_radref(x)); } arb-2.8.1/arb/submul.c000066400000000000000000000103211264125401100144760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_submul_arf(arb_t z, const arb_t x, const arf_t y, slong prec) { mag_t ym; int inexact; if (arb_is_exact(x)) { inexact = arf_submul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); } else if (ARB_IS_LAGOM(x) && ARF_IS_LAGOM(y) && ARB_IS_LAGOM(z)) { mag_fast_init_set_arf(ym, y); mag_fast_addmul(arb_radref(z), ym, arb_radref(x)); inexact = arf_submul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_fast_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); } else { mag_init_set_arf(ym, y); mag_addmul(arb_radref(z), ym, arb_radref(x)); inexact = arf_submul(arb_midref(z), arb_midref(x), y, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(z), arb_radref(z), arb_midref(z), prec); mag_clear(ym); } } void arb_submul(arb_t z, const arb_t x, const arb_t y, slong prec) { mag_t zr, xm, ym; int inexact; if (arb_is_exact(y)) { arb_submul_arf(z, x, arb_midref(y), prec); } else if (arb_is_exact(x)) { arb_submul_arf(z, y, arb_midref(x), prec); } else if (ARB_IS_LAGOM(x) && ARB_IS_LAGOM(y) && ARB_IS_LAGOM(z)) { mag_fast_init_set_arf(xm, arb_midref(x)); mag_fast_init_set_arf(ym, arb_midref(y)); mag_fast_init_set(zr, arb_radref(z)); mag_fast_addmul(zr, xm, arb_radref(y)); mag_fast_addmul(zr, ym, arb_radref(x)); mag_fast_addmul(zr, arb_radref(x), arb_radref(y)); inexact = arf_submul(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARF_RND_DOWN); if (inexact) arf_mag_fast_add_ulp(zr, zr, arb_midref(z), prec); *arb_radref(z) = *zr; } else { mag_init_set_arf(xm, arb_midref(x)); mag_init_set_arf(ym, arb_midref(y)); mag_init_set(zr, arb_radref(z)); mag_addmul(zr, xm, arb_radref(y)); mag_addmul(zr, ym, arb_radref(x)); mag_addmul(zr, arb_radref(x), arb_radref(y)); inexact = arf_submul(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARF_RND_DOWN); if (inexact) arf_mag_add_ulp(arb_radref(z), zr, arb_midref(z), prec); else mag_set(arb_radref(z), zr); mag_clear(zr); mag_clear(xm); mag_clear(ym); } } void arb_submul_si(arb_t z, const arb_t x, slong y, slong prec) { arf_t t; arf_init_set_si(t, y); /* no need to free */ arb_submul_arf(z, x, t, prec); } void arb_submul_ui(arb_t z, const arb_t x, ulong y, slong prec) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ arb_submul_arf(z, x, t, prec); } void arb_submul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) { arf_t t; if (!COEFF_IS_MPZ(*y)) { arf_init_set_si(t, *y); /* no need to free */ arb_submul_arf(z, x, t, prec); } else { arf_init(t); arf_set_fmpz(t, y); arb_submul_arf(z, x, t, prec); arf_clear(t); } } arb-2.8.1/arb/tan.c000066400000000000000000000023701264125401100137560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_tan(arb_t y, const arb_t x, slong prec) { arb_t u; arb_init(u); arb_sin_cos(y, u, x, prec + 4); arb_div(y, y, u, prec); arb_clear(u); } arb-2.8.1/arb/tan_pi.c000066400000000000000000000023761264125401100144540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_tan_pi(arb_t y, const arb_t x, slong prec) { arb_t u; arb_init(u); arb_sin_cos_pi(y, u, x, prec + 4); arb_div(y, y, u, prec); arb_clear(u); } arb-2.8.1/arb/tanh.c000066400000000000000000000035261264125401100141320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_tanh(arb_t y, const arb_t x, slong prec) { arb_t t, u; int sign = arf_sgn(arb_midref(x)) < 0; arb_init(t); arb_init(u); arb_mul_2exp_si(t, x, 1); if (!sign) arb_neg(t, t); if (arf_cmpabs_2exp_si(arb_midref(x), 1) > 0) { /* tanh(x) = 1 - 2 exp(-2x) / (1 + exp(-2x)) */ arb_exp(t, t, prec + 4); arb_add_ui(u, t, 1, prec + 4); arb_div(y, t, u, prec + 4); arb_mul_2exp_si(y, y, 1); arb_sub_ui(y, y, 1, prec); } else { /* tanh(x) = (exp(2x) - 1) / (exp(2x) + 1) */ arb_expm1(t, t, prec + 4); arb_add_ui(y, t, 2, prec + 4); arb_div(y, t, y, prec); } if (!sign) arb_neg(y, y); arb_clear(t); arb_clear(u); } arb-2.8.1/arb/test/000077500000000000000000000000001264125401100140055ustar00rootroot00000000000000arb-2.8.1/arb/test/t-acos.c000066400000000000000000000071061264125401100153430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("acos...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_acos(t, t, MPFR_RNDN); arb_acos(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_printd(a, 100); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 100); flint_printf("\n\n"); abort(); } arb_acos(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100); arb_acos(b, a, prec1); arb_acos(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check sin(asin(x)) = x */ arb_cos(c, b, prec1); if (!arb_contains(c, a)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-acosh.c000066400000000000000000000057451264125401100155220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("acosh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(x); arb_init(a); arb_init(b); arb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_acosh(a, x, prec1); arb_acosh(b, x, prec2); /* check consistency */ if (!arb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check cosh(acosh(x)) = x */ arb_cosh(b, b, prec1); if (!arb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); abort(); } arb_acosh(x, x, prec1); if (!arb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(a); arb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-add.c000066400000000000000000000116601264125401100151460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t x, y, z; arb_init(a); arb_init(b); arb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_add(c, a, b, 2 + n_randint(state, 200)); fmpq_add(z, x, y); if (!arb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_add(a, a, b, 2 + n_randint(state, 200)); fmpq_add(z, x, y); if (!arb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_add(b, a, b, 2 + n_randint(state, 200)); fmpq_add(z, x, y); if (!arb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-add_arf.c000066400000000000000000000067771264125401100160130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("add_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_add_arf(c, a, x, prec); arb_add(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arf_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_add_arf(c, a, x, prec); arb_add_arf(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-add_error.c000066400000000000000000000211531264125401100163550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("add_error...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t m, r; arb_init(a); arb_init(b); arb_init(c); arf_init(m); arf_init(r); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 10); arf_randtest_special(m, state, 1 + n_randint(state, 2000), 10); arf_randtest_special(r, state, 1 + n_randint(state, 2000), 10); /* c = a plus error bounds */ arb_set(c, a); arf_set(arb_midref(b), m); arf_get_mag(arb_radref(b), r); arb_add_error(c, b); /* b = a + random point */ arb_set(b, a); if (n_randint(state, 2)) arf_add(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN); else arf_sub(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN); if (n_randint(state, 2)) arf_add(arb_midref(b), arb_midref(b), r, ARF_PREC_EXACT, ARF_RND_DOWN); else arf_sub(arb_midref(b), arb_midref(b), r, ARF_PREC_EXACT, ARF_RND_DOWN); /* should this be done differently? */ if (arf_is_nan(arb_midref(b))) arf_zero(arb_midref(b)); if (!arb_contains(c, b)) { flint_printf("FAIL (arb_add_error)\n\n"); flint_printf("a = "); arb_printn(a, 50, 0); flint_printf("\n\n"); flint_printf("b = "); arb_printn(b, 50, 0); flint_printf("\n\n"); flint_printf("c = "); arb_printn(c, 50, 0); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(m); arf_clear(r); } for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t m; arb_init(a); arb_init(b); arb_init(c); arf_init(m); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 10); arf_randtest_special(m, state, 1 + n_randint(state, 2000), 10); /* c = a plus error bounds */ arb_set(c, a); arb_add_error_arf(c, m); /* b = a + random point */ arb_set(b, a); if (n_randint(state, 2)) arf_add(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN); else arf_sub(arb_midref(b), arb_midref(b), m, ARF_PREC_EXACT, ARF_RND_DOWN); /* should this be done differently? */ if (arf_is_nan(arb_midref(b))) arf_zero(arb_midref(b)); if (!arb_contains(c, b)) { flint_printf("FAIL (arb_add_error_arf)\n\n"); flint_printf("a = "); arb_printn(a, 50, 0); flint_printf("\n\n"); flint_printf("b = "); arb_printn(b, 50, 0); flint_printf("\n\n"); flint_printf("c = "); arb_printn(c, 50, 0); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(m); } for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t t; mag_t r; arb_init(a); arb_init(b); arb_init(c); mag_init(r); arf_init(t); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10); mag_randtest(r, state, 10); /* c = a plus error bounds */ arb_set(c, a); arb_add_error_mag(c, r); /* b = a + random point */ arb_set(b, a); arf_set_mag(t, r); if (n_randint(state, 2)) arf_add(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN); else arf_sub(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN); /* should this be done differently? */ if (arf_is_nan(arb_midref(b))) arf_zero(arb_midref(b)); if (!arb_contains(c, b)) { flint_printf("FAIL (arb_add_error_mag)\n\n"); flint_printf("a = "); arb_printn(a, 50, 0); flint_printf("\n\n"); flint_printf("b = "); arb_printn(b, 50, 0); flint_printf("\n\n"); flint_printf("c = "); arb_printn(c, 50, 0); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); mag_clear(r); arf_clear(t); } for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t t; slong e; arb_init(a); arb_init(b); arb_init(c); arf_init(t); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10); e = n_randint(state, 10) - 10; /* c = a plus error bounds */ arb_set(c, a); arb_add_error_2exp_si(c, e); /* b = a + random point */ arb_set(b, a); arf_one(t); arf_mul_2exp_si(t, t, e); if (n_randint(state, 2)) arf_add(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN); else arf_sub(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN); /* should this be done differently? */ if (arf_is_nan(arb_midref(b))) arf_zero(arb_midref(b)); if (!arb_contains(c, b)) { flint_printf("FAIL (arb_add_error_2exp_si)\n\n"); flint_printf("a = "); arb_printn(a, 50, 0); flint_printf("\n\n"); flint_printf("b = "); arb_printn(b, 50, 0); flint_printf("\n\n"); flint_printf("c = "); arb_printn(c, 50, 0); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(t); } for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t t; fmpz_t e; arb_init(a); arb_init(b); arb_init(c); arf_init(t); fmpz_init(e); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 10); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 10); fmpz_randtest(e, state, 10); /* c = a plus error bounds */ arb_set(c, a); arb_add_error_2exp_fmpz(c, e); /* b = a + random point */ arb_set(b, a); arf_one(t); arf_mul_2exp_fmpz(t, t, e); if (n_randint(state, 2)) arf_add(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN); else arf_sub(arb_midref(b), arb_midref(b), t, ARF_PREC_EXACT, ARF_RND_DOWN); /* should this be done differently? */ if (arf_is_nan(arb_midref(b))) arf_zero(arb_midref(b)); if (!arb_contains(c, b)) { flint_printf("FAIL (arb_add_error_2exp_fmpz)\n\n"); flint_printf("a = "); arb_printn(a, 50, 0); flint_printf("\n\n"); flint_printf("b = "); arb_printn(b, 50, 0); flint_printf("\n\n"); flint_printf("c = "); arb_printn(c, 50, 0); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(t); fmpz_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-add_fmpz.c000066400000000000000000000067631264125401100162120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("add_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_add_fmpz(c, a, x, prec); arb_add(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_add_fmpz(c, a, x, prec); arb_add_fmpz(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpz_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-add_fmpz_2exp.c000066400000000000000000000070271264125401100171420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("add_fmpz_2exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t x, e; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(x); fmpz_init(e); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); fmpz_randtest(e, state, 1 + n_randint(state, 200)); prec = 2 + n_randint(state, 2000); arb_set_fmpz_2exp(b, x, e); arb_add_fmpz_2exp(c, a, x, e, prec); arb_add(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(x); fmpz_clear(e); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, c; fmpz_t x, e; slong prec; arb_init(a); arb_init(c); fmpz_init(x); fmpz_init(e); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); fmpz_randtest(e, state, 1 + n_randint(state, 200)); prec = 2 + n_randint(state, 2000); arb_add_fmpz_2exp(c, a, x, e, prec); arb_add_fmpz_2exp(a, a, x, e, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(c); fmpz_clear(x); fmpz_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-add_si.c000066400000000000000000000065501264125401100156430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("add_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_add_si(c, a, x, prec); arb_add(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_add_si(c, a, x, prec); arb_add_si(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-add_ui.c000066400000000000000000000065511264125401100156460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "ulong_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("add_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_add_ui(c, a, x, prec); arb_add(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_add_ui(c, a, x, prec); arb_add_ui(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-addmul.c000066400000000000000000000231651264125401100156670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int mag_close(const mag_t am, const mag_t bm) { arf_t t, a, b; int res1, res2; arf_init(t); arf_init(a); arf_init(b); arf_set_mag(a, am); arf_set_mag(b, bm); arf_mul_ui(t, b, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res1 = arf_cmp(a, t) <= 0; arf_mul_ui(t, a, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res2 = arf_cmp(b, t) <= 0; arf_clear(t); arf_clear(a); arf_clear(b); return res1 && res2; } void arb_addmul_naive(arb_t z, const arb_t x, const arb_t y, slong prec) { arb_t t; arb_init(t); arb_mul(t, x, y, ARF_PREC_EXACT); arb_add(z, z, t, prec); arb_clear(t); } int main() { slong iter, iter2; flint_rand_t state; flint_printf("addmul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t x, y, z; arb_init(a); arb_init(b); arb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_get_rand_fmpq(z, state, c, 1 + n_randint(state, 200)); arb_addmul(c, a, b, 2 + n_randint(state, 200)); fmpq_addmul(z, x, y); if (!arb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, x); arb_addmul(a, a, b, 2 + n_randint(state, 200)); fmpq_addmul(z, x, y); if (!arb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, y); arb_addmul(b, a, b, 2 + n_randint(state, 200)); fmpq_addmul(z, x, y); if (!arb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* main test */ for (iter = 0; iter < 10000; iter++) { arb_t x, y, z, v; slong prec; arb_init(x); arb_init(y); arb_init(z); arb_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arb_randtest_special(x, state, n_randint(state,2) ? 2000 : 200, 200); arb_randtest_special(y, state, n_randint(state,2) ? 2000 : 200, 200); arb_randtest_special(z, state, n_randint(state,2) ? 2000 : 200, 200); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 5)) { case 0: arb_set(v, z); arb_addmul(z, x, y, prec); arb_addmul_naive(v, x, y, prec); if (!arf_equal(arb_midref(z), arb_midref(v)) || !mag_close(arb_radref(z), arb_radref(v))) { flint_printf("FAIL!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 1: arb_set(y, x); arb_set(z, v); arb_addmul(z, x, y, prec); arb_addmul(v, x, x, prec); if (!arf_equal(arb_midref(z), arb_midref(v)) || !mag_close(arb_radref(z), arb_radref(v))) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 2: arb_set(v, x); arb_addmul(v, x, x, prec); arb_addmul(x, x, x, prec); if (!arf_equal(arb_midref(x), arb_midref(v)) || !mag_close(arb_radref(x), arb_radref(v))) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 3: arb_set(v, x); arb_addmul(v, x, y, prec); arb_addmul(x, x, y, prec); if (!arf_equal(arb_midref(x), arb_midref(v)) || !mag_close(arb_radref(x), arb_radref(v))) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; default: arb_set(v, x); arb_addmul(v, x, y, prec); arb_addmul(x, y, x, prec); if (!arf_equal(arb_midref(x), arb_midref(v)) || !mag_close(arb_radref(x), arb_radref(v))) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; } } arb_clear(x); arb_clear(y); arb_clear(z); arb_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-addmul_arf.c000066400000000000000000000070741264125401100165200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("addmul_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_set(d, c); arb_addmul_arf(c, a, x, prec); arb_addmul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arf_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_set(c, a); arb_addmul_arf(c, a, x, prec); arb_addmul_arf(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-addmul_fmpz.c000066400000000000000000000070601264125401100167170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("addmul_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_set(d, c); arb_addmul_fmpz(c, a, x, prec); arb_addmul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_set(c, a); arb_addmul_fmpz(c, a, x, prec); arb_addmul_fmpz(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpz_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-addmul_si.c000066400000000000000000000066451264125401100163660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("addmul_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_set(d, c); arb_addmul_si(c, a, x, prec); arb_addmul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_set(c, a); arb_addmul_si(c, a, x, prec); arb_addmul_si(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-addmul_ui.c000066400000000000000000000066461264125401100163710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "ulong_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("addmul_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_set(d, c); arb_addmul_ui(c, a, x, prec); arb_addmul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_set(c, a); arb_addmul_ui(c, a, x, prec); arb_addmul_ui(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-agm.c000066400000000000000000000061461264125401100151650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("agm...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t q, r; mpfr_t t, u; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); fmpq_init(q); fmpq_init(r); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_randtest(c, state, 1 + n_randint(state, 200), 3); arb_agm(c, a, b, prec); if (arb_equal(a, b)) { if (!arb_contains(c, a)) { flint_printf("FAIL: containment (identity)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } } else { arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(r, state, b, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); fmpq_get_mpfr(u, r, MPFR_RNDN); mpfr_agm(t, t, u, MPFR_RNDN); if (!arb_contains_mpfr(c, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(q); fmpq_clear(r); mpfr_clear(t); mpfr_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-asin.c000066400000000000000000000070721264125401100153520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("asin...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_asin(t, t, MPFR_RNDN); arb_asin(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_asin(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100); arb_asin(b, a, prec1); arb_asin(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check sin(asin(x)) = x */ arb_sin(c, b, prec1); if (!arb_contains(c, a)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-asinh.c000066400000000000000000000057451264125401100155270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("asinh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(x); arb_init(a); arb_init(b); arb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_asinh(a, x, prec1); arb_asinh(b, x, prec2); /* check consistency */ if (!arb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check sinh(asinh(x)) = x */ arb_sinh(b, b, prec1); if (!arb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); abort(); } arb_asinh(x, x, prec1); if (!arb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(a); arb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atan.c000066400000000000000000000144651264125401100153470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("atan...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_atan(t, t, MPFR_RNDN); arb_atan(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_atan(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100); arb_atan(b, a, prec1); arb_atan(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check tan(atan(x)) = x */ arb_sin_cos(c, d, b, prec1); arb_div(c, c, d, prec1); if (!arb_contains(c, a)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* higher precision */ for (iter = 0; iter < 2000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 5000); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 5000), 8); arb_randtest(b, state, 1 + n_randint(state, 5000), 8); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_atan(t, t, MPFR_RNDN); arb_atan(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 50); flint_printf("\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 50); flint_printf("\n\n"); abort(); } arb_atan(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* higher precision */ /* check large arguments */ for (iter = 0; iter < 2000; iter++) { arb_t a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 5000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_precise(a, state, 1 + n_randint(state, 5000), 100); arb_atan(b, a, prec1); arb_atan(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check tan(atan(x)) = x */ arb_sin_cos(c, d, b, prec1); arb_div(c, c, d, prec1); if (!arb_contains(c, a)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atan2.c000066400000000000000000000051621264125401100154230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("atan2...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t q, r; mpfr_t t, u; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); fmpq_init(q); fmpq_init(r); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_randtest(c, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(r, state, b, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); fmpq_get_mpfr(u, r, MPFR_RNDN); mpfr_atan2(t, u, t, MPFR_RNDN); arb_atan2(c, b, a, prec); if (!arb_contains_mpfr(c, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(q); fmpq_clear(r); mpfr_clear(t); mpfr_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atan_arf.c000066400000000000000000000062401264125401100161670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("atan_arf...."); fflush(stdout); flint_randinit(state); /* self-consistency test */ for (iter = 0; iter < 5000; iter++) { arf_t x; arb_t y1, y2; slong prec1, prec2, acc1, acc2; prec1 = 2 + n_randint(state, 9000); prec2 = 2 + n_randint(state, 9000); arf_init(x); arb_init(y1); arb_init(y2); arf_randtest_special(x, state, 1 + n_randint(state, 9000), 200); arb_randtest_special(y1, state, 1 + n_randint(state, 9000), 200); arb_randtest_special(y2, state, 1 + n_randint(state, 9000), 200); if (n_randint(state, 2)) arf_add_ui(x, x, 1, 2 + n_randint(state, 9000), ARF_RND_DOWN); arb_atan_arf(y1, x, prec1); arb_atan_arf(y2, x, prec2); if (!arb_overlaps(y1, y2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("prec1 = %wd, prec2 = %wd\n\n", prec1, prec2); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y1 = "); arb_print(y1); flint_printf("\n\n"); flint_printf("y2 = "); arb_print(y2); flint_printf("\n\n"); abort(); } acc1 = arb_rel_accuracy_bits(y1); acc2 = arb_rel_accuracy_bits(y2); if (!arf_is_nan(x)) { if (acc1 < prec1 - 2 || acc2 < prec2 - 2) { flint_printf("FAIL: accuracy\n\n"); flint_printf("prec1 = %wd, prec2 = %wd\n\n", prec1, prec2); flint_printf("acc1 = %wd, acc2 = %wd\n\n", acc1, acc2); flint_printf("x = "); arf_printd(x, 50); flint_printf("\n\n"); flint_printf("y1 = "); arb_printd(y1, 50); flint_printf("\n\n"); flint_printf("y2 = "); arb_printd(y2, 50); flint_printf("\n\n"); abort(); } } arf_clear(x); arb_clear(y1); arb_clear(y2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atan_arf_bb.c000066400000000000000000000071121264125401100166310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_atan_arf_via_mpfr(arb_t z, const arf_t x, slong prec) { mpfr_t t, u; int exact; mpfr_init2(t, 2 + arf_bits(x)); mpfr_init2(u, prec); mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); arf_get_mpfr(t, x, MPFR_RNDD); exact = (mpfr_atan(u, t, MPFR_RNDD) == 0); arf_set_mpfr(arb_midref(z), u); if (!exact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); mpfr_clear(t); mpfr_clear(u); } int main() { slong iter; flint_rand_t state; flint_printf("atan_arf_bb...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arb_t x, y, z; slong prec, prec2; arb_init(x); arb_init(y); arb_init(z); prec = 2 + n_randint(state, 8000); arb_randtest(x, state, 1 + n_randint(state, 8000), 3); mag_zero(arb_radref(x)); if (n_randint(state, 2)) arb_mul_2exp_si(x, x, 1 + n_randint(state, 40)); else arb_mul_2exp_si(x, x, -n_randint(state, 1.5 * prec)); if (!arf_is_special(arb_midref(x))) prec2 = prec + 100 + 2 * (-ARF_EXP(arb_midref(x))); else prec2 = prec + 100; arb_atan_arf_via_mpfr(y, arb_midref(x), prec2); arb_atan_arf_bb(z, arb_midref(x), prec); if (!arb_contains(z, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n\n", prec); flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n"); flint_printf("z = "); arb_printd(z, 50); flint_printf("\n\n"); abort(); } if (arb_rel_accuracy_bits(z) < prec - 2) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd, acc = %wd\n\n", prec, arb_rel_accuracy_bits(z)); flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n"); flint_printf("z = "); arb_printd(z, 50); flint_printf("\n\n"); abort(); } arb_atan_arf_bb(x, arb_midref(x), prec); if (!arb_overlaps(x, z)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(x); arb_clear(y); arb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atan_sum_bs_powtab.c000066400000000000000000000051321264125401100202620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("atan_sum_bs_powtab...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2500; iter++) { slong N; fmpz_t x, T, Q; fmpq_t S, V; mp_bitcnt_t Qexp, r; fmpz_init(x); fmpz_init(T); fmpz_init(Q); fmpq_init(S); fmpq_init(V); N = 1 + n_randint(state, 200); r = n_randint(state, 10); fmpz_randtest(x, state, 30); _arb_atan_sum_bs_simple(T, Q, &Qexp, x, r, N); fmpq_set_fmpz_frac(S, T, Q); fmpq_div_2exp(S, S, Qexp); _arb_atan_sum_bs_powtab(T, Q, &Qexp, x, r, N); fmpq_set_fmpz_frac(V, T, Q); fmpq_div_2exp(V, V, Qexp); if (!fmpq_equal(S, V)) { flint_printf("FAIL\n\n"); flint_printf("N = %wd\n\n", N); flint_printf("r = %wu\n\n", r); flint_printf("x = "); fmpz_print(x); flint_printf("\n\n"); flint_printf("T = "); fmpz_print(T); flint_printf("\n\n"); flint_printf("Q = "); fmpz_print(T); flint_printf("\n\n"); flint_printf("V = "); fmpq_print(V); flint_printf("\n\n"); flint_printf("S = "); fmpq_print(S); flint_printf("\n\n"); abort(); } fmpz_clear(x); fmpz_clear(T); fmpz_clear(Q); fmpq_clear(S); fmpq_clear(V); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atan_tab.c000066400000000000000000000133451264125401100161710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong i; mpfr_t tabx, atanx, y1, y2; mpz_t tt; flint_printf("atan_tab...."); fflush(stdout); { slong prec, bits, num; prec = ARB_ATAN_TAB1_LIMBS * FLINT_BITS; bits = ARB_ATAN_TAB1_BITS; num = 1 << ARB_ATAN_TAB1_BITS; mpfr_init2(tabx, prec); mpfr_init2(atanx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_atan_tab1[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(atanx, i, MPFR_RNDD); mpfr_div_2ui(atanx, atanx, bits, MPFR_RNDD); mpfr_atan(atanx, atanx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, atanx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(atanx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_ATAN_TAB2_LIMBS * FLINT_BITS; bits = ARB_ATAN_TAB21_BITS; num = 1 << ARB_ATAN_TAB21_BITS; mpfr_init2(tabx, prec); mpfr_init2(atanx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_atan_tab21[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(atanx, i, MPFR_RNDD); mpfr_div_2ui(atanx, atanx, bits, MPFR_RNDD); mpfr_atan(atanx, atanx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, atanx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(atanx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_ATAN_TAB2_LIMBS * FLINT_BITS; bits = ARB_ATAN_TAB21_BITS + ARB_ATAN_TAB22_BITS; num = 1 << ARB_ATAN_TAB22_BITS; mpfr_init2(tabx, prec); mpfr_init2(atanx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_atan_tab22[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(atanx, i, MPFR_RNDD); mpfr_div_2ui(atanx, atanx, bits, MPFR_RNDD); mpfr_atan(atanx, atanx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, atanx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(atanx); mpfr_clear(y1); mpfr_clear(y2); } flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atan_taylor_rf.c000066400000000000000000000057351264125401100174300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "mpn_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("atan_taylor_rf...."); fflush(stdout); flint_randinit(state); _flint_rand_init_gmp(state); for (iter = 0; iter < 100000; iter++) { mp_ptr x, y1, y2, t; mp_limb_t err1, err2; ulong N; mp_size_t xn; int alternating, cmp, result; N = n_randint(state, 256); alternating = n_randint(state, 2); xn = 1 + n_randint(state, 20); x = flint_malloc(sizeof(mp_limb_t) * xn); y1 = flint_malloc(sizeof(mp_limb_t) * xn); y2 = flint_malloc(sizeof(mp_limb_t) * xn); t = flint_malloc(sizeof(mp_limb_t) * xn); flint_mpn_rrandom(x, state->gmp_state, xn); x[xn - 1] &= (LIMB_ONES >> 4); _arb_atan_taylor_naive(y1, &err1, x, xn, N, alternating); _arb_atan_taylor_rs(y2, &err2, x, xn, N, alternating); cmp = mpn_cmp(y1, y2, xn); if (cmp == 0) { result = 1; } else if (cmp > 0) { mpn_sub_n(t, y1, y2, xn); result = flint_mpn_zero_p(t + 1, xn - 1) && (t[0] <= err2); } else { mpn_sub_n(t, y2, y1, xn); result = flint_mpn_zero_p(t + 1, xn - 1) && (t[0] <= err2); } if (!result) { flint_printf("FAIL\n"); flint_printf("N = %wd xn = %wd alternating = %d\n", N, xn, alternating); flint_printf("x ="); flint_mpn_debug(x, xn); flint_printf("y1 ="); flint_mpn_debug(y1, xn); flint_printf("y2 ="); flint_mpn_debug(y2, xn); abort(); } flint_free(x); flint_free(y1); flint_free(y2); flint_free(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-atanh.c000066400000000000000000000057451264125401100155200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("atanh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t x, a, b; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(x); arb_init(a); arb_init(b); arb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100)); arb_atanh(a, x, prec1); arb_atanh(b, x, prec2); /* check consistency */ if (!arb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); abort(); } /* check tanh(atanh(x)) = x */ arb_tanh(b, b, prec1); if (!arb_contains(b, x)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); abort(); } arb_atanh(x, x, prec1); if (!arb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(a); arb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-bell_fmpz.c000066400000000000000000000060611264125401100163670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("bell_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arb_t b1, b2; fmpz_t n; slong prec1, prec2, acc1, acc2; fmpz_init(n); arb_init(b1); arb_init(b2); if (iter % 100 == 0) { fmpz_randtest(n, state, 1 + n_randint(state, 100)); fmpz_abs(n, n); prec1 = 2 + n_randint(state, 200); prec2 = 2 + n_randint(state, 200); } else { fmpz_randtest(n, state, 1 + n_randint(state, 20)); fmpz_abs(n, n); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); } arb_bell_fmpz(b1, n, prec1); arb_bell_fmpz(b2, n, prec2); if (!arb_overlaps(b1, b2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = "); fmpz_print(n); flint_printf("\n\n"); flint_printf("b1 = "); arb_printn(b1, 50, 0); flint_printf("\n\n"); flint_printf("b2 = "); arb_printn(b2, 50, 0); flint_printf("\n\n"); abort(); } acc1 = arb_rel_accuracy_bits(b1); acc2 = arb_rel_accuracy_bits(b2); if (acc1 < prec1 - 4 || acc2 < prec2 - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec1 = %wd, acc1 = %wd\n", prec1, acc1); flint_printf("prec2 = %wd, acc2 = %wd\n", prec2, acc2); flint_printf("n = "); fmpz_print(n); flint_printf("\n\n"); flint_printf("b1 = "); arb_printn(b1, 50, 0); flint_printf("\n\n"); flint_printf("b2 = "); arb_printn(b2, 50, 0); flint_printf("\n\n"); abort(); } arb_clear(b1); arb_clear(b2); fmpz_clear(n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-bell_sum_taylor.c000066400000000000000000000052351264125401100176130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("bell_sum_taylor...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t s1, s2; fmpz_t a, b, n; slong prec; arb_init(s1); arb_init(s2); fmpz_init(a); fmpz_init(b); fmpz_init(n); prec = 2 + n_randint(state, 300); fmpz_randtest_unsigned(n, state, 1 + n_randint(state, 100)); fmpz_randtest_unsigned(a, state, 1 + n_randint(state, 100)); fmpz_add_ui(b, a, n_randint(state, 100)); arb_bell_sum_bsplit(s1, n, a, b, NULL, prec); arb_bell_sum_taylor(s2, n, a, b, NULL, prec); if (!arb_overlaps(s1, s2) || (arb_rel_accuracy_bits(s1) < prec - 4) || (arb_rel_accuracy_bits(s2) < prec - 4)) { flint_printf("FAIL: overlap or accuracy\n\n"); flint_printf("prec = %wd\n\n", prec); flint_printf("n = "); fmpz_print(n); flint_printf("\n\n"); flint_printf("a = "); fmpz_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("s1 = "); arb_printn(s1, 100, 0); flint_printf("\n\n"); flint_printf("s2 = "); arb_printn(s2, 100, 0); flint_printf("\n\n"); abort(); } arb_clear(s1); arb_clear(s2); fmpz_clear(a); fmpz_clear(b); fmpz_clear(n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-bernoulli_ui.c000066400000000000000000000050631264125401100171060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("bernoulli_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t b1, b2; ulong n; slong prec1, prec2, acc1, acc2; n = n_randint(state, 10000); prec1 = 2 + n_randint(state, 10000); prec2 = prec1 + 100; arb_init(b1); arb_init(b2); arb_bernoulli_ui(b1, n, prec1); arb_bernoulli_ui(b2, n, prec2); if (!arb_overlaps(b1, b2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("b1 = "); arb_print(b1); flint_printf("\n\n"); flint_printf("b2 = "); arb_print(b2); flint_printf("\n\n"); abort(); } acc1 = arb_rel_accuracy_bits(b1); acc2 = arb_rel_accuracy_bits(b2); if (acc1 < prec1 - 2 || acc2 < prec2 - 2) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec1 = %wd\n", prec1); flint_printf("prec2 = %wd\n", prec2); flint_printf("b1 = "); arb_printd(b1, prec1 / 3.33); flint_printf("\n\n"); flint_printf("b2 = "); arb_printd(b2, prec2 / 3.33); flint_printf("\n\n"); abort(); } arb_clear(b1); arb_clear(b2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-ceil.c000066400000000000000000000051721264125401100153330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("ceil...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t x; fmpz_t y; slong prec; arb_init(a); arb_init(b); fmpq_init(x); fmpz_init(y); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_ceil(b, a, prec); fmpz_cdiv_q(y, fmpq_numref(x), fmpq_denref(x)); if (!arb_contains_fmpz(b, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); abort(); } arb_ceil(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpz_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-chebyshev_t_ui.c000066400000000000000000000076471264125401100174300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("chebyshev_t_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; ulong n; slong prec; n = n_randtest(state); prec = 2 + n_randint(state, 300); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest(a, state, 1 + n_randint(state, 300), 5); arb_randtest(c, state, 1 + n_randint(state, 300), 5); arb_cos(b, a, prec); arb_chebyshev_t_ui(c, n, b, prec); arb_mul_ui(d, a, n, prec); arb_cos(d, d, prec); if (!arb_overlaps(c, d)) { flint_printf("FAIL: c = T_n(cos(a)) = d = cos(n*a)\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("d = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_chebyshev_t_ui(b, n, b, prec); if (!arb_equal(b, c)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_randtest(a, state, 1 + n_randint(state, 300), 5); arb_randtest(b, state, 1 + n_randint(state, 300), 5); arb_randtest(c, state, 1 + n_randint(state, 300), 5); arb_chebyshev_t2_ui(b, c, n, a, prec); arb_chebyshev_t_ui(d, n, a, prec); if (!arb_overlaps(b, d)) { flint_printf("FAIL: T_n\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } if (n == 0) arb_set(d, a); else arb_chebyshev_t_ui(d, n - 1, a, prec); if (!arb_overlaps(c, d)) { flint_printf("FAIL: T_{n-1}\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-chebyshev_u_ui.c000066400000000000000000000105471264125401100174220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("chebyshev_u_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d, e; ulong n; slong prec; n = n_randtest(state); prec = 2 + n_randint(state, 300); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_init(e); arb_randtest_precise(a, state, 1 + n_randint(state, 300), 5); arb_randtest_precise(c, state, 1 + n_randint(state, 300), 5); arb_sin_cos(d, b, a, prec); arb_chebyshev_u_ui(c, n, b, prec); arb_mul(d, c, d, prec); if (n == LIMB_ONES) arb_mul_2exp_si(e, a, FLINT_BITS); else arb_mul_ui(e, a, n + 1, prec); arb_sin(e, e, prec); if (!arb_overlaps(d, e)) { flint_printf("FAIL: sin(a)*U_n(cos(a)) = sin((n+1)a)\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_printd(d, 15); flint_printf("\n\n"); flint_printf("e = "); arb_printd(e, 15); flint_printf("\n\n"); abort(); } arb_chebyshev_u_ui(b, n, b, prec); if (!arb_equal(b, c)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_printd(c, 15); flint_printf("\n\n"); abort(); } arb_randtest(a, state, 1 + n_randint(state, 300), 5); arb_randtest(b, state, 1 + n_randint(state, 300), 5); arb_randtest(c, state, 1 + n_randint(state, 300), 5); arb_chebyshev_u2_ui(b, c, n, a, prec); arb_chebyshev_u_ui(d, n, a, prec); if (!arb_overlaps(b, d)) { flint_printf("FAIL: U_n\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } if (n == 0) arb_zero(d); else arb_chebyshev_u_ui(d, n - 1, a, prec); if (!arb_overlaps(c, d)) { flint_printf("FAIL: U_{n-1}\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arb_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_apery.c000066400000000000000000000043461264125401100167470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_apery...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r; mpfr_t s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 17)); arb_init(r); mpfr_init2(s, prec + 1000); arb_const_apery(r, prec); mpfr_zeta_ui(s, 3, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_catalan.c000066400000000000000000000043551264125401100172320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_catalan...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r; mpfr_t s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 16)); arb_init(r); mpfr_init2(s, prec + 1000); arb_const_catalan(r, prec); mpfr_const_catalan(s, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_e.c000066400000000000000000000044001264125401100160420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_e...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r; mpfr_t s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 16)); arb_init(r); mpfr_init2(s, prec + 1000); arb_const_e(r, prec); mpfr_set_ui(s, 1, MPFR_RNDN); mpfr_exp(s, s, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_euler.c000066400000000000000000000043471264125401100167440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_euler...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r; mpfr_t s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 16)); arb_init(r); mpfr_init2(s, prec + 1000); arb_const_euler(r, prec); mpfr_const_euler(s, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_glaisher.c000066400000000000000000000055341264125401100174250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_glaisher...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r, s, t; fmpz_t v; slong accuracy, prec; prec = 2 + n_randint(state, 2000); arb_init(r); arb_init(s); arb_init(t); fmpz_init(v); arb_const_glaisher(r, prec); arb_const_glaisher(s, prec + 100); if (!arb_overlaps(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } if (n_randint(state, 30) == 0) { flint_cleanup(); } fmpz_set_str(v, "128242712910062263687534256886979172776768892732500", 10); arb_set_fmpz(t, v); mag_one(arb_radref(t)); fmpz_ui_pow_ui(v, 10, 50); arb_div_fmpz(t, t, v, 170); if (!arb_overlaps(r, t)) { flint_printf("FAIL: reference value\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); arb_clear(s); arb_clear(t); fmpz_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_khinchin.c000066400000000000000000000043161264125401100174170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_khinchin...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r, s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 14)); arb_init(r); arb_init(s); arb_const_khinchin(r, prec); arb_const_khinchin(s, prec + 1000); if (!arb_overlaps(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); arb_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_log10.c000066400000000000000000000044111264125401100165420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_log10...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r; mpfr_t s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 16)); arb_init(r); mpfr_init2(s, prec + 1000); arb_const_log10(r, prec); mpfr_set_ui(s, 10, MPFR_RNDN); mpfr_log(s, s, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_log2.c000066400000000000000000000043441264125401100164700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_log2...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r; mpfr_t s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 16)); arb_init(r); mpfr_init2(s, prec + 1000); arb_const_log2(r, prec); mpfr_const_log2(s, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-const_pi.c000066400000000000000000000043361264125401100162360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("const_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 250; iter++) { arb_t r; mpfr_t s; slong accuracy, prec; prec = 2 + n_randint(state, 1 << n_randint(state, 18)); arb_init(r); mpfr_init2(s, prec + 1000); arb_const_pi(r, prec); mpfr_const_pi(s, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-contains.c000066400000000000000000000060361264125401100162350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("contains...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t am, ar, bm, br, t, u; int c1, c2; arb_init(a); arb_init(b); fmpq_init(am); fmpq_init(ar); fmpq_init(bm); fmpq_init(br); fmpq_init(t); fmpq_init(u); arb_randtest(a, state, 1 + n_randint(state, 500), 14); arb_randtest(b, state, 1 + n_randint(state, 500), 14); arf_get_fmpq(am, arb_midref(a)); mag_get_fmpq(ar, arb_radref(a)); arf_get_fmpq(bm, arb_midref(b)); mag_get_fmpq(br, arb_radref(b)); c1 = arb_contains(a, b); fmpq_sub(t, am, ar); fmpq_sub(u, bm, br); c2 = fmpq_cmp(t, u) <= 0; fmpq_add(t, am, ar); fmpq_add(u, bm, br); c2 = c2 && (fmpq_cmp(t, u) >= 0); if (c1 != c2) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("am = "); fmpq_print(am); flint_printf("\n\n"); flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n"); flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n"); flint_printf("br = "); fmpq_print(br); flint_printf("\n\n"); flint_printf("t = "); fmpq_print(t); flint_printf("\n\n"); flint_printf("u = "); fmpq_print(u); flint_printf("\n\n"); flint_printf("c1 = %d, c2 = %d\n\n", c1, c2); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(am); fmpq_clear(ar); fmpq_clear(bm); fmpq_clear(br); fmpq_clear(t); fmpq_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-contains_arf.c000066400000000000000000000053231264125401100170630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("contains_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a; arf_t b; fmpq_t am, ar, bm, t; int c1, c2; arb_init(a); arf_init(b); fmpq_init(am); fmpq_init(ar); fmpq_init(bm); fmpq_init(t); arb_randtest(a, state, 1 + n_randint(state, 500), 14); arf_randtest(b, state, 1 + n_randint(state, 500), 14); arf_get_fmpq(am, arb_midref(a)); mag_get_fmpq(ar, arb_radref(a)); arf_get_fmpq(bm, b); c1 = arb_contains_arf(a, b); fmpq_sub(t, am, ar); c2 = fmpq_cmp(t, bm) <= 0; fmpq_add(t, am, ar); c2 = c2 && (fmpq_cmp(t, bm) >= 0); if (c1 != c2) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("am = "); fmpq_print(am); flint_printf("\n\n"); flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n"); flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n"); flint_printf("t = "); fmpq_print(t); flint_printf("\n\n"); flint_printf("c1 = %d, c2 = %d\n\n", c1, c2); abort(); } arb_clear(a); arf_clear(b); fmpq_clear(am); fmpq_clear(ar); fmpq_clear(bm); fmpq_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-contains_int.c000066400000000000000000000037651264125401100171150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("contains_int...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a; slong c; int r, ok; arb_init(a); arb_randtest_special(a, state, 1 + n_randint(state, 500), 2); r = arb_contains_int(a); ok = !r; for (c = 0; c < 10; c++) { if (arb_contains_si(a, c) || arb_contains_si(a, -c)) { ok = !ok; break; } } if (!ok) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_printd(a, 30); flint_printf("\n\n"); flint_printf("r = %d\n\n", r); abort(); } arb_clear(a); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-cos.c000066400000000000000000000102631264125401100152000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("cos...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec0, prec; prec0 = 400; if (iter % 100 == 0) prec0 = 8000; prec = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec0 + 100); arb_randtest(a, state, 1 + n_randint(state, prec0), 6); arb_randtest(b, state, 1 + n_randint(state, prec0), 6); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_cos(t, t, MPFR_RNDN); arb_cos(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_cos(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 1000000; iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), prec0); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(d, state, 1 + n_randint(state, prec0), 100); arb_cos(b, a, prec1); arb_cos(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check cos(2a) = 2cos(a)^2-1 */ arb_mul_2exp_si(c, a, 1); arb_cos(c, c, prec1); arb_mul(b, b, b, prec1); arb_mul_2exp_si(b, b, 1); arb_sub_ui(b, b, 1, prec1); if (!arb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-cos_pi.c000066400000000000000000000043171264125401100156730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("cos_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, b, c; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_const_pi(b, prec); arb_mul(b, b, a, prec); arb_cos(b, b, prec); arb_cos_pi(c, a, prec); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-cos_pi_fmpq.c000066400000000000000000000043271264125401100167170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("cos_pi_fmpq...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t c1, c2; fmpq_t x; slong prec; prec = 2 + n_randint(state, 5000); arb_init(c1); arb_init(c2); fmpq_init(x); fmpq_randtest(x, state, 1 + n_randint(state, 200)); arb_cos_pi_fmpq(c1, x, prec); arb_const_pi(c2, prec); arb_mul_fmpz(c2, c2, fmpq_numref(x), prec); arb_div_fmpz(c2, c2, fmpq_denref(x), prec); arb_cos(c2, c2, prec); if (!arb_overlaps(c1, c2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n"); flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n"); abort(); } arb_clear(c1); arb_clear(c2); fmpq_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-cos_pi_fmpq_algebraic.c000066400000000000000000000052641264125401100207110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("cos_pi_fmpq_algebraic...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t c1, c2; ulong p, q, g; slong prec; prec = 2 + n_randint(state, 5000); q = 1 + n_randint(state, 500); p = n_randint(state, q / 2 + 1); g = n_gcd(q, p); q /= g; p /= g; arb_init(c1); arb_init(c2); _arb_cos_pi_fmpq_algebraic(c1, p, q, prec); arb_const_pi(c2, prec); arb_mul_ui(c2, c2, p, prec); arb_div_ui(c2, c2, q, prec); arb_cos(c2, c2, prec); if (!arb_overlaps(c1, c2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n"); flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n"); abort(); } if (arb_rel_accuracy_bits(c1) < prec - 2) { flint_printf("FAIL: accuracy\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("prec=%wd eff=%wd\n", prec, arb_rel_accuracy_bits(c1)); flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n"); flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n"); abort(); } arb_clear(c1); arb_clear(c2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-cosh.c000066400000000000000000000045601264125401100153530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("cosh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_cosh(t, t, MPFR_RNDN); arb_cosh(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_cosh(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-coth.c000066400000000000000000000064661264125401100153630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("coth...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t x, y, a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(x); arb_init(y); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_precise(x, state, 1 + n_randint(state, 1000), 100); arb_randtest_precise(y, state, 1 + n_randint(state, 1000), 100); arb_coth(a, x, prec1); arb_coth(b, x, prec2); /* check consistency */ if (!arb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } /* check coth(x+y) = (1 + coth(x) coth(y)) / (coth(x) + coth(y)) */ arb_add(b, x, y, prec1); arb_coth(b, b, prec1); arb_coth(c, y, prec1); arb_add(d, a, c, prec1); arb_mul(c, a, c, prec1); arb_add_ui(c, c, 1, prec1); arb_div(d, c, d, prec1); if (!arb_overlaps(b, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_coth(x, x, prec1); if (!arb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(y); arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-digamma.c000066400000000000000000000057561264125401100160260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("digamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { arb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 10); arb_digamma(b, a, prec1); arb_digamma(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_set(c, a); arb_digamma(c, c, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check digamma(z+1) = digamma(z) + 1/z */ arb_inv(c, a, prec1); arb_add(b, b, c, prec1); arb_add_ui(c, a, 1, prec1); arb_digamma(c, c, prec1); if (!arb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-digits_round_inplace.c000066400000000000000000000061541264125401100206050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" int main() { flint_rand_t state; flint_printf("digits_round_inplace...."); fflush(stdout); flint_randinit(state); { char s[30]; slong i, j, len, n; mp_bitcnt_t shift; fmpz_t inp, out, err, t; arf_rnd_t rnd; fmpz_init(inp); fmpz_init(out); fmpz_init(err); fmpz_init(t); for (i = 0; i < 100000; i++) { len = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); s[0] = (n_randint(state, 9) + '1'); for (j = 1; j < len; j++) s[j] = (n_randint(state, 10) + '0'); s[len] = '\0'; fmpz_set_str(inp, s, 10); switch (n_randint(state, 3)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; default: rnd = ARF_RND_NEAR; break; } _arb_digits_round_inplace(s, &shift, err, n, rnd); fmpz_set_str(out, s, 10); fmpz_set_ui(t, 10); fmpz_pow_ui(t, t, shift); fmpz_mul(t, t, out); fmpz_add(t, t, err); if (!fmpz_equal(t, inp) || (rnd == ARF_RND_UP && fmpz_sgn(err) > 0)) { flint_printf("FAIL!\n"); flint_printf("inp = "); fmpz_print(inp); flint_printf("\n\n"); flint_printf("shift = %wd\n\n", shift); flint_printf("err = "); fmpz_print(err); flint_printf("\n\n"); flint_printf("out = "); fmpz_print(out); flint_printf("\n\n"); flint_printf(" t = "); fmpz_print(t); flint_printf("\n\n"); abort(); } } fmpz_clear(inp); fmpz_clear(out); fmpz_clear(err); fmpz_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-div.c000066400000000000000000000143011264125401100151730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("div...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t x, y, z; arb_init(a); arb_init(b); arb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); do { arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); } while (fmpq_is_zero(y)); arb_div(c, a, b, 2 + n_randint(state, 200)); fmpq_div(z, x, y); if (!arb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); do { arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); } while (fmpq_is_zero(y)); arb_div(a, a, b, 2 + n_randint(state, 200)); fmpq_div(z, x, y); if (!arb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); do { arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); } while (fmpq_is_zero(y)); arb_div(b, a, b, 2 + n_randint(state, 200)); fmpq_div(z, x, y); if (!arb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* test special values */ for (iter = 0; iter < 100000; iter++) { arb_t a, b, c, d; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 200), 1 + n_randint(state, 100)); arb_randtest_special(b, state, 1 + n_randint(state, 200), 1 + n_randint(state, 100)); arb_randtest_special(c, state, 1 + n_randint(state, 200), 1 + n_randint(state, 100)); arb_div(c, a, b, 2 + n_randint(state, 200)); arb_mul(d, c, b, 2 + n_randint(state, 200)); if (!arb_contains(d, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_printd(d, 15); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-div_2expm1_ui.c000066400000000000000000000065231264125401100170730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("div_2expm1_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; ulong n; slong prec, acc1, acc2; fmpz_t t; arb_init(a); arb_init(b); arb_init(c); fmpz_init(t); prec = 2 + n_randint(state, 10000); arb_randtest(a, state, 1 + n_randint(state, 10000), 10); if (n_randint(state, 2)) n = 1 + (n_randtest(state) % (10 * prec)); else n = n_randtest(state); arb_div_2expm1_ui(b, a, n, prec); arb_one(c); if (n >= (UWORD(1) << (FLINT_BITS-1))) { arb_mul_2exp_si(c, c, (UWORD(1) << (FLINT_BITS-2))); arb_mul_2exp_si(c, c, (UWORD(1) << (FLINT_BITS-2))); arb_mul_2exp_si(c, c, n - (UWORD(1) << (FLINT_BITS-1))); } else { arb_mul_2exp_si(c, c, n); } arb_sub_ui(c, c, 1, prec); arb_div(c, a, c, prec); acc1 = arb_rel_accuracy_bits(a); acc2 = arb_rel_accuracy_bits(b); if (!arb_overlaps(b, c)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } if (n > 0 && (acc2 < FLINT_MIN(prec, acc1) - 10) && !(acc1 == -ARF_PREC_EXACT && acc2 == -ARF_PREC_EXACT)) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec=%wd, acc1=%wd, acc2=%wd\n\n", prec, acc1, acc2); flint_printf("n = %wu\n\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpz_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-div_arf.c000066400000000000000000000067771264125401100160450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("div_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_div_arf(c, a, x, prec); arb_div(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arf_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_div_arf(c, a, x, prec); arb_div_arf(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-div_fmpz.c000066400000000000000000000067631264125401100162440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("div_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_div_fmpz(c, a, x, prec); arb_div(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_div_fmpz(c, a, x, prec); arb_div_fmpz(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpz_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-div_si.c000066400000000000000000000065501264125401100156750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("div_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_div_si(c, a, x, prec); arb_div(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_div_si(c, a, x, prec); arb_div_si(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-div_ui.c000066400000000000000000000065511264125401100157000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "ulong_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("div_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_div_ui(c, a, x, prec); arb_div(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_div_ui(c, a, x, prec); arb_div_ui(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-doublefac_ui.c000066400000000000000000000042731264125401100170410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("doublefac_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, b, c; ulong n; slong prec1, prec2; prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); arb_init(a); arb_init(b); arb_init(c); n = n_randtest(state); if (n + 1 == 0 || n + 2 == 0) n -= 2; arb_doublefac_ui(a, n, prec1); arb_doublefac_ui(b, n + 2, prec1); arb_mul_ui(c, a, n + 2, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-exp.c000066400000000000000000000107001264125401100152040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec0, prec; prec0 = 400; if (iter % 100 == 0) prec0 = 10000; prec = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, prec0), 4); arb_randtest(b, state, 1 + n_randint(state, prec0), 4); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_exp(t, t, MPFR_RNDN); arb_exp(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("iter = %wd, prec = %wd\n\n", iter, prec); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_exp(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("iter = %wd, prec = %wd\n\n", iter, prec); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 100000; iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_exp(b, a, prec1); arb_exp(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); /* check exp(a)*exp(b) = exp(a+b) */ arb_exp(c, a, prec1); arb_exp(d, b, prec1); arb_mul(c, c, d, prec1); arb_add(d, a, b, prec1); arb_exp(d, d, prec1); if (!arb_overlaps(c, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-exp_arf_bb.c000066400000000000000000000070271264125401100165070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_exp_arf_via_mpfr(arb_t z, const arf_t x, slong prec) { mpfr_t t, u; int exact; mpfr_init2(t, 2 + arf_bits(x)); mpfr_init2(u, prec); mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); arf_get_mpfr(t, x, MPFR_RNDD); exact = (mpfr_exp(u, t, MPFR_RNDD) == 0); arf_set_mpfr(arb_midref(z), u); if (!exact) arf_mag_set_ulp(arb_radref(z), arb_midref(z), prec); mpfr_clear(t); mpfr_clear(u); } int main() { slong iter; flint_rand_t state; flint_printf("exp_arf_bb...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arb_t x, y, z; slong prec = 2 + n_randint(state, 8000); arb_init(x); arb_init(y); arb_init(z); arb_randtest(x, state, 1 + n_randint(state, 8000), 3); mag_zero(arb_radref(x)); if (n_randint(state, 2)) { #if FLINT_BITS == 64 arb_mul_2exp_si(x, x, 1 + n_randint(state, 40)); #else arb_mul_2exp_si(x, x, 1 + n_randint(state, 20)); #endif } else { arb_mul_2exp_si(x, x, -n_randint(state, 1.5 * prec)); } arb_exp_arf_via_mpfr(y, arb_midref(x), prec + 100); arb_exp_arf_bb(z, arb_midref(x), prec, 0); if (!arb_contains(z, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n\n", prec); flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n"); flint_printf("z = "); arb_printd(z, 50); flint_printf("\n\n"); abort(); } if (arb_rel_accuracy_bits(z) < prec - 2) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd, acc = %wd\n\n", prec, arb_rel_accuracy_bits(z)); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); abort(); } arb_exp_arf_bb(x, arb_midref(x), prec, 0); if (!arb_overlaps(x, z)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(x); arb_clear(y); arb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-exp_invexp.c000066400000000000000000000056501264125401100166050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_invexp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong prec; if (iter % 10 == 0) prec = 10000; else prec = 1000; prec = 2 + n_randint(state, prec); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec), 1 + n_randint(state, 100)); arb_randtest_special(b, state, 1 + n_randint(state, prec), 1 + n_randint(state, 100)); arb_randtest_special(c, state, 1 + n_randint(state, prec), 1 + n_randint(state, 100)); arb_exp_invexp(b, c, a, prec); arb_exp(d, a, prec); if (!arb_overlaps(b, d)) { flint_printf("FAIL: overlap 1\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_neg(d, a); arb_exp(d, d, prec); if (!arb_overlaps(c, d)) { flint_printf("FAIL: overlap 2\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-exp_sum_bs_powtab.c000066400000000000000000000051301264125401100201310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_sum_bs_powtab...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong N; fmpz_t x, T, Q; fmpq_t S, V; mp_bitcnt_t Qexp, r; fmpz_init(x); fmpz_init(T); fmpz_init(Q); fmpq_init(S); fmpq_init(V); N = 1 + n_randint(state, 300); r = n_randint(state, 10); fmpz_randtest(x, state, 80); _arb_exp_sum_bs_simple(T, Q, &Qexp, x, r, N); fmpq_set_fmpz_frac(S, T, Q); fmpq_div_2exp(S, S, Qexp); _arb_exp_sum_bs_powtab(T, Q, &Qexp, x, r, N); fmpq_set_fmpz_frac(V, T, Q); fmpq_div_2exp(V, V, Qexp); if (!fmpq_equal(S, V)) { flint_printf("FAIL\n\n"); flint_printf("N = %wd\n\n", N); flint_printf("r = %wu\n\n", r); flint_printf("x = "); fmpz_print(x); flint_printf("\n\n"); flint_printf("T = "); fmpz_print(T); flint_printf("\n\n"); flint_printf("Q = "); fmpz_print(T); flint_printf("\n\n"); flint_printf("V = "); fmpq_print(V); flint_printf("\n\n"); flint_printf("S = "); fmpq_print(S); flint_printf("\n\n"); abort(); } fmpz_clear(x); fmpz_clear(T); fmpz_clear(Q); fmpq_clear(S); fmpq_clear(V); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-exp_tab.c000066400000000000000000000132651264125401100160430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong i; mpfr_t tabx, expx, y1, y2; mpz_t tt; flint_printf("exp_tab...."); fflush(stdout); { slong prec, bits, num; prec = ARB_EXP_TAB1_LIMBS * FLINT_BITS; bits = ARB_EXP_TAB1_BITS; num = ARB_EXP_TAB1_NUM; mpfr_init2(tabx, prec); mpfr_init2(expx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_exp_tab1[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(expx, i, MPFR_RNDD); mpfr_div_2ui(expx, expx, bits, MPFR_RNDD); mpfr_exp(expx, expx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, expx, prec - 1, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(expx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_EXP_TAB2_LIMBS * FLINT_BITS; bits = ARB_EXP_TAB21_BITS; num = ARB_EXP_TAB21_NUM; mpfr_init2(tabx, prec); mpfr_init2(expx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_exp_tab21[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(expx, i, MPFR_RNDD); mpfr_div_2ui(expx, expx, bits, MPFR_RNDD); mpfr_exp(expx, expx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, expx, prec - 1, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(expx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_EXP_TAB2_LIMBS * FLINT_BITS; bits = ARB_EXP_TAB21_BITS + ARB_EXP_TAB22_BITS; num = ARB_EXP_TAB22_NUM; mpfr_init2(tabx, prec); mpfr_init2(expx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_exp_tab22[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(expx, i, MPFR_RNDD); mpfr_div_2ui(expx, expx, bits, MPFR_RNDD); mpfr_exp(expx, expx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, expx, prec - 1, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(expx); mpfr_clear(y1); mpfr_clear(y2); } flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-exp_taylor_rf.c000066400000000000000000000057761264125401100173060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "mpn_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_taylor_rf...."); fflush(stdout); flint_randinit(state); _flint_rand_init_gmp(state); for (iter = 0; iter < 100000; iter++) { mp_ptr x, y1, y2, t; mp_limb_t err1, err2; ulong N; mp_size_t xn; int cmp, result; N = n_randint(state, 288 - 1); xn = 1 + n_randint(state, 20); x = flint_malloc(sizeof(mp_limb_t) * xn); y1 = flint_malloc(sizeof(mp_limb_t) * (xn + 1)); y2 = flint_malloc(sizeof(mp_limb_t) * (xn + 1)); t = flint_malloc(sizeof(mp_limb_t) * (xn + 1)); flint_mpn_rrandom(x, state->gmp_state, xn); flint_mpn_rrandom(y1, state->gmp_state, xn + 1); flint_mpn_rrandom(y2, state->gmp_state, xn + 1); x[xn - 1] &= (LIMB_ONES >> 4); _arb_exp_taylor_naive(y1, &err1, x, xn, N); _arb_exp_taylor_rs(y2, &err2, x, xn, N); cmp = mpn_cmp(y1, y2, xn + 1); if (cmp == 0) { result = 1; } else if (cmp > 0) { mpn_sub_n(t, y1, y2, xn + 1); result = flint_mpn_zero_p(t + 1, xn) && (t[0] <= err2); } else { mpn_sub_n(t, y2, y1, xn + 1); result = flint_mpn_zero_p(t + 1, xn) && (t[0] <= err2); } if (!result) { flint_printf("FAIL\n"); flint_printf("N = %wd xn = %wd\n", N, xn); flint_printf("x ="); flint_mpn_debug(x, xn); flint_printf("y1 ="); flint_mpn_debug(y1, xn + 1); flint_printf("y2 ="); flint_mpn_debug(y2, xn + 1); abort(); } flint_free(x); flint_free(y1); flint_free(y2); flint_free(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-expm1.c000066400000000000000000000106031264125401100154440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("expm1...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec0, prec; prec0 = 400; if (iter % 100 == 0) prec0 = 10000; prec = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, prec0), 4); arb_randtest(b, state, 1 + n_randint(state, prec0), 4); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_expm1(t, t, MPFR_RNDN); arb_expm1(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("iter = %wd, prec = %wd\n\n", iter, prec); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_expm1(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("iter = %wd, prec = %wd\n\n", iter, prec); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 100000; iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_expm1(b, a, prec1); arb_expm1(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); /* compare with exp */ arb_expm1(c, a, prec1); arb_exp(d, a, prec1); arb_sub_ui(d, d, 1, prec1); if (!arb_overlaps(c, d)) { flint_printf("FAIL: comparison with exp\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-fac_ui.c000066400000000000000000000042301264125401100156370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("fac_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, b, c; ulong n; slong prec1, prec2; prec1 = 2 + n_randint(state, 300); prec2 = 2 + n_randint(state, 300); arb_init(a); arb_init(b); arb_init(c); n = n_randtest(state); if (n + 1 == 0) n--; arb_fac_ui(a, n, prec1); arb_fac_ui(b, n + 1, prec1); arb_mul_ui(c, a, n + 1, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-floor.c000066400000000000000000000051751264125401100155430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("floor...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t x; fmpz_t y; slong prec; arb_init(a); arb_init(b); fmpq_init(x); fmpz_init(y); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); prec = 2 + n_randint(state, 200); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_floor(b, a, prec); fmpz_fdiv_q(y, fmpq_numref(x), fmpq_denref(x)); if (!arb_contains_fmpz(b, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); abort(); } arb_floor(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpz_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-gamma.c000066400000000000000000000050711264125401100154770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { arb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 3); arb_gamma(b, a, prec1); arb_gamma(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check gamma(z+1) = z gamma(z) */ arb_mul(b, b, a, prec1); arb_add_ui(c, a, 1, prec1); arb_gamma(c, c, prec1); if (!arb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-gamma_fmpq.c000066400000000000000000000054771264125401100165340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma_fmpq...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t r, s; fmpq_t q; slong accuracy, prec, pp, qq; prec = 2 + n_randint(state, 1 << n_randint(state, 12)); prec += 20; arb_init(r); arb_init(s); fmpq_init(q); pp = -100 + n_randint(state, 10000); qq = 1 + n_randint(state, 20); fmpq_set_si(q, pp, qq); arb_gamma_fmpq(r, q, prec); arb_set_fmpq(s, q, prec); arb_gamma(s, s, prec); if (!arb_overlaps(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("q = "); fmpq_print(q); flint_printf("\n\n"); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); arb_printd(s, prec / 3.33); flint_printf("\n\n"); abort(); } if (!(fmpz_is_one(fmpq_denref(q)) && fmpz_sgn(fmpq_numref(q)) <= 0) && FLINT_ABS(pp / qq) < 10) { accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 6) { flint_printf("FAIL: poor accuracy\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("q = "); fmpq_print(q); flint_printf("\n\n"); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } } arb_clear(r); arb_clear(s); fmpq_clear(q); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_fmpz_mid_rad_10exp.c000066400000000000000000000063521264125401100207270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_fmpz_mid_rad_10exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arb_t x, y, t; fmpz_t mid, rad, exp; slong n, prec; arb_init(x); arb_init(y); arb_init(t); fmpz_init(mid); fmpz_init(rad); fmpz_init(exp); arb_randtest_special(x, state, 1 + n_randint(state, 500), 1 + n_randint(state, 500)); n = 1 + n_randint(state, 500); prec = 2 + n_randint(state, 1500); arb_get_fmpz_mid_rad_10exp(mid, rad, exp, x, n); arf_set_fmpz(arb_midref(y), mid); mag_set_fmpz(arb_radref(y), rad); arb_set_ui(t, 10); arb_pow_fmpz(t, t, exp, prec); arb_mul(y, y, t, prec); if (arb_is_finite(x) && !arb_is_zero(x) && fmpz_sizeinbase(mid, 10) < n && fmpz_sizeinbase(rad, 10) < n) { flint_printf("FAIL (too few digits):\n\n"); flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n"); flint_printf("mid = "); fmpz_print(mid); flint_printf("\n\n"); flint_printf("rad = "); fmpz_print(rad); flint_printf("\n\n"); flint_printf("exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } if (arb_is_finite(x) && !arb_contains(y, x)) { flint_printf("FAIL (containment):\n\n"); flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n"); flint_printf("mid = "); fmpz_print(mid); flint_printf("\n\n"); flint_printf("rad = "); fmpz_print(rad); flint_printf("\n\n"); flint_printf("exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(y); arb_clear(t); fmpz_clear(mid); fmpz_clear(rad); fmpz_clear(exp); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_interval_arf.c000066400000000000000000000042311264125401100177250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_interval_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x, y; arf_t a, b; arb_init(x); arf_init(a); arf_init(b); arb_init(y); arb_randtest_special(x, state, 200, 100); arb_get_interval_arf(a, b, x, 2 + n_randint(state, 200)); arb_set_interval_arf(y, a, b, 2 + n_randint(state, 200)); if (!arb_contains(y, x)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); abort(); } arb_clear(x); arf_clear(a); arf_clear(b); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_interval_fmpz_2exp.c000066400000000000000000000047011264125401100210710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_interval_fmpz_2exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x; arf_t y; fmpz_t a, b, exp; arb_init(x); arf_init(y); fmpz_init(a); fmpz_init(b); fmpz_init(exp); arb_randtest(x, state, 200, 10); arb_get_interval_fmpz_2exp(a, b, exp, x); arf_set_fmpz_2exp(y, a, exp); if (!arb_contains_arf(x, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); fmpz_print(a); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } arf_set_fmpz_2exp(y, b, exp); if (!arb_contains_arf(x, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } arb_clear(x); arf_clear(y); fmpz_clear(a); fmpz_clear(b); fmpz_clear(exp); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_interval_mpfr.c000066400000000000000000000043431264125401100201250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_interval_mpfr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x, y; mpfr_t aa, bb; arb_init(x); arb_init(y); mpfr_init2(aa, 2 + n_randint(state, 200)); mpfr_init2(bb, 2 + n_randint(state, 200)); arb_randtest_special(x, state, 200, 10); arb_get_interval_mpfr(aa, bb, x); arb_set_interval_mpfr(y, aa, bb, 2 + n_randint(state, 200)); if (!arb_contains(y, x)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("aa = "); mpfr_printf("%.50Rg", aa); flint_printf("\n\n"); flint_printf("bb = "); mpfr_printf("%.50Rg", bb); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(y); mpfr_clear(aa); mpfr_clear(bb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_mag.c000066400000000000000000000042041264125401100160150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_mag...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; mag_t m; arb_init(a); arb_init(b); mag_init(m); arb_randtest_special(a, state, 200, 1 + n_randint(state, 100)); arb_get_mag(m, a); MAG_CHECK_BITS(m) if (arf_is_nan(arb_midref(a))) arf_nan(arb_midref(b)); else arf_zero(arb_midref(b)); mag_set(arb_radref(b), m); if (!arb_contains(b, a)) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("m = "); mag_print(m); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); mag_clear(m); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_mag_lower.c000066400000000000000000000051341264125401100172300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_mag_lower...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a; mag_t m; int result; arf_struct t[3]; arf_t s; arb_init(a); mag_init(m); arf_init(s); arb_randtest_special(a, state, 200, 1 + n_randint(state, 100)); arb_get_mag_lower(m, a); MAG_CHECK_BITS(m) if (arb_contains_zero(a)) { result = mag_is_zero(m); } else if (arb_contains_negative(a)) { arf_init_set_shallow(t + 0, arb_midref(a)); arf_init_set_mag_shallow(t + 1, arb_radref(a)); arf_init_set_mag_shallow(t + 2, m); arf_sum(s, t, 3, 16, ARF_RND_DOWN); result = (arf_sgn(s) <= 0); } else { arf_init_set_shallow(t + 0, arb_midref(a)); arf_init_neg_mag_shallow(t + 1, arb_radref(a)); arf_init_neg_mag_shallow(t + 2, m); result = (arf_sgn(s) >= 0); } if (!result) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("m = "); mag_print(m); flint_printf("\n\n"); abort(); } arb_clear(a); mag_clear(m); arf_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_mag_lower_nonnegative.c000066400000000000000000000045601264125401100216270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_mag_lower_nonnegative...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a; mag_t m; int result; arf_struct t[3]; arf_t s; arb_init(a); mag_init(m); arf_init(s); arb_randtest_special(a, state, 200, 1 + n_randint(state, 100)); arb_get_mag_lower_nonnegative(m, a); MAG_CHECK_BITS(m) if (arb_contains_nonpositive(a)) { result = mag_is_zero(m); } else { arf_init_set_shallow(t + 0, arb_midref(a)); arf_init_neg_mag_shallow(t + 1, arb_radref(a)); arf_init_neg_mag_shallow(t + 2, m); arf_sum(s, t, 3, 16, ARF_RND_DOWN); result = (arf_sgn(s) >= 0); } if (!result) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("m = "); mag_print(m); flint_printf("\n\n"); abort(); } arb_clear(a); mag_clear(m); arf_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_mpn_fixed_mod_log2.c000066400000000000000000000072451264125401100210140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec); int main() { slong iter; flint_rand_t state; flint_printf("get_mpn_fixed_mod_log2...."); fflush(stdout); flint_randinit(state); /* _flint_rand_init_gmp(state); */ for (iter = 0; iter < 100000; iter++) { arf_t x; fmpz_t q; mp_ptr w; arb_t wb, t; mp_size_t wn; slong prec, prec2; int success; mp_limb_t error; prec = 2 + n_randint(state, 10000); wn = 1 + n_randint(state, 200); prec2 = FLINT_MAX(prec, wn * FLINT_BITS) + 100; arf_init(x); arb_init(wb); arb_init(t); fmpz_init(q); w = flint_malloc(sizeof(mp_limb_t) * wn); arf_randtest(x, state, prec, 14); /* this should generate numbers close to multiples of log(2) */ if (n_randint(state, 4) == 0) { arb_const_log2(t, prec); fmpz_randtest(q, state, 200); arb_mul_fmpz(t, t, q, prec); arf_add(x, x, arb_midref(t), prec, ARF_RND_DOWN); } success = _arb_get_mpn_fixed_mod_log2(w, q, &error, x, wn); if (success) { _arf_set_mpn_fixed(arb_midref(wb), w, wn, wn, 0, FLINT_BITS * wn); mag_set_ui_2exp_si(arb_radref(wb), error, -FLINT_BITS * wn); arb_const_log2(t, prec2); arb_mul_fmpz(t, t, q, prec2); arb_add(t, t, wb, prec2); if (!arb_contains_arf(t, x)) { flint_printf("FAIL (containment)\n"); flint_printf("x = "); arf_printd(x, 50); flint_printf("\n\n"); flint_printf("q = "); fmpz_print(q); flint_printf("\n\n"); flint_printf("w = "); arb_printd(wb, 50); flint_printf("\n\n"); flint_printf("t = "); arb_printd(t, 50); flint_printf("\n\n"); abort(); } arb_const_log2(t, prec2); if (arf_sgn(arb_midref(wb)) < 0 || arf_cmp(arb_midref(wb), arb_midref(t)) >= 0) { flint_printf("FAIL (expected 0 <= w < log(2))\n"); flint_printf("x = "); arf_printd(x, 50); flint_printf("\n\n"); flint_printf("w = "); arb_printd(wb, 50); flint_printf("\n\n"); abort(); } } flint_free(w); fmpz_clear(q); arf_clear(x); arb_clear(wb); arb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_mpn_fixed_mod_pi4.c000066400000000000000000000101571264125401100206410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int _arf_set_mpn_fixed(arf_t z, mp_srcptr xp, mp_size_t xn, mp_size_t fixn, int negative, slong prec); int main() { slong iter; flint_rand_t state; flint_printf("get_mpn_fixed_mod_pi4...."); fflush(stdout); flint_randinit(state); /* _flint_rand_init_gmp(state); */ for (iter = 0; iter < 100000; iter++) { arf_t x; int octant; fmpz_t q; mp_ptr w; arb_t wb, t, u; mp_size_t wn; slong prec, prec2; int success; mp_limb_t error; prec = 2 + n_randint(state, 10000); wn = 1 + n_randint(state, 200); prec2 = FLINT_MAX(prec, wn * FLINT_BITS) + 100; arf_init(x); arb_init(wb); arb_init(t); arb_init(u); fmpz_init(q); w = flint_malloc(sizeof(mp_limb_t) * wn); arf_randtest(x, state, prec, 14); /* this should generate numbers close to multiples of pi/4 */ if (n_randint(state, 4) == 0) { arb_const_pi(t, prec); arb_mul_2exp_si(t, t, -2); fmpz_randtest(q, state, 200); arb_mul_fmpz(t, t, q, prec); arf_add(x, x, arb_midref(t), prec, ARF_RND_DOWN); } arf_abs(x, x); success = _arb_get_mpn_fixed_mod_pi4(w, q, &octant, &error, x, wn); if (success) { /* could round differently */ if (fmpz_fdiv_ui(q, 8) != octant) { flint_printf("bad octant\n"); abort(); } _arf_set_mpn_fixed(arb_midref(wb), w, wn, wn, 0, FLINT_BITS * wn); mag_set_ui_2exp_si(arb_radref(wb), error, -FLINT_BITS * wn); arb_const_pi(u, prec2); arb_mul_2exp_si(u, u, -2); arb_set(t, wb); if (octant % 2 == 1) arb_sub(t, u, t, prec2); arb_addmul_fmpz(t, u, q, prec2); if (!arb_contains_arf(t, x)) { flint_printf("FAIL (containment)\n"); flint_printf("x = "); arf_printd(x, 50); flint_printf("\n\n"); flint_printf("q = "); fmpz_print(q); flint_printf("\n\n"); flint_printf("w = "); arb_printd(wb, 50); flint_printf("\n\n"); flint_printf("t = "); arb_printd(t, 50); flint_printf("\n\n"); abort(); } arb_const_pi(t, prec2); arb_mul_2exp_si(t, t, -2); if (arf_sgn(arb_midref(wb)) < 0 || arf_cmp(arb_midref(wb), arb_midref(t)) >= 0) { flint_printf("FAIL (expected 0 <= w < pi/4)\n"); flint_printf("x = "); arf_printd(x, 50); flint_printf("\n\n"); flint_printf("w = "); arb_printd(wb, 50); flint_printf("\n\n"); abort(); } } flint_free(w); fmpz_clear(q); arf_clear(x); arb_clear(wb); arb_clear(t); arb_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_rand_fmpq.c000066400000000000000000000036331264125401100172250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_rand_fmpq...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x; fmpq_t q; arb_init(x); fmpq_init(q); arb_randtest(x, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(q, state, x, 1 + n_randint(state, 200)); if (!arb_contains_fmpq(x, q) || !fmpq_is_canonical(q)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("q = "); fmpq_print(q); flint_printf("\n\n"); abort(); } arb_clear(x); fmpq_clear(q); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_str.c000066400000000000000000000056051264125401100160670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" int main() { flint_rand_t state; slong iter; flint_printf("get_str...."); fflush(stdout); flint_randinit(state); /* just test no crashing... */ for (iter = 0; iter < 10000; iter++) { arb_t x; char * s; slong n; arb_init(x); arb_randtest_special(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); n = 1 + n_randint(state, 300); s = arb_get_str(x, n, (n_randint(state, 2) * ARB_STR_MORE) | (n_randint(state, 2) * ARB_STR_NO_RADIUS) | (ARB_STR_CONDENSE * n_randint(state, 50))); flint_free(s); arb_clear(x); } for (iter = 0; iter < 100000; iter++) { arb_t x, y; char * s; slong n, prec; int conversion_error; arb_init(x); arb_init(y); arb_randtest_special(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); arb_randtest_special(y, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); n = 1 + n_randint(state, 300); prec = 2 + n_randint(state, 1000); s = arb_get_str(x, n, n_randint(state, 2) * ARB_STR_MORE); conversion_error = arb_set_str(y, s, prec); if (conversion_error || !arb_contains(y, x)) { flint_printf("FAIL (roundtrip) iter = %wd\n", iter); flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n"); flint_printf("s = %s", s); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n"); abort(); } flint_free(s); arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-get_unique_fmpz.c000066400000000000000000000076251264125401100176250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_unique_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x, z; fmpz_t y, a, b, exp; int unique, unique2; arb_init(x); arb_init(z); fmpz_init(y); fmpz_init(a); fmpz_init(b); fmpz_init(exp); arb_randtest(x, state, 2000, 10); unique = arb_get_unique_fmpz(y, x); arb_get_interval_fmpz_2exp(a, b, exp, x); if (fmpz_sgn(exp) >= 0) { fmpz_mul_2exp(a, a, fmpz_get_si(exp)); fmpz_mul_2exp(b, b, fmpz_get_si(exp)); } else { fmpz_cdiv_q_2exp(a, a, -fmpz_get_si(exp)); fmpz_fdiv_q_2exp(b, b, -fmpz_get_si(exp)); } unique2 = fmpz_equal(a, b); if ((unique != unique2) || (unique && !fmpz_equal(y, a))) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("unique = %d, unique2 = %d\n\n", unique, unique2); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("a = "); fmpz_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } if (unique) { arb_set_fmpz(z, y); arb_set_round(z, z, 2 + n_randint(state, 1000)); if (!arb_overlaps(x, z)) { flint_printf("FAIL (overlap):\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); abort(); } fmpz_add_ui(b, y, 1); if (arb_contains_fmpz(x, b)) { flint_printf("FAIL (contains a + 1):\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); abort(); } fmpz_sub_ui(b, y, 1); if (arb_contains_fmpz(x, b)) { flint_printf("FAIL (contains a - 1):\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); abort(); } } arb_clear(x); arb_clear(z); fmpz_clear(y); fmpz_clear(a); fmpz_clear(b); fmpz_clear(exp); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-hurwitz_zeta.c000066400000000000000000000053621264125401100171570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "acb.h" int main() { slong iter; flint_rand_t state; flint_printf("hurwitz_zeta...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, b, c; acb_t d, e, f; slong prec; prec = 2 + n_randint(state, 300); arb_init(a); arb_init(b); arb_init(c); acb_init(d); acb_init(e); acb_init(f); arb_randtest_precise(a, state, 1 + n_randint(state, 300), 5); arb_randtest_precise(b, state, 1 + n_randint(state, 300), 5); arb_randtest_precise(c, state, 1 + n_randint(state, 300), 5); acb_set_arb(d, a); acb_set_arb(e, b); arb_hurwitz_zeta(c, a, b, prec); acb_hurwitz_zeta(f, d, e, prec); if (!arb_overlaps(c, acb_realref(f)) || (arb_is_finite(c) && !arb_contains_zero(acb_imagref(f)))) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_printd(d, 15); flint_printf("\n\n"); flint_printf("e = "); acb_printd(e, 15); flint_printf("\n\n"); flint_printf("f = "); acb_printd(f, 15); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); acb_clear(d); acb_clear(e); acb_clear(f); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-lgamma.c000066400000000000000000000043461264125401100156570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("lgamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { arb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 3); arb_lgamma(b, a, prec1); arb_lgamma(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_lgamma(a, a, prec2); if (!arb_equal(a, c)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-log.c000066400000000000000000000122241264125401100151740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("log...."); fflush(stdout); flint_randinit(state); /* compare with mpfr */ for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 300); do { arb_randtest(a, state, 1 + n_randint(state, 200), 10); } while (arb_contains_nonpositive(a)); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_log(t, t, MPFR_RNDN); arb_log(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_log(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* compare with mpfr (higher precision) */ for (iter = 0; iter < 1000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 6000); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 7000); do { arb_randtest(a, state, 1 + n_randint(state, 6000), 10); } while (arb_contains_nonpositive(a)); arb_randtest(b, state, 1 + n_randint(state, 6000), 10); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_log(t, t, MPFR_RNDN); arb_log(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_log(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* test large numbers */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, ab, lab, la, lb, lalb; slong prec = 2 + n_randint(state, 6000); arb_init(a); arb_init(b); arb_init(ab); arb_init(lab); arb_init(la); arb_init(lb); arb_init(lalb); arb_randtest(a, state, 1 + n_randint(state, 400), 400); arb_randtest(b, state, 1 + n_randint(state, 400), 400); arb_log(la, a, prec); arb_log(lb, b, prec); arb_mul(ab, a, b, prec); arb_log(lab, ab, prec); arb_add(lalb, la, lb, prec); if (!arb_overlaps(lab, lalb)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("la = "); arb_print(la); flint_printf("\n\n"); flint_printf("lb = "); arb_print(lb); flint_printf("\n\n"); flint_printf("ab = "); arb_print(ab); flint_printf("\n\n"); flint_printf("lab = "); arb_print(lab); flint_printf("\n\n"); flint_printf("lalb = "); arb_print(lalb); flint_printf("\n\n"); abort(); } arb_log(a, a, prec); if (!arb_overlaps(a, la)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(ab); arb_clear(lab); arb_clear(la); arb_clear(lb); arb_clear(lalb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-log1p.c000066400000000000000000000062651264125401100154450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("log1p...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 20000; iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100); arb_log1p(b, a, prec1); arb_log1p(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* compare with log */ arb_add_ui(d, a, 1, prec2); arb_log(d, d, prec2); if (!arb_overlaps(c, d)) { flint_printf("FAIL: comparison with log\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_log1p(a, a, prec1); if (!arb_overlaps(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-log_arf.c000066400000000000000000000061561264125401100160330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("log_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arf_t x; arb_t y1, y2; slong prec1, prec2, acc1, acc2; prec1 = 2 + n_randint(state, 9000); prec2 = 2 + n_randint(state, 9000); arf_init(x); arb_init(y1); arb_init(y2); arf_randtest_special(x, state, 1 + n_randint(state, 9000), 200); arb_randtest_special(y1, state, 1 + n_randint(state, 9000), 200); arb_randtest_special(y2, state, 1 + n_randint(state, 9000), 200); if (n_randint(state, 2)) arf_add_ui(x, x, 1, 2 + n_randint(state, 9000), ARF_RND_DOWN); arb_log_arf(y1, x, prec1); arb_log_arf(y2, x, prec2); if (!arb_overlaps(y1, y2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("prec1 = %wd, prec2 = %wd\n\n", prec1, prec2); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y1 = "); arb_print(y1); flint_printf("\n\n"); flint_printf("y2 = "); arb_print(y2); flint_printf("\n\n"); abort(); } acc1 = arb_rel_accuracy_bits(y1); acc2 = arb_rel_accuracy_bits(y2); if (arf_sgn(x) > 0) { if (acc1 < prec1 - 2 || acc2 < prec2 - 2) { flint_printf("FAIL: accuracy\n\n"); flint_printf("prec1 = %wd, prec2 = %wd\n\n", prec1, prec2); flint_printf("acc1 = %wd, acc2 = %wd\n\n", acc1, acc2); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y1 = "); arb_print(y1); flint_printf("\n\n"); flint_printf("y2 = "); arb_print(y2); flint_printf("\n\n"); abort(); } } arf_clear(x); arb_clear(y1); arb_clear(y2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-log_tab.c000066400000000000000000000165701264125401100160320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong i; mpfr_t tabx, logx, y1, y2; mpz_t tt; flint_printf("log_tab...."); fflush(stdout); { slong prec, bits, num; prec = ARB_LOG_TAB1_LIMBS * FLINT_BITS; bits = ARB_LOG_TAB11_BITS; num = 1 << ARB_LOG_TAB11_BITS; mpfr_init2(tabx, prec); mpfr_init2(logx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_log_tab11[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(logx, i, MPFR_RNDD); mpfr_div_2ui(logx, logx, bits, MPFR_RNDD); mpfr_add_ui(logx, logx, 1, MPFR_RNDD); mpfr_log(logx, logx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(logx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_LOG_TAB1_LIMBS * FLINT_BITS; bits = ARB_LOG_TAB11_BITS + ARB_LOG_TAB12_BITS; num = 1 << ARB_LOG_TAB12_BITS; mpfr_init2(tabx, prec); mpfr_init2(logx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_log_tab12[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(logx, i, MPFR_RNDD); mpfr_div_2ui(logx, logx, bits, MPFR_RNDD); mpfr_add_ui(logx, logx, 1, MPFR_RNDD); mpfr_log(logx, logx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(logx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_LOG_TAB2_LIMBS * FLINT_BITS; bits = ARB_LOG_TAB21_BITS; num = 1 << ARB_LOG_TAB21_BITS; mpfr_init2(tabx, prec); mpfr_init2(logx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_log_tab21[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(logx, i, MPFR_RNDD); mpfr_div_2ui(logx, logx, bits, MPFR_RNDD); mpfr_add_ui(logx, logx, 1, MPFR_RNDD); mpfr_log(logx, logx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(logx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_LOG_TAB2_LIMBS * FLINT_BITS; bits = ARB_LOG_TAB21_BITS + ARB_LOG_TAB22_BITS; num = 1 << ARB_LOG_TAB22_BITS; mpfr_init2(tabx, prec); mpfr_init2(logx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_log_tab22[i]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(logx, i, MPFR_RNDD); mpfr_div_2ui(logx, logx, bits, MPFR_RNDD); mpfr_add_ui(logx, logx, 1, MPFR_RNDD); mpfr_log(logx, logx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, logx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } mpfr_clear(tabx); mpfr_clear(logx); mpfr_clear(y1); mpfr_clear(y2); } flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-log_ui_from_prev.c000066400000000000000000000051741264125401100177560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("log_ui_from_prev...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t z1, z2, z3; ulong n1, n2; slong prec, accuracy; prec = 2 + n_randint(state, 3000); n1 = n_randint(state, 100000); n2 = n1 + 1 + n_randint(state, 1000); arb_init(z1); arb_init(z2); arb_init(z3); arb_log_ui(z1, n1, prec); arb_log_ui(z2, n2, prec); arb_log_ui_from_prev(z3, n2, z1, n1, prec); if (!arb_overlaps(z2, z3)) { flint_printf("FAIL: overlap\n\n"); flint_printf("prec = %wd, n1 = %wu, n2 = %wu\n\n", prec, n1, n2); flint_printf("z1 = "); arb_printd(z1, prec / 3.33); flint_printf("\n\n"); flint_printf("z2 = "); arb_printd(z2, prec / 3.33); flint_printf("\n\n"); flint_printf("z3 = "); arb_printd(z3, prec / 3.33); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(z3); if (accuracy < prec - 4) { flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec); flint_printf("n1 = %wu, n2 = %wu\n\n", n1, n2); flint_printf("z3 = "); arb_printd(z3, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(z1); arb_clear(z2); arb_clear(z3); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-mul.c000066400000000000000000000224031264125401100152100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int mag_close(const mag_t am, const mag_t bm) { arf_t t, a, b; int res1, res2; arf_init(t); arf_init(a); arf_init(b); arf_set_mag(a, am); arf_set_mag(b, bm); arf_mul_ui(t, b, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res1 = arf_cmp(a, t) <= 0; arf_mul_ui(t, a, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res2 = arf_cmp(b, t) <= 0; arf_clear(t); arf_clear(a); arf_clear(b); return res1 && res2; } void arb_mul_naive(arb_t z, const arb_t x, const arb_t y, slong prec) { fmprb_t c, a, b; fmprb_init(a); fmprb_init(b); fmprb_init(c); arb_get_fmprb(a, x); arb_get_fmprb(b, y); fmprb_mul(c, a, b, prec); arb_set_fmprb(z, c); fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t x, y, z; arb_init(a); arb_init(b); arb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_mul(c, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!arb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_mul(a, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!arb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_mul(b, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!arb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* main test */ for (iter = 0; iter < 10000; iter++) { arb_t x, y, z, v; slong prec; arb_init(x); arb_init(y); arb_init(z); arb_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arb_randtest_special(x, state, n_randint(state,2) ? 2000 : 200, 200); arb_randtest_special(y, state, n_randint(state,2) ? 2000 : 200, 200); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 5)) { case 0: arb_mul(z, x, y, prec); arb_mul_naive(v, x, y, prec); if (!arf_equal(arb_midref(z), arb_midref(v)) || !mag_close(arb_radref(z), arb_radref(v))) { flint_printf("FAIL!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 1: arb_set(y, x); arb_mul(z, x, y, prec); arb_mul(v, x, x, prec); if (!arf_equal(arb_midref(z), arb_midref(v)) || !mag_close(arb_radref(z), arb_radref(v))) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 2: arb_mul(v, x, x, prec); arb_mul(x, x, x, prec); if (!arb_equal(v, x)) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 3: arb_mul(v, x, y, prec); arb_mul(x, x, y, prec); if (!arb_equal(v, x)) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; default: arb_mul(v, x, y, prec); arb_mul(x, y, x, prec); if (!arf_equal(arb_midref(x), arb_midref(v)) || !mag_close(arb_radref(x), arb_radref(v))) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; } } arb_clear(x); arb_clear(y); arb_clear(z); arb_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-mul_arf.c000066400000000000000000000067771264125401100160600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_mul_arf(c, a, x, prec); arb_mul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arf_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_mul_arf(c, a, x, prec); arb_mul_arf(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-mul_fmpz.c000066400000000000000000000067631264125401100162570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_mul_fmpz(c, a, x, prec); arb_mul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_mul_fmpz(c, a, x, prec); arb_mul_fmpz(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpz_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-mul_more.c000066400000000000000000000116651264125401100162420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_more...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t x, y, z; arb_init(a); arb_init(b); arb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_mul(c, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!arb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_mul(a, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!arb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_mul(b, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!arb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-mul_si.c000066400000000000000000000065501264125401100157100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_mul_si(c, a, x, prec); arb_mul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_mul_si(c, a, x, prec); arb_mul_si(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-mul_ui.c000066400000000000000000000065511264125401100157130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "ulong_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_mul_ui(c, a, x, prec); arb_mul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_mul_ui(c, a, x, prec); arb_mul_ui(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-overlaps.c000066400000000000000000000057561264125401100162620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("overlaps...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t am, ar, bm, br, t, u; int c1, c2; arb_init(a); arb_init(b); fmpq_init(am); fmpq_init(ar); fmpq_init(bm); fmpq_init(br); fmpq_init(t); fmpq_init(u); arb_randtest(a, state, 1 + n_randint(state, 500), 14); arb_randtest(b, state, 1 + n_randint(state, 500), 14); arf_get_fmpq(am, arb_midref(a)); mag_get_fmpq(ar, arb_radref(a)); arf_get_fmpq(bm, arb_midref(b)); mag_get_fmpq(br, arb_radref(b)); fmpq_sub(t, am, bm); fmpz_abs(fmpq_numref(t), fmpq_numref(t)); fmpq_add(u, ar, br); c1 = arb_overlaps(a, b); c2 = (fmpq_cmp(t, u) <= 0); if (c1 != c2) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("am = "); fmpq_print(am); flint_printf("\n\n"); flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n"); flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n"); flint_printf("br = "); fmpq_print(br); flint_printf("\n\n"); flint_printf("t = "); fmpq_print(t); flint_printf("\n\n"); flint_printf("u = "); fmpq_print(u); flint_printf("\n\n"); flint_printf("c1 = %d, c2 = %d\n\n", c1, c2); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(am); fmpq_clear(ar); fmpq_clear(bm); fmpq_clear(br); fmpq_clear(t); fmpq_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-pow.c000066400000000000000000000100531264125401100152160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("pow...."); fflush(stdout); flint_randinit(state); /* check large arguments */ for (iter = 0; iter < 20000; iter++) { arb_t a, b, c, d, e, f; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_init(e); arb_init(f); arb_randtest(a, state, 1 + n_randint(state, 1000), 200); arb_randtest(b, state, 1 + n_randint(state, 1000), 200); arb_pow(c, a, b, prec1); arb_pow(d, a, b, prec2); if (!arb_overlaps(c, d)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_randtest(c, state, 1 + n_randint(state, 1000), 200); /* check a^(b+c) = a^b*a^c */ arb_add(e, b, c, prec1); arb_pow(d, a, e, prec1); arb_pow(e, a, b, prec1); arb_pow(f, a, c, prec1); arb_mul(e, e, f, prec1); if (!arb_overlaps(d, e)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_printf("e = "); arb_print(e); flint_printf("\n\n"); abort(); } arb_pow(c, a, b, prec1); arb_set(d, a); arb_pow(d, d, b, prec2); if (!arb_overlaps(c, d)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_set(d, b); arb_pow(d, a, d, prec2); if (!arb_overlaps(c, d)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arb_clear(e); arb_clear(f); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-pow_fmpq.c000066400000000000000000000064411264125401100162470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_fmpq...."); fflush(stdout); flint_randinit(state); /* check large arguments */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpq_t e1, e2, e3; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpq_init(e1); fmpq_init(e2); fmpq_init(e3); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 200); arb_randtest_precise(b, state, 1 + n_randint(state, 1000), 200); fmpq_randtest(e1, state, 200); fmpq_randtest(e2, state, 200); arb_pow_fmpq(b, a, e1, prec1); arb_pow_fmpq(c, a, e1, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("e1 = "); fmpq_print(e1); flint_printf("\n\n"); abort(); } /* check a^(e1+e2) = a^e1*a^e2 */ arb_pow_fmpq(c, a, e2, prec1); arb_mul(d, b, c, prec1); fmpq_add(e3, e1, e2); arb_pow_fmpq(c, a, e3, prec1); if (!arb_overlaps(c, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_printf("e1 = "); fmpq_print(e1); flint_printf("\n\n"); flint_printf("e2 = "); fmpq_print(e2); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpq_clear(e1); fmpq_clear(e2); fmpq_clear(e3); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-pow_fmpz.c000066400000000000000000000064411264125401100162600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_fmpz...."); fflush(stdout); flint_randinit(state); /* check large arguments */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t e1, e2, e3; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(e1); fmpz_init(e2); fmpz_init(e3); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 200); arb_randtest_precise(b, state, 1 + n_randint(state, 1000), 200); fmpz_randtest(e1, state, 200); fmpz_randtest(e2, state, 200); arb_pow_fmpz(b, a, e1, prec1); arb_pow_fmpz(c, a, e1, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("e1 = "); fmpz_print(e1); flint_printf("\n\n"); abort(); } /* check a^(e1+e2) = a^e1*a^e2 */ arb_pow_fmpz(c, a, e2, prec1); arb_mul(d, b, c, prec1); fmpz_add(e3, e1, e2); arb_pow_fmpz(c, a, e3, prec1); if (!arb_overlaps(c, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_printf("e1 = "); fmpz_print(e1); flint_printf("\n\n"); flint_printf("e2 = "); fmpz_print(e2); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(e1); fmpz_clear(e2); fmpz_clear(e3); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-power_sum_vec.c000066400000000000000000000051451264125401100172740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("power_sum_vec...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, b, s, t; arb_ptr res; slong aa, bb, k, n, len; slong prec; len = n_randint(state, 30); prec = 2 + n_randint(state, 500); aa = n_randint(state, 50) - 50; bb = aa + n_randint(state, 50); arb_init(a); arb_init(b); arb_init(s); arb_init(t); res = _arb_vec_init(len); arb_set_si(a, aa); arb_set_si(b, bb); arb_power_sum_vec(res, a, b, len, prec); for (n = 0; n < len; n++) { arb_zero(s); for (k = aa; k < bb; k++) { arb_set_si(t, k); arb_pow_ui(t, t, n, prec); arb_add(s, s, t, prec); } if (!arb_overlaps(res + n, s)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = %wd, b = %wd, n = %wd\n\n", aa, bb, n); flint_printf("res = "); arb_printd(res + n, 30); flint_printf("\n\n"); flint_printf("s = "); arb_printd(s, 30); flint_printf("\n\n"); abort(); } } arb_clear(a); arb_clear(b); arb_clear(s); arb_clear(t); _arb_vec_clear(res, len); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rgamma.c000066400000000000000000000051021264125401100156540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("rgamma...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { arb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 3); arb_rgamma(b, a, prec1); arb_rgamma(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check 1/gamma(z+1) = 1/gamma(z)/z */ arb_div(b, b, a, prec1); arb_add_ui(c, a, 1, prec1); arb_rgamma(c, c, prec1); if (!arb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-richcmp.c000066400000000000000000000105411264125401100160400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" static void arb_supremum(arf_t res, const arb_t x) { if (arf_is_nan(arb_midref(x))) { arf_nan(res); } else if (mag_is_inf(arb_radref(x))) { arf_pos_inf(res); } else { arf_set_mag(res, arb_radref(x)); arf_add(res, res, arb_midref(x), ARF_PREC_EXACT, ARF_RND_CEIL); } } static void arb_infimum(arf_t res, const arb_t x) { if (arf_is_nan(arb_midref(x))) { arf_nan(res); } else if (mag_is_inf(arb_radref(x))) { arf_neg_inf(res); } else { arf_set_mag(res, arb_radref(x)); arf_sub(res, arb_midref(x), res, ARF_PREC_EXACT, ARF_RND_FLOOR); } } int arb_richcmp(const arb_t x, const arb_t y, int op) { switch (op) { case 0: return arb_eq(x, y); case 1: return arb_ne(x, y); case 2: return arb_le(x, y); case 3: return arb_lt(x, y); case 4: return arb_ge(x, y); default: return arb_gt(x, y); } } int arb_richcmp_fallback(const arb_t x, const arb_t y, int op) { arf_t xa, xb, ya, yb; int res; arf_init(xa); arf_init(xb); arf_init(ya); arf_init(yb); arb_infimum(xa, x); arb_supremum(xb, x); arb_infimum(ya, y); arb_supremum(yb, y); if (arf_is_nan(xa) || arf_is_nan(ya)) { res = 0; } else { if (op == 0) /* eq */ { res = arf_equal(xa, xb) && arf_equal(ya, yb) && arf_equal(xa, ya); } else if (op == 1) /* ne */ { res = (arf_cmp(yb, xa) < 0) || (arf_cmp(xb, ya) < 0); } else if (op == 2) /* le */ { res = (arf_cmp(xb, ya) <= 0); } else if (op == 3) /* lt */ { res = (arf_cmp(xb, ya) < 0); } else if (op == 4) /* ge */ { res = (arf_cmp(xa, yb) >= 0); } else /* gt */ { res = (arf_cmp(xa, yb) > 0); } } arf_clear(xa); arf_clear(xb); arf_clear(ya); arf_clear(yb); return res; } int main() { slong iter; flint_rand_t state; flint_printf("richcmp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000000; iter++) { arb_t a, b; int op, res1, res2; arb_init(a); arb_init(b); arb_randtest_special(a, state, 1 + n_randint(state, 100), 5); arb_randtest_special(b, state, 1 + n_randint(state, 100), 5); op = n_randint(state, 6); res1 = arb_richcmp(a, b, op); res2 = arb_richcmp_fallback(a, b, op); if (res1 != res2) { flint_printf("FAIL:\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 30); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 30); flint_printf("\n\n"); flint_printf("op = %d\n\n", op); flint_printf("res1 (cmp) = %d\n\n", res1); flint_printf("res2 (fallback) = %d\n\n", res2); abort(); } arb_clear(a); arb_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rising2_ui.c000066400000000000000000000076031264125401100164720ustar00rootroot00000000000000/*============================================================================= This file is part of arb. arb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with arb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising2_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, u, v, u2, v2; fmpz *f; arb_ptr g; ulong n; slong i, prec; arb_init(a); arb_init(u); arb_init(v); arb_init(u2); arb_init(v2); arb_randtest(a, state, 1 + n_randint(state, 4000), 10); arb_randtest(u, state, 1 + n_randint(state, 4000), 10); arb_randtest(v, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 120); f = _fmpz_vec_init(n + 1); g = _arb_vec_init(n + 1); prec = 2 + n_randint(state, 4000); arb_rising2_ui(u, v, a, n, prec); arith_stirling_number_1u_vec(f, n, n + 1); for (i = 0; i <= n; i++) arb_set_fmpz(g + i, f + i); _arb_poly_evaluate(u2, g, n + 1, a, prec); _arb_poly_derivative(g, g, n + 1, prec); _arb_poly_evaluate(v2, g, n, a, prec); if (!arb_overlaps(u, u2) || !arb_overlaps(v, v2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n"); flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n"); abort(); } arb_set(u2, a); arb_rising2_ui(u2, v, u2, n, prec); if (!arb_equal(u2, u)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_set(v2, a); arb_rising2_ui(u, v2, v2, n, prec); if (!arb_equal(v2, v)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_clear(a); arb_clear(u); arb_clear(v); arb_clear(u2); arb_clear(v2); _fmpz_vec_clear(f, n + 1); _arb_vec_clear(g, n + 1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rising2_ui_bs.c000066400000000000000000000076171264125401100171630ustar00rootroot00000000000000/*============================================================================= This file is part of arb. arb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with arb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising2_ui_bs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, u, v, u2, v2; fmpz *f; arb_ptr g; ulong n; slong i, prec; arb_init(a); arb_init(u); arb_init(v); arb_init(u2); arb_init(v2); arb_randtest(a, state, 1 + n_randint(state, 4000), 10); arb_randtest(u, state, 1 + n_randint(state, 4000), 10); arb_randtest(v, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 120); f = _fmpz_vec_init(n + 1); g = _arb_vec_init(n + 1); prec = 2 + n_randint(state, 4000); arb_rising2_ui_bs(u, v, a, n, prec); arith_stirling_number_1u_vec(f, n, n + 1); for (i = 0; i <= n; i++) arb_set_fmpz(g + i, f + i); _arb_poly_evaluate(u2, g, n + 1, a, prec); _arb_poly_derivative(g, g, n + 1, prec); _arb_poly_evaluate(v2, g, n, a, prec); if (!arb_overlaps(u, u2) || !arb_overlaps(v, v2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n"); flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n"); abort(); } arb_set(u2, a); arb_rising2_ui_bs(u2, v, u2, n, prec); if (!arb_equal(u2, u)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_set(v2, a); arb_rising2_ui_bs(u, v2, v2, n, prec); if (!arb_equal(v2, v)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_clear(a); arb_clear(u); arb_clear(v); arb_clear(u2); arb_clear(v2); _fmpz_vec_clear(f, n + 1); _arb_vec_clear(g, n + 1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rising2_ui_rs.c000066400000000000000000000076301264125401100171760ustar00rootroot00000000000000/*============================================================================= This file is part of arb. arb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with arb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising2_ui_rs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, u, v, u2, v2; fmpz *f; arb_ptr g; ulong n; slong i, prec; arb_init(a); arb_init(u); arb_init(v); arb_init(u2); arb_init(v2); arb_randtest(a, state, 1 + n_randint(state, 4000), 10); arb_randtest(u, state, 1 + n_randint(state, 4000), 10); arb_randtest(v, state, 1 + n_randint(state, 4000), 10); n = n_randint(state, 120); f = _fmpz_vec_init(n + 1); g = _arb_vec_init(n + 1); prec = 2 + n_randint(state, 4000); arb_rising2_ui_rs(u, v, a, n, 0, prec); arith_stirling_number_1u_vec(f, n, n + 1); for (i = 0; i <= n; i++) arb_set_fmpz(g + i, f + i); _arb_poly_evaluate(u2, g, n + 1, a, prec); _arb_poly_derivative(g, g, n + 1, prec); _arb_poly_evaluate(v2, g, n, a, prec); if (!arb_overlaps(u, u2) || !arb_overlaps(v, v2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n"); flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n"); abort(); } arb_set(u2, a); arb_rising2_ui_rs(u2, v, u2, n, 0, prec); if (!arb_equal(u2, u)) { flint_printf("FAIL: aliasing 1\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n"); flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_set(v2, a); arb_rising2_ui_rs(u, v2, v2, n, 0, prec); if (!arb_equal(v2, v)) { flint_printf("FAIL: aliasing 2\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n"); flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_clear(a); arb_clear(u); arb_clear(v); arb_clear(u2); arb_clear(v2); _fmpz_vec_clear(f, n + 1); _arb_vec_clear(g, n + 1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rising_ui.c000066400000000000000000000066031264125401100164070ustar00rootroot00000000000000/*============================================================================= This file is part of arb. arb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with arb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui...."); fflush(stdout); flint_randinit(state); /* compare with fmpq */ for (iter = 0; iter < 1000; iter++) { arb_t a, b; fmpq_t x, y, z; ulong n; slong i; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 1000), 10); arb_randtest(b, state, 1 + n_randint(state, 1000), 10); n = n_randint(state, 80); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 10)); arb_rising_ui(b, a, n, 2 + n_randint(state, 1000)); fmpq_one(y); for (i = 0; i < n; i++) { fmpq_set_si(z, i, 1); fmpq_add(z, x, z); fmpq_mul(y, y, z); } if (!arb_contains_fmpq(b, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 500; iter++) { arb_t x, y; ulong n; slong prec; arb_init(x); arb_init(y); arb_randtest(x, state, 1 + n_randint(state, 200), 10); arb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); prec = 2 + n_randint(state, 1000); arb_rising_ui(y, x, n, prec); arb_rising_ui(x, x, n, prec); if (!arb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rising_ui_bs.c000066400000000000000000000066171264125401100171000ustar00rootroot00000000000000/*============================================================================= This file is part of arb. arb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with arb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_bs...."); fflush(stdout); flint_randinit(state); /* compare with fmpq */ for (iter = 0; iter < 1000; iter++) { arb_t a, b; fmpq_t x, y, z; ulong n; slong i; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 1000), 10); arb_randtest(b, state, 1 + n_randint(state, 1000), 10); n = n_randint(state, 80); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 10)); arb_rising_ui_bs(b, a, n, 2 + n_randint(state, 1000)); fmpq_one(y); for (i = 0; i < n; i++) { fmpq_set_si(z, i, 1); fmpq_add(z, x, z); fmpq_mul(y, y, z); } if (!arb_contains_fmpq(b, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 500; iter++) { arb_t x, y; ulong n; slong prec; arb_init(x); arb_init(y); arb_randtest(x, state, 1 + n_randint(state, 200), 10); arb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); prec = 2 + n_randint(state, 1000); arb_rising_ui_bs(y, x, n, prec); arb_rising_ui_bs(x, x, n, prec); if (!arb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rising_ui_rec.c000066400000000000000000000066231264125401100172420ustar00rootroot00000000000000/*============================================================================= This file is part of arb. arb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with arb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_rec...."); fflush(stdout); flint_randinit(state); /* compare with fmpq */ for (iter = 0; iter < 1000; iter++) { arb_t a, b; fmpq_t x, y, z; ulong n; slong i; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 1000), 10); arb_randtest(b, state, 1 + n_randint(state, 1000), 10); n = n_randint(state, 80); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 10)); arb_rising_ui_rec(b, a, n, 2 + n_randint(state, 1000)); fmpq_one(y); for (i = 0; i < n; i++) { fmpq_set_si(z, i, 1); fmpq_add(z, x, z); fmpq_mul(y, y, z); } if (!arb_contains_fmpq(b, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 500; iter++) { arb_t x, y; ulong n; slong prec; arb_init(x); arb_init(y); arb_randtest(x, state, 1 + n_randint(state, 200), 10); arb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); prec = 2 + n_randint(state, 1000); arb_rising_ui_rec(y, x, n, prec); arb_rising_ui_rec(x, x, n, prec); if (!arb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rising_ui_rs.c000066400000000000000000000067701264125401100171200ustar00rootroot00000000000000/*============================================================================= This file is part of arb. arb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with arb; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_rs...."); fflush(stdout); flint_randinit(state); /* compare with fmpq */ for (iter = 0; iter < 1000; iter++) { arb_t a, b; fmpq_t x, y, z; ulong n, step; slong i; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 1000), 10); arb_randtest(b, state, 1 + n_randint(state, 1000), 10); n = n_randint(state, 80); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 10)); step = n_randint(state, 20); arb_rising_ui_rs(b, a, n, step, 2 + n_randint(state, 1000)); fmpq_one(y); for (i = 0; i < n; i++) { fmpq_set_si(z, i, 1); fmpq_add(z, x, z); fmpq_mul(y, y, z); } if (!arb_contains_fmpq(b, y)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n", n); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of y and x */ for (iter = 0; iter < 500; iter++) { arb_t x, y; ulong n, step; slong prec; arb_init(x); arb_init(y); arb_randtest(x, state, 1 + n_randint(state, 200), 10); arb_randtest(y, state, 1 + n_randint(state, 200), 10); n = n_randint(state, 100); prec = 2 + n_randint(state, 1000); step = n_randint(state, 20); arb_rising_ui_rs(y, x, n, step, prec); arb_rising_ui_rs(x, x, n, step, prec); if (!arb_equal(x, y)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("n = %wu\n", n); abort(); } arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-root_ui.c000066400000000000000000000046331264125401100161000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("root_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; ulong k; slong prec; prec = 2 + n_randint(state, 2000); k = n_randtest_not_zero(state); arb_init(a); arb_init(b); arb_init(c); arb_randtest(a, state, 1 + n_randint(state, 2000), 1 + n_randint(state, 100)); arb_randtest(b, state, 1 + n_randint(state, 2000), 1 + n_randint(state, 100)); arb_root_ui(b, a, k, prec); arb_pow_ui(c, b, k, prec); if (!arb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("k = %wu\n", k); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_root_ui(a, a, k, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-rsqrt.c000066400000000000000000000043071264125401100155710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("rsqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_rsqrt(b, a, prec); arb_inv(c, b, prec); arb_mul(c, c, c, prec); if (!arb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_rsqrt(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-set_interval_arf.c000066400000000000000000000041561264125401100177470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("set_interval_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x; arf_t a, b; arb_init(x); arf_init(a); arf_init(b); arf_randtest_special(a, state, 200, 10); arf_randtest_special(b, state, 200, 10); if (arf_cmp(a, b) > 0) arf_swap(a, b); arb_set_interval_arf(x, a, b, 2 + n_randint(state, 200)); if (!arb_contains_arf(x, a) || !arb_contains_arf(x, b)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); abort(); } arb_clear(x); arf_clear(a); arf_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-set_interval_mpfr.c000066400000000000000000000045041264125401100201400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("set_interval_mpfr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x; arf_t a, b; mpfr_t aa, bb; arb_init(x); arf_init(a); arf_init(b); mpfr_init2(aa, 200); mpfr_init2(bb, 200); arf_randtest_special(a, state, 200, 10); arf_randtest_special(b, state, 200, 10); if (arf_cmp(a, b) > 0) arf_swap(a, b); arf_get_mpfr(aa, a, MPFR_RNDD); arf_get_mpfr(bb, b, MPFR_RNDU); arb_set_interval_mpfr(x, aa, bb, 2 + n_randint(state, 200)); if (!arb_contains_arf(x, a) || !arb_contains_arf(x, b)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); abort(); } arb_clear(x); arf_clear(a); arf_clear(b); mpfr_clear(aa); mpfr_clear(bb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-set_str.c000066400000000000000000000154111264125401100160770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" const char * testdata_floats[] = { "0", /* repeated to test empty string later */ "0", "0.0", "0.", ".0", "+0", "+0.0", "+0.", " +.0 ", "-0", "-0.0", "-0.", "-.0", " 0e3", "0.0e3", "0.e3", " .0e3", "+0e3", "+0.0e3", "+0.e3", "+.0e3", "-0e3", "-0.0e3", "-0.e3", "-.0e3", "0e+3", "0.0e+3", "0.e+3", " .0e+3", "+0e+3", "+0.0e+3", "+0.e+3", "+.0e+3", "-0E+3", "-0.0E+3 ", "-0.e+3", "-.0e+3", "0e-3", "0.0e-3", "0.e-3", ".0E-3", "+0e-3", "+0.0e-3", "+0.E-3", "+.0e-3", "-0e-3", "-0.0e-3", "-0.e-3", "-.0e-3", "03.125", "+03.125", "-03.125", "03.12500", "+03.12500", "-03.12500", "03.125e+3", "+03.125e+3", " -03.125e+3 ", "03.12500e+3", "+03.12500e+3", "-03.12500e+3", "03.125e3", "+03.125E3", "-03.125e3", "03.12500e3", "+03.12500E3", "-03.12500E3", "25000.0e-2", "-25000.0e-2", " 25000.0000000000000000000e-2", "-25000.0000000000000000000e-2", " 000025000.0000000000000000000e-2 ", "-000025000.0000000000000000000e-2", "25000.e-2", "-25000.e-2", "12345.125", "-12345.125", "+12345.125", "inf", "-inf", "+inf", "Inf", "-INF", "+Inf", "NAN", "-NaN", "+NAN", NULL, }; const char * testdata_invalid[] = { "", ".", "+.", "-.", ".e+3", "-.e+5", "+.e-5", "2+3", "150a.25", "-e+4", "10.25x", "10.3.5", "125e3.6", "125e-3.6", "3.14 e+5", "3.140 e3", "3.14+e5", "3.14e+ 5", " 3.14e- 5", "3.14e+-5", "3.14e+/-5", ".0.", "..", ":)", " +/- ", " 0 0", " +/- EEE ", "-3.5e+x5 +/-", "4.7 +/- -3.5e+x5", "4.7 +/-", NULL, }; int main() { flint_rand_t state; arb_t t, u, v; double x; int error, bracket; char tmp[256]; slong i, j; flint_printf("set_str...."); fflush(stdout); flint_randinit(state); arb_init(t); arb_init(u); arb_init(v); flint_randinit(state); for (i = 0; testdata_floats[i] != NULL; i++) { arb_const_pi(t, 53); error = arb_set_str(t, testdata_floats[i], 53); x = strtod(testdata_floats[i], NULL); if (x != x) { arb_indeterminate(u); } else { arf_set_d(arb_midref(u), x); mag_zero(arb_radref(u)); } if (error != 0 || !arb_equal(t, u)) { flint_printf("FAIL (valid input): %s\n", testdata_floats[i]); arb_printd(t, 15); flint_printf("\n"); arb_printd(u, 15); flint_printf("\n"); abort(); } } for (i = 0; testdata_floats[i] != NULL; i++) { for (j = 0; testdata_floats[j] != NULL; j++) { for (bracket = 0; bracket < 2; bracket++) { arb_const_pi(t, 53); bracket = n_randint(state, 2); strcpy(tmp, ""); if (bracket) strcat(tmp, "["); /* allow empty string for midpoint */ strcat(tmp, (i == 0) ? "" : testdata_floats[i]); strcat(tmp, "+/-"); strcat(tmp, testdata_floats[j]); if (bracket) strcat(tmp, "]"); error = arb_set_str(t, tmp, 53); x = strtod((i == 0) ? "0" : testdata_floats[i], NULL); if (x != x) { arb_indeterminate(u); } else { arf_set_d(arb_midref(u), x); mag_zero(arb_radref(u)); } x = strtod(testdata_floats[j], NULL); arf_set_d(arb_midref(v), x); mag_zero(arb_radref(v)); arb_abs(v, v); arb_add_error(u, v); if (error != 0 || !arb_equal(t, u)) { flint_printf("FAIL (valid input): %s\n", tmp); arb_printd(t, 15); flint_printf("\n"); arb_printd(u, 15); flint_printf("\n"); abort(); } } } } for (i = 0; testdata_invalid[i] != NULL; i++) { arb_const_pi(t, 53); error = arb_set_str(t, testdata_invalid[i], 53); if (error == 0) { flint_printf("FAIL (invalid input): %s\n", testdata_invalid[i]); arb_printd(t, 15); flint_printf("\n"); abort(); } } for (i = 0; testdata_invalid[i] != NULL; i++) { for (j = 0; testdata_invalid[j] != NULL; j++) { for (bracket = 0; bracket < 2; bracket++) { arb_const_pi(t, 53); bracket = n_randint(state, 2); strcpy(tmp, ""); if (bracket) strcat(tmp, "["); strcat(tmp, testdata_invalid[i]); strcat(tmp, "+/-"); strcat(tmp, testdata_invalid[j]); if (bracket) strcat(tmp, "]"); error = arb_set_str(t, tmp, 53); if (error == 0) { flint_printf("FAIL (invalid input): %s\n", tmp); arb_printd(t, 15); flint_printf("\n"); abort(); } } } } arb_clear(t); arb_clear(u); arb_clear(v); flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin.c000066400000000000000000000102571264125401100152100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec0, prec; prec0 = 400; if (iter % 100 == 0) prec0 = 8000; prec = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec0 + 100); arb_randtest(a, state, 1 + n_randint(state, prec0), 6); arb_randtest(b, state, 1 + n_randint(state, prec0), 6); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_sin(t, t, MPFR_RNDN); arb_sin(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_sin(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 1000000; iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), prec0); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(d, state, 1 + n_randint(state, prec0), 100); arb_sin(b, a, prec1); arb_sin(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check sin(2a) = 2sin(a)cos(a) */ arb_mul_2exp_si(c, a, 1); arb_sin(c, c, prec1); arb_cos(d, a, prec1); arb_mul(b, b, d, prec1); arb_mul_2exp_si(b, b, 1); if (!arb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_cos.c000066400000000000000000000115451264125401100160550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t q; mpfr_t t, u; slong prec0, prec; prec0 = 400; if (iter % 100 == 0) prec0 = 8000; prec = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); fmpq_init(q); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); arb_randtest(a, state, 1 + n_randint(state, prec0), 6); arb_randtest(b, state, 1 + n_randint(state, prec0), 6); arb_randtest(c, state, 1 + n_randint(state, prec0), 6); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_sin_cos(t, u, t, MPFR_RNDN); arb_sin_cos(b, c, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment (sin)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } if (!arb_contains_mpfr(c, u)) { flint_printf("FAIL: containment (cos)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(q); mpfr_clear(t); mpfr_clear(u); } /* check large arguments */ for (iter = 0; iter < 1000000; iter++) { arb_t a, b, c, d, e; slong prec0, prec1, prec2, prec3; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); if (iter % 10 == 0) prec3 = 50000; else prec3 = 100; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_init(e); arb_randtest_special(a, state, 1 + n_randint(state, prec0), prec3); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(d, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(e, state, 1 + n_randint(state, prec0), 100); arb_sin_cos(b, c, a, prec1); arb_sin_cos(d, e, a, prec2); if (!arb_overlaps(b, d) || !arb_overlaps(c, e)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_printf("e = "); arb_print(e); flint_printf("\n\n"); abort(); } /* check sin(a)^2 + cos(a)^2 = 1 */ arb_mul(d, b, b, prec1); arb_mul(e, c, c, prec1); arb_add(d, d, e, prec1); arb_sub_ui(d, d, 1, prec1); if (!arb_contains_zero(d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arb_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_cos_pi.c000066400000000000000000000051361264125401100165440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, b, c, d, e; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_init(e); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_randtest(d, state, 1 + n_randint(state, 200), 10); arb_randtest(e, state, 1 + n_randint(state, 200), 10); arb_const_pi(b, prec); arb_mul(b, b, a, prec); arb_sin_cos(b, d, b, prec); arb_sin_cos_pi(c, e, a, prec); if (!arb_overlaps(b, c) || !arb_overlaps(d, e)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_printf("e = "); arb_print(e); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arb_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_cos_pi_fmpq.c000066400000000000000000000050001264125401100175550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_pi_fmpq...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t s1, c1, s2, c2; fmpq_t x; slong prec; prec = 2 + n_randint(state, 5000); arb_init(s1); arb_init(c1); arb_init(s2); arb_init(c2); fmpq_init(x); fmpq_randtest(x, state, 1 + n_randint(state, 200)); arb_sin_cos_pi_fmpq(s1, c1, x, prec); arb_const_pi(s2, prec); arb_mul_fmpz(s2, s2, fmpq_numref(x), prec); arb_div_fmpz(s2, s2, fmpq_denref(x), prec); arb_sin_cos(s2, c2, s2, prec); if (!arb_overlaps(s1, s2) || !arb_overlaps(c1, c2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("s1 = "); arb_printd(s1, 15); flint_printf("\n\n"); flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n"); flint_printf("s2 = "); arb_printd(s2, 15); flint_printf("\n\n"); flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n"); abort(); } arb_clear(s1); arb_clear(c1); arb_clear(s2); arb_clear(c2); fmpq_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_cos_pi_fmpq_algebraic.c000066400000000000000000000071051264125401100215560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_pi_fmpq_algebraic...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t s1, s2, c1, c2; ulong p, q, g; slong prec; prec = 2 + n_randint(state, 5000); q = 1 + n_randint(state, 500); p = n_randint(state, q / 2 + 1); g = n_gcd(q, p); q /= g; p /= g; arb_init(s1); arb_init(s2); arb_init(c1); arb_init(c2); _arb_sin_cos_pi_fmpq_algebraic(s1, c1, p, q, prec); arb_const_pi(s2, prec); arb_mul_ui(s2, s2, p, prec); arb_div_ui(s2, s2, q, prec); arb_sin_cos(s2, c2, s2, prec); if (!arb_overlaps(s1, s2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("s1 = "); arb_printd(s1, 15); flint_printf("\n\n"); flint_printf("s2 = "); arb_printd(s2, 15); flint_printf("\n\n"); abort(); } if (!arb_overlaps(c1, c2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n"); flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n"); abort(); } if (arb_rel_accuracy_bits(s1) < prec - 2) { flint_printf("FAIL: accuracy\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("prec=%wd eff=%wd\n", prec, arb_rel_accuracy_bits(s1)); flint_printf("s1 = "); arb_printd(s1, 15); flint_printf("\n\n"); flint_printf("s2 = "); arb_printd(s2, 15); flint_printf("\n\n"); abort(); } if (arb_rel_accuracy_bits(c1) < prec - 2) { flint_printf("FAIL: accuracy\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("prec=%wd eff=%wd\n", prec, arb_rel_accuracy_bits(c1)); flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n"); flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n"); abort(); } arb_clear(s1); arb_clear(s2); arb_clear(c1); arb_clear(c2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_cos_tab.c000066400000000000000000000170121264125401100166760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong i, which; mpfr_t tabx, sinx, y1, y2; mpz_t tt; flint_printf("sin_cos_tab...."); fflush(stdout); { slong prec, bits, num; prec = ARB_SIN_COS_TAB1_LIMBS * FLINT_BITS; bits = ARB_SIN_COS_TAB1_BITS; num = ARB_SIN_COS_TAB1_NUM; mpfr_init2(tabx, prec); mpfr_init2(sinx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (which = 0; which < 2; which++) { for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_sin_cos_tab1[2 * i + which]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(sinx, i, MPFR_RNDD); mpfr_div_2ui(sinx, sinx, bits, MPFR_RNDD); if (which) mpfr_cos(sinx, sinx, MPFR_RNDD); else mpfr_sin(sinx, sinx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, sinx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (which && i == 0) /* special case */ { mpfr_set_ui(y2, 1, MPFR_RNDD); mpfr_mul_2ui(y2, y2, prec, MPFR_RNDD); mpfr_sub_ui(y2, y2, 1, MPFR_RNDD); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); } if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: which = %wd, i = %wd, bits = %wd, prec = %wd\n", which, i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } } mpfr_clear(tabx); mpfr_clear(sinx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_SIN_COS_TAB2_LIMBS * FLINT_BITS; bits = ARB_SIN_COS_TAB21_BITS; num = ARB_SIN_COS_TAB21_NUM; mpfr_init2(tabx, prec); mpfr_init2(sinx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (which = 0; which < 2; which++) { for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_sin_cos_tab21[2 * i + which]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(sinx, i, MPFR_RNDD); mpfr_div_2ui(sinx, sinx, bits, MPFR_RNDD); if (which) mpfr_cos(sinx, sinx, MPFR_RNDD); else mpfr_sin(sinx, sinx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, sinx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (which && i == 0) /* special case */ { mpfr_set_ui(y2, 1, MPFR_RNDD); mpfr_mul_2ui(y2, y2, prec, MPFR_RNDD); mpfr_sub_ui(y2, y2, 1, MPFR_RNDD); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); } if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } } mpfr_clear(tabx); mpfr_clear(sinx); mpfr_clear(y1); mpfr_clear(y2); } { slong prec, bits, num; prec = ARB_SIN_COS_TAB2_LIMBS * FLINT_BITS; bits = ARB_SIN_COS_TAB21_BITS + ARB_SIN_COS_TAB22_BITS; num = ARB_SIN_COS_TAB22_NUM; mpfr_init2(tabx, prec); mpfr_init2(sinx, prec); mpfr_init2(y1, prec); mpfr_init2(y2, prec); for (which = 0; which < 2; which++) { for (i = 0; i < num; i++) { tt->_mp_d = (mp_ptr) arb_sin_cos_tab22[2 * i + which]; tt->_mp_size = prec / FLINT_BITS; tt->_mp_alloc = tt->_mp_size; while (tt->_mp_size > 0 && tt->_mp_d[tt->_mp_size-1] == 0) tt->_mp_size--; mpfr_set_z(tabx, tt, MPFR_RNDD); mpfr_div_2ui(tabx, tabx, prec, MPFR_RNDD); mpfr_set_ui(sinx, i, MPFR_RNDD); mpfr_div_2ui(sinx, sinx, bits, MPFR_RNDD); if (which) mpfr_cos(sinx, sinx, MPFR_RNDD); else mpfr_sin(sinx, sinx, MPFR_RNDD); mpfr_mul_2ui(y1, tabx, prec, MPFR_RNDD); mpfr_floor(y1, y1); mpfr_div_2ui(y1, y1, prec, MPFR_RNDD); mpfr_mul_2ui(y2, sinx, prec, MPFR_RNDD); mpfr_floor(y2, y2); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); if (which && i == 0) /* special case */ { mpfr_set_ui(y2, 1, MPFR_RNDD); mpfr_mul_2ui(y2, y2, prec, MPFR_RNDD); mpfr_sub_ui(y2, y2, 1, MPFR_RNDD); mpfr_div_2ui(y2, y2, prec, MPFR_RNDD); } if (!mpfr_equal_p(y1, y2)) { flint_printf("FAIL: i = %wd, bits = %wd, prec = %wd\n", i, bits, prec); mpfr_printf("y1 = %.1500Rg\n", y1); mpfr_printf("y2 = %.1500Rg\n", y2); abort(); } } } mpfr_clear(tabx); mpfr_clear(sinx); mpfr_clear(y1); mpfr_clear(y2); } flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_cos_taylor_rf.c000066400000000000000000000100411264125401100201240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "mpn_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_taylor_rf...."); fflush(stdout); flint_randinit(state); _flint_rand_init_gmp(state); for (iter = 0; iter < 100000; iter++) { mp_ptr x, y1s, y1c, y2s, y2c, t; mp_limb_t err1, err2; ulong N; mp_size_t xn; int cmp, result; N = n_randint(state, 144 - 1); xn = 1 + n_randint(state, 20); x = flint_malloc(sizeof(mp_limb_t) * xn); y1s = flint_malloc(sizeof(mp_limb_t) * xn); y1c = flint_malloc(sizeof(mp_limb_t) * xn); y2s = flint_malloc(sizeof(mp_limb_t) * xn); y2c = flint_malloc(sizeof(mp_limb_t) * xn); t = flint_malloc(sizeof(mp_limb_t) * xn); flint_mpn_rrandom(x, state->gmp_state, xn); flint_mpn_rrandom(y1s, state->gmp_state, xn); flint_mpn_rrandom(y1c, state->gmp_state, xn); flint_mpn_rrandom(y2s, state->gmp_state, xn); flint_mpn_rrandom(y2c, state->gmp_state, xn); x[xn - 1] &= (LIMB_ONES >> 4); _arb_sin_cos_taylor_naive(y1s, y1c, &err1, x, xn, N); _arb_sin_cos_taylor_rs(y2s, y2c, &err2, x, xn, N, 0, 1); cmp = mpn_cmp(y1s, y2s, xn); if (cmp == 0) { result = 1; } else if (cmp > 0) { mpn_sub_n(t, y1s, y2s, xn); result = flint_mpn_zero_p(t + 1, xn - 1) && (t[0] <= err2); } else { mpn_sub_n(t, y2s, y1s, xn); result = flint_mpn_zero_p(t + 1, xn - 1) && (t[0] <= err2); } if (!result) { flint_printf("FAIL\n"); flint_printf("N = %wd xn = %wd\n", N, xn); flint_printf("x ="); flint_mpn_debug(x, xn); flint_printf("y1s ="); flint_mpn_debug(y1s, xn); flint_printf("y2s ="); flint_mpn_debug(y2s, xn); abort(); } cmp = mpn_cmp(y1c, y2c, xn); if (cmp == 0) { result = 1; } else if (cmp > 0) { mpn_sub_n(t, y1c, y2c, xn); result = flint_mpn_zero_p(t + 1, xn - 1) && (t[0] <= err2); } else { mpn_sub_n(t, y2c, y1c, xn); result = flint_mpn_zero_p(t + 1, xn - 1) && (t[0] <= err2); } if (!result) { flint_printf("FAIL\n"); flint_printf("N = %wd xn = %wd\n", N, xn); flint_printf("x ="); flint_mpn_debug(x, xn); flint_printf("y1c ="); flint_mpn_debug(y1c, xn); flint_printf("y2c ="); flint_mpn_debug(y2c, xn); abort(); } flint_free(x); flint_free(y1s); flint_free(y1c); flint_free(y2s); flint_free(y2c); flint_free(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_pi.c000066400000000000000000000043171264125401100157000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_pi...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t a, b, c; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_const_pi(b, prec); arb_mul(b, b, a, prec); arb_sin(b, b, prec); arb_sin_pi(c, a, prec); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_pi_fmpq.c000066400000000000000000000043271264125401100167240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_pi_fmpq...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t s1, s2; fmpq_t x; slong prec; prec = 2 + n_randint(state, 5000); arb_init(s1); arb_init(s2); fmpq_init(x); fmpq_randtest(x, state, 1 + n_randint(state, 200)); arb_sin_pi_fmpq(s1, x, prec); arb_const_pi(s2, prec); arb_mul_fmpz(s2, s2, fmpq_numref(x), prec); arb_div_fmpz(s2, s2, fmpq_denref(x), prec); arb_sin(s2, s2, prec); if (!arb_overlaps(s1, s2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("s1 = "); arb_printd(s1, 15); flint_printf("\n\n"); flint_printf("s2 = "); arb_printd(s2, 15); flint_printf("\n\n"); abort(); } arb_clear(s1); arb_clear(s2); fmpq_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sin_pi_fmpq_algebraic.c000066400000000000000000000052641264125401100207160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_pi_fmpq_algebraic...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t s1, s2; ulong p, q, g; slong prec; prec = 2 + n_randint(state, 5000); q = 1 + n_randint(state, 500); p = n_randint(state, q / 2 + 1); g = n_gcd(q, p); q /= g; p /= g; arb_init(s1); arb_init(s2); _arb_sin_pi_fmpq_algebraic(s1, p, q, prec); arb_const_pi(s2, prec); arb_mul_ui(s2, s2, p, prec); arb_div_ui(s2, s2, q, prec); arb_sin(s2, s2, prec); if (!arb_overlaps(s1, s2)) { flint_printf("FAIL: overlap\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("s1 = "); arb_printd(s1, 15); flint_printf("\n\n"); flint_printf("s2 = "); arb_printd(s2, 15); flint_printf("\n\n"); abort(); } if (arb_rel_accuracy_bits(s1) < prec - 2) { flint_printf("FAIL: accuracy\n\n"); flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n"); flint_printf("prec=%wd eff=%wd\n", prec, arb_rel_accuracy_bits(s1)); flint_printf("s1 = "); arb_printd(s1, 15); flint_printf("\n\n"); flint_printf("s2 = "); arb_printd(s2, 15); flint_printf("\n\n"); abort(); } arb_clear(s1); arb_clear(s2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sinc.c000066400000000000000000000063141264125401100153520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sinc...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t x, a; slong prec, mag_bits; prec = 2 + n_randint(state, 500); mag_bits = 6 + n_randint(state, 500); arb_init(x); arb_randtest(x, state, 1 + n_randint(state, prec), mag_bits); arb_init(a); arb_sinc(a, x, prec); /* sinc(x) in [-2, 2] */ { arb_t b; arb_init(b); arb_zero(b); mag_one(arb_radref(b)); mag_mul_2exp_si(arb_radref(b), arb_radref(b), 1); if (!arb_contains(b, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(b); } /* sinc(x) * x = sin(x) */ { arb_t b, c; arb_init(b); arb_init(c); arb_mul(b, a, x, prec); arb_sin(c, x, prec); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap (sin)\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(b); arb_clear(c); } /* aliasing */ { arb_t b; arb_init(b); arb_set(b, x); arb_sinc(b, b, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(b); } arb_clear(x); arb_clear(a); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sinh.c000066400000000000000000000045601264125401100153600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sinh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_sinh(t, t, MPFR_RNDN); arb_sinh(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_sinh(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sinh_cosh.c000066400000000000000000000052611264125401100163730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sinh_cosh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t q; mpfr_t t, u; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); fmpq_init(q); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_randtest(c, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_sinh_cosh(t, u, t, MPFR_RNDN); arb_sinh_cosh(b, c, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment (sin)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } if (!arb_contains_mpfr(c, u)) { flint_printf("FAIL: containment (cos)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(q); mpfr_clear(t); mpfr_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-special.c000066400000000000000000000657401264125401100160460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define ASSERT(cond) if (!(cond)) { flint_printf("FAIL: %d\n", __LINE__); abort(); } int main() { arb_t zero, pos, neg, pos_inf, neg_inf, pos_inf_err, neg_inf_err, zero_pm_inf, pos_pm_inf, neg_pm_inf, indet_exact, indet_pos_rad, indet_inf_rad; flint_printf("special...."); fflush(stdout); arb_init(zero); arb_init(pos); arb_init(neg); arb_init(pos_inf); arb_init(neg_inf); arb_init(pos_inf_err); arb_init(neg_inf_err); arb_init(zero_pm_inf); arb_init(pos_pm_inf); arb_init(neg_pm_inf); arb_init(indet_exact); arb_init(indet_pos_rad); arb_init(indet_inf_rad); arb_set_si(pos, 3); arb_div_ui(pos, pos, 5, 53); arb_neg(neg, pos); arb_pos_inf(pos_inf); arb_neg_inf(neg_inf); arb_pos_inf(pos_inf_err); arf_get_mag(arb_radref(pos_inf_err), arb_midref(pos)); arb_neg(neg_inf_err, pos_inf_err); arb_zero_pm_inf(zero_pm_inf); arf_set_si(arb_midref(pos_pm_inf), 3); mag_inf(arb_radref(pos_pm_inf)); arf_set_si(arb_midref(neg_pm_inf), -3); mag_inf(arb_radref(neg_pm_inf)); arf_nan(arb_midref(indet_exact)); mag_zero(arb_radref(indet_exact)); arf_nan(arb_midref(indet_pos_rad)); arf_get_mag(arb_radref(indet_pos_rad), arb_midref(pos)); arf_nan(arb_midref(indet_inf_rad)); arf_get_mag(arb_radref(indet_inf_rad), arb_midref(pos)); ASSERT(arb_is_zero(zero)); ASSERT(!arb_is_zero(pos)); ASSERT(!arb_is_zero(neg)); ASSERT(!arb_is_zero(pos_inf)); ASSERT(!arb_is_zero(neg_inf)); ASSERT(!arb_is_zero(pos_inf_err)); ASSERT(!arb_is_zero(neg_inf_err)); ASSERT(!arb_is_zero(zero_pm_inf)); ASSERT(!arb_is_zero(pos_pm_inf)); ASSERT(!arb_is_zero(neg_pm_inf)); ASSERT(!arb_is_zero(indet_exact)); ASSERT(!arb_is_zero(indet_pos_rad)); ASSERT(!arb_is_zero(indet_inf_rad)); ASSERT(!arb_is_nonzero(zero)); ASSERT(arb_is_nonzero(pos)); ASSERT(arb_is_nonzero(neg)); ASSERT(arb_is_nonzero(pos_inf)); ASSERT(arb_is_nonzero(neg_inf)); ASSERT(arb_is_nonzero(pos_inf_err)); ASSERT(arb_is_nonzero(neg_inf_err)); ASSERT(!arb_is_nonzero(zero_pm_inf)); ASSERT(!arb_is_nonzero(pos_pm_inf)); ASSERT(!arb_is_nonzero(neg_pm_inf)); ASSERT(!arb_is_nonzero(indet_exact)); ASSERT(!arb_is_nonzero(indet_pos_rad)); ASSERT(!arb_is_nonzero(indet_inf_rad)); ASSERT(!arb_is_positive(zero)); ASSERT(arb_is_positive(pos)); ASSERT(!arb_is_positive(neg)); ASSERT(arb_is_positive(pos_inf)); ASSERT(!arb_is_positive(neg_inf)); ASSERT(arb_is_positive(pos_inf_err)); ASSERT(!arb_is_positive(neg_inf_err)); ASSERT(!arb_is_positive(zero_pm_inf)); ASSERT(!arb_is_positive(pos_pm_inf)); ASSERT(!arb_is_positive(neg_pm_inf)); ASSERT(!arb_is_positive(indet_exact)); ASSERT(!arb_is_positive(indet_pos_rad)); ASSERT(!arb_is_positive(indet_inf_rad)); ASSERT(!arb_is_negative(zero)); ASSERT(!arb_is_negative(pos)); ASSERT(arb_is_negative(neg)); ASSERT(!arb_is_negative(pos_inf)); ASSERT(arb_is_negative(neg_inf)); ASSERT(!arb_is_negative(pos_inf_err)); ASSERT(arb_is_negative(neg_inf_err)); ASSERT(!arb_is_negative(zero_pm_inf)); ASSERT(!arb_is_negative(pos_pm_inf)); ASSERT(!arb_is_negative(neg_pm_inf)); ASSERT(!arb_is_negative(indet_exact)); ASSERT(!arb_is_negative(indet_pos_rad)); ASSERT(!arb_is_negative(indet_inf_rad)); ASSERT(arb_is_nonnegative(zero)); ASSERT(arb_is_nonnegative(pos)); ASSERT(!arb_is_nonnegative(neg)); ASSERT(arb_is_nonnegative(pos_inf)); ASSERT(!arb_is_nonnegative(neg_inf)); ASSERT(arb_is_nonnegative(pos_inf_err)); ASSERT(!arb_is_nonnegative(neg_inf_err)); ASSERT(!arb_is_nonnegative(zero_pm_inf)); ASSERT(!arb_is_nonnegative(pos_pm_inf)); ASSERT(!arb_is_nonnegative(neg_pm_inf)); ASSERT(!arb_is_nonnegative(indet_exact)); ASSERT(!arb_is_nonnegative(indet_pos_rad)); ASSERT(!arb_is_nonnegative(indet_inf_rad)); ASSERT(arb_is_nonpositive(zero)); ASSERT(!arb_is_nonpositive(pos)); ASSERT(arb_is_nonpositive(neg)); ASSERT(!arb_is_nonpositive(pos_inf)); ASSERT(arb_is_nonpositive(neg_inf)); ASSERT(!arb_is_nonpositive(pos_inf_err)); ASSERT(arb_is_nonpositive(neg_inf_err)); ASSERT(!arb_is_nonpositive(zero_pm_inf)); ASSERT(!arb_is_nonpositive(pos_pm_inf)); ASSERT(!arb_is_nonpositive(neg_pm_inf)); ASSERT(!arb_is_nonpositive(indet_exact)); ASSERT(!arb_is_nonpositive(indet_pos_rad)); ASSERT(!arb_is_nonpositive(indet_inf_rad)); ASSERT(!arb_contains_negative(zero)); ASSERT(!arb_contains_negative(pos)); ASSERT(arb_contains_negative(neg)); ASSERT(!arb_contains_negative(pos_inf)); ASSERT(arb_contains_negative(neg_inf)); ASSERT(!arb_contains_negative(pos_inf_err)); ASSERT(arb_contains_negative(neg_inf_err)); ASSERT(arb_contains_negative(zero_pm_inf)); ASSERT(arb_contains_negative(pos_pm_inf)); ASSERT(arb_contains_negative(neg_pm_inf)); ASSERT(arb_contains_negative(indet_exact)); ASSERT(arb_contains_negative(indet_pos_rad)); ASSERT(arb_contains_negative(indet_inf_rad)); ASSERT(arb_contains_nonpositive(zero)); ASSERT(!arb_contains_nonpositive(pos)); ASSERT(arb_contains_nonpositive(neg)); ASSERT(!arb_contains_nonpositive(pos_inf)); ASSERT(arb_contains_nonpositive(neg_inf)); ASSERT(!arb_contains_nonpositive(pos_inf_err)); ASSERT(arb_contains_nonpositive(neg_inf_err)); ASSERT(arb_contains_nonpositive(zero_pm_inf)); ASSERT(arb_contains_nonpositive(pos_pm_inf)); ASSERT(arb_contains_nonpositive(neg_pm_inf)); ASSERT(arb_contains_nonpositive(indet_exact)); ASSERT(arb_contains_nonpositive(indet_pos_rad)); ASSERT(arb_contains_nonpositive(indet_inf_rad)); ASSERT(!arb_contains_positive(zero)); ASSERT(arb_contains_positive(pos)); ASSERT(!arb_contains_positive(neg)); ASSERT(arb_contains_positive(pos_inf)); ASSERT(!arb_contains_positive(neg_inf)); ASSERT(arb_contains_positive(pos_inf_err)); ASSERT(!arb_contains_positive(neg_inf_err)); ASSERT(arb_contains_positive(zero_pm_inf)); ASSERT(arb_contains_positive(pos_pm_inf)); ASSERT(arb_contains_positive(neg_pm_inf)); ASSERT(arb_contains_positive(indet_exact)); ASSERT(arb_contains_positive(indet_pos_rad)); ASSERT(arb_contains_positive(indet_inf_rad)); ASSERT(arb_contains_nonnegative(zero)); ASSERT(arb_contains_nonnegative(pos)); ASSERT(!arb_contains_nonnegative(neg)); ASSERT(arb_contains_nonnegative(pos_inf)); ASSERT(!arb_contains_nonnegative(neg_inf)); ASSERT(arb_contains_nonnegative(pos_inf_err)); ASSERT(!arb_contains_nonnegative(neg_inf_err)); ASSERT(arb_contains_nonnegative(zero_pm_inf)); ASSERT(arb_contains_nonnegative(pos_pm_inf)); ASSERT(arb_contains_nonnegative(neg_pm_inf)); ASSERT(arb_contains_nonnegative(indet_exact)); ASSERT(arb_contains_nonnegative(indet_pos_rad)); ASSERT(arb_contains_nonnegative(indet_inf_rad)); ASSERT(arb_is_finite(zero)); ASSERT(arb_is_finite(pos)); ASSERT(arb_is_finite(neg)); ASSERT(!arb_is_finite(pos_inf)); ASSERT(!arb_is_finite(neg_inf)); ASSERT(!arb_is_finite(pos_inf_err)); ASSERT(!arb_is_finite(neg_inf_err)); ASSERT(!arb_is_finite(zero_pm_inf)); ASSERT(!arb_is_finite(pos_pm_inf)); ASSERT(!arb_is_finite(neg_pm_inf)); ASSERT(!arb_is_finite(indet_exact)); ASSERT(!arb_is_finite(indet_pos_rad)); ASSERT(!arb_is_finite(indet_inf_rad)); ASSERT(arb_contains(zero, zero)); ASSERT(!arb_contains(zero, pos)); ASSERT(!arb_contains(zero, neg)); ASSERT(!arb_contains(zero, pos_inf)); ASSERT(!arb_contains(zero, neg_inf)); ASSERT(!arb_contains(zero, pos_inf_err)); ASSERT(!arb_contains(zero, neg_inf_err)); ASSERT(!arb_contains(zero, zero_pm_inf)); ASSERT(!arb_contains(zero, pos_pm_inf)); ASSERT(!arb_contains(zero, neg_pm_inf)); ASSERT(!arb_contains(zero, indet_exact)); ASSERT(!arb_contains(zero, indet_pos_rad)); ASSERT(!arb_contains(zero, indet_inf_rad)); ASSERT(!arb_contains(pos, zero)); ASSERT(arb_contains(pos, pos)); ASSERT(!arb_contains(pos, neg)); ASSERT(!arb_contains(pos, pos_inf)); ASSERT(!arb_contains(pos, neg_inf)); ASSERT(!arb_contains(pos, pos_inf_err)); ASSERT(!arb_contains(pos, neg_inf_err)); ASSERT(!arb_contains(pos, zero_pm_inf)); ASSERT(!arb_contains(pos, pos_pm_inf)); ASSERT(!arb_contains(pos, neg_pm_inf)); ASSERT(!arb_contains(pos, indet_exact)); ASSERT(!arb_contains(pos, indet_pos_rad)); ASSERT(!arb_contains(pos, indet_inf_rad)); ASSERT(!arb_contains(neg, zero)); ASSERT(!arb_contains(neg, pos)); ASSERT(arb_contains(neg, neg)); ASSERT(!arb_contains(neg, pos_inf)); ASSERT(!arb_contains(neg, neg_inf)); ASSERT(!arb_contains(neg, pos_inf_err)); ASSERT(!arb_contains(neg, neg_inf_err)); ASSERT(!arb_contains(neg, zero_pm_inf)); ASSERT(!arb_contains(neg, pos_pm_inf)); ASSERT(!arb_contains(neg, neg_pm_inf)); ASSERT(!arb_contains(neg, indet_exact)); ASSERT(!arb_contains(neg, indet_pos_rad)); ASSERT(!arb_contains(neg, indet_inf_rad)); ASSERT(!arb_contains(pos_inf, zero)); ASSERT(!arb_contains(pos_inf, pos)); ASSERT(!arb_contains(pos_inf, neg)); ASSERT(arb_contains(pos_inf, pos_inf)); ASSERT(!arb_contains(pos_inf, neg_inf)); ASSERT(arb_contains(pos_inf, pos_inf_err)); ASSERT(!arb_contains(pos_inf, neg_inf_err)); ASSERT(!arb_contains(pos_inf, zero_pm_inf)); ASSERT(!arb_contains(pos_inf, pos_pm_inf)); ASSERT(!arb_contains(pos_inf, neg_pm_inf)); ASSERT(!arb_contains(pos_inf, indet_exact)); ASSERT(!arb_contains(pos_inf, indet_pos_rad)); ASSERT(!arb_contains(pos_inf, indet_inf_rad)); ASSERT(!arb_contains(neg_inf, zero)); ASSERT(!arb_contains(neg_inf, pos)); ASSERT(!arb_contains(neg_inf, neg)); ASSERT(!arb_contains(neg_inf, pos_inf)); ASSERT(arb_contains(neg_inf, neg_inf)); ASSERT(!arb_contains(neg_inf, pos_inf_err)); ASSERT(arb_contains(neg_inf, neg_inf_err)); ASSERT(!arb_contains(neg_inf, zero_pm_inf)); ASSERT(!arb_contains(neg_inf, pos_pm_inf)); ASSERT(!arb_contains(neg_inf, neg_pm_inf)); ASSERT(!arb_contains(neg_inf, indet_exact)); ASSERT(!arb_contains(neg_inf, indet_pos_rad)); ASSERT(!arb_contains(neg_inf, indet_inf_rad)); ASSERT(!arb_contains(pos_inf_err, zero)); ASSERT(!arb_contains(pos_inf_err, pos)); ASSERT(!arb_contains(pos_inf_err, neg)); ASSERT(arb_contains(pos_inf_err, pos_inf)); ASSERT(!arb_contains(pos_inf_err, neg_inf)); ASSERT(arb_contains(pos_inf_err, pos_inf_err)); ASSERT(!arb_contains(pos_inf_err, neg_inf_err)); ASSERT(!arb_contains(pos_inf_err, zero_pm_inf)); ASSERT(!arb_contains(pos_inf_err, pos_pm_inf)); ASSERT(!arb_contains(pos_inf_err, neg_pm_inf)); ASSERT(!arb_contains(pos_inf_err, indet_exact)); ASSERT(!arb_contains(pos_inf_err, indet_pos_rad)); ASSERT(!arb_contains(pos_inf_err, indet_inf_rad)); ASSERT(!arb_contains(neg_inf_err, zero)); ASSERT(!arb_contains(neg_inf_err, pos)); ASSERT(!arb_contains(neg_inf_err, neg)); ASSERT(!arb_contains(neg_inf_err, pos_inf)); ASSERT(arb_contains(neg_inf_err, neg_inf)); ASSERT(!arb_contains(neg_inf_err, pos_inf_err)); ASSERT(arb_contains(neg_inf_err, neg_inf_err)); ASSERT(!arb_contains(neg_inf_err, zero_pm_inf)); ASSERT(!arb_contains(neg_inf_err, pos_pm_inf)); ASSERT(!arb_contains(neg_inf_err, neg_pm_inf)); ASSERT(!arb_contains(neg_inf_err, indet_exact)); ASSERT(!arb_contains(neg_inf_err, indet_pos_rad)); ASSERT(!arb_contains(neg_inf_err, indet_inf_rad)); ASSERT(arb_contains(zero_pm_inf, zero)); ASSERT(arb_contains(zero_pm_inf, pos)); ASSERT(arb_contains(zero_pm_inf, neg)); ASSERT(arb_contains(zero_pm_inf, pos_inf)); ASSERT(arb_contains(zero_pm_inf, neg_inf)); ASSERT(arb_contains(zero_pm_inf, pos_inf_err)); ASSERT(arb_contains(zero_pm_inf, neg_inf_err)); ASSERT(arb_contains(zero_pm_inf, zero_pm_inf)); ASSERT(arb_contains(zero_pm_inf, pos_pm_inf)); ASSERT(arb_contains(zero_pm_inf, neg_pm_inf)); ASSERT(!arb_contains(zero_pm_inf, indet_exact)); ASSERT(!arb_contains(zero_pm_inf, indet_pos_rad)); ASSERT(!arb_contains(zero_pm_inf, indet_inf_rad)); ASSERT(arb_contains(pos_pm_inf, zero)); ASSERT(arb_contains(pos_pm_inf, pos)); ASSERT(arb_contains(pos_pm_inf, neg)); ASSERT(arb_contains(pos_pm_inf, pos_inf)); ASSERT(arb_contains(pos_pm_inf, neg_inf)); ASSERT(arb_contains(pos_pm_inf, pos_inf_err)); ASSERT(arb_contains(pos_pm_inf, neg_inf_err)); ASSERT(arb_contains(pos_pm_inf, zero_pm_inf)); ASSERT(arb_contains(pos_pm_inf, pos_pm_inf)); ASSERT(arb_contains(pos_pm_inf, neg_pm_inf)); ASSERT(!arb_contains(pos_pm_inf, indet_exact)); ASSERT(!arb_contains(pos_pm_inf, indet_pos_rad)); ASSERT(!arb_contains(pos_pm_inf, indet_inf_rad)); ASSERT(arb_contains(neg_pm_inf, zero)); ASSERT(arb_contains(neg_pm_inf, pos)); ASSERT(arb_contains(neg_pm_inf, neg)); ASSERT(arb_contains(neg_pm_inf, pos_inf)); ASSERT(arb_contains(neg_pm_inf, neg_inf)); ASSERT(arb_contains(neg_pm_inf, pos_inf_err)); ASSERT(arb_contains(neg_pm_inf, neg_inf_err)); ASSERT(arb_contains(neg_pm_inf, zero_pm_inf)); ASSERT(arb_contains(neg_pm_inf, pos_pm_inf)); ASSERT(arb_contains(neg_pm_inf, neg_pm_inf)); ASSERT(!arb_contains(neg_pm_inf, indet_exact)); ASSERT(!arb_contains(neg_pm_inf, indet_pos_rad)); ASSERT(!arb_contains(neg_pm_inf, indet_inf_rad)); ASSERT(arb_contains(indet_exact, zero)); ASSERT(arb_contains(indet_exact, pos)); ASSERT(arb_contains(indet_exact, neg)); ASSERT(arb_contains(indet_exact, pos_inf)); ASSERT(arb_contains(indet_exact, neg_inf)); ASSERT(arb_contains(indet_exact, pos_inf_err)); ASSERT(arb_contains(indet_exact, neg_inf_err)); ASSERT(arb_contains(indet_exact, zero_pm_inf)); ASSERT(arb_contains(indet_exact, pos_pm_inf)); ASSERT(arb_contains(indet_exact, neg_pm_inf)); ASSERT(arb_contains(indet_exact, indet_exact)); ASSERT(arb_contains(indet_exact, indet_pos_rad)); ASSERT(arb_contains(indet_exact, indet_inf_rad)); ASSERT(arb_contains(indet_pos_rad, zero)); ASSERT(arb_contains(indet_pos_rad, pos)); ASSERT(arb_contains(indet_pos_rad, neg)); ASSERT(arb_contains(indet_pos_rad, pos_inf)); ASSERT(arb_contains(indet_pos_rad, neg_inf)); ASSERT(arb_contains(indet_pos_rad, pos_inf_err)); ASSERT(arb_contains(indet_pos_rad, neg_inf_err)); ASSERT(arb_contains(indet_pos_rad, zero_pm_inf)); ASSERT(arb_contains(indet_pos_rad, pos_pm_inf)); ASSERT(arb_contains(indet_pos_rad, neg_pm_inf)); ASSERT(arb_contains(indet_pos_rad, indet_exact)); ASSERT(arb_contains(indet_pos_rad, indet_pos_rad)); ASSERT(arb_contains(indet_pos_rad, indet_inf_rad)); ASSERT(arb_contains(indet_inf_rad, zero)); ASSERT(arb_contains(indet_inf_rad, pos)); ASSERT(arb_contains(indet_inf_rad, neg)); ASSERT(arb_contains(indet_inf_rad, pos_inf)); ASSERT(arb_contains(indet_inf_rad, neg_inf)); ASSERT(arb_contains(indet_inf_rad, pos_inf_err)); ASSERT(arb_contains(indet_inf_rad, neg_inf_err)); ASSERT(arb_contains(indet_inf_rad, zero_pm_inf)); ASSERT(arb_contains(indet_inf_rad, pos_pm_inf)); ASSERT(arb_contains(indet_inf_rad, neg_pm_inf)); ASSERT(arb_contains(indet_inf_rad, indet_exact)); ASSERT(arb_contains(indet_inf_rad, indet_pos_rad)); ASSERT(arb_contains(indet_inf_rad, indet_inf_rad)); ASSERT(arb_overlaps(zero, zero)); ASSERT(!arb_overlaps(zero, pos)); ASSERT(!arb_overlaps(zero, neg)); ASSERT(!arb_overlaps(zero, pos_inf)); ASSERT(!arb_overlaps(zero, neg_inf)); ASSERT(!arb_overlaps(zero, pos_inf_err)); ASSERT(!arb_overlaps(zero, neg_inf_err)); ASSERT(arb_overlaps(zero, zero_pm_inf)); ASSERT(arb_overlaps(zero, pos_pm_inf)); ASSERT(arb_overlaps(zero, neg_pm_inf)); ASSERT(arb_overlaps(zero, indet_exact)); ASSERT(arb_overlaps(zero, indet_pos_rad)); ASSERT(arb_overlaps(zero, indet_inf_rad)); ASSERT(!arb_overlaps(pos, zero)); ASSERT(arb_overlaps(pos, pos)); ASSERT(!arb_overlaps(pos, neg)); ASSERT(!arb_overlaps(pos, pos_inf)); ASSERT(!arb_overlaps(pos, neg_inf)); ASSERT(!arb_overlaps(pos, pos_inf_err)); ASSERT(!arb_overlaps(pos, neg_inf_err)); ASSERT(arb_overlaps(pos, zero_pm_inf)); ASSERT(arb_overlaps(pos, pos_pm_inf)); ASSERT(arb_overlaps(pos, neg_pm_inf)); ASSERT(arb_overlaps(pos, indet_exact)); ASSERT(arb_overlaps(pos, indet_pos_rad)); ASSERT(arb_overlaps(pos, indet_inf_rad)); ASSERT(!arb_overlaps(neg, zero)); ASSERT(!arb_overlaps(neg, pos)); ASSERT(arb_overlaps(neg, neg)); ASSERT(!arb_overlaps(neg, pos_inf)); ASSERT(!arb_overlaps(neg, neg_inf)); ASSERT(!arb_overlaps(neg, pos_inf_err)); ASSERT(!arb_overlaps(neg, neg_inf_err)); ASSERT(arb_overlaps(neg, zero_pm_inf)); ASSERT(arb_overlaps(neg, pos_pm_inf)); ASSERT(arb_overlaps(neg, neg_pm_inf)); ASSERT(arb_overlaps(neg, indet_exact)); ASSERT(arb_overlaps(neg, indet_pos_rad)); ASSERT(arb_overlaps(neg, indet_inf_rad)); ASSERT(!arb_overlaps(pos_inf, zero)); ASSERT(!arb_overlaps(pos_inf, pos)); ASSERT(!arb_overlaps(pos_inf, neg)); ASSERT(arb_overlaps(pos_inf, pos_inf)); ASSERT(!arb_overlaps(pos_inf, neg_inf)); ASSERT(arb_overlaps(pos_inf, pos_inf_err)); ASSERT(!arb_overlaps(pos_inf, neg_inf_err)); ASSERT(arb_overlaps(pos_inf, zero_pm_inf)); ASSERT(arb_overlaps(pos_inf, pos_pm_inf)); ASSERT(arb_overlaps(pos_inf, neg_pm_inf)); ASSERT(arb_overlaps(pos_inf, indet_exact)); ASSERT(arb_overlaps(pos_inf, indet_pos_rad)); ASSERT(arb_overlaps(pos_inf, indet_inf_rad)); ASSERT(!arb_overlaps(neg_inf, zero)); ASSERT(!arb_overlaps(neg_inf, pos)); ASSERT(!arb_overlaps(neg_inf, neg)); ASSERT(!arb_overlaps(neg_inf, pos_inf)); ASSERT(arb_overlaps(neg_inf, neg_inf)); ASSERT(!arb_overlaps(neg_inf, pos_inf_err)); ASSERT(arb_overlaps(neg_inf, neg_inf_err)); ASSERT(arb_overlaps(neg_inf, zero_pm_inf)); ASSERT(arb_overlaps(neg_inf, pos_pm_inf)); ASSERT(arb_overlaps(neg_inf, neg_pm_inf)); ASSERT(arb_overlaps(neg_inf, indet_exact)); ASSERT(arb_overlaps(neg_inf, indet_pos_rad)); ASSERT(arb_overlaps(neg_inf, indet_inf_rad)); ASSERT(!arb_overlaps(pos_inf_err, zero)); ASSERT(!arb_overlaps(pos_inf_err, pos)); ASSERT(!arb_overlaps(pos_inf_err, neg)); ASSERT(arb_overlaps(pos_inf_err, pos_inf)); ASSERT(!arb_overlaps(pos_inf_err, neg_inf)); ASSERT(arb_overlaps(pos_inf_err, pos_inf_err)); ASSERT(!arb_overlaps(pos_inf_err, neg_inf_err)); ASSERT(arb_overlaps(pos_inf_err, zero_pm_inf)); ASSERT(arb_overlaps(pos_inf_err, pos_pm_inf)); ASSERT(arb_overlaps(pos_inf_err, neg_pm_inf)); ASSERT(arb_overlaps(pos_inf_err, indet_exact)); ASSERT(arb_overlaps(pos_inf_err, indet_pos_rad)); ASSERT(arb_overlaps(pos_inf_err, indet_inf_rad)); ASSERT(!arb_overlaps(neg_inf_err, zero)); ASSERT(!arb_overlaps(neg_inf_err, pos)); ASSERT(!arb_overlaps(neg_inf_err, neg)); ASSERT(!arb_overlaps(neg_inf_err, pos_inf)); ASSERT(arb_overlaps(neg_inf_err, neg_inf)); ASSERT(!arb_overlaps(neg_inf_err, pos_inf_err)); ASSERT(arb_overlaps(neg_inf_err, neg_inf_err)); ASSERT(arb_overlaps(neg_inf_err, zero_pm_inf)); ASSERT(arb_overlaps(neg_inf_err, pos_pm_inf)); ASSERT(arb_overlaps(neg_inf_err, neg_pm_inf)); ASSERT(arb_overlaps(neg_inf_err, indet_exact)); ASSERT(arb_overlaps(neg_inf_err, indet_pos_rad)); ASSERT(arb_overlaps(neg_inf_err, indet_inf_rad)); ASSERT(arb_overlaps(zero_pm_inf, zero)); ASSERT(arb_overlaps(zero_pm_inf, pos)); ASSERT(arb_overlaps(zero_pm_inf, neg)); ASSERT(arb_overlaps(zero_pm_inf, pos_inf)); ASSERT(arb_overlaps(zero_pm_inf, neg_inf)); ASSERT(arb_overlaps(zero_pm_inf, pos_inf_err)); ASSERT(arb_overlaps(zero_pm_inf, neg_inf_err)); ASSERT(arb_overlaps(zero_pm_inf, zero_pm_inf)); ASSERT(arb_overlaps(zero_pm_inf, pos_pm_inf)); ASSERT(arb_overlaps(zero_pm_inf, neg_pm_inf)); ASSERT(arb_overlaps(zero_pm_inf, indet_exact)); ASSERT(arb_overlaps(zero_pm_inf, indet_pos_rad)); ASSERT(arb_overlaps(zero_pm_inf, indet_inf_rad)); ASSERT(arb_overlaps(pos_pm_inf, zero)); ASSERT(arb_overlaps(pos_pm_inf, pos)); ASSERT(arb_overlaps(pos_pm_inf, neg)); ASSERT(arb_overlaps(pos_pm_inf, pos_inf)); ASSERT(arb_overlaps(pos_pm_inf, neg_inf)); ASSERT(arb_overlaps(pos_pm_inf, pos_inf_err)); ASSERT(arb_overlaps(pos_pm_inf, neg_inf_err)); ASSERT(arb_overlaps(pos_pm_inf, zero_pm_inf)); ASSERT(arb_overlaps(pos_pm_inf, pos_pm_inf)); ASSERT(arb_overlaps(pos_pm_inf, neg_pm_inf)); ASSERT(arb_overlaps(pos_pm_inf, indet_exact)); ASSERT(arb_overlaps(pos_pm_inf, indet_pos_rad)); ASSERT(arb_overlaps(pos_pm_inf, indet_inf_rad)); ASSERT(arb_overlaps(neg_pm_inf, zero)); ASSERT(arb_overlaps(neg_pm_inf, pos)); ASSERT(arb_overlaps(neg_pm_inf, neg)); ASSERT(arb_overlaps(neg_pm_inf, pos_inf)); ASSERT(arb_overlaps(neg_pm_inf, neg_inf)); ASSERT(arb_overlaps(neg_pm_inf, pos_inf_err)); ASSERT(arb_overlaps(neg_pm_inf, neg_inf_err)); ASSERT(arb_overlaps(neg_pm_inf, zero_pm_inf)); ASSERT(arb_overlaps(neg_pm_inf, pos_pm_inf)); ASSERT(arb_overlaps(neg_pm_inf, neg_pm_inf)); ASSERT(arb_overlaps(neg_pm_inf, indet_exact)); ASSERT(arb_overlaps(neg_pm_inf, indet_pos_rad)); ASSERT(arb_overlaps(neg_pm_inf, indet_inf_rad)); ASSERT(arb_overlaps(indet_exact, zero)); ASSERT(arb_overlaps(indet_exact, pos)); ASSERT(arb_overlaps(indet_exact, neg)); ASSERT(arb_overlaps(indet_exact, pos_inf)); ASSERT(arb_overlaps(indet_exact, neg_inf)); ASSERT(arb_overlaps(indet_exact, pos_inf_err)); ASSERT(arb_overlaps(indet_exact, neg_inf_err)); ASSERT(arb_overlaps(indet_exact, zero_pm_inf)); ASSERT(arb_overlaps(indet_exact, pos_pm_inf)); ASSERT(arb_overlaps(indet_exact, neg_pm_inf)); ASSERT(arb_overlaps(indet_exact, indet_exact)); ASSERT(arb_overlaps(indet_exact, indet_pos_rad)); ASSERT(arb_overlaps(indet_exact, indet_inf_rad)); ASSERT(arb_overlaps(indet_pos_rad, zero)); ASSERT(arb_overlaps(indet_pos_rad, pos)); ASSERT(arb_overlaps(indet_pos_rad, neg)); ASSERT(arb_overlaps(indet_pos_rad, pos_inf)); ASSERT(arb_overlaps(indet_pos_rad, neg_inf)); ASSERT(arb_overlaps(indet_pos_rad, pos_inf_err)); ASSERT(arb_overlaps(indet_pos_rad, neg_inf_err)); ASSERT(arb_overlaps(indet_pos_rad, zero_pm_inf)); ASSERT(arb_overlaps(indet_pos_rad, pos_pm_inf)); ASSERT(arb_overlaps(indet_pos_rad, neg_pm_inf)); ASSERT(arb_overlaps(indet_pos_rad, indet_exact)); ASSERT(arb_overlaps(indet_pos_rad, indet_pos_rad)); ASSERT(arb_overlaps(indet_pos_rad, indet_inf_rad)); ASSERT(arb_overlaps(indet_inf_rad, zero)); ASSERT(arb_overlaps(indet_inf_rad, pos)); ASSERT(arb_overlaps(indet_inf_rad, neg)); ASSERT(arb_overlaps(indet_inf_rad, pos_inf)); ASSERT(arb_overlaps(indet_inf_rad, neg_inf)); ASSERT(arb_overlaps(indet_inf_rad, pos_inf_err)); ASSERT(arb_overlaps(indet_inf_rad, neg_inf_err)); ASSERT(arb_overlaps(indet_inf_rad, zero_pm_inf)); ASSERT(arb_overlaps(indet_inf_rad, pos_pm_inf)); ASSERT(arb_overlaps(indet_inf_rad, neg_pm_inf)); ASSERT(arb_overlaps(indet_inf_rad, indet_exact)); ASSERT(arb_overlaps(indet_inf_rad, indet_pos_rad)); ASSERT(arb_overlaps(indet_inf_rad, indet_inf_rad)); { fmpz_t t; fmpz_init(t); ASSERT(arb_get_unique_fmpz(t, zero)); ASSERT(!arb_get_unique_fmpz(t, pos_inf)); ASSERT(!arb_get_unique_fmpz(t, neg_inf)); ASSERT(!arb_get_unique_fmpz(t, pos_inf_err)); ASSERT(!arb_get_unique_fmpz(t, neg_inf_err)); ASSERT(!arb_get_unique_fmpz(t, zero_pm_inf)); ASSERT(!arb_get_unique_fmpz(t, pos_pm_inf)); ASSERT(!arb_get_unique_fmpz(t, neg_pm_inf)); ASSERT(!arb_get_unique_fmpz(t, indet_exact)); ASSERT(!arb_get_unique_fmpz(t, indet_pos_rad)); ASSERT(!arb_get_unique_fmpz(t, indet_inf_rad)); fmpz_clear(t); } { arf_t b; slong wp = 30; arf_init(b); arb_get_abs_ubound_arf(b, zero, wp); ASSERT(arf_is_zero(b)); arb_get_abs_ubound_arf(b, pos, wp); ASSERT(arf_sgn(b) > 0); arb_get_abs_ubound_arf(b, neg, wp); ASSERT(arf_sgn(b) > 0); arb_get_abs_ubound_arf(b, pos_inf, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_ubound_arf(b, neg_inf, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_ubound_arf(b, pos_inf_err, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_ubound_arf(b, neg_inf_err, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_ubound_arf(b, zero_pm_inf, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_ubound_arf(b, indet_exact, wp); ASSERT(arf_is_nan(b)); arb_get_abs_ubound_arf(b, indet_pos_rad, wp); ASSERT(arf_is_nan(b)); arb_get_abs_ubound_arf(b, indet_inf_rad, wp); ASSERT(arf_is_nan(b)); arb_get_abs_lbound_arf(b, zero, wp); ASSERT(arf_is_zero(b)); arb_get_abs_lbound_arf(b, pos, wp); ASSERT(arf_sgn(b) > 0); arb_get_abs_lbound_arf(b, neg, wp); ASSERT(arf_sgn(b) > 0); arb_get_abs_lbound_arf(b, pos_inf, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_lbound_arf(b, neg_inf, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_lbound_arf(b, pos_inf_err, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_lbound_arf(b, neg_inf_err, wp); ASSERT(arf_is_pos_inf(b)); arb_get_abs_lbound_arf(b, zero_pm_inf, wp); ASSERT(arf_is_zero(b)); arb_get_abs_lbound_arf(b, indet_exact, wp); ASSERT(arf_is_nan(b)); arb_get_abs_lbound_arf(b, indet_pos_rad, wp); ASSERT(arf_is_nan(b)); arb_get_abs_lbound_arf(b, indet_inf_rad, wp); ASSERT(arf_is_nan(b)); arf_clear(b); } arb_clear(zero); arb_clear(pos); arb_clear(neg); arb_clear(pos_inf); arb_clear(neg_inf); arb_clear(pos_inf_err); arb_clear(neg_inf_err); arb_clear(zero_pm_inf); arb_clear(pos_pm_inf); arb_clear(neg_pm_inf); arb_clear(indet_exact); arb_clear(indet_pos_rad); arb_clear(indet_inf_rad); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sqrt.c000066400000000000000000000042571264125401100154130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 200), 100); arb_sqrt(b, a, prec); arb_mul(c, b, b, prec); if (!arb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_sqrt(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sqrt1pm1.c000066400000000000000000000063471264125401100161140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt1pm1...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 20000; iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100); arb_sqrt1pm1(b, a, prec1); arb_sqrt1pm1(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* compare with sqrt */ arb_add_ui(d, a, 1, prec2); arb_sqrt(d, d, prec2); arb_sub_ui(d, d, 1, prec2); if (!arb_overlaps(c, d)) { flint_printf("FAIL: comparison with log\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_sqrt1pm1(a, a, prec1); if (!arb_overlaps(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sqrtpos.c000066400000000000000000000044261264125401100161330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrtpos...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); do { arb_randtest(a, state, 1 + n_randint(state, 200), 10); } while (arb_contains_negative(a)); arb_sqrtpos(b, a, prec); arb_mul(c, b, b, prec); if (!arb_contains(c, a) || arb_contains_negative(b)) { flint_printf("FAIL: containment / positivity\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_sqrtpos(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sub.c000066400000000000000000000116601264125401100152070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sub...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t x, y, z; arb_init(a); arb_init(b); arb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_sub(c, a, b, 2 + n_randint(state, 200)); fmpq_sub(z, x, y); if (!arb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_sub(a, a, b, 2 + n_randint(state, 200)); fmpq_sub(z, x, y); if (!arb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_sub(b, a, b, 2 + n_randint(state, 200)); fmpq_sub(z, x, y); if (!arb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sub_arf.c000066400000000000000000000067771264125401100160540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sub_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_sub_arf(c, a, x, prec); arb_sub(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arf_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_sub_arf(c, a, x, prec); arb_sub_arf(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sub_fmpz.c000066400000000000000000000067631264125401100162530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("sub_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_sub_fmpz(c, a, x, prec); arb_sub(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_sub_fmpz(c, a, x, prec); arb_sub_fmpz(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpz_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sub_si.c000066400000000000000000000065501264125401100157040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("sub_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_sub_si(c, a, x, prec); arb_sub(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_sub_si(c, a, x, prec); arb_sub_si(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-sub_ui.c000066400000000000000000000065511264125401100157070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "ulong_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("sub_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_sub_ui(c, a, x, prec); arb_sub(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_sub_ui(c, a, x, prec); arb_sub_ui(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-submul.c000066400000000000000000000231651264125401100157300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int mag_close(const mag_t am, const mag_t bm) { arf_t t, a, b; int res1, res2; arf_init(t); arf_init(a); arf_init(b); arf_set_mag(a, am); arf_set_mag(b, bm); arf_mul_ui(t, b, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res1 = arf_cmp(a, t) <= 0; arf_mul_ui(t, a, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res2 = arf_cmp(b, t) <= 0; arf_clear(t); arf_clear(a); arf_clear(b); return res1 && res2; } void arb_submul_naive(arb_t z, const arb_t x, const arb_t y, slong prec) { arb_t t; arb_init(t); arb_mul(t, x, y, ARF_PREC_EXACT); arb_sub(z, z, t, prec); arb_clear(t); } int main() { slong iter, iter2; flint_rand_t state; flint_printf("submul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t x, y, z; arb_init(a); arb_init(b); arb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_randtest(c, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); arb_get_rand_fmpq(z, state, c, 1 + n_randint(state, 200)); arb_submul(c, a, b, 2 + n_randint(state, 200)); fmpq_submul(z, x, y); if (!arb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, x); arb_submul(a, a, b, 2 + n_randint(state, 200)); fmpq_submul(z, x, y); if (!arb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t x, y, z; arb_init(a); arb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); arb_randtest(a, state, 1 + n_randint(state, 200), 10); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, y); arb_submul(b, a, b, 2 + n_randint(state, 200)); fmpq_submul(z, x, y); if (!arb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* main test */ for (iter = 0; iter < 10000; iter++) { arb_t x, y, z, v; slong prec; arb_init(x); arb_init(y); arb_init(z); arb_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arb_randtest_special(x, state, n_randint(state,2) ? 2000 : 200, 200); arb_randtest_special(y, state, n_randint(state,2) ? 2000 : 200, 200); arb_randtest_special(z, state, n_randint(state,2) ? 2000 : 200, 200); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 5)) { case 0: arb_set(v, z); arb_submul(z, x, y, prec); arb_submul_naive(v, x, y, prec); if (!arf_equal(arb_midref(z), arb_midref(v)) || !mag_close(arb_radref(z), arb_radref(v))) { flint_printf("FAIL!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 1: arb_set(y, x); arb_set(z, v); arb_submul(z, x, y, prec); arb_submul(v, x, x, prec); if (!arf_equal(arb_midref(z), arb_midref(v)) || !mag_close(arb_radref(z), arb_radref(v))) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 2: arb_set(v, x); arb_submul(v, x, x, prec); arb_submul(x, x, x, prec); if (!arf_equal(arb_midref(x), arb_midref(v)) || !mag_close(arb_radref(x), arb_radref(v))) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; case 3: arb_set(v, x); arb_submul(v, x, y, prec); arb_submul(x, x, y, prec); if (!arf_equal(arb_midref(x), arb_midref(v)) || !mag_close(arb_radref(x), arb_radref(v))) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; default: arb_set(v, x); arb_submul(v, x, y, prec); arb_submul(x, y, x, prec); if (!arf_equal(arb_midref(x), arb_midref(v)) || !mag_close(arb_radref(x), arb_radref(v))) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("v = "); arb_print(v); flint_printf("\n\n"); abort(); } break; } } arb_clear(x); arb_clear(y); arb_clear(z); arb_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-submul_arf.c000066400000000000000000000070741264125401100165610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("submul_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_set(d, c); arb_submul_arf(c, a, x, prec); arb_submul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arf_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; arf_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arf_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); arf_randtest_special(x, state, 1 + n_randint(state, 2000), 100); prec = 2 + n_randint(state, 2000); arb_set_arf(b, x); arb_set(c, a); arb_submul_arf(c, a, x, prec); arb_submul_arf(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arf_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-submul_fmpz.c000066400000000000000000000070601264125401100167600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("submul_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_set(d, c); arb_submul_fmpz(c, a, x, prec); arb_submul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); fmpz_clear(x); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; fmpz_t x; slong prec; arb_init(a); arb_init(b); arb_init(c); fmpz_init(x); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); fmpz_randtest(x, state, 1 + n_randint(state, 2000)); prec = 2 + n_randint(state, 2000); arb_set_fmpz(b, x); arb_set(c, a); arb_submul_fmpz(c, a, x, prec); arb_submul_fmpz(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpz_clear(x); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-submul_si.c000066400000000000000000000066451264125401100164270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("submul_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_set(d, c); arb_submul_si(c, a, x, prec); arb_submul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; slong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = z_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_si(b, x); arb_set(c, a); arb_submul_si(c, a, x, prec); arb_submul_si(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-submul_ui.c000066400000000000000000000066461264125401100164320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "ulong_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("submul_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b, c, d; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_set(d, c); arb_submul_ui(c, a, x, prec); arb_submul(d, a, b, prec); if (!arb_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* aliasing */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; ulong x; slong prec; arb_init(a); arb_init(b); arb_init(c); arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100); arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100); x = n_randtest(state); prec = 2 + n_randint(state, 2000); arb_set_ui(b, x); arb_set(c, a); arb_submul_ui(c, a, x, prec); arb_submul_ui(a, a, x, prec); if (!arb_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-tanh.c000066400000000000000000000064661264125401100153600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("tanh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t x, y, a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(x); arb_init(y); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_precise(x, state, 1 + n_randint(state, 1000), 100); arb_randtest_precise(y, state, 1 + n_randint(state, 1000), 100); arb_tanh(a, x, prec1); arb_tanh(b, x, prec2); /* check consistency */ if (!arb_overlaps(a, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } /* check tanh(x+y) = (tanh(x) + tanh(y)) / (1 + tanh(x) tanh(y)) */ arb_add(b, x, y, prec1); arb_tanh(b, b, prec1); arb_tanh(c, y, prec1); arb_add(d, a, c, prec1); arb_mul(c, a, c, prec1); arb_add_ui(c, c, 1, prec1); arb_div(d, d, c, prec1); if (!arb_overlaps(b, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); abort(); } arb_tanh(x, x, prec1); if (!arb_overlaps(a, x)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(y); arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-trim.c000066400000000000000000000051501264125401100153660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("trim...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x, y; slong acc1, acc2; int accuracy_ok; arb_init(x); arb_init(y); arb_randtest_special(x, state, 1000, 100); arb_trim(y, x); if (!arb_contains(y, x)) { flint_printf("FAIL (containment):\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); abort(); } acc1 = arb_rel_accuracy_bits(x); acc2 = arb_rel_accuracy_bits(y); accuracy_ok = (acc1 < 0 && acc2 <= acc1) || (acc2 >= acc1 - 1); if (!accuracy_ok) { flint_printf("FAIL (accuracy):\n\n"); flint_printf("x: %wd, y = %wd\n\n", acc1, acc2); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); abort(); } arb_trim(x, x); if (!arb_equal(y, x)) { flint_printf("FAIL (aliasing):\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-union.c000066400000000000000000000052441264125401100155470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("union...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x, y, z; slong prec; int alias; arb_init(x); arb_init(y); arb_init(z); arb_randtest_special(x, state, 200, 10); arb_randtest_special(y, state, 200, 10); arb_randtest_special(z, state, 200, 10); prec = 2 + n_randint(state, 200); arb_union(z, x, y, prec); if (!arb_contains(z, x) || !arb_contains(z, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); abort(); } if (n_randint(state, 2)) { arb_union(x, x, y, prec); alias = arb_equal(x, z); } else { arb_union(y, x, y, prec); alias = arb_equal(y, z); } if (!alias) { flint_printf("FAIL (aliasing):\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); flint_printf("z = "); arb_print(z); flint_printf("\n\n"); abort(); } arb_clear(x); arb_clear(y); arb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta.c000066400000000000000000000041121264125401100153530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { arb_t a, b, c; slong prec1, prec2; prec1 = 2 + n_randint(state, 500); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 500), 5); arb_zeta(b, a, prec1); arb_zeta(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta_ui.c000066400000000000000000000046011264125401100160530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t r; ulong n; mpfr_t s; slong prec, accuracy; prec = 2 + n_randint(state, 1 << n_randint(state, 14)); arb_init(r); mpfr_init2(s, prec + 100); do { n = n_randint(state, 1 << n_randint(state, 10)); } while (n == 1); arb_zeta_ui(r, n, prec); mpfr_zeta_ui(s, n, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta_ui_asymp.c000066400000000000000000000041221264125401100172620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_ui_asymp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t r; ulong n; mpfr_t s; slong prec; prec = 2 + n_randint(state, 1 << n_randint(state, 10)); arb_init(r); mpfr_init2(s, prec + 100); n = 2 + n_randint(state, 1 << n_randint(state, 10)); arb_zeta_ui_asymp(r, n, prec); mpfr_zeta_ui(s, n, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta_ui_bernoulli.c000066400000000000000000000046521264125401100201340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_ui_bernoulli...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t r; ulong n; mpfr_t s; slong prec, accuracy; prec = 2 + n_randint(state, 1 << n_randint(state, 14)); arb_init(r); mpfr_init2(s, prec + 100); do { n = n_randint(state, 1 << n_randint(state, 10)); } while (n % 2 || n == 0); arb_zeta_ui_bernoulli(r, n, prec); mpfr_zeta_ui(s, n, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta_ui_borwein_bsplit.c000066400000000000000000000046371264125401100211660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_ui_borwein_bsplit...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t r; ulong n; mpfr_t s; slong prec, accuracy; prec = 2 + n_randint(state, 1 << n_randint(state, 14)); arb_init(r); mpfr_init2(s, prec + 100); do { n = n_randint(state, 1 << n_randint(state, 10)); } while (n == 1); arb_zeta_ui_borwein_bsplit(r, n, prec); mpfr_zeta_ui(s, n, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta_ui_euler_product.c000066400000000000000000000046111264125401100210100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_ui_euler_product...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_t r; ulong n; mpfr_t s; slong prec, accuracy; do { n = n_randint(state, 1 << n_randint(state, 10)); } while (n < 6); prec = 2 + n_randint(state, 12 * n); arb_init(r); mpfr_init2(s, prec + 100); arb_zeta_ui_euler_product(r, n, prec); mpfr_zeta_ui(s, n, MPFR_RNDN); if (!arb_contains_mpfr(r, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r); if (accuracy < prec - 4) { flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec); flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n"); abort(); } arb_clear(r); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta_ui_vec.c000066400000000000000000000052441264125401100167140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_ui_vec...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { arb_ptr r; ulong n; slong i, num; mpfr_t s; slong prec, accuracy; prec = 2 + n_randint(state, 1 << n_randint(state, 13)); num = 1 + n_randint(state, 20); r = _arb_vec_init(num); mpfr_init2(s, prec + 100); do { n = n_randint(state, 1 << n_randint(state, 10)); } while (n < 2); arb_zeta_ui_vec(r, n, num, prec); for (i = 0; i < num; i++) { mpfr_zeta_ui(s, n + i, MPFR_RNDN); if (!arb_contains_mpfr(r + i, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n\n", n + i); flint_printf("r = "); arb_printd(r + i, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r + i); if (accuracy < prec - 4) { flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec); flint_printf("n = %wu\n\n", n + i); flint_printf("r = "); arb_printd(r + i, prec / 3.33); flint_printf("\n\n"); abort(); } } _arb_vec_clear(r, num); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/test/t-zeta_ui_vec_borwein.c000066400000000000000000000053751264125401100204460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_ui_vec_borwein...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100; iter++) { arb_ptr r; ulong n; slong i, num, step; mpfr_t s; slong prec, accuracy; prec = 2 + n_randint(state, 1 << n_randint(state, 13)); num = 1 + n_randint(state, 20); step = 1 + n_randint(state, 5); r = _arb_vec_init(num); mpfr_init2(s, prec + 100); do { n = n_randint(state, 1 << n_randint(state, 10)); } while (n < 2); arb_zeta_ui_vec_borwein(r, n, num, step, prec); for (i = 0; i < num; i++) { mpfr_zeta_ui(s, n + i * step, MPFR_RNDN); if (!arb_contains_mpfr(r + i, s)) { flint_printf("FAIL: containment\n\n"); flint_printf("n = %wu\n\n", n + i * step); flint_printf("r = "); arb_printd(r + i, prec / 3.33); flint_printf("\n\n"); flint_printf("s = "); mpfr_printf("%.275Rf\n", s); flint_printf("\n\n"); abort(); } accuracy = arb_rel_accuracy_bits(r + i); if (accuracy < prec - 4) { flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec); flint_printf("n = %wu\n\n", n + i * step); flint_printf("r = "); arb_printd(r + i, prec / 3.33); flint_printf("\n\n"); abort(); } } _arb_vec_clear(r, num); mpfr_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb/trim.c000066400000000000000000000040041264125401100141430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013-2014 Fredrik Johansson ******************************************************************************/ #include "arb.h" #define TRIM_PADDING 16 void arb_trim(arb_t y, const arb_t x) { if (mag_is_zero(arb_radref(x)) || arf_is_special(arb_midref(x))) { arb_set(y, x); } else if (mag_is_special(arb_radref(x))) { /* midpoint must be finite, so set to 0 +/- inf */ arb_zero_pm_inf(y); } else { slong bits, accuracy; bits = arb_bits(x); accuracy = arb_rel_accuracy_bits(x); if (accuracy < -TRIM_PADDING) { mag_t t; /* set to 0 +/- r */ mag_init(t); arf_get_mag(t, arb_midref(x)); mag_add(arb_radref(y), t, arb_radref(x)); mag_clear(t); arf_zero(arb_midref(y)); } else if (accuracy < bits - TRIM_PADDING) { arb_set_round(y, x, FLINT_MAX(0, accuracy) + TRIM_PADDING); } else { arb_set(y, x); } } } arb-2.8.1/arb/union.c000066400000000000000000000026231264125401100143250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_union(arb_t z, const arb_t x, const arb_t y, slong prec) { fmprb_t t, u, v; fmprb_init(t); fmprb_init(u); fmprb_init(v); arb_get_fmprb(t, x); arb_get_fmprb(u, y); fmprb_union(v, t, u, prec); arb_set_fmprb(z, v); fmprb_clear(t); fmprb_clear(u); fmprb_clear(v); } arb-2.8.1/arb/version.c000066400000000000000000000021671264125401100146650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb.h" const char * arb_version = "2.8.1"; arb-2.8.1/arb/zeta.c000066400000000000000000000024331264125401100141370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "acb.h" void arb_zeta(arb_t y, const arb_t s, slong prec) { acb_t t; acb_init(t); acb_set_arb(t, s), acb_zeta(t, t, prec); arb_set(y, acb_realref(t)); acb_clear(t); } arb-2.8.1/arb/zeta_ui.c000066400000000000000000000047131264125401100146370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include "arith.h" #include "arb.h" void arb_zeta_ui(arb_t x, ulong n, slong prec) { if (n == 0) { arb_set_si(x, -1); arb_mul_2exp_si(x, x, -1); } else if (n == 1) { arb_indeterminate(x); } /* fast detection of asymptotic case */ else if (n > 0.7 * prec) { arb_zeta_ui_asymp(x, n, prec); } else { /* even */ if (n % 2 == 0) { if (((prec < 10000) && (n < 40 + 0.11*prec)) || ((prec >= 10000) && (arith_bernoulli_number_size(n) * 0.9 < prec))) { arb_zeta_ui_bernoulli(x, n, prec); } else { arb_zeta_ui_euler_product(x, n, prec); } } else { if (n == 3) { arb_const_apery(x, prec); } else if (n < prec * 0.0006) { /* small odd n, extremely high precision */ arb_zeta_ui_borwein_bsplit(x, n, prec); } else if (prec > 20 && n > 6 && n > 0.4 * pow(prec, 0.8)) { /* large n */ arb_zeta_ui_euler_product(x, n, prec); } else { /* fallback */ arb_zeta_ui_vec_borwein(x, n, 1, 0, prec); } } } } arb-2.8.1/arb/zeta_ui_asymp.c000066400000000000000000000026731264125401100160530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_zeta_ui_asymp(arb_t x, ulong s, slong prec) { arb_one(x); if (s != 2 && s > prec) { arb_add_error_2exp_si(x, -prec); } else { arf_t t; arf_init(t); arf_set_ui_2exp_si(t, 1, -s); arb_add_arf(x, x, t, prec); arb_add_error_2exp_si(x, 2 - (3 * s) / 2); arf_clear(t); } } arb-2.8.1/arb/zeta_ui_bernoulli.c000066400000000000000000000032331264125401100167060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" #include "bernoulli.h" void arb_zeta_ui_bernoulli(arb_t x, ulong n, slong prec) { fmpq_t b; arb_t t, f; slong wp; if (n % 2) abort(); wp = prec + FLINT_BIT_COUNT(n) + 2; fmpq_init(b); arb_init(t); arb_init(f); bernoulli_fmpq_ui(b, n); arb_set_fmpq(x, b, wp); arb_const_pi(t, wp); arb_mul_2exp_si(t, t, 1); arb_pow_ui(t, t, n, wp); arb_fac_ui(f, n, wp); arb_div(t, t, f, wp); arb_mul(x, x, t, wp); arb_abs(x, x); arb_mul_2exp_si(x, x, -1); arb_clear(t); arb_clear(f); fmpq_clear(b); } arb-2.8.1/arb/zeta_ui_borwein_bsplit.c000066400000000000000000000111671264125401100177420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* With parameter n, the error is bounded by 3/(3+sqrt(8))^n */ #define ERROR_A 1.5849625007211561815 /* log2(3) */ #define ERROR_B 2.5431066063272239453 /* log2(3+sqrt(8)) */ typedef struct { arb_t A; arb_t B; arb_t C; arb_t D; arb_t Q1; arb_t Q2; arb_t Q3; } zeta_bsplit_state; typedef zeta_bsplit_state zeta_bsplit_t[1]; static __inline__ void zeta_bsplit_init(zeta_bsplit_t S) { arb_init(S->A); arb_init(S->B); arb_init(S->C); arb_init(S->D); arb_init(S->Q1); arb_init(S->Q2); arb_init(S->Q3); } static __inline__ void zeta_bsplit_clear(zeta_bsplit_t S) { arb_clear(S->A); arb_clear(S->B); arb_clear(S->C); arb_clear(S->D); arb_clear(S->Q1); arb_clear(S->Q2); arb_clear(S->Q3); } static __inline__ void zeta_coeff_k(zeta_bsplit_t S, slong k, slong n, slong s) { arb_set_si(S->D, 2 * (n + k)); arb_mul_si(S->D, S->D, n - k, ARF_PREC_EXACT); arb_set_si(S->Q1, k + 1); arb_mul_si(S->Q1, S->Q1, 2*k + 1, ARF_PREC_EXACT); if (k == 0) { arb_zero(S->A); arb_one(S->Q2); } else { arb_set_si(S->A, k % 2 ? 1 : -1); arb_mul(S->A, S->A, S->Q1, ARF_PREC_EXACT); arb_ui_pow_ui(S->Q2, k, s, ARF_PREC_EXACT); } arb_mul(S->Q3, S->Q1, S->Q2, ARF_PREC_EXACT); arb_zero(S->B); arb_set(S->C, S->Q1); } static void zeta_bsplit(zeta_bsplit_t L, slong a, slong b, slong n, slong s, int cont, slong bits) { if (a + 1 == b) { zeta_coeff_k(L, a, n, s); } else { zeta_bsplit_t R; slong m = (a + b) / 2; zeta_bsplit(L, m, b, n, s, 1, bits); zeta_bsplit_init(R); zeta_bsplit(R, a, m, n, s, 1, bits); arb_mul(L->B, L->B, R->D, bits); arb_addmul(L->B, L->A, R->C, bits); arb_mul(L->B, L->B, R->Q2, bits); arb_addmul(L->B, R->B, L->Q3, bits); arb_mul(L->A, L->A, R->Q3, bits); arb_addmul(L->A, R->A, L->Q3, bits); arb_mul(L->C, L->C, R->D, bits); arb_addmul(L->C, R->C, L->Q1, bits); if (cont) { arb_mul(L->D, L->D, R->D, bits); arb_mul(L->Q2, L->Q2, R->Q2, bits); } arb_mul(L->Q1, L->Q1, R->Q1, bits); arb_mul(L->Q3, L->Q3, R->Q3, bits); zeta_bsplit_clear(R); } } /* The error for eta(s) is bounded by 3/(3+sqrt(8))^n */ void mag_borwein_error(mag_t err, slong n) { /* upper bound for 1/(3+sqrt(8)) */ mag_set_ui_2exp_si(err, 736899889, -32); mag_pow_ui(err, err, n); mag_mul_ui(err, err, 3); } void arb_zeta_ui_borwein_bsplit(arb_t x, ulong s, slong prec) { zeta_bsplit_t sum; mag_t err; slong wp, n; /* zeta(0) = -1/2 */ if (s == 0) { arb_set_si(x, -1); arb_mul_2exp_si(x, x, -1); return; } if (s == 1) { flint_printf("zeta_ui_borwein_bsplit: zeta(1)"); abort(); } n = prec / ERROR_B + 2; wp = prec + 30; zeta_bsplit_init(sum); zeta_bsplit(sum, 0, n + 1, n, s, 0, wp); /* A/Q3 - B/Q3 / (C/Q1) = (A*C - B*Q1) / (Q3*C) */ arb_mul(sum->A, sum->A, sum->C, wp); arb_mul(sum->B, sum->B, sum->Q1, wp); arb_sub(sum->A, sum->A, sum->B, wp); arb_mul(sum->Q3, sum->Q3, sum->C, wp); arb_div(sum->C, sum->A, sum->Q3, wp); mag_init(err); mag_borwein_error(err, n); mag_add(arb_radref(sum->C), arb_radref(sum->C), err); mag_clear(err); /* convert from eta(s) to zeta(s) */ arb_div_2expm1_ui(x, sum->C, s - 1, wp); arb_mul_2exp_si(x, x, s - 1); zeta_bsplit_clear(sum); } arb-2.8.1/arb/zeta_ui_euler_product.c000066400000000000000000000062401264125401100175700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include "arb.h" /* Let P(a,b) = prod_{a <= p <= b} (1 - p^(-s)). Then 1/zeta(s) = P(a,M) * P(M+1,inf). According to the analysis in S. Fillebrown, "Faster Computation of Bernoulli Numbers", Journal of Algorithms 13, 431-445 (1992), it holds for all s >= 6 and M >= 1 that (1/P(M+1,inf) - 1) <= 2 * M^(1-s) / (s/2 - 1). Writing 1/zeta(s) = P(a,M) * (1 - eps) and solving for eps gives 1/(1-eps) <= 1 + 2 * M^(1-s) / (s/2 - 1), so we have eps <= 2 * M^(1-s) / (s/2 - 1) = 4 * M^(1-s) / (s-2). Since 0 < P(a,M) <= 1, this bounds the absolute error of 1/zeta(s). */ static void add_error(arb_t z, ulong M, ulong s) { mag_t t, u; mag_init(t); mag_init(u); mag_set_ui(t, M); mag_pow_ui_lower(t, t, s - 1); mag_mul_ui_lower(t, t, s - 2); mag_set_ui(u, 4); mag_div(t, u, t); mag_add(arb_radref(z), arb_radref(z), t); mag_clear(t); mag_clear(u); } void arb_zeta_inv_ui_euler_product(arb_t z, ulong s, slong prec) { slong wp, powprec; double powmag; arb_t t, u; ulong M; mp_limb_t p; if (s < 6) { flint_printf("too small s!\n"); abort(); } /* heuristic */ wp = prec + FLINT_BIT_COUNT(prec) + (prec/s) + 4; arb_init(t); arb_init(u); /* z = 1 - 2^(-s) */ arb_set_ui(z, UWORD(1)); arf_set_ui_2exp_si(arb_midref(t), 1, -s); arb_sub(z, z, t, wp); M = 2; p = UWORD(3); while (1) { /* approximate magnitude of p^s */ powmag = s * log(p) * 1.4426950408889634; powprec = FLINT_MAX(wp - powmag, 8); /* see error analysis */ if ((powmag >= prec) && ((1.-s)*log(M-1.)) - log(s-2.) + 2 <= -(prec+1) * 0.69314718055995) break; M = p; arb_ui_pow_ui(t, p, s, powprec); arb_set_round(u, z, powprec); arb_div(t, u, t, powprec); arb_sub(z, z, t, wp); p = n_nextprime(p, 0); } add_error(z, M, s); arb_clear(t); arb_clear(u); } void arb_zeta_ui_euler_product(arb_t z, ulong s, slong prec) { arb_zeta_inv_ui_euler_product(z, s, prec); arb_inv(z, z, prec); } arb-2.8.1/arb/zeta_ui_vec.c000066400000000000000000000034651264125401100154770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_zeta_ui_vec(arb_ptr x, ulong start, slong num, slong prec) { slong i, num_odd, num_even, start_odd; arb_ptr tmp; num_odd = num / 2 + (start & num & 1); num_even = num - num_odd; start_odd = start % 2; arb_zeta_ui_vec_even(x, start + start_odd, num_even, prec); arb_zeta_ui_vec_odd(x + num_even, start + !start_odd, num_odd, prec); /* interleave */ tmp = flint_malloc(sizeof(arb_struct) * num); for (i = 0; i < num_even; i++) tmp[i] = x[i]; for (i = 0; i < num_odd; i++) tmp[num_even + i] = x[num_even + i]; for (i = 0; i < num_even; i++) x[start_odd + 2 * i] = tmp[i]; for (i = 0; i < num_odd; i++) x[!start_odd + 2 * i] = tmp[num_even + i]; flint_free(tmp); } arb-2.8.1/arb/zeta_ui_vec_borwein.c000066400000000000000000000060441264125401100172200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb.h" /* With parameter n, the error is bounded by 3/(3+sqrt(8))^n */ #define ERROR_A 1.5849625007211561815 /* log2(3) */ #define ERROR_B 2.5431066063272239453 /* log2(3+sqrt(8)) */ void mag_borwein_error(mag_t err, slong n); void arb_zeta_ui_vec_borwein(arb_ptr z, ulong start, slong num, ulong step, slong prec) { slong j, k, s, n, wp; fmpz_t c, d, t, u; fmpz * zeta; mag_t err; if (num < 1) return; wp = prec + FLINT_BIT_COUNT(prec); n = wp / 2.5431066063272239453 + 1; fmpz_init(c); fmpz_init(d); fmpz_init(t); fmpz_init(u); zeta = _fmpz_vec_init(num); fmpz_set_ui(c, 1); fmpz_mul_2exp(c, c, 2 * n - 1); fmpz_set(d, c); for (k = n; k > 0; k--) { /* divide by first k^s */ fmpz_ui_pow_ui(u, k, start); fmpz_tdiv_q(t, d, u); if (k % 2 == 0) fmpz_neg(t, t); fmpz_add(zeta, zeta, t); /* remaining k^s */ fmpz_ui_pow_ui(u, k, step); for (j = 1; j < num; j++) { fmpz_tdiv_q(t, t, u); fmpz_add(zeta + j, zeta + j, t); } /* hypergeometric recurrence */ fmpz_mul2_uiui(c, c, k, 2 * k - 1); fmpz_divexact2_uiui(c, c, 2 * (n - k + 1), n + k - 1); fmpz_add(d, d, c); } mag_init(err); mag_borwein_error(err, n); for (k = 0; k < num; k++) { arb_ptr x = z + k; s = start + step * k; arb_set_fmpz(x, zeta + k); /* the error in each term in the main loop is < 2 */ mag_set_ui(arb_radref(x), 2 * n); arb_div_fmpz(x, x, d, wp); /* mathematical error for eta(s), bounded by 3/(3+sqrt(8))^n */ mag_add(arb_radref(x), arb_radref(x), err); /* convert from eta(s) to zeta(s) */ arb_div_2expm1_ui(x, x, s - 1, wp); arb_mul_2exp_si(x, x, s - 1); } mag_clear(err); fmpz_clear(c); fmpz_clear(d); fmpz_clear(t); fmpz_clear(u); _fmpz_vec_clear(zeta, num); } arb-2.8.1/arb/zeta_ui_vec_even.c000066400000000000000000000024031264125401100165030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_zeta_ui_vec_even(arb_ptr x, ulong start, slong num, slong prec) { slong i; for (i = 0; i < num; i++) arb_zeta_ui(x + i, start + 2 * i, prec); } arb-2.8.1/arb/zeta_ui_vec_odd.c000066400000000000000000000030611264125401100163150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb.h" void arb_zeta_ui_vec_odd(arb_ptr x, ulong start, slong num, slong prec) { slong i, num_borwein; ulong cutoff; cutoff = 40 + 0.3 * prec; if (cutoff > start) { num_borwein = 1 + (cutoff - start) / 2; num_borwein = FLINT_MIN(num_borwein, num); } else num_borwein = 0; arb_zeta_ui_vec_borwein(x, start, num_borwein, 2, prec); for (i = num_borwein; i < num; i++) arb_zeta_ui(x + i, start + 2 * i, prec); } arb-2.8.1/arb_calc.h000066400000000000000000000077121264125401100141700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #ifndef ARB_CALC_H #define ARB_CALC_H #include "arb.h" #include "arb_poly.h" #include "arb_mat.h" #ifdef __cplusplus extern "C" { #endif extern TLS_PREFIX int arb_calc_verbose; typedef int (*arb_calc_func_t)(arb_ptr out, const arb_t inp, void * param, slong order, slong prec); #define ARB_CALC_SUCCESS 0 #define ARB_CALC_IMPRECISE_INPUT 1 #define ARB_CALC_NO_CONVERGENCE 2 /* Root-finding */ typedef struct { arf_struct a; arf_struct b; } arf_interval_struct; typedef arf_interval_struct arf_interval_t[1]; typedef arf_interval_struct * arf_interval_ptr; typedef const arf_interval_struct * arf_interval_srcptr; static __inline__ void arf_interval_init(arf_interval_t v) { arf_init(&v->a); arf_init(&v->b); } static __inline__ void arf_interval_clear(arf_interval_t v) { arf_clear(&v->a); arf_clear(&v->b); } static __inline__ arf_interval_ptr _arf_interval_vec_init(slong n) { slong i; arf_interval_ptr v = (arf_interval_ptr) flint_malloc(sizeof(arf_interval_struct) * n); for (i = 0; i < n; i++) arf_interval_init(v + i); return v; } static __inline__ void _arf_interval_vec_clear(arf_interval_ptr v, slong n) { slong i; for (i = 0; i < n; i++) arf_interval_clear(v + i); flint_free(v); } static __inline__ void arf_interval_set(arf_interval_t v, const arf_interval_t u) { arf_set(&v->a, &u->a); arf_set(&v->b, &u->b); } static __inline__ void arf_interval_swap(arf_interval_t v, arf_interval_t u) { arf_swap(&v->a, &u->a); arf_swap(&v->b, &u->b); } static __inline__ void arf_interval_get_arb(arb_t x, const arf_interval_t v, slong prec) { arb_set_interval_arf(x, &v->a, &v->b, prec); } static __inline__ void arf_interval_printd(const arf_interval_t v, slong n) { flint_printf("["); arf_printd(&v->a, n); flint_printf(", "); arf_printd(&v->b, n); flint_printf("]"); } /* bisection */ int arb_calc_partition(arf_interval_t L, arf_interval_t R, arb_calc_func_t func, void * param, const arf_interval_t block, slong prec); slong arb_calc_isolate_roots(arf_interval_ptr * blocks, int ** flags, arb_calc_func_t func, void * param, const arf_interval_t block, slong maxdepth, slong maxeval, slong maxfound, slong prec); int arb_calc_refine_root_bisect(arf_interval_t r, arb_calc_func_t func, void * param, const arf_interval_t start, slong iter, slong prec); /* newton iteration */ void arb_calc_newton_conv_factor(arf_t conv_factor, arb_calc_func_t func, void * param, const arb_t conv_region, slong prec); int arb_calc_newton_step(arb_t xnew, arb_calc_func_t func, void * param, const arb_t x, const arb_t conv_region, const arf_t conv_factor, slong prec); int arb_calc_refine_root_newton(arb_t r, arb_calc_func_t func, void * param, const arb_t start, const arb_t conv_region, const arf_t conv_factor, slong eval_extra_prec, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/arb_calc/000077500000000000000000000000001264125401100140105ustar00rootroot00000000000000arb-2.8.1/arb_calc/isolate_roots.c000066400000000000000000000131251264125401100170440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_calc.h" #define BLOCK_NO_ZERO 0 #define BLOCK_ISOLATED_ZERO 1 #define BLOCK_UNKNOWN 2 /* 0 means that it *could* be zero; otherwise +/- 1 */ static __inline__ int _arb_sign(const arb_t t) { if (arb_is_positive(t)) return 1; else if (arb_is_negative(t)) return -1; else return 0; } static int check_block(arb_calc_func_t func, void * param, const arf_interval_t block, int asign, int bsign, slong prec) { arb_struct t[2]; arb_t x; int result; arb_init(t + 0); arb_init(t + 1); arb_init(x); arf_interval_get_arb(x, block, prec); func(t, x, param, 1, prec); result = BLOCK_UNKNOWN; if (arb_is_positive(t) || arb_is_negative(t)) { result = BLOCK_NO_ZERO; } else { if ((asign < 0 && bsign > 0) || (asign > 0 && bsign < 0)) { func(t, x, param, 2, prec); if (arb_is_finite(t + 1) && !arb_contains_zero(t + 1)) { result = BLOCK_ISOLATED_ZERO; } } } arb_clear(t + 0); arb_clear(t + 1); arb_clear(x); return result; } #define ADD_BLOCK \ if (*length >= *alloc) \ { \ slong new_alloc; \ new_alloc = (*alloc == 0) ? 1 : 2 * (*alloc); \ *blocks = flint_realloc(*blocks, sizeof(arf_interval_struct) * new_alloc); \ *flags = flint_realloc(*flags, sizeof(int) * new_alloc); \ *alloc = new_alloc; \ } \ arf_interval_init((*blocks) + *length); \ arf_interval_set((*blocks) + *length, block); \ (*flags)[*length] = status; \ (*length)++; \ static void isolate_roots_recursive(arf_interval_ptr * blocks, int ** flags, slong * length, slong * alloc, arb_calc_func_t func, void * param, const arf_interval_t block, int asign, int bsign, slong depth, slong * eval_count, slong * found_count, slong prec) { int status; if (*found_count <= 0 || *eval_count <= 0) { status = BLOCK_UNKNOWN; ADD_BLOCK } else { *eval_count -= 1; status = check_block(func, param, block, asign, bsign, prec); if (status != BLOCK_NO_ZERO) { if (status == BLOCK_ISOLATED_ZERO || depth <= 0) { if (status == BLOCK_ISOLATED_ZERO) { if (arb_calc_verbose) { flint_printf("found isolated root in: "); arf_interval_printd(block, 15); flint_printf("\n"); } *found_count -= 1; } ADD_BLOCK } else { arf_interval_t L, R; int msign; arf_interval_init(L); arf_interval_init(R); msign = arb_calc_partition(L, R, func, param, block, prec); if (msign == 0 && arb_calc_verbose) { flint_printf("possible zero at midpoint: "); arf_interval_printd(block, 15); flint_printf("\n"); } isolate_roots_recursive(blocks, flags, length, alloc, func, param, L, asign, msign, depth - 1, eval_count, found_count, prec); isolate_roots_recursive(blocks, flags, length, alloc, func, param, R, msign, bsign, depth - 1, eval_count, found_count, prec); arf_interval_clear(L); arf_interval_clear(R); } } } } slong arb_calc_isolate_roots(arf_interval_ptr * blocks, int ** flags, arb_calc_func_t func, void * param, const arf_interval_t block, slong maxdepth, slong maxeval, slong maxfound, slong prec) { int asign, bsign; slong length, alloc; arb_t m, v; *blocks = NULL; *flags = NULL; length = 0; alloc = 0; arb_init(m); arb_init(v); arb_set_arf(m, &block->a); func(v, m, param, 1, prec); asign = _arb_sign(v); arb_set_arf(m, &block->b); func(v, m, param, 1, prec); bsign = _arb_sign(v); arb_clear(m); arb_clear(v); isolate_roots_recursive(blocks, flags, &length, &alloc, func, param, block, asign, bsign, maxdepth, &maxeval, &maxfound, prec); *blocks = flint_realloc(*blocks, length * sizeof(arf_interval_struct)); *flags = flint_realloc(*flags, length * sizeof(int)); return length; } arb-2.8.1/arb_calc/newton_conv_factor.c000066400000000000000000000030231264125401100200470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_calc.h" void arb_calc_newton_conv_factor(arf_t conv_factor, arb_calc_func_t func, void * param, const arb_t conv_region, slong prec) { arb_struct t[3]; arb_init(t); arb_init(t + 1); arb_init(t + 2); func(t, conv_region, param, 3, prec); arb_div(t, t + 2, t + 1, prec); arb_mul_2exp_si(t, t, -1); arb_get_abs_ubound_arf(conv_factor, t, prec); arb_clear(t); arb_clear(t + 1); arb_clear(t + 2); } arb-2.8.1/arb_calc/newton_step.c000066400000000000000000000041301264125401100165170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_calc.h" int arb_calc_newton_step(arb_t xnew, arb_calc_func_t func, void * param, const arb_t x, const arb_t conv_region, const arf_t conv_factor, slong prec) { mag_t err, v; arb_t t; arb_struct u[2]; int result; mag_init(err); mag_init(v); arb_init(t); arb_init(u + 0); arb_init(u + 1); mag_mul(err, arb_radref(x), arb_radref(x)); arf_get_mag(v, conv_factor); mag_mul(err, err, v); arf_set(arb_midref(t), arb_midref(x)); mag_zero(arb_radref(t)); func(u, t, param, 2, prec); arb_div(u, u, u + 1, prec); arb_sub(u, t, u, prec); mag_add(arb_radref(u), arb_radref(u), err); if (arb_contains(conv_region, u) && (mag_cmp(arb_radref(u), arb_radref(x)) < 0)) { arb_swap(xnew, u); result = ARB_CALC_SUCCESS; } else { arb_set(xnew, x); result = ARB_CALC_NO_CONVERGENCE; } arb_clear(t); arb_clear(u); arb_clear(u + 1); mag_clear(err); mag_clear(v); return result; } arb-2.8.1/arb_calc/refine_root_bisect.c000066400000000000000000000066761264125401100200370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_calc.h" /* TODO: refactor/combine some of this code with isolate_roots.c */ /* 0 means that it *could* be zero; otherwise +/- 1 */ static __inline__ int _arb_sign(const arb_t t) { if (arb_is_positive(t)) return 1; else if (arb_is_negative(t)) return -1; else return 0; } int arb_calc_partition(arf_interval_t L, arf_interval_t R, arb_calc_func_t func, void * param, const arf_interval_t block, slong prec) { arb_t t, m; arf_t u; int msign; arb_init(t); arb_init(m); arf_init(u); /* Compute the midpoint (TODO: try other points) */ arf_add(u, &block->a, &block->b, ARF_PREC_EXACT, ARF_RND_DOWN); arf_mul_2exp_si(u, u, -1); /* Evaluate and get sign at midpoint */ arb_set_arf(m, u); func(t, m, param, 1, prec); msign = _arb_sign(t); /* L, R = block, split at midpoint */ arf_set(&L->a, &block->a); arf_set(&R->b, &block->b); arf_set(&L->b, u); arf_set(&R->a, u); arb_clear(t); arb_clear(m); arf_clear(u); return msign; } int arb_calc_refine_root_bisect(arf_interval_t r, arb_calc_func_t func, void * param, const arf_interval_t start, slong iter, slong prec) { int asign, bsign, msign, result; slong i; arf_interval_t t, u; arb_t m, v; arf_interval_init(t); arf_interval_init(u); arb_init(m); arb_init(v); arb_set_arf(m, &start->a); func(v, m, param, 1, prec); asign = _arb_sign(v); arb_set_arf(m, &start->b); func(v, m, param, 1, prec); bsign = _arb_sign(v); /* must have proper sign changes */ if (asign == 0 || bsign == 0 || asign == bsign) { result = ARB_CALC_IMPRECISE_INPUT; } else { arf_interval_set(r, start); result = ARB_CALC_SUCCESS; for (i = 0; i < iter; i++) { msign = arb_calc_partition(t, u, func, param, r, prec); /* the algorithm fails if the value at the midpoint cannot be distinguished from zero */ if (msign == 0) { result = ARB_CALC_NO_CONVERGENCE; break; } if (msign == asign) arf_interval_swap(r, u); else arf_interval_swap(r, t); } } arf_interval_clear(t); arf_interval_clear(u); arb_clear(m); arb_clear(v); return result; } arb-2.8.1/arb_calc/refine_root_newton.c000066400000000000000000000046131264125401100200650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_calc.h" int arb_calc_refine_root_newton(arb_t r, arb_calc_func_t func, void * param, const arb_t start, const arb_t conv_region, const arf_t conv_factor, slong eval_extra_prec, slong prec) { slong precs[FLINT_BITS]; slong i, iters, wp, padding, start_prec; int result; start_prec = arb_rel_accuracy_bits(start); if (arb_calc_verbose) flint_printf("newton initial accuracy: %wd\n", start_prec); padding = arf_abs_bound_lt_2exp_si(conv_factor); padding = FLINT_MIN(padding, prec) + 5; padding = FLINT_MAX(0, padding); precs[0] = prec + padding; iters = 1; while ((iters < FLINT_BITS) && (precs[iters-1] + padding > 2*start_prec)) { precs[iters] = (precs[iters-1] / 2) + padding; iters++; if (iters == FLINT_BITS) { return ARB_CALC_IMPRECISE_INPUT; } } arb_set(r, start); for (i = iters - 1; i >= 0; i--) { wp = precs[i] + eval_extra_prec; if (arb_calc_verbose) flint_printf("newton step: wp = %wd + %wd = %wd\n", precs[i], eval_extra_prec, wp); if ((result = arb_calc_newton_step(r, func, param, r, conv_region, conv_factor, wp)) != ARB_CALC_SUCCESS) { return result; } } return ARB_CALC_SUCCESS; } arb-2.8.1/arb_calc/test/000077500000000000000000000000001264125401100147675ustar00rootroot00000000000000arb-2.8.1/arb_calc/test/t-isolate_roots.c000066400000000000000000000111571264125401100202670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_calc.h" /* sin((pi/2)x) */ static int sin_pi2_x(arb_ptr out, const arb_t inp, void * params, slong order, slong prec) { arb_ptr x; x = _arb_vec_init(2); arb_set(x, inp); arb_one(x + 1); arb_const_pi(out, prec); arb_mul_2exp_si(out, out, -1); _arb_vec_scalar_mul(x, x, 2, out, prec); _arb_poly_sin_series(out, x, order, order, prec); _arb_vec_clear(x, 2); return 0; } int main() { slong iter; flint_rand_t state; flint_printf("isolate_roots...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 40; iter++) { slong m, r, a, b, maxdepth, maxeval, maxfound, prec, i, j, num; arf_interval_ptr blocks; int * info; arf_interval_t interval; arb_t t; fmpz_t nn; prec = 2 + n_randint(state, 50); m = n_randint(state, 80); r = 1 + n_randint(state, 80); a = m - r; b = m + r; maxdepth = 1 + n_randint(state, 60); maxeval = 1 + n_randint(state, 5000); maxfound = 1 + n_randint(state, 100); arf_interval_init(interval); arb_init(t); fmpz_init(nn); arf_set_si(&interval->a, a); arf_set_si(&interval->b, b); num = arb_calc_isolate_roots(&blocks, &info, sin_pi2_x, NULL, interval, maxdepth, maxeval, maxfound, prec); /* check that all roots are accounted for */ for (i = a; i <= b; i++) { if (i % 2 == 0) { int found = 0; for (j = 0; j < num; j++) { arf_interval_get_arb(t, blocks + j, ARF_PREC_EXACT); if (arb_contains_si(t, i)) { found = 1; break; } } if (!found) { flint_printf("FAIL: missing root %wd\n", i); flint_printf("a = %wd, b = %wd, maxdepth = %wd, maxeval = %wd, maxfound = %wd, prec = %wd\n", a, b, maxdepth, maxeval, maxfound, prec); for (j = 0; j < num; j++) { arf_interval_printd(blocks + j, 15); flint_printf(" %d \n", info[i]); } abort(); } } } /* check that all reported single roots are good */ for (i = 0; i < num; i++) { if (info[i] == 1) { /* b contains unique 2n -> b/2 contains unique n */ arf_interval_get_arb(t, blocks + i, ARF_PREC_EXACT); arb_mul_2exp_si(t, t, -1); if (!arb_get_unique_fmpz(nn, t)) { flint_printf("FAIL: bad root %wd\n", i); flint_printf("a = %wd, b = %wd, maxdepth = %wd, maxeval = %wd, maxfound = %wd, prec = %wd\n", a, b, maxdepth, maxeval, maxfound, prec); for (j = 0; j < num; j++) { arf_interval_printd(blocks + j, 15); flint_printf(" %d \n", info[i]); } abort(); } } } _arf_interval_vec_clear(blocks, num); flint_free(info); arf_interval_clear(interval); arb_clear(t); fmpz_clear(nn); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_calc/verbose.c000066400000000000000000000021751264125401100156260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_calc.h" int TLS_PREFIX arb_calc_verbose = 0; arb-2.8.1/arb_mat.h000066400000000000000000000177411264125401100140520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef ARB_MAT_H #define ARB_MAT_H #ifdef ARB_MAT_INLINES_C #define ARB_MAT_INLINE #else #define ARB_MAT_INLINE static __inline__ #endif #include "arb.h" #include "fmpz_mat.h" #include "fmpq_mat.h" #include "perm.h" #include "arb_poly.h" #ifdef __cplusplus extern "C" { #endif typedef struct { arb_ptr entries; slong r; slong c; arb_ptr * rows; } arb_mat_struct; typedef arb_mat_struct arb_mat_t[1]; #define arb_mat_entry(mat,i,j) ((mat)->rows[i] + (j)) #define arb_mat_nrows(mat) ((mat)->r) #define arb_mat_ncols(mat) ((mat)->c) ARB_MAT_INLINE arb_ptr arb_mat_entry_ptr(arb_mat_t mat, slong i, slong j) { return arb_mat_entry(mat, i, j); } /* Memory management */ void arb_mat_init(arb_mat_t mat, slong r, slong c); void arb_mat_clear(arb_mat_t mat); ARB_MAT_INLINE void arb_mat_swap(arb_mat_t mat1, arb_mat_t mat2) { arb_mat_struct t = *mat1; *mat1 = *mat2; *mat2 = t; } /* Conversions */ void arb_mat_set(arb_mat_t dest, const arb_mat_t src); void arb_mat_set_fmpz_mat(arb_mat_t dest, const fmpz_mat_t src); void arb_mat_set_round_fmpz_mat(arb_mat_t dest, const fmpz_mat_t src, slong prec); void arb_mat_set_fmpq_mat(arb_mat_t dest, const fmpq_mat_t src, slong prec); /* Random generation */ void arb_mat_randtest(arb_mat_t mat, flint_rand_t state, slong prec, slong mag_bits); /* I/O */ void arb_mat_printd(const arb_mat_t mat, slong digits); /* Comparisons */ int arb_mat_eq(const arb_mat_t mat1, const arb_mat_t mat2); int arb_mat_ne(const arb_mat_t mat1, const arb_mat_t mat2); int arb_mat_equal(const arb_mat_t mat1, const arb_mat_t mat2); int arb_mat_overlaps(const arb_mat_t mat1, const arb_mat_t mat2); int arb_mat_contains(const arb_mat_t mat1, const arb_mat_t mat2); int arb_mat_contains_fmpq_mat(const arb_mat_t mat1, const fmpq_mat_t mat2); int arb_mat_contains_fmpz_mat(const arb_mat_t mat1, const fmpz_mat_t mat2); /* Special matrices */ void arb_mat_zero(arb_mat_t mat); void arb_mat_one(arb_mat_t mat); void arb_mat_transpose(arb_mat_t mat1, const arb_mat_t mat2); /* Norms */ void arb_mat_bound_inf_norm(mag_t b, const arb_mat_t A); /* Arithmetic */ void arb_mat_neg(arb_mat_t dest, const arb_mat_t src); void arb_mat_add(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec); void arb_mat_sub(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec); void arb_mat_mul(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec); void arb_mat_mul_classical(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec); void arb_mat_mul_threaded(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec); void arb_mat_sqr(arb_mat_t B, const arb_mat_t A, slong prec); void arb_mat_sqr_classical(arb_mat_t B, const arb_mat_t A, slong prec); void arb_mat_pow_ui(arb_mat_t B, const arb_mat_t A, ulong exp, slong prec); /* Scalar arithmetic */ ARB_MAT_INLINE void arb_mat_scalar_mul_2exp_si(arb_mat_t B, const arb_mat_t A, slong c) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_mul_2exp_si(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c); } ARB_MAT_INLINE void arb_mat_scalar_addmul_si(arb_mat_t B, const arb_mat_t A, slong c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_addmul_si(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_mul_si(arb_mat_t B, const arb_mat_t A, slong c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_mul_si(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_div_si(arb_mat_t B, const arb_mat_t A, slong c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_div_si(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_addmul_fmpz(arb_mat_t B, const arb_mat_t A, const fmpz_t c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_addmul_fmpz(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_mul_fmpz(arb_mat_t B, const arb_mat_t A, const fmpz_t c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_mul_fmpz(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_div_fmpz(arb_mat_t B, const arb_mat_t A, const fmpz_t c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_div_fmpz(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_addmul_arb(arb_mat_t B, const arb_mat_t A, const arb_t c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_addmul(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_mul_arb(arb_mat_t B, const arb_mat_t A, const arb_t c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_mul(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } ARB_MAT_INLINE void arb_mat_scalar_div_arb(arb_mat_t B, const arb_mat_t A, const arb_t c, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(A); i++) for (j = 0; j < arb_mat_ncols(A); j++) arb_div(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), c, prec); } /* Solving */ ARB_MAT_INLINE void arb_mat_swap_rows(arb_mat_t mat, slong * perm, slong r, slong s) { if (r != s) { arb_ptr u; slong t; if (perm != NULL) { t = perm[s]; perm[s] = perm[r]; perm[r] = t; } u = mat->rows[s]; mat->rows[s] = mat->rows[r]; mat->rows[r] = u; } } slong arb_mat_find_pivot_partial(const arb_mat_t mat, slong start_row, slong end_row, slong c); int arb_mat_lu(slong * P, arb_mat_t LU, const arb_mat_t A, slong prec); void arb_mat_solve_lu_precomp(arb_mat_t X, const slong * perm, const arb_mat_t A, const arb_mat_t B, slong prec); int arb_mat_solve(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec); int arb_mat_inv(arb_mat_t X, const arb_mat_t A, slong prec); void arb_mat_det(arb_t det, const arb_mat_t A, slong prec); /* Special functions */ void arb_mat_exp(arb_mat_t B, const arb_mat_t A, slong prec); void _arb_mat_charpoly(arb_ptr cp, const arb_mat_t mat, slong prec); void arb_mat_charpoly(arb_poly_t cp, const arb_mat_t mat, slong prec); void arb_mat_trace(arb_t trace, const arb_mat_t mat, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/arb_mat/000077500000000000000000000000001264125401100136675ustar00rootroot00000000000000arb-2.8.1/arb_mat/add.c000066400000000000000000000026661264125401100145750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_add(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) arb_add(arb_mat_entry(res, i, j), arb_mat_entry(mat1, i, j), arb_mat_entry(mat2, i, j), prec); } arb-2.8.1/arb_mat/bound_inf_norm.c000066400000000000000000000031241264125401100170310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_bound_inf_norm(mag_t b, const arb_mat_t A) { slong i, j, r, c; mag_t s, t; r = arb_mat_nrows(A); c = arb_mat_ncols(A); mag_zero(b); if (r == 0 || c == 0) return; mag_init(s); mag_init(t); for (i = 0; i < r; i++) { mag_zero(s); for (j = 0; j < c; j++) { arb_get_mag(t, arb_mat_entry(A, i, j)); mag_add(s, s, t); } mag_max(b, b, s); } mag_clear(s); mag_clear(t); } arb-2.8.1/arb_mat/charpoly.c000066400000000000000000000061641264125401100156630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Sebastian Pancratz ******************************************************************************/ #include "arb_mat.h" void _arb_mat_charpoly(arb_ptr cp, const arb_mat_t mat, slong prec) { const slong n = mat->r; if (n == 0) { arb_one(cp); } else if (n == 1) { arb_neg(cp + 0, arb_mat_entry(mat, 0, 0)); arb_one(cp + 1); } else { slong i, j, k, t; arb_ptr a, A, s; a = _arb_vec_init(n * n); A = a + (n - 1) * n; _arb_vec_zero(cp, n + 1); arb_neg(cp + 0, arb_mat_entry(mat, 0, 0)); for (t = 1; t < n; t++) { for (i = 0; i <= t; i++) { arb_set(a + 0 * n + i, arb_mat_entry(mat, i, t)); } arb_set(A + 0, arb_mat_entry(mat, t, t)); for (k = 1; k < t; k++) { for (i = 0; i <= t; i++) { s = a + k * n + i; arb_zero(s); for (j = 0; j <= t; j++) arb_addmul(s, arb_mat_entry(mat, i, j), a + (k - 1) * n + j, prec); } arb_set(A + k, a + k * n + t); } arb_zero(A + t); for (j = 0; j <= t; j++) arb_addmul(A + t, arb_mat_entry(mat, t, j), a + (t - 1) * n + j, prec); for (k = 0; k <= t; k++) { for (j = 0; j < k; j++) arb_submul(cp + k, A + j, cp + (k - j - 1), prec); arb_sub(cp + k, cp + k, A + k, prec); } } /* Shift all coefficients up by one */ for (i = n; i > 0; i--) arb_swap(cp + i, cp + (i - 1)); arb_one(cp + 0); _arb_poly_reverse(cp, cp, n + 1, n + 1); _arb_vec_clear(a, n * n); } } void arb_mat_charpoly(arb_poly_t cp, const arb_mat_t mat, slong prec) { if (mat->r != mat->c) { flint_printf("Exception (arb_mat_charpoly). Non-square matrix.\n"); abort(); } arb_poly_fit_length(cp, mat->r + 1); _arb_poly_set_length(cp, mat->r + 1); _arb_mat_charpoly(cp->coeffs, mat, prec); } arb-2.8.1/arb_mat/clear.c000066400000000000000000000023741264125401100151270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_clear(arb_mat_t mat) { if (mat->entries != NULL) { _arb_vec_clear(mat->entries, mat->r * mat->c); flint_free(mat->rows); } } arb-2.8.1/arb_mat/contains.c000066400000000000000000000030131264125401100156460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_contains(const arb_mat_t mat1, const arb_mat_t mat2) { slong i, j; if ((arb_mat_nrows(mat1) != arb_mat_nrows(mat2)) || (arb_mat_ncols(mat1) != arb_mat_ncols(mat2))) return 0; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) if (!arb_contains(arb_mat_entry(mat1, i, j), arb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/arb_mat/contains_fmpq_mat.c000066400000000000000000000030531264125401100175360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_contains_fmpq_mat(const arb_mat_t mat1, const fmpq_mat_t mat2) { slong i, j; if ((arb_mat_nrows(mat1) != arb_mat_nrows(mat2)) || (arb_mat_ncols(mat1) != arb_mat_ncols(mat2))) return 0; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) if (!arb_contains_fmpq(arb_mat_entry(mat1, i, j), fmpq_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/arb_mat/contains_fmpz_mat.c000066400000000000000000000030531264125401100175470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_contains_fmpz_mat(const arb_mat_t mat1, const fmpz_mat_t mat2) { slong i, j; if ((arb_mat_nrows(mat1) != arb_mat_nrows(mat2)) || (arb_mat_ncols(mat1) != arb_mat_ncols(mat2))) return 0; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) if (!arb_contains_fmpz(arb_mat_entry(mat1, i, j), fmpz_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/arb_mat/det.c000066400000000000000000000073641264125401100146210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" slong arb_mat_gauss_partial(arb_mat_t A, slong prec) { arb_t e; arb_ptr * a; slong j, m, n, r, rank, row, col, sign; m = A->r; n = A->c; a = A->rows; rank = row = col = 0; sign = 1; arb_init(e); while (row < m && col < n) { r = arb_mat_find_pivot_partial(A, row, m, col); if (r == -1) { break; } else if (r != row) { arb_mat_swap_rows(A, NULL, row, r); sign *= -1; } rank++; for (j = row + 1; j < m; j++) { arb_div(e, a[j] + col, a[row] + col, prec); arb_neg(e, e); _arb_vec_scalar_addmul(a[j] + col + 1, a[row] + col + 1, n - col - 1, e, prec); } row++; col++; } arb_clear(e); return rank * sign; } void arb_vec_get_arf_2norm_squared_bound(arf_t s, arb_srcptr vec, slong len, slong prec) { slong i; arf_t t; arf_init(t); arf_zero(s); for (i = 0; i < len; i++) { arb_get_abs_ubound_arf(t, vec + i, prec); arf_addmul(s, t, t, prec, ARF_RND_UP); } arf_clear(t); } void arb_mat_det_inplace(arb_t det, arb_mat_t A, slong prec) { slong i, n, sign, rank; n = arb_mat_nrows(A); rank = arb_mat_gauss_partial(A, prec); sign = (rank < 0) ? -1 : 1; rank = FLINT_ABS(rank); arb_set_si(det, sign); for (i = 0; i < rank; i++) arb_mul(det, det, arb_mat_entry(A, i, i), prec); /* bound unreduced part using Hadamard's inequality */ if (rank < n) { arf_t t; arf_t d; arb_t b; arf_init(t); arf_init(d); arb_init(b); arf_one(d); for (i = rank; i < n; i++) { arb_vec_get_arf_2norm_squared_bound(t, A->rows[i] + rank, n - rank, MAG_BITS); arf_mul(d, d, t, MAG_BITS, ARF_RND_UP); } arf_sqrt(d, d, MAG_BITS, ARF_RND_UP); arb_add_error_arf(b, d); arb_mul(det, det, b, prec); arf_clear(d); arf_clear(t); arb_clear(b); } } void arb_mat_det(arb_t det, const arb_mat_t A, slong prec) { slong n = arb_mat_nrows(A); if (n == 0) { arb_one(det); } else if (n == 1) { arb_set(det, arb_mat_entry(A, 0, 0)); } else if (n == 2) { arb_mul(det, arb_mat_entry(A, 0, 0), arb_mat_entry(A, 1, 1), prec); arb_submul(det, arb_mat_entry(A, 0, 1), arb_mat_entry(A, 1, 0), prec); } else { arb_mat_t T; arb_mat_init(T, arb_mat_nrows(A), arb_mat_ncols(A)); arb_mat_set(T, A); arb_mat_det_inplace(det, T, prec); arb_mat_clear(T); } } arb-2.8.1/arb_mat/eq.c000066400000000000000000000030131264125401100144350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "arb_mat.h" int arb_mat_eq(const arb_mat_t mat1, const arb_mat_t mat2) { slong i, j; if ((arb_mat_nrows(mat1) != arb_mat_nrows(mat2)) || (arb_mat_ncols(mat1) != arb_mat_ncols(mat2))) return 0; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) if (!arb_eq(arb_mat_entry(mat1, i, j), arb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/arb_mat/equal.c000066400000000000000000000030251264125401100151420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_equal(const arb_mat_t mat1, const arb_mat_t mat2) { slong i, j; if ((arb_mat_nrows(mat1) != arb_mat_nrows(mat2)) || (arb_mat_ncols(mat1) != arb_mat_ncols(mat2))) return 0; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) if (!arb_equal(arb_mat_entry(mat1, i, j), arb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/arb_mat/exp.c000066400000000000000000000130141264125401100146260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "double_extras.h" #include "arb_mat.h" #define LOG2_OVER_E 0.25499459743395350926 slong _arb_mat_exp_choose_N(const mag_t norm, slong prec) { if (mag_is_special(norm) || mag_cmp_2exp_si(norm, 30) > 0 || mag_cmp_2exp_si(norm, -prec) < 0) { return 1; } else if (mag_cmp_2exp_si(norm, -300) < 0) { slong N = -MAG_EXP(norm); return (prec + N - 1) / N; } else { double c, t; c = mag_get_d(norm); t = d_lambertw(prec * LOG2_OVER_E / c); t = c * exp(t + 1.0); return FLINT_MIN((slong) (t + 1.0), 2 * prec); } } /* evaluates the truncated Taylor series (assumes no aliasing) */ void _arb_mat_exp_taylor(arb_mat_t S, const arb_mat_t A, slong N, slong prec) { if (N == 1) { arb_mat_one(S); } else if (N == 2) { arb_mat_one(S); arb_mat_add(S, S, A, prec); } else if (N == 3) { arb_mat_t T; arb_mat_init(T, arb_mat_nrows(A), arb_mat_nrows(A)); arb_mat_sqr(T, A, prec); arb_mat_scalar_mul_2exp_si(T, T, -1); arb_mat_add(S, A, T, prec); arb_mat_one(T); arb_mat_add(S, S, T, prec); arb_mat_clear(T); } else { slong i, lo, hi, m, w, dim; arb_mat_struct * pows; arb_mat_t T, U; fmpz_t c, f; dim = arb_mat_nrows(A); m = n_sqrt(N); w = (N + m - 1) / m; fmpz_init(c); fmpz_init(f); pows = flint_malloc(sizeof(arb_mat_t) * (m + 1)); arb_mat_init(T, dim, dim); arb_mat_init(U, dim, dim); for (i = 0; i <= m; i++) { arb_mat_init(pows + i, dim, dim); if (i == 0) arb_mat_one(pows + i); else if (i == 1) arb_mat_set(pows + i, A); else arb_mat_mul(pows + i, pows + i - 1, A, prec); } arb_mat_zero(S); fmpz_one(f); for (i = w - 1; i >= 0; i--) { lo = i * m; hi = FLINT_MIN(N - 1, lo + m - 1); arb_mat_zero(T); fmpz_one(c); while (hi >= lo) { arb_mat_scalar_addmul_fmpz(T, pows + hi - lo, c, prec); if (hi != 0) fmpz_mul_ui(c, c, hi); hi--; } arb_mat_mul(U, pows + m, S, prec); arb_mat_scalar_mul_fmpz(S, T, f, prec); arb_mat_add(S, S, U, prec); fmpz_mul(f, f, c); } arb_mat_scalar_div_fmpz(S, S, f, prec); fmpz_clear(c); fmpz_clear(f); for (i = 0; i <= m; i++) arb_mat_clear(pows + i); flint_free(pows); arb_mat_clear(T); arb_mat_clear(U); } } void arb_mat_exp(arb_mat_t B, const arb_mat_t A, slong prec) { slong i, j, dim, wp, N, q, r; mag_t norm, err; arb_mat_t T; dim = arb_mat_nrows(A); if (dim != arb_mat_ncols(A)) { flint_printf("arb_mat_exp: a square matrix is required!\n"); abort(); } if (dim == 0) { return; } else if (dim == 1) { arb_exp(arb_mat_entry(B, 0, 0), arb_mat_entry(A, 0, 0), prec); return; } wp = prec + 3 * FLINT_BIT_COUNT(prec); mag_init(norm); mag_init(err); arb_mat_init(T, dim, dim); arb_mat_bound_inf_norm(norm, A); if (mag_is_zero(norm)) { arb_mat_one(B); } else { q = pow(wp, 0.25); /* wanted magnitude */ if (mag_cmp_2exp_si(norm, 2 * wp) > 0) /* too big */ r = 2 * wp; else if (mag_cmp_2exp_si(norm, -q) < 0) /* tiny, no need to reduce */ r = 0; else r = FLINT_MAX(0, q + MAG_EXP(norm)); /* reduce to magnitude 2^(-r) */ arb_mat_scalar_mul_2exp_si(T, A, -r); mag_mul_2exp_si(norm, norm, -r); N = _arb_mat_exp_choose_N(norm, wp); mag_exp_tail(err, norm, N); _arb_mat_exp_taylor(B, T, N, wp); for (i = 0; i < dim; i++) for (j = 0; j < dim; j++) arb_add_error_mag(arb_mat_entry(B, i, j), err); for (i = 0; i < r; i++) { arb_mat_sqr(T, B, wp); arb_mat_swap(T, B); } for (i = 0; i < dim; i++) for (j = 0; j < dim; j++) arb_set_round(arb_mat_entry(B, i, j), arb_mat_entry(B, i, j), prec); } mag_clear(norm); mag_clear(err); arb_mat_clear(T); } arb-2.8.1/arb_mat/find_pivot_partial.c000066400000000000000000000034131264125401100177110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" slong arb_mat_find_pivot_partial(const arb_mat_t mat, slong start_row, slong end_row, slong c) { slong best_row, i; best_row = -1; for (i = start_row; i < end_row; i++) { if (!arb_contains_zero(arb_mat_entry(mat, i, c))) { if (best_row == -1) { best_row = i; } /* todo: should take the radius into account */ else if (arf_cmpabs(arb_midref(arb_mat_entry(mat, i, c)), arb_midref(arb_mat_entry(mat, best_row, c))) > 0) { best_row = i; } } } return best_row; } arb-2.8.1/arb_mat/init.c000066400000000000000000000027161264125401100150040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_init(arb_mat_t mat, slong r, slong c) { if (r != 0 && c != 0) { slong i; mat->entries = _arb_vec_init(r * c); mat->rows = (arb_ptr *) flint_malloc(r * sizeof(arb_ptr)); for (i = 0; i < r; i++) mat->rows[i] = mat->entries + i * c; } else mat->entries = NULL; mat->r = r; mat->c = c; } arb-2.8.1/arb_mat/inlines.c000066400000000000000000000021601264125401100154730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define ARB_MAT_INLINES_C #include "arb_mat.h" arb-2.8.1/arb_mat/inv.c000066400000000000000000000026761264125401100146420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_inv(arb_mat_t X, const arb_mat_t A, slong prec) { if (X == A) { int r; arb_mat_t T; arb_mat_init(T, arb_mat_nrows(A), arb_mat_ncols(A)); r = arb_mat_inv(T, A, prec); arb_mat_swap(T, X); arb_mat_clear(T); return r; } arb_mat_one(X); return arb_mat_solve(X, A, X, prec); } arb-2.8.1/arb_mat/lu.c000066400000000000000000000042451264125401100144600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_lu(slong * P, arb_mat_t LU, const arb_mat_t A, slong prec) { arb_t d, e; arb_ptr * a; slong i, j, m, n, r, row, col; int result; m = arb_mat_nrows(A); n = arb_mat_ncols(A); result = 1; if (m == 0 || n == 0) return result; arb_mat_set(LU, A); a = LU->rows; row = col = 0; for (i = 0; i < m; i++) P[i] = i; arb_init(d); arb_init(e); while (row < m && col < n) { r = arb_mat_find_pivot_partial(LU, row, m, col); if (r == -1) { result = 0; break; } else if (r != row) arb_mat_swap_rows(LU, P, row, r); arb_set(d, a[row] + col); for (j = row + 1; j < m; j++) { arb_div(e, a[j] + col, d, prec); arb_neg(e, e); _arb_vec_scalar_addmul(a[j] + col, a[row] + col, n - col, e, prec); arb_zero(a[j] + col); arb_neg(a[j] + row, e); } row++; col++; } arb_clear(d); arb_clear(e); return result; } arb-2.8.1/arb_mat/mul.c000066400000000000000000000027371264125401100146410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_mul(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec) { if (flint_get_num_threads() > 1 && ((double) arb_mat_nrows(A) * (double) arb_mat_nrows(B) * (double) arb_mat_ncols(B) * (double) prec > 100000)) { arb_mat_mul_threaded(C, A, B, prec); } else { arb_mat_mul_classical(C, A, B, prec); } } arb-2.8.1/arb_mat/mul_classical.c000066400000000000000000000043131264125401100166470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_mul_classical(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec) { slong ar, ac, br, bc, i, j, k; ar = arb_mat_nrows(A); ac = arb_mat_ncols(A); br = arb_mat_nrows(B); bc = arb_mat_ncols(B); if (ac != br || ar != arb_mat_nrows(C) || bc != arb_mat_ncols(C)) { flint_printf("arb_mat_mul: incompatible dimensions\n"); abort(); } if (br == 0) { arb_mat_zero(C); return; } if (A == C || B == C) { arb_mat_t T; arb_mat_init(T, ar, bc); arb_mat_mul(T, A, B, prec); arb_mat_swap(T, C); arb_mat_clear(T); return; } for (i = 0; i < ar; i++) { for (j = 0; j < bc; j++) { arb_mul(arb_mat_entry(C, i, j), arb_mat_entry(A, i, 0), arb_mat_entry(B, 0, j), prec); for (k = 1; k < br; k++) { arb_addmul(arb_mat_entry(C, i, j), arb_mat_entry(A, i, k), arb_mat_entry(B, k, j), prec); } } } } arb-2.8.1/arb_mat/mul_threaded.c000066400000000000000000000067561264125401100165060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" #include "pthread.h" typedef struct { arb_ptr * C; const arb_ptr * A; const arb_ptr * B; slong ar0; slong ar1; slong bc0; slong bc1; slong br; slong prec; } arb_mat_mul_arg_t; void * _arb_mat_mul_thread(void * arg_ptr) { arb_mat_mul_arg_t arg = *((arb_mat_mul_arg_t *) arg_ptr); slong i, j, k; for (i = arg.ar0; i < arg.ar1; i++) { for (j = arg.bc0; j < arg.bc1; j++) { arb_mul(arg.C[i] + j, arg.A[i] + 0, arg.B[0] + j, arg.prec); for (k = 1; k < arg.br; k++) { arb_addmul(arg.C[i] + j, arg.A[i] + k, arg.B[k] + j, arg.prec); } } } flint_cleanup(); return NULL; } void arb_mat_mul_threaded(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec) { slong ar, ac, br, bc, i, num_threads; pthread_t * threads; arb_mat_mul_arg_t * args; ar = arb_mat_nrows(A); ac = arb_mat_ncols(A); br = arb_mat_nrows(B); bc = arb_mat_ncols(B); if (ac != br || ar != arb_mat_nrows(C) || bc != arb_mat_ncols(C)) { flint_printf("arb_mat_mul_threaded: incompatible dimensions\n"); abort(); } if (br == 0) { arb_mat_zero(C); return; } if (A == C || B == C) { arb_mat_t T; arb_mat_init(T, ar, bc); arb_mat_mul_threaded(T, A, B, prec); arb_mat_swap(T, C); arb_mat_clear(T); return; } num_threads = flint_get_num_threads(); threads = flint_malloc(sizeof(pthread_t) * num_threads); args = flint_malloc(sizeof(arb_mat_mul_arg_t) * num_threads); for (i = 0; i < num_threads; i++) { args[i].C = C->rows; args[i].A = A->rows; args[i].B = B->rows; if (ar >= bc) { args[i].ar0 = (ar * i) / num_threads; args[i].ar1 = (ar * (i + 1)) / num_threads; args[i].bc0 = 0; args[i].bc1 = bc; } else { args[i].ar0 = 0; args[i].ar1 = ar; args[i].bc0 = (bc * i) / num_threads; args[i].bc1 = (bc * (i + 1)) / num_threads; } args[i].br = br; args[i].prec = prec; pthread_create(&threads[i], NULL, _arb_mat_mul_thread, &args[i]); } for (i = 0; i < num_threads; i++) { pthread_join(threads[i], NULL); } flint_free(threads); flint_free(args); } arb-2.8.1/arb_mat/ne.c000066400000000000000000000030121264125401100144310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "arb_mat.h" int arb_mat_ne(const arb_mat_t mat1, const arb_mat_t mat2) { slong i, j; if ((arb_mat_nrows(mat1) != arb_mat_nrows(mat2)) || (arb_mat_ncols(mat1) != arb_mat_ncols(mat2))) return 1; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) if (arb_ne(arb_mat_entry(mat1, i, j), arb_mat_entry(mat2, i, j))) return 1; return 0; } arb-2.8.1/arb_mat/neg.c000066400000000000000000000025311264125401100146050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_neg(arb_mat_t dest, const arb_mat_t src) { slong i, j; for (i = 0; i < arb_mat_nrows(src); i++) for (j = 0; j < arb_mat_ncols(src); j++) arb_neg(arb_mat_entry(dest, i, j), arb_mat_entry(src, i, j)); } arb-2.8.1/arb_mat/one.c000066400000000000000000000025711264125401100146210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_one(arb_mat_t mat) { slong i, j; for (i = 0; i < arb_mat_nrows(mat); i++) for (j = 0; j < arb_mat_ncols(mat); j++) if (i == j) arb_one(arb_mat_entry(mat, i, j)); else arb_zero(arb_mat_entry(mat, i, j)); } arb-2.8.1/arb_mat/overlaps.c000066400000000000000000000030131264125401100156630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_overlaps(const arb_mat_t mat1, const arb_mat_t mat2) { slong i, j; if ((arb_mat_nrows(mat1) != arb_mat_nrows(mat2)) || (arb_mat_ncols(mat1) != arb_mat_ncols(mat2))) return 0; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) if (!arb_overlaps(arb_mat_entry(mat1, i, j), arb_mat_entry(mat2, i, j))) return 0; return 1; } arb-2.8.1/arb_mat/pow_ui.c000066400000000000000000000041371264125401100153420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_pow_ui(arb_mat_t B, const arb_mat_t A, ulong exp, slong prec) { slong d = arb_mat_nrows(A); if (exp <= 2 || d <= 1) { if (exp == 0 || d == 0) { arb_mat_one(B); } else if (d == 1) { arb_pow_ui(arb_mat_entry(B, 0, 0), arb_mat_entry(A, 0, 0), exp, prec); } else if (exp == 1) { arb_mat_set(B, A); } else if (exp == 2) { arb_mat_sqr(B, A, prec); } } else { arb_mat_t T, U; slong i; arb_mat_init(T, d, d); arb_mat_set(T, A); arb_mat_init(U, d, d); for (i = ((slong) FLINT_BIT_COUNT(exp)) - 2; i >= 0; i--) { arb_mat_sqr(U, T, prec); if (exp & (WORD(1) << i)) arb_mat_mul(T, U, A, prec); else arb_mat_swap(T, U); } arb_mat_swap(B, T); arb_mat_clear(T); arb_mat_clear(U); } } arb-2.8.1/arb_mat/printd.c000066400000000000000000000027451264125401100153430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_printd(const arb_mat_t mat, slong digits) { slong i, j; for (i = 0; i < arb_mat_nrows(mat); i++) { flint_printf("["); for (j = 0; j < arb_mat_ncols(mat); j++) { arb_printd(arb_mat_entry(mat, i, j), digits); if (j < arb_mat_ncols(mat) - 1) flint_printf(", "); } flint_printf("]\n"); } } arb-2.8.1/arb_mat/randtest.c000066400000000000000000000031311264125401100156550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_randtest(arb_mat_t mat, flint_rand_t state, slong prec, slong mag_bits) { slong i, j; if (n_randint(state, 2)) for (i = 0; i < arb_mat_nrows(mat); i++) for (j = 0; j < arb_mat_ncols(mat); j++) arb_randtest(arb_mat_entry(mat, i, j), state, prec, mag_bits); else for (i = 0; i < arb_mat_nrows(mat); i++) for (j = 0; j < arb_mat_ncols(mat); j++) arb_randtest_precise(arb_mat_entry(mat, i, j), state, prec, mag_bits); } arb-2.8.1/arb_mat/set.c000066400000000000000000000026451264125401100146350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_set(arb_mat_t dest, const arb_mat_t src) { slong i, j; if (dest != src && arb_mat_ncols(src) != 0) { for (i = 0; i < arb_mat_nrows(src); i++) for (j = 0; j < arb_mat_ncols(src); j++) arb_set(arb_mat_entry(dest, i, j), arb_mat_entry(src, i, j)); } } arb-2.8.1/arb_mat/set_fmpq_mat.c000066400000000000000000000026731264125401100165220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_set_fmpq_mat(arb_mat_t dest, const fmpq_mat_t src, slong prec) { slong i, j; if (arb_mat_ncols(dest) != 0) { for (i = 0; i < arb_mat_nrows(dest); i++) for (j = 0; j < arb_mat_ncols(dest); j++) arb_set_fmpq(arb_mat_entry(dest, i, j), fmpq_mat_entry(src, i, j), prec); } } arb-2.8.1/arb_mat/set_fmpz_mat.c000066400000000000000000000026511264125401100165270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_set_fmpz_mat(arb_mat_t dest, const fmpz_mat_t src) { slong i, j; if (arb_mat_ncols(dest) != 0) { for (i = 0; i < arb_mat_nrows(dest); i++) for (j = 0; j < arb_mat_ncols(dest); j++) arb_set_fmpz(arb_mat_entry(dest, i, j), fmpz_mat_entry(src, i, j)); } } arb-2.8.1/arb_mat/set_round_fmpz_mat.c000066400000000000000000000027031264125401100177340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Tommy Hofmann ******************************************************************************/ #include "arb_mat.h" void arb_mat_set_round_fmpz_mat(arb_mat_t dest, const fmpz_mat_t src, slong prec) { slong i, j; if (arb_mat_ncols(dest) != 0) { for (i = 0; i < arb_mat_nrows(dest); i++) for (j = 0; j < arb_mat_ncols(dest); j++) arb_set_round_fmpz(arb_mat_entry(dest, i, j), fmpz_mat_entry(src, i, j), prec); } } arb-2.8.1/arb_mat/solve.c000066400000000000000000000030661264125401100151700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int arb_mat_solve(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec) { int result; slong n, m, *perm; arb_mat_t LU; n = arb_mat_nrows(A); m = arb_mat_ncols(X); if (n == 0 || m == 0) return 1; perm = _perm_init(n); arb_mat_init(LU, n, n); result = arb_mat_lu(perm, LU, A, prec); if (result) arb_mat_solve_lu_precomp(X, perm, LU, B, prec); arb_mat_clear(LU); _perm_clear(perm); return result; } arb-2.8.1/arb_mat/solve_lu_precomp.c000066400000000000000000000050201264125401100174050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_solve_lu_precomp(arb_mat_t X, const slong * perm, const arb_mat_t A, const arb_mat_t B, slong prec) { slong i, j, c, n, m; n = arb_mat_nrows(X); m = arb_mat_ncols(X); if (X == B) { arb_ptr tmp = flint_malloc(sizeof(arb_struct) * n); for (c = 0; c < m; c++) { for (i = 0; i < n; i++) tmp[i] = B->rows[perm[i]][c]; for (i = 0; i < n; i++) X->rows[i][c] = tmp[i]; } flint_free(tmp); } else { for (c = 0; c < m; c++) { for (i = 0; i < n; i++) { arb_set(arb_mat_entry(X, i, c), arb_mat_entry(B, perm[i], c)); } } } for (c = 0; c < m; c++) { /* solve Ly = b */ for (i = 1; i < n; i++) { for (j = 0; j < i; j++) { arb_submul(arb_mat_entry(X, i, c), arb_mat_entry(A, i, j), arb_mat_entry(X, j, c), prec); } } /* solve Ux = y */ for (i = n - 1; i >= 0; i--) { for (j = i + 1; j < n; j++) { arb_submul(arb_mat_entry(X, i, c), arb_mat_entry(A, i, j), arb_mat_entry(X, j, c), prec); } arb_div(arb_mat_entry(X, i, c), arb_mat_entry(X, i, c), arb_mat_entry(A, i, i), prec); } } } arb-2.8.1/arb_mat/sqr.c000066400000000000000000000026301264125401100146410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "arb_mat.h" void arb_mat_sqr(arb_mat_t B, const arb_mat_t A, slong prec) { double d = (double) arb_mat_nrows(A); if (flint_get_num_threads() > 1 && d*d*d * (double) prec > 100000) { arb_mat_mul_threaded(B, A, A, prec); /* todo: sqr threaded */ } else { arb_mat_sqr_classical(B, A, prec); } } arb-2.8.1/arb_mat/sqr_classical.c000066400000000000000000000065341264125401100166660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "arb_mat.h" void arb_mat_sqr_classical(arb_mat_t B, const arb_mat_t A, slong prec) { slong n, i, j, k; arb_t p, s; n = arb_mat_nrows(A); if (arb_mat_ncols(A) != n || arb_mat_nrows(B) != n || arb_mat_ncols(B) != n) { flint_printf("arb_mat_sqr: incompatible dimensions\n"); abort(); } if (n == 0) { arb_mat_zero(B); return; } if (n == 1) { arb_mul(arb_mat_entry(B, 0, 0), arb_mat_entry(A, 0, 0), arb_mat_entry(A, 0, 0), prec); return; } if (A == B) { arb_mat_t T; arb_mat_init(T, n, n); arb_mat_sqr(T, A, prec); arb_mat_swap(T, B); arb_mat_clear(T); return; } arb_init(p); arb_init(s); /* contribution of diagonal of A to diagonal of B */ for (i = 0; i < n; i++) { arb_mul(arb_mat_entry(B, i, i), arb_mat_entry(A, i, i), arb_mat_entry(A, i, i), prec); } for (i = 0; i < n; i++) { for (j = 0; j < i; j++) { /* contribution of off-diagonal of A to diagonal of B */ arb_mul(p, arb_mat_entry(A, i, j), arb_mat_entry(A, j, i), prec); arb_add(arb_mat_entry(B, i, i), arb_mat_entry(B, i, i), p, prec); arb_add(arb_mat_entry(B, j, j), arb_mat_entry(B, j, j), p, prec); /* contribution of diagonal of A to off-diagonal of B */ arb_add(s, arb_mat_entry(A, i, i), arb_mat_entry(A, j, j), prec); arb_mul(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), s, prec); arb_mul(arb_mat_entry(B, j, i), arb_mat_entry(A, j, i), s, prec); } } /* contribution of off-diagonal of A to off-diagonal of B */ if (n > 2) { for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { for (k = 0; k < n; k++) { if (i != j && j != k && k != i) { arb_addmul(arb_mat_entry(B, i, j), arb_mat_entry(A, i, k), arb_mat_entry(A, k, j), prec); } } } } } arb_clear(p); arb_clear(s); } arb-2.8.1/arb_mat/sub.c000066400000000000000000000026661264125401100146360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_sub(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec) { slong i, j; for (i = 0; i < arb_mat_nrows(mat1); i++) for (j = 0; j < arb_mat_ncols(mat1); j++) arb_sub(arb_mat_entry(res, i, j), arb_mat_entry(mat1, i, j), arb_mat_entry(mat2, i, j), prec); } arb-2.8.1/arb_mat/test/000077500000000000000000000000001264125401100146465ustar00rootroot00000000000000arb-2.8.1/arb_mat/test/t-charpoly.c000066400000000000000000000052321264125401100170760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main(void) { slong iter; flint_rand_t state; flint_printf("charpoly...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arb_mat_t A, B, C, D; arb_poly_t f, g; slong m, n; m = n_randint(state, 8); n = m; arb_mat_init(A, m, n); arb_mat_init(B, m, n); arb_mat_init(C, m, m); arb_mat_init(D, n, n); arb_poly_init(f); arb_poly_init(g); arb_mat_randtest(A, state, 1 + n_randint(state, 1000), 10); arb_mat_randtest(B, state, 1 + n_randint(state, 1000), 10); arb_mat_mul(C, A, B, 2 + n_randint(state, 1000)); arb_mat_mul(D, B, A, 2 + n_randint(state, 1000)); arb_mat_charpoly(f, C, 2 + n_randint(state, 1000)); arb_mat_charpoly(g, D, 2 + n_randint(state, 1000)); if (!arb_poly_overlaps(f, g)) { flint_printf("FAIL: charpoly(AB) != charpoly(BA).\n"); flint_printf("Matrix A:\n"), arb_mat_printd(A, 15), flint_printf("\n"); flint_printf("Matrix B:\n"), arb_mat_printd(B, 15), flint_printf("\n"); flint_printf("cp(AB) = "), arb_poly_printd(f, 15), flint_printf("\n"); flint_printf("cp(BA) = "), arb_poly_printd(g, 15), flint_printf("\n"); abort(); } arb_mat_clear(A); arb_mat_clear(B); arb_mat_clear(C); arb_mat_clear(D); arb_poly_clear(f); arb_poly_clear(g); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/arb_mat/test/t-det.c000066400000000000000000000051371264125401100160350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("det...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpq_mat_t Q; fmpq_t Qdet; arb_mat_t A; arb_t Adet; slong n, qbits, prec; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_init(Qdet); arb_mat_init(A, n, n); arb_init(Adet); fmpq_mat_randtest(Q, state, qbits); fmpq_mat_det(Qdet, Q); arb_mat_set_fmpq_mat(A, Q, prec); arb_mat_det(Adet, A, prec); if (!arb_contains_fmpq(Adet, Qdet)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("Qdet = \n"); fmpq_print(Qdet); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Adet = \n"); arb_printd(Adet, 15); flint_printf("\n\n"); flint_printf("Adet = \n"); arb_print(Adet); flint_printf("\n\n"); abort(); } fmpq_mat_clear(Q); fmpq_clear(Qdet); arb_mat_clear(A); arb_clear(Adet); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-exp.c000066400000000000000000000061501264125401100160510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("exp...."); fflush(stdout); flint_randinit(state); /* check exp(A)*exp(c*A) = exp((1+c)*A) */ for (iter = 0; iter < 1000; iter++) { arb_mat_t A, E, F, EF, G; fmpq_mat_t Q; arb_t c, d; slong n, qbits, prec; n = n_randint(state, 5); qbits = 2 + n_randint(state, 300); prec = 2 + n_randint(state, 300); arb_init(c); arb_init(d); fmpq_mat_init(Q, n, n); arb_mat_init(A, n, n); arb_mat_init(E, n, n); arb_mat_init(F, n, n); arb_mat_init(EF, n, n); arb_mat_init(G, n, n); fmpq_mat_randtest(Q, state, qbits); arb_mat_set_fmpq_mat(A, Q, prec); arb_mat_exp(E, A, prec); arb_randtest(c, state, prec, 10); arb_mat_scalar_mul_arb(F, A, c, prec); arb_mat_exp(F, F, prec); arb_add_ui(d, c, 1, prec); arb_mat_scalar_mul_arb(G, A, d, prec); arb_mat_exp(G, G, prec); arb_mat_mul(EF, E, F, prec); if (!arb_mat_overlaps(EF, G)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("c = \n"); arb_printd(c, 15); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("E = \n"); arb_mat_printd(E, 15); flint_printf("\n\n"); flint_printf("F = \n"); arb_mat_printd(F, 15); flint_printf("\n\n"); flint_printf("E*F = \n"); arb_mat_printd(EF, 15); flint_printf("\n\n"); flint_printf("G = \n"); arb_mat_printd(G, 15); flint_printf("\n\n"); abort(); } arb_clear(c); arb_clear(d); fmpq_mat_clear(Q); arb_mat_clear(A); arb_mat_clear(E); arb_mat_clear(F); arb_mat_clear(EF); arb_mat_clear(G); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-inv.c000066400000000000000000000106701264125401100160530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("inv...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpq_mat_t Q, Qinv; arb_mat_t A, Ainv; slong n, qbits, prec; int q_invertible, r_invertible, r_invertible2; n = n_randint(state, 8); qbits = 1 + n_randint(state, 30); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_mat_init(Qinv, n, n); arb_mat_init(A, n, n); arb_mat_init(Ainv, n, n); fmpq_mat_randtest(Q, state, qbits); q_invertible = fmpq_mat_inv(Qinv, Q); if (!q_invertible) { arb_mat_set_fmpq_mat(A, Q, prec); r_invertible = arb_mat_inv(Ainv, A, prec); if (r_invertible) { flint_printf("FAIL: matrix is singular over Q but not over R\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n"); abort(); } } else { /* now this must converge */ while (1) { arb_mat_set_fmpq_mat(A, Q, prec); r_invertible = arb_mat_inv(Ainv, A, prec); if (r_invertible) { break; } else { if (prec > 10000) { flint_printf("FAIL: failed to converge at 10000 bits\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); abort(); } prec *= 2; } } if (!arb_mat_contains_fmpq_mat(Ainv, Qinv)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("Qinv = \n"); fmpq_mat_print(Qinv); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n"); abort(); } /* test aliasing */ r_invertible2 = arb_mat_inv(A, A, prec); if (!arb_mat_equal(A, Ainv) || r_invertible != r_invertible2) { flint_printf("FAIL (aliasing)\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Ainv = \n"); arb_mat_printd(Ainv, 15); flint_printf("\n\n"); abort(); } } fmpq_mat_clear(Q); fmpq_mat_clear(Qinv); arb_mat_clear(A); arb_mat_clear(Ainv); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-lu.c000066400000000000000000000116211264125401100156740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int fmpq_mat_is_invertible(const fmpq_mat_t A) { int r; fmpq_t t; fmpq_init(t); fmpq_mat_det(t, A); r = !fmpq_is_zero(t); fmpq_clear(t); return r; } int main() { slong iter; flint_rand_t state; flint_printf("lu...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpq_mat_t Q; arb_mat_t A, LU, P, L, U, T; slong i, j, n, qbits, prec, *perm; int q_invertible, r_invertible; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 202); fmpq_mat_init(Q, n, n); arb_mat_init(A, n, n); arb_mat_init(LU, n, n); arb_mat_init(P, n, n); arb_mat_init(L, n, n); arb_mat_init(U, n, n); arb_mat_init(T, n, n); perm = _perm_init(n); fmpq_mat_randtest(Q, state, qbits); q_invertible = fmpq_mat_is_invertible(Q); if (!q_invertible) { arb_mat_set_fmpq_mat(A, Q, prec); r_invertible = arb_mat_lu(perm, LU, A, prec); if (r_invertible) { flint_printf("FAIL: matrix is singular over Q but not over R\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("LU = \n"); arb_mat_printd(LU, 15); flint_printf("\n\n"); } } else { /* now this must converge */ while (1) { arb_mat_set_fmpq_mat(A, Q, prec); r_invertible = arb_mat_lu(perm, LU, A, prec); if (r_invertible) { break; } else { if (prec > 10000) { flint_printf("FAIL: failed to converge at 10000 bits\n"); abort(); } prec *= 2; } } arb_mat_one(L); for (i = 0; i < n; i++) for (j = 0; j < i; j++) arb_set(arb_mat_entry(L, i, j), arb_mat_entry(LU, i, j)); for (i = 0; i < n; i++) for (j = i; j < n; j++) arb_set(arb_mat_entry(U, i, j), arb_mat_entry(LU, i, j)); for (i = 0; i < n; i++) arb_one(arb_mat_entry(P, perm[i], i)); arb_mat_mul(T, P, L, prec); arb_mat_mul(T, T, U, prec); if (!arb_mat_contains_fmpq_mat(T, Q)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("LU = \n"); arb_mat_printd(LU, 15); flint_printf("\n\n"); flint_printf("L = \n"); arb_mat_printd(L, 15); flint_printf("\n\n"); flint_printf("U = \n"); arb_mat_printd(U, 15); flint_printf("\n\n"); flint_printf("P*L*U = \n"); arb_mat_printd(T, 15); flint_printf("\n\n"); abort(); } } fmpq_mat_clear(Q); arb_mat_clear(A); arb_mat_clear(LU); arb_mat_clear(P); arb_mat_clear(L); arb_mat_clear(U); arb_mat_clear(T); _perm_clear(perm); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-mul.c000066400000000000000000000075401264125401100160560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, k, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_mat_t A, B, C; arb_mat_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); k = n_randint(state, 10); fmpq_mat_init(A, m, n); fmpq_mat_init(B, n, k); fmpq_mat_init(C, m, k); arb_mat_init(a, m, n); arb_mat_init(b, n, k); arb_mat_init(c, m, k); arb_mat_init(d, m, k); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_randtest(B, state, qbits2); fmpq_mat_mul(C, A, B); arb_mat_set_fmpq_mat(a, A, rbits1); arb_mat_set_fmpq_mat(b, B, rbits2); arb_mat_mul(c, a, b, rbits3); if (!arb_mat_contains_fmpq_mat(c, C)) { flint_printf("FAIL\n\n"); flint_printf("m = %wd, n = %wd, k = %wd, bits3 = %wd\n", m, n, k, rbits3); flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_mat_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_mat_printd(c, 15); flint_printf("\n\n"); abort(); } /* test aliasing with a */ if (arb_mat_nrows(a) == arb_mat_nrows(c) && arb_mat_ncols(a) == arb_mat_ncols(c)) { arb_mat_set(d, a); arb_mat_mul(d, d, b, rbits3); if (!arb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } } /* test aliasing with b */ if (arb_mat_nrows(b) == arb_mat_nrows(c) && arb_mat_ncols(b) == arb_mat_ncols(c)) { arb_mat_set(d, b); arb_mat_mul(d, a, d, rbits3); if (!arb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(C); arb_mat_clear(a); arb_mat_clear(b); arb_mat_clear(c); arb_mat_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-mul_threaded.c000066400000000000000000000077641264125401100177260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_threaded...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, k, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_mat_t A, B, C; arb_mat_t a, b, c, d; flint_set_num_threads(1 + n_randint(state, 5)); qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); k = n_randint(state, 10); fmpq_mat_init(A, m, n); fmpq_mat_init(B, n, k); fmpq_mat_init(C, m, k); arb_mat_init(a, m, n); arb_mat_init(b, n, k); arb_mat_init(c, m, k); arb_mat_init(d, m, k); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_randtest(B, state, qbits2); fmpq_mat_mul(C, A, B); arb_mat_set_fmpq_mat(a, A, rbits1); arb_mat_set_fmpq_mat(b, B, rbits2); arb_mat_mul_threaded(c, a, b, rbits3); if (!arb_mat_contains_fmpq_mat(c, C)) { flint_printf("FAIL\n\n"); flint_printf("threads = %d, m = %wd, n = %wd, k = %wd, bits3 = %wd\n", flint_get_num_threads(), m, n, k, rbits3); flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_mat_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_mat_printd(c, 15); flint_printf("\n\n"); abort(); } /* test aliasing with a */ if (arb_mat_nrows(a) == arb_mat_nrows(c) && arb_mat_ncols(a) == arb_mat_ncols(c)) { arb_mat_set(d, a); arb_mat_mul_threaded(d, d, b, rbits3); if (!arb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } } /* test aliasing with b */ if (arb_mat_nrows(b) == arb_mat_nrows(c) && arb_mat_ncols(b) == arb_mat_ncols(c)) { arb_mat_set(d, b); arb_mat_mul_threaded(d, a, d, rbits3); if (!arb_mat_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } } fmpq_mat_clear(A); fmpq_mat_clear(B); fmpq_mat_clear(C); arb_mat_clear(a); arb_mat_clear(b); arb_mat_clear(c); arb_mat_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-solve.c000066400000000000000000000122561264125401100164110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("solve...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpq_mat_t Q, QX, QB; arb_mat_t A, X, B; slong n, m, qbits, prec; int q_invertible, r_invertible, r_invertible2; n = n_randint(state, 8); m = n_randint(state, 8); qbits = 1 + n_randint(state, 30); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_mat_init(QX, n, m); fmpq_mat_init(QB, n, m); arb_mat_init(A, n, n); arb_mat_init(X, n, m); arb_mat_init(B, n, m); fmpq_mat_randtest(Q, state, qbits); fmpq_mat_randtest(QB, state, qbits); q_invertible = fmpq_mat_solve_fraction_free(QX, Q, QB); if (!q_invertible) { arb_mat_set_fmpq_mat(A, Q, prec); r_invertible = arb_mat_solve(X, A, B, prec); if (r_invertible) { flint_printf("FAIL: matrix is singular over Q but not over R\n"); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n"); flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); abort(); } } else { /* now this must converge */ while (1) { arb_mat_set_fmpq_mat(A, Q, prec); arb_mat_set_fmpq_mat(B, QB, prec); r_invertible = arb_mat_solve(X, A, B, prec); if (r_invertible) { break; } else { if (prec > 10000) { flint_printf("FAIL: failed to converge at 10000 bits\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n"); flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); abort(); } prec *= 2; } } if (!arb_mat_contains_fmpq_mat(X, QX)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("QB = \n"); fmpq_mat_print(QB); flint_printf("\n\n"); flint_printf("QX = \n"); fmpq_mat_print(QX); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n"); flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n"); abort(); } /* test aliasing */ r_invertible2 = arb_mat_solve(B, A, B, prec); if (!arb_mat_equal(X, B) || r_invertible != r_invertible2) { flint_printf("FAIL (aliasing)\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("B = \n"); arb_mat_printd(B, 15); flint_printf("\n\n"); flint_printf("X = \n"); arb_mat_printd(X, 15); flint_printf("\n\n"); abort(); } } fmpq_mat_clear(Q); fmpq_mat_clear(QB); fmpq_mat_clear(QX); arb_mat_clear(A); arb_mat_clear(B); arb_mat_clear(X); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-sqr.c000066400000000000000000000054051264125401100160640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("sqr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong n, qbits1, rbits1, rbits2; fmpq_mat_t A, B; arb_mat_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = n_randint(state, 10); fmpq_mat_init(A, n, n); fmpq_mat_init(B, n, n); arb_mat_init(a, n, n); arb_mat_init(b, n, n); arb_mat_init(c, n, n); fmpq_mat_randtest(A, state, qbits1); fmpq_mat_mul(B, A, A); arb_mat_set_fmpq_mat(a, A, rbits1); arb_mat_sqr(b, a, rbits2); if (!arb_mat_contains_fmpq_mat(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_mat_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_mat_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_mat_printd(b, 15); flint_printf("\n\n"); abort(); } /* test aliasing */ arb_mat_set(c, a); arb_mat_sqr(c, c, rbits2); if (!arb_mat_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_mat_clear(A); fmpq_mat_clear(B); arb_mat_clear(a); arb_mat_clear(b); arb_mat_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-trace.c000066400000000000000000000104501264125401100163510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("trace...."); fflush(stdout); flint_randinit(state); /* check that the arb trace contains the fmpq trace */ for (iter = 0; iter < 10000; iter++) { fmpq_mat_t Q; fmpq_t Qtrace; arb_mat_t A; arb_t Atrace; slong n, qbits, prec; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_init(Qtrace); arb_mat_init(A, n, n); arb_init(Atrace); fmpq_mat_randtest(Q, state, qbits); fmpq_mat_trace(Qtrace, Q); arb_mat_set_fmpq_mat(A, Q, prec); arb_mat_trace(Atrace, A, prec); if (!arb_contains_fmpq(Atrace, Qtrace)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("Qtrace = \n"); fmpq_print(Qtrace); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("Atrace = \n"); arb_printd(Atrace, 15); flint_printf("\n\n"); flint_printf("Atrace = \n"); arb_print(Atrace); flint_printf("\n\n"); abort(); } fmpq_mat_clear(Q); fmpq_clear(Qtrace); arb_mat_clear(A); arb_clear(Atrace); } /* check trace(A*B) = trace(B*A) */ for (iter = 0; iter < 10000; iter++) { slong m, n, prec; arb_mat_t a, b, ab, ba; arb_t trab, trba; prec = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); arb_mat_init(a, m, n); arb_mat_init(b, n, m); arb_mat_init(ab, m, m); arb_mat_init(ba, n, n); arb_init(trab); arb_init(trba); arb_mat_randtest(a, state, 2 + n_randint(state, 100), 10); arb_mat_randtest(b, state, 2 + n_randint(state, 100), 10); arb_mat_mul(ab, a, b, prec); arb_mat_mul(ba, b, a, prec); arb_mat_trace(trab, ab, prec); arb_mat_trace(trba, ba, prec); if (!arb_overlaps(trab, trba)) { flint_printf("FAIL (overlap, iter = %wd)\n", iter); flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec); flint_printf("\n"); flint_printf("a = \n"); arb_mat_printd(a, 15); flint_printf("\n\n"); flint_printf("b = \n"); arb_mat_printd(b, 15); flint_printf("\n\n"); flint_printf("ab = \n"); arb_mat_printd(ab, 15); flint_printf("\n\n"); flint_printf("ba = \n"); arb_mat_printd(ba, 15); flint_printf("\n\n"); flint_printf("trace(ab) = \n"); arb_printd(trab, 15); flint_printf("\n\n"); flint_printf("trace(ba) = \n"); arb_printd(trba, 15); flint_printf("\n\n"); } arb_clear(trab); arb_clear(trba); arb_mat_clear(a); arb_mat_clear(b); arb_mat_clear(ab); arb_mat_clear(ba); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/test/t-transpose.c000066400000000000000000000045661264125401100173040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" int main() { slong iter; flint_rand_t state; flint_printf("transpose...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n; arb_mat_t a, b, c; m = n_randint(state, 10); n = n_randint(state, 10); arb_mat_init(a, m, n); arb_mat_init(b, n, m); arb_mat_init(c, m, n); arb_mat_randtest(a, state, 2 + n_randint(state, 100), 10); arb_mat_randtest(b, state, 2 + n_randint(state, 100), 10); arb_mat_randtest(c, state, 2 + n_randint(state, 100), 10); arb_mat_transpose(b, a); arb_mat_transpose(c, b); if (!arb_mat_equal(c, a)) { flint_printf("FAIL\n\n"); flint_printf("m = %wd, n = %wd\n", m, n); abort(); } if (arb_mat_nrows(a) == arb_mat_ncols(a)) { arb_mat_transpose(c, a); arb_mat_transpose(a, a); if (!arb_mat_equal(a, c)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } } arb_mat_clear(a); arb_mat_clear(b); arb_mat_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_mat/trace.c000066400000000000000000000026561264125401100151420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Arb authors ******************************************************************************/ #include "arb_mat.h" void arb_mat_trace(arb_t trace, const arb_mat_t mat, slong prec) { slong i, n = arb_mat_nrows(mat); if (n == 0) { arb_zero(trace); } else { arb_set(trace, arb_mat_entry(mat, 0, 0)); for (i = 1; i < n; i++) { arb_add(trace, trace, arb_mat_entry(mat, i, i), prec); } } } arb-2.8.1/arb_mat/transpose.c000066400000000000000000000037371264125401100160630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Tommy Hofmann ******************************************************************************/ #include "arb_mat.h" void arb_mat_transpose(arb_mat_t B, const arb_mat_t A) { arb_struct tmp; slong i, j; if (arb_mat_nrows(B) != arb_mat_ncols(A) || arb_mat_ncols(B) != arb_mat_nrows(A)) { flint_printf("Exception (arb_mat_transpose). Incompatible dimensions.\n"); abort(); } if (A == B) /* In-place, guaranteed to be square */ { for (i = 0; i < arb_mat_nrows(A) - 1; i++) { for (j = i + 1; j < arb_mat_ncols(A); j++) { tmp = *arb_mat_entry(A, i, j); *arb_mat_entry(A, i, j) = *arb_mat_entry(A, j, i); *arb_mat_entry(A, j, i) = tmp; } } } else /* Not aliased; general case */ { for (i = 0; i < arb_mat_nrows(B); i++) for (j = 0; j < arb_mat_ncols(B); j++) arb_set(arb_mat_entry(B, i, j), arb_mat_entry(A, j, i)); } } arb-2.8.1/arb_mat/zero.c000066400000000000000000000024321264125401100150130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_mat.h" void arb_mat_zero(arb_mat_t mat) { slong i, j; for (i = 0; i < arb_mat_nrows(mat); i++) for (j = 0; j < arb_mat_ncols(mat); j++) arb_zero(arb_mat_entry(mat, i, j)); } arb-2.8.1/arb_poly.h000066400000000000000000000603251264125401100142500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef ARB_POLY_H #define ARB_POLY_H #ifdef ARB_POLY_INLINES_C #define ARB_POLY_INLINE #else #define ARB_POLY_INLINE static __inline__ #endif #include "arb.h" #include "acb.h" #include "fmpz_poly.h" #include "fmpq_poly.h" #ifdef __cplusplus extern "C" { #endif typedef struct { arb_ptr coeffs; slong length; slong alloc; } arb_poly_struct; typedef arb_poly_struct arb_poly_t[1]; /* Memory management */ void arb_poly_init(arb_poly_t poly); void arb_poly_init2(arb_poly_t poly, slong len); void arb_poly_clear(arb_poly_t poly); void arb_poly_fit_length(arb_poly_t poly, slong len); void _arb_poly_set_length(arb_poly_t poly, slong len); void _arb_poly_normalise(arb_poly_t poly); ARB_POLY_INLINE void arb_poly_swap(arb_poly_t poly1, arb_poly_t poly2) { arb_poly_struct t = *poly1; *poly1 = *poly2; *poly2 = t; } void arb_poly_set(arb_poly_t poly, const arb_poly_t src); void arb_poly_set_round(arb_poly_t poly, const arb_poly_t src, slong prec); /* Basic manipulation */ ARB_POLY_INLINE slong arb_poly_length(const arb_poly_t poly) { return poly->length; } ARB_POLY_INLINE slong arb_poly_degree(const arb_poly_t poly) { return poly->length - 1; } ARB_POLY_INLINE void arb_poly_zero(arb_poly_t poly) { poly->length = 0; } ARB_POLY_INLINE void arb_poly_one(arb_poly_t poly) { arb_poly_fit_length(poly, 1); arb_one(poly->coeffs); _arb_poly_set_length(poly, 1); } void arb_poly_set_coeff_si(arb_poly_t poly, slong n, slong x); void arb_poly_set_coeff_arb(arb_poly_t poly, slong n, const arb_t x); void arb_poly_get_coeff_arb(arb_t x, const arb_poly_t poly, slong n); #define arb_poly_get_coeff_ptr(poly, n) \ ((n) < (poly)->length ? (poly)->coeffs + (n) : NULL) void _arb_poly_reverse(arb_ptr res, arb_srcptr poly, slong len, slong n); void _arb_poly_shift_right(arb_ptr res, arb_srcptr poly, slong len, slong n); void arb_poly_shift_right(arb_poly_t res, const arb_poly_t poly, slong n); void _arb_poly_shift_left(arb_ptr res, arb_srcptr poly, slong len, slong n); void arb_poly_shift_left(arb_poly_t res, const arb_poly_t poly, slong n); ARB_POLY_INLINE void arb_poly_truncate(arb_poly_t poly, slong newlen) { if (poly->length > newlen) { slong i; for (i = newlen; i < poly->length; i++) arb_zero(poly->coeffs + i); poly->length = newlen; _arb_poly_normalise(poly); } } /* Conversions */ void arb_poly_set_fmpz_poly(arb_poly_t poly, const fmpz_poly_t src, slong prec); void arb_poly_set_fmpq_poly(arb_poly_t poly, const fmpq_poly_t src, slong prec); ARB_POLY_INLINE void arb_poly_set_arb(arb_poly_t poly, const arb_t c) { arb_poly_fit_length(poly, 1); arb_set(poly->coeffs, c); _arb_poly_set_length(poly, !arb_is_zero(poly->coeffs)); } void arb_poly_set_si(arb_poly_t poly, slong c); int arb_poly_get_unique_fmpz_poly(fmpz_poly_t res, const arb_poly_t src); /* Comparisons */ int arb_poly_contains(const arb_poly_t poly1, const arb_poly_t poly2); int arb_poly_contains_fmpz_poly(const arb_poly_t poly1, const fmpz_poly_t poly2); int arb_poly_contains_fmpq_poly(const arb_poly_t poly1, const fmpq_poly_t poly2); int arb_poly_equal(const arb_poly_t A, const arb_poly_t B); int _arb_poly_overlaps(arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2); int arb_poly_overlaps(const arb_poly_t poly1, const arb_poly_t poly2); /* Bounds */ void _arb_poly_majorant(arb_ptr res, arb_srcptr vec, slong len, slong prec); void arb_poly_majorant(arb_poly_t res, const arb_poly_t poly, slong prec); /* IO */ void arb_poly_printd(const arb_poly_t poly, slong digits); /* Random generation */ void arb_poly_randtest(arb_poly_t poly, flint_rand_t state, slong len, slong prec, slong mag_bits); /* Arithmetic */ void _arb_poly_add(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec); void arb_poly_add(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec); void arb_poly_add_si(arb_poly_t res, const arb_poly_t poly, slong c, slong prec); void _arb_poly_sub(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec); void arb_poly_sub(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec); ARB_POLY_INLINE void arb_poly_neg(arb_poly_t res, const arb_poly_t poly) { arb_poly_fit_length(res, poly->length); _arb_vec_neg(res->coeffs, poly->coeffs, poly->length); _arb_poly_set_length(res, poly->length); } ARB_POLY_INLINE void arb_poly_scalar_mul_2exp_si(arb_poly_t res, const arb_poly_t poly, slong c) { arb_poly_fit_length(res, poly->length); _arb_vec_scalar_mul_2exp_si(res->coeffs, poly->coeffs, poly->length, c); _arb_poly_set_length(res, poly->length); } void _arb_poly_mullow_ztrunc(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec); void arb_poly_mullow_ztrunc(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec); void _arb_poly_mullow_classical(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec); void arb_poly_mullow_classical(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec); void _arb_poly_mullow_block(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong n, slong prec); void arb_poly_mullow_block(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong len, slong prec); void _arb_poly_mullow(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong n, slong prec); void arb_poly_mullow(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong len, slong prec); void _arb_poly_mul(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec); void arb_poly_mul(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec); ARB_POLY_INLINE void _arb_poly_mul_monic(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) { if (len1 + len2 - 2 > 0) _arb_poly_mullow(res, poly1, len1, poly2, len2, len1 + len2 - 2, prec); arb_one(res + len1 + len2 - 2); } void _arb_poly_inv_series(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong len, slong prec); void arb_poly_inv_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec); void _arb_poly_div_series(arb_ptr Q, arb_srcptr A, slong Alen, arb_srcptr B, slong Blen, slong n, slong prec); void arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, slong n, slong prec); void _arb_poly_div(arb_ptr Q, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec); void _arb_poly_divrem(arb_ptr Q, arb_ptr R, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec); void _arb_poly_rem(arb_ptr R, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec); int arb_poly_divrem(arb_poly_t Q, arb_poly_t R, const arb_poly_t A, const arb_poly_t B, slong prec); void _arb_poly_div_root(arb_ptr Q, arb_t R, arb_srcptr A, slong len, const arb_t c, slong prec); /* Product trees */ void _arb_poly_product_roots(arb_ptr poly, arb_srcptr xs, slong n, slong prec); void arb_poly_product_roots(arb_poly_t poly, arb_srcptr xs, slong n, slong prec); arb_ptr * _arb_poly_tree_alloc(slong len); void _arb_poly_tree_free(arb_ptr * tree, slong len); void _arb_poly_tree_build(arb_ptr * tree, arb_srcptr roots, slong len, slong prec); /* Composition */ void _arb_poly_compose(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec); void arb_poly_compose(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec); void _arb_poly_compose_horner(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec); void arb_poly_compose_horner(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec); void _arb_poly_compose_divconquer(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec); void arb_poly_compose_divconquer(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec); void _arb_poly_compose_series_horner(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec); void arb_poly_compose_series_horner(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec); void _arb_poly_compose_series(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec); void arb_poly_compose_series(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec); /* Reversion */ void _arb_poly_revert_series_lagrange(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec); void arb_poly_revert_series_lagrange(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec); void _arb_poly_revert_series_newton(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec); void arb_poly_revert_series_newton(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec); void _arb_poly_revert_series_lagrange_fast(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec); void arb_poly_revert_series_lagrange_fast(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec); void _arb_poly_revert_series(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec); void arb_poly_revert_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec); /* Evaluation and interpolation */ void _arb_poly_evaluate_horner(arb_t res, arb_srcptr f, slong len, const arb_t a, slong prec); void arb_poly_evaluate_horner(arb_t res, const arb_poly_t f, const arb_t a, slong prec); void _arb_poly_evaluate_rectangular(arb_t y, arb_srcptr poly, slong len, const arb_t x, slong prec); void arb_poly_evaluate_rectangular(arb_t res, const arb_poly_t f, const arb_t a, slong prec); void _arb_poly_evaluate(arb_t res, arb_srcptr f, slong len, const arb_t a, slong prec); void arb_poly_evaluate(arb_t res, const arb_poly_t f, const arb_t a, slong prec); void _arb_poly_evaluate2_horner(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec); void arb_poly_evaluate2_horner(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec); void _arb_poly_evaluate2_rectangular(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec); void arb_poly_evaluate2_rectangular(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec); void _arb_poly_evaluate2(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec); void arb_poly_evaluate2(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec); void _arb_poly_evaluate_vec_iter(arb_ptr ys, arb_srcptr poly, slong plen, arb_srcptr xs, slong n, slong prec); void arb_poly_evaluate_vec_iter(arb_ptr ys, const arb_poly_t poly, arb_srcptr xs, slong n, slong prec); void _arb_poly_evaluate_vec_fast_precomp(arb_ptr vs, arb_srcptr poly, slong plen, arb_ptr * tree, slong len, slong prec); void _arb_poly_evaluate_vec_fast(arb_ptr ys, arb_srcptr poly, slong plen, arb_srcptr xs, slong n, slong prec); void arb_poly_evaluate_vec_fast(arb_ptr ys, const arb_poly_t poly, arb_srcptr xs, slong n, slong prec); void _arb_poly_interpolate_newton(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec); void arb_poly_interpolate_newton(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec); void _arb_poly_interpolate_barycentric(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec); void arb_poly_interpolate_barycentric(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec); void _arb_poly_interpolation_weights(arb_ptr w, arb_ptr * tree, slong len, slong prec); void _arb_poly_interpolate_fast_precomp(arb_ptr poly, arb_srcptr ys, arb_ptr * tree, arb_srcptr weights, slong len, slong prec); void _arb_poly_interpolate_fast(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong len, slong prec); void arb_poly_interpolate_fast(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec); /* Derivative and integral */ void _arb_poly_derivative(arb_ptr res, arb_srcptr poly, slong len, slong prec); void arb_poly_derivative(arb_poly_t res, const arb_poly_t poly, slong prec); void _arb_poly_integral(arb_ptr res, arb_srcptr poly, slong len, slong prec); void arb_poly_integral(arb_poly_t res, const arb_poly_t poly, slong prec); /* Transforms */ void arb_poly_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec); void _arb_poly_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec); void arb_poly_inv_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec); void _arb_poly_inv_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec); void _arb_poly_binomial_transform_basecase(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec); void arb_poly_binomial_transform_basecase(arb_poly_t b, const arb_poly_t a, slong len, slong prec); void _arb_poly_binomial_transform_convolution(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec); void arb_poly_binomial_transform_convolution(arb_poly_t b, const arb_poly_t a, slong len, slong prec); void _arb_poly_binomial_transform(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec); void arb_poly_binomial_transform(arb_poly_t b, const arb_poly_t a, slong len, slong prec); /* Special functions */ void _arb_poly_pow_ui_trunc_binexp(arb_ptr res, arb_srcptr f, slong flen, ulong exp, slong len, slong prec); void arb_poly_pow_ui_trunc_binexp(arb_poly_t res, const arb_poly_t poly, ulong exp, slong len, slong prec); void _arb_poly_pow_ui(arb_ptr res, arb_srcptr f, slong flen, ulong exp, slong prec); void arb_poly_pow_ui(arb_poly_t res, const arb_poly_t poly, ulong exp, slong prec); void _arb_poly_pow_series(arb_ptr h, arb_srcptr f, slong flen, arb_srcptr g, slong glen, slong len, slong prec); void arb_poly_pow_series(arb_poly_t h, const arb_poly_t f, const arb_poly_t g, slong len, slong prec); void _arb_poly_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec); void arb_poly_pow_arb_series(arb_poly_t h, const arb_poly_t f, const arb_t g, slong len, slong prec); void _arb_poly_binomial_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec); void _arb_poly_rsqrt_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_rsqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_sqrt_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_sqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_log_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec); void arb_poly_log_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_atan_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec); void arb_poly_atan_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_asin_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec); void arb_poly_asin_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_acos_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec); void arb_poly_acos_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_exp_series_basecase(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec); void arb_poly_exp_series_basecase(arb_poly_t f, const arb_poly_t h, slong n, slong prec); void _arb_poly_exp_series(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec); void arb_poly_exp_series(arb_poly_t f, const arb_poly_t h, slong n, slong prec); void _arb_poly_sin_cos_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec, int times_pi); void arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec, int times_pi); void _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong len, slong prec, int times_pi); void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec, int times_pi); void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_sin_cos_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec); void _arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_sin_cos_pi_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec); void _arb_poly_sin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec); void arb_poly_sin_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_cos_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec); void arb_poly_cos_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_sin_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec); void arb_poly_sin_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_cos_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec); void arb_poly_cos_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_cot_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec); void arb_poly_cot_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_tan_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec); void _arb_poly_compose_series_brent_kung(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec); void arb_poly_compose_series_brent_kung(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec); void _arb_poly_evaluate_acb_horner(acb_t res, arb_srcptr f, slong len, const acb_t x, slong prec); void arb_poly_evaluate_acb_horner(acb_t res, const arb_poly_t f, const acb_t a, slong prec); void _arb_poly_evaluate_acb_rectangular(acb_t y, arb_srcptr poly, slong len, const acb_t x, slong prec); void arb_poly_evaluate_acb_rectangular(acb_t res, const arb_poly_t f, const acb_t a, slong prec); void _arb_poly_evaluate_acb(acb_t res, arb_srcptr f, slong len, const acb_t x, slong prec); void arb_poly_evaluate_acb(acb_t res, const arb_poly_t f, const acb_t a, slong prec); void _arb_poly_evaluate2_acb_horner(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec); void arb_poly_evaluate2_acb_horner(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec); void _arb_poly_evaluate2_acb_rectangular(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec); void arb_poly_evaluate2_acb_rectangular(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec); void _arb_poly_evaluate2_acb(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec); void arb_poly_evaluate2_acb(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec); void _arb_poly_gamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_gamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_rgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_rgamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_lgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_lgamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_digamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_digamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec); void _arb_poly_rising_ui_series(arb_ptr res, arb_srcptr f, slong flen, ulong r, slong trunc, slong prec); void arb_poly_rising_ui_series(arb_poly_t res, const arb_poly_t f, ulong r, slong trunc, slong prec); void _arb_poly_zeta_series(arb_ptr res, arb_srcptr h, slong hlen, const arb_t a, int deflate, slong len, slong prec); void arb_poly_zeta_series(arb_poly_t res, const arb_poly_t f, const arb_t a, int deflate, slong n, slong prec); void _arb_poly_riemann_siegel_theta_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_riemann_siegel_theta_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec); void _arb_poly_riemann_siegel_z_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec); void arb_poly_riemann_siegel_z_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec); slong _arb_poly_swinnerton_dyer_ui_prec(ulong n); void _arb_poly_swinnerton_dyer_ui(arb_ptr T, ulong n, slong trunc, slong prec); void arb_poly_swinnerton_dyer_ui(arb_poly_t poly, ulong n, slong prec); /* Root-finding */ void _arb_poly_newton_convergence_factor(arf_t convergence_factor, arb_srcptr poly, slong len, const arb_t convergence_interval, slong prec); int _arb_poly_newton_step(arb_t xnew, arb_srcptr poly, slong len, const arb_t x, const arb_t convergence_interval, const arf_t convergence_factor, slong prec); void _arb_poly_newton_refine_root(arb_t r, arb_srcptr poly, slong len, const arb_t start, const arb_t convergence_interval, const arf_t convergence_factor, slong eval_extra_prec, slong prec); void _arb_poly_root_bound_fujiwara(mag_t bound, arb_srcptr poly, slong len); void arb_poly_root_bound_fujiwara(mag_t bound, arb_poly_t poly); /* Macros */ /* counts zero bits in the binary representation of e */ ARB_POLY_INLINE int n_zerobits(mp_limb_t e) { int zeros = 0; while (e > 1) { zeros += !(e & 1); e >>= 1; } return zeros; } ARB_POLY_INLINE slong poly_pow_length(slong poly_len, ulong exp, slong trunc) { mp_limb_t hi, lo; umul_ppmm(hi, lo, poly_len - 1, exp); add_ssaaaa(hi, lo, hi, lo, 0, 1); if (hi != 0 || lo > (mp_limb_t) WORD_MAX) return trunc; return FLINT_MIN((slong) lo, trunc); } #ifndef NEWTON_INIT #define NEWTON_INIT(from, to) \ { \ slong __steps[FLINT_BITS], __i, __from, __to; \ __steps[__i = 0] = __to = (to); \ __from = (from); \ while (__to > __from) \ __steps[++__i] = (__to = (__to + 1) / 2); \ #define NEWTON_BASECASE(bc_to) { slong bc_to = __to; #define NEWTON_END_BASECASE } #define NEWTON_LOOP(step_from, step_to) \ { \ for (__i--; __i >= 0; __i--) \ { \ slong step_from = __steps[__i+1]; \ slong step_to = __steps[__i]; \ #define NEWTON_END_LOOP }} #define NEWTON_END } #endif #ifdef __cplusplus } #endif #endif arb-2.8.1/arb_poly/000077500000000000000000000000001264125401100140715ustar00rootroot00000000000000arb-2.8.1/arb_poly/acos_series.c000066400000000000000000000051001264125401100165300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_acos_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) { arb_t c; arb_init(c); arb_acos(c, h, prec); hlen = FLINT_MIN(hlen, n); if (hlen == 1) { _arb_vec_zero(g + 1, n - 1); } else { arb_ptr t, u; slong ulen; t = _arb_vec_init(n); u = _arb_vec_init(n); /* acos(h(x)) = integral(-h'(x)/sqrt(1-h(x)^2)) */ ulen = FLINT_MIN(n, 2 * hlen - 1); _arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec); arb_sub_ui(u, u, 1, prec); _arb_vec_neg(u, u, ulen); _arb_poly_rsqrt_series(t, u, ulen, n, prec); _arb_poly_derivative(u, h, hlen, prec); _arb_poly_mullow(g, t, n, u, hlen - 1, n, prec); _arb_poly_integral(g, g, n, prec); _arb_vec_neg(g, g, n); _arb_vec_clear(t, n); _arb_vec_clear(u, n); } arb_swap(g, c); arb_clear(c); } void arb_poly_acos_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0) { if (n == 0) arb_poly_zero(g); else { arb_poly_fit_length(g, 1); arb_const_pi(g->coeffs, prec); arb_mul_2exp_si(g->coeffs, g->coeffs, -1); _arb_poly_set_length(g, 1); } return; } arb_poly_fit_length(g, n); _arb_poly_acos_series(g->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/add.c000066400000000000000000000035641264125401100147750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_add(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) { slong i, min = FLINT_MIN(len1, len2); for (i = 0; i < min; i++) arb_add(res + i, poly1 + i, poly2 + i, prec); for (i = min; i < len1; i++) arb_set_round(res + i, poly1 + i, prec); for (i = min; i < len2; i++) arb_set_round(res + i, poly2 + i, prec); } void arb_poly_add(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) { slong max = FLINT_MAX(poly1->length, poly2->length); arb_poly_fit_length(res, max); _arb_poly_add(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); _arb_poly_set_length(res, max); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/add_si.c000066400000000000000000000030341264125401100154600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_add_si(arb_poly_t res, const arb_poly_t x, slong y, slong prec) { slong len = x->length; if (len == 0) { arb_poly_set_si(res, y); } else { arb_poly_fit_length(res, len); arb_add_si(res->coeffs, x->coeffs, y, prec); if (res != x) _arb_vec_set(res->coeffs + 1, x->coeffs + 1, len - 1); _arb_poly_set_length(res, len); _arb_poly_normalise(res); } } arb-2.8.1/arb_poly/asin_series.c000066400000000000000000000045001264125401100165400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_asin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) { arb_t c; arb_init(c); arb_asin(c, h, prec); hlen = FLINT_MIN(hlen, n); if (hlen == 1) { _arb_vec_zero(g + 1, n - 1); } else { arb_ptr t, u; slong ulen; t = _arb_vec_init(n); u = _arb_vec_init(n); /* asin(h(x)) = integral(h'(x)/sqrt(1-h(x)^2)) */ ulen = FLINT_MIN(n, 2 * hlen - 1); _arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec); arb_sub_ui(u, u, 1, prec); _arb_vec_neg(u, u, ulen); _arb_poly_rsqrt_series(t, u, ulen, n, prec); _arb_poly_derivative(u, h, hlen, prec); _arb_poly_mullow(g, t, n, u, hlen - 1, n, prec); _arb_poly_integral(g, g, n, prec); _arb_vec_clear(t, n); _arb_vec_clear(u, n); } arb_swap(g, c); arb_clear(c); } void arb_poly_asin_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { arb_poly_zero(g); return; } arb_poly_fit_length(g, n); _arb_poly_asin_series(g->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/atan_series.c000066400000000000000000000043561264125401100165420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_atan_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) { arb_t c; arb_init(c); arb_atan(c, h, prec); hlen = FLINT_MIN(hlen, n); if (hlen == 1) { _arb_vec_zero(g + 1, n - 1); } else { arb_ptr t, u; slong ulen; t = _arb_vec_init(n); u = _arb_vec_init(n); /* atan(h(x)) = integral(h'(x)/(1+h(x)^2)) */ ulen = FLINT_MIN(n, 2 * hlen - 1); _arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec); arb_add_ui(u, u, 1, prec); _arb_poly_derivative(t, h, hlen, prec); _arb_poly_div_series(g, t, hlen - 1, u, ulen, n, prec); _arb_poly_integral(g, g, n, prec); _arb_vec_clear(t, n); _arb_vec_clear(u, n); } arb_swap(g, c); arb_clear(c); } void arb_poly_atan_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { arb_poly_zero(g); return; } arb_poly_fit_length(g, n); _arb_poly_atan_series(g->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/binomial_transform.c000066400000000000000000000037221264125401100201260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_binomial_transform(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec) { if (alen < 10 || len < 10) _arb_poly_binomial_transform_basecase(b, a, alen, len, prec); else _arb_poly_binomial_transform_convolution(b, a, alen, len, prec); } void arb_poly_binomial_transform(arb_poly_t b, const arb_poly_t a, slong len, slong prec) { if (len == 0 || a->length == 0) { arb_poly_zero(b); return; } if (b == a) { arb_poly_t c; arb_poly_init2(c, len); _arb_poly_binomial_transform(c->coeffs, a->coeffs, a->length, len, prec); arb_poly_swap(b, c); arb_poly_clear(c); } else { arb_poly_fit_length(b, len); _arb_poly_binomial_transform(b->coeffs, a->coeffs, a->length, len, prec); } _arb_poly_set_length(b, len); _arb_poly_normalise(b); } arb-2.8.1/arb_poly/binomial_transform_basecase.c000066400000000000000000000044411264125401100217530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_binomial_transform_basecase(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec) { slong n, k; fmpz_t t; fmpz_init(t); for (n = 0; n < len; n++) { arb_zero(b + n); for (k = 0; k < FLINT_MIN(n + 1, alen); k++) { if (k == 0) { fmpz_one(t); } else { fmpz_mul_si(t, t, -(n - k + 1)); fmpz_divexact_ui(t, t, k); } arb_addmul_fmpz(b + n, a + k, t, prec); } } fmpz_clear(t); } void arb_poly_binomial_transform_basecase(arb_poly_t b, const arb_poly_t a, slong len, slong prec) { if (len == 0 || a->length == 0) { arb_poly_zero(b); return; } if (b == a) { arb_poly_t c; arb_poly_init2(c, len); _arb_poly_binomial_transform_basecase(c->coeffs, a->coeffs, a->length, len, prec); arb_poly_swap(b, c); arb_poly_clear(c); } else { arb_poly_fit_length(b, len); _arb_poly_binomial_transform_basecase(b->coeffs, a->coeffs, a->length, len, prec); } _arb_poly_set_length(b, len); _arb_poly_normalise(b); } arb-2.8.1/arb_poly/binomial_transform_convolution.c000066400000000000000000000045161264125401100225670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include #include "arb_poly.h" void _arb_poly_binomial_transform_convolution(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec) { slong i; arb_ptr c, d; alen = FLINT_MIN(alen, len); c = _arb_vec_init(alen); d = _arb_vec_init(len); _arb_poly_borel_transform(c, a, alen, prec); for (i = 1; i < alen; i += 2) arb_neg(c + i, c + i); arb_one(d); for (i = 1; i < len; i++) arb_div_ui(d + i, d + i - 1, i, prec); _arb_poly_mullow(b, d, len, c, alen, len, prec); _arb_poly_inv_borel_transform(b, b, len, prec); _arb_vec_clear(c, alen); _arb_vec_clear(d, len); } void arb_poly_binomial_transform_convolution(arb_poly_t b, const arb_poly_t a, slong len, slong prec) { if (len == 0 || a->length == 0) { arb_poly_zero(b); return; } if (b == a) { arb_poly_t c; arb_poly_init2(c, len); _arb_poly_binomial_transform_convolution(c->coeffs, a->coeffs, a->length, len, prec); arb_poly_swap(b, c); arb_poly_clear(c); } else { arb_poly_fit_length(b, len); _arb_poly_binomial_transform_convolution(b->coeffs, a->coeffs, a->length, len, prec); } _arb_poly_set_length(b, len); _arb_poly_normalise(b); } arb-2.8.1/arb_poly/borel_transform.c000066400000000000000000000032561264125401100174410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec) { slong i; arb_t t; arb_init(t); arb_one(t); for (i = 0; i < len; i++) { if (i > 1) arb_mul_ui(t, t, i, prec); arb_div(res + i, poly + i, t, prec); } arb_clear(t); } void arb_poly_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec) { arb_poly_fit_length(res, poly->length); _arb_poly_borel_transform(res->coeffs, poly->coeffs, poly->length, prec); _arb_poly_set_length(res, poly->length); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/clear.c000066400000000000000000000023701264125401100153250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_clear(arb_poly_t poly) { slong i; for (i = 0; i < poly->alloc; i++) arb_clear(poly->coeffs + i); flint_free(poly->coeffs); } arb-2.8.1/arb_poly/compose.c000066400000000000000000000061601264125401100157050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 William Hart Copyright (C) 2012 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_compose(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) { if (len2 == 1) { _arb_poly_evaluate(res, poly1, len1, poly2, prec); } else if (_arb_vec_is_zero(poly2, len2 - 1)) /* poly2 is a monomial */ { slong i; arb_t t; arb_init(t); arb_set(t, poly2 + len2 - 1); arb_set_round(res, poly1, prec); for (i = 1; i < len1; i++) { arb_mul(res + i * (len2 - 1), poly1 + i, t, prec); if (i + 1 < len1) arb_mul(t, t, poly2 + len2 - 1, prec); _arb_vec_zero(res + (i - 1) * (len2 - 1) + 1, len2 - 2); } arb_clear(t); } else if (len1 <= 7) { _arb_poly_compose_horner(res, poly1, len1, poly2, len2, prec); } else { _arb_poly_compose_divconquer(res, poly1, len1, poly2, len2, prec); } } void arb_poly_compose(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) { const slong len1 = poly1->length; const slong len2 = poly2->length; if (len1 == 0) { arb_poly_zero(res); } else if (len1 == 1 || len2 == 0) { arb_poly_set_arb(res, poly1->coeffs); } else { const slong lenr = (len1 - 1) * (len2 - 1) + 1; if (res != poly1 && res != poly2) { arb_poly_fit_length(res, lenr); _arb_poly_compose(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); } else { arb_poly_t t; arb_poly_init2(t, lenr); _arb_poly_compose(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); arb_poly_swap(res, t); arb_poly_clear(t); } _arb_poly_set_length(res, lenr); _arb_poly_normalise(res); } } arb-2.8.1/arb_poly/compose_divconquer.c000066400000000000000000000131041264125401100201400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 William Hart Copyright (C) 2012 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_compose_divconquer(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) { slong i, j, k, n; slong *hlen, alloc, powlen; arb_ptr v, pow, temp; arb_ptr * h; if (len1 == 1) { arb_set(res, poly1); return; } if (len2 == 1) { _arb_poly_evaluate(res, poly1, len1, poly2, prec); return; } if (len1 == 2) { _arb_poly_compose_horner(res, poly1, len1, poly2, len2, prec); return; } /* Initialisation */ hlen = (slong *) flint_malloc(((len1 + 1) / 2) * sizeof(slong)); for (k = 1; (2 << k) < len1; k++) ; hlen[0] = hlen[1] = ((1 << k) - 1) * (len2 - 1) + 1; for (i = k - 1; i > 0; i--) { slong hi = (len1 + (1 << i) - 1) / (1 << i); for (n = (hi + 1) / 2; n < hi; n++) hlen[n] = ((1 << i) - 1) * (len2 - 1) + 1; } powlen = (1 << k) * (len2 - 1) + 1; alloc = 0; for (i = 0; i < (len1 + 1) / 2; i++) alloc += hlen[i]; v = _arb_vec_init(alloc + 2 * powlen); h = (arb_ptr *) flint_malloc(((len1 + 1) / 2) * sizeof(arb_ptr)); h[0] = v; for (i = 0; i < (len1 - 1) / 2; i++) { h[i + 1] = h[i] + hlen[i]; hlen[i] = 0; } hlen[(len1 - 1) / 2] = 0; pow = v + alloc; temp = pow + powlen; /* Let's start the actual work */ for (i = 0, j = 0; i < len1 / 2; i++, j += 2) { if (!arb_is_zero(poly1 + j + 1)) { _arb_vec_scalar_mul(h[i], poly2, len2, poly1 + j + 1, prec); arb_add(h[i], h[i], poly1 + j, prec); hlen[i] = len2; } else if (!arb_is_zero(poly1 + j)) { arb_set(h[i], poly1 + j); hlen[i] = 1; } } if ((len1 & WORD(1))) { if (!arb_is_zero(poly1 + j)) { arb_set(h[i], poly1 + j); hlen[i] = 1; } } _arb_poly_mul(pow, poly2, len2, poly2, len2, prec); powlen = 2 * len2 - 1; for (n = (len1 + 1) / 2; n > 2; n = (n + 1) / 2) { if (hlen[1] > 0) { slong templen = powlen + hlen[1] - 1; _arb_poly_mul(temp, pow, powlen, h[1], hlen[1], prec); _arb_poly_add(h[0], temp, templen, h[0], hlen[0], prec); hlen[0] = FLINT_MAX(hlen[0], templen); } for (i = 1; i < n / 2; i++) { if (hlen[2*i + 1] > 0) { _arb_poly_mul(h[i], pow, powlen, h[2*i + 1], hlen[2*i + 1], prec); hlen[i] = hlen[2*i + 1] + powlen - 1; } else hlen[i] = 0; _arb_poly_add(h[i], h[i], hlen[i], h[2*i], hlen[2*i], prec); hlen[i] = FLINT_MAX(hlen[i], hlen[2*i]); } if ((n & WORD(1))) { _arb_vec_set(h[i], h[2*i], hlen[2*i]); hlen[i] = hlen[2*i]; } _arb_poly_mul(temp, pow, powlen, pow, powlen, prec); powlen += powlen - 1; { arb_ptr t = pow; pow = temp; temp = t; } } _arb_poly_mul(res, pow, powlen, h[1], hlen[1], prec); _arb_vec_add(res, res, h[0], hlen[0], prec); _arb_vec_clear(v, alloc + 2 * powlen); flint_free(h); flint_free(hlen); } void arb_poly_compose_divconquer(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) { const slong len1 = poly1->length; const slong len2 = poly2->length; if (len1 == 0) { arb_poly_zero(res); } else if (len1 == 1 || len2 == 0) { arb_poly_set_arb(res, poly1->coeffs); } else { const slong lenr = (len1 - 1) * (len2 - 1) + 1; if (res != poly1 && res != poly2) { arb_poly_fit_length(res, lenr); _arb_poly_compose_divconquer(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); } else { arb_poly_t t; arb_poly_init2(t, lenr); _arb_poly_compose_divconquer(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); arb_poly_swap(res, t); arb_poly_clear(t); } _arb_poly_set_length(res, lenr); _arb_poly_normalise(res); } } arb-2.8.1/arb_poly/compose_horner.c000066400000000000000000000070441264125401100172640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 William Hart Copyright (C) 2012 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_compose_horner(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) { if (len1 == 1) { arb_set(res, poly1); } else if (len2 == 1) { _arb_poly_evaluate(res, poly1, len1, poly2, prec); } else if (len1 == 2) { _arb_vec_scalar_mul(res, poly2, len2, poly1 + 1, prec); arb_add(res, res, poly1, prec); } else { const slong alloc = (len1 - 1) * (len2 - 1) + 1; slong i = len1 - 1, lenr = len2; arb_ptr t, t1, t2; t = _arb_vec_init(alloc); if (len1 % 2 == 0) { t1 = res; t2 = t; } else { t1 = t; t2 = res; } /* Perform the first two steps as one, "res = a(m) * poly2 + a(m-1)". */ { _arb_vec_scalar_mul(t1, poly2, len2, poly1 + i, prec); i--; arb_add(t1 + 0, t1 + 0, poly1 + i, prec); } while (i--) { _arb_poly_mul(t2, t1, lenr, poly2, len2, prec); lenr += len2 - 1; { void *t_ = t1; t1 = t2; t2 = t_; } arb_add(t1 + 0, t1 + 0, poly1 + i, prec); } _arb_vec_clear(t, alloc); } } void arb_poly_compose_horner(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) { const slong len1 = poly1->length; const slong len2 = poly2->length; if (len1 == 0) { arb_poly_zero(res); } else if (len1 == 1 || len2 == 0) { arb_poly_set_arb(res, poly1->coeffs); } else { const slong lenr = (len1 - 1) * (len2 - 1) + 1; if (res != poly1 && res != poly2) { arb_poly_fit_length(res, lenr); _arb_poly_compose_horner(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); } else { arb_poly_t t; arb_poly_init2(t, lenr); _arb_poly_compose_horner(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, prec); arb_poly_swap(res, t); arb_poly_clear(t); } _arb_poly_set_length(res, lenr); _arb_poly_normalise(res); } } arb-2.8.1/arb_poly/compose_series.c000066400000000000000000000071221264125401100172560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_compose_series(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) { if (len2 == 1) { arb_set_round(res, poly1, prec); _arb_vec_zero(res + 1, n - 1); } else if (_arb_vec_is_zero(poly2 + 1, len2 - 2)) /* poly2 is a monomial */ { slong i, j; arb_t t; arb_init(t); arb_set(t, poly2 + len2 - 1); arb_set_round(res, poly1, prec); for (i = 1, j = len2 - 1; i < len1 && j < n; i++, j += len2 - 1) { arb_mul(res + j, poly1 + i, t, prec); if (i + 1 < len1 && j + len2 - 1 < n) arb_mul(t, t, poly2 + len2 - 1, prec); } if (len2 != 2) for (i = 1; i < n; i++) if (i % (len2 - 1) != 0) arb_zero(res + i); arb_clear(t); } else if (len1 < 6 || n < 6) { _arb_poly_compose_series_horner(res, poly1, len1, poly2, len2, n, prec); } else { _arb_poly_compose_series_brent_kung(res, poly1, len1, poly2, len2, n, prec); } } void arb_poly_compose_series(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) { slong len1 = poly1->length; slong len2 = poly2->length; slong lenr; if (len2 != 0 && !arb_is_zero(poly2->coeffs)) { flint_printf("exception: compose_series: inner " "polynomial must have zero constant term\n"); abort(); } if (len1 == 0 || n == 0) { arb_poly_zero(res); return; } if (len2 == 0 || len1 == 1) { arb_poly_set_arb(res, poly1->coeffs); return; } lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n); len1 = FLINT_MIN(len1, lenr); len2 = FLINT_MIN(len2, lenr); if ((res != poly1) && (res != poly2)) { arb_poly_fit_length(res, lenr); _arb_poly_compose_series(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _arb_poly_set_length(res, lenr); _arb_poly_normalise(res); } else { arb_poly_t t; arb_poly_init2(t, lenr); _arb_poly_compose_series(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _arb_poly_set_length(t, lenr); _arb_poly_normalise(t); arb_poly_swap(res, t); arb_poly_clear(t); } } arb-2.8.1/arb_poly/compose_series_brent_kung.c000066400000000000000000000075231264125401100215010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #include "arb_mat.h" void _arb_poly_compose_series_brent_kung(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) { arb_mat_t A, B, C; arb_ptr t, h; slong i, m; if (n == 1) { arb_set(res, poly1); return; } m = n_sqrt(n) + 1; arb_mat_init(A, m, n); arb_mat_init(B, m, m); arb_mat_init(C, m, n); h = _arb_vec_init(n); t = _arb_vec_init(n); /* Set rows of B to the segments of poly1 */ for (i = 0; i < len1 / m; i++) _arb_vec_set(B->rows[i], poly1 + i*m, m); _arb_vec_set(B->rows[i], poly1 + i*m, len1 % m); /* Set rows of A to powers of poly2 */ arb_set_ui(A->rows[0] + 0, UWORD(1)); _arb_vec_set(A->rows[1], poly2, len2); for (i = 2; i < m; i++) _arb_poly_mullow(A->rows[i], A->rows[(i + 1) / 2], n, A->rows[i / 2], n, n, prec); arb_mat_mul(C, B, A, prec); /* Evaluate block composition using the Horner scheme */ _arb_vec_set(res, C->rows[m - 1], n); _arb_poly_mullow(h, A->rows[m - 1], n, poly2, len2, n, prec); for (i = m - 2; i >= 0; i--) { _arb_poly_mullow(t, res, n, h, n, n, prec); _arb_poly_add(res, t, n, C->rows[i], n, prec); } _arb_vec_clear(h, n); _arb_vec_clear(t, n); arb_mat_clear(A); arb_mat_clear(B); arb_mat_clear(C); } void arb_poly_compose_series_brent_kung(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) { slong len1 = poly1->length; slong len2 = poly2->length; slong lenr; if (len2 != 0 && !arb_is_zero(poly2->coeffs)) { flint_printf("exception: compose_series: inner " "polynomial must have zero constant term\n"); abort(); } if (len1 == 0 || n == 0) { arb_poly_zero(res); return; } if (len2 == 0 || len1 == 1) { arb_poly_set_arb(res, poly1->coeffs); return; } lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n); len1 = FLINT_MIN(len1, lenr); len2 = FLINT_MIN(len2, lenr); if ((res != poly1) && (res != poly2)) { arb_poly_fit_length(res, lenr); _arb_poly_compose_series_brent_kung(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _arb_poly_set_length(res, lenr); _arb_poly_normalise(res); } else { arb_poly_t t; arb_poly_init2(t, lenr); _arb_poly_compose_series_brent_kung(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _arb_poly_set_length(t, lenr); _arb_poly_normalise(t); arb_poly_swap(res, t); arb_poly_clear(t); } } arb-2.8.1/arb_poly/compose_series_horner.c000066400000000000000000000066771264125401100206510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_compose_series_horner(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) { if (n == 1) { arb_set(res, poly1); } else { slong i = len1 - 1; slong lenr; arb_ptr t = _arb_vec_init(n); lenr = len2; _arb_vec_scalar_mul(res, poly2, len2, poly1 + i, prec); i--; arb_add(res, res, poly1 + i, prec); while (i > 0) { i--; if (lenr + len2 - 1 < n) { _arb_poly_mul(t, res, lenr, poly2, len2, prec); lenr = lenr + len2 - 1; } else { _arb_poly_mullow(t, res, lenr, poly2, len2, n, prec); lenr = n; } _arb_poly_add(res, t, lenr, poly1 + i, 1, prec); } _arb_vec_zero(res + lenr, n - lenr); _arb_vec_clear(t, n); } } void arb_poly_compose_series_horner(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) { slong len1 = poly1->length; slong len2 = poly2->length; slong lenr; if (len2 != 0 && !arb_is_zero(poly2->coeffs)) { flint_printf("exception: compose_series: inner " "polynomial must have zero constant term\n"); abort(); } if (len1 == 0 || n == 0) { arb_poly_zero(res); return; } if (len2 == 0 || len1 == 1) { arb_poly_set_arb(res, poly1->coeffs); return; } lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n); len1 = FLINT_MIN(len1, lenr); len2 = FLINT_MIN(len2, lenr); if ((res != poly1) && (res != poly2)) { arb_poly_fit_length(res, lenr); _arb_poly_compose_series_horner(res->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _arb_poly_set_length(res, lenr); _arb_poly_normalise(res); } else { arb_poly_t t; arb_poly_init2(t, lenr); _arb_poly_compose_series_horner(t->coeffs, poly1->coeffs, len1, poly2->coeffs, len2, lenr, prec); _arb_poly_set_length(t, lenr); _arb_poly_normalise(t); arb_poly_swap(res, t); arb_poly_clear(t); } } arb-2.8.1/arb_poly/contains.c000066400000000000000000000030011264125401100160450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int arb_poly_contains(const arb_poly_t poly1, const arb_poly_t poly2) { slong i; if (poly2->length > poly1->length) return 0; for (i = 0; i < poly2->length; i++) { if (!arb_contains(poly1->coeffs + i, poly2->coeffs + i)) return 0; } for (i = poly2->length; i < poly1->length; i++) if (!arb_contains_zero(poly1->coeffs + i)) return 0; return 1; } arb-2.8.1/arb_poly/contains_fmpq_poly.c000066400000000000000000000032241264125401100201420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int arb_poly_contains_fmpq_poly(const arb_poly_t poly1, const fmpq_poly_t poly2) { slong i; fmpq_t t; if (poly2->length > poly1->length) return 0; fmpq_init(t); for (i = 0; i < poly2->length; i++) { fmpq_poly_get_coeff_fmpq(t, poly2, i); if (!arb_contains_fmpq(poly1->coeffs + i, t)) { fmpq_clear(t); return 0; } } fmpq_clear(t); for (i = poly2->length; i < poly1->length; i++) if (!arb_contains_zero(poly1->coeffs + i)) return 0; return 1; } arb-2.8.1/arb_poly/contains_fmpz_poly.c000066400000000000000000000030061264125401100201510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int arb_poly_contains_fmpz_poly(const arb_poly_t poly1, const fmpz_poly_t poly2) { slong i; if (poly2->length > poly1->length) return 0; for (i = 0; i < poly2->length; i++) if (!arb_contains_fmpz(poly1->coeffs + i, poly2->coeffs + i)) return 0; for (i = poly2->length; i < poly1->length; i++) if (!arb_contains_zero(poly1->coeffs + i)) return 0; return 1; } arb-2.8.1/arb_poly/cos_pi_series.c000066400000000000000000000042701264125401100170660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_cos_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_cos_pi(g, h, prec); _arb_vec_zero(g + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_sin_cos_pi(t, g, h, prec); arb_neg(t, t); arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ arb_const_pi(t, prec); arb_mul(g + 1, g + 1, t, prec); arb_clear(t); } else { arb_ptr t = _arb_vec_init(n); _arb_poly_sin_cos_pi_series(t, g, h, hlen, n, prec); _arb_vec_clear(t, n); } } void arb_poly_cos_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { arb_poly_zero(g); return; } if (hlen == 0) { arb_poly_one(g); return; } if (hlen == 1) n = 1; arb_poly_fit_length(g, n); _arb_poly_cos_pi_series(g->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/cos_series.c000066400000000000000000000041371264125401100164000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_cos_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_cos(g, h, prec); _arb_vec_zero(g + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_sin_cos(t, g, h, prec); arb_neg(t, t); arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ arb_clear(t); } else { arb_ptr t = _arb_vec_init(n); _arb_poly_sin_cos_series(t, g, h, hlen, n, prec); _arb_vec_clear(t, n); } } void arb_poly_cos_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { arb_poly_zero(g); return; } if (hlen == 0) { arb_poly_one(g); return; } if (hlen == 1) n = 1; arb_poly_fit_length(g, n); _arb_poly_cos_series(g->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/cot_pi_series.c000066400000000000000000000037271264125401100170750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_cot_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); if (hlen == 1) { arb_cot_pi(g, h, prec); _arb_vec_zero(g + 1, len - 1); } else { arb_ptr t, u; t = _arb_vec_init(len); u = _arb_vec_init(len); _arb_poly_sin_cos_pi_series(t, u, h, hlen, len, prec); _arb_poly_div_series(g, u, len, t, len, len, prec); _arb_vec_clear(t, len); _arb_vec_clear(u, len); } } void arb_poly_cot_pi_series(arb_poly_t res, const arb_poly_t f, slong len, slong prec) { arb_poly_fit_length(res, len); if (f->length == 0 || len == 0) _arb_vec_indeterminate(res->coeffs, len); else _arb_poly_cot_pi_series(res->coeffs, f->coeffs, f->length, len, prec); _arb_poly_set_length(res, len); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/derivative.c000066400000000000000000000031431264125401100164000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_derivative(arb_ptr res, arb_srcptr poly, slong len, slong prec) { slong i; for (i = 1; i < len; i++) arb_mul_ui(res + i - 1, poly + i, i, prec); } void arb_poly_derivative(arb_poly_t res, const arb_poly_t poly, slong prec) { slong len = poly->length; if (len < 2) { arb_poly_zero(res); } else { arb_poly_fit_length(res, len - 1); _arb_poly_derivative(res->coeffs, poly->coeffs, len, prec); _arb_poly_set_length(res, len - 1); } } arb-2.8.1/arb_poly/digamma_series.c000066400000000000000000000127601264125401100172140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const arb_t x, int use_reflect, int digamma, slong prec); void _arb_poly_gamma_stirling_eval2(arb_ptr res, const arb_t z, slong n, slong num, int diff, slong prec); void _arb_poly_digamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec) { int reflect; slong i, r, n, rflen, wp; arb_t zr; arb_ptr t, u, v; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { arb_digamma(res, h, prec); if (arb_is_finite(res)) _arb_vec_zero(res + 1, len - 1); else _arb_vec_indeterminate(res + 1, len - 1); return; } wp = prec + FLINT_BIT_COUNT(prec); t = _arb_vec_init(len + 1); u = _arb_vec_init(len + 1); v = _arb_vec_init(len + 1); arb_init(zr); /* use zeta values at small integers */ if (arb_is_int(h) && (arf_cmpabs_ui(arb_midref(h), prec / 2) < 0)) { r = arf_get_si(arb_midref(h), ARF_RND_DOWN); if (r <= 0) { _arb_vec_indeterminate(res, len); goto cleanup; } else if (r == 1) { arb_const_euler(u, prec); arb_zeta_ui_vec(u + 1, 2, len - 1, prec); for (i = 0; i < len; i += 2) arb_neg(u + i, u + i); } else { arb_one(v); arb_one(v + 1); rflen = FLINT_MIN(len + 1, r); _arb_poly_rising_ui_series(u, v, 2, r - 1, rflen, wp); _arb_poly_derivative(v, u, rflen, wp); _arb_poly_div_series(t, v, rflen - 1, u, rflen, len, wp); arb_const_euler(u, prec); arb_zeta_ui_vec(u + 1, 2, len - 1, prec); for (i = 0; i < len; i += 2) arb_neg(u + i, u + i); _arb_vec_add(u, u, t, len, wp); } } else { /* use Stirling series */ arb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 1, wp); /* psi(x) = psi((1-x)+r) - h(1-x,r) - pi*cot(pi*x) */ if (reflect) { if (r != 0) /* otherwise t = 0 */ { arb_sub_ui(v, h, 1, wp); arb_neg(v, v); arb_one(v + 1); rflen = FLINT_MIN(len + 1, r + 1); _arb_poly_rising_ui_series(u, v, 2, r, rflen, wp); _arb_poly_derivative(v, u, rflen, wp); _arb_poly_div_series(t, v, rflen - 1, u, rflen, len, wp); for (i = 1; i < len; i += 2) arb_neg(t + i, t + i); } arb_sub_ui(zr, h, r + 1, wp); arb_neg(zr, zr); _arb_poly_gamma_stirling_eval2(u, zr, n, len + 1, 1, wp); for (i = 1; i < len; i += 2) arb_neg(u + i, u + i); _arb_vec_sub(u, u, t, len, wp); arb_set(t, h); arb_one(t + 1); _arb_poly_cot_pi_series(t, t, 2, len, wp); arb_const_pi(v, wp); _arb_vec_scalar_mul(t, t, len, v, wp); _arb_vec_sub(u, u, t, len, wp); } else { if (r == 0) { arb_add_ui(zr, h, r, wp); _arb_poly_gamma_stirling_eval2(u, zr, n, len + 1, 1, wp); } else { arb_set(v, h); arb_one(v + 1); rflen = FLINT_MIN(len + 1, r + 1); _arb_poly_rising_ui_series(u, v, 2, r, rflen, wp); _arb_poly_derivative(v, u, rflen, wp); _arb_poly_div_series(t, v, rflen - 1, u, rflen, len, wp); arb_add_ui(zr, h, r, wp); _arb_poly_gamma_stirling_eval2(u, zr, n, len + 1, 1, wp); _arb_vec_sub(u, u, t, len, wp); } } } /* compose with nonconstant part */ arb_zero(t); _arb_vec_set(t + 1, h + 1, hlen - 1); _arb_poly_compose_series(res, u, len, t, hlen, len, prec); cleanup: arb_clear(zr); _arb_vec_clear(t, len + 1); _arb_vec_clear(u, len + 1); _arb_vec_clear(v, len + 1); } void arb_poly_digamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) { arb_poly_fit_length(res, n); if (f->length == 0 || n == 0) _arb_vec_indeterminate(res->coeffs, n); else _arb_poly_digamma_series(res->coeffs, f->coeffs, f->length, n, prec); _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/div_root.c000066400000000000000000000033701264125401100160650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 William Hart Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_div_root(arb_ptr Q, arb_t R, arb_srcptr A, slong len, const arb_t c, slong prec) { arb_t r, t; slong i; if (len < 2) { arb_zero(R); return; } arb_init(r); arb_init(t); arb_set(t, A + len - 2); arb_set(Q + len - 2, A + len - 1); arb_set(r, Q + len - 2); /* TODO: avoid the extra assignments (but still support aliasing) */ for (i = len - 2; i > 0; i--) { arb_mul(r, r, c, prec); arb_add(r, r, t, prec); arb_set(t, A + i - 1); arb_set(Q + i - 1, r); } arb_mul(r, r, c, prec); arb_add(R, r, t, prec); } arb-2.8.1/arb_poly/div_series.c000066400000000000000000000055171264125401100164010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_div_series(arb_ptr Q, arb_srcptr A, slong Alen, arb_srcptr B, slong Blen, slong n, slong prec) { Alen = FLINT_MIN(Alen, n); Blen = FLINT_MIN(Blen, n); if (Blen == 1) { _arb_vec_scalar_div(Q, A, Alen, B, prec); _arb_vec_zero(Q + Alen, n - Alen); } else if (n == 2) { if (Alen == 1) { arb_div(Q, A, B, prec); arb_div(Q + 1, Q, B, prec); arb_mul(Q + 1, Q + 1, B + 1, prec); arb_neg(Q + 1, Q + 1); } else { arb_div(Q, A, B, prec); arb_mul(Q + 1, Q, B + 1, prec); arb_sub(Q + 1, A + 1, Q + 1, prec); arb_div(Q + 1, Q + 1, B, prec); } } else { arb_ptr Binv; Binv = _arb_vec_init(n); _arb_poly_inv_series(Binv, B, Blen, n, prec); _arb_poly_mullow(Q, Binv, n, A, Alen, n, prec); _arb_vec_clear(Binv, n); } } void arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, slong n, slong prec) { if (n == 0) { arb_poly_zero(Q); return; } if (B->length == 0) { arb_poly_fit_length(Q, n); _arb_vec_indeterminate(Q->coeffs, n); _arb_poly_set_length(Q, n); return; } if (A->length == 0) { arb_poly_zero(Q); return; } if (Q == A || Q == B) { arb_poly_t t; arb_poly_init(t); arb_poly_div_series(t, A, B, n, prec); arb_poly_swap(Q, t); arb_poly_clear(t); return; } arb_poly_fit_length(Q, n); _arb_poly_div_series(Q->coeffs, A->coeffs, A->length, B->coeffs, B->length, n, prec); _arb_poly_set_length(Q, n); _arb_poly_normalise(Q); } arb-2.8.1/arb_poly/divrem.c000066400000000000000000000071721264125401100155320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 William Hart Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" /* TODO: tighten this code */ void _arb_poly_div(arb_ptr Q, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) { slong lenQ, lenB2; arb_ptr Arev, Brev; lenQ = lenA - lenB + 1; Arev = _arb_vec_init(2 * lenQ); Brev = Arev + lenQ; _arb_poly_reverse(Arev, A + (lenA - lenQ), lenQ, lenQ); if (lenB >= lenQ) { _arb_poly_reverse(Brev, B + (lenB - lenQ), lenQ, lenQ); lenB2 = lenQ; } else { _arb_poly_reverse(Brev, B, lenB, lenB); lenB2 = lenB; } _arb_poly_div_series(Q, Arev, lenQ, Brev, lenB2, lenQ, prec); _arb_poly_reverse(Q, Q, lenQ, lenQ); _arb_vec_clear(Arev, 2 * lenQ); } void _arb_poly_divrem(arb_ptr Q, arb_ptr R, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) { const slong lenQ = lenA - lenB + 1; _arb_poly_div(Q, A, lenA, B, lenB, prec); if (lenB > 1) { if (lenQ >= lenB - 1) _arb_poly_mullow(R, Q, lenQ, B, lenB - 1, lenB - 1, prec); else _arb_poly_mullow(R, B, lenB - 1, Q, lenQ, lenB - 1, prec); _arb_vec_sub(R, A, R, lenB - 1, prec); } } void _arb_poly_rem(arb_ptr R, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) { const slong lenQ = lenA - lenB + 1; arb_ptr Q = _arb_vec_init(lenQ); _arb_poly_divrem(Q, R, A, lenA, B, lenB, prec); _arb_vec_clear(Q, lenQ); } int arb_poly_divrem(arb_poly_t Q, arb_poly_t R, const arb_poly_t A, const arb_poly_t B, slong prec) { const slong lenA = A->length, lenB = B->length; if (lenB == 0 || arb_contains_zero(B->coeffs + lenB - 1)) { return 0; } if (lenA < lenB) { arb_poly_set(R, A); arb_poly_zero(Q); return 1; } if (Q == A || Q == B) { arb_poly_t T; arb_poly_init(T); arb_poly_divrem(T, R, A, B, prec); arb_poly_swap(Q, T); arb_poly_clear(T); return 1; } if (R == A || R == B) { arb_poly_t U; arb_poly_init(U); arb_poly_divrem(Q, U, A, B, prec); arb_poly_swap(R, U); arb_poly_clear(U); return 1; } arb_poly_fit_length(Q, lenA - lenB + 1); arb_poly_fit_length(R, lenB - 1); _arb_poly_divrem(Q->coeffs, R->coeffs, A->coeffs, lenA, B->coeffs, lenB, prec); _arb_poly_set_length(Q, lenA - lenB + 1); _arb_poly_set_length(R, lenB - 1); _arb_poly_normalise(R); return 1; } arb-2.8.1/arb_poly/equal.c000066400000000000000000000025261264125401100153510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int arb_poly_equal(const arb_poly_t A, const arb_poly_t B) { slong i; if (A->length != B->length) return 0; for (i = 0; i < A->length; i++) if (!arb_equal(A->coeffs + i, B->coeffs + i)) return 0; return 1; } arb-2.8.1/arb_poly/evaluate.c000066400000000000000000000032361264125401100160470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate(arb_t res, arb_srcptr f, slong len, const arb_t x, slong prec) { if ((prec >= 1024) && (len >= 5 + 20000 / prec)) { slong fbits; fbits = _arb_vec_bits(f, len); if (fbits <= prec / 2) { _arb_poly_evaluate_rectangular(res, f, len, x, prec); return; } } _arb_poly_evaluate_horner(res, f, len, x, prec); } void arb_poly_evaluate(arb_t res, const arb_poly_t f, const arb_t a, slong prec) { _arb_poly_evaluate(res, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate2.c000066400000000000000000000032311264125401100161240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate2(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec) { if ((prec >= 1024) && (len >= 5 + 20000 / prec)) { slong fbits; fbits = _arb_vec_bits(f, len); if (fbits <= prec / 2) { _arb_poly_evaluate2_rectangular(y, z, f, len, x, prec); return; } } _arb_poly_evaluate2_horner(y, z, f, len, x, prec); } void arb_poly_evaluate2(arb_t r, arb_t s, const arb_poly_t f, const arb_t a, slong prec) { _arb_poly_evaluate2(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate2_acb.c000066400000000000000000000026431264125401100167370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate2_acb(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec) { _arb_poly_evaluate2_acb_rectangular(y, z, f, len, x, prec); } void arb_poly_evaluate2_acb(acb_t r, acb_t s, const arb_poly_t f, const acb_t a, slong prec) { _arb_poly_evaluate2_acb(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate2_acb_horner.c000066400000000000000000000045531264125401100203160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate2_acb_horner(acb_t y, acb_t z, arb_srcptr poly, slong len, const acb_t x, slong prec) { if (len == 0) { acb_zero(y); acb_zero(z); } else if (len == 1) { acb_set_round_arb(y, poly + 0, prec); acb_zero(z); } else if (acb_is_zero(x)) { acb_set_round_arb(y, poly + 0, prec); acb_set_round_arb(z, poly + 1, prec); } else if (len == 2) { acb_mul_arb(y, x, poly + 1, prec); acb_add_arb(y, y, poly + 0, prec); acb_set_round_arb(z, poly + 1, prec); } else { acb_t t, u, v; slong i; acb_init(t); acb_init(u); acb_init(v); acb_set_round_arb(u, poly + len - 1, prec); acb_zero(v); for (i = len - 2; i >= 0; i--) { acb_mul(t, v, x, prec); acb_add(v, u, t, prec); acb_mul(t, u, x, prec); acb_add_arb(u, t, poly + i, prec); } acb_swap(y, u); acb_swap(z, v); acb_clear(t); acb_clear(u); acb_clear(v); } } void arb_poly_evaluate2_acb_horner(acb_t r, acb_t s, const arb_poly_t f, const acb_t a, slong prec) { _arb_poly_evaluate2_acb_horner(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate2_acb_rectangular.c000066400000000000000000000064651264125401100213340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate2_acb_rectangular(acb_t y, acb_t z, arb_srcptr poly, slong len, const acb_t x, slong prec) { slong i, j, m, r; acb_ptr xs; acb_t s, t; arb_t c; if (len < 3) { if (len == 0) { acb_zero(y); acb_zero(z); } else if (len == 1) { acb_set_round_arb(y, poly + 0, prec); acb_zero(z); } else if (len == 2) { acb_mul_arb(y, x, poly + 1, prec); acb_add_arb(y, y, poly + 0, prec); acb_set_round_arb(z, poly + 1, prec); } return; } m = n_sqrt(len) + 1; m *= 1; r = (len + m - 1) / m; xs = _acb_vec_init(m + 1); acb_init(s); acb_init(t); arb_init(c); _acb_vec_set_powers(xs, x, m + 1, prec); acb_set_arb(y, poly + (r - 1) * m); for (j = 1; (r - 1) * m + j < len; j++) acb_addmul_arb(y, xs + j, poly + (r - 1) * m + j, prec); for (i = r - 2; i >= 0; i--) { acb_set_arb(s, poly + i * m); for (j = 1; j < m; j++) acb_addmul_arb(s, xs + j, poly + i * m + j, prec); acb_mul(y, y, xs + m, prec); acb_add(y, y, s, prec); } len -= 1; r = (len + m - 1) / m; arb_mul_ui(acb_realref(z), poly + (r - 1) * m + 1, (r - 1) * m + 1, ARF_PREC_EXACT); arb_zero(acb_imagref(z)); for (j = 1; (r - 1) * m + j < len; j++) { arb_mul_ui(c, poly + (r - 1) * m + j + 1, (r - 1) * m + j + 1, ARF_PREC_EXACT); acb_addmul_arb(z, xs + j, c, prec); } for (i = r - 2; i >= 0; i--) { arb_mul_ui(acb_realref(s), poly + i * m + 1, i * m + 1, ARF_PREC_EXACT); arb_zero(acb_imagref(s)); for (j = 1; j < m; j++) { arb_mul_ui(c, poly + i * m + j + 1, i * m + j + 1, ARF_PREC_EXACT); acb_addmul_arb(s, xs + j, c, prec); } acb_mul(z, z, xs + m, prec); acb_add(z, z, s, prec); } _acb_vec_clear(xs, m + 1); acb_clear(s); acb_clear(t); arb_clear(c); } void arb_poly_evaluate2_acb_rectangular(acb_t r, acb_t s, const arb_poly_t f, const acb_t a, slong prec) { _arb_poly_evaluate2_acb_rectangular(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate2_horner.c000066400000000000000000000045031264125401100175040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate2_horner(arb_t y, arb_t z, arb_srcptr poly, slong len, const arb_t x, slong prec) { if (len == 0) { arb_zero(y); arb_zero(z); } else if (len == 1) { arb_set_round(y, poly + 0, prec); arb_zero(z); } else if (arb_is_zero(x)) { arb_set_round(y, poly + 0, prec); arb_set_round(z, poly + 1, prec); } else if (len == 2) { arb_mul(y, x, poly + 1, prec); arb_add(y, y, poly + 0, prec); arb_set_round(z, poly + 1, prec); } else { arb_t t, u, v; slong i; arb_init(t); arb_init(u); arb_init(v); arb_set_round(u, poly + len - 1, prec); arb_zero(v); for (i = len - 2; i >= 0; i--) { arb_mul(t, v, x, prec); arb_add(v, u, t, prec); arb_mul(t, u, x, prec); arb_add(u, t, poly + i, prec); } arb_swap(y, u); arb_swap(z, v); arb_clear(t); arb_clear(u); arb_clear(v); } } void arb_poly_evaluate2_horner(arb_t r, arb_t s, const arb_poly_t f, const arb_t a, slong prec) { _arb_poly_evaluate2_horner(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate2_rectangular.c000066400000000000000000000062351264125401100205220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate2_rectangular(arb_t y, arb_t z, arb_srcptr poly, slong len, const arb_t x, slong prec) { slong i, j, m, r; arb_ptr xs; arb_t s, t, c; if (len < 3) { if (len == 0) { arb_zero(y); arb_zero(z); } else if (len == 1) { arb_set_round(y, poly + 0, prec); arb_zero(z); } else if (len == 2) { arb_mul(y, x, poly + 1, prec); arb_add(y, y, poly + 0, prec); arb_set_round(z, poly + 1, prec); } return; } m = n_sqrt(len) + 1; m *= 1; r = (len + m - 1) / m; xs = _arb_vec_init(m + 1); arb_init(s); arb_init(t); arb_init(c); _arb_vec_set_powers(xs, x, m + 1, prec); arb_set(y, poly + (r - 1) * m); for (j = 1; (r - 1) * m + j < len; j++) arb_addmul(y, xs + j, poly + (r - 1) * m + j, prec); for (i = r - 2; i >= 0; i--) { arb_set(s, poly + i * m); for (j = 1; j < m; j++) arb_addmul(s, xs + j, poly + i * m + j, prec); arb_mul(y, y, xs + m, prec); arb_add(y, y, s, prec); } len -= 1; r = (len + m - 1) / m; arb_mul_ui(z, poly + (r - 1) * m + 1, (r - 1) * m + 1, ARF_PREC_EXACT); for (j = 1; (r - 1) * m + j < len; j++) { arb_mul_ui(c, poly + (r - 1) * m + j + 1, (r - 1) * m + j + 1, ARF_PREC_EXACT); arb_addmul(z, xs + j, c, prec); } for (i = r - 2; i >= 0; i--) { arb_mul_ui(s, poly + i * m + 1, i * m + 1, ARF_PREC_EXACT); for (j = 1; j < m; j++) { arb_mul_ui(c, poly + i * m + j + 1, i * m + j + 1, ARF_PREC_EXACT); arb_addmul(s, xs + j, c, prec); } arb_mul(z, z, xs + m, prec); arb_add(z, z, s, prec); } _arb_vec_clear(xs, m + 1); arb_clear(s); arb_clear(t); arb_clear(c); } void arb_poly_evaluate2_rectangular(arb_t r, arb_t s, const arb_poly_t f, const arb_t a, slong prec) { _arb_poly_evaluate2_rectangular(r, s, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate_acb.c000066400000000000000000000026521264125401100166550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate_acb(acb_t res, arb_srcptr f, slong len, const acb_t x, slong prec) { _arb_poly_evaluate_acb_rectangular(res, f, len, x, prec); } void arb_poly_evaluate_acb(acb_t res, const arb_poly_t f, const acb_t a, slong prec) { _arb_poly_evaluate_acb(res, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate_acb_horner.c000066400000000000000000000040131264125401100202230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate_acb_horner(acb_t y, arb_srcptr f, slong len, const acb_t x, slong prec) { if (len == 0) { acb_zero(y); } else if (len == 1 || acb_is_zero(x)) { acb_set_round_arb(y, f, prec); } else if (len == 2) { acb_mul_arb(y, x, f + 1, prec); acb_add_arb(y, y, f + 0, prec); } else { slong i = len - 1; acb_t t, u; acb_init(t); acb_init(u); acb_set_arb(u, f + i); for (i = len - 2; i >= 0; i--) { acb_mul(t, u, x, prec); acb_add_arb(u, t, f + i, prec); } acb_swap(y, u); acb_clear(t); acb_clear(u); } } void arb_poly_evaluate_acb_horner(acb_t res, const arb_poly_t f, const acb_t a, slong prec) { _arb_poly_evaluate_acb_horner(res, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate_acb_rectangular.c000066400000000000000000000046551264125401100212510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate_acb_rectangular(acb_t y, arb_srcptr poly, slong len, const acb_t x, slong prec) { slong i, j, m, r; acb_ptr xs; acb_t s, t, c; if (len < 3) { if (len == 0) { acb_zero(y); } else if (len == 1) { acb_set_round_arb(y, poly + 0, prec); } else if (len == 2) { acb_mul_arb(y, x, poly + 1, prec); acb_add_arb(y, y, poly + 0, prec); } return; } m = n_sqrt(len) + 1; r = (len + m - 1) / m; xs = _acb_vec_init(m + 1); acb_init(s); acb_init(t); acb_init(c); _acb_vec_set_powers(xs, x, m + 1, prec); acb_set_arb(y, poly + (r - 1) * m); for (j = 1; (r - 1) * m + j < len; j++) acb_addmul_arb(y, xs + j, poly + (r - 1) * m + j, prec); for (i = r - 2; i >= 0; i--) { acb_set_arb(s, poly + i * m); for (j = 1; j < m; j++) acb_addmul_arb(s, xs + j, poly + i * m + j, prec); acb_mul(y, y, xs + m, prec); acb_add(y, y, s, prec); } _acb_vec_clear(xs, m + 1); acb_clear(s); acb_clear(t); acb_clear(c); } void arb_poly_evaluate_acb_rectangular(acb_t res, const arb_poly_t f, const acb_t a, slong prec) { _arb_poly_evaluate_acb_rectangular(res, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate_horner.c000066400000000000000000000037531264125401100174300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate_horner(arb_t y, arb_srcptr f, slong len, const arb_t x, slong prec) { if (len == 0) { arb_zero(y); } else if (len == 1 || arb_is_zero(x)) { arb_set_round(y, f, prec); } else if (len == 2) { arb_mul(y, x, f + 1, prec); arb_add(y, y, f + 0, prec); } else { slong i = len - 1; arb_t t, u; arb_init(t); arb_init(u); arb_set(u, f + i); for (i = len - 2; i >= 0; i--) { arb_mul(t, u, x, prec); arb_add(u, f + i, t, prec); } arb_swap(y, u); arb_clear(t); arb_clear(u); } } void arb_poly_evaluate_horner(arb_t res, const arb_poly_t f, const arb_t a, slong prec) { _arb_poly_evaluate_horner(res, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate_rectangular.c000066400000000000000000000046051264125401100204370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate_rectangular(arb_t y, arb_srcptr poly, slong len, const arb_t x, slong prec) { slong i, j, m, r; arb_ptr xs; arb_t s, t, c; if (len < 3) { if (len == 0) { arb_zero(y); } else if (len == 1) { arb_set_round(y, poly + 0, prec); } else if (len == 2) { arb_mul(y, x, poly + 1, prec); arb_add(y, y, poly + 0, prec); } return; } m = n_sqrt(len) + 1; r = (len + m - 1) / m; xs = _arb_vec_init(m + 1); arb_init(s); arb_init(t); arb_init(c); _arb_vec_set_powers(xs, x, m + 1, prec); arb_set(y, poly + (r - 1) * m); for (j = 1; (r - 1) * m + j < len; j++) arb_addmul(y, xs + j, poly + (r - 1) * m + j, prec); for (i = r - 2; i >= 0; i--) { arb_set(s, poly + i * m); for (j = 1; j < m; j++) arb_addmul(s, xs + j, poly + i * m + j, prec); arb_mul(y, y, xs + m, prec); arb_add(y, y, s, prec); } _arb_vec_clear(xs, m + 1); arb_clear(s); arb_clear(t); arb_clear(c); } void arb_poly_evaluate_rectangular(arb_t res, const arb_poly_t f, const arb_t a, slong prec) { _arb_poly_evaluate_rectangular(res, f->coeffs, f->length, a, prec); } arb-2.8.1/arb_poly/evaluate_vec_fast.c000066400000000000000000000102171264125401100177160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" /* This gives some speedup for small lengths. */ static __inline__ void _arb_poly_rem_2(arb_ptr r, arb_srcptr a, slong al, arb_srcptr b, slong bl, slong prec) { if (al == 2) { arb_mul(r + 0, a + 1, b + 0, prec); arb_sub(r + 0, a + 0, r + 0, prec); } else { _arb_poly_rem(r, a, al, b, bl, prec); } } void _arb_poly_evaluate_vec_fast_precomp(arb_ptr vs, arb_srcptr poly, slong plen, arb_ptr * tree, slong len, slong prec) { slong height, i, j, pow, left; slong tree_height; slong tlen; arb_ptr t, u, swap, pa, pb, pc; /* avoid worrying about some degenerate cases */ if (len < 2 || plen < 2) { if (len == 1) { arb_t tmp; arb_init(tmp); arb_neg(tmp, tree[0] + 0); _arb_poly_evaluate(vs + 0, poly, plen, tmp, prec); arb_clear(tmp); } else if (len != 0 && plen == 0) { _arb_vec_zero(vs, len); } else if (len != 0 && plen == 1) { for (i = 0; i < len; i++) arb_set(vs + i, poly + 0); } return; } t = _arb_vec_init(len); u = _arb_vec_init(len); left = len; /* Initial reduction. We allow the polynomial to be larger or smaller than the number of points. */ height = FLINT_BIT_COUNT(plen - 1) - 1; tree_height = FLINT_CLOG2(len); while (height >= tree_height) height--; pow = WORD(1) << height; for (i = j = 0; i < len; i += pow, j += (pow + 1)) { tlen = ((i + pow) <= len) ? pow : len % pow; _arb_poly_rem(t + i, poly, plen, tree[height] + j, tlen + 1, prec); } for (i = height - 1; i >= 0; i--) { pow = WORD(1) << i; left = len; pa = tree[i]; pb = t; pc = u; while (left >= 2 * pow) { _arb_poly_rem_2(pc, pb, 2 * pow, pa, pow + 1, prec); _arb_poly_rem_2(pc + pow, pb, 2 * pow, pa + pow + 1, pow + 1, prec); pa += 2 * pow + 2; pb += 2 * pow; pc += 2 * pow; left -= 2 * pow; } if (left > pow) { _arb_poly_rem(pc, pb, left, pa, pow + 1, prec); _arb_poly_rem(pc + pow, pb, left, pa + pow + 1, left - pow + 1, prec); } else if (left > 0) _arb_vec_set(pc, pb, left); swap = t; t = u; u = swap; } _arb_vec_set(vs, t, len); _arb_vec_clear(t, len); _arb_vec_clear(u, len); } void _arb_poly_evaluate_vec_fast(arb_ptr ys, arb_srcptr poly, slong plen, arb_srcptr xs, slong n, slong prec) { arb_ptr * tree; tree = _arb_poly_tree_alloc(n); _arb_poly_tree_build(tree, xs, n, prec); _arb_poly_evaluate_vec_fast_precomp(ys, poly, plen, tree, n, prec); _arb_poly_tree_free(tree, n); } void arb_poly_evaluate_vec_fast(arb_ptr ys, const arb_poly_t poly, arb_srcptr xs, slong n, slong prec) { _arb_poly_evaluate_vec_fast(ys, poly->coeffs, poly->length, xs, n, prec); } arb-2.8.1/arb_poly/evaluate_vec_iter.c000066400000000000000000000030371264125401100177260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_evaluate_vec_iter(arb_ptr ys, arb_srcptr poly, slong plen, arb_srcptr xs, slong n, slong prec) { slong i; for (i = 0; i < n; i++) _arb_poly_evaluate(ys + i, poly, plen, xs + i, prec); } void arb_poly_evaluate_vec_iter(arb_ptr ys, const arb_poly_t poly, arb_srcptr xs, slong n, slong prec) { _arb_poly_evaluate_vec_iter(ys, poly->coeffs, poly->length, xs, n, prec); } arb-2.8.1/arb_poly/exp_series.c000066400000000000000000000123551264125401100164110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define NEWTON_EXP_CUTOFF 200 /* with inverse=1 simultaneously computes g = exp(-x) to length n with inverse=0 uses g as scratch space, computing g = exp(-x) only to length (n+1)/2 */ static void _arb_poly_exp_series_newton(arb_ptr f, arb_ptr g, arb_srcptr h, slong len, slong prec, int inverse, slong cutoff) { slong alloc; arb_ptr T, U, hprime; alloc = 3 * len; T = _arb_vec_init(alloc); U = T + len; hprime = U + len; _arb_poly_derivative(hprime, h, len, prec); arb_zero(hprime + len - 1); NEWTON_INIT(cutoff, len) /* f := exp(h) + O(x^m), g := exp(-h) + O(x^m2) */ NEWTON_BASECASE(n) _arb_poly_exp_series_basecase(f, h, n, n, prec); _arb_poly_inv_series(g, f, (n + 1) / 2, (n + 1) / 2, prec); NEWTON_END_BASECASE /* extend from length m to length n */ NEWTON_LOOP(m, n) slong m2 = (m + 1) / 2; slong l = m - 1; /* shifted for derivative */ /* g := exp(-h) + O(x^m) */ _arb_poly_mullow(T, f, m, g, m2, m, prec); _arb_poly_mullow(g + m2, g, m2, T + m2, m - m2, m - m2, prec); _arb_vec_neg(g + m2, g + m2, m - m2); /* U := h' + g (f' - f h') + O(x^(n-1)) Note: should replace h' by h' mod x^(m-1) */ _arb_vec_zero(f + m, n - m); _arb_poly_mullow(T, f, n, hprime, n, n, prec); /* should be mulmid */ _arb_poly_derivative(U, f, n, prec); arb_zero(U + n - 1); /* should skip low terms */ _arb_vec_sub(U + l, U + l, T + l, n - l, prec); _arb_poly_mullow(T + l, g, n - m, U + l, n - m, n - m, prec); _arb_vec_add(U + l, hprime + l, T + l, n - m, prec); /* f := f + f * (h - int U) + O(x^n) = exp(h) + O(x^n) */ _arb_poly_integral(U, U, n, prec); /* should skip low terms */ _arb_vec_sub(U + m, h + m, U + m, n - m, prec); _arb_poly_mullow(f + m, f, n - m, U + m, n - m, n - m, prec); /* g := exp(-h) + O(x^n) */ /* not needed if we only want exp(x) */ if (n == len && inverse) { _arb_poly_mullow(T, f, n, g, m, n, prec); _arb_poly_mullow(g + m, g, m, T + m, n - m, n - m, prec); _arb_vec_neg(g + m, g + m, n - m); } NEWTON_END_LOOP NEWTON_END _arb_vec_clear(T, alloc); } void _arb_poly_exp_series(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_exp(f, h, prec); _arb_vec_zero(f + 1, n - 1); } else if (n == 2) { arb_exp(f, h, prec); arb_mul(f + 1, f, h + 1, prec); /* safe since hlen >= 2 */ } else if (_arb_vec_is_zero(h + 1, hlen - 2)) /* h = a + bx^d */ { slong i, j, d = hlen - 1; arb_t t; arb_init(t); arb_set(t, h + d); arb_exp(f, h, prec); for (i = 1, j = d; j < n; j += d, i++) { arb_mul(f + j, f + j - d, t, prec); arb_div_ui(f + j, f + j, i, prec); _arb_vec_zero(f + j - d + 1, hlen - 2); } _arb_vec_zero(f + j - d + 1, n - (j - d + 1)); arb_clear(t); } else if (hlen <= NEWTON_EXP_CUTOFF) { _arb_poly_exp_series_basecase(f, h, hlen, n, prec); } else { arb_ptr g, t; arb_t u; int fix; g = _arb_vec_init((n + 1) / 2); fix = (hlen < n || h == f || !arb_is_zero(h)); if (fix) { t = _arb_vec_init(n); _arb_vec_set(t + 1, h + 1, hlen - 1); } else t = (arb_ptr) h; arb_init(u); arb_exp(u, h, prec); _arb_poly_exp_series_newton(f, g, t, n, prec, 0, NEWTON_EXP_CUTOFF); if (!arb_is_one(u)) _arb_vec_scalar_mul(f, f, n, u, prec); _arb_vec_clear(g, (n + 1) / 2); if (fix) _arb_vec_clear(t, n); arb_clear(u); } } void arb_poly_exp_series(arb_poly_t f, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { arb_poly_zero(f); return; } if (hlen == 0) { arb_poly_one(f); return; } if (hlen == 1) n = 1; arb_poly_fit_length(f, n); _arb_poly_exp_series(f->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(f, n); _arb_poly_normalise(f); } arb-2.8.1/arb_poly/exp_series_basecase.c000066400000000000000000000057571264125401100202470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define MUL_CUTOFF 60 static void _arb_poly_exp_series_basecase_rec(arb_ptr f, arb_ptr a, arb_srcptr h, slong hlen, slong n, slong prec) { slong j, k; arb_t s; arb_init(s); arb_exp(f, h, prec); for (k = 1; k < hlen; k++) arb_mul_ui(a + k, h + k, k, prec); for (k = 1; k < n; k++) { arb_zero(s); for (j = 1; j < FLINT_MIN(k + 1, hlen); j++) arb_addmul(s, a + j, f + k - j, prec); arb_div_ui(f + k, s, k, prec); } arb_clear(s); } void _arb_poly_exp_series_basecase(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(n, hlen); if (n < MUL_CUTOFF || hlen < 0.9 * n) { arb_ptr t = _arb_vec_init(hlen); _arb_poly_exp_series_basecase_rec(f, t, h, hlen, n, prec); _arb_vec_clear(t, hlen); } else { slong m, v; arb_ptr t, u; m = (n + 2) / 3; v = m * 2; t = _arb_vec_init(n); u = _arb_vec_init(n - m); _arb_poly_mullow(t, h + m, hlen - m, h + m, hlen - m, n - v, prec); _arb_vec_scalar_mul_2exp_si(t, t, n - v, -1); _arb_vec_set(u, h + m, v - m); _arb_poly_add(u + v - m, t, n - v, h + v, hlen - v, prec); _arb_poly_exp_series_basecase_rec(f, t, h, m, n, prec); _arb_poly_mullow(t, f, n, u, n - m, n - m, prec); _arb_poly_add(f + m, f + m, n - m, t, n - m, prec); _arb_vec_clear(t, n); _arb_vec_clear(u, n - m); } } void arb_poly_exp_series_basecase(arb_poly_t f, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { arb_poly_zero(f); return; } if (hlen == 0) { arb_poly_one(f); return; } arb_poly_fit_length(f, n); _arb_poly_exp_series_basecase(f->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(f, n); _arb_poly_normalise(f); } arb-2.8.1/arb_poly/fit_length.c000066400000000000000000000027271264125401100163700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_fit_length(arb_poly_t poly, slong len) { slong i; if (len > poly->alloc) { if (len < 2 * poly->alloc) len = 2 * poly->alloc; poly->coeffs = flint_realloc(poly->coeffs, len * sizeof(arb_struct)); for (i = poly->alloc; i < len; i++) arb_init(poly->coeffs + i); poly->alloc = len; } } arb-2.8.1/arb_poly/gamma_series.c000066400000000000000000000253541264125401100167020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_gamma_stirling_bound(mag_ptr err, const arb_t x, slong k0, slong knum, slong n); void arb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const arb_t x, int use_reflect, int digamma, slong prec); void arb_gamma_stirling_coeff(arb_t b, ulong k, int digamma, slong prec); void _arb_poly_lgamma_series_at_one(arb_ptr u, slong len, slong prec) { slong i; if (len > 0) arb_zero(u); if (len > 1) arb_const_euler(u + 1, prec); if (len > 2) arb_zeta_ui_vec(u + 2, 2, len - 2, prec); for (i = 2; i < len; i++) arb_div_ui(u + i, u + i, i, prec); for (i = 1; i < len; i += 2) arb_neg(u + i, u + i); } static void bsplit(arb_ptr Q, arb_ptr T, const arb_t z, slong a, slong b, slong num, slong prec) { if (b - a == 1) { arb_gamma_stirling_coeff(T, a, 0, prec); if (a == 1) { /* (z + t) */ arb_set(Q, z); if (num > 1) arb_one(Q + 1); if (num > 2) arb_zero(Q + 2); } else { /* (z + t)^2 */ arb_mul(Q, z, z, prec); /* TODO: precompute */ if (num > 1) arb_mul_2exp_si(Q + 1, z, 1); if (num > 2) arb_one(Q + 2); } } else { slong m, n1, n2, q1len, q2len, t1len, t2len, qlen, tlen, alloc; arb_ptr Q1, T1, Q2, T2; m = a + (b - a) / 2; n1 = m - a; n2 = b - m; q1len = FLINT_MIN(2 * n1 + 1, num); t1len = FLINT_MIN(2 * n1 - 1, num); q2len = FLINT_MIN(2 * n2 + 1, num); t2len = FLINT_MIN(2 * n2 - 1, num); qlen = FLINT_MIN(q1len + q2len - 1, num); tlen = FLINT_MIN(t1len + q2len - 1, num); alloc = q1len + q2len + t1len + t2len; Q1 = _arb_vec_init(alloc); Q2 = Q1 + q1len; T1 = Q2 + q2len; T2 = T1 + t1len; bsplit(Q1, T1, z, a, m, num, prec); bsplit(Q2, T2, z, m, b, num, prec); _arb_poly_mullow(Q, Q2, q2len, Q1, q1len, qlen, prec); _arb_poly_mullow(T, Q2, q2len, T1, t1len, tlen, prec); _arb_poly_add(T, T, tlen, T2, t2len, prec); _arb_vec_clear(Q1, alloc); } } void _arb_poly_mullow_cpx(arb_ptr res, arb_srcptr src, slong len, const arb_t c, slong trunc, slong prec) { slong i; if (len < trunc) arb_set(res + len, src + len - 1); for (i = len - 1; i > 0; i--) { arb_mul(res + i, src + i, c, prec); arb_add(res + i, res + i, src + i - 1, prec); } arb_mul(res, src, c, prec); } void _arb_poly_log_cpx_series(arb_ptr res, const arb_t c, slong num, slong prec) { slong i; for (i = 0; i < num; i++) { if (i == 0) arb_log(res + i, c, prec); else if (i == 1) arb_inv(res + i, c, prec); else arb_mul(res + i, res + i - 1, res + 1, prec); } for (i = 2; i < num; i++) { arb_div_ui(res + i, res + i, i, prec); if (i % 2 == 0) arb_neg(res + i, res + i); } } void _arb_poly_gamma_stirling_eval2(arb_ptr res, const arb_t z, slong n, slong num, int diff, slong prec) { slong k, tlen, qlen; arb_ptr T, Q; mag_ptr err; arb_t c; T = _arb_vec_init(num); Q = _arb_vec_init(num); err = _mag_vec_init(num); arb_init(c); arb_gamma_stirling_bound(err, z, 0, num, n); if (n <= 1) { _arb_vec_zero(res, num); } else { qlen = FLINT_MIN(2 * (n - 1) + 1, num); tlen = FLINT_MIN(2 * (n - 1) - 1, num); bsplit(Q, T, z, 1, n, num, prec); _arb_poly_div_series(res, T, tlen, Q, qlen, num, prec); } if (diff) { _arb_vec_add_error_mag_vec(res, err, num); _arb_poly_derivative(res, res, num, prec); if (num > 1) { /* add log(z+x) - 1/(2(z+x)) */ arb_inv(c, z, prec); _arb_vec_set_powers(T, c, num, prec); for (k = 1; k < num - 1; k++) { arb_mul_2exp_si(T, z, 1); arb_div_ui(T, T, k, prec); arb_add_ui(T, T, 1, prec); arb_mul_2exp_si(T, T, -1); if (k % 2 == 0) arb_submul(res + k, T, T + k + 1, prec); else arb_addmul(res + k, T, T + k + 1, prec); } arb_mul_2exp_si(c, c, -1); arb_sub(res, res, c, prec); arb_log(c, z, prec); arb_add(res, res, c, prec); } } else { /* ((z-1/2) + t) * log(z+t) */ _arb_poly_log_cpx_series(T, z, num, prec); arb_one(c); arb_mul_2exp_si(c, c, -1); arb_sub(c, z, c, prec); _arb_poly_mullow_cpx(T, T, num, c, num, prec); /* constant term */ arb_const_log_sqrt2pi(c, prec); arb_add(T, T, c, prec); /* subtract (z+t) */ arb_sub(T, T, z, prec); if (num > 1) arb_sub_ui(T + 1, T + 1, 1, prec); _arb_vec_add(res, res, T, num, prec); _arb_vec_add_error_mag_vec(res, err, num); } _arb_vec_clear(T, num); _arb_vec_clear(Q, num); _mag_vec_clear(err, num); arb_clear(c); } void _arb_poly_gamma_stirling_eval(arb_ptr res, const arb_t z, slong n, slong num, slong prec) { _arb_poly_gamma_stirling_eval2(res, z, n, num, 0, prec); } void _arb_poly_gamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec) { int reflect; slong i, rflen, r, n, wp; arb_ptr t, u, v; arb_struct f[2]; if (hlen == 1) { arb_gamma(res, h, prec); if (arb_is_finite(res)) _arb_vec_zero(res + 1, len - 1); else _arb_vec_indeterminate(res + 1, len - 1); return; } hlen = FLINT_MIN(hlen, len); wp = prec + FLINT_BIT_COUNT(prec); t = _arb_vec_init(len); u = _arb_vec_init(len); v = _arb_vec_init(len); arb_init(f); arb_init(f + 1); /* use zeta values at small integers */ if (arb_is_int(h) && (arf_cmpabs_ui(arb_midref(h), prec / 2) < 0)) { r = arf_get_si(arb_midref(h), ARF_RND_DOWN); if (r <= 0) { _arb_vec_indeterminate(v, len); } else if (r == 1) { _arb_poly_lgamma_series_at_one(u, len, wp); _arb_poly_exp_series(v, u, len, len, wp); } else { _arb_poly_lgamma_series_at_one(u, len, wp); _arb_poly_exp_series(t, u, len, len, wp); arb_one(f); arb_one(f + 1); rflen = FLINT_MIN(len, r); _arb_poly_rising_ui_series(u, f, FLINT_MIN(2, len), r - 1, rflen, wp); _arb_poly_mullow(v, t, len, u, rflen, len, wp); } } else { /* otherwise use Stirling series */ arb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 0, wp); /* gamma(h) = (rf(1-h, r) * pi) / (gamma(1-h+r) sin(pi h)), h = h0 + t*/ if (reflect) { /* u = 1/gamma(r+1-h) */ arb_sub_ui(f, h, r + 1, wp); arb_neg(f, f); _arb_poly_gamma_stirling_eval(t, f, n, len, wp); _arb_vec_neg(t, t, len); _arb_poly_exp_series(u, t, len, len, wp); for (i = 1; i < len; i += 2) arb_neg(u + i, u + i); /* v = 1/sin(pi x) */ arb_set(f, h); arb_one(f + 1); _arb_poly_sin_pi_series(t, f, 2, len, wp); _arb_poly_inv_series(v, t, len, len, wp); _arb_poly_mullow(t, u, len, v, len, len, wp); /* rf(1-h,r) * pi */ if (r == 0) { rflen = 1; arb_const_pi(u, wp); } else { arb_sub_ui(f, h, 1, wp); arb_neg(f, f); arb_set_si(f + 1, -1); rflen = FLINT_MIN(len, r + 1); _arb_poly_rising_ui_series(u, f, FLINT_MIN(2, len), r, rflen, wp); arb_const_pi(v, wp); _arb_vec_scalar_mul(u, u, rflen, v, wp); } /* multiply by rising factorial */ _arb_poly_mullow(v, t, len, u, rflen, len, wp); } else { /* gamma(h) = gamma(h+r) / rf(h,r) */ if (r == 0) { arb_add_ui(f, h, r, wp); _arb_poly_gamma_stirling_eval(t, f, n, len, wp); _arb_poly_exp_series(v, t, len, len, wp); } else { /* TODO: div_series may be better (once it has a good basecase), if the rising factorial is short */ arb_set(f, h); arb_one(f + 1); rflen = FLINT_MIN(len, r + 1); _arb_poly_rising_ui_series(u, f, FLINT_MIN(2, len), r, rflen, wp); _arb_poly_inv_series(t, u, rflen, len, wp); arb_add_ui(f, h, r, wp); _arb_poly_gamma_stirling_eval(v, f, n, len, wp); _arb_poly_exp_series(u, v, len, len, wp); _arb_poly_mullow(v, u, len, t, len, len, wp); } } } /* compose with nonconstant part */ arb_zero(t); _arb_vec_set(t + 1, h + 1, hlen - 1); _arb_poly_compose_series(res, v, len, t, hlen, len, prec); arb_clear(f); arb_clear(f + 1); _arb_vec_clear(t, len); _arb_vec_clear(u, len); _arb_vec_clear(v, len); } void arb_poly_gamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) { arb_poly_fit_length(res, n); if (f->length == 0 || n == 0) _arb_vec_indeterminate(res->coeffs, n); else _arb_poly_gamma_series(res->coeffs, f->coeffs, f->length, n, prec); _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/get_coeff_arb.c000066400000000000000000000023771264125401100170130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_get_coeff_arb(arb_t x, const arb_poly_t poly, slong n) { if (n < poly->length) arb_set(x, poly->coeffs + n); else arb_zero(x); } arb-2.8.1/arb_poly/get_unique_fmpz_poly.c000066400000000000000000000026261264125401100205070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int arb_poly_get_unique_fmpz_poly(fmpz_poly_t res, const arb_poly_t src) { int success; fmpz_poly_fit_length(res, src->length); success = _arb_vec_get_unique_fmpz_vec(res->coeffs, src->coeffs, src->length); _fmpz_poly_set_length(res, src->length); _fmpz_poly_normalise(res); return success; } arb-2.8.1/arb_poly/init.c000066400000000000000000000024651264125401100152070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_init(arb_poly_t poly) { poly->coeffs = NULL; poly->length = 0; poly->alloc = 0; } void arb_poly_init2(arb_poly_t poly, slong len) { arb_poly_init(poly); arb_poly_fit_length(poly, len); } arb-2.8.1/arb_poly/inlines.c000066400000000000000000000021621264125401100156770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define ARB_POLY_INLINES_C #include "arb_poly.h" arb-2.8.1/arb_poly/integral.c000066400000000000000000000031031264125401100160370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_integral(arb_ptr res, arb_srcptr poly, slong len, slong prec) { slong k = len - 1; for (k = len - 1; k > 0; k--) arb_div_ui(res + k, poly + k - 1, k, prec); arb_zero(res); } void arb_poly_integral(arb_poly_t res, const arb_poly_t poly, slong prec) { arb_poly_fit_length(res, poly->length + 1); _arb_poly_integral(res->coeffs, poly->coeffs, poly->length + 1, prec); _arb_poly_set_length(res, poly->length + 1); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/interpolate_barycentric.c000066400000000000000000000047171264125401100211610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_interpolate_barycentric(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) { arb_ptr P, Q, w; arb_t t; slong i, j; if (n == 1) { arb_set(poly, ys); return; } P = _arb_vec_init(n + 1); Q = _arb_vec_init(n); w = _arb_vec_init(n); arb_init(t); _arb_poly_product_roots(P, xs, n, prec); for (i = 0; i < n; i++) { arb_one(w + i); for (j = 0; j < n; j++) { if (i != j) { arb_sub(t, xs + i, xs + j, prec); arb_mul(w + i, w + i, t, prec); } } arb_inv(w + i, w + i, prec); } _arb_vec_zero(poly, n); for (i = 0; i < n; i++) { _arb_poly_div_root(Q, t, P, n + 1, xs + i, prec); arb_mul(t, w + i, ys + i, prec); _arb_vec_scalar_addmul(poly, Q, n, t, prec); } _arb_vec_clear(P, n + 1); _arb_vec_clear(Q, n); _arb_vec_clear(w, n); arb_clear(t); } void arb_poly_interpolate_barycentric(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) { if (n == 0) { arb_poly_zero(poly); } else { arb_poly_fit_length(poly, n); _arb_poly_set_length(poly, n); _arb_poly_interpolate_barycentric(poly->coeffs, xs, ys, n, prec); _arb_poly_normalise(poly); } } arb-2.8.1/arb_poly/interpolate_fast.c000066400000000000000000000072521264125401100176060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_interpolation_weights(arb_ptr w, arb_ptr * tree, slong len, slong prec) { arb_ptr tmp; slong i, n, height; if (len == 0) return; if (len == 1) { arb_one(w); return; } tmp = _arb_vec_init(len + 1); height = FLINT_CLOG2(len); n = WORD(1) << (height - 1); _arb_poly_mul_monic(tmp, tree[height-1], n + 1, tree[height-1] + (n + 1), (len - n + 1), prec); _arb_poly_derivative(tmp, tmp, len + 1, prec); _arb_poly_evaluate_vec_fast_precomp(w, tmp, len, tree, len, prec); for (i = 0; i < len; i++) arb_inv(w + i, w + i, prec); _arb_vec_clear(tmp, len + 1); } void _arb_poly_interpolate_fast_precomp(arb_ptr poly, arb_srcptr ys, arb_ptr * tree, arb_srcptr weights, slong len, slong prec) { arb_ptr t, u, pa, pb; slong i, pow, left; if (len == 0) return; t = _arb_vec_init(len); u = _arb_vec_init(len); for (i = 0; i < len; i++) arb_mul(poly + i, weights + i, ys + i, prec); for (i = 0; i < FLINT_CLOG2(len); i++) { pow = (WORD(1) << i); pa = tree[i]; pb = poly; left = len; while (left >= 2 * pow) { _arb_poly_mul(t, pa, pow + 1, pb + pow, pow, prec); _arb_poly_mul(u, pa + pow + 1, pow + 1, pb, pow, prec); _arb_vec_add(pb, t, u, 2 * pow, prec); left -= 2 * pow; pa += 2 * pow + 2; pb += 2 * pow; } if (left > pow) { _arb_poly_mul(t, pa, pow + 1, pb + pow, left - pow, prec); _arb_poly_mul(u, pb, pow, pa + pow + 1, left - pow + 1, prec); _arb_vec_add(pb, t, u, left, prec); } } _arb_vec_clear(t, len); _arb_vec_clear(u, len); } void _arb_poly_interpolate_fast(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong len, slong prec) { arb_ptr * tree; arb_ptr w; tree = _arb_poly_tree_alloc(len); _arb_poly_tree_build(tree, xs, len, prec); w = _arb_vec_init(len); _arb_poly_interpolation_weights(w, tree, len, prec); _arb_poly_interpolate_fast_precomp(poly, ys, tree, w, len, prec); _arb_vec_clear(w, len); _arb_poly_tree_free(tree, len); } void arb_poly_interpolate_fast(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) { if (n == 0) { arb_poly_zero(poly); } else { arb_poly_fit_length(poly, n); _arb_poly_set_length(poly, n); _arb_poly_interpolate_fast(poly->coeffs, xs, ys, n, prec); _arb_poly_normalise(poly); } } arb-2.8.1/arb_poly/interpolate_newton.c000066400000000000000000000056221264125401100201620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" static void _interpolate_newton(arb_ptr ys, arb_srcptr xs, slong n, slong prec) { arb_t p, q, t; slong i, j; arb_init(p); arb_init(q); arb_init(t); for (i = 1; i < n; i++) { arb_set(t, ys + i - 1); for (j = i; j < n; j++) { arb_sub(p, ys + j, t, prec); arb_sub(q, xs + j, xs + j - i, prec); arb_set(t, ys + j); arb_div(ys + j, p, q, prec); } } arb_clear(p); arb_clear(q); arb_clear(t); } static void _newton_to_monomial(arb_ptr ys, arb_srcptr xs, slong n, slong prec) { arb_t t, u; slong i, j; arb_init(t); arb_init(u); for (i = n - 2; i >= 0; i--) { arb_set(t, ys + i); arb_set(ys + i, ys + i + 1); for (j = i + 1; j < n - 1; j++) { arb_mul(u, ys + j, xs + i, prec); arb_sub(ys + j, ys + j + 1, u, prec); } arb_mul(u, ys + n - 1, xs + i, prec); arb_sub(ys + n - 1, t, u, prec); } _arb_poly_reverse(ys, ys, n, n); arb_clear(t); arb_clear(u); } void _arb_poly_interpolate_newton(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) { if (n == 1) { arb_set(poly, ys); } else { _arb_vec_set(poly, ys, n); _interpolate_newton(poly, xs, n, prec); while (n > 0 && arb_is_zero(poly + n - 1)) n--; _newton_to_monomial(poly, xs, n, prec); } } void arb_poly_interpolate_newton(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) { if (n == 0) { arb_poly_zero(poly); } else { arb_poly_fit_length(poly, n); _arb_poly_set_length(poly, n); _arb_poly_interpolate_newton(poly->coeffs, xs, ys, n, prec); _arb_poly_normalise(poly); } } arb-2.8.1/arb_poly/inv_borel_transform.c000066400000000000000000000032721264125401100203130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_inv_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec) { slong i; arb_t t; arb_init(t); arb_one(t); for (i = 0; i < len; i++) { if (i > 1) arb_mul_ui(t, t, i, prec); arb_mul(res + i, poly + i, t, prec); } arb_clear(t); } void arb_poly_inv_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec) { arb_poly_fit_length(res, poly->length); _arb_poly_inv_borel_transform(res->coeffs, poly->coeffs, poly->length, prec); _arb_poly_set_length(res, poly->length); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/inv_series.c000066400000000000000000000055111264125401100164050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define MULLOW(z, x, xn, y, yn, nn, prec) \ if ((xn) >= (yn)) \ _arb_poly_mullow(z, x, xn, y, yn, nn, prec); \ else \ _arb_poly_mullow(z, y, yn, x, xn, nn, prec); \ void _arb_poly_inv_series(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong len, slong prec) { arb_inv(Qinv, Q, prec); if (Qlen == 1) { _arb_vec_zero(Qinv + 1, len - 1); } else if (len == 2) { arb_div(Qinv + 1, Qinv, Q, prec); arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec); arb_neg(Qinv + 1, Qinv + 1); } else { slong Qnlen, Wlen, W2len; arb_ptr W; W = _arb_vec_init(len); NEWTON_INIT(1, len) NEWTON_LOOP(m, n) Qnlen = FLINT_MIN(Qlen, n); Wlen = FLINT_MIN(Qnlen + m - 1, n); W2len = Wlen - m; MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec); MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec); _arb_vec_neg(Qinv + m, Qinv + m, n - m); NEWTON_END_LOOP NEWTON_END _arb_vec_clear(W, len); } } void arb_poly_inv_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec) { if (n == 0) { arb_poly_zero(Qinv); return; } if (Q->length == 0) { arb_poly_fit_length(Qinv, n); _arb_vec_indeterminate(Qinv->coeffs, n); _arb_poly_set_length(Qinv, n); return; } if (Qinv == Q) { arb_poly_t t; arb_poly_init(t); arb_poly_inv_series(t, Q, n, prec); arb_poly_swap(Qinv, t); arb_poly_clear(t); return; } arb_poly_fit_length(Qinv, n); _arb_poly_inv_series(Qinv->coeffs, Q->coeffs, Q->length, n, prec); _arb_poly_set_length(Qinv, n); _arb_poly_normalise(Qinv); } arb-2.8.1/arb_poly/lgamma_series.c000066400000000000000000000076101264125401100170510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" slong arf_get_si(const arf_t x, arf_rnd_t rnd); void _arb_poly_lgamma_series_at_one(arb_ptr u, slong len, slong prec); void arb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const arb_t x, int use_reflect, int digamma, slong prec); void _arb_poly_gamma_stirling_eval(arb_ptr res, const arb_t z, slong n, slong num, slong prec); static __inline__ void _log_rising_ui_series(arb_ptr t, const arb_t x, slong r, slong len, slong prec) { arb_struct f[2]; slong rflen; arb_init(f); arb_init(f + 1); arb_set(f, x); arb_one(f + 1); rflen = FLINT_MIN(len, r + 1); _arb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, prec); _arb_poly_log_series(t, t, rflen, len, prec); arb_clear(f); arb_clear(f + 1); } void _arb_poly_lgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec) { int reflect; slong r, n, wp; arb_t zr; arb_ptr t, u; if (!arb_is_positive(h)) { _arb_vec_indeterminate(res, len); return; } hlen = FLINT_MIN(hlen, len); wp = prec + FLINT_BIT_COUNT(prec); t = _arb_vec_init(len); u = _arb_vec_init(len); arb_init(zr); /* use zeta values at small integers */ if (arb_is_int(h) && (arf_cmpabs_ui(arb_midref(h), prec / 2) < 0)) { r = arf_get_si(arb_midref(h), ARF_RND_DOWN); if (r <= 0) { _arb_vec_indeterminate(res, len); goto cleanup; } else { _arb_poly_lgamma_series_at_one(u, len, wp); if (r != 1) { arb_one(zr); _log_rising_ui_series(t, zr, r - 1, len, wp); _arb_vec_add(u, u, t, len, wp); } } } else if (len <= 2) { arb_lgamma(u, h, wp); if (len == 2) arb_digamma(u + 1, h, wp); } else { /* otherwise use Stirling series */ arb_gamma_stirling_choose_param(&reflect, &r, &n, h, 0, 0, wp); arb_add_ui(zr, h, r, wp); _arb_poly_gamma_stirling_eval(u, zr, n, len, wp); if (r != 0) { _log_rising_ui_series(t, h, r, len, wp); _arb_vec_sub(u, u, t, len, wp); } } /* compose with nonconstant part */ arb_zero(t); _arb_vec_set(t + 1, h + 1, hlen - 1); _arb_poly_compose_series(res, u, len, t, hlen, len, prec); cleanup: arb_clear(zr); _arb_vec_clear(t, len); _arb_vec_clear(u, len); } void arb_poly_lgamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) { arb_poly_fit_length(res, n); if (f->length == 0 || n == 0) _arb_vec_indeterminate(res->coeffs, n); else _arb_poly_lgamma_series(res->coeffs, f->coeffs, f->length, n, prec); _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/log_series.c000066400000000000000000000060101264125401100163650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_log_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec) { flen = FLINT_MIN(flen, n); if (flen == 1) { arb_log(res, f, prec); _arb_vec_zero(res + 1, n - 1); } else if (n == 2) { arb_div(res + 1, f + 1, f + 0, prec); /* safe since hlen >= 2 */ arb_log(res, f, prec); } else if (_arb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */ { slong i, j, d = flen - 1; for (i = 1, j = d; j < n; j += d, i++) { if (i == 1) arb_div(res + j, f + d, f + 0, prec); else arb_mul(res + j, res + j - d, res + d, prec); _arb_vec_zero(res + j - d + 1, flen - 2); } _arb_vec_zero(res + j - d + 1, n - (j - d + 1)); for (i = 2, j = 2 * d; j < n; j += d, i++) arb_div_si(res + j, res + j, i % 2 ? i : -i, prec); arb_log(res, f, prec); /* done last to allow aliasing */ } else { arb_ptr f_diff, f_inv; arb_t a; slong alloc; alloc = n + flen - 1; f_inv = _arb_vec_init(alloc); f_diff = f_inv + n; arb_init(a); arb_log(a, f, prec); _arb_poly_derivative(f_diff, f, flen, prec); _arb_poly_inv_series(f_inv, f, flen, n, prec); _arb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec); _arb_poly_integral(res, res, n, prec); arb_swap(res, a); arb_clear(a); _arb_vec_clear(f_inv, alloc); } } void arb_poly_log_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) { if (n == 0) { arb_poly_zero(res); return; } arb_poly_fit_length(res, n); if (f->length == 0) _arb_vec_indeterminate(res->coeffs, n); else _arb_poly_log_series(res->coeffs, f->coeffs, f->length, n, prec); _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/majorant.c000066400000000000000000000030721264125401100160520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_majorant(arb_ptr res, arb_srcptr vec, slong len, slong prec) { slong i; for (i = 0; i < len; i++) { arb_get_abs_ubound_arf(arb_midref(res + i), vec + i, prec); mag_zero(arb_radref(res + i)); } } void arb_poly_majorant(arb_poly_t res, const arb_poly_t poly, slong prec) { arb_poly_fit_length(res, poly->length); _arb_poly_majorant(res->coeffs, poly->coeffs, poly->length, prec); _arb_poly_set_length(res, poly->length); } arb-2.8.1/arb_poly/mul.c000066400000000000000000000041611264125401100150340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_mul(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) { _arb_poly_mullow(C, A, lenA, B, lenB, lenA + lenB - 1, prec); } void arb_poly_mul(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) { slong len_out; if ((poly1->length == 0) || (poly2->length == 0)) { arb_poly_zero(res); return; } len_out = poly1->length + poly2->length - 1; if (res == poly1 || res == poly2) { arb_poly_t temp; arb_poly_init2(temp, len_out); _arb_poly_mul(temp->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); arb_poly_swap(res, temp); arb_poly_clear(temp); } else { arb_poly_fit_length(res, len_out); _arb_poly_mul(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); } _arb_poly_set_length(res, len_out); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/mullow.c000066400000000000000000000050411264125401100155540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define BLOCK_CUTOFF 16 void _arb_poly_mullow(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) { if (n == 1) { arb_mul(res, poly1, poly2, prec); } else { if (n < BLOCK_CUTOFF || len1 < BLOCK_CUTOFF || len2 < BLOCK_CUTOFF) _arb_poly_mullow_classical(res, poly1, len1, poly2, len2, n, prec); else _arb_poly_mullow_block(res, poly1, len1, poly2, len2, n, prec); } } void arb_poly_mullow(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) { slong len_out; if (poly1->length == 0 || poly2->length == 0 || n == 0) { arb_poly_zero(res); return; } len_out = poly1->length + poly2->length - 1; if (n > len_out) n = len_out; if (res == poly1 || res == poly2) { arb_poly_t t; arb_poly_init2(t, n); _arb_poly_mullow(t->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, prec); arb_poly_swap(res, t); arb_poly_clear(t); } else { arb_poly_fit_length(res, n); _arb_poly_mullow(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, prec); } _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/mullow_block.c000066400000000000000000000476541264125401100167460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include #include "arb_poly.h" void _arb_poly_get_scale(fmpz_t scale, arb_srcptr x, slong xlen, arb_srcptr y, slong ylen) { slong xa, xb, ya, yb, den; fmpz_zero(scale); /* ignore zeros (and infs/nans!); find the first and last finite nonzero entries to determine the scale */ xa = 0; xb = xlen - 1; while (xa < xlen && arf_is_special(arb_midref(x + xa))) xa++; while (xb > xa && arf_is_special(arb_midref(x + xb))) xb--; ya = 0; yb = ylen - 1; while (ya < ylen && arf_is_special(arb_midref(y + ya))) ya++; while (yb > ya && arf_is_special(arb_midref(y + yb))) yb--; /* compute average of exponent differences, weighted by the lengths */ if (xa <= xb && ya <= yb && (xa < xb || ya < yb)) { fmpz_add(scale, scale, ARF_EXPREF(arb_midref(x + xb))); fmpz_sub(scale, scale, ARF_EXPREF(arb_midref(x + xa))); fmpz_add(scale, scale, ARF_EXPREF(arb_midref(y + yb))); fmpz_sub(scale, scale, ARF_EXPREF(arb_midref(y + ya))); den = (xb - xa) + (yb - ya); /* scale = floor(scale / den + 1/2) = floor((2 scale + den) / (2 den)) */ fmpz_mul_2exp(scale, scale, 1); fmpz_add_ui(scale, scale, den); fmpz_fdiv_q_ui(scale, scale, 2 * den); } } /* Break vector into same-exponent blocks where the largest block has a height of at most ALPHA*prec + BETA bits. These are just tuning parameters. Note that ALPHA * MAG_BITS + BETA should be smaller than DOUBLE_BLOCK_MAX_HEIGHT if we want to use doubles for error bounding. */ #define ALPHA 3.0 #define BETA 512 /* Maximum length of block for which we use double multiplication (for longer blocks, we use fmpz_poly multiplication). This is essentially just a tuning parameter, but note that it must be considered when compensating for rounding error below. */ #define DOUBLE_BLOCK_MAX_LENGTH 1000 /* Computing a dot product of length DOUBLE_BLOCK_MAX_LENGTH involving only nonnegative numbers, and then multiplying by this factor, must give an upper bound for the exact dot product (we can assume that no overflow or underflow occurs). The following is certainly sufficient, but it would be nice to include a formal proof here. */ #define DOUBLE_ROUNDING_FACTOR (1.0 + 1e-9) /* Maximum height for which we use double multiplication. Since the dynamic exponent range of doubles is about +/- 1024, this must be less than about 1024 (to allow the product of two numbers). This must also account for adding MAG_BITS bits. */ #define DOUBLE_BLOCK_MAX_HEIGHT 800 /* We divide coefficients by 2^DOUBLE_BLOCK_SHIFT when converting them to doubles, in order to use the whole exponent range. Note that this means numbers of size (2^(-DOUBLE_BLOCK_SHIFT))^2 must not underflow. */ #define DOUBLE_BLOCK_SHIFT (DOUBLE_BLOCK_MAX_HEIGHT / 2) static __inline__ void _mag_vec_get_fmpz_2exp_blocks(fmpz * coeffs, double * dblcoeffs, fmpz * exps, slong * blocks, const fmpz_t scale, arb_srcptr x, mag_srcptr xm, slong len) { fmpz_t top, bot, t, b, v, block_top, block_bot; slong i, j, s, block, bits, maxheight; int in_zero; mag_srcptr cur; fmpz_init(top); fmpz_init(bot); fmpz_init(t); fmpz_init(b); fmpz_init(v); fmpz_init(block_top); fmpz_init(block_bot); blocks[0] = 0; block = 0; in_zero = 1; maxheight = ALPHA * MAG_BITS + BETA; if (maxheight > DOUBLE_BLOCK_MAX_HEIGHT) abort(); for (i = 0; i < len; i++) { cur = (x == NULL) ? (xm + i) : arb_radref(x + i); /* Skip (must be zero, since we assume there are no Infs/NaNs). */ if (mag_is_special(cur)) continue; /* Bottom and top exponent of current number */ bits = MAG_BITS; fmpz_set(top, MAG_EXPREF(cur)); fmpz_submul_ui(top, scale, i); fmpz_sub_ui(bot, top, bits); /* Extend current block. */ if (in_zero) { fmpz_swap(block_top, top); fmpz_swap(block_bot, bot); } else { fmpz_max(t, top, block_top); fmpz_min(b, bot, block_bot); fmpz_sub(v, t, b); /* extend current block */ if (fmpz_cmp_ui(v, maxheight) < 0) { fmpz_swap(block_top, t); fmpz_swap(block_bot, b); } else /* start new block */ { /* write exponent for previous block */ fmpz_set(exps + block, block_bot); block++; blocks[block] = i; fmpz_swap(block_top, top); fmpz_swap(block_bot, bot); } } in_zero = 0; } /* write exponent for last block */ fmpz_set(exps + block, block_bot); /* end marker */ blocks[block + 1] = len; /* write the block data */ for (i = 0; blocks[i] != len; i++) { for (j = blocks[i]; j < blocks[i + 1]; j++) { cur = (x == NULL) ? (xm + j) : arb_radref(x + j); if (mag_is_special(cur)) { fmpz_zero(coeffs + j); dblcoeffs[j] = 0.0; } else { mp_limb_t man; double c; man = MAG_MAN(cur); /* TODO: only write and use doubles when block is short? */ /* Divide by 2^(scale * j) */ fmpz_mul_ui(t, scale, j); fmpz_sub(t, MAG_EXPREF(cur), t); fmpz_sub_ui(t, t, MAG_BITS); /* bottom exponent */ s = _fmpz_sub_small(t, exps + i); if (s < 0) abort(); /* Bug catcher */ fmpz_set_ui(coeffs + j, man); fmpz_mul_2exp(coeffs + j, coeffs + j, s); c = man; c = ldexp(c, s - DOUBLE_BLOCK_SHIFT); if (c < 1e-150 || c > 1e150) /* Bug catcher */ abort(); dblcoeffs[j] = c; } } } fmpz_clear(top); fmpz_clear(bot); fmpz_clear(t); fmpz_clear(b); fmpz_clear(v); fmpz_clear(block_top); fmpz_clear(block_bot); } static __inline__ void _arb_vec_get_fmpz_2exp_blocks(fmpz * coeffs, fmpz * exps, slong * blocks, const fmpz_t scale, arb_srcptr x, slong len, slong prec) { fmpz_t top, bot, t, b, v, block_top, block_bot; slong i, j, s, block, bits, maxheight; int in_zero; fmpz_init(top); fmpz_init(bot); fmpz_init(t); fmpz_init(b); fmpz_init(v); fmpz_init(block_top); fmpz_init(block_bot); blocks[0] = 0; block = 0; in_zero = 1; if (prec == ARF_PREC_EXACT) maxheight = ARF_PREC_EXACT; else maxheight = ALPHA * prec + BETA; for (i = 0; i < len; i++) { bits = arf_bits(arb_midref(x + i)); /* Skip (must be zero, since we assume there are no Infs/NaNs). */ if (bits == 0) continue; /* Bottom and top exponent of current number */ fmpz_set(top, ARF_EXPREF(arb_midref(x + i))); fmpz_submul_ui(top, scale, i); fmpz_sub_ui(bot, top, bits); /* Extend current block. */ if (in_zero) { fmpz_swap(block_top, top); fmpz_swap(block_bot, bot); } else { fmpz_max(t, top, block_top); fmpz_min(b, bot, block_bot); fmpz_sub(v, t, b); /* extend current block */ if (fmpz_cmp_ui(v, maxheight) < 0) { fmpz_swap(block_top, t); fmpz_swap(block_bot, b); } else /* start new block */ { /* write exponent for previous block */ fmpz_set(exps + block, block_bot); block++; blocks[block] = i; fmpz_swap(block_top, top); fmpz_swap(block_bot, bot); } } in_zero = 0; } /* write exponent for last block */ fmpz_set(exps + block, block_bot); /* end marker */ blocks[block + 1] = len; /* write the block data */ for (i = 0; blocks[i] != len; i++) { for (j = blocks[i]; j < blocks[i + 1]; j++) { if (arf_is_special(arb_midref(x + j))) { fmpz_zero(coeffs + j); } else { /* TODO: make this a single operation */ arf_get_fmpz_2exp(coeffs + j, bot, arb_midref(x + j)); fmpz_mul_ui(t, scale, j); fmpz_sub(t, bot, t); s = _fmpz_sub_small(t, exps + i); if (s < 0) abort(); /* Bug catcher */ fmpz_mul_2exp(coeffs + j, coeffs + j, s); } } } fmpz_clear(top); fmpz_clear(bot); fmpz_clear(t); fmpz_clear(b); fmpz_clear(v); fmpz_clear(block_top); fmpz_clear(block_bot); } static __inline__ void _arb_poly_addmullow_rad(arb_ptr z, fmpz * zz, const fmpz * xz, const double * xdbl, const fmpz * xexps, const slong * xblocks, slong xlen, const fmpz * yz, const double * ydbl, const fmpz * yexps, const slong * yblocks, slong ylen, slong n) { slong i, j, k, ii, xp, yp, xl, yl, bn; fmpz_t zexp; mag_t t; fmpz_init(zexp); mag_init(t); for (i = 0; (xp = xblocks[i]) != xlen; i++) { for (j = 0; (yp = yblocks[j]) != ylen; j++) { if (xp + yp >= n) continue; xl = xblocks[i + 1] - xp; yl = yblocks[j + 1] - yp; bn = FLINT_MIN(xl + yl - 1, n - xp - yp); xl = FLINT_MIN(xl, bn); yl = FLINT_MIN(yl, bn); fmpz_add_inline(zexp, xexps + i, yexps + j); if (xl > 1 && yl > 1 && (xl < DOUBLE_BLOCK_MAX_LENGTH || yl < DOUBLE_BLOCK_MAX_LENGTH)) { fmpz_add_ui(zexp, zexp, 2 * DOUBLE_BLOCK_SHIFT); for (k = 0; k < bn; k++) { /* Classical multiplication (may round down!) */ double ss = 0.0; for (ii = FLINT_MAX(0, k - yl + 1); ii <= FLINT_MIN(xl - 1, k); ii++) { ss += xdbl[xp + ii] * ydbl[yp + k - ii]; } /* Compensate for rounding error */ ss *= DOUBLE_ROUNDING_FACTOR; mag_set_d_2exp_fmpz(t, ss, zexp); mag_add(arb_radref(z + xp + yp + k), arb_radref(z + xp + yp + k), t); } } else { if (xl >= yl) _fmpz_poly_mullow(zz, xz + xp, xl, yz + yp, yl, bn); else _fmpz_poly_mullow(zz, yz + yp, yl, xz + xp, xl, bn); for (k = 0; k < bn; k++) { mag_set_fmpz_2exp_fmpz(t, zz + k, zexp); mag_add(arb_radref(z + xp + yp + k), arb_radref(z + xp + yp + k), t); } } } } fmpz_clear(zexp); mag_clear(t); } static __inline__ void _arb_poly_addmullow_block(arb_ptr z, fmpz * zz, const fmpz * xz, const fmpz * xexps, const slong * xblocks, slong xlen, const fmpz * yz, const fmpz * yexps, const slong * yblocks, slong ylen, slong n, slong prec, int squaring) { slong i, j, k, xp, yp, xl, yl, bn; fmpz_t zexp; fmpz_init(zexp); if (squaring) { for (i = 0; (xp = xblocks[i]) != xlen; i++) { if (2 * xp >= n) continue; xl = xblocks[i + 1] - xp; bn = FLINT_MIN(2 * xl - 1, n - 2 * xp); xl = FLINT_MIN(xl, bn); _fmpz_poly_sqrlow(zz, xz + xp, xl, bn); _fmpz_add2_fast(zexp, xexps + i, xexps + i, 0); for (k = 0; k < bn; k++) arb_add_fmpz_2exp(z + 2 * xp + k, z + 2 * xp + k, zz + k, zexp, prec); } } for (i = 0; (xp = xblocks[i]) != xlen; i++) { for (j = squaring ? i + 1 : 0; (yp = yblocks[j]) != ylen; j++) { if (xp + yp >= n) continue; xl = xblocks[i + 1] - xp; yl = yblocks[j + 1] - yp; bn = FLINT_MIN(xl + yl - 1, n - xp - yp); xl = FLINT_MIN(xl, bn); yl = FLINT_MIN(yl, bn); if (xl >= yl) _fmpz_poly_mullow(zz, xz + xp, xl, yz + yp, yl, bn); else _fmpz_poly_mullow(zz, yz + yp, yl, xz + xp, xl, bn); _fmpz_add2_fast(zexp, xexps + i, yexps + j, squaring); for (k = 0; k < bn; k++) arb_add_fmpz_2exp(z + xp + yp + k, z + xp + yp + k, zz + k, zexp, prec); } } fmpz_clear(zexp); } void _arb_poly_mullow_block(arb_ptr z, arb_srcptr x, slong xlen, arb_srcptr y, slong ylen, slong n, slong prec) { slong xmlen, xrlen, ymlen, yrlen, i; fmpz *xz, *yz, *zz; fmpz *xe, *ye; slong *xblocks, *yblocks; int squaring; fmpz_t scale, t; xlen = FLINT_MIN(xlen, n); ylen = FLINT_MIN(ylen, n); squaring = (x == y) && (xlen == ylen); /* Strip trailing zeros */ xmlen = xrlen = xlen; while (xmlen > 0 && arf_is_zero(arb_midref(x + xmlen - 1))) xmlen--; while (xrlen > 0 && mag_is_zero(arb_radref(x + xrlen - 1))) xrlen--; if (squaring) { ymlen = xmlen; yrlen = xrlen; } else { ymlen = yrlen = ylen; while (ymlen > 0 && arf_is_zero(arb_midref(y + ymlen - 1))) ymlen--; while (yrlen > 0 && mag_is_zero(arb_radref(y + yrlen - 1))) yrlen--; } /* We don't know how to deal with infinities or NaNs */ if (!_arb_vec_is_finite(x, xlen) || (!squaring && !_arb_vec_is_finite(y, ylen))) { _arb_poly_mullow_classical(z, x, xlen, y, ylen, n, prec); return; } xlen = FLINT_MAX(xmlen, xrlen); ylen = FLINT_MAX(ymlen, yrlen); /* Start with the zero polynomial */ _arb_vec_zero(z, n); /* Nothing to do */ if (xlen == 0 || ylen == 0) return; n = FLINT_MIN(n, xlen + ylen - 1); fmpz_init(scale); fmpz_init(t); xz = _fmpz_vec_init(xlen); yz = _fmpz_vec_init(ylen); zz = _fmpz_vec_init(n); xe = _fmpz_vec_init(xlen); ye = _fmpz_vec_init(ylen); xblocks = flint_malloc(sizeof(slong) * (xlen + 1)); yblocks = flint_malloc(sizeof(slong) * (ylen + 1)); _arb_poly_get_scale(scale, x, xlen, y, ylen); /* Error propagation */ /* (xm + xr)*(ym + yr) = (xm*ym) + (xr*ym + xm*yr + xr*yr) = (xm*ym) + (xm*yr + xr*(ym + yr)) */ if (xrlen != 0 || yrlen != 0) { mag_ptr tmp; double *xdbl, *ydbl; tmp = _mag_vec_init(FLINT_MAX(xlen, ylen)); xdbl = flint_malloc(sizeof(double) * xlen); ydbl = flint_malloc(sizeof(double) * ylen); /* (xm + xr)^2 = (xm*ym) + (xr^2 + 2 xm xr) = (xm*ym) + xr*(2 xm + xr) */ if (squaring) { _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen); for (i = 0; i < xlen; i++) { arf_get_mag(tmp + i, arb_midref(x + i)); mag_mul_2exp_si(tmp + i, tmp + i, 1); mag_add(tmp + i, tmp + i, arb_radref(x + i)); } _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, xlen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, xlen, n); } else if (yrlen == 0) { /* xr * |ym| */ _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen); for (i = 0; i < ymlen; i++) arf_get_mag(tmp + i, arb_midref(y + i)); _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, ymlen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, ymlen, n); } else { /* |xm| * yr */ for (i = 0; i < xmlen; i++) arf_get_mag(tmp + i, arb_midref(x + i)); _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, NULL, tmp, xmlen); _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, y, NULL, yrlen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xmlen, yz, ydbl, ye, yblocks, yrlen, n); /* xr*(|ym| + yr) */ if (xrlen != 0) { _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen); for (i = 0; i < ylen; i++) arb_get_mag(tmp + i, y + i); _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, ylen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, ylen, n); } } _mag_vec_clear(tmp, FLINT_MAX(xlen, ylen)); flint_free(xdbl); flint_free(ydbl); } /* multiply midpoints */ if (xmlen != 0 && ymlen != 0) { _arb_vec_get_fmpz_2exp_blocks(xz, xe, xblocks, scale, x, xmlen, prec); if (squaring) { _arb_poly_addmullow_block(z, zz, xz, xe, xblocks, xmlen, xz, xe, xblocks, xmlen, n, prec, 1); } else { _arb_vec_get_fmpz_2exp_blocks(yz, ye, yblocks, scale, y, ymlen, prec); _arb_poly_addmullow_block(z, zz, xz, xe, xblocks, xmlen, yz, ye, yblocks, ymlen, n, prec, 0); } } /* Unscale. */ if (!fmpz_is_zero(scale)) { fmpz_zero(t); for (i = 0; i < n; i++) { arb_mul_2exp_fmpz(z + i, z + i, t); fmpz_add(t, t, scale); } } _fmpz_vec_clear(xz, xlen); _fmpz_vec_clear(yz, ylen); _fmpz_vec_clear(zz, n); _fmpz_vec_clear(xe, xlen); _fmpz_vec_clear(ye, ylen); flint_free(xblocks); flint_free(yblocks); fmpz_clear(scale); fmpz_clear(t); } void arb_poly_mullow_block(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) { slong xlen, ylen, zlen; xlen = poly1->length; ylen = poly2->length; if (xlen == 0 || ylen == 0 || n == 0) { arb_poly_zero(res); return; } xlen = FLINT_MIN(xlen, n); ylen = FLINT_MIN(ylen, n); zlen = FLINT_MIN(xlen + ylen - 1, n); if (res == poly1 || res == poly2) { arb_poly_t tmp; arb_poly_init2(tmp, zlen); _arb_poly_mullow_block(tmp->coeffs, poly1->coeffs, xlen, poly2->coeffs, ylen, zlen, prec); arb_poly_swap(res, tmp); arb_poly_clear(tmp); } else { arb_poly_fit_length(res, zlen); _arb_poly_mullow_block(res->coeffs, poly1->coeffs, xlen, poly2->coeffs, ylen, zlen, prec); } _arb_poly_set_length(res, zlen); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/mullow_classical.c000066400000000000000000000070661264125401100176030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2008, 2009 William Hart Copyright (C) 2011 Sebastian Pancratz Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_mullow_classical(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) { len1 = FLINT_MIN(len1, n); len2 = FLINT_MIN(len2, n); if (n == 1) { arb_mul(res, poly1, poly2, prec); } else if (poly1 == poly2 && len1 == len2) { slong i; _arb_vec_scalar_mul(res, poly1, FLINT_MIN(len1, n), poly1, prec); _arb_vec_scalar_mul(res + len1, poly1 + 1, n - len1, poly1 + len1 - 1, prec); for (i = 1; i < len1 - 1; i++) _arb_vec_scalar_addmul(res + i + 1, poly1 + 1, FLINT_MIN(i - 1, n - (i + 1)), poly1 + i, prec); for (i = 1; i < FLINT_MIN(2 * len1 - 2, n); i++) arb_mul_2exp_si(res + i, res + i, 1); for (i = 1; i < FLINT_MIN(len1 - 1, (n + 1) / 2); i++) arb_addmul(res + 2 * i, poly1 + i, poly1 + i, prec); } else { slong i; _arb_vec_scalar_mul(res, poly1, FLINT_MIN(len1, n), poly2, prec); if (n > len1) _arb_vec_scalar_mul(res + len1, poly2 + 1, n - len1, poly1 + len1 - 1, prec); for (i = 0; i < FLINT_MIN(len1, n) - 1; i++) _arb_vec_scalar_addmul(res + i + 1, poly2 + 1, FLINT_MIN(len2, n - i) - 1, poly1 + i, prec); } } void arb_poly_mullow_classical(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) { slong len_out; if (poly1->length == 0 || poly2->length == 0 || n == 0) { arb_poly_zero(res); return; } len_out = poly1->length + poly2->length - 1; if (n > len_out) n = len_out; if (res == poly1 || res == poly2) { arb_poly_t t; arb_poly_init2(t, n); _arb_poly_mullow_classical(t->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, prec); arb_poly_swap(res, t); arb_poly_clear(t); } else { arb_poly_fit_length(res, n); _arb_poly_mullow_classical(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, n, prec); } _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/newton_convergence_factor.c000066400000000000000000000034231264125401100214650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_newton_convergence_factor(arf_t convergence_factor, arb_srcptr poly, slong len, const arb_t convergence_interval, slong prec) { arb_ptr deriv; arb_t t, u; arb_init(t); arb_init(u); deriv = _arb_vec_init(len - 1); _arb_poly_derivative(deriv, poly, len, prec); _arb_poly_evaluate(t, deriv, len - 1, convergence_interval, prec); _arb_poly_derivative(deriv, deriv, len - 1, prec); _arb_poly_evaluate(u, deriv, len - 2, convergence_interval, prec); arb_div(t, u, t, prec); arb_mul_2exp_si(t, t, -1); arb_get_abs_ubound_arf(convergence_factor, t, prec); _arb_vec_clear(deriv, len - 1); arb_clear(t); arb_clear(u); } arb-2.8.1/arb_poly/newton_refine_root.c000066400000000000000000000044321264125401100201450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" static __inline__ slong _arf_mag(const arf_t c) { slong m = arf_abs_bound_lt_2exp_si(c); return FLINT_MAX(m, 0); } void _arb_poly_newton_refine_root(arb_t r, arb_srcptr poly, slong len, const arb_t start, const arb_t convergence_interval, const arf_t convergence_factor, slong eval_extra_prec, slong prec) { slong precs[FLINT_BITS]; slong i, iters, wp, padding, start_prec; start_prec = arb_rel_accuracy_bits(start); padding = 5 + _arf_mag(convergence_factor); precs[0] = prec + padding; iters = 1; while ((iters < FLINT_BITS) && (precs[iters-1] + padding > 2*start_prec)) { precs[iters] = (precs[iters-1] / 2) + padding; iters++; if (iters == FLINT_BITS) { flint_printf("newton_refine_root: initial value too imprecise\n"); abort(); } } arb_set(r, start); for (i = iters - 1; i >= 0; i--) { wp = precs[i] + eval_extra_prec; if (!_arb_poly_newton_step(r, poly, len, r, convergence_interval, convergence_factor, wp)) { flint_printf("warning: newton_refine_root: improvement failed\n"); break; } } } arb-2.8.1/arb_poly/newton_step.c000066400000000000000000000040631264125401100166050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int _arb_poly_newton_step(arb_t xnew, arb_srcptr poly, slong len, const arb_t x, const arb_t convergence_interval, const arf_t convergence_factor, slong prec) { arf_t err; arb_t t, u, v; int result; arf_init(err); arb_init(t); arb_init(u); arb_init(v); arf_set_mag(err, arb_radref(x)); arf_mul(err, err, err, MAG_BITS, ARF_RND_UP); arf_mul(err, err, convergence_factor, MAG_BITS, ARF_RND_UP); arf_set(arb_midref(t), arb_midref(x)); mag_zero(arb_radref(t)); _arb_poly_evaluate2(u, v, poly, len, t, prec); arb_div(u, u, v, prec); arb_sub(u, t, u, prec); arb_add_error_arf(u, err); if (arb_contains(convergence_interval, u) && (mag_cmp(arb_radref(u), arb_radref(x)) < 0)) { arb_swap(xnew, u); result = 1; } else { arb_set(xnew, x); result = 0; } arb_clear(t); arb_clear(u); arb_clear(v); arf_clear(err); return result; } arb-2.8.1/arb_poly/normalise.c000066400000000000000000000024061264125401100162300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_normalise(arb_poly_t poly) { slong i; for (i = poly->length - 1; (i >= 0) && arb_is_zero(poly->coeffs + i); i--); poly->length = i + 1; } arb-2.8.1/arb_poly/overlaps.c000066400000000000000000000033431264125401100160730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int _arb_poly_overlaps(arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2) { slong i; for (i = 0; i < len2; i++) if (!arb_overlaps(poly1 + i, poly2 + i)) return 0; for (i = len2; i < len1; i++) if (!arb_contains_zero(poly1 + i)) return 0; return 1; } int arb_poly_overlaps(const arb_poly_t poly1, const arb_poly_t poly2) { slong len1 = poly1->length; slong len2 = poly2->length; if (len1 >= len2) return _arb_poly_overlaps(poly1->coeffs, len1, poly2->coeffs, len2); else return _arb_poly_overlaps(poly2->coeffs, len2, poly1->coeffs, len1); } arb-2.8.1/arb_poly/pow_arb_series.c000066400000000000000000000106061264125401100172430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" /* (a + bx^c)^g where a = f[0] and b = f[flen-1] */ void _arb_poly_binomial_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec) { slong i, j, d; arb_t t; arb_init(t); d = flen - 1; arb_pow(h, f, g, prec); arb_div(t, f + d, f, prec); for (i = 1, j = d; j < len; i++, j += d) { arb_sub_ui(h + j, g, i - 1, prec); arb_mul(h + j, h + j, h + j - d, prec); arb_mul(h + j, h + j, t, prec); arb_div_ui(h + j, h + j, i, prec); } if (d > 1) { for (i = 1; i < len; i++) if (i % d != 0) arb_zero(h + i); } arb_clear(t); return; } void _arb_poly_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec) { int f_binomial, g_exact, g_int; while (flen > 0 && arb_is_zero(f + flen - 1)) flen--; if (flen <= 1) { arb_pow(h, f, g, prec); _arb_vec_zero(h + 1, len - 1); return; } g_exact = arb_is_exact(g); g_int = arb_is_int(g); f_binomial = _arb_vec_is_zero(f + 1, flen - 2); /* g = small integer */ if (g_exact && g_int && arf_cmpabs_2exp_si(arb_midref(g), FLINT_BITS - 1) < 0) { slong e, hlen; e = arf_get_si(arb_midref(g), ARF_RND_DOWN); hlen = poly_pow_length(flen, FLINT_ABS(e), len); if (e >= 0) { _arb_poly_pow_ui_trunc_binexp(h, f, flen, e, hlen, prec); _arb_vec_zero(h + hlen, len - hlen); return; } else if (!f_binomial) { arb_ptr t; t = _arb_vec_init(hlen); _arb_poly_pow_ui_trunc_binexp(t, f, flen, -e, hlen, prec); _arb_poly_inv_series(h, t, hlen, len, prec); _arb_vec_clear(t, hlen); return; } } /* (a + bx^c)^g */ if (f_binomial) { _arb_poly_binomial_pow_arb_series(h, f, flen, g, len, prec); return; } /* g = +/- 1/2 */ if (g_exact && arf_cmpabs_2exp_si(arb_midref(g), -1) == 0) { if (arf_sgn(arb_midref(g)) > 0) _arb_poly_sqrt_series(h, f, flen, len, prec); else _arb_poly_rsqrt_series(h, f, flen, len, prec); return; } /* f^g = exp(g*log(f)) */ _arb_poly_log_series(h, f, flen, len, prec); _arb_vec_scalar_mul(h, h, len, g, prec); _arb_poly_exp_series(h, h, len, len, prec); } void arb_poly_pow_arb_series(arb_poly_t h, const arb_poly_t f, const arb_t g, slong len, slong prec) { slong flen; flen = f->length; flen = FLINT_MIN(flen, len); if (len == 0) { arb_poly_zero(h); return; } if (arb_is_zero(g)) { arb_poly_one(h); return; } if (flen == 0) { arb_poly_zero(h); return; } if (f == h) { arb_poly_t t; arb_poly_init2(t, len); _arb_poly_pow_arb_series(t->coeffs, f->coeffs, flen, g, len, prec); _arb_poly_set_length(t, len); _arb_poly_normalise(t); arb_poly_swap(t, h); arb_poly_clear(t); } else { arb_poly_fit_length(h, len); _arb_poly_pow_arb_series(h->coeffs, f->coeffs, flen, g, len, prec); _arb_poly_set_length(h, len); _arb_poly_normalise(h); } } arb-2.8.1/arb_poly/pow_series.c000066400000000000000000000060261264125401100164200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_pow_series(arb_ptr h, arb_srcptr f, slong flen, arb_srcptr g, slong glen, slong len, slong prec) { if (glen == 1) { _arb_poly_pow_arb_series(h, f, flen, g, len, prec); return; } /* f^g = exp(g * log(f)) */ if (flen == 1) { arb_t t; arb_init(t); arb_log(t, f, prec); _arb_vec_scalar_mul(h, g, glen, t, prec); _arb_poly_exp_series(h, h, glen, len, prec); arb_clear(t); } else { arb_ptr t; t = _arb_vec_init(len); _arb_poly_log_series(t, f, flen, len, prec); _arb_poly_mullow(h, t, len, g, glen, len, prec); _arb_poly_exp_series(h, h, len, len, prec); _arb_vec_clear(t, len); } } void arb_poly_pow_series(arb_poly_t h, const arb_poly_t f, const arb_poly_t g, slong len, slong prec) { slong flen, glen; flen = f->length; glen = g->length; flen = FLINT_MIN(flen, len); glen = FLINT_MIN(glen, len); if (len == 0) { arb_poly_zero(h); return; } if (glen == 0) { arb_poly_one(h); return; } if (flen == 0) { arb_poly_zero(h); return; } if (flen == 1 && glen == 1) { arb_poly_fit_length(h, 1); arb_pow(h->coeffs, f->coeffs, g->coeffs, prec); _arb_poly_set_length(h, 1); _arb_poly_normalise(h); return; } if (f == h || g == h) { arb_poly_t t; arb_poly_init2(t, len); _arb_poly_pow_series(t->coeffs, f->coeffs, flen, g->coeffs, glen, len, prec); _arb_poly_set_length(t, len); _arb_poly_normalise(t); arb_poly_swap(t, h); arb_poly_clear(t); } else { arb_poly_fit_length(h, len); _arb_poly_pow_series(h->coeffs, f->coeffs, flen, g->coeffs, glen, len, prec); _arb_poly_set_length(h, len); _arb_poly_normalise(h); } } arb-2.8.1/arb_poly/pow_ui.c000066400000000000000000000042221264125401100155370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_pow_ui(arb_ptr res, arb_srcptr f, slong flen, ulong exp, slong prec) { _arb_poly_pow_ui_trunc_binexp(res, f, flen, exp, exp * (flen - 1) + 1, prec); } void arb_poly_pow_ui(arb_poly_t res, const arb_poly_t poly, ulong exp, slong prec) { slong flen, rlen; flen = poly->length; if (exp == 0) { arb_poly_one(res); } else if (flen == 0) { arb_poly_zero(res); } else { rlen = exp * (flen - 1) + 1; if (res != poly) { arb_poly_fit_length(res, rlen); _arb_poly_pow_ui(res->coeffs, poly->coeffs, flen, exp, prec); _arb_poly_set_length(res, rlen); _arb_poly_normalise(res); } else { arb_poly_t t; arb_poly_init2(t, rlen); _arb_poly_pow_ui(t->coeffs, poly->coeffs, flen, exp, prec); _arb_poly_set_length(t, rlen); _arb_poly_normalise(t); arb_poly_swap(res, t); arb_poly_clear(t); } } } arb-2.8.1/arb_poly/pow_ui_trunc_binexp.c000066400000000000000000000076221264125401100203260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define MUL(z, zlen, x, xlen, y, ylen, trunc, prec) \ do { \ slong slen = FLINT_MIN(xlen + ylen - 1, trunc); \ _arb_poly_mullow(z, x, xlen, y, ylen, slen, prec); \ zlen = slen; \ } while (0) void _arb_poly_pow_ui_trunc_binexp(arb_ptr res, arb_srcptr f, slong flen, ulong exp, slong len, slong prec) { arb_ptr v, R, S, T; slong rlen; ulong bit; if (exp <= 1) { if (exp == 0) arb_one(res); else if (exp == 1) _arb_vec_set_round(res, f, len, prec); return; } /* (f * x^r)^m = x^(rm) * f^m */ while (flen > 1 && arb_is_zero(f)) { if (((ulong) len) > exp) { _arb_vec_zero(res, exp); len -= exp; res += exp; } else { _arb_vec_zero(res, len); return; } f++; flen--; } if (exp == 2) { _arb_poly_mullow(res, f, flen, f, flen, len, prec); return; } if (flen == 1) { arb_pow_ui(res, f, exp, prec); return; } v = _arb_vec_init(len); bit = UWORD(1) << (FLINT_BIT_COUNT(exp) - 2); if (n_zerobits(exp) % 2) { R = res; S = v; } else { R = v; S = res; } MUL(R, rlen, f, flen, f, flen, len, prec); if (bit & exp) { MUL(S, rlen, R, rlen, f, flen, len, prec); T = R; R = S; S = T; } while (bit >>= 1) { if (bit & exp) { MUL(S, rlen, R, rlen, R, rlen, len, prec); MUL(R, rlen, S, rlen, f, flen, len, prec); } else { MUL(S, rlen, R, rlen, R, rlen, len, prec); T = R; R = S; S = T; } } _arb_vec_clear(v, len); } void arb_poly_pow_ui_trunc_binexp(arb_poly_t res, const arb_poly_t poly, ulong exp, slong len, slong prec) { slong flen, rlen; flen = poly->length; if (exp == 0 && len != 0) { arb_poly_one(res); } else if (flen == 0 || len == 0) { arb_poly_zero(res); } else { rlen = poly_pow_length(flen, exp, len); if (res != poly) { arb_poly_fit_length(res, rlen); _arb_poly_pow_ui_trunc_binexp(res->coeffs, poly->coeffs, flen, exp, rlen, prec); _arb_poly_set_length(res, rlen); _arb_poly_normalise(res); } else { arb_poly_t t; arb_poly_init2(t, rlen); _arb_poly_pow_ui_trunc_binexp(t->coeffs, poly->coeffs, flen, exp, rlen, prec); _arb_poly_set_length(t, rlen); _arb_poly_normalise(t); arb_poly_swap(res, t); arb_poly_clear(t); } } } arb-2.8.1/arb_poly/printd.c000066400000000000000000000026651264125401100155460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_printd(const arb_poly_t poly, slong digits) { slong i; flint_printf("["); for (i = 0; i < poly->length; i++) { flint_printf("("); arb_printd(poly->coeffs + i, digits); flint_printf(")"); if (i + 1 < poly->length) flint_printf(", "); } flint_printf("]"); } arb-2.8.1/arb_poly/product_roots.c000066400000000000000000000041171264125401100171460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 William Hart Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_product_roots(arb_ptr poly, arb_srcptr xs, slong n, slong prec) { if (n == 0) { arb_one(poly); } else if (n == 1) { arb_neg(poly, xs); arb_one(poly + 1); } else if (n == 2) { arb_mul(poly, xs + 0, xs + 1, prec); arb_add(poly + 1, xs + 0, xs + 1, prec); arb_neg(poly + 1, poly + 1); arb_one(poly + 2); } else { const slong m = (n + 1) / 2; arb_ptr tmp; tmp = _arb_vec_init(n + 2); _arb_poly_product_roots(tmp, xs, m, prec); _arb_poly_product_roots(tmp + m + 1, xs + m, n - m, prec); _arb_poly_mul_monic(poly, tmp, m + 1, tmp + m + 1, n - m + 1, prec); _arb_vec_clear(tmp, n + 2); } } void arb_poly_product_roots(arb_poly_t poly, arb_srcptr xs, slong n, slong prec) { arb_poly_fit_length(poly, n + 1); _arb_poly_product_roots(poly->coeffs, xs, n, prec); _arb_poly_set_length(poly, n + 1); } arb-2.8.1/arb_poly/randtest.c000066400000000000000000000030571264125401100160660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_randtest(arb_poly_t poly, flint_rand_t state, slong len, slong prec, slong mag_bits) { slong i; arb_poly_fit_length(poly, len); if (n_randint(state, 2)) for (i = 0; i < len; i++) arb_randtest(poly->coeffs + i, state, prec, mag_bits); else for (i = 0; i < len; i++) arb_randtest_precise(poly->coeffs + i, state, prec, mag_bits); _arb_poly_set_length(poly, len); _arb_poly_normalise(poly); } arb-2.8.1/arb_poly/reverse.c000066400000000000000000000032141264125401100157100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_reverse(arb_ptr res, arb_srcptr poly, slong len, slong n) { if (res == poly) { slong i; for (i = 0; i < n / 2; i++) { arb_struct t = res[i]; res[i] = res[n - 1 - i]; res[n - 1 - i] = t; } for (i = 0; i < n - len; i++) arb_zero(res + i); } else { slong i; for (i = 0; i < n - len; i++) arb_zero(res + i); for (i = 0; i < len; i++) arb_set(res + (n - len) + i, poly + (len - 1) - i); } } arb-2.8.1/arb_poly/revert_series.c000066400000000000000000000041121264125401100171140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_revert_series(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec) { _arb_poly_revert_series_lagrange_fast(Qinv, Q, Qlen, n, prec); } void arb_poly_revert_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !arb_is_zero(Q->coeffs) || arb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (arb_poly_revert_series). Input must \n" "have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { arb_poly_fit_length(Qinv, n); _arb_poly_revert_series(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { arb_poly_t t; arb_poly_init2(t, n); _arb_poly_revert_series(t->coeffs, Q->coeffs, Qlen, n, prec); arb_poly_swap(Qinv, t); arb_poly_clear(t); } _arb_poly_set_length(Qinv, n); _arb_poly_normalise(Qinv); } arb-2.8.1/arb_poly/revert_series_lagrange.c000066400000000000000000000054121264125401100207600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_revert_series_lagrange(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec) { slong i; arb_ptr R, S, T, tmp; if (n <= 2) { if (n >= 1) arb_zero(Qinv); if (n == 2) arb_inv(Qinv + 1, Q + 1, prec); return; } R = _arb_vec_init(n - 1); S = _arb_vec_init(n - 1); T = _arb_vec_init(n - 1); arb_zero(Qinv); arb_inv(Qinv + 1, Q + 1, prec); _arb_poly_inv_series(R, Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec); _arb_vec_set(S, R, n - 1); for (i = 2; i < n; i++) { _arb_poly_mullow(T, S, n - 1, R, n - 1, n - 1, prec); arb_div_ui(Qinv + i, T + i - 1, i, prec); tmp = S; S = T; T = tmp; } _arb_vec_clear(R, n - 1); _arb_vec_clear(S, n - 1); _arb_vec_clear(T, n - 1); } void arb_poly_revert_series_lagrange(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !arb_is_zero(Q->coeffs) || arb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (arb_poly_revert_series_lagrange). Input must \n" "have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { arb_poly_fit_length(Qinv, n); _arb_poly_revert_series_lagrange(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { arb_poly_t t; arb_poly_init2(t, n); _arb_poly_revert_series_lagrange(t->coeffs, Q->coeffs, Qlen, n, prec); arb_poly_swap(Qinv, t); arb_poly_clear(t); } _arb_poly_set_length(Qinv, n); _arb_poly_normalise(Qinv); } arb-2.8.1/arb_poly/revert_series_lagrange_fast.c000066400000000000000000000067421264125401100220040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" /* pointer to (x/Q)^i */ #define Ri(ii) (R + (n-1)*((ii)-1)) void _arb_poly_revert_series_lagrange_fast(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec) { slong i, j, k, m; arb_ptr R, S, T, tmp; arb_t t; if (n <= 2) { if (n >= 1) arb_zero(Qinv); if (n == 2) arb_inv(Qinv + 1, Q + 1, prec); return; } m = n_sqrt(n); arb_init(t); R = _arb_vec_init((n - 1) * m); S = _arb_vec_init(n - 1); T = _arb_vec_init(n - 1); arb_zero(Qinv); arb_inv(Qinv + 1, Q + 1, prec); _arb_poly_inv_series(Ri(1), Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec); for (i = 2; i <= m; i++) _arb_poly_mullow(Ri(i), Ri((i + 1) / 2), n - 1, Ri(i / 2), n - 1, n - 1, prec); for (i = 2; i < m; i++) arb_div_ui(Qinv + i, Ri(i) + i - 1, i, prec); _arb_vec_set(S, Ri(m), n - 1); for (i = m; i < n; i += m) { arb_div_ui(Qinv + i, S + i - 1, i, prec); for (j = 1; j < m && i + j < n; j++) { arb_mul(t, S + 0, Ri(j) + i + j - 1, prec); for (k = 1; k <= i + j - 1; k++) arb_addmul(t, S + k, Ri(j) + i + j - 1 - k, prec); arb_div_ui(Qinv + i + j, t, i + j, prec); } if (i + 1 < n) { _arb_poly_mullow(T, S, n - 1, Ri(m), n - 1, n - 1, prec); tmp = S; S = T; T = tmp; } } arb_clear(t); _arb_vec_clear(R, (n - 1) * m); _arb_vec_clear(S, n - 1); _arb_vec_clear(T, n - 1); } void arb_poly_revert_series_lagrange_fast(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !arb_is_zero(Q->coeffs) || arb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (arb_poly_revert_series_lagrange_fast). Input \n" "must have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { arb_poly_fit_length(Qinv, n); _arb_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { arb_poly_t t; arb_poly_init2(t, n); _arb_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n, prec); arb_poly_swap(Qinv, t); arb_poly_clear(t); } _arb_poly_set_length(Qinv, n); _arb_poly_normalise(Qinv); } arb-2.8.1/arb_poly/revert_series_newton.c000066400000000000000000000060671264125401100205210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define CUTOFF 5 void _arb_poly_revert_series_newton(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec) { slong i, k, a[FLINT_BITS]; arb_ptr T, U, V; if (n <= 2) { if (n >= 1) arb_zero(Qinv); if (n == 2) arb_inv(Qinv + 1, Q + 1, prec); return; } T = _arb_vec_init(n); U = _arb_vec_init(n); V = _arb_vec_init(n); k = n; for (i = 1; (WORD(1) << i) < k; i++); a[i = 0] = k; while (k >= CUTOFF) a[++i] = (k = (k + 1) / 2); _arb_poly_revert_series_lagrange(Qinv, Q, Qlen, k, prec); _arb_vec_zero(Qinv + k, n - k); for (i--; i >= 0; i--) { k = a[i]; _arb_poly_compose_series(T, Q, FLINT_MIN(Qlen, k), Qinv, k, k, prec); _arb_poly_derivative(U, T, k, prec); arb_zero(U + k - 1); arb_zero(T + 1); _arb_poly_div_series(V, T, k, U, k, k, prec); _arb_poly_derivative(T, Qinv, k, prec); _arb_poly_mullow(U, V, k, T, k, k, prec); _arb_vec_sub(Qinv, Qinv, U, k, prec); } _arb_vec_clear(T, n); _arb_vec_clear(U, n); _arb_vec_clear(V, n); } void arb_poly_revert_series_newton(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec) { slong Qlen = Q->length; if (Qlen < 2 || !arb_is_zero(Q->coeffs) || arb_contains_zero(Q->coeffs + 1)) { flint_printf("Exception (arb_poly_revert_series_newton). Input must \n" "have zero constant term and nonzero coefficient of x^1.\n"); abort(); } if (Qinv != Q) { arb_poly_fit_length(Qinv, n); _arb_poly_revert_series_newton(Qinv->coeffs, Q->coeffs, Qlen, n, prec); } else { arb_poly_t t; arb_poly_init2(t, n); _arb_poly_revert_series_newton(t->coeffs, Q->coeffs, Qlen, n, prec); arb_poly_swap(Qinv, t); arb_poly_clear(t); } _arb_poly_set_length(Qinv, n); _arb_poly_normalise(Qinv); } arb-2.8.1/arb_poly/rgamma_series.c000066400000000000000000000146271264125401100170650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" slong arf_get_si(const arf_t x, arf_rnd_t rnd); void _arb_poly_lgamma_series_at_one(arb_ptr u, slong len, slong prec); void arb_gamma_stirling_choose_param(int * reflect, slong * r, slong * n, const arb_t x, int use_reflect, int digamma, slong prec); void _arb_poly_gamma_stirling_eval(arb_ptr res, const arb_t z, slong n, slong num, slong prec); void _arb_poly_rgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec) { int reflect, isint; slong i, rflen, r, n, wp; arb_ptr t, u, v; arb_struct f[2]; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { arb_rgamma(res, h, prec); _arb_vec_zero(res + 1, len - 1); return; } isint = arb_is_int(h); if (len <= 2 && isint && arf_sgn(arb_midref(h)) <= 0) { int even = arf_is_int_2exp_si(arb_midref(h), 1); /* use res[0] as tmp to allow aliasing */ arb_sub_ui(res, h, 1, prec); arb_neg(res, res); arb_gamma(res, res, prec); arb_mul(res + 1, h + 1, res, prec); if (!even) arb_neg(res + 1, res + 1); arb_zero(res); return; } wp = prec + FLINT_BIT_COUNT(prec); t = _arb_vec_init(len); u = _arb_vec_init(len); v = _arb_vec_init(len); arb_init(f); arb_init(f + 1); /* use zeta values at small integers */ if (isint && (arf_cmpabs_ui(arb_midref(h), prec / 2) < 0)) { r = arf_get_si(arb_midref(h), ARF_RND_DOWN); _arb_poly_lgamma_series_at_one(u, len, wp); _arb_vec_neg(u, u, len); _arb_poly_exp_series(t, u, len, len, wp); if (r == 1) { _arb_vec_swap(v, t, len); } else if (r <= 0) { arb_set(f, h); arb_one(f + 1); rflen = FLINT_MIN(len, 2 - r); _arb_poly_rising_ui_series(u, f, FLINT_MIN(2, len), 1 - r, rflen, wp); _arb_poly_mullow(v, t, len, u, rflen, len, wp); } else { arb_one(f); arb_one(f + 1); rflen = FLINT_MIN(len, r); _arb_poly_rising_ui_series(v, f, FLINT_MIN(2, len), r - 1, rflen, wp); /* TODO: use div_series? */ _arb_poly_inv_series(u, v, rflen, len, wp); _arb_poly_mullow(v, t, len, u, len, len, wp); } } else { /* otherwise use Stirling series */ arb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 0, wp); /* rgamma(h) = (gamma(1-h+r) sin(pi h)) / (rf(1-h, r) * pi), h = h0 + t*/ if (reflect) { /* u = gamma(r+1-h) */ arb_sub_ui(f, h, r + 1, wp); arb_neg(f, f); _arb_poly_gamma_stirling_eval(t, f, n, len, wp); _arb_poly_exp_series(u, t, len, len, wp); for (i = 1; i < len; i += 2) arb_neg(u + i, u + i); /* v = sin(pi x) */ arb_set(f, h); arb_one(f + 1); _arb_poly_sin_pi_series(v, f, 2, len, wp); _arb_poly_mullow(t, u, len, v, len, len, wp); /* rf(1-h,r) * pi */ if (r == 0) { arb_const_pi(u, wp); _arb_vec_scalar_div(v, t, len, u, wp); } else { arb_sub_ui(f, h, 1, wp); arb_neg(f, f); arb_set_si(f + 1, -1); rflen = FLINT_MIN(len, r + 1); _arb_poly_rising_ui_series(v, f, FLINT_MIN(2, len), r, rflen, wp); arb_const_pi(u, wp); _arb_vec_scalar_mul(v, v, rflen, u, wp); /* divide by rising factorial */ /* TODO: might better to use div_series, when it has a good basecase */ _arb_poly_inv_series(u, v, rflen, len, wp); _arb_poly_mullow(v, t, len, u, len, len, wp); } } else { /* rgamma(h) = rgamma(h+r) rf(h,r) */ if (r == 0) { arb_add_ui(f, h, r, wp); _arb_poly_gamma_stirling_eval(t, f, n, len, wp); _arb_vec_neg(t, t, len); _arb_poly_exp_series(v, t, len, len, wp); } else { arb_set(f, h); arb_one(f + 1); rflen = FLINT_MIN(len, r + 1); _arb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, wp); arb_add_ui(f, h, r, wp); _arb_poly_gamma_stirling_eval(v, f, n, len, wp); _arb_vec_neg(v, v, len); _arb_poly_exp_series(u, v, len, len, wp); _arb_poly_mullow(v, u, len, t, rflen, len, wp); } } } /* compose with nonconstant part */ arb_zero(t); _arb_vec_set(t + 1, h + 1, hlen - 1); _arb_poly_compose_series(res, v, len, t, hlen, len, prec); arb_clear(f); arb_clear(f + 1); _arb_vec_clear(t, len); _arb_vec_clear(u, len); _arb_vec_clear(v, len); } void arb_poly_rgamma_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) { if (f->length == 0 || n == 0) { arb_poly_zero(res); } else { arb_poly_fit_length(res, n); _arb_poly_rgamma_series(res->coeffs, f->coeffs, f->length, n, prec); _arb_poly_set_length(res, n); _arb_poly_normalise(res); } } arb-2.8.1/arb_poly/riemann_siegel_theta_series.c000066400000000000000000000051621264125401100217610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #include "acb_poly.h" void _arb_poly_riemann_siegel_theta_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec) { acb_ptr s; arb_t u; slong i; hlen = FLINT_MIN(hlen, len); s = _acb_vec_init(len); arb_init(u); /* s = 1/4 + (1/2) i h */ for (i = 0; i < hlen; i++) arb_mul_2exp_si(acb_imagref(s + i), h + i, -1); arb_one(u); arb_mul_2exp_si(u, u, -2); arb_add(acb_realref(s), acb_realref(s), u, prec); /* log gamma */ _acb_poly_lgamma_series(s, s, hlen, len, prec); /* imaginary part */ for (i = 0; i < len; i++) arb_set(res + i, acb_imagref(s + i)); /* subtract log(pi)/2 * h */ arb_const_pi(u, prec); arb_log(u, u, prec); arb_mul_2exp_si(u, u, -1); arb_neg(u, u); _arb_vec_scalar_addmul(res, h, hlen, u, prec); _acb_vec_clear(s, len); arb_clear(u); } void arb_poly_riemann_siegel_theta_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) { if (n == 0 || f->length == 0) { arb_poly_zero(res); return; } if (res == f) { arb_poly_t tmp; arb_poly_init2(tmp, n); _arb_poly_riemann_siegel_theta_series(tmp->coeffs, f->coeffs, f->length, n, prec); arb_poly_swap(res, tmp); arb_poly_clear(tmp); } else { arb_poly_fit_length(res, n); _arb_poly_riemann_siegel_theta_series(res->coeffs, f->coeffs, f->length, n, prec); } _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/riemann_siegel_z_series.c000066400000000000000000000063321264125401100211250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #include "acb_poly.h" void _arb_poly_riemann_siegel_z_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec) { slong i, alloc; arb_ptr t, u, v, w, q; hlen = FLINT_MIN(hlen, len); alloc = 5 * len; t = _arb_vec_init(alloc); u = t + len; v = u + len; w = v + len; q = w + len; /* (v + wi) = zeta(1/2 + i (s+x)) */ { acb_ptr sx, z; acb_t a; slong slen = FLINT_MIN(len, 2); z = _acb_vec_init(len); sx = _acb_vec_init(slen); acb_init(a); acb_one(a); acb_one(sx); acb_mul_2exp_si(sx, sx, -1); arb_set(acb_imagref(sx), h); if (slen > 1) arb_one(acb_imagref(sx + 1)); _acb_poly_zeta_series(z, sx, slen, a, 0, len, prec); for (i = 0; i < len; i++) { arb_set(v + i, acb_realref(z + i)); arb_set(w + i, acb_imagref(z + i)); } acb_clear(a); _acb_vec_clear(z, len); _acb_vec_clear(sx, slen); } /* (t + ui) = exp(i theta(s+x)) */ arb_set(u, h); if (len > 1) arb_one(u + 1); _arb_poly_riemann_siegel_theta_series(t, u, 2, len, prec); _arb_poly_sin_cos_series(u, t, t, len, len, prec); /* (t+ui)(v+wi) = (tv-uw) + (tw+uv)i */ _arb_poly_mullow(q, t, len, v, len, len, prec); _arb_poly_mullow(t, u, len, w, len, len, prec); _arb_vec_sub(t, q, t, len, prec); /* compose with nonconstant part */ arb_zero(u); _arb_vec_set(u + 1, h + 1, hlen - 1); _arb_poly_compose_series(res, t, len, u, hlen, len, prec); _arb_vec_clear(t, alloc); } void arb_poly_riemann_siegel_z_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) { if (n == 0) { arb_poly_zero(res); return; } arb_poly_fit_length(res, n); if (f->length == 0) { arb_t t; arb_init(t); _arb_poly_riemann_siegel_z_series(res->coeffs, t, 1, n, prec); arb_clear(t); } else { _arb_poly_riemann_siegel_z_series(res->coeffs, f->coeffs, f->length, n, prec); } _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/rising_ui_series.c000066400000000000000000000062411264125401100176020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" static void _arb_poly_rising_ui_series_bsplit(arb_ptr res, arb_srcptr f, slong flen, ulong a, ulong b, slong trunc, slong prec) { flen = FLINT_MIN(flen, trunc); if (b - a == 1) { arb_add_ui(res, f, a, prec); _arb_vec_set(res + 1, f + 1, flen - 1); } else { arb_ptr L, R; slong len1, len2; slong m = a + (b - a) / 2; len1 = poly_pow_length(flen, m - a, trunc); len2 = poly_pow_length(flen, b - m, trunc); L = _arb_vec_init(len1 + len2); R = L + len1; _arb_poly_rising_ui_series_bsplit(L, f, flen, a, m, trunc, prec); _arb_poly_rising_ui_series_bsplit(R, f, flen, m, b, trunc, prec); _arb_poly_mullow(res, L, len1, R, len2, FLINT_MIN(trunc, len1 + len2 - 1), prec); _arb_vec_clear(L, len1 + len2); } } void _arb_poly_rising_ui_series(arb_ptr res, arb_srcptr f, slong flen, ulong r, slong trunc, slong prec) { if (trunc == 1 || flen == 1) { arb_rising_ui(res, f, r, prec); _arb_vec_zero(res + 1, trunc - 1); } else if (trunc == 2) { arb_rising2_ui(res, res + 1, f, r, prec); arb_mul(res + 1, res + 1, f + 1, prec); } else { _arb_poly_rising_ui_series_bsplit(res, f, flen, 0, r, trunc, prec); } } void arb_poly_rising_ui_series(arb_poly_t res, const arb_poly_t f, ulong r, slong trunc, slong prec) { slong len; if ((f->length == 0 && r != 0) || trunc == 0) { arb_poly_zero(res); return; } if (r == 0) { arb_poly_one(res); return; } len = poly_pow_length(f->length, r, trunc); if (f == res) { arb_poly_t tmp; arb_poly_init(tmp); arb_poly_rising_ui_series(tmp, f, r, len, prec); arb_poly_swap(tmp, res); arb_poly_clear(tmp); } else { arb_poly_fit_length(res, len); _arb_poly_rising_ui_series(res->coeffs, f->coeffs, f->length, r, len, prec); _arb_poly_set_length(res, len); _arb_poly_normalise(res); } } arb-2.8.1/arb_poly/root_bound_fujiwara.c000066400000000000000000000036241264125401100203040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_root_bound_fujiwara(mag_t bound, arb_srcptr poly, slong len) { mag_t t, u, v; slong i; if (len <= 1) { mag_inf(bound); return; } mag_init(t); mag_init(u); mag_init(v); /* u = 1/leading */ arb_get_mag_lower(t, poly + len - 1); mag_one(u); mag_div(u, u, t); mag_zero(v); for (i = 0; i < len - 1; i++) { arb_get_mag(t, poly + len - 2 - i); mag_mul(t, t, u); if (i == len - 2) mag_mul_2exp_si(t, t, -1); mag_root(t, t, i + 1); mag_max(v, v, t); } mag_mul_2exp_si(bound, v, 1); mag_clear(t); mag_clear(u); mag_clear(v); } void arb_poly_root_bound_fujiwara(mag_t bound, arb_poly_t poly) { _arb_poly_root_bound_fujiwara(bound, poly->coeffs, poly->length); } arb-2.8.1/arb_poly/rsqrt_series.c000066400000000000000000000057641264125401100167760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_rsqrt_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); while (hlen > 0 && arb_is_zero(h + hlen - 1)) hlen--; if (hlen <= 1) { arb_rsqrt(g, h, prec); _arb_vec_zero(g + 1, len - 1); } else if (len == 2) { arb_rsqrt(g, h, prec); arb_div(g + 1, h + 1, h, prec); arb_mul(g + 1, g + 1, g, prec); arb_mul_2exp_si(g + 1, g + 1, -1); arb_neg(g + 1, g + 1); } else if (_arb_vec_is_zero(h + 1, hlen - 2)) { arb_t t; arb_init(t); arf_set_si_2exp_si(arb_midref(t), -1, -1); _arb_poly_binomial_pow_arb_series(g, h, hlen, t, len, prec); arb_clear(t); } else { arb_ptr t, u; slong tlen; t = _arb_vec_init(2 * len); u = t + len; arb_rsqrt(g, h, prec); NEWTON_INIT(1, len) NEWTON_LOOP(m, n) tlen = FLINT_MIN(2 * m - 1, n); _arb_poly_mullow(t, g, m, g, m, tlen, prec); _arb_poly_mullow(u, g, m, t, tlen, n, prec); _arb_poly_mullow(t, u, n, h, hlen, n, prec); _arb_vec_scalar_mul_2exp_si(g + m, t + m, n - m, -1); _arb_vec_neg(g + m, g + m, n - m); NEWTON_END_LOOP NEWTON_END _arb_vec_clear(t, 2 * len); } } void arb_poly_rsqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { if (n == 0) { arb_poly_zero(g); return; } if (g == h) { arb_poly_t t; arb_poly_init(t); arb_poly_rsqrt_series(t, h, n, prec); arb_poly_swap(g, t); arb_poly_clear(t); return; } arb_poly_fit_length(g, n); if (h->length == 0) _arb_vec_indeterminate(g->coeffs, n); else _arb_poly_rsqrt_series(g->coeffs, h->coeffs, h->length, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/set.c000066400000000000000000000024661264125401100150400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_set(arb_poly_t dest, const arb_poly_t src) { slong len = arb_poly_length(src); arb_poly_fit_length(dest, len); _arb_vec_set(dest->coeffs, src->coeffs, len); _arb_poly_set_length(dest, len); } arb-2.8.1/arb_poly/set_coeff_arb.c000066400000000000000000000026301264125401100170170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_set_coeff_arb(arb_poly_t poly, slong n, const arb_t x) { arb_poly_fit_length(poly, n + 1); if (n + 1 > poly->length) { _arb_vec_zero(poly->coeffs + poly->length, n - poly->length); poly->length = n + 1; } arb_set(poly->coeffs + n, x); _arb_poly_normalise(poly); } arb-2.8.1/arb_poly/set_coeff_si.c000066400000000000000000000026241264125401100166710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_set_coeff_si(arb_poly_t poly, slong n, slong x) { arb_poly_fit_length(poly, n + 1); if (n + 1 > poly->length) { _arb_vec_zero(poly->coeffs + poly->length, n - poly->length); poly->length = n + 1; } arb_set_si(poly->coeffs + n, x); _arb_poly_normalise(poly); } arb-2.8.1/arb_poly/set_fmpq_poly.c000066400000000000000000000027151264125401100171230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_set_fmpq_poly(arb_poly_t poly, const fmpq_poly_t src, slong prec) { slong i, len = src->length; arb_poly_fit_length(poly, len); _arb_poly_set_length(poly, len); for (i = 0; i < len; i++) { fmpq t; t.num = (fmpz) src->coeffs[i]; t.den = (fmpz) *src->den; arb_set_fmpq(poly->coeffs + i, &t, prec); } } arb-2.8.1/arb_poly/set_fmpz_poly.c000066400000000000000000000026031264125401100171300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_set_fmpz_poly(arb_poly_t poly, const fmpz_poly_t src, slong prec) { slong i, len = fmpz_poly_length(src); arb_poly_fit_length(poly, len); _arb_poly_set_length(poly, len); for (i = 0; i < len; i++) arb_set_round_fmpz(poly->coeffs + i, src->coeffs + i, prec); } arb-2.8.1/arb_poly/set_length.c000066400000000000000000000024651264125401100164000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_set_length(arb_poly_t poly, slong len) { slong i; if (poly->length > len) { for (i = len; i < poly->length; i++) arb_zero(poly->coeffs + i); } poly->length = len; } arb-2.8.1/arb_poly/set_round.c000066400000000000000000000025251264125401100162430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_set_round(arb_poly_t dest, const arb_poly_t src, slong prec) { slong len = arb_poly_length(src); arb_poly_fit_length(dest, len); _arb_vec_set_round(dest->coeffs, src->coeffs, len, prec); _arb_poly_set_length(dest, len); } arb-2.8.1/arb_poly/set_si.c000066400000000000000000000025131264125401100155240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void arb_poly_set_si(arb_poly_t poly, slong c) { if (c == 0) { arb_poly_zero(poly); } else { arb_poly_fit_length(poly, 1); arb_set_si(poly->coeffs, c); _arb_poly_set_length(poly, 1); } } arb-2.8.1/arb_poly/shift_left.c000066400000000000000000000037501264125401100163710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2008, 2009 William Hart Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_shift_left(arb_ptr res, arb_srcptr poly, slong len, slong n) { slong i; /* Copy in reverse to avoid writing over unshifted coefficients */ if (res != poly) { for (i = len; i--; ) arb_set(res + n + i, poly + i); } else { for (i = len; i--; ) arb_swap(res + n + i, res + i); } for (i = 0; i < n; i++) arb_zero(res + i); } void arb_poly_shift_left(arb_poly_t res, const arb_poly_t poly, slong n) { if (n == 0) { arb_poly_set(res, poly); return; } if (poly->length == 0) { arb_poly_zero(res); return; } arb_poly_fit_length(res, poly->length + n); _arb_poly_shift_left(res->coeffs, poly->coeffs, poly->length, n); _arb_poly_set_length(res, poly->length + n); } arb-2.8.1/arb_poly/shift_right.c000066400000000000000000000037141264125401100165540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2008, 2009 William Hart Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_shift_right(arb_ptr res, arb_srcptr poly, slong len, slong n) { slong i; /* Copy in forward order to avoid writing over unshifted coefficients */ if (res != poly) { for (i = 0; i < len - n; i++) arb_set(res + i, poly + n + i); } else { for (i = 0; i < len - n; i++) arb_swap(res + i, res + n + i); } } void arb_poly_shift_right(arb_poly_t res, const arb_poly_t poly, slong n) { if (n == 0) { arb_poly_set(res, poly); return; } if (poly->length <= n) { arb_poly_zero(res); return; } arb_poly_fit_length(res, poly->length - n); _arb_poly_shift_right(res->coeffs, poly->coeffs, poly->length, n); _arb_poly_set_length(res, poly->length - n); } arb-2.8.1/arb_poly/sin_cos_pi_series.c000066400000000000000000000050131264125401100177330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define TANGENT_CUTOFF 240 void _arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_sin_cos_pi(s, c, h, prec); _arb_vec_zero(s + 1, n - 1); _arb_vec_zero(c + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_const_pi(t, prec); arb_mul(t, t, h + 1, prec); arb_sin_cos_pi(s, c, h, prec); arb_mul(s + 1, c, t, prec); arb_neg(t, t); arb_mul(c + 1, s, t, prec); arb_clear(t); } else if (hlen < TANGENT_CUTOFF) _arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 1); else _arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 1); } void arb_poly_sin_cos_pi_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { arb_poly_zero(s); arb_poly_zero(c); return; } if (hlen == 0) { arb_poly_zero(s); arb_poly_one(c); return; } if (hlen == 1) n = 1; arb_poly_fit_length(s, n); arb_poly_fit_length(c, n); _arb_poly_sin_cos_pi_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(s, n); _arb_poly_normalise(s); _arb_poly_set_length(c, n); _arb_poly_normalise(c); } arb-2.8.1/arb_poly/sin_cos_series.c000066400000000000000000000047241264125401100172530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define TANGENT_CUTOFF 240 void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_sin_cos(s, c, h, prec); _arb_vec_zero(s + 1, n - 1); _arb_vec_zero(c + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_set(t, h + 1); arb_sin_cos(s, c, h, prec); arb_mul(s + 1, c, t, prec); arb_neg(t, t); arb_mul(c + 1, s, t, prec); arb_clear(t); } else if (hlen < TANGENT_CUTOFF) _arb_poly_sin_cos_series_basecase(s, c, h, hlen, n, prec, 0); else _arb_poly_sin_cos_series_tangent(s, c, h, hlen, n, prec, 0); } void arb_poly_sin_cos_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { arb_poly_zero(s); arb_poly_zero(c); return; } if (hlen == 0) { arb_poly_zero(s); arb_poly_one(c); return; } if (hlen == 1) n = 1; arb_poly_fit_length(s, n); arb_poly_fit_length(c, n); _arb_poly_sin_cos_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(s, n); _arb_poly_normalise(s); _arb_poly_set_length(c, n); _arb_poly_normalise(c); } arb-2.8.1/arb_poly/sin_cos_series_basecase.c000066400000000000000000000054421264125401100210770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_sin_cos_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec, int times_pi) { slong j, k, alen = FLINT_MIN(n, hlen); arb_ptr a; arb_t t, u; if (times_pi) arb_sin_cos_pi(s, c, h, prec); else arb_sin_cos(s, c, h, prec); if (hlen == 1) { _arb_vec_zero(s + 1, n - 1); _arb_vec_zero(c + 1, n - 1); return; } arb_init(t); arb_init(u); a = _arb_vec_init(alen); for (k = 1; k < alen; k++) arb_mul_ui(a + k, h + k, k, prec); if (times_pi) { arb_const_pi(t, prec); _arb_vec_scalar_mul(a + 1, a + 1, alen - 1, t, prec); } for (k = 1; k < n; k++) { arb_zero(t); arb_zero(u); for (j = 1; j < FLINT_MIN(k + 1, hlen); j++) { arb_submul(t, a + j, s + k - j, prec); arb_addmul(u, a + j, c + k - j, prec); } arb_div_ui(c + k, t, k, prec); arb_div_ui(s + k, u, k, prec); } arb_clear(t); arb_clear(u); _arb_vec_clear(a, alen); } void arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec, int times_pi) { slong hlen = h->length; if (n == 0) { arb_poly_zero(s); arb_poly_zero(c); return; } if (hlen == 0) { arb_poly_zero(s); arb_poly_one(c); return; } arb_poly_fit_length(s, n); arb_poly_fit_length(c, n); _arb_poly_sin_cos_series_basecase(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi); _arb_poly_set_length(s, n); _arb_poly_normalise(s); _arb_poly_set_length(c, n); _arb_poly_normalise(c); } arb-2.8.1/arb_poly/sin_cos_series_tangent.c000066400000000000000000000073141264125401100207710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong len, slong prec, int times_pi) { arb_ptr t, u, v; arb_t s0, c0; hlen = FLINT_MIN(hlen, len); if (hlen == 1) { if (times_pi) arb_sin_cos_pi(s, c, h, prec); else arb_sin_cos(s, c, h, prec); _arb_vec_zero(s + 1, len - 1); _arb_vec_zero(c + 1, len - 1); return; } /* sin(x) = 2*tan(x/2)/(1+tan(x/2)^2) cos(x) = (1-tan(x/2)^2)/(1+tan(x/2)^2) */ arb_init(s0); arb_init(c0); t = _arb_vec_init(3 * len); u = t + len; v = u + len; /* sin, cos of h0 */ if (times_pi) arb_sin_cos_pi(s0, c0, h, prec); else arb_sin_cos(s0, c0, h, prec); /* t = tan((h-h0)/2) */ arb_zero(u); _arb_vec_scalar_mul_2exp_si(u + 1, h + 1, hlen - 1, -1); if (times_pi) { arb_const_pi(t, prec); _arb_vec_scalar_mul(u + 1, u + 1, hlen - 1, t, prec); } _arb_poly_tan_series(t, u, hlen, len, prec); /* v = 1 + t^2 */ _arb_poly_mullow(v, t, len, t, len, len, prec); arb_add_ui(v, v, 1, prec); /* u = 1/(1+t^2) */ _arb_poly_inv_series(u, v, len, len, prec); /* sine */ _arb_poly_mullow(s, t, len, u, len, len, prec); _arb_vec_scalar_mul_2exp_si(s, s, len, 1); /* cosine */ arb_sub_ui(v, v, 2, prec); _arb_vec_neg(v, v, len); _arb_poly_mullow(c, v, len, u, len, len, prec); /* sin(h0 + h1) = cos(h0) sin(h1) + sin(h0) cos(h1) cos(h0 + h1) = cos(h0) cos(h1) - sin(h0) sin(h1) */ if (!arb_is_zero(s0)) { _arb_vec_scalar_mul(t, s, len, c0, prec); _arb_vec_scalar_mul(u, c, len, s0, prec); _arb_vec_scalar_mul(v, s, len, s0, prec); _arb_vec_add(s, t, u, len, prec); _arb_vec_scalar_mul(t, c, len, c0, prec); _arb_vec_sub(c, t, v, len, prec); } _arb_vec_clear(t, 3 * len); arb_clear(s0); arb_clear(c0); } void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec, int times_pi) { slong hlen = h->length; if (n == 0) { arb_poly_zero(s); arb_poly_zero(c); return; } if (hlen == 0) { arb_poly_zero(s); arb_poly_one(c); return; } arb_poly_fit_length(s, n); arb_poly_fit_length(c, n); _arb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi); _arb_poly_set_length(s, n); _arb_poly_normalise(s); _arb_poly_set_length(c, n); _arb_poly_normalise(c); } arb-2.8.1/arb_poly/sin_pi_series.c000066400000000000000000000041451264125401100170740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_sin_pi_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_sin_pi(g, h, prec); _arb_vec_zero(g + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_sin_cos_pi(g, t, h, prec); arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ arb_const_pi(t, prec); arb_mul(g + 1, g + 1, t, prec); arb_clear(t); } else { arb_ptr t = _arb_vec_init(n); _arb_poly_sin_cos_pi_series(g, t, h, hlen, n, prec); _arb_vec_clear(t, n); } } void arb_poly_sin_pi_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { arb_poly_zero(g); return; } if (hlen == 1) n = 1; arb_poly_fit_length(g, n); _arb_poly_sin_pi_series(g->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/sin_series.c000066400000000000000000000040141264125401100163770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_sin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) { hlen = FLINT_MIN(hlen, n); if (hlen == 1) { arb_sin(g, h, prec); _arb_vec_zero(g + 1, n - 1); } else if (n == 2) { arb_t t; arb_init(t); arb_sin_cos(g, t, h, prec); arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */ arb_clear(t); } else { arb_ptr t = _arb_vec_init(n); _arb_poly_sin_cos_series(g, t, h, hlen, n, prec); _arb_vec_clear(t, n); } } void arb_poly_sin_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (hlen == 0 || n == 0) { arb_poly_zero(g); return; } if (hlen == 1) n = 1; arb_poly_fit_length(g, n); _arb_poly_sin_series(g->coeffs, h->coeffs, hlen, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/sqrt_series.c000066400000000000000000000051251264125401100166030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_sqrt_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); while (hlen > 0 && arb_is_zero(h + hlen - 1)) hlen--; if (hlen <= 1) { arb_sqrt(g, h, prec); _arb_vec_zero(g + 1, len - 1); } else if (len == 2) { arb_sqrt(g, h, prec); arb_div(g + 1, h + 1, h, prec); arb_mul(g + 1, g + 1, g, prec); arb_mul_2exp_si(g + 1, g + 1, -1); } else if (_arb_vec_is_zero(h + 1, hlen - 2)) { arb_t t; arb_init(t); arf_set_si_2exp_si(arb_midref(t), 1, -1); _arb_poly_binomial_pow_arb_series(g, h, hlen, t, len, prec); arb_clear(t); } else { arb_ptr t; t = _arb_vec_init(len); _arb_poly_rsqrt_series(t, h, hlen, len, prec); _arb_poly_mullow(g, t, len, h, hlen, len, prec); _arb_vec_clear(t, len); } } void arb_poly_sqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { if (n == 0) { arb_poly_zero(g); return; } if (g == h) { arb_poly_t t; arb_poly_init(t); arb_poly_sqrt_series(t, h, n, prec); arb_poly_swap(g, t); arb_poly_clear(t); return; } arb_poly_fit_length(g, n); if (h->length == 0) _arb_vec_indeterminate(g->coeffs, n); else _arb_poly_sqrt_series(g->coeffs, h->coeffs, h->length, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/sub.c000066400000000000000000000035641264125401100150360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" void _arb_poly_sub(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) { slong i, min = FLINT_MIN(len1, len2); for (i = 0; i < min; i++) arb_sub(res + i, poly1 + i, poly2 + i, prec); for (i = min; i < len1; i++) arb_set_round(res + i, poly1 + i, prec); for (i = min; i < len2; i++) arb_neg_round(res + i, poly2 + i, prec); } void arb_poly_sub(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) { slong max = FLINT_MAX(poly1->length, poly2->length); arb_poly_fit_length(res, max); _arb_poly_sub(res->coeffs, poly1->coeffs, poly1->length, poly2->coeffs, poly2->length, prec); _arb_poly_set_length(res, max); _arb_poly_normalise(res); } arb-2.8.1/arb_poly/swinnerton_dyer_ui.c000066400000000000000000000071401264125401100201650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" /* Bound based on binomial theorem */ slong _arb_poly_swinnerton_dyer_ui_prec(ulong n) { slong i; double u, N; N = UWORD(1) << n; /* u = (sum of square roots)^(2^n) */ u = 0; for (i = 0; i < n; i++) u += sqrt(n_nth_prime(1 + i)); u = N * log(u) * 1.44269504088897; /* Central binomial coefficient C(N,N/2) < 2^N / sqrt(3*N/2) */ u += N - 0.5*(n-1) - 0.792481250360578; /* log(sqrt(3)) */ /* experimental heuristic: the bound is 2x too large */ return u * 0.5 + 15; } void _arb_poly_swinnerton_dyer_ui(arb_ptr T, ulong n, slong trunc, slong prec) { arb_ptr square_roots, tmp1, tmp2, tmp3; arb_t one; slong i, j, k, N; if (n == 0) { arb_zero(T); arb_one(T + 1); return; } if (prec == 0) prec = _arb_poly_swinnerton_dyer_ui_prec(n); N = WORD(1) << n; trunc = FLINT_MIN(trunc, N + 1); arb_init(one); arb_one(one); square_roots = _arb_vec_init(n); tmp1 = flint_malloc((N/2 + 1) * sizeof(arb_struct)); tmp2 = flint_malloc((N/2 + 1) * sizeof(arb_struct)); tmp3 = _arb_vec_init(N); for (i = 0; i < n; i++) arb_sqrt_ui(square_roots + i, n_nth_prime(i + 1), prec); /* Build linear factors */ for (i = 0; i < N; i++) { arb_zero(T + i); for (j = 0; j < n; j++) { if ((i >> j) & 1) arb_add(T + i, T + i, square_roots + j, prec); else arb_sub(T + i, T + i, square_roots + j, prec); } } /* For each level... */ for (i = 0; i < n; i++) { slong stride = UWORD(1) << i; for (j = 0; j < N; j += 2*stride) { for (k = 0; k < stride; k++) { tmp1[k] = T[j + k]; tmp2[k] = T[j + stride + k]; } tmp1[stride] = *one; tmp2[stride] = *one; _arb_poly_mullow(tmp3, tmp1, stride + 1, tmp2, stride + 1, FLINT_MIN(2 * stride, trunc), prec); _arb_vec_set(T + j, tmp3, FLINT_MIN(2 * stride, trunc)); } } arb_one(T + N); _arb_vec_clear(square_roots, n); flint_free(tmp1); flint_free(tmp2); _arb_vec_clear(tmp3, UWORD(1) << n); arb_clear(one); } void arb_poly_swinnerton_dyer_ui(arb_poly_t poly, ulong n, slong prec) { slong N = WORD(1) << n; arb_poly_fit_length(poly, N + 1); _arb_poly_swinnerton_dyer_ui(poly->coeffs, n, N + 1, prec); _arb_poly_set_length(poly, N + 1); _arb_poly_normalise(poly); } arb-2.8.1/arb_poly/tan_series.c000066400000000000000000000054651264125401100164030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #define TAN_NEWTON_CUTOFF 20 void _arb_poly_tan_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec) { hlen = FLINT_MIN(hlen, len); if (hlen == 1) { arb_tan(g, h, prec); _arb_vec_zero(g + 1, len - 1); } else if (len == 2) { arb_t t; arb_init(t); arb_tan(g, h, prec); arb_mul(t, g, g, prec); arb_add_ui(t, t, 1, prec); arb_mul(g + 1, t, h + 1, prec); /* safe since hlen >= 2 */ arb_clear(t); } else { arb_ptr t, u; t = _arb_vec_init(2 * len); u = t + len; NEWTON_INIT(TAN_NEWTON_CUTOFF, len) NEWTON_BASECASE(n) _arb_poly_sin_cos_series_basecase(t, u, h, hlen, n, prec, 0); _arb_poly_div_series(g, t, n, u, n, n, prec); NEWTON_END_BASECASE NEWTON_LOOP(m, n) _arb_poly_mullow(u, g, m, g, m, n, prec); arb_add_ui(u, u, 1, prec); _arb_poly_atan_series(t, g, m, n, prec); _arb_poly_sub(t + m, h + m, FLINT_MAX(0, hlen - m), t + m, n - m, prec); _arb_poly_mullow(g + m, u, n, t + m, n - m, n - m, prec); NEWTON_END_LOOP NEWTON_END _arb_vec_clear(t, 2 * len); } } void arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) { if (h->length == 0 || n == 0) { arb_poly_zero(g); return; } if (g == h) { arb_poly_t t; arb_poly_init(t); arb_poly_tan_series(t, h, n, prec); arb_poly_swap(g, t); arb_poly_clear(t); return; } arb_poly_fit_length(g, n); _arb_poly_tan_series(g->coeffs, h->coeffs, h->length, n, prec); _arb_poly_set_length(g, n); _arb_poly_normalise(g); } arb-2.8.1/arb_poly/test/000077500000000000000000000000001264125401100150505ustar00rootroot00000000000000arb-2.8.1/arb_poly/test/t-acos_series.c000066400000000000000000000060301264125401100177530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("acos_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5); arb_poly_acos_series(b, a, n, rbits2); /* Check cos(acos(x)) = x */ arb_poly_sin_cos_series_basecase(d, c, b, n, rbits2, 0); fmpq_poly_truncate(A, n); if (!arb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_acos_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-add.c000066400000000000000000000057161264125401100162160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; arb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_add(C, A, B); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_add(c, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-add_si.c000066400000000000000000000047511264125401100167070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("add_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t a, b, c, d; slong v; arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_randtest(a, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); arb_poly_randtest(b, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); arb_poly_randtest(c, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); arb_poly_randtest(d, state, 1 + n_randint(state, 10), 1 + n_randint(state, 200), 10); v = n_randtest(state); arb_poly_set_si(b, v); arb_poly_add(c, a, b, 2 + n_randint(state, 200)); arb_poly_add_si(d, a, v, 2 + n_randint(state, 200)); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); abort(); } arb_poly_add_si(a, a, v, 2 + n_randint(state, 200)); if (!arb_poly_overlaps(a, d)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-asin_series.c000066400000000000000000000060301264125401100177600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("asin_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5); arb_poly_asin_series(b, a, n, rbits2); /* Check sin(asin(x)) = x */ arb_poly_sin_cos_series_basecase(c, d, b, n, rbits2, 0); fmpq_poly_truncate(A, n); if (!arb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_asin_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-atan_series.c000066400000000000000000000067321264125401100177620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("atan_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5); arb_poly_atan_series(b, a, n, rbits2); /* Check 2 atan(x) = atan(2x/(1-x^2)) + C */ arb_poly_mullow(c, a, a, n, rbits2); arb_poly_one(d); arb_poly_sub(c, d, c, rbits2); arb_poly_add(d, a, a, rbits2); if (arb_poly_length(c) != 0) { arb_poly_div_series(c, d, c, n, rbits2); arb_poly_atan_series(c, c, n, rbits2); arb_poly_add(d, b, b, rbits2); /* TODO: also check the first coefficient */ arb_poly_set_coeff_si(c, 0, 0); arb_poly_set_coeff_si(d, 0, 0); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } } arb_poly_atan_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-binomial_transform.c000066400000000000000000000073041264125401100213460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("binomial_transform...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arb_poly_t a, b, c, d; slong j, n, prec; arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); n = n_randint(state, 20); prec = 2 + n_randint(state, 200); arb_poly_randtest(a, state, n, prec, 10); arb_poly_randtest(b, state, n, prec, 10); arb_poly_randtest(c, state, n, prec, 10); /* check self-inversion property */ arb_poly_binomial_transform(b, a, n, prec); arb_poly_binomial_transform(c, b, n, prec); arb_poly_set(d, a); arb_poly_truncate(d, n); if (!arb_poly_contains(c, d)) { flint_printf("FAIL (containment)\n\n"); flint_printf("n = %wd, prec = %wd\n\n", n, prec); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c: "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d: "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_binomial_transform(d, d, n, prec); if (!arb_poly_equal(d, b)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d: "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } /* compare with power series operations */ arb_poly_zero(d); for (j = 1; j < n; j++) arb_poly_set_coeff_si(d, j, -1); arb_poly_compose_series(c, a, d, n, prec); for (j = 0; j < n; j++) arb_poly_set_coeff_si(d, j, 1); arb_poly_mullow(c, c, d, n, prec); if (!arb_poly_overlaps(b, c)) { flint_printf("FAIL (power series)\n\n"); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c: "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-binomial_transform_basecase.c000066400000000000000000000073501264125401100231750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("binomial_transform_basecase...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arb_poly_t a, b, c, d; slong j, n, prec; arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); n = n_randint(state, 20); prec = 2 + n_randint(state, 200); arb_poly_randtest(a, state, n, prec, 10); arb_poly_randtest(b, state, n, prec, 10); arb_poly_randtest(c, state, n, prec, 10); /* check self-inversion property */ arb_poly_binomial_transform_basecase(b, a, n, prec); arb_poly_binomial_transform_basecase(c, b, n, prec); arb_poly_set(d, a); arb_poly_truncate(d, n); if (!arb_poly_contains(c, d)) { flint_printf("FAIL (containment)\n\n"); flint_printf("n = %wd, prec = %wd\n\n", n, prec); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c: "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d: "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_binomial_transform_basecase(d, d, n, prec); if (!arb_poly_equal(d, b)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d: "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } /* compare with power series operations */ arb_poly_zero(d); for (j = 1; j < n; j++) arb_poly_set_coeff_si(d, j, -1); arb_poly_compose_series(c, a, d, n, prec); for (j = 0; j < n; j++) arb_poly_set_coeff_si(d, j, 1); arb_poly_mullow(c, c, d, n, prec); if (!arb_poly_overlaps(b, c)) { flint_printf("FAIL (power series)\n\n"); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c: "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-binomial_transform_convolution.c000066400000000000000000000073641264125401100240130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("binomial_transform_convolution...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 5000; iter++) { arb_poly_t a, b, c, d; slong j, n, prec; arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); n = n_randint(state, 20); prec = 2 + n_randint(state, 200); arb_poly_randtest(a, state, n, prec, 10); arb_poly_randtest(b, state, n, prec, 10); arb_poly_randtest(c, state, n, prec, 10); /* check self-inversion property */ arb_poly_binomial_transform_convolution(b, a, n, prec); arb_poly_binomial_transform_convolution(c, b, n, prec); arb_poly_set(d, a); arb_poly_truncate(d, n); if (!arb_poly_contains(c, d)) { flint_printf("FAIL (containment)\n\n"); flint_printf("n = %wd, prec = %wd\n\n", n, prec); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c: "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d: "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_binomial_transform_convolution(d, d, n, prec); if (!arb_poly_equal(d, b)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d: "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } /* compare with power series operations */ arb_poly_zero(d); for (j = 1; j < n; j++) arb_poly_set_coeff_si(d, j, -1); arb_poly_compose_series(c, a, d, n, prec); for (j = 0; j < n; j++) arb_poly_set_coeff_si(d, j, 1); arb_poly_mullow(c, c, d, n, prec); if (!arb_poly_overlaps(b, c)) { flint_printf("FAIL (power series)\n\n"); flint_printf("a: "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b: "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c: "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-borel_transform.c000066400000000000000000000047571264125401100206700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("borel_transform...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t a, b, c, d; slong n, prec; arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); n = n_randint(state, 30); prec = n_randint(state, 200); arb_poly_randtest(a, state, n, prec, 10); arb_poly_randtest(b, state, n, prec, 10); arb_poly_randtest(c, state, n, prec, 10); arb_poly_borel_transform(b, a, prec); arb_poly_inv_borel_transform(c, b, prec); if (!arb_poly_contains(c, a)) { flint_printf("FAIL (containment)\n\n"); abort(); } arb_poly_set(d, a); arb_poly_borel_transform(d, d, prec); if (!arb_poly_equal(d, b)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_inv_borel_transform(d, d, prec); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-compose.c000066400000000000000000000067511264125401100171330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 20), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_compose(C, A, B); arb_poly_randtest(c, state, 1 + n_randint(state, 20), rbits1, 4); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_compose(c, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_compose(d, d, b, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_compose(d, a, d, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-compose_divconquer.c000066400000000000000000000067121264125401100213670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_divconquer...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 20), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_compose(C, A, B); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_compose_divconquer(c, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_compose_divconquer(d, d, b, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_compose_divconquer(d, a, d, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-compose_horner.c000066400000000000000000000066721264125401100205120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 20), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_compose(C, A, B); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_compose_horner(c, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_compose_horner(d, d, b, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_compose_horner(d, a, d, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-compose_series.c000066400000000000000000000071661264125401100205060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, n; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 25), qbits2); fmpq_poly_set_coeff_ui(B, 0, 0); fmpq_poly_compose_series(C, A, B, n); arb_poly_randtest(c, state, 1 + n_randint(state, 20), rbits1, 4); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_compose_series(c, a, b, n, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits3 = %wd\n", n, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_compose_series(d, d, b, n, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_compose_series(d, a, d, n, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-compose_series_brent_kung.c000066400000000000000000000071271264125401100227210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_series_brent_kung...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, n; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 25), qbits2); fmpq_poly_set_coeff_ui(B, 0, 0); fmpq_poly_compose_series(C, A, B, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_compose_series_brent_kung(c, a, b, n, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits3 = %wd\n", n, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_compose_series_brent_kung(d, d, b, n, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_compose_series_brent_kung(d, a, d, n, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-compose_series_horner.c000066400000000000000000000071071264125401100220560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("compose_series_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, n; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 25), qbits2); fmpq_poly_set_coeff_ui(B, 0, 0); fmpq_poly_compose_series(C, A, B, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_compose_series_horner(c, a, b, n, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits3 = %wd\n", n, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_compose_series_horner(d, d, b, n, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_compose_series_horner(d, a, d, n, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-cos_pi_series.c000066400000000000000000000057231264125401100203120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("cos_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, bits1, bits2, bits3; arb_poly_t S, A, B, C; arb_t pi; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); arb_poly_init(S); arb_poly_init(A); arb_poly_init(B); arb_poly_init(C); arb_init(pi); arb_poly_randtest(S, state, m, bits1, 3); arb_poly_randtest(A, state, m, bits1, 3); arb_poly_randtest(B, state, m, bits1, 3); arb_poly_cos_pi_series(A, S, n1, bits2); arb_const_pi(pi, bits3); arb_poly_set_arb(B, pi); arb_poly_mul(B, S, B, bits3); arb_poly_cos_series(B, B, n2, bits3); arb_poly_set(C, A); arb_poly_truncate(C, FLINT_MIN(n1, n2)); arb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); arb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); arb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } arb_poly_cos_pi_series(S, S, n1, bits2); if (!arb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(S); arb_poly_clear(A); arb_poly_clear(B); arb_poly_clear(C); arb_clear(pi); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-cot_pi_series.c000066400000000000000000000053001264125401100203020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("cot_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, bits1, bits2, bits3; arb_poly_t S, A, B, C; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); arb_poly_init(S); arb_poly_init(A); arb_poly_init(B); arb_poly_init(C); arb_poly_randtest(S, state, m, bits1, 10); arb_poly_randtest(A, state, m, bits1, 10); arb_poly_randtest(B, state, m, bits1, 10); arb_poly_cot_pi_series(A, S, n1, bits2); arb_poly_sin_cos_pi_series(B, C, S, n1, bits3); arb_poly_div_series(B, C, B, n1, bits3); if (!arb_poly_overlaps(A, B)) { flint_printf("FAIL\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); arb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); arb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } arb_poly_cot_pi_series(S, S, n1, bits2); if (!arb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(S); arb_poly_clear(A); arb_poly_clear(B); arb_poly_clear(C); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-digamma_series.c000066400000000000000000000067501264125401100204360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("digamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; arb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 300); rbits2 = 2 + n_randint(state, 300); rbits3 = 2 + n_randint(state, 300); m = n_randint(state, 25); n1 = n_randint(state, 25); n2 = n_randint(state, 25); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_randtest(a, state, m, rbits1, 10); arb_poly_digamma_series(b, a, n1, rbits2); arb_poly_digamma_series(c, a, n2, rbits3); arb_poly_set(d, b); arb_poly_truncate(d, FLINT_MIN(n1, n2)); arb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); arb_poly_printd(a, 50); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 50); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 50); flint_printf("\n\n"); abort(); } /* check psi(a) + 1/a = psi(a+1) */ arb_poly_inv_series(c, a, n1, rbits2); arb_poly_add(c, b, c, rbits2); arb_poly_add_si(d, a, 1, rbits2); arb_poly_digamma_series(d, d, n1, rbits2); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_digamma_series(a, a, n1, rbits2); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-div_series.c000066400000000000000000000073321264125401100176160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("div_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, p, qbits, rbits1, rbits2; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); p = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); do { fmpq_poly_randtest_not_zero(B, state, n, qbits); } while (B->coeffs[0] == 0); fmpq_poly_div_series(C, A, B, p); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits1); arb_poly_div_series(c, a, b, p, rbits2); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_div_series(d, d, b, p, rbits2); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_div_series(d, a, d, p, rbits2); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_div_series(c, d, d, p, rbits2); arb_poly_div_series(d, d, d, p, rbits2); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 3)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-divrem.c000066400000000000000000000101171264125401100167430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("divrem...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong m, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, Q, R; arb_poly_t a, b, q, r; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(Q); fmpq_poly_init(R); arb_poly_init(a); arb_poly_init(b); arb_poly_init(q); arb_poly_init(r); fmpq_poly_randtest(A, state, m, qbits1); fmpq_poly_randtest_not_zero(B, state, n, qbits2); fmpq_poly_divrem(Q, R, A, B); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_divrem(q, r, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(q, Q) || !arb_poly_contains_fmpq_poly(r, R)) { flint_printf("FAIL\n\n"); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("Q = "); fmpq_poly_print(Q); flint_printf("\n\n"); flint_printf("R = "); fmpq_poly_print(R); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("q = "); arb_poly_printd(q, 15); flint_printf("\n\n"); flint_printf("r = "); arb_poly_printd(r, 15); flint_printf("\n\n"); abort(); } arb_poly_divrem(a, r, a, b, rbits3); if (!arb_poly_equal(a, q)) { flint_printf("FAIL (aliasing q, a)\n\n"); } arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_divrem(b, r, a, b, rbits3); if (!arb_poly_equal(b, q)) { flint_printf("FAIL (aliasing q, b)\n\n"); abort(); } arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_divrem(q, a, a, b, rbits3); if (!arb_poly_equal(a, r)) { flint_printf("FAIL (aliasing r, a)\n\n"); abort(); } arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_divrem(q, b, a, b, rbits3); if (!arb_poly_equal(b, r)) { flint_printf("FAIL (aliasing r, b)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(Q); fmpq_poly_clear(R); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(q); arb_poly_clear(r); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate.c000066400000000000000000000060371264125401100172710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq_t X, Y; arb_poly_t f; arb_t x, y; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(F); fmpq_init(X); fmpq_init(Y); arb_poly_init(f); arb_init(x); arb_init(y); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); fmpq_randtest(X, state, qbits2); fmpq_poly_evaluate_fmpq(Y, F, X); arb_poly_set_fmpq_poly(f, F, rbits1); arb_set_fmpq(x, X, rbits2); arb_poly_evaluate(y, f, x, rbits3); if (!arb_contains_fmpq(y, Y)) { flint_printf("FAIL\n\n"); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y); flint_printf("\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 15); flint_printf("\n\n"); abort(); } /* aliasing */ arb_poly_evaluate(x, f, x, rbits3); if (!arb_contains_fmpq(x, Y)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(F); fmpq_clear(X); fmpq_clear(Y); arb_poly_clear(f); arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate2.c000066400000000000000000000055541264125401100173560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate2...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t f, g; arb_t x, y1, z1, y2, z2; arb_init(x); arb_init(y1); arb_init(z1); arb_init(y2); arb_init(z2); arb_poly_init(f); arb_poly_init(g); arb_randtest(x, state, 2 + n_randint(state, 1000), 5); arb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); arb_poly_derivative(g, f, 2 + n_randint(state, 1000)); arb_poly_evaluate2(y1, z1, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000)); if (!arb_overlaps(y1, y2) || !arb_overlaps(z1, z2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); arb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); arb_printd(y1, 15); flint_printf("\n\n"); flint_printf("z1 = "); arb_printd(z1, 15); flint_printf("\n\n"); flint_printf("y2 = "); arb_printd(y2, 15); flint_printf("\n\n"); flint_printf("z2 = "); arb_printd(z2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(f); arb_poly_clear(g); arb_clear(x); arb_clear(y1); arb_clear(z1); arb_clear(y2); arb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate2_acb_rectangular.c000066400000000000000000000056241264125401100225500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate2_acb_rectangular...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t f, g; acb_t x, y1, z1, y2, z2; acb_init(x); acb_init(y1); acb_init(z1); acb_init(y2); acb_init(z2); arb_poly_init(f); arb_poly_init(g); acb_randtest(x, state, 2 + n_randint(state, 1000), 5); arb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); arb_poly_derivative(g, f, 2 + n_randint(state, 1000)); arb_poly_evaluate2_acb_rectangular(y1, z1, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_acb_horner(y2, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_acb_horner(z2, g, x, 2 + n_randint(state, 1000)); if (!acb_overlaps(y1, y2) || !acb_overlaps(z1, z2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); arb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(f); arb_poly_clear(g); acb_clear(x); acb_clear(y1); acb_clear(z1); acb_clear(y2); acb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate2_horner.c000066400000000000000000000055721264125401100207330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate2_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t f, g; arb_t x, y1, z1, y2, z2; arb_init(x); arb_init(y1); arb_init(z1); arb_init(y2); arb_init(z2); arb_poly_init(f); arb_poly_init(g); arb_randtest(x, state, 2 + n_randint(state, 1000), 5); arb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); arb_poly_derivative(g, f, 2 + n_randint(state, 1000)); arb_poly_evaluate2_horner(y1, z1, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000)); if (!arb_overlaps(y1, y2) || !arb_overlaps(z1, z2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); arb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); arb_printd(y1, 15); flint_printf("\n\n"); flint_printf("z1 = "); arb_printd(z1, 15); flint_printf("\n\n"); flint_printf("y2 = "); arb_printd(y2, 15); flint_printf("\n\n"); flint_printf("z2 = "); arb_printd(z2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(f); arb_poly_clear(g); arb_clear(x); arb_clear(y1); arb_clear(z1); arb_clear(y2); arb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate2_rectangular.c000066400000000000000000000056041264125401100217410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate2_rectangular...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t f, g; arb_t x, y1, z1, y2, z2; arb_init(x); arb_init(y1); arb_init(z1); arb_init(y2); arb_init(z2); arb_poly_init(f); arb_poly_init(g); arb_randtest(x, state, 2 + n_randint(state, 1000), 5); arb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); arb_poly_derivative(g, f, 2 + n_randint(state, 1000)); arb_poly_evaluate2_rectangular(y1, z1, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_horner(z2, g, x, 2 + n_randint(state, 1000)); if (!arb_overlaps(y1, y2) || !arb_overlaps(z1, z2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); arb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); arb_printd(y1, 15); flint_printf("\n\n"); flint_printf("z1 = "); arb_printd(z1, 15); flint_printf("\n\n"); flint_printf("y2 = "); arb_printd(y2, 15); flint_printf("\n\n"); flint_printf("z2 = "); arb_printd(z2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(f); arb_poly_clear(g); arb_clear(x); arb_clear(y1); arb_clear(z1); arb_clear(y2); arb_clear(z2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate_acb_rectangular.c000066400000000000000000000045451264125401100224670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_acb_rectangular...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t f; acb_t x, y1, y2; acb_init(x); acb_init(y1); acb_init(y2); arb_poly_init(f); acb_randtest(x, state, 2 + n_randint(state, 1000), 5); arb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); arb_poly_evaluate_acb_rectangular(y1, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_acb_horner(y2, f, x, 2 + n_randint(state, 1000)); if (!acb_overlaps(y1, y2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); acb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); acb_printd(y1, 15); flint_printf("\n\n"); flint_printf("y2 = "); acb_printd(y2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(f); acb_clear(x); acb_clear(y1); acb_clear(y2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate_horner.c000066400000000000000000000060641264125401100206460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_horner...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq_t X, Y; arb_poly_t f; arb_t x, y; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(F); fmpq_init(X); fmpq_init(Y); arb_poly_init(f); arb_init(x); arb_init(y); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); fmpq_randtest(X, state, qbits2); fmpq_poly_evaluate_fmpq(Y, F, X); arb_poly_set_fmpq_poly(f, F, rbits1); arb_set_fmpq(x, X, rbits2); arb_poly_evaluate_horner(y, f, x, rbits3); if (!arb_contains_fmpq(y, Y)) { flint_printf("FAIL\n\n"); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y); flint_printf("\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y, 15); flint_printf("\n\n"); abort(); } /* aliasing */ arb_poly_evaluate_horner(x, f, x, rbits3); if (!arb_contains_fmpq(x, Y)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(F); fmpq_clear(X); fmpq_clear(Y); arb_poly_clear(f); arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate_rectangular.c000066400000000000000000000045311264125401100216550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_rectangular...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t f; arb_t x, y1, y2; arb_init(x); arb_init(y1); arb_init(y2); arb_poly_init(f); arb_randtest(x, state, 2 + n_randint(state, 1000), 5); arb_poly_randtest(f, state, 2 + n_randint(state, 100), 2 + n_randint(state, 1000), 5); arb_poly_evaluate_rectangular(y1, f, x, 2 + n_randint(state, 1000)); arb_poly_evaluate_horner(y2, f, x, 2 + n_randint(state, 1000)); if (!arb_overlaps(y1, y2)) { flint_printf("FAIL\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n"); flint_printf("y1 = "); arb_printd(y1, 15); flint_printf("\n\n"); flint_printf("y2 = "); arb_printd(y2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(f); arb_clear(x); arb_clear(y1); arb_clear(y2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate_vec_fast.c000066400000000000000000000063541264125401100211450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_vec_fast...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq * X, * Y; arb_poly_t f; arb_ptr x, y; qbits1 = 2 + n_randint(state, 100); qbits2 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = n_randint(state, 10); fmpq_poly_init(F); X = _fmpq_vec_init(n); Y = _fmpq_vec_init(n); arb_poly_init(f); x = _arb_vec_init(n); y = _arb_vec_init(n); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); for (i = 0; i < n; i++) fmpq_randtest(X + i, state, qbits2); for (i = 0; i < n; i++) fmpq_poly_evaluate_fmpq(Y + i, F, X + i); arb_poly_set_fmpq_poly(f, F, rbits1); for (i = 0; i < n; i++) arb_set_fmpq(x + i, X + i, rbits2); arb_poly_evaluate_vec_fast(y, f, x, n, rbits3); for (i = 0; i < n; i++) { if (!arb_contains_fmpq(y + i, Y + i)) { flint_printf("FAIL (%wd of %wd)\n\n", i, n); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X + i); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y + i); flint_printf("\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x + i, 15); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y + i, 15); flint_printf("\n\n"); abort(); } } fmpq_poly_clear(F); _fmpq_vec_clear(X, n); _fmpq_vec_clear(Y, n); arb_poly_clear(f); _arb_vec_clear(x, n); _arb_vec_clear(y, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-evaluate_vec_iter.c000066400000000000000000000063541264125401100211530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("evaluate_vec_iter...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t F; fmpq * X, * Y; arb_poly_t f; arb_ptr x, y; qbits1 = 2 + n_randint(state, 100); qbits2 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); n = n_randint(state, 10); fmpq_poly_init(F); X = _fmpq_vec_init(n); Y = _fmpq_vec_init(n); arb_poly_init(f); x = _arb_vec_init(n); y = _arb_vec_init(n); fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1); for (i = 0; i < n; i++) fmpq_randtest(X + i, state, qbits2); for (i = 0; i < n; i++) fmpq_poly_evaluate_fmpq(Y + i, F, X + i); arb_poly_set_fmpq_poly(f, F, rbits1); for (i = 0; i < n; i++) arb_set_fmpq(x + i, X + i, rbits2); arb_poly_evaluate_vec_iter(y, f, x, n, rbits3); for (i = 0; i < n; i++) { if (!arb_contains_fmpq(y + i, Y + i)) { flint_printf("FAIL (%wd of %wd)\n\n", i, n); flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n"); flint_printf("X = "); fmpq_print(X + i); flint_printf("\n\n"); flint_printf("Y = "); fmpq_print(Y + i); flint_printf("\n\n"); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("x = "); arb_printd(x + i, 15); flint_printf("\n\n"); flint_printf("y = "); arb_printd(y + i, 15); flint_printf("\n\n"); abort(); } } fmpq_poly_clear(F); _fmpq_vec_clear(X, n); _fmpq_vec_clear(Y, n); arb_poly_clear(f); _arb_vec_clear(x, n); _arb_vec_clear(y, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-exp_series.c000066400000000000000000000143321264125401100176260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" /* hack: avoid overflow since exp currently uses mpfr */ void fmpq_poly_randtest_small(fmpq_poly_t A, flint_rand_t state, slong len, slong bits) { fmpq_poly_randtest(A, state, len, bits); if (A->length > 0) { bits = _fmpz_vec_max_bits(A->coeffs, A->length); bits = FLINT_ABS(bits); fmpz_mul_2exp(A->den, A->den, bits); _fmpq_poly_normalise(A); } } int main() { slong iter; flint_rand_t state; flint_printf("exp_series...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); fmpq_poly_randtest(A, state, m, qbits); fmpq_poly_set_coeff_ui(A, 0, UWORD(0)); arb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); fmpq_poly_exp_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_exp_series(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); } /* test aliasing */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); if (n_randint(state, 100) == 0) { m = 1 + n_randint(state, 600); n = 1 + n_randint(state, 600); } else { m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); } fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); fmpq_poly_randtest_small(A, state, m, qbits); arb_poly_randtest(a, state, 1 + n_randint(state, 300), rbits1, 5); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_exp_series(b, a, n, rbits2); arb_poly_exp_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); } /* test that log(exp(f)) contains f */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; arb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); if (n_randint(state, 100) == 0) { m = 1 + n_randint(state, 600); n = 1 + n_randint(state, 600); } else { m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); } fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_randtest(b, state, 1 + n_randint(state, 300), rbits1, 5); do { fmpq_poly_randtest_small(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_exp_series(b, a, n, rbits3); } while (b->length == 0 || arb_contains_zero(b->coeffs)); arb_poly_log_series(c, b, n, rbits2); fmpq_poly_truncate(A, n); if (!arb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-exp_series_basecase.c000066400000000000000000000132601264125401100214530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" /* hack: avoid overflow since exp currently uses mpfr */ void fmpq_poly_randtest_small(fmpq_poly_t A, flint_rand_t state, slong len, slong bits) { fmpq_poly_randtest(A, state, len, bits); if (A->length > 0) { bits = _fmpz_vec_max_bits(A->coeffs, A->length); bits = FLINT_ABS(bits); fmpz_mul_2exp(A->den, A->den, bits); _fmpq_poly_normalise(A); } } int main() { slong iter; flint_rand_t state; flint_printf("exp_series_basecase...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 40); n = 1 + n_randint(state, 40); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); fmpq_poly_randtest(A, state, m, qbits); fmpq_poly_set_coeff_ui(A, 0, UWORD(0)); fmpq_poly_exp_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_exp_series_basecase(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); } /* test aliasing */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 40); n = 1 + n_randint(state, 40); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); fmpq_poly_randtest_small(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_exp_series_basecase(b, a, n, rbits2); arb_poly_exp_series_basecase(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); } /* test that log(exp(f)) contains f */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; arb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 40); n = 1 + n_randint(state, 40); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); do { fmpq_poly_randtest_small(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_exp_series_basecase(b, a, n, rbits3); } while (b->length == 0 || arb_contains_zero(b->coeffs)); arb_poly_log_series(c, b, n, rbits2); fmpq_poly_truncate(A, n); if (!arb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-gamma_series.c000066400000000000000000000075041264125401100201170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("gamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { slong m, n1, n2, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; arb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 400); rbits2 = 2 + n_randint(state, 400); rbits3 = 2 + n_randint(state, 400); m = 1 + n_randint(state, 25); n1 = 1 + n_randint(state, 25); n2 = 1 + n_randint(state, 25); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest_not_zero(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_gamma_series(b, a, n1, rbits2); arb_poly_gamma_series(c, a, n2, rbits3); arb_poly_set(d, b); arb_poly_truncate(d, FLINT_MIN(n1, n2)); arb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check gamma(a) * a = gamma(a+1) */ arb_poly_mullow(c, b, a, n1, rbits2); arb_poly_set(d, a); arb_add_ui(d->coeffs, d->coeffs, 1, rbits2); arb_poly_gamma_series(d, d, n1, rbits2); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation, n1 = %wd)\n\n", n1); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_gamma_series(a, a, n1, rbits2); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-get_coeff_ptr.c000066400000000000000000000042201264125401100202610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2010 Sebastian Pancratz Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main(void) { int i, result; flint_rand_t state; flint_printf("get_coeff_ptr...."); fflush(stdout); flint_randinit(state); for (i = 0; i < 1000; i++) { arb_poly_t A; arb_t a; slong n = n_randint(state, 100); arb_poly_init(A); arb_poly_randtest(A, state, n_randint(state, 100), 100, 10); arb_init(a); arb_poly_get_coeff_arb(a, A, n); result = n < arb_poly_length(A) ? arb_equal(a, arb_poly_get_coeff_ptr(A, n)) : arb_poly_get_coeff_ptr(A, n) == NULL; if (!result) { flint_printf("FAIL:\n"); flint_printf("A = "), arb_poly_printd(A, 10), flint_printf("\n\n"); flint_printf("a = "), arb_print(a), flint_printf("\n\n"); flint_printf("n = %wd\n\n", n); abort(); } arb_poly_clear(A); arb_clear(a); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/arb_poly/test/t-get_set_coeff_arb.c000066400000000000000000000044511264125401100211010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2009 William Hart Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main(void) { int i, j, result; flint_rand_t state; flint_printf("get/set_coeff_arb...."); fflush(stdout); flint_randinit(state); for (i = 0; i < 100; i++) { arb_poly_t a; arb_t x1, x2; slong coeff, len; arb_poly_init(a); arb_init(x1); arb_init(x2); len = n_randint(state, 100) + 1; for (j = 0; j < 100; j++) { arb_randtest(x1, state, 2 + n_randint(state, 200), 10); coeff = n_randint(state, len); arb_poly_set_coeff_arb(a, coeff, x1); arb_poly_get_coeff_arb(x2, a, coeff); result = (arb_equal(x1, x2)); if (!result) { flint_printf("FAIL:\n"); flint_printf("x1 = "), arb_print(x1), flint_printf("\n"); flint_printf("x2 = "), arb_print(x2), flint_printf("\n"); flint_printf("coeff = %wd, length = %wd\n", coeff, len); abort(); } } arb_clear(x1); arb_clear(x2); arb_poly_clear(a); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/arb_poly/test/t-get_unique_fmpz_poly.c000066400000000000000000000054261264125401100217300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("get_unique_fmpz_poly...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong prec, c; fmpz_poly_t A, B; arb_poly_t a, b; fmpz_poly_init(A); fmpz_poly_init(B); arb_poly_init(a); arb_poly_init(b); fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); fmpz_poly_randtest(B, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); c = 1 + n_randint(state, 1000); prec = 2 + n_randint(state, 100); for ( ; ; ) { arb_poly_set_fmpz_poly(a, A, prec); arb_poly_set_fmpz_poly(b, B, prec); arb_poly_scalar_mul_2exp_si(b, b, -c); arb_poly_add(a, a, b, prec); arb_poly_sub(a, a, b, prec); if (arb_poly_get_unique_fmpz_poly(B, a)) { if (!fmpz_poly_equal(A, B)) { flint_printf("FAIL\n\n"); flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); abort(); } break; } else { prec *= 2; } } fmpz_poly_clear(A); fmpz_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-interpolate_barycentric.c000066400000000000000000000061761264125401100224020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("interpolate_barycentric...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t P; arb_poly_t R, S; fmpq_t t, u; arb_ptr xs, ys; fmpq_poly_init(P); arb_poly_init(R); arb_poly_init(S); fmpq_init(t); fmpq_init(u); qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 5); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1); n = P->length; xs = _arb_vec_init(n); ys = _arb_vec_init(n); arb_poly_set_fmpq_poly(R, P, rbits1); if (n > 0) { fmpq_randtest(t, state, qbits2); arb_set_fmpq(xs, t, rbits2); for (i = 1; i < n; i++) { fmpq_randtest_not_zero(u, state, qbits2); fmpq_abs(u, u); fmpq_add(t, t, u); arb_set_fmpq(xs + i, t, rbits2); } } for (i = 0; i < n; i++) arb_poly_evaluate(ys + i, R, xs + i, rbits2); arb_poly_interpolate_barycentric(S, xs, ys, n, rbits3); if (!arb_poly_contains_fmpq_poly(S, P)) { flint_printf("FAIL:\n"); flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n"); flint_printf("R = "); arb_poly_printd(R, 15); flint_printf("\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(P); arb_poly_clear(R); arb_poly_clear(S); fmpq_clear(t); fmpq_clear(u); _arb_vec_clear(xs, n); _arb_vec_clear(ys, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-interpolate_fast.c000066400000000000000000000061601264125401100210230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("interpolate_fast...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t P; arb_poly_t R, S; fmpq_t t, u; arb_ptr xs, ys; fmpq_poly_init(P); arb_poly_init(R); arb_poly_init(S); fmpq_init(t); fmpq_init(u); qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 5); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1); n = P->length; xs = _arb_vec_init(n); ys = _arb_vec_init(n); arb_poly_set_fmpq_poly(R, P, rbits1); if (n > 0) { fmpq_randtest(t, state, qbits2); arb_set_fmpq(xs, t, rbits2); for (i = 1; i < n; i++) { fmpq_randtest_not_zero(u, state, qbits2); fmpq_abs(u, u); fmpq_add(t, t, u); arb_set_fmpq(xs + i, t, rbits2); } } for (i = 0; i < n; i++) arb_poly_evaluate(ys + i, R, xs + i, rbits2); arb_poly_interpolate_fast(S, xs, ys, n, rbits3); if (!arb_poly_contains_fmpq_poly(S, P)) { flint_printf("FAIL:\n"); flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n"); flint_printf("R = "); arb_poly_printd(R, 15); flint_printf("\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(P); arb_poly_clear(R); arb_poly_clear(S); fmpq_clear(t); fmpq_clear(u); _arb_vec_clear(xs, n); _arb_vec_clear(ys, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-interpolate_newton.c000066400000000000000000000061641264125401100214040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("interpolate_newton...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t P; arb_poly_t R, S; fmpq_t t, u; arb_ptr xs, ys; fmpq_poly_init(P); arb_poly_init(R); arb_poly_init(S); fmpq_init(t); fmpq_init(u); qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 5); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1); n = P->length; xs = _arb_vec_init(n); ys = _arb_vec_init(n); arb_poly_set_fmpq_poly(R, P, rbits1); if (n > 0) { fmpq_randtest(t, state, qbits2); arb_set_fmpq(xs, t, rbits2); for (i = 1; i < n; i++) { fmpq_randtest_not_zero(u, state, qbits2); fmpq_abs(u, u); fmpq_add(t, t, u); arb_set_fmpq(xs + i, t, rbits2); } } for (i = 0; i < n; i++) arb_poly_evaluate(ys + i, R, xs + i, rbits2); arb_poly_interpolate_newton(S, xs, ys, n, rbits3); if (!arb_poly_contains_fmpq_poly(S, P)) { flint_printf("FAIL:\n"); flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n"); flint_printf("R = "); arb_poly_printd(R, 15); flint_printf("\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(P); arb_poly_clear(R); arb_poly_clear(S); fmpq_clear(t); fmpq_clear(u); _arb_vec_clear(xs, n); _arb_vec_clear(ys, n); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-inv_series.c000066400000000000000000000055451264125401100176340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("inv_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (A->coeffs[0] == 0); arb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); fmpq_poly_inv_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_inv_series(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } arb_poly_inv_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-lgamma_series.c000066400000000000000000000076261264125401100203000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("lgamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; arb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 400); rbits2 = 2 + n_randint(state, 400); rbits3 = 2 + n_randint(state, 400); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest_not_zero(A, state, m, qbits); fmpz_abs(A->coeffs, A->coeffs); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_lgamma_series(b, a, n1, rbits2); arb_poly_lgamma_series(c, a, n2, rbits3); arb_poly_set(d, b); arb_poly_truncate(d, FLINT_MIN(n1, n2)); arb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check loggamma(a) + log(a) = loggamma(a+1) */ arb_poly_log_series(c, a, n1, rbits2); arb_poly_add(c, b, c, rbits2); arb_poly_set(d, a); arb_add_ui(d->coeffs, d->coeffs, 1, rbits2); arb_poly_lgamma_series(d, d, n1, rbits2); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_lgamma_series(a, a, n1, rbits2); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-log_series.c000066400000000000000000000127121264125401100176130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("log_series...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); fmpq_poly_randtest_not_zero(A, state, m, qbits); fmpq_poly_set_coeff_ui(A, 0, UWORD(1)); fmpq_poly_log_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); arb_poly_log_series(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); } /* test aliasing */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (fmpz_sgn(A->coeffs + 0) <= 0); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_log_series(b, a, n, rbits2); arb_poly_log_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); } /* test that exp(log(f)) contains f */ for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; arb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (fmpz_sgn(A->coeffs + 0) <= 0); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); arb_poly_log_series(b, a, n, rbits2); arb_poly_exp_series_basecase(c, b, n, rbits3); fmpq_poly_truncate(A, n); if (!arb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-mul.c000066400000000000000000000105141264125401100162530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mul(C, A, B); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_mul(c, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_mul(d, d, b, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_mul(d, a, d, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ arb_poly_set(b, a); arb_poly_mul(c, a, b, rbits3); arb_poly_mul(d, a, a, rbits3); if (!arb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_mul(a, a, a, rbits3); if (!arb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-mullow.c000066400000000000000000000110251264125401100167730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mullow...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 100000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mullow(C, A, B, trunc); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_mullow(c, a, b, trunc, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_mullow(d, d, b, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_mullow(d, a, d, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ arb_poly_set(b, a); arb_poly_mullow(c, a, b, trunc, rbits3); arb_poly_mullow(d, a, a, trunc, rbits3); if (!arb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_mullow(a, a, a, trunc, rbits3); if (!arb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-mullow_block.c000066400000000000000000000165441264125401100201600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mullow_block...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 1000); qbits2 = 2 + n_randint(state, 1000); rbits1 = 2 + n_randint(state, 1000); rbits2 = 2 + n_randint(state, 1000); rbits3 = 2 + n_randint(state, 1000); trunc = n_randint(state, 100); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 100), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 100), qbits2); fmpq_poly_mullow(C, A, B, trunc); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_mullow_block(c, a, b, trunc, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_mullow_block(d, d, b, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_mullow_block(d, a, d, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ arb_poly_set(b, a); arb_poly_mullow_block(c, a, b, trunc, rbits3); arb_poly_mullow_block(d, a, a, trunc, rbits3); if (!arb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_mullow_block(a, a, a, trunc, rbits3); if (!arb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } for (iter = 0; iter < 3000; iter++) { slong rbits1, rbits2, rbits3, trunc; arb_poly_t a, b, c, ab, ac, bc, abc, abc2; rbits1 = 2 + n_randint(state, 300); rbits2 = 2 + n_randint(state, 300); rbits3 = 2 + n_randint(state, 300); trunc = n_randint(state, 100); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(ab); arb_poly_init(ac); arb_poly_init(bc); arb_poly_init(abc); arb_poly_init(abc2); arb_poly_randtest(a, state, 1 + n_randint(state, 100), rbits1, 1 + n_randint(state, 100)); arb_poly_randtest(b, state, 1 + n_randint(state, 100), rbits2, 1 + n_randint(state, 100)); arb_poly_randtest(c, state, 1 + n_randint(state, 100), rbits2, 1 + n_randint(state, 100)); /* check a*(b+c) = a*b + a*c */ arb_poly_mullow_block(ab, a, b, trunc, rbits3); arb_poly_mullow_block(ac, a, c, trunc, rbits3); arb_poly_add(abc, ab, ac, rbits3); arb_poly_add(bc, b, c, rbits3); arb_poly_mullow_block(abc2, a, bc, trunc, rbits3); if (!arb_poly_overlaps(abc, abc2)) { flint_printf("FAIL (a*(b+c) = a*b + a*c) \n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check (b+c)^2 = b^2 + 2bc + c^2 */ arb_poly_mullow_block(a, b, c, trunc, rbits3); arb_poly_scalar_mul_2exp_si(a, a, 1); arb_poly_mullow_block(abc, b, b, trunc, rbits3); arb_poly_mullow_block(abc2, c, c, trunc, rbits3); arb_poly_add(abc, abc, a, rbits3); arb_poly_add(abc, abc, abc2, rbits3); arb_poly_mullow_block(abc2, bc, bc, trunc, rbits3); if (!arb_poly_overlaps(abc, abc2)) { flint_printf("FAIL ((b+c)^2 = b^2 + 2bc + c^2) \n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("abc = "); arb_poly_printd(abc, 15); flint_printf("\n\n"); flint_printf("abc2 = "); arb_poly_printd(abc2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(ab); arb_poly_clear(ac); arb_poly_clear(bc); arb_poly_clear(abc); arb_poly_clear(abc2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-mullow_classical.c000066400000000000000000000111331264125401100210110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("mullow_classical...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 100000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mullow(C, A, B, trunc); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_mullow_classical(c, a, b, trunc, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_mullow_classical(d, d, b, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_mullow_classical(d, a, d, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ arb_poly_set(b, a); arb_poly_mullow_classical(c, a, b, trunc, rbits3); arb_poly_mullow_classical(d, a, a, trunc, rbits3); if (!arb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_mullow_classical(a, a, a, trunc, rbits3); if (!arb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-pow_arb_series.c000066400000000000000000000065151264125401100204670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_arb_series...."); fflush(stdout); flint_randinit(state); /* compare with exp/log */ for (iter = 0; iter < 10000; iter++) { slong prec, trunc; arb_poly_t f, g, h1, h2; arb_t c; prec = 2 + n_randint(state, 200); trunc = n_randint(state, 20); arb_poly_init(f); arb_poly_init(g); arb_poly_init(h1); arb_poly_init(h2); arb_init(c); /* generate binomials */ if (n_randint(state, 20) == 0) { arb_randtest(c, state, prec, 10); arb_poly_set_coeff_arb(f, 0, c); arb_randtest(c, state, prec, 10); arb_poly_set_coeff_arb(f, 1 + n_randint(state, 20), c); } else { arb_poly_randtest(f, state, 1 + n_randint(state, 20), prec, 10); } arb_poly_randtest(h1, state, 1 + n_randint(state, 20), prec, 10); arb_randtest(c, state, prec, 10); arb_poly_set_arb(g, c); /* f^c */ arb_poly_pow_arb_series(h1, f, c, trunc, prec); /* f^c = exp(c*log(f)) */ arb_poly_log_series(h2, f, trunc, prec); arb_poly_mullow(h2, h2, g, trunc, prec); arb_poly_exp_series(h2, h2, trunc, prec); if (!arb_poly_overlaps(h1, h2)) { flint_printf("FAIL\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("trunc = %wd\n", trunc); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("c = "); arb_printd(c, 15); flint_printf("\n\n"); flint_printf("h1 = "); arb_poly_printd(h1, 15); flint_printf("\n\n"); flint_printf("h2 = "); arb_poly_printd(h2, 15); flint_printf("\n\n"); abort(); } arb_poly_pow_arb_series(f, f, c, trunc, prec); if (!arb_poly_overlaps(f, h1)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(f); arb_poly_clear(g); arb_poly_clear(h1); arb_poly_clear(h2); arb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-pow_series.c000066400000000000000000000070071264125401100176400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 50000; iter++) { slong rbits1, rbits2, len; arb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); len = n_randint(state, 25); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); if (n_randint(state, 4) == 0) arb_poly_randtest(a, state, 1, rbits1, 25); else arb_poly_randtest(a, state, 1 + n_randint(state, 20), rbits1, 5); if (n_randint(state, 4) == 0) arb_poly_randtest(b, state, 1, rbits1, 25); else arb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); arb_poly_randtest(c, state, 1 + n_randint(state, 20), rbits1, 5); arb_poly_pow_series(c, a, b, len, rbits2); /* a^b = exp(b log a) */ arb_poly_log_series(d, a, len, rbits2); arb_poly_mullow(d, d, b, len, rbits2); arb_poly_exp_series(d, d, len, rbits2); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL (iter %wd)\n\n", iter); flint_printf("bits2 = %wd\n", rbits2); flint_printf("len = %wd\n", len); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } /* check aliasing */ if (iter < 5000) { arb_poly_set(d, a); arb_poly_pow_series(d, d, b, len, rbits2); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL (aliasing 1)\n"); abort(); } arb_poly_set(d, b); arb_poly_pow_series(d, a, d, len, rbits2); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL (aliasing 2)\n"); abort(); } } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-pow_ui.c000066400000000000000000000054131264125401100167620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_ui...."); fflush(stdout); flint_randinit(state); /* compare with fmpz_poly */ for (iter = 0; iter < 10000; iter++) { slong zbits1, rbits1, rbits2; ulong e; fmpz_poly_t A, B; arb_poly_t a, b; zbits1 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); e = n_randint(state, 30); fmpz_poly_init(A); fmpz_poly_init(B); arb_poly_init(a); arb_poly_init(b); fmpz_poly_randtest(A, state, 1 + n_randint(state, 8), zbits1); fmpz_poly_pow(B, A, e); arb_poly_set_fmpz_poly(a, A, rbits1); arb_poly_pow_ui(b, a, e, rbits2); if (!arb_poly_contains_fmpz_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("e = %wu\n", e); flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } arb_poly_pow_ui(a, a, e, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpz_poly_clear(A); fmpz_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-pow_ui_trunc_binexp.c000066400000000000000000000056551264125401100215520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_ui_trunc_binexp...."); fflush(stdout); flint_randinit(state); /* compare with fmpz_poly */ for (iter = 0; iter < 10000; iter++) { slong zbits1, rbits1, rbits2, trunc; ulong e; fmpz_poly_t A, B; arb_poly_t a, b; zbits1 = 2 + n_randint(state, 100); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); e = n_randint(state, 50); trunc = n_randint(state, 40); fmpz_poly_init(A); fmpz_poly_init(B); arb_poly_init(a); arb_poly_init(b); fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), zbits1); fmpz_poly_pow_trunc(B, A, e, trunc); arb_poly_set_fmpz_poly(a, A, rbits1); arb_poly_pow_ui_trunc_binexp(b, a, e, trunc, rbits2); if (!arb_poly_contains_fmpz_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("e = %wu\n", e); flint_printf("trunc = %wd\n", trunc); flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } arb_poly_pow_ui_trunc_binexp(a, a, e, trunc, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpz_poly_clear(A); fmpz_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-revert_series.c000066400000000000000000000056651264125401100203520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; arb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_revert_series(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } arb_poly_set(c, a); arb_poly_revert_series(c, c, n, rbits2); if (!arb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-revert_series_lagrange.c000066400000000000000000000057201264125401100222020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series_lagrange...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; arb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_revert_series_lagrange(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } arb_poly_set(c, a); arb_poly_revert_series_lagrange(c, c, n, rbits2); if (!arb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-revert_series_lagrange_fast.c000066400000000000000000000057371264125401100232270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series_lagrange_fast...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; arb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_revert_series_lagrange_fast(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } arb_poly_set(c, a); arb_poly_revert_series_lagrange_fast(c, c, n, rbits2); if (!arb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-revert_series_newton.c000066400000000000000000000057121264125401100217350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("revert_series_newton...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong qbits1, rbits1, rbits2, n; fmpq_poly_t A, B; arb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); n = 2 + n_randint(state, 25); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); do { fmpq_poly_randtest(A, state, 1 + n_randint(state, 25), qbits1); fmpq_poly_set_coeff_ui(A, 0, 0); } while (A->length < 2 || fmpz_is_zero(A->coeffs + 1)); fmpq_poly_revert_series(B, A, n); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_revert_series_newton(b, a, n, rbits2); if (!arb_poly_contains_fmpq_poly(b, B)) { flint_printf("FAIL\n\n"); flint_printf("n = %wd, bits2 = %wd\n", n, rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); abort(); } arb_poly_set(c, a); arb_poly_revert_series_newton(c, c, n, rbits2); if (!arb_poly_equal(c, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-rgamma_series.c000066400000000000000000000074401264125401100203000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rgamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { slong m, n1, n2, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; arb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 400); rbits2 = 2 + n_randint(state, 400); rbits3 = 2 + n_randint(state, 400); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest_not_zero(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_rgamma_series(b, a, n1, rbits2); arb_poly_rgamma_series(c, a, n2, rbits3); arb_poly_set(d, b); arb_poly_truncate(d, FLINT_MIN(n1, n2)); arb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check rgamma(a) = a gamma(a+1) */ arb_poly_add_si(d, a, 1, rbits2); arb_poly_rgamma_series(d, d, n1, rbits2); arb_poly_mullow(c, d, a, n1, rbits2); if (!arb_poly_overlaps(b, c)) { flint_printf("FAIL (functional equation, n1 = %wd)\n\n", n1); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_rgamma_series(a, a, n1, rbits2); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-riemann_siegel_theta_series.c000066400000000000000000000072651264125401100232070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("riemann_siegel_theta_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 300; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; arb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 150); rbits2 = 2 + n_randint(state, 150); rbits3 = 2 + n_randint(state, 150); m = 1 + n_randint(state, 15); n1 = 1 + n_randint(state, 15); n2 = 1 + n_randint(state, 15); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_randtest(a, state, m, rbits1, 10); /* if (a->length != 0) arb_randtest_precise(a->coeffs, state, rbits1, 1); */ arb_poly_randtest(b, state, m, rbits1, 10); arb_poly_randtest(c, state, m, rbits1, 10); arb_poly_riemann_siegel_theta_series(b, a, n1, rbits2); arb_poly_riemann_siegel_theta_series(c, a, n2, rbits3); arb_poly_set(d, b); arb_poly_truncate(d, FLINT_MIN(n1, n2)); arb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check theta(a) = -theta(-a) */ arb_poly_neg(d, a); arb_poly_riemann_siegel_theta_series(c, d, n1, rbits2); arb_poly_neg(c, c); if (!arb_poly_overlaps(b, c)) { flint_printf("FAIL (symmetry, n1 = %wd)\n\n", n1); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_riemann_siegel_theta_series(a, a, n1, rbits2); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-riemann_siegel_z_series.c000066400000000000000000000071661264125401100223530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("riemann_siegel_z_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 300; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; arb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 150); rbits2 = 2 + n_randint(state, 150); rbits3 = 2 + n_randint(state, 150); m = 1 + n_randint(state, 15); n1 = 1 + n_randint(state, 15); n2 = 1 + n_randint(state, 15); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_randtest(a, state, m, rbits1, 10); if (a->length != 0) arb_randtest_precise(a->coeffs, state, rbits1, 1); arb_poly_randtest(b, state, m, rbits1, 10); arb_poly_randtest(c, state, m, rbits1, 10); arb_poly_riemann_siegel_z_series(b, a, n1, rbits2); arb_poly_riemann_siegel_z_series(c, a, n2, rbits3); arb_poly_set(d, b); arb_poly_truncate(d, FLINT_MIN(n1, n2)); arb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check Z(a) = Z(-a) */ arb_poly_neg(d, a); arb_poly_riemann_siegel_z_series(c, d, n1, rbits2); if (!arb_poly_overlaps(b, c)) { flint_printf("FAIL (symmetry, n1 = %wd)\n\n", n1); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_riemann_siegel_z_series(a, a, n1, rbits2); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-rising_ui_series.c000066400000000000000000000077311264125401100210270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rising_ui_series...."); fflush(stdout); flint_randinit(state); /* check rf(f, a) * rf(f + a, b) = rf(f, a + b) */ for (iter = 0; iter < 1000; iter++) { slong bits, trunc; ulong a, b; arb_poly_t f, g, h1, h2, h1h2, h3; bits = 2 + n_randint(state, 200); trunc = 1 + n_randint(state, 20); a = n_randint(state, 10); b = n_randint(state, 10); arb_poly_init(f); arb_poly_init(g); arb_poly_init(h1); arb_poly_init(h2); arb_poly_init(h1h2); arb_poly_init(h3); arb_poly_randtest(f, state, 1 + n_randint(state, 20), bits, 4); arb_poly_set(g, f); /* g = f + 1 */ if (g->length == 0) { arb_poly_fit_length(g, 1); arb_set_ui(g->coeffs, a); _arb_poly_set_length(g, 1); _arb_poly_normalise(g); } else { arb_add_ui(g->coeffs, g->coeffs, a, bits); _arb_poly_normalise(g); } arb_poly_rising_ui_series(h1, f, a, trunc, bits); arb_poly_rising_ui_series(h2, g, b, trunc, bits); arb_poly_rising_ui_series(h3, f, a + b, trunc, bits); arb_poly_mullow(h1h2, h1, h2, trunc, bits); if (!arb_poly_overlaps(h1h2, h3)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = %wu\n", a); flint_printf("b = %wu\n", a); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("g = "); arb_poly_printd(g, 15); flint_printf("\n\n"); flint_printf("h1 = "); arb_poly_printd(h1, 15); flint_printf("\n\n"); flint_printf("h2 = "); arb_poly_printd(h2, 15); flint_printf("\n\n"); flint_printf("h1h2 = "); arb_poly_printd(h1h2, 15); flint_printf("\n\n"); flint_printf("h3 = "); arb_poly_printd(h3, 15); flint_printf("\n\n"); abort(); } arb_poly_rising_ui_series(f, f, a, trunc, bits); if (!arb_poly_equal(f, h1)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("trunc = %wd\n", trunc); flint_printf("a = %wu\n", a); flint_printf("b = %wu\n", a); flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("h1 = "); arb_poly_printd(h1, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(f); arb_poly_clear(g); arb_poly_clear(h1); arb_poly_clear(h2); arb_poly_clear(h1h2); arb_poly_clear(h3); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-root_bound_fujiwara.c000066400000000000000000000057641264125401100215330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("root_bound_fujiwara...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_poly_t a; arb_ptr roots; arb_t t; mag_t mag1, mag2; slong i, deg, prec; prec = 10 + n_randint(state, 400); deg = n_randint(state, 10); arb_init(t); arb_poly_init(a); mag_init(mag1); mag_init(mag2); roots = _arb_vec_init(deg); for (i = 0; i < deg; i++) arb_randtest(roots + i, state, prec, 1 + n_randint(state, 20)); arb_poly_product_roots(a, roots, deg, prec); arb_randtest(t, state, prec, 1 + n_randint(state, 20)); _arb_vec_scalar_mul(a->coeffs, a->coeffs, a->length, t, prec); arb_poly_root_bound_fujiwara(mag1, a); for (i = 0; i < deg; i++) { arb_get_mag(mag2, roots + i); /* arb_get_mag gives an upper bound which due to rounding could be larger than mag1, so we pick a slightly smaller number */ mag_mul_ui(mag2, mag2, 10000); mag_div_ui(mag2, mag2, 10001); if (mag_cmp(mag2, mag1) > 0) { flint_printf("FAIL\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("root = "); arb_printd(roots + i, 15); flint_printf("\n\n"); flint_printf("mag1 = "); mag_printd(mag1, 10); flint_printf("\n\n"); flint_printf("mag2 = "); mag_printd(mag2, 10); flint_printf("\n\n"); abort(); } } _arb_vec_clear(roots, deg); arb_clear(t); arb_poly_clear(a); mag_clear(mag1); mag_clear(mag2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-rsqrt_series.c000066400000000000000000000056731264125401100202150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("rsqrt_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); fmpq_poly_randtest_not_zero(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5); arb_poly_rsqrt_series(b, a, n, rbits2); /* Check 1/((1/sqrt(a))^2) = a */ arb_poly_mullow(c, b, b, n, rbits2); arb_poly_inv_series(c, c, n, rbits2); fmpq_poly_truncate(A, n); if (!arb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_rsqrt_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-shift_left_right.c000066400000000000000000000070551264125401100210100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2009 William Hart Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main(void) { int i, result; flint_rand_t state; flint_printf("shift_left/right...."); fflush(stdout); flint_randinit(state); /* Check aliasing of a and b for left shift */ for (i = 0; i < 1000; i++) { arb_poly_t a, b; slong shift = n_randint(state, 100); arb_poly_init(a); arb_poly_init(b); arb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); arb_poly_shift_left(b, a, shift); arb_poly_shift_left(a, a, shift); result = (arb_poly_equal(a, b)); if (!result) { flint_printf("FAIL:\n"); arb_poly_printd(a, 10), flint_printf("\n\n"); arb_poly_printd(b, 10), flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); } /* Check aliasing of a and b for right shift */ for (i = 0; i < 1000; i++) { arb_poly_t a, b; slong shift = n_randint(state, 100); arb_poly_init(a); arb_poly_init(b); arb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); arb_poly_shift_right(b, a, shift); arb_poly_shift_right(a, a, shift); result = (arb_poly_equal(a, b)); if (!result) { flint_printf("FAIL:\n"); arb_poly_printd(a, 10), flint_printf("\n\n"); arb_poly_printd(b, 10), flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); } /* Check shift left then right does nothing */ for (i = 0; i < 1000; i++) { arb_poly_t a, b, c; slong shift = n_randint(state, 100); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); arb_poly_shift_left(b, a, shift); arb_poly_shift_right(c, b, shift); result = (arb_poly_equal(c, a)); if (!result) { flint_printf("FAIL:\n"); arb_poly_printd(a, 10), flint_printf("\n\n"); arb_poly_printd(b, 10), flint_printf("\n\n"); arb_poly_printd(c, 10), flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/arb_poly/test/t-sin_cos_pi_series.c000066400000000000000000000066071264125401100211650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b, c, d, e; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_sin_cos_pi_series(b, c, a, n, rbits2); /* Check sin(x)^2 + cos(x)^2 = 1 */ arb_poly_mullow(d, b, b, n, rbits2); arb_poly_mullow(e, c, c, n, rbits2); arb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!arb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_pi_series(d, c, d, n, rbits2); if (!arb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_pi_series(b, d, d, n, rbits2); if (!arb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); arb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-sin_cos_series.c000066400000000000000000000065731264125401100204770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b, c, d, e; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_sin_cos_series(b, c, a, n, rbits2); /* Check sin(x)^2 + cos(x)^2 = 1 */ arb_poly_mullow(d, b, b, n, rbits2); arb_poly_mullow(e, c, c, n, rbits2); arb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!arb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_series(d, c, d, n, rbits2); if (!arb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_series(b, d, d, n, rbits2); if (!arb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); arb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-sin_cos_series_basecase.c000066400000000000000000000067741264125401100223300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_series_basecase...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b, c, d, e; int times_pi; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); times_pi = n_randint(state, 2); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_sin_cos_series_basecase(b, c, a, n, rbits2, times_pi); /* Check sin(x)^2 + cos(x)^2 = 1 */ arb_poly_mullow(d, b, b, n, rbits2); arb_poly_mullow(e, c, c, n, rbits2); arb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!arb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_series_basecase(d, c, d, n, rbits2, times_pi); if (!arb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_series_basecase(b, d, d, n, rbits2, times_pi); if (!arb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); arb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-sin_cos_series_tangent.c000066400000000000000000000067701264125401100222160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_series_tangent...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b, c, d, e; int times_pi; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); times_pi = n_randint(state, 2); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_sin_cos_series_tangent(b, c, a, n, rbits2, times_pi); /* Check sin(x)^2 + cos(x)^2 = 1 */ arb_poly_mullow(d, b, b, n, rbits2); arb_poly_mullow(e, c, c, n, rbits2); arb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!arb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_series_tangent(d, c, d, n, rbits2, times_pi); if (!arb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_series_tangent(b, d, d, n, rbits2, times_pi); if (!arb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); arb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-sin_pi_series.c000066400000000000000000000057231264125401100203170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, bits1, bits2, bits3; arb_poly_t S, A, B, C; arb_t pi; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); arb_poly_init(S); arb_poly_init(A); arb_poly_init(B); arb_poly_init(C); arb_init(pi); arb_poly_randtest(S, state, m, bits1, 3); arb_poly_randtest(A, state, m, bits1, 3); arb_poly_randtest(B, state, m, bits1, 3); arb_poly_sin_pi_series(A, S, n1, bits2); arb_const_pi(pi, bits3); arb_poly_set_arb(B, pi); arb_poly_mul(B, S, B, bits3); arb_poly_sin_series(B, B, n2, bits3); arb_poly_set(C, A); arb_poly_truncate(C, FLINT_MIN(n1, n2)); arb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); arb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); arb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } arb_poly_sin_pi_series(S, S, n1, bits2); if (!arb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(S); arb_poly_clear(A); arb_poly_clear(B); arb_poly_clear(C); arb_clear(pi); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-sin_series_cos_series.c000066400000000000000000000066331264125401100220460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sin_series/cos_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b, c, d, e; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_sin_series(b, a, n, rbits2); arb_poly_cos_series(c, a, n, rbits2); /* Check sin(x)^2 + cos(x)^2 = 1 */ arb_poly_mullow(d, b, b, n, rbits2); arb_poly_mullow(e, c, c, n, rbits2); arb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!arb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_series(d, d, n, rbits2); if (!arb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, a); arb_poly_cos_series(d, d, n, rbits2); if (!arb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); arb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-sqrt_series.c000066400000000000000000000054671264125401100200340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); fmpq_poly_randtest_not_zero(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_sqrt_series(b, a, n, rbits2); /* Check sqrt(a)^2 = a */ arb_poly_mullow(c, b, b, n, rbits2); fmpq_poly_truncate(A, n); if (!arb_poly_contains_fmpq_poly(c, A)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_sqrt_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-sub.c000066400000000000000000000057161264125401100162570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("sub...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; arb_poly_t a, b, c; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); fmpq_poly_randtest(A, state, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_sub(C, A, B); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_sub(c, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-swinnerton_dyer_ui.c000066400000000000000000000052201264125401100214020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("swinnerton_dyer_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 50; iter++) { arb_poly_t a, b; arb_t x, y; fmpz_poly_t c; slong i, n, prec; arb_poly_init(a); arb_poly_init(b); fmpz_poly_init(c); arb_init(x); arb_init(y); n = n_randint(state, 10); arb_poly_swinnerton_dyer_ui(a, n, 0); prec = 2 + n_randint(state, 10000); if (!arb_poly_get_unique_fmpz_poly(c, a)) { flint_printf("FAIL (uniqueness)\n\n"); abort(); } arb_poly_set_fmpz_poly(b, c, prec); arb_zero(x); for (i = 0; i < n; i++) { arb_sqrt_ui(y, n_nth_prime(i + 1), prec); if (n_randint(state, 2)) arb_add(x, x, y, prec); else arb_sub(x, x, y, prec); } arb_poly_evaluate(y, b, x, prec); if (!arb_contains_zero(y)) { flint_printf("FAIL (containment)\n\n"); abort(); } arb_poly_swinnerton_dyer_ui(b, n, 2 + n_randint(state, 1000)); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (overlap)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); fmpz_poly_clear(c); arb_clear(x); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-tan_series.c000066400000000000000000000063111264125401100176120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("tan_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_poly_t a, b, c, d, e; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 50); n = 1 + n_randint(state, 50); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 50), rbits1, 5); arb_poly_tan_series(b, a, n, rbits2); /* check tan(x) = 2*tan(x/2)/(1-tan(x/2)^2) */ arb_poly_scalar_mul_2exp_si(c, a, -1); arb_poly_tan_series(c, c, n, rbits2); arb_poly_mullow(d, c, c, n, rbits2); arb_poly_one(e); arb_poly_sub(e, e, d, rbits2); arb_poly_div_series(c, c, e, n, rbits2); arb_poly_scalar_mul_2exp_si(c, c, 1); if (!arb_poly_overlaps(b, c)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_tan_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); arb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/test/t-zeta_series.c000066400000000000000000000102341264125401100177720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" int main() { slong iter; flint_rand_t state; flint_printf("zeta_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 500; iter++) { slong m, n1, n2, bits1, bits2, bits3; int deflate; arb_poly_t S, A, B, C, D, E, F; arb_t a, a1; bits1 = 2 + n_randint(state, 300); bits2 = 2 + n_randint(state, 300); bits3 = 2 + n_randint(state, 300); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); arb_poly_init(S); arb_poly_init(A); arb_poly_init(B); arb_poly_init(C); arb_poly_init(D); arb_poly_init(E); arb_poly_init(F); arb_init(a); arb_init(a1); deflate = n_randint(state, 2); arb_poly_randtest(S, state, m, bits1, 3); arb_randtest_precise(a, state, bits1, 3); arb_poly_set_coeff_arb(S, 0, a); if (n_randint(state, 2)) arb_randtest(a, state, bits1, 3); else arb_one(a); arb_poly_zeta_series(A, S, a, deflate, n1, bits2); arb_poly_zeta_series(B, S, a, deflate, n2, bits3); arb_poly_set(C, A); arb_poly_truncate(C, FLINT_MIN(n1, n2)); arb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(B, C)) { flint_printf("FAIL\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("A = "); arb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); arb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } /* check zeta(s,a) = zeta(s,a+1) + a^(-s) */ arb_poly_set_arb(D, a); arb_poly_log_series(D, D, n1, bits2); arb_poly_mullow(D, D, S, n1, bits2); arb_poly_neg(D, D); arb_poly_exp_series(D, D, n1, bits2); arb_add_ui(a1, a, 1, bits2); arb_poly_zeta_series(E, S, a1, deflate, n1, bits2); arb_poly_add(E, E, D, bits2); if (!arb_poly_overlaps(A, E)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("S = "); arb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("A = "); arb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("E = "); arb_poly_printd(A, 15); flint_printf("\n\n"); abort(); } arb_poly_zeta_series(S, S, a, deflate, n1, bits2); if (!arb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(S); arb_poly_clear(A); arb_poly_clear(B); arb_poly_clear(C); arb_poly_clear(D); arb_poly_clear(E); arb_poly_clear(F); arb_clear(a); arb_clear(a1); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arb_poly/tree.c000066400000000000000000000062701264125401100152010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" arb_ptr * _arb_poly_tree_alloc(slong len) { arb_ptr * tree = NULL; if (len) { slong i, height = FLINT_CLOG2(len); tree = flint_malloc(sizeof(arb_ptr) * (height + 1)); for (i = 0; i <= height; i++) tree[i] = _arb_vec_init(len + (len >> i) + 1); } return tree; } void _arb_poly_tree_free(arb_ptr * tree, slong len) { if (len) { slong i, height = FLINT_CLOG2(len); for (i = 0; i <= height; i++) _arb_vec_clear(tree[i], len + (len >> i) + 1); flint_free(tree); } } void _arb_poly_tree_build(arb_ptr * tree, arb_srcptr roots, slong len, slong prec) { slong height, pow, left, i; arb_ptr pa, pb; arb_srcptr a, b; if (len == 0) return; height = FLINT_CLOG2(len); /* zeroth level, (x-a) */ for (i = 0; i < len; i++) { arb_one(tree[0] + (2 * i + 1)); arb_neg(tree[0] + (2 * i), roots + i); } /* first level, (x-a)(x-b) = x^2 + (-a-b)*x + a*b */ if (height > 1) { pa = tree[1]; for (i = 0; i < len / 2; i++) { a = (arb_srcptr) (roots + (2 * i)); b = (arb_srcptr) (roots + (2 * i + 1)); arb_mul(pa + (3 * i), a, b, prec); arb_add(pa + (3 * i + 1), a, b, prec); arb_neg(pa + (3 * i + 1), pa + (3 * i + 1)); arb_one(pa + (3 * i + 2)); } if (len & 1) { arb_neg(pa + (3 * (len / 2)), roots + len - 1); arb_one(pa + (3 * (len / 2) + 1)); } } for (i = 1; i < height - 1; i++) { left = len; pow = WORD(1) << i; pa = tree[i]; pb = tree[i + 1]; while (left >= 2 * pow) { _arb_poly_mul_monic(pb, pa, pow + 1, pa + pow + 1, pow + 1, prec); left -= 2 * pow; pa += 2 * pow + 2; pb += 2 * pow + 1; } if (left > pow) { _arb_poly_mul_monic(pb, pa, pow + 1, pa + pow + 1, left - pow + 1, prec); } else if (left > 0) _arb_vec_set(pb, pa, left + 1); } } arb-2.8.1/arb_poly/zeta_series.c000066400000000000000000000124121264125401100165520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arb_poly.h" #include "acb_poly.h" static __inline__ void _arb_vec_printd(arb_srcptr vec, slong len, slong digits) { slong i; for (i = 0; i < len; i++) arb_printd(vec + i, digits), flint_printf("\n"); } /* series of c^(d+x) */ static __inline__ void _arb_poly_pow_cpx(arb_ptr res, const arb_t c, const arb_t d, slong trunc, slong prec) { slong i; arb_t logc; arb_init(logc); arb_log(logc, c, prec); arb_mul(res + 0, logc, d, prec); arb_exp(res + 0, res + 0, prec); for (i = 1; i < trunc; i++) { arb_mul(res + i, res + i - 1, logc, prec); arb_div_ui(res + i, res + i, i, prec); } arb_clear(logc); } void _arb_poly_zeta_series(arb_ptr res, arb_srcptr h, slong hlen, const arb_t a, int deflate, slong len, slong prec) { slong i; acb_t cs, ca; acb_ptr z; arb_ptr t, u; if (arb_contains_nonpositive(a)) { _arb_vec_indeterminate(res, len); return; } hlen = FLINT_MIN(hlen, len); z = _acb_vec_init(len); t = _arb_vec_init(len); u = _arb_vec_init(len); acb_init(cs); acb_init(ca); /* use reflection formula */ if (arf_sgn(arb_midref(h)) < 0 && arb_is_one(a)) { /* zeta(s) = (2*pi)**s * sin(pi*s/2) / pi * gamma(1-s) * zeta(1-s) */ arb_t pi; arb_ptr f, s1, s2, s3, s4; arb_init(pi); f = _arb_vec_init(2); s1 = _arb_vec_init(len); s2 = _arb_vec_init(len); s3 = _arb_vec_init(len); s4 = _arb_vec_init(len); arb_const_pi(pi, prec); /* s1 = (2*pi)**s */ arb_mul_2exp_si(pi, pi, 1); _arb_poly_pow_cpx(s1, pi, h, len, prec); arb_mul_2exp_si(pi, pi, -1); /* s2 = sin(pi*s/2) / pi */ arb_set(f, h); arb_one(f + 1); arb_mul_2exp_si(f, f, -1); arb_mul_2exp_si(f + 1, f + 1, -1); _arb_poly_sin_pi_series(s2, f, 2, len, prec); _arb_vec_scalar_div(s2, s2, len, pi, prec); /* s3 = gamma(1-s) */ arb_sub_ui(f, h, 1, prec); arb_neg(f, f); arb_set_si(f + 1, -1); _arb_poly_gamma_series(s3, f, 2, len, prec); /* s4 = zeta(1-s) */ arb_sub_ui(f, h, 1, prec); arb_neg(f, f); acb_set_arb(cs, f); acb_one(ca); _acb_poly_zeta_cpx_series(z, cs, ca, 0, len, prec); for (i = 0; i < len; i++) arb_set(s4 + i, acb_realref(z + i)); for (i = 1; i < len; i += 2) arb_neg(s4 + i, s4 + i); _arb_poly_mullow(u, s1, len, s2, len, len, prec); _arb_poly_mullow(s1, s3, len, s4, len, len, prec); _arb_poly_mullow(t, u, len, s1, len, len, prec); /* add 1/(1-(s+t)) = 1/(1-s) + t/(1-s)^2 + ... */ if (deflate) { arb_sub_ui(u, h, 1, prec); arb_neg(u, u); arb_inv(u, u, prec); for (i = 1; i < len; i++) arb_mul(u + i, u + i - 1, u, prec); _arb_vec_add(t, t, u, len, prec); } arb_clear(pi); _arb_vec_clear(f, 2); _arb_vec_clear(s1, len); _arb_vec_clear(s2, len); _arb_vec_clear(s3, len); _arb_vec_clear(s4, len); } else { acb_set_arb(cs, h); acb_set_arb(ca, a); _acb_poly_zeta_cpx_series(z, cs, ca, deflate, len, prec); for (i = 0; i < len; i++) arb_set(t + i, acb_realref(z + i)); } /* compose with nonconstant part */ arb_zero(u); _arb_vec_set(u + 1, h + 1, hlen - 1); _arb_poly_compose_series(res, t, len, u, hlen, len, prec); _acb_vec_clear(z, len); _arb_vec_clear(t, len); _arb_vec_clear(u, len); acb_init(cs); acb_init(ca); } void arb_poly_zeta_series(arb_poly_t res, const arb_poly_t f, const arb_t a, int deflate, slong n, slong prec) { if (n == 0) { arb_poly_zero(res); return; } arb_poly_fit_length(res, n); if (f->length == 0) { arb_t t; arb_init(t); _arb_poly_zeta_series(res->coeffs, t, 1, a, deflate, n, prec); arb_clear(t); } else { _arb_poly_zeta_series(res->coeffs, f->coeffs, f->length, a, deflate, n, prec); } _arb_poly_set_length(res, n); _arb_poly_normalise(res); } arb-2.8.1/arf.h000066400000000000000000000777211264125401100132210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson 2x2 mul code taken from MPFR 2.3.0 (Copyright (C) 1991-2007 Free Software Foundation, Inc.) ******************************************************************************/ #ifndef ARF_H #define ARF_H #ifdef ARF_INLINES_C #define ARF_INLINE #else #define ARF_INLINE static __inline__ #endif #include #include "flint.h" #include "fmpr.h" #include "mag.h" #ifdef __cplusplus extern "C" { #endif #define arf_rnd_t fmpr_rnd_t #define ARF_RND_DOWN FMPR_RND_DOWN #define ARF_RND_UP FMPR_RND_UP #define ARF_RND_FLOOR FMPR_RND_FLOOR #define ARF_RND_CEIL FMPR_RND_CEIL #define ARF_RND_NEAR FMPR_RND_NEAR ARF_INLINE int arf_rounds_down(arf_rnd_t rnd, int sgnbit) { if (rnd == ARF_RND_DOWN) return 1; if (rnd == ARF_RND_UP) return 0; if (rnd == ARF_RND_FLOOR) return !sgnbit; return sgnbit; } ARF_INLINE int arf_rounds_up(arf_rnd_t rnd, int sgnbit) { if (rnd == ARF_RND_DOWN) return 0; if (rnd == ARF_RND_UP) return 1; if (rnd == ARF_RND_FLOOR) return sgnbit; return !sgnbit; } ARF_INLINE mpfr_rnd_t arf_rnd_to_mpfr(arf_rnd_t rnd) { if (rnd == ARF_RND_DOWN) return MPFR_RNDZ; else if (rnd == ARF_RND_UP) return MPFR_RNDA; else if (rnd == ARF_RND_FLOOR) return MPFR_RNDD; else if (rnd == ARF_RND_CEIL) return MPFR_RNDU; else return MPFR_RNDN; } /* Allow 'infinite' precision for operations where a result can be computed exactly. */ #define ARF_PREC_EXACT WORD_MAX #define ARF_PREC_ADD(prec,extra) ((prec) == ARF_PREC_EXACT ? ARF_PREC_EXACT : (prec) + (extra)) #define ARF_RESULT_EXACT 0 #define ARF_RESULT_INEXACT 1 /* Range where we can skip fmpz overflow checks for exponent manipulation. */ #define ARF_MAX_LAGOM_EXP MAG_MAX_LAGOM_EXP #define ARF_MIN_LAGOM_EXP MAG_MIN_LAGOM_EXP /* Exponent values used to encode special values. */ #define ARF_EXP_ZERO 0 #define ARF_EXP_NAN COEFF_MIN #define ARF_EXP_POS_INF (COEFF_MIN+1) #define ARF_EXP_NEG_INF (COEFF_MIN+2) /* Direct access to the exponent. */ #define ARF_EXP(x) ((x)->exp) #define ARF_EXPREF(x) (&(x)->exp) /* Finite and with lagom big exponents. */ #define ARF_IS_LAGOM(x) (ARF_EXP(x) >= ARF_MIN_LAGOM_EXP && \ ARF_EXP(x) <= ARF_MAX_LAGOM_EXP) /* More than two limbs (needs pointer). */ #define ARF_HAS_PTR(x) ((x)->size > ((2 << 1) + 1)) /* Raw size field (encodes both limb size and sign). */ #define ARF_XSIZE(x) ((x)->size) /* Construct size field value from size in limbs and sign bit. */ #define ARF_MAKE_XSIZE(size, sgnbit) ((((mp_size_t) size) << 1) | sgnbit) /* The limb size, and the sign bit. */ #define ARF_SIZE(x) (ARF_XSIZE(x) >> 1) #define ARF_SGNBIT(x) (ARF_XSIZE(x) & 1) /* Assumes non-special value */ #define ARF_NEG(x) (ARF_XSIZE(x) ^= 1) /* Note: may also be hardcoded in a few places. */ #define ARF_NOPTR_LIMBS 2 /* Direct access to the limb data. */ #define ARF_NOPTR_D(x) ((x)->d.noptr.d) #define ARF_PTR_D(x) ((x)->d.ptr.d) #define ARF_PTR_ALLOC(x) ((x)->d.ptr.alloc) /* Encoding for special values. */ #define ARF_IS_SPECIAL(x) (ARF_XSIZE(x) == 0) /* Value is +/- a power of two */ #define ARF_IS_POW2(x) (ARF_SIZE(x) == 1) && (ARF_NOPTR_D(x)[0] == LIMB_TOP) /* To set a special value, first call this and then set the exponent. */ #define ARF_MAKE_SPECIAL(x) \ do { \ fmpz_clear(ARF_EXPREF(x)); \ ARF_DEMOTE(x); \ ARF_XSIZE(x) = 0; \ } while (0) typedef struct { mp_limb_t d[ARF_NOPTR_LIMBS]; } mantissa_noptr_struct; typedef struct { mp_size_t alloc; mp_ptr d; } mantissa_ptr_struct; typedef union { mantissa_noptr_struct noptr; mantissa_ptr_struct ptr; } mantissa_struct; typedef struct { fmpz exp; mp_size_t size; mantissa_struct d; } arf_struct; typedef arf_struct arf_t[1]; typedef arf_struct * arf_ptr; typedef const arf_struct * arf_srcptr; void _arf_promote(arf_t x, mp_size_t n); void _arf_demote(arf_t x); /* Warning: does not set size! -- also doesn't demote exponent. */ #define ARF_DEMOTE(x) \ do { \ if (ARF_HAS_PTR(x)) \ _arf_demote(x); \ } while (0) /* Get mpn pointer and size (xptr, xn) for read-only use. */ #define ARF_GET_MPN_READONLY(xptr, xn, x) \ do { \ xn = ARF_SIZE(x); \ if (xn <= ARF_NOPTR_LIMBS) \ xptr = ARF_NOPTR_D(x); \ else \ xptr = ARF_PTR_D(x); \ } while (0) /* Assumes non-special! */ #define ARF_GET_TOP_LIMB(lmb, x) \ do { \ mp_srcptr __xptr; \ mp_size_t __xn; \ ARF_GET_MPN_READONLY(__xptr, __xn, (x)); \ (lmb) = __xptr[__xn - 1]; \ } while (0) /* Get mpn pointer xptr for writing *exactly* xn limbs to x. */ #define ARF_GET_MPN_WRITE(xptr, xn, x) \ do { \ mp_size_t __xn = (xn); \ if ((__xn) <= ARF_NOPTR_LIMBS) \ { \ ARF_DEMOTE(x); \ xptr = ARF_NOPTR_D(x); \ } \ else \ { \ if (!ARF_HAS_PTR(x)) \ { \ _arf_promote(x, __xn); \ } \ else if (ARF_PTR_ALLOC(x) < (__xn)) \ { \ ARF_PTR_D(x) = (mp_ptr) \ flint_realloc(ARF_PTR_D(x), \ (xn) * sizeof(mp_limb_t)); \ ARF_PTR_ALLOC(x) = (__xn); \ } \ xptr = ARF_PTR_D(x); \ } \ ARF_XSIZE(x) = ARF_MAKE_XSIZE(__xn, 0); \ } while (0) ARF_INLINE void arf_init(arf_t x) { fmpz_init(ARF_EXPREF(x)); ARF_XSIZE(x) = 0; } ARF_INLINE void arf_clear(arf_t x) { fmpz_clear(ARF_EXPREF(x)); ARF_DEMOTE(x); } ARF_INLINE void arf_zero(arf_t x) { ARF_MAKE_SPECIAL(x); ARF_EXP(x) = ARF_EXP_ZERO; } ARF_INLINE void arf_pos_inf(arf_t x) { ARF_MAKE_SPECIAL(x); ARF_EXP(x) = ARF_EXP_POS_INF; } ARF_INLINE void arf_neg_inf(arf_t x) { ARF_MAKE_SPECIAL(x); ARF_EXP(x) = ARF_EXP_NEG_INF; } ARF_INLINE void arf_nan(arf_t x) { ARF_MAKE_SPECIAL(x); ARF_EXP(x) = ARF_EXP_NAN; } ARF_INLINE int arf_is_special(const arf_t x) { return ARF_IS_SPECIAL(x); } ARF_INLINE int arf_is_zero(const arf_t x) { return ARF_IS_SPECIAL(x) && (ARF_EXP(x) == ARF_EXP_ZERO); } ARF_INLINE int arf_is_pos_inf(const arf_t x) { return ARF_IS_SPECIAL(x) && (ARF_EXP(x) == ARF_EXP_POS_INF); } ARF_INLINE int arf_is_neg_inf(const arf_t x) { return ARF_IS_SPECIAL(x) && (ARF_EXP(x) == ARF_EXP_NEG_INF); } ARF_INLINE int arf_is_nan(const arf_t x) { return ARF_IS_SPECIAL(x) && (ARF_EXP(x) == ARF_EXP_NAN); } ARF_INLINE int arf_is_normal(const arf_t x) { return !ARF_IS_SPECIAL(x); } ARF_INLINE int arf_is_finite(const arf_t x) { return !ARF_IS_SPECIAL(x) || (ARF_EXP(x) == ARF_EXP_ZERO); } ARF_INLINE int arf_is_inf(const arf_t x) { return ARF_IS_SPECIAL(x) && (ARF_EXP(x) == ARF_EXP_POS_INF || ARF_EXP(x) == ARF_EXP_NEG_INF); } ARF_INLINE void arf_one(arf_t x) { fmpz_clear(ARF_EXPREF(x)); ARF_DEMOTE(x); ARF_EXP(x) = 1; ARF_XSIZE(x) = ARF_MAKE_XSIZE(1, 0); ARF_NOPTR_D(x)[0] = LIMB_TOP; } ARF_INLINE int arf_is_one(const arf_t x) { return (ARF_EXP(x) == 1) && (ARF_XSIZE(x) == ARF_MAKE_XSIZE(1, 0)) && ARF_NOPTR_D(x)[0] == LIMB_TOP; } ARF_INLINE int arf_sgn(const arf_t x) { if (arf_is_special(x)) { if (arf_is_zero(x) || arf_is_nan(x)) return 0; return arf_is_pos_inf(x) ? 1 : -1; } else { return ARF_SGNBIT(x) ? -1 : 1; } } int arf_cmp(const arf_t x, const arf_t y); int arf_cmpabs(const arf_t x, const arf_t y); ARF_INLINE void arf_swap(arf_t y, arf_t x) { if (x != y) { arf_struct t = *x; *x = *y; *y = t; } } ARF_INLINE void arf_set(arf_t y, const arf_t x) { if (x != y) { /* Fast path */ if (!COEFF_IS_MPZ(ARF_EXP(x)) && !COEFF_IS_MPZ(ARF_EXP(y))) ARF_EXP(y) = ARF_EXP(x); else fmpz_set(ARF_EXPREF(y), ARF_EXPREF(x)); /* Fast path */ if (!ARF_HAS_PTR(x)) { ARF_DEMOTE(y); (y)->d = (x)->d; } else { mp_ptr yptr; mp_srcptr xptr; mp_size_t n; ARF_GET_MPN_READONLY(xptr, n, x); ARF_GET_MPN_WRITE(yptr, n, y); flint_mpn_copyi(yptr, xptr, n); } /* Important. */ ARF_XSIZE(y) = ARF_XSIZE(x); } } ARF_INLINE void arf_neg(arf_t y, const arf_t x) { arf_set(y, x); if (arf_is_special(y)) { if (arf_is_pos_inf(y)) arf_neg_inf(y); else if (arf_is_neg_inf(y)) arf_pos_inf(y); } else { ARF_NEG(y); } } ARF_INLINE void arf_init_set_ui(arf_t x, ulong v) { if (v == 0) { ARF_EXP(x) = ARF_EXP_ZERO; ARF_XSIZE(x) = 0; } else { unsigned int c; count_leading_zeros(c, v); ARF_EXP(x) = FLINT_BITS - c; ARF_NOPTR_D(x)[0] = v << c; ARF_XSIZE(x) = ARF_MAKE_XSIZE(1, 0); } } ARF_INLINE void arf_init_set_si(arf_t x, slong v) { arf_init_set_ui(x, FLINT_ABS(v)); if (v < 0) ARF_NEG(x); } ARF_INLINE void arf_set_ui(arf_t x, ulong v) { ARF_DEMOTE(x); _fmpz_demote(ARF_EXPREF(x)); if (v == 0) { ARF_EXP(x) = ARF_EXP_ZERO; ARF_XSIZE(x) = 0; } else { unsigned int c; count_leading_zeros(c, v); ARF_EXP(x) = FLINT_BITS - c; ARF_NOPTR_D(x)[0] = v << c; ARF_XSIZE(x) = ARF_MAKE_XSIZE(1, 0); } } ARF_INLINE void arf_set_si(arf_t x, slong v) { arf_set_ui(x, FLINT_ABS(v)); if (v < 0) ARF_NEG(x); } ARF_INLINE int arf_cmpabs_ui(const arf_t x, ulong y) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ return arf_cmpabs(x, t); } ARF_INLINE void arf_init_set_shallow(arf_t z, const arf_t x) { *z = *x; } ARF_INLINE void arf_init_neg_shallow(arf_t z, const arf_t x) { *z = *x; arf_neg(z, z); } ARF_INLINE void arf_init_set_mag_shallow(arf_t y, const mag_t x) { mp_limb_t t = MAG_MAN(x); ARF_XSIZE(y) = ARF_MAKE_XSIZE(t != 0, 0); ARF_EXP(y) = MAG_EXP(x); ARF_NOPTR_D(y)[0] = t << (FLINT_BITS - MAG_BITS); } ARF_INLINE void arf_init_neg_mag_shallow(arf_t z, const mag_t x) { arf_init_set_mag_shallow(z, x); arf_neg(z, z); } ARF_INLINE int arf_cmpabs_mag(const arf_t x, const mag_t y) { arf_t t; arf_init_set_mag_shallow(t, y); /* no need to free */ return arf_cmpabs(x, t); } ARF_INLINE int arf_mag_cmpabs(const mag_t x, const arf_t y) { arf_t t; arf_init_set_mag_shallow(t, x); /* no need to free */ return arf_cmpabs(t, y); } /* Assumes xn > 0, x[xn-1] != 0. */ /* TBD: 1, 2 limb versions */ void arf_set_mpn(arf_t y, mp_srcptr x, mp_size_t xn, int sgnbit); ARF_INLINE void arf_set_mpz(arf_t y, const mpz_t x) { slong size = x->_mp_size; if (size == 0) arf_zero(y); else arf_set_mpn(y, x->_mp_d, FLINT_ABS(size), size < 0); } ARF_INLINE void arf_set_fmpz(arf_t y, const fmpz_t x) { if (!COEFF_IS_MPZ(*x)) arf_set_si(y, *x); else arf_set_mpz(y, COEFF_TO_PTR(*x)); } int _arf_set_round_ui(arf_t x, ulong v, int sgnbit, slong prec, arf_rnd_t rnd); /* TODO: document */ int _arf_set_round_uiui(arf_t z, slong * fix, mp_limb_t hi, mp_limb_t lo, int sgnbit, slong prec, arf_rnd_t rnd); /* Assumes xn > 0, x[xn-1] != 0. */ int _arf_set_round_mpn(arf_t y, slong * exp_shift, mp_srcptr x, mp_size_t xn, int sgnbit, slong prec, arf_rnd_t rnd); ARF_INLINE int arf_set_round_ui(arf_t x, ulong v, slong prec, arf_rnd_t rnd) { return _arf_set_round_ui(x, v, 0, prec, rnd); } ARF_INLINE int arf_set_round_si(arf_t x, slong v, slong prec, arf_rnd_t rnd) { return _arf_set_round_ui(x, FLINT_ABS(v), v < 0, prec, rnd); } ARF_INLINE int arf_set_round_mpz(arf_t y, const mpz_t x, slong prec, arf_rnd_t rnd) { int inexact; slong size = x->_mp_size; slong fix; if (size == 0) { arf_zero(y); return 0; } inexact = _arf_set_round_mpn(y, &fix, x->_mp_d, FLINT_ABS(size), (size < 0), prec, rnd); _fmpz_demote(ARF_EXPREF(y)); ARF_EXP(y) = FLINT_ABS(size) * FLINT_BITS + fix; return inexact; } ARF_INLINE int arf_set_round_fmpz(arf_t y, const fmpz_t x, slong prec, arf_rnd_t rnd) { if (!COEFF_IS_MPZ(*x)) return arf_set_round_si(y, *x, prec, rnd); else return arf_set_round_mpz(y, COEFF_TO_PTR(*x), prec, rnd); } int arf_set_round(arf_t y, const arf_t x, slong prec, arf_rnd_t rnd); int arf_neg_round(arf_t y, const arf_t x, slong prec, arf_rnd_t rnd); void arf_get_fmpr(fmpr_t y, const arf_t x); void arf_set_fmpr(arf_t y, const fmpr_t x); int arf_get_mpfr(mpfr_t x, const arf_t y, mpfr_rnd_t rnd); void arf_set_mpfr(arf_t x, const mpfr_t y); int arf_equal(const arf_t x, const arf_t y); int arf_equal_si(const arf_t x, slong y); ARF_INLINE void arf_min(arf_t z, const arf_t a, const arf_t b) { if (arf_cmp(a, b) <= 0) arf_set(z, a); else arf_set(z, b); } ARF_INLINE void arf_max(arf_t z, const arf_t a, const arf_t b) { if (arf_cmp(a, b) > 0) arf_set(z, a); else arf_set(z, b); } ARF_INLINE void arf_abs(arf_t y, const arf_t x) { if (arf_sgn(x) < 0) arf_neg(y, x); else arf_set(y, x); } ARF_INLINE slong arf_bits(const arf_t x) { if (arf_is_special(x)) return 0; else { mp_srcptr xp; mp_size_t xn; slong c; ARF_GET_MPN_READONLY(xp, xn, x); count_trailing_zeros(c, xp[0]); return xn * FLINT_BITS - c; } } ARF_INLINE void arf_bot(fmpz_t e, const arf_t x) { if (arf_is_special(x)) fmpz_zero(e); else fmpz_sub_si(e, ARF_EXPREF(x), arf_bits(x)); } ARF_INLINE int arf_is_int(const arf_t x) { if (arf_is_special(x)) return arf_is_zero(x); else { fmpz_t t; int r; fmpz_init(t); arf_bot(t, x); r = fmpz_sgn(t) >= 0; fmpz_clear(t); return r; } } ARF_INLINE int arf_is_int_2exp_si(const arf_t x, slong e) { if (arf_is_special(x)) return arf_is_zero(x); else { fmpz_t t; int r; fmpz_init(t); arf_bot(t, x); r = fmpz_cmp_si(t, e) >= 0; fmpz_clear(t); return r; } } int arf_cmp_2exp_si(const arf_t x, slong e); int arf_cmpabs_2exp_si(const arf_t x, slong e); ARF_INLINE void arf_set_si_2exp_si(arf_t x, slong man, slong exp) { arf_set_si(x, man); if (man != 0) fmpz_add_si_inline(ARF_EXPREF(x), ARF_EXPREF(x), exp); } ARF_INLINE void arf_set_ui_2exp_si(arf_t x, ulong man, slong exp) { arf_set_ui(x, man); if (man != 0) fmpz_add_si_inline(ARF_EXPREF(x), ARF_EXPREF(x), exp); } ARF_INLINE void arf_mul_2exp_si(arf_t y, const arf_t x, slong e) { arf_set(y, x); if (!arf_is_special(y)) fmpz_add_si_inline(ARF_EXPREF(y), ARF_EXPREF(y), e); } ARF_INLINE void arf_mul_2exp_fmpz(arf_t y, const arf_t x, const fmpz_t e) { arf_set(y, x); if (!arf_is_special(y)) fmpz_add_inline(ARF_EXPREF(y), ARF_EXPREF(y), e); } ARF_INLINE int arf_set_round_fmpz_2exp(arf_t y, const fmpz_t x, const fmpz_t exp, slong prec, arf_rnd_t rnd) { if (fmpz_is_zero(x)) { arf_zero(y); return 0; } else { int r = arf_set_round_fmpz(y, x, prec, rnd); fmpz_add_inline(ARF_EXPREF(y), ARF_EXPREF(y), exp); return r; } } ARF_INLINE void arf_abs_bound_lt_2exp_fmpz(fmpz_t b, const arf_t x) { if (arf_is_special(x)) fmpz_zero(b); else fmpz_set(b, ARF_EXPREF(x)); } ARF_INLINE void arf_abs_bound_le_2exp_fmpz(fmpz_t b, const arf_t x) { if (arf_is_special(x)) fmpz_zero(b); else if (ARF_IS_POW2(x)) fmpz_sub_ui(b, ARF_EXPREF(x), 1); else fmpz_set(b, ARF_EXPREF(x)); } slong arf_abs_bound_lt_2exp_si(const arf_t x); void arf_get_fmpz_2exp(fmpz_t man, fmpz_t exp, const arf_t x); void arf_get_fmpz(fmpz_t z, const arf_t x, arf_rnd_t rnd); slong arf_get_si(const arf_t x, arf_rnd_t rnd); ARF_INLINE int arf_get_fmpz_fixed_fmpz(fmpz_t y, const arf_t x, const fmpz_t e) { int r; fmpr_t t; fmpr_init(t); arf_get_fmpr(t, x); r = fmpr_get_fmpz_fixed_fmpz(y, t, e); fmpr_clear(t); return r; } ARF_INLINE int arf_get_fmpz_fixed_si(fmpz_t y, const arf_t x, slong e) { int r; fmpr_t t; fmpr_init(t); arf_get_fmpr(t, x); r = fmpr_get_fmpz_fixed_si(y, t, e); fmpr_clear(t); return r; } ARF_INLINE void arf_set_fmpz_2exp(arf_t x, const fmpz_t man, const fmpz_t exp) { arf_set_fmpz(x, man); if (!arf_is_zero(x)) fmpz_add_inline(ARF_EXPREF(x), ARF_EXPREF(x), exp); } void arf_floor(arf_t z, const arf_t x); void arf_ceil(arf_t z, const arf_t x); void arf_debug(const arf_t x); void arf_print(const arf_t x); void arf_printd(const arf_t y, slong d); void arf_randtest(arf_t x, flint_rand_t state, slong bits, slong mag_bits); void arf_randtest_not_zero(arf_t x, flint_rand_t state, slong bits, slong mag_bits); void arf_randtest_special(arf_t x, flint_rand_t state, slong bits, slong mag_bits); #define MUL_MPFR_MIN_LIMBS 25 #define MUL_MPFR_MAX_LIMBS 10000 #define nn_mul_2x1(r2, r1, r0, a1, a0, b0) \ do { \ mp_limb_t t1; \ umul_ppmm(r1, r0, a0, b0); \ umul_ppmm(r2, t1, a1, b0); \ add_ssaaaa(r2, r1, r2, r1, 0, t1); \ } while (0) #define nn_mul_2x2(r3, r2, r1, r0, a1, a0, b1, b0) \ do { \ mp_limb_t t1, t2, t3; \ umul_ppmm(r1, r0, a0, b0); \ umul_ppmm(r2, t1, a1, b0); \ add_ssaaaa(r2, r1, r2, r1, 0, t1); \ umul_ppmm(t1, t2, a0, b1); \ umul_ppmm(r3, t3, a1, b1); \ add_ssaaaa(r3, t1, r3, t1, 0, t3); \ add_ssaaaa(r2, r1, r2, r1, t1, t2); \ r3 += r2 < t1; \ } while (0) #define ARF_MPN_MUL(_z, _x, _xn, _y, _yn) \ if ((_xn) == (_yn)) \ { \ if ((_xn) == 1) \ { \ umul_ppmm((_z)[1], (_z)[0], (_x)[0], (_y)[0]); \ } \ else if ((_xn) == 2) \ { \ mp_limb_t __arb_x1, __arb_x0, __arb_y1, __arb_y0; \ __arb_x0 = (_x)[0]; \ __arb_x1 = (_x)[1]; \ __arb_y0 = (_y)[0]; \ __arb_y1 = (_y)[1]; \ nn_mul_2x2((_z)[3], (_z)[2], (_z)[1], (_z)[0], __arb_x1, __arb_x0, __arb_y1, __arb_y0); \ } \ else if ((_x) == (_y)) \ { \ mpn_sqr((_z), (_x), (_xn)); \ } \ else \ { \ mpn_mul_n((_z), (_x), (_y), (_xn)); \ } \ } \ else if ((_xn) > (_yn)) \ { \ if ((_yn) == 1) \ (_z)[(_xn) + (_yn) - 1] = mpn_mul_1((_z), (_x), (_xn), (_y)[0]); \ else \ mpn_mul((_z), (_x), (_xn), (_y), (_yn)); \ } \ else \ { \ if ((_xn) == 1) \ (_z)[(_xn) + (_yn) - 1] = mpn_mul_1((_z), (_y), (_yn), (_x)[0]); \ else \ mpn_mul((_z), (_y), (_yn), (_x), (_xn)); \ } #define ARF_MUL_STACK_ALLOC 40 #define ARF_MUL_TLS_ALLOC 1000 extern TLS_PREFIX mp_ptr __arf_mul_tmp; extern TLS_PREFIX slong __arf_mul_alloc; extern void _arf_mul_tmp_cleanup(void); #define ARF_MUL_TMP_DECL \ mp_limb_t tmp_stack[ARF_MUL_STACK_ALLOC]; \ #define ARF_MUL_TMP_ALLOC(tmp, alloc) \ if (alloc <= ARF_MUL_STACK_ALLOC) \ { \ tmp = tmp_stack; \ } \ else if (alloc <= ARF_MUL_TLS_ALLOC) \ { \ if (__arf_mul_alloc < alloc) \ { \ if (__arf_mul_alloc == 0) \ { \ flint_register_cleanup_function(_arf_mul_tmp_cleanup); \ } \ __arf_mul_tmp = flint_realloc(__arf_mul_tmp, sizeof(mp_limb_t) * alloc); \ __arf_mul_alloc = alloc; \ } \ tmp = __arf_mul_tmp; \ } \ else \ { \ tmp = flint_malloc(sizeof(mp_limb_t) * alloc); \ } #define ARF_MUL_TMP_FREE(tmp, alloc) \ if (alloc > ARF_MUL_TLS_ALLOC) \ flint_free(tmp); void arf_mul_special(arf_t z, const arf_t x, const arf_t y); int arf_mul_via_mpfr(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd); int arf_mul_rnd_any(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd); int arf_mul_rnd_down(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec); #define arf_mul(z, x, y, prec, rnd) \ ((rnd == FMPR_RND_DOWN) \ ? arf_mul_rnd_down(z, x, y, prec) \ : arf_mul_rnd_any(z, x, y, prec, rnd)) ARF_INLINE int arf_neg_mul(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { if (arf_is_special(y)) { arf_mul(z, x, y, prec, rnd); arf_neg(z, z); return 0; } else { arf_t t; *t = *y; ARF_NEG(t); return arf_mul(z, x, t, prec, rnd); } } ARF_INLINE int arf_mul_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ return arf_mul(z, x, t, prec, rnd); } ARF_INLINE int arf_mul_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_si(t, y); /* no need to free */ return arf_mul(z, x, t, prec, rnd); } int arf_mul_mpz(arf_ptr z, arf_srcptr x, const mpz_t y, slong prec, arf_rnd_t rnd); ARF_INLINE int arf_mul_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd) { if (!COEFF_IS_MPZ(*y)) return arf_mul_si(z, x, *y, prec, rnd); else return arf_mul_mpz(z, x, COEFF_TO_PTR(*y), prec, rnd); } #define ARF_ADD_STACK_ALLOC 40 #define ARF_ADD_TLS_ALLOC 1000 extern TLS_PREFIX mp_ptr __arf_add_tmp; extern TLS_PREFIX slong __arf_add_alloc; extern void _arf_add_tmp_cleanup(void); #define ARF_ADD_TMP_DECL \ mp_limb_t tmp_stack[ARF_ADD_STACK_ALLOC]; \ #define ARF_ADD_TMP_ALLOC(tmp, alloc) \ if (alloc <= ARF_ADD_STACK_ALLOC) \ { \ tmp = tmp_stack; \ } \ else if (alloc <= ARF_ADD_TLS_ALLOC) \ { \ if (__arf_add_alloc < alloc) \ { \ if (__arf_add_alloc == 0) \ { \ flint_register_cleanup_function(_arf_add_tmp_cleanup); \ } \ __arf_add_tmp = flint_realloc(__arf_add_tmp, sizeof(mp_limb_t) * alloc); \ __arf_add_alloc = alloc; \ } \ tmp = __arf_add_tmp; \ } \ else \ { \ tmp = flint_malloc(sizeof(mp_limb_t) * alloc); \ } #define ARF_ADD_TMP_FREE(tmp, alloc) \ if (alloc > ARF_ADD_TLS_ALLOC) \ flint_free(tmp); int _arf_add_mpn(arf_t z, mp_srcptr xp, mp_size_t xn, int xsgnbit, const fmpz_t xexp, mp_srcptr yp, mp_size_t yn, int ysgnbit, mp_bitcnt_t shift, slong prec, arf_rnd_t rnd); int arf_add(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd); int arf_add_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd); int arf_add_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd); int arf_add_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd); int arf_add_fmpz_2exp(arf_ptr z, arf_srcptr x, const fmpz_t y, const fmpz_t exp, slong prec, arf_rnd_t rnd); int arf_sub(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd); int arf_sub_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd); int arf_sub_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd); int arf_sub_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd); int arf_addmul(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd); ARF_INLINE int arf_addmul_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ return arf_addmul(z, x, t, prec, rnd); } ARF_INLINE int arf_addmul_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_si(t, y); /* no need to free */ return arf_addmul(z, x, t, prec, rnd); } int arf_addmul_mpz(arf_ptr z, arf_srcptr x, const mpz_t y, slong prec, arf_rnd_t rnd); ARF_INLINE int arf_addmul_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd) { if (!COEFF_IS_MPZ(*y)) return arf_addmul_si(z, x, *y, prec, rnd); else return arf_addmul_mpz(z, x, COEFF_TO_PTR(*y), prec, rnd); } int arf_submul(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd); ARF_INLINE int arf_submul_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ return arf_submul(z, x, t, prec, rnd); } ARF_INLINE int arf_submul_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_si(t, y); /* no need to free */ return arf_submul(z, x, t, prec, rnd); } int arf_submul_mpz(arf_ptr z, arf_srcptr x, const mpz_t y, slong prec, arf_rnd_t rnd); ARF_INLINE int arf_submul_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd) { if (!COEFF_IS_MPZ(*y)) return arf_submul_si(z, x, *y, prec, rnd); else return arf_submul_mpz(z, x, COEFF_TO_PTR(*y), prec, rnd); } int arf_div(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd); ARF_INLINE int arf_div_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_ui(t, y); /* no need to free */ return arf_div(z, x, t, prec, rnd); } ARF_INLINE int arf_ui_div(arf_ptr z, ulong x, arf_srcptr y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_ui(t, x); /* no need to free */ return arf_div(z, t, y, prec, rnd); } ARF_INLINE int arf_div_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_si(t, y); /* no need to free */ return arf_div(z, x, t, prec, rnd); } ARF_INLINE int arf_si_div(arf_ptr z, slong x, arf_srcptr y, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_si(t, x); /* no need to free */ return arf_div(z, t, y, prec, rnd); } ARF_INLINE int arf_div_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz(t, y); r = arf_div(z, x, t, prec, rnd); arf_clear(t); return r; } ARF_INLINE int arf_fmpz_div(arf_ptr z, const fmpz_t x, arf_srcptr y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz(t, x); r = arf_div(z, t, y, prec, rnd); arf_clear(t); return r; } ARF_INLINE int arf_fmpz_div_fmpz(arf_ptr z, const fmpz_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t, u; int r; arf_init(t); arf_init(u); arf_set_fmpz(t, x); arf_set_fmpz(u, y); r = arf_div(z, t, u, prec, rnd); arf_clear(t); arf_clear(u); return r; } int arf_sqrt(arf_ptr z, arf_srcptr x, slong prec, arf_rnd_t rnd); int arf_sqrt_ui(arf_t z, ulong x, slong prec, arf_rnd_t rnd); int arf_sqrt_fmpz(arf_t z, const fmpz_t x, slong prec, arf_rnd_t rnd); int arf_rsqrt(arf_ptr z, arf_srcptr x, slong prec, arf_rnd_t rnd); int arf_root(arf_t z, const arf_t x, ulong k, slong prec, arf_rnd_t rnd); /* Magnitude bounds */ void arf_get_mag(mag_t y, const arf_t x); void arf_get_mag_lower(mag_t y, const arf_t x); ARF_INLINE void arf_set_mag(arf_t y, const mag_t x) { if (mag_is_zero(x)) { arf_zero(y); } else if (mag_is_inf(x)) { arf_pos_inf(y); } else { _fmpz_set_fast(ARF_EXPREF(y), MAG_EXPREF(x)); ARF_DEMOTE(y); ARF_XSIZE(y) = ARF_MAKE_XSIZE(1, 0); ARF_NOPTR_D(y)[0] = MAG_MAN(x) << (FLINT_BITS - MAG_BITS); } } ARF_INLINE void mag_init_set_arf(mag_t y, const arf_t x) { mag_init(y); arf_get_mag(y, x); } ARF_INLINE void mag_fast_init_set_arf(mag_t y, const arf_t x) { if (ARF_IS_SPECIAL(x)) /* x == 0 */ { mag_fast_zero(y); } else { mp_srcptr xp; mp_size_t xn; ARF_GET_MPN_READONLY(xp, xn, x); MAG_MAN(y) = (xp[xn - 1] >> (FLINT_BITS - MAG_BITS)) + LIMB_ONE; MAG_EXP(y) = ARF_EXP(x); MAG_FAST_ADJUST_ONE_TOO_LARGE(y); } } ARF_INLINE void arf_mag_fast_add_ulp(mag_t z, const mag_t x, const arf_t y, slong prec) { mag_fast_add_2exp_si(z, x, ARF_EXP(y) - prec); } ARF_INLINE void arf_mag_add_ulp(mag_t z, const mag_t x, const arf_t y, slong prec) { if (ARF_IS_SPECIAL(y)) { flint_printf("error: ulp error not defined for special value!\n"); abort(); } else if (MAG_IS_LAGOM(z) && MAG_IS_LAGOM(x) && ARF_IS_LAGOM(y)) { arf_mag_fast_add_ulp(z, x, y, prec); } else { fmpz_t e; fmpz_init(e); fmpz_sub_ui(e, ARF_EXPREF(y), prec); mag_add_2exp_fmpz(z, x, e); fmpz_clear(e); } } ARF_INLINE void arf_mag_set_ulp(mag_t z, const arf_t y, slong prec) { if (ARF_IS_SPECIAL(y)) { flint_printf("error: ulp error not defined for special value!\n"); abort(); } else { _fmpz_add_fast(MAG_EXPREF(z), ARF_EXPREF(y), 1 - prec); MAG_MAN(z) = MAG_ONE_HALF; } } void arf_get_fmpq(fmpq_t y, const arf_t x); ARF_INLINE int arf_set_fmpq(arf_t y, const fmpq_t x, slong prec, arf_rnd_t rnd) { return arf_fmpz_div_fmpz(y, fmpq_numref(x), fmpq_denref(x), prec, rnd); } int arf_complex_mul(arf_t e, arf_t f, const arf_t a, const arf_t b, const arf_t c, const arf_t d, slong prec, arf_rnd_t rnd); int arf_complex_mul_fallback(arf_t e, arf_t f, const arf_t a, const arf_t b, const arf_t c, const arf_t d, slong prec, arf_rnd_t rnd); int arf_complex_sqr(arf_t e, arf_t f, const arf_t a, const arf_t b, slong prec, arf_rnd_t rnd); int arf_sum(arf_t s, arf_srcptr terms, slong len, slong prec, arf_rnd_t rnd); double arf_get_d(const arf_t x, arf_rnd_t rnd); void arf_set_d(arf_t x, double v); #ifdef __cplusplus } #endif #endif arb-2.8.1/arf/000077500000000000000000000000001264125401100130325ustar00rootroot00000000000000arb-2.8.1/arf/abs_bound_lt_2exp_si.c000066400000000000000000000032361264125401100172660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" slong arf_abs_bound_lt_2exp_si(const arf_t x) { slong res; if (arf_is_special(x)) { if (arf_is_zero(x)) return -ARF_PREC_EXACT; else return ARF_PREC_EXACT; } if (!COEFF_IS_MPZ(ARF_EXP(x))) return ARF_EXP(x); if (fmpz_fits_si(ARF_EXPREF(x))) res = fmpz_get_si(ARF_EXPREF(x)); else res = fmpz_sgn(ARF_EXPREF(x)) < 0 ? -ARF_PREC_EXACT : ARF_PREC_EXACT; if (res < -ARF_PREC_EXACT) res = -ARF_PREC_EXACT; if (res > ARF_PREC_EXACT) res = ARF_PREC_EXACT; return res; } arb-2.8.1/arf/add.c000066400000000000000000000151761264125401100137400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_add_special(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { if (arf_is_zero(x)) { if (arf_is_zero(y)) { arf_zero(z); return 0; } else return arf_set_round(z, y, prec, rnd); } else if (arf_is_zero(y)) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_nan(x) || arf_is_nan(y) || (arf_is_pos_inf(x) && arf_is_neg_inf(y)) || (arf_is_neg_inf(x) && arf_is_pos_inf(y))) { arf_nan(z); return 0; } else if (arf_is_special(x)) { arf_set(z, x); return 0; } else { arf_set(z, y); return 0; } } int arf_add(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; slong shift; if (arf_is_special(x) || arf_is_special(y)) { return arf_add_special(z, x, y, prec, rnd); } shift = _fmpz_sub_small(ARF_EXPREF(x), ARF_EXPREF(y)); if (shift < 0) { arf_srcptr __t; __t = x; x = y; y = __t; shift = -shift; } ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); return _arf_add_mpn(z, xptr, xn, ARF_SGNBIT(x), ARF_EXPREF(x), yptr, yn, ARF_SGNBIT(y), shift, prec, rnd); } int arf_add_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; mp_limb_t ytmp; int xsgnbit, ysgnbit; fmpz yexp; slong shift; if (y == 0) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_special(x)) { if (arf_is_zero(x)) return arf_set_round_si(z, y, prec, rnd); else { arf_set(z, x); return 0; } } ysgnbit = (y < 0); if (ysgnbit) ytmp = -y; else ytmp = y; yptr = &ytmp; yn = 1; yexp = FLINT_BITS; /* XXX: worth the trouble to top-align y? */ shift = _fmpz_sub_small(ARF_EXPREF(x), &yexp); xsgnbit = ARF_SGNBIT(x); ARF_GET_MPN_READONLY(xptr, xn, x); if (shift >= 0) return _arf_add_mpn(z, xptr, xn, xsgnbit, ARF_EXPREF(x), yptr, yn, ysgnbit, shift, prec, rnd); else return _arf_add_mpn(z, yptr, yn, ysgnbit, &yexp, xptr, xn, xsgnbit, -shift, prec, rnd); } int arf_add_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; mp_limb_t ytmp; int xsgnbit, ysgnbit; fmpz yexp; slong shift; if (y == 0) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_special(x)) { if (arf_is_zero(x)) return arf_set_round_ui(z, y, prec, rnd); else { arf_set(z, x); return 0; } } ysgnbit = 0; ytmp = y; yptr = &ytmp; yn = 1; yexp = FLINT_BITS; shift = _fmpz_sub_small(ARF_EXPREF(x), &yexp); xsgnbit = ARF_SGNBIT(x); ARF_GET_MPN_READONLY(xptr, xn, x); if (shift >= 0) return _arf_add_mpn(z, xptr, xn, xsgnbit, ARF_EXPREF(x), yptr, yn, ysgnbit, shift, prec, rnd); else return _arf_add_mpn(z, yptr, yn, ysgnbit, &yexp, xptr, xn, xsgnbit, -shift, prec, rnd); } int arf_add_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; mp_limb_t ytmp; int xsgnbit, ysgnbit; fmpz yexp; slong shift; if (fmpz_is_zero(y)) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_special(x)) { if (arf_is_zero(x)) return arf_set_round_fmpz(z, y, prec, rnd); else { arf_set(z, x); return 0; } } FMPZ_GET_MPN_READONLY(ysgnbit, yn, yptr, ytmp, *y) yexp = yn * FLINT_BITS; shift = _fmpz_sub_small(ARF_EXPREF(x), &yexp); xsgnbit = ARF_SGNBIT(x); ARF_GET_MPN_READONLY(xptr, xn, x); if (shift >= 0) return _arf_add_mpn(z, xptr, xn, xsgnbit, ARF_EXPREF(x), yptr, yn, ysgnbit, shift, prec, rnd); else return _arf_add_mpn(z, yptr, yn, ysgnbit, &yexp, xptr, xn, xsgnbit, -shift, prec, rnd); } int arf_add_fmpz_2exp(arf_ptr z, arf_srcptr x, const fmpz_t y, const fmpz_t exp, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; mp_limb_t ytmp; int xsgnbit, ysgnbit, inexact; fmpz_t yexp; slong shift; if (fmpz_is_zero(y)) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_special(x)) { if (arf_is_zero(x)) { inexact = arf_set_round_fmpz(z, y, prec, rnd); arf_mul_2exp_fmpz(z, z, exp); return inexact; } else { arf_set(z, x); return 0; } } FMPZ_GET_MPN_READONLY(ysgnbit, yn, yptr, ytmp, *y) fmpz_init(yexp); fmpz_add_ui(yexp, exp, yn * FLINT_BITS); shift = _fmpz_sub_small(ARF_EXPREF(x), yexp); xsgnbit = ARF_SGNBIT(x); ARF_GET_MPN_READONLY(xptr, xn, x); if (shift >= 0) inexact = _arf_add_mpn(z, xptr, xn, xsgnbit, ARF_EXPREF(x), yptr, yn, ysgnbit, shift, prec, rnd); else inexact = _arf_add_mpn(z, yptr, yn, ysgnbit, yexp, xptr, xn, xsgnbit, -shift, prec, rnd); fmpz_clear(yexp); return inexact; } arb-2.8.1/arf/add_mpn.c000066400000000000000000000265521264125401100146120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" TLS_PREFIX mp_ptr __arf_add_tmp = NULL; TLS_PREFIX slong __arf_add_alloc = 0; void _arf_add_tmp_cleanup(void) { flint_free(__arf_add_tmp); __arf_add_tmp = NULL; __arf_add_alloc = 0; } /* Assumptions: top limbs of x and y nonzero. */ int _arf_add_mpn(arf_t z, mp_srcptr xp, mp_size_t xn, int xsgnbit, const fmpz_t xexp, mp_srcptr yp, mp_size_t yn, int ysgnbit, mp_bitcnt_t shift, slong prec, arf_rnd_t rnd) { mp_size_t wn, zn, zn_original, alloc, xbase, wbase; mp_size_t shift_limbs; mp_bitcnt_t shift_bits; int inexact; slong fix; mp_limb_t cy; mp_ptr tmp; ARF_ADD_TMP_DECL /* very fast case */ if (xn == 1 && yn == 1 && shift < FLINT_BITS - 1) { mp_limb_t hi, lo, xhi, xlo, yhi, ylo; xhi = xp[0]; yhi = yp[0]; xlo = xhi << (FLINT_BITS - 1); xhi = xhi >> 1; ylo = yhi << (FLINT_BITS - (shift + 1)); yhi = yhi >> (shift + 1); if (xsgnbit == ysgnbit) { add_ssaaaa(hi, lo, xhi, xlo, yhi, ylo); } else { if (xhi > yhi) { sub_ddmmss(hi, lo, xhi, xlo, yhi, ylo); } else if (xhi < yhi) { sub_ddmmss(hi, lo, yhi, ylo, xhi, xlo); xsgnbit = ysgnbit; } else { if (xlo > ylo) { sub_ddmmss(hi, lo, xhi, xlo, yhi, ylo); } else if (xlo < ylo) { sub_ddmmss(hi, lo, yhi, ylo, xhi, xlo); xsgnbit = ysgnbit; } else { arf_zero(z); return 0; } } } inexact = _arf_set_round_uiui(z, &fix, hi, lo, xsgnbit, prec, rnd); _fmpz_add_fast(ARF_EXPREF(z), xexp, fix + 1); return inexact; } /* somewhat fast case */ if (xn <= 2 && yn <= 2 && shift <= 2 * FLINT_BITS) { mp_limb_t t[5], xtmp[4], ytmp[4], yhi, ylo; slong fix2; xtmp[0] = 0; xtmp[1] = 0; if (xn == 1) { xtmp[2] = 0; xtmp[3] = xp[0]; } else { xtmp[2] = xp[0]; xtmp[3] = xp[1]; } ytmp[0] = 0; ytmp[1] = 0; ytmp[2] = 0; ytmp[3] = 0; if (yn == 1) { yhi = yp[0]; ylo = 0; } else { yhi = yp[1]; ylo = yp[0]; } shift_limbs = shift / FLINT_BITS; shift_bits = shift % FLINT_BITS; if (shift_bits == 0) { ytmp[3 - shift_limbs] = yhi; ytmp[2 - shift_limbs] = ylo; } else { ytmp[3 - shift_limbs] = yhi >> shift_bits; ytmp[2 - shift_limbs] = (yhi << (FLINT_BITS - shift_bits)) | (ylo >> (shift_bits)); ytmp[1 - shift_limbs] = ylo << (FLINT_BITS - shift_bits); } if (xsgnbit == ysgnbit) { t[4] = cy = mpn_add_n(t, xtmp, ytmp, 4); fix2 = cy * FLINT_BITS; zn = 4 + cy; while (t[zn - 1] == 0) { zn--; fix2 -= FLINT_BITS; } } else { #if 1 cy = mpn_sub_n(t, xtmp, ytmp, 4); if (cy) { mpn_neg_n(t, t, 4); xsgnbit = ysgnbit; } zn = 4; fix2 = 0; while (t[zn - 1] == 0) { zn--; fix2 -= FLINT_BITS; if (zn == 0) { arf_zero(z); return 0; } } #else int cmp; cmp = mpn_cmp(xtmp, ytmp, 4); if (cmp > 0) { mpn_sub_n(t, xtmp, ytmp, 4); } else if (cmp < 0) { mpn_sub_n(t, ytmp, xtmp, 4); xsgnbit = ysgnbit; } else { arf_zero(z); return 0; } fix2 = 0; zn = 4; while (t[zn - 1] == 0) { zn--; fix2 -= FLINT_BITS; } #endif } inexact = _arf_set_round_mpn(z, &fix, t, zn, xsgnbit, prec, rnd); _fmpz_add_fast(ARF_EXPREF(z), xexp, fix + fix2); return inexact; } /* x +/- eps */ if (shift > prec + FLINT_BITS + 1 && prec != ARF_PREC_EXACT && shift > (xn + 1) * FLINT_BITS) { zn = (prec + FLINT_BITS - 1) / FLINT_BITS; zn_original = zn = FLINT_MAX(zn, xn) + 2; shift_limbs = zn - xn; alloc = zn + 1; ARF_ADD_TMP_ALLOC(tmp, alloc) flint_mpn_zero(tmp, shift_limbs); flint_mpn_copyi(tmp + shift_limbs, xp, xn); if (xsgnbit == ysgnbit) { tmp[0] = 1; } else { mpn_sub_1(tmp, tmp, zn, 1); while (tmp[zn-1] == 0) zn--; } _arf_set_round_mpn(z, &fix, tmp, zn, xsgnbit, prec, rnd); fix += (zn - zn_original) * FLINT_BITS; _fmpz_add_fast(ARF_EXPREF(z), xexp, fix); ARF_ADD_TMP_FREE(tmp, alloc) return 1; } shift_limbs = shift / FLINT_BITS; shift_bits = shift % FLINT_BITS; /* TODO: shift == 0 optimization! (common case) */ /* w = y shifted */ wn = yn + (shift_bits != 0); /* Size of sum (possibly one more limb than this for carry). */ zn_original = zn = FLINT_MAX(xn, wn + shift_limbs); alloc = zn + 1; ARF_ADD_TMP_ALLOC(tmp, alloc) /* Low limbs of both operands */ xbase = zn - xn; wbase = zn - shift_limbs - wn; /* Shift y to its correct offset in the sum. */ if (shift_bits == 0) flint_mpn_copyi(tmp + wbase, yp, yn); else tmp[wbase] = cy = mpn_rshift(tmp + wbase + 1, yp, yn, shift_bits); if (xsgnbit == ysgnbit) { if (shift_limbs >= xn) { /* XXXXXX WWWWWWW */ flint_mpn_zero(tmp + wn, zn - xn - wn); flint_mpn_copyi(tmp + zn - xn, xp, xn); cy = 0; } else if (shift_limbs == 0) { /* XXXXXX or XXXXX WWWW WWWWWWW */ if (wn < xn) { flint_mpn_copyi(tmp, xp, xn - wn); cy = mpn_add_n(tmp + wbase, xp + wbase, tmp + wbase, wn); } else { cy = mpn_add_n(tmp + xbase, xp, tmp + xbase, xn); } } else if (xbase >= wbase) { /* XXXXXX or XXXXXX WWWWWWW WWWW */ cy = mpn_add_n(tmp + xbase, tmp + xbase, xp, wn - xbase); cy = mpn_add_1(tmp + wn, xp + wn - xbase, zn - wn, cy); } else { /* XXXXXXXX todo: merge with above? WWW */ flint_mpn_copyi(tmp, xp, wbase); cy = mpn_add_n(tmp + wbase, tmp + wbase, xp + wbase, wn); cy = mpn_add_1(tmp + zn - shift_limbs, xp + xn - shift_limbs, shift_limbs, cy); } /* There could be a carry. */ tmp[zn] = cy; zn += cy; } else { if (shift_limbs >= xn) { /* XXXXXX WWWWWWW */ mpn_neg(tmp, tmp, wn); flint_mpn_store(tmp + wn, zn - xn - wn, -LIMB_ONE); mpn_sub_1(tmp + zn - xn, xp, xn, 1); } else if (shift_limbs == 0) { /* XXXXXX (1) or XXXXX (2) WWWW WWWWWWW */ if (wn <= xn) /* (1) */ { if (mpn_cmp(xp + wbase, tmp + wbase, wn) >= 0) { flint_mpn_copyi(tmp, xp, wbase); mpn_sub_n(tmp + wbase, xp + wbase, tmp + wbase, wn); } else { xsgnbit = ysgnbit; mpn_sub_n(tmp + wbase, tmp + wbase, xp + wbase, wn); if (wbase != 0) { cy = mpn_neg_n(tmp, xp, wbase); mpn_sub_1(tmp + wbase, tmp + wbase, wn, cy); } } } else /* (2) */ { if (mpn_cmp(tmp + xbase, xp, xn) >= 0) { xsgnbit = ysgnbit; mpn_sub_n(tmp + xbase, tmp + xbase, xp, xn); } else { cy = mpn_neg(tmp, tmp, xbase); mpn_sub_n(tmp + xbase, xp, tmp + xbase, xn); mpn_sub_1(tmp + xbase, tmp + xbase, xn, cy); } } } else if (xbase >= wbase) { /* XXXXXX or XXXXXX WWWWWWW WWWW */ if (xbase > 0) { cy = mpn_sub_n(tmp + xbase, xp, tmp + xbase, wn - xbase); cy = mpn_sub_1(tmp + wn, xp + xn - shift_limbs, shift_limbs, cy); cy = mpn_neg(tmp, tmp, xbase); mpn_sub_1(tmp + xbase, tmp + xbase, xn, cy); } else { cy = mpn_sub_n(tmp, xp, tmp, wn); cy = mpn_sub_1(tmp + wn, xp + wn, xn - wn, cy); } } else { /* XXXXXXXX WWW */ flint_mpn_copyi(tmp, xp, wbase); cy = mpn_sub_n(tmp + wbase, xp + wbase, tmp + wbase, wn); mpn_sub_1(tmp + zn - shift_limbs, xp + xn - shift_limbs, shift_limbs, cy); } /* There could be cancellation. */ while (zn > 0 && tmp[zn - 1] == 0) zn--; } if (zn == 0) { arf_zero(z); inexact = 0; } else { inexact = _arf_set_round_mpn(z, &fix, tmp, zn, xsgnbit, prec, rnd); fix += (zn - zn_original) * FLINT_BITS; _fmpz_add_fast(ARF_EXPREF(z), xexp, fix); } ARF_ADD_TMP_FREE(tmp, alloc) return inexact; } arb-2.8.1/arf/addmul.c000066400000000000000000000106621264125401100144510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_addmul(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn, zn, tn, alloc; mp_srcptr xptr, yptr, zptr; mp_ptr tptr, tptr2; fmpz_t texp; slong shift; int tsgnbit, inexact; ARF_MUL_TMP_DECL if (arf_is_special(x) || arf_is_special(y) || arf_is_special(z)) { if (arf_is_zero(z)) { return arf_mul(z, x, y, prec, rnd); } else if (arf_is_finite(x) && arf_is_finite(y)) { return arf_set_round(z, z, prec, rnd); } else { /* todo: speed up */ arf_t t; arf_init(t); arf_mul(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_add(z, z, t, prec, rnd); arf_clear(t); return inexact; } } tsgnbit = ARF_SGNBIT(x) ^ ARF_SGNBIT(y); ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); ARF_GET_MPN_READONLY(zptr, zn, z); fmpz_init(texp); _fmpz_add2_fast(texp, ARF_EXPREF(x), ARF_EXPREF(y), 0); shift = _fmpz_sub_small(ARF_EXPREF(z), texp); alloc = tn = xn + yn; ARF_MUL_TMP_ALLOC(tptr2, alloc) tptr = tptr2; ARF_MPN_MUL(tptr, xptr, xn, yptr, yn); tn -= (tptr[0] == 0); tptr += (tptr[0] == 0); if (shift >= 0) inexact = _arf_add_mpn(z, zptr, zn, ARF_SGNBIT(z), ARF_EXPREF(z), tptr, tn, tsgnbit, shift, prec, rnd); else inexact = _arf_add_mpn(z, tptr, tn, tsgnbit, texp, zptr, zn, ARF_SGNBIT(z), -shift, prec, rnd); ARF_MUL_TMP_FREE(tptr2, alloc) fmpz_clear(texp); return inexact; } int arf_addmul_mpz(arf_ptr z, arf_srcptr x, const mpz_t y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn, zn, tn, alloc; mp_srcptr xptr, yptr, zptr; mp_ptr tptr, tptr2; fmpz_t texp, yexp; slong shift; int tsgnbit, ysgnbit, inexact; ARF_MUL_TMP_DECL yn = FLINT_ABS(y->_mp_size); if (arf_is_special(x) || yn == 0 || arf_is_special(z)) { if (arf_is_zero(z)) { return arf_mul_mpz(z, x, y, prec, rnd); } else if (arf_is_finite(x)) { return arf_set_round(z, z, prec, rnd); } else { /* todo: speed up */ arf_t t; arf_init(t); arf_mul_mpz(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_add(z, z, t, prec, rnd); arf_clear(t); return inexact; } } ARF_GET_MPN_READONLY(xptr, xn, x); yptr = y->_mp_d; ysgnbit = (y->_mp_size < 0); *yexp = yn * FLINT_BITS; ARF_GET_MPN_READONLY(zptr, zn, z); fmpz_init(texp); tsgnbit = ARF_SGNBIT(x) ^ ysgnbit; alloc = tn = xn + yn; ARF_MUL_TMP_ALLOC(tptr2, alloc) tptr = tptr2; ARF_MPN_MUL(tptr, xptr, xn, yptr, yn); shift = (tptr[tn - 1] == 0) * FLINT_BITS; tn -= (tptr[tn - 1] == 0); _fmpz_add2_fast(texp, ARF_EXPREF(x), yexp, -shift); shift = _fmpz_sub_small(ARF_EXPREF(z), texp); if (shift >= 0) inexact = _arf_add_mpn(z, zptr, zn, ARF_SGNBIT(z), ARF_EXPREF(z), tptr, tn, tsgnbit, shift, prec, rnd); else inexact = _arf_add_mpn(z, tptr, tn, tsgnbit, texp, zptr, zn, ARF_SGNBIT(z), -shift, prec, rnd); ARF_MUL_TMP_FREE(tptr2, alloc) fmpz_clear(texp); return inexact; } arb-2.8.1/arf/ceil.c000066400000000000000000000033041264125401100141120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_ceil(arf_t z, const arf_t x) { if (arf_is_special(x) || arf_is_int(x)) { arf_set(z, x); } else { slong exp = ARF_EXP(x); /* now exp cannot be too large, as we would have caught this in arf_is_int() */ if (COEFF_IS_MPZ(exp) || exp <= 0) { if (ARF_SGNBIT(x)) arf_zero(z); else arf_one(z); } else if (exp == 1) { arf_set_si(z, ARF_SGNBIT(x) ? -1 : 2); } else { arf_set_round(z, x, exp, ARF_RND_CEIL); } } } arb-2.8.1/arf/cmp.c000066400000000000000000000041161264125401100137570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_cmp(const arf_t x, const arf_t y) { int xs, ys, ec, mc; mp_size_t xn, yn; mp_srcptr xp, yp; if (arf_is_special(x) || arf_is_special(y)) { if (arf_equal(x, y)) return 0; if (arf_is_nan(x) || arf_is_nan(y)) return 0; if (arf_is_zero(y)) return arf_sgn(x); if (arf_is_zero(x)) return -arf_sgn(y); if (arf_is_pos_inf(x)) return 1; if (arf_is_neg_inf(y)) return 1; return -1; } xs = ARF_SGNBIT(x); ys = ARF_SGNBIT(y); if (xs != ys) return xs ? -1 : 1; ec = fmpz_cmp(ARF_EXPREF(x), ARF_EXPREF(y)); if (ec != 0) return ((ec < 0) ^ xs) ? -1 : 1; ARF_GET_MPN_READONLY(xp, xn, x); ARF_GET_MPN_READONLY(yp, yn, y); if (xn >= yn) mc = mpn_cmp(xp + xn - yn, yp, yn); else mc = mpn_cmp(xp, yp + yn - xn, xn); if (mc != 0) return ((mc < 0) ^ xs) ? -1 : 1; if (xn != yn) return ((xn < yn) ^ xs) ? -1 : 1; return 0; } arb-2.8.1/arf/cmp_2exp_si.c000066400000000000000000000035561264125401100154170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_cmp_2exp_si(const arf_t x, slong e) { if (arf_is_special(x)) { if (arf_is_zero(x)) return -1; if (arf_is_pos_inf(x)) return 1; if (arf_is_neg_inf(x)) return -1; return 0; } if (ARF_SGNBIT(x)) return -1; /* Fast path. */ if (!COEFF_IS_MPZ(ARF_EXP(x))) { if (ARF_IS_POW2(x) && (ARF_EXP(x) - 1 == e)) return 0; else return (ARF_EXP(x) <= e) ? -1 : 1; } if (ARF_IS_POW2(x)) { fmpz_t t; fmpz_init(t); fmpz_one(t); fmpz_add_si(t, t, e); if (fmpz_equal(ARF_EXPREF(x), t)) { fmpz_clear(t); return 0; } fmpz_clear(t); } return (fmpz_cmp_si(ARF_EXPREF(x), e) <= 0) ? -1 : 1; } arb-2.8.1/arf/cmpabs.c000066400000000000000000000037171264125401100144530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_cmpabs(const arf_t x, const arf_t y) { int ec, mc; mp_size_t xn, yn; mp_srcptr xp, yp; if (arf_is_special(x) || arf_is_special(y)) { if (arf_equal(x, y)) return 0; if (arf_is_nan(x) || arf_is_nan(y)) return 0; if (arf_is_zero(x)) return -1; if (arf_is_zero(y)) return 1; if (arf_is_inf(x)) return arf_is_inf(y) ? 0 : 1; if (arf_is_inf(y)) return -1; return -1; } ec = fmpz_cmp(ARF_EXPREF(x), ARF_EXPREF(y)); if (ec != 0) return (ec < 0) ? -1 : 1; ARF_GET_MPN_READONLY(xp, xn, x); ARF_GET_MPN_READONLY(yp, yn, y); if (xn >= yn) mc = mpn_cmp(xp + xn - yn, yp, yn); else mc = mpn_cmp(xp, yp + yn - xn, xn); if (mc != 0) return (mc < 0) ? -1 : 1; if (xn != yn) return (xn < yn) ? -1 : 1; return 0; } arb-2.8.1/arf/cmpabs_2exp_si.c000066400000000000000000000034331264125401100160770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_cmpabs_2exp_si(const arf_t x, slong e) { if (arf_is_special(x)) { if (arf_is_zero(x)) return -1; if (arf_is_inf(x)) return 1; return 0; } /* Fast path. */ if (!COEFF_IS_MPZ(ARF_EXP(x))) { if (ARF_IS_POW2(x) && (ARF_EXP(x) - 1 == e)) return 0; else return (ARF_EXP(x) <= e) ? -1 : 1; } if (ARF_IS_POW2(x)) { fmpz_t t; fmpz_init(t); fmpz_one(t); fmpz_add_si(t, t, e); if (fmpz_equal(ARF_EXPREF(x), t)) { fmpz_clear(t); return 0; } fmpz_clear(t); } return (fmpz_cmp_si(ARF_EXPREF(x), e) <= 0) ? -1 : 1; } arb-2.8.1/arf/complex_mul.c000066400000000000000000000204021264125401100155200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_complex_mul_fallback(arf_t e, arf_t f, const arf_t a, const arf_t b, const arf_t c, const arf_t d, slong prec, arf_rnd_t rnd) { int inex1, inex2; /* here the operations are ordered to allow aliasing */ if (arf_is_zero(d)) { /* (a + bi) * c */ inex2 = arf_mul(f, b, c, prec, rnd); inex1 = arf_mul(e, a, c, prec, rnd); } else if (arf_is_zero(b)) { /* a * (c + di) */ inex2 = arf_mul(f, a, d, prec, rnd); inex1 = arf_mul(e, a, c, prec, rnd); } else if (arf_is_zero(c)) { /* (a + bi) * di = -bd + adi */ inex2 = arf_mul(e, a, d, prec, rnd); inex1 = arf_neg_mul(f, b, d, prec, rnd); arf_swap(e, f); } else if (arf_is_zero(a)) { /* bi * (c + di) = -bd + bci */ inex2 = arf_mul(e, b, c, prec, rnd); inex1 = arf_neg_mul(f, b, d, prec, rnd); arf_swap(e, f); } else { arf_t t, u, v, w; arf_init(t); arf_init(u); arf_init(v); arf_init(w); arf_mul(t, a, c, ARF_PREC_EXACT, ARF_RND_DOWN); arf_mul(u, b, d, ARF_PREC_EXACT, ARF_RND_DOWN); arf_mul(v, b, c, ARF_PREC_EXACT, ARF_RND_DOWN); arf_mul(w, a, d, ARF_PREC_EXACT, ARF_RND_DOWN); inex1 = arf_sub(e, t, u, prec, rnd); inex2 = arf_add(f, v, w, prec, rnd); arf_clear(t); arf_clear(u); arf_clear(v); arf_clear(w); } return inex1 | (inex2 << 1); } int arf_complex_mul(arf_t e, arf_t f, const arf_t a, const arf_t b, const arf_t c, const arf_t d, slong prec, arf_rnd_t rnd) { mp_srcptr ap, bp, cp, dp; int asgn, bsgn, csgn, dsgn, inex1, inex2; mp_ptr tmp, acp, bdp, adp, bcp; mp_size_t an, bn, cn, dn, acn, bdn, adn, bcn, alloc; slong shift; slong aexp, bexp, cexp, dexp; fmpz texp, uexp; if (!ARF_IS_LAGOM(a) || !ARF_IS_LAGOM(b) || !ARF_IS_LAGOM(c) || !ARF_IS_LAGOM(d) || ARF_IS_SPECIAL(d) || ARF_IS_SPECIAL(a) || ARF_IS_SPECIAL(b) || ARF_IS_SPECIAL(c)) { return arf_complex_mul_fallback(e, f, a, b, c, d, prec, rnd); } ARF_GET_MPN_READONLY(ap, an, a); asgn = ARF_SGNBIT(a); aexp = ARF_EXP(a); ARF_GET_MPN_READONLY(bp, bn, b); bsgn = ARF_SGNBIT(b); bexp = ARF_EXP(b); ARF_GET_MPN_READONLY(cp, cn, c); csgn = ARF_SGNBIT(c); cexp = ARF_EXP(c); ARF_GET_MPN_READONLY(dp, dn, d); dsgn = ARF_SGNBIT(d); dexp = ARF_EXP(d); /* Gauss multiplication e = ac - bd f = (a+b)(c+d) - ac - bd */ if (an >= 20 && cn >= 20 && FLINT_ABS(an - bn) <= 2 && FLINT_ABS(cn - dn) <= 2 && FLINT_ABS(aexp - bexp) <= 64 && FLINT_ABS(cexp - dexp) <= 64) { fmpz_t za, zb, zc, zd, t, u, v; slong abot, bbot, cbot, dbot; abot = aexp - an * FLINT_BITS; bbot = bexp - bn * FLINT_BITS; cbot = cexp - cn * FLINT_BITS; dbot = dexp - dn * FLINT_BITS; texp = FLINT_MIN(abot, bbot); uexp = FLINT_MIN(cbot, dbot); fmpz_init(za); fmpz_init(zb); fmpz_init(zc); fmpz_init(zd); fmpz_init(t); fmpz_init(u); fmpz_init(v); /* todo: could avoid two copies */ fmpz_lshift_mpn(za, ap, an, asgn, abot - texp); fmpz_lshift_mpn(zb, bp, bn, bsgn, bbot - texp); fmpz_lshift_mpn(zc, cp, cn, csgn, cbot - uexp); fmpz_lshift_mpn(zd, dp, dn, dsgn, dbot - uexp); fmpz_add(t, za, zb); fmpz_add(v, zc, zd); fmpz_mul(u, t, v); fmpz_mul(t, za, zc); fmpz_mul(v, zb, zd); fmpz_sub(u, u, t); fmpz_sub(u, u, v); fmpz_sub(t, t, v); texp += uexp; inex1 = arf_set_round_fmpz_2exp(e, t, &texp, prec, rnd); inex2 = arf_set_round_fmpz_2exp(f, u, &texp, prec, rnd); fmpz_clear(za); fmpz_clear(zb); fmpz_clear(zc); fmpz_clear(zd); fmpz_clear(t); fmpz_clear(u); fmpz_clear(v); } else { ARF_MUL_TMP_DECL acn = an + cn; bdn = bn + dn; adn = an + dn; bcn = bn + cn; alloc = acn + bdn + adn + bcn; ARF_MUL_TMP_ALLOC(tmp, alloc) acp = tmp; bdp = acp + acn; adp = bdp + bdn; bcp = adp + adn; ARF_MPN_MUL(acp, ap, an, cp, cn) acn -= (acp[0] == 0); acp += (acp[0] == 0); ARF_MPN_MUL(bdp, bp, bn, dp, dn) bdn -= (bdp[0] == 0); bdp += (bdp[0] == 0); ARF_MPN_MUL(adp, ap, an, dp, dn) adn -= (adp[0] == 0); adp += (adp[0] == 0); ARF_MPN_MUL(bcp, bp, bn, cp, cn) bcn -= (bcp[0] == 0); bcp += (bcp[0] == 0); texp = aexp + cexp; uexp = bexp + dexp; shift = texp - uexp; if (shift >= 0) inex1 = _arf_add_mpn(e, acp, acn, asgn ^ csgn, &texp, bdp, bdn, bsgn ^ dsgn ^ 1, shift, prec, rnd); else inex1 = _arf_add_mpn(e, bdp, bdn, bsgn ^ dsgn ^ 1, &uexp, acp, acn, asgn ^ csgn, -shift, prec, rnd); texp = aexp + dexp; uexp = bexp + cexp; shift = texp - uexp; if (shift >= 0) inex2 = _arf_add_mpn(f, adp, adn, asgn ^ dsgn, &texp, bcp, bcn, bsgn ^ csgn, shift, prec, rnd); else inex2 = _arf_add_mpn(f, bcp, bcn, bsgn ^ csgn, &uexp, adp, adn, asgn ^ dsgn, -shift, prec, rnd); ARF_MUL_TMP_FREE(tmp, alloc) } return inex1 | (inex2 << 1); } int arf_complex_sqr(arf_t e, arf_t f, const arf_t a, const arf_t b, slong prec, arf_rnd_t rnd) { if (!ARF_IS_LAGOM(a) || !ARF_IS_LAGOM(b) || ARF_IS_SPECIAL(a) || ARF_IS_SPECIAL(b)) { return arf_complex_mul_fallback(e, f, a, b, a, b, prec, rnd); } else { mp_srcptr ap, bp; int inex1, inex2; mp_ptr tmp, aap, bbp; mp_size_t an, bn, aan, bbn, alloc; slong shift; slong aexp, bexp; fmpz texp, uexp; TMP_INIT; ARF_GET_MPN_READONLY(ap, an, a); aexp = ARF_EXP(a); ARF_GET_MPN_READONLY(bp, bn, b); bexp = ARF_EXP(b); aan = 2 * an; bbn = 2 * bn; alloc = aan + bbn; TMP_START; tmp = TMP_ALLOC(alloc * sizeof(mp_limb_t)); aap = tmp; bbp = tmp + aan; ARF_MPN_MUL(aap, ap, an, ap, an) aan -= (aap[0] == 0); aap += (aap[0] == 0); ARF_MPN_MUL(bbp, bp, bn, bp, bn) bbn -= (bbp[0] == 0); bbp += (bbp[0] == 0); texp = aexp + aexp; uexp = bexp + bexp; shift = texp - uexp; inex2 = arf_mul(f, a, b, prec, rnd); ARF_EXP(f) += 1; if (shift >= 0) inex1 = _arf_add_mpn(e, aap, aan, 0, &texp, bbp, bbn, 1, shift, prec, rnd); else inex1 = _arf_add_mpn(e, bbp, bbn, 1, &uexp, aap, aan, 0, -shift, prec, rnd); TMP_END; return inex1 | (inex2 << 1); } } arb-2.8.1/arf/debug.c000066400000000000000000000026511264125401100142700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_debug(const arf_t x) { mp_srcptr d; mp_size_t n; slong i; flint_printf("{exp="); fmpz_print(&x->exp); flint_printf("; size=%wu; sgnbit=%wd; digits=[", ARF_SIZE(x), ARF_SGNBIT(x)); ARF_GET_MPN_READONLY(d, n, x); for (i = 0; i < n; i++) flint_printf(" %wu", d[i]); flint_printf("]}"); } arb-2.8.1/arf/div.c000066400000000000000000000107761264125401100137730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "mpn_extras.h" #if !defined(__MPIR_VERSION) #define USE_GMP_DIV_Q 1 void __gmpn_div_q(mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr); #else #define USE_GMP_DIV_Q 0 #endif void arf_div_special(arf_t z, const arf_t x, const arf_t y) { if ((arf_is_zero(x) && !arf_is_zero(y) && !arf_is_nan(y)) || (arf_is_inf(y) && !arf_is_special(x))) { arf_zero(z); } else if (arf_is_zero(y) || (arf_is_special(x) && arf_is_special(y)) || arf_is_nan(x) || arf_is_nan(y)) { arf_nan(z); } else if (arf_sgn(x) == arf_sgn(y)) arf_pos_inf(z); else arf_neg_inf(z); } int arf_div(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn, zn, sn, tn, alloc; mp_srcptr xptr, yptr; mp_ptr tmp; mp_ptr tptr, zptr; int inexact; slong fix, fix2; ARF_MUL_TMP_DECL if (arf_is_special(x) || arf_is_special(y)) { arf_div_special(z, x, y); return 0; } ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); /* Division by a power of two */ if (yn == 1 && yptr[0] == LIMB_TOP) { fmpz_t t; fmpz_init_set(t, ARF_EXPREF(y)); if (ARF_SGNBIT(y)) inexact = arf_neg_round(z, x, prec, rnd); else inexact = arf_set_round(z, x, prec, rnd); _fmpz_sub2_fast(ARF_EXPREF(z), ARF_EXPREF(z), t, 1); fmpz_clear(t); return inexact; } sn = FLINT_MAX(prec - xn * FLINT_BITS + yn * FLINT_BITS, 0) + 32; sn = (sn + FLINT_BITS - 1) / FLINT_BITS; /* Need space for numerator (tn), quotient (zn), and one extra limb at the top of tptr for the multiplication to check the remainder. */ tn = xn + sn; zn = tn - yn + 1; alloc = zn + (tn + 1); /* need tn + 1 extra temporary limbs, which we store at the end of tptr */ #if USE_GMP_DIV_Q alloc += tn + 1; #endif ARF_MUL_TMP_ALLOC(tmp, alloc) zptr = tmp; tptr = tmp + zn; flint_mpn_zero(tptr, sn); flint_mpn_copyi(tptr + sn, xptr, xn); /* uses tn + 1 extra temporary limbs, tn limbs after tptr */ #if USE_GMP_DIV_Q __gmpn_div_q(zptr, tptr, tn, yptr, yn, tptr + tn); #else mpn_tdiv_q(zptr, tptr, tn, yptr, yn); #endif if (zptr[zn - 1] == 0) { zn--; fix2 = 0; } else { fix2 = FLINT_BITS; } /* The remainder can only be zero if the last several bits of the extended quotient are zero. */ if ((zptr[0] & ((LIMB_ONE << 24) - 1)) == 0) { /* The quotient is exact iff multiplying by y gives back the input. Note: the multiplication may write sn + xn + 1 limbs, but tptr[sn + xn] is guaranteed to be zero in that case since the approximate quotient cannot be larger than the true quotient. */ if (zn >= yn) mpn_mul(tptr, zptr, zn, yptr, yn); else mpn_mul(tptr, yptr, yn, zptr, zn); /* The quotient is not exact. Perturbing the approximate quotient and rounding gives the correct the result. */ if (!flint_mpn_zero_p(tptr, sn) || mpn_cmp(tptr + sn, xptr, xn) != 0) { zptr[0]++; } } inexact = _arf_set_round_mpn(z, &fix, zptr, zn, ARF_SGNBIT(x) ^ ARF_SGNBIT(y), prec, rnd); _fmpz_sub2_fast(ARF_EXPREF(z), ARF_EXPREF(x), ARF_EXPREF(y), fix + fix2); ARF_MUL_TMP_FREE(tmp, alloc) return inexact; } arb-2.8.1/arf/equal.c000066400000000000000000000033741264125401100143140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_equal(const arf_t x, const arf_t y) { mp_size_t n; if (x == y) return 1; if (ARF_XSIZE(x) != ARF_XSIZE(y)) return 0; if (!fmpz_equal(ARF_EXPREF(x), ARF_EXPREF(y))) return 0; n = ARF_SIZE(x); if (n == 0) return 1; if (n == 1) return ARF_NOPTR_D(x)[0] == ARF_NOPTR_D(y)[0]; if (n == 2) return (ARF_NOPTR_D(x)[0] == ARF_NOPTR_D(y)[0] && ARF_NOPTR_D(x)[1] == ARF_NOPTR_D(y)[1]); return mpn_cmp(ARF_PTR_D(x), ARF_PTR_D(y), n) == 0; } int arf_equal_si(const arf_t x, slong y) { arf_t t; arf_init_set_si(t, y); return arf_equal(x, t); /* no need to free */ } arb-2.8.1/arf/floor.c000066400000000000000000000033151264125401100143210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_floor(arf_t z, const arf_t x) { if (arf_is_special(x) || arf_is_int(x)) { arf_set(z, x); } else { slong exp = ARF_EXP(x); /* now exp cannot be too large, as we would have caught this in arf_is_int() */ if (COEFF_IS_MPZ(exp) || exp <= 0) { if (ARF_SGNBIT(x)) arf_set_si(z, -1); else arf_zero(z); } else if (exp == 1) { arf_set_si(z, ARF_SGNBIT(x) ? -2 : 1); } else { arf_set_round(z, x, exp, ARF_RND_FLOOR); } } } arb-2.8.1/arf/get_d.c000066400000000000000000000062221264125401100142620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "double_extras.h" /* most double: (2^53-1) * 2^971 */ /* least normal: 2^-1022 */ /* least subnormal: 2^-1074 */ static double huge_double(arf_rnd_t rnd, int negative) { double v; if (rnd == ARF_RND_NEAR || rounds_up(rnd, negative)) v = D_INF; else v = ldexp(9007199254740991.0, 971); return negative ? -v : v; } static double tiny_double(arf_rnd_t rnd, int negative) { double v; if (rnd == ARF_RND_NEAR || !rounds_up(rnd, negative)) v = 0.0; else v = ldexp(1.0, -1074); return negative ? -v : v; } double arf_get_d(const arf_t x, arf_rnd_t rnd) { if (arf_is_special(x)) { if (arf_is_zero(x)) return 0.0; else if (arf_is_pos_inf(x)) return D_INF; else if (arf_is_neg_inf(x)) return -D_INF; else return D_NAN; } else { arf_t t; mp_srcptr tp; mp_size_t tn; double v; /* also catches bignum exponents */ if (ARF_EXP(x) > 1030 || ARF_EXP(x) < -1080) { if (fmpz_sgn(ARF_EXPREF(x)) > 0) return huge_double(rnd, ARF_SGNBIT(x)); else return tiny_double(rnd, ARF_SGNBIT(x)); } /* allow mpfr to take care of corner cases for now */ if (ARF_EXP(x) > 1020 || ARF_EXP(x) <= -1020 || rnd == ARF_RND_NEAR) { mpfr_t xx; ARF_GET_MPN_READONLY(tp, tn, x); xx->_mpfr_d = (mp_ptr) tp; xx->_mpfr_prec = tn * FLINT_BITS; xx->_mpfr_sign = ARF_SGNBIT(x) ? -1 : 1; xx->_mpfr_exp = ARF_EXP(x); return mpfr_get_d(xx, rnd_to_mpfr(rnd)); } arf_init(t); arf_set_round(t, x, 53, rnd); ARF_GET_MPN_READONLY(tp, tn, t); if (tn == 1) v = (double)(tp[0]); else v = (double)(tp[1]) + (double)(tp[0]) * ldexp(1,-32); v = ldexp(v, ARF_EXP(t) - FLINT_BITS); if (ARF_SGNBIT(t)) v = -v; arf_clear(t); return v; } } arb-2.8.1/arf/get_fmpq.c000066400000000000000000000035211264125401100150010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_get_fmpq(fmpq_t y, const arf_t x) { if (arf_is_zero(x)) { fmpq_zero(y); } else if (arf_is_special(x) || !ARF_IS_LAGOM(x)) { flint_printf("exception: arf_get_fmpq: cannot convert to rational\n"); abort(); } else { fmpz_t man, exp; slong e; fmpz_init(man); fmpz_init(exp); arf_get_fmpz_2exp(man, exp, x); e = *exp; fmpz_set_ui(fmpq_denref(y), UWORD(1)); if (e >= 0) { fmpz_mul_2exp(fmpq_numref(y), man, e); } else { fmpz_set(fmpq_numref(y), man); fmpz_mul_2exp(fmpq_denref(y), fmpq_denref(y), -e); } fmpz_clear(man); fmpz_clear(exp); } } arb-2.8.1/arf/get_fmpr.c000066400000000000000000000027321264125401100150050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_get_fmpr(fmpr_t y, const arf_t x) { if (arf_is_special(x)) { if (arf_is_zero(x)) fmpr_zero(y); else if (arf_is_pos_inf(x)) fmpr_pos_inf(y); else if (arf_is_neg_inf(x)) fmpr_neg_inf(y); else fmpr_nan(y); } else { arf_get_fmpz_2exp(fmpr_manref(y), fmpr_expref(y), x); } } arb-2.8.1/arf/get_fmpz.c000066400000000000000000000130571264125401100150170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" /* assumes xp[0] is nonzero and xp[xn-1] has the top bit set */ /* assumes that the correct number of limbs for y has been allocated (no zero-extension is done) */ /* truncates, returns inexact */ int _arf_get_integer_mpn(mp_ptr y, mp_srcptr x, mp_size_t xn, slong exp) { slong bot_exp = exp - xn * FLINT_BITS; if (bot_exp >= 0) { mp_size_t bot_limbs; mp_bitcnt_t bot_bits; bot_limbs = bot_exp / FLINT_BITS; bot_bits = bot_exp % FLINT_BITS; flint_mpn_zero(y, bot_limbs); if (bot_bits == 0) flint_mpn_copyi(y + bot_limbs, x, xn); else y[bot_limbs + xn] = mpn_lshift(y + bot_limbs, x, xn, bot_bits); /* exact */ return 0; } else if (exp <= 0) { /* inexact */ return 1; } else { mp_size_t top_limbs; mp_bitcnt_t top_bits; mp_limb_t cy; top_limbs = exp / FLINT_BITS; top_bits = exp % FLINT_BITS; if (top_bits == 0) { flint_mpn_copyi(y, x + xn - top_limbs, top_limbs); /* inexact */ return 1; } else { /* can be inexact */ cy = mpn_rshift(y, x + xn - top_limbs - 1, top_limbs + 1, FLINT_BITS - top_bits); return (cy != 0) || (top_limbs + 1 != xn); } } } void arf_get_fmpz(fmpz_t z, const arf_t x, arf_rnd_t rnd) { if (arf_is_special(x)) { if (arf_is_zero(x)) { fmpz_zero(z); } else { flint_printf("arf_get_fmpz: cannot convert infinity or nan to integer\n"); abort(); } } else if (COEFF_IS_MPZ(*ARF_EXPREF(x))) { /* tiny */ if (fmpz_sgn(ARF_EXPREF(x)) < 0) { int negative = ARF_SGNBIT(x); if (rnd == ARF_RND_NEAR || rnd == ARF_RND_DOWN || (rnd == ARF_RND_FLOOR && !negative) || (rnd == ARF_RND_CEIL && negative)) { fmpz_zero(z); } else { fmpz_set_si(z, negative ? -1 : 1); } } else { flint_printf("arf_get_fmpz: number too large to convert to integer\n"); abort(); } } else { slong exp; int negative, inexact; mp_size_t xn, zn; mp_srcptr xp; __mpz_struct * zz; /* TBD: implement efficiently */ if (rnd == ARF_RND_NEAR) { fmpr_t t; fmpr_init(t); arf_get_fmpr(t, x); fmpr_get_fmpz(z, t, rnd); fmpr_clear(t); return; } exp = ARF_EXP(x); negative = ARF_SGNBIT(x); /* |x| < 1 */ if (exp <= 0) { if (rnd == ARF_RND_DOWN || (rnd == ARF_RND_FLOOR && !negative) || (rnd == ARF_RND_CEIL && negative)) { fmpz_zero(z); } else { fmpz_set_si(z, negative ? -1 : 1); } return; } ARF_GET_MPN_READONLY(xp, xn, x); /* |x| < 2^31 or 2^63 (must save 1 bit for rounding up!) */ if (exp < FLINT_BITS) { mp_limb_t v, v2; v = xp[xn - 1]; v2 = v >> (FLINT_BITS - exp); inexact = (xn > 1) || ((v2 << (FLINT_BITS - exp)) != v); if (inexact && rnd != ARF_RND_DOWN) { if (negative && (rnd == ARF_RND_UP || rnd == ARF_RND_FLOOR)) v2++; if (!negative && (rnd == ARF_RND_UP || rnd == ARF_RND_CEIL)) v2++; } if (negative) fmpz_neg_ui(z, v2); else fmpz_set_ui(z, v2); return; } /* |x| >= 1 */ zn = (exp + FLINT_BITS - 1) / FLINT_BITS; zz = _fmpz_promote(z); if (zz->_mp_alloc < zn) mpz_realloc2(zz, zn * FLINT_BITS); inexact = _arf_get_integer_mpn(zz->_mp_d, xp, xn, exp); zz->_mp_size = negative ? -zn : zn; _fmpz_demote_val(z); if (inexact && rnd != ARF_RND_DOWN) { if (negative && (rnd == ARF_RND_UP || rnd == ARF_RND_FLOOR)) fmpz_sub_ui(z, z, 1); if (!negative && (rnd == ARF_RND_UP || rnd == ARF_RND_CEIL)) fmpz_add_ui(z, z, 1); } } } arb-2.8.1/arf/get_fmpz_2exp.c000066400000000000000000000040671264125401100157560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_get_fmpz_2exp(fmpz_t man, fmpz_t exp, const arf_t x) { if (arf_is_special(x)) { fmpz_zero(man); fmpz_zero(exp); } else { mp_srcptr xptr; mp_size_t xn; int shift; ARF_GET_MPN_READONLY(xptr, xn, x); count_trailing_zeros(shift, xptr[0]); fmpz_sub_ui(exp, ARF_EXPREF(x), xn * FLINT_BITS - shift); if (xn == 1) { if (ARF_SGNBIT(x)) fmpz_neg_ui(man, xptr[0] >> shift); else fmpz_set_ui(man, xptr[0] >> shift); } else { __mpz_struct * z = _fmpz_promote(man); if (z->_mp_alloc < xn) mpz_realloc(z, xn); if (shift == 0) flint_mpn_copyi(z->_mp_d, xptr, xn); else mpn_rshift(z->_mp_d, xptr, xn, shift); /* top limb cannot be zero */ z->_mp_size = ARF_SGNBIT(x) ? -xn : xn; } } } arb-2.8.1/arf/get_mag.c000066400000000000000000000036511264125401100146060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_get_mag(mag_t y, const arf_t x) { if (arf_is_zero(x)) { mag_zero(y); } else if (arf_is_special(x)) { mag_inf(y); } else { mp_limb_t t, u; ARF_GET_TOP_LIMB(t, x); t = (t >> (FLINT_BITS - MAG_BITS)) + LIMB_ONE; u = t >> MAG_BITS; t = (t >> u) + u; _fmpz_add_fast(MAG_EXPREF(y), ARF_EXPREF(x), u); MAG_MAN(y) = t; } } void arf_get_mag_lower(mag_t y, const arf_t x) { if (arf_is_zero(x)) { mag_zero(y); } else if (arf_is_special(x)) { if (arf_is_nan(x)) mag_zero(y); else mag_inf(y); } else { mp_limb_t t; ARF_GET_TOP_LIMB(t, x); MAG_MAN(y) = t >> (FLINT_BITS - MAG_BITS); _fmpz_set_fast(MAG_EXPREF(y), ARF_EXPREF(x)); } } arb-2.8.1/arf/get_mpfr.c000066400000000000000000000036401264125401100150040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_get_mpfr(mpfr_t x, const arf_t y, mpfr_rnd_t rnd) { int r; if (arf_is_special(y)) { if (arf_is_zero(y)) mpfr_set_zero(x, 0); else if (arf_is_pos_inf(y)) mpfr_set_inf(x, 1); else if (arf_is_neg_inf(y)) mpfr_set_inf(x, -1); else mpfr_set_nan(x); r = 0; } else if (COEFF_IS_MPZ(*ARF_EXPREF(y))) { flint_printf("exception: exponent too large to convert to mpfr"); abort(); } else { __mpfr_struct t; mp_size_t n; mp_srcptr d; ARF_GET_MPN_READONLY(d, n, y); t._mpfr_d = (mp_ptr) d; t._mpfr_exp = ARF_EXP(y); t._mpfr_prec = n * FLINT_BITS; t._mpfr_sign = ARF_SGNBIT(y) ? -1 : 1; r = mpfr_set(x, &t, rnd); } return r; } arb-2.8.1/arf/get_si.c000066400000000000000000000026151264125401100144540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" slong arf_get_si(const arf_t x, arf_rnd_t rnd) { fmpz_t t; slong v; fmpz_init(t); arf_get_fmpz(t, x, rnd); if (!fmpz_fits_si(t)) { flint_printf("arf_get_si: result does not fit in a signed slong\n"); abort(); } v = fmpz_get_si(t); fmpz_clear(t); return v; } arb-2.8.1/arf/inlines.c000066400000000000000000000021501264125401100146350ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define ARF_INLINES_C #include "arf.h" arb-2.8.1/arf/memory_manager.c000066400000000000000000000055561264125401100162130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" #define ARF_USE_CACHE 0 #define ARF_MAX_CACHE_LIMBS 64 FLINT_TLS_PREFIX mp_ptr * arf_free_arr = NULL; FLINT_TLS_PREFIX ulong arf_free_num = 0; FLINT_TLS_PREFIX ulong arf_free_alloc = 0; FLINT_TLS_PREFIX int arf_have_registered_cleanup = 0; void _arf_cleanup(void) { slong i; for (i = 0; i < arf_free_num; i++) flint_free(arf_free_arr[i]); flint_free(arf_free_arr); arf_free_arr = NULL; arf_free_num = 0; arf_free_alloc = 0; } void _arf_promote(arf_t x, mp_size_t n) { if (ARF_USE_CACHE && n <= ARF_MAX_CACHE_LIMBS && arf_free_num != 0) { mp_ptr ptr; mp_size_t alloc; ptr = arf_free_arr[--arf_free_num]; alloc = ptr[0]; if (alloc >= n) { ARF_PTR_ALLOC(x) = ptr[0]; ARF_PTR_D(x) = ptr; } else { ptr = flint_realloc(ptr, n * sizeof(mp_limb_t)); ARF_PTR_ALLOC(x) = n; ARF_PTR_D(x) = ptr; } } else { ARF_PTR_ALLOC(x) = n; ARF_PTR_D(x) = flint_malloc(n * sizeof(mp_limb_t)); } } void _arf_demote(arf_t x) { mp_ptr ptr; mp_size_t alloc; alloc = ARF_PTR_ALLOC(x); ptr = ARF_PTR_D(x); if (ARF_USE_CACHE && alloc <= ARF_MAX_CACHE_LIMBS) { if (arf_free_num == arf_free_alloc) { if (!arf_have_registered_cleanup) { flint_register_cleanup_function(_arf_cleanup); arf_have_registered_cleanup = 1; } arf_free_alloc = FLINT_MAX(64, arf_free_alloc * 2); arf_free_arr = flint_realloc(arf_free_arr, arf_free_alloc * sizeof(mp_ptr)); } ptr[0] = alloc; arf_free_arr[arf_free_num++] = ptr; } else { flint_free(ptr); } } arb-2.8.1/arf/mul_rnd_any.c000066400000000000000000000052051264125401100155070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" TLS_PREFIX mp_ptr __arf_mul_tmp = NULL; TLS_PREFIX slong __arf_mul_alloc = 0; void _arf_mul_tmp_cleanup(void) { flint_free(__arf_mul_tmp); __arf_mul_tmp = NULL; __arf_mul_alloc = 0; } int arf_mul_rnd_any(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; slong fix; int sgnbit, inexact; xn = ARF_XSIZE(x); yn = ARF_XSIZE(y); sgnbit = (xn ^ yn) & 1; xn >>= 1; yn >>= 1; if (yn > xn) { arf_srcptr __t; mp_size_t __u; __t = x; x = y; y = __t; __u = xn; xn = yn; yn = __u; } /* Either operand is a special value. */ if (yn == 0) { arf_mul_special(z, x, y); return 0; } else { mp_size_t zn, alloc; mp_srcptr xptr, yptr; mp_ptr tmp; ARF_MUL_TMP_DECL ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); alloc = zn = xn + yn; ARF_MUL_TMP_ALLOC(tmp, alloc) if (yn == 1) { tmp[zn - 1] = mpn_mul_1(tmp, xptr, xn, yptr[0]); } else if (xn == yn) { if (xptr == yptr) mpn_sqr(tmp, xptr, xn); else mpn_mul_n(tmp, xptr, yptr, yn); } else { mpn_mul(tmp, xptr, xn, yptr, yn); } inexact = _arf_set_round_mpn(z, &fix, tmp, zn, sgnbit, prec, rnd); _fmpz_add2_fast(ARF_EXPREF(z), ARF_EXPREF(x), ARF_EXPREF(y), fix); ARF_MUL_TMP_FREE(tmp, alloc) return inexact; } } arb-2.8.1/arf/mul_rnd_down.c000066400000000000000000000170541264125401100156740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_mul_rnd_down(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec) { mp_size_t xn, yn, zn; mp_limb_t hi, lo; slong expfix; int sgnbit, ret, fix; mp_ptr zptr; xn = ARF_XSIZE(x); yn = ARF_XSIZE(y); sgnbit = (xn ^ yn) & 1; xn >>= 1; yn >>= 1; if (yn > xn) { arf_srcptr __t; mp_size_t __u; __t = x; x = y; y = __t; __u = xn; xn = yn; yn = __u; } /* Either operand is a special value. */ if (yn == 0) { arf_mul_special(z, x, y); return 0; } /* xn == yn == 1 */ if (xn == 1) { lo = ARF_NOPTR_D(x)[0]; hi = ARF_NOPTR_D(y)[0]; umul_ppmm(hi, lo, hi, lo); /* Shift so that the top bit is set (branch free version). */ fix = !(hi >> (FLINT_BITS - 1)); hi = (hi << fix) | ((lo >> (FLINT_BITS - 1)) & fix); lo = (lo << fix); ARF_DEMOTE(z); if (lo == 0) { zn = 1; if (prec >= FLINT_BITS) { lo = hi; ret = 0; } else { lo = MASK_LIMB(hi, FLINT_BITS - prec); ret = (lo != hi); } } else { zn = 2; if (prec <= FLINT_BITS) /* Must be inexact. */ { lo = MASK_LIMB(hi, FLINT_BITS - prec); zn = ret = 1; } else if (prec >= 2 * FLINT_BITS) /* Must be exact. */ { ret = 0; } else /* prec < FLINT_BITS < 2 * FLINT_BITS */ { ret = MASK_LIMB(lo, 2 * FLINT_BITS - prec) != lo; lo = MASK_LIMB(lo, 2 * FLINT_BITS - prec); if (lo == 0) { zn = 1; lo = hi; } } } _fmpz_add2_fast(ARF_EXPREF(z), ARF_EXPREF(x), ARF_EXPREF(y), -fix); ARF_XSIZE(z) = ARF_MAKE_XSIZE(zn, sgnbit); zptr = ARF_NOPTR_D(z); zptr[0] = lo; zptr[1] = hi; return ret; } else if (xn == 2) { mp_limb_t zz[4]; mp_limb_t x1, x0, y1, y0; x0 = ARF_NOPTR_D(x)[0]; x1 = ARF_NOPTR_D(x)[1]; if (yn == 2) { y0 = ARF_NOPTR_D(y)[0]; y1 = ARF_NOPTR_D(y)[1]; nn_mul_2x2(zz[3], zz[2], zz[1], zz[0], x1, x0, y1, y0); /* Likely case, must be inexact */ if (prec <= 2 * FLINT_BITS) { ARF_DEMOTE(z); fix = !(zz[3] >> (FLINT_BITS - 1)); zz[3] = (zz[3] << fix) | ((zz[2] >> (FLINT_BITS - 1)) & fix); zz[2] = (zz[2] << fix) | ((zz[1] >> (FLINT_BITS - 1)) & fix); _fmpz_add2_fast(ARF_EXPREF(z), ARF_EXPREF(x), ARF_EXPREF(y), -fix); /* Rounding */ if (prec != 2 * FLINT_BITS) { if (prec > FLINT_BITS) { zz[2] &= (LIMB_ONES << (2 * FLINT_BITS - prec)); } else if (prec == FLINT_BITS) { zz[2] = 0; } else { zz[3] &= (LIMB_ONES << (FLINT_BITS - prec)); zz[2] = 0; } } if (zz[2] == 0) { ARF_XSIZE(z) = ARF_MAKE_XSIZE(1, sgnbit); ARF_NOPTR_D(z)[0] = zz[3]; } else { ARF_XSIZE(z) = ARF_MAKE_XSIZE(2, sgnbit); ARF_NOPTR_D(z)[0] = zz[2]; ARF_NOPTR_D(z)[1] = zz[3]; } return 1; } } else { y0 = ARF_NOPTR_D(y)[0]; nn_mul_2x1(zz[2], zz[1], zz[0], x1, x0, y0); } zn = xn + yn; ret = _arf_set_round_mpn(z, &expfix, zz, zn, sgnbit, prec, ARF_RND_DOWN); _fmpz_add2_fast(ARF_EXPREF(z), ARF_EXPREF(x), ARF_EXPREF(y), expfix); return ret; } else if (yn > MUL_MPFR_MIN_LIMBS && prec != ARF_PREC_EXACT && xn + yn > 1.25 * prec / FLINT_BITS && xn < MUL_MPFR_MAX_LIMBS) /* FIXME: proper cutoffs */ { return arf_mul_via_mpfr(z, x, y, prec, ARF_RND_DOWN); } else { mp_size_t zn, alloc; mp_srcptr xptr, yptr; mp_ptr tmp; ARF_MUL_TMP_DECL ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); alloc = zn = xn + yn; ARF_MUL_TMP_ALLOC(tmp, alloc) if (xn == yn) { if (xptr == yptr) mpn_sqr(tmp, xptr, xn); else mpn_mul_n(tmp, xptr, yptr, yn); } else if (yn == 1) { tmp[zn - 1] = mpn_mul_1(tmp, xptr, xn, yptr[0]); } else { mpn_mul(tmp, xptr, xn, yptr, yn); } ret = _arf_set_round_mpn(z, &expfix, tmp, zn, sgnbit, prec, ARF_RND_DOWN); _fmpz_add2_fast(ARF_EXPREF(z), ARF_EXPREF(x), ARF_EXPREF(y), expfix); ARF_MUL_TMP_FREE(tmp, alloc) return ret; } } int arf_mul_mpz(arf_ptr z, arf_srcptr x, const mpz_t y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; slong fix, shift; int sgnbit, inexact; yn = FLINT_ABS(y->_mp_size); xn = ARF_XSIZE(x); xn >>= 1; sgnbit = ARF_SGNBIT(x) ^ (y->_mp_size < 0); /* Either operand is a special value. */ if (xn == 0 || yn == 0) { if (arf_is_finite(x)) { arf_zero(z); } else { arf_t t; arf_init_set_si(t, mpz_sgn(y)); arf_mul(z, x, t, prec, rnd); arf_clear(t); } return 0; } else { mp_size_t zn, alloc; mp_srcptr xptr, yptr; mp_ptr tmp; ARF_MUL_TMP_DECL ARF_GET_MPN_READONLY(xptr, xn, x); yptr = y->_mp_d; alloc = zn = xn + yn; ARF_MUL_TMP_ALLOC(tmp, alloc) ARF_MPN_MUL(tmp, xptr, xn, yptr, yn); shift = yn * FLINT_BITS - (tmp[zn - 1] == 0) * FLINT_BITS; zn -= (tmp[zn - 1] == 0); inexact = _arf_set_round_mpn(z, &fix, tmp, zn, sgnbit, prec, rnd); _fmpz_add_fast(ARF_EXPREF(z), ARF_EXPREF(x), fix + shift); ARF_MUL_TMP_FREE(tmp, alloc) return inexact; } } arb-2.8.1/arf/mul_special.c000066400000000000000000000030711264125401100154740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_mul_special(arf_t z, const arf_t x, const arf_t y) { if (arf_is_zero(x)) { if (arf_is_finite(y)) arf_zero(z); else arf_nan(z); } else if (arf_is_zero(y)) { if (arf_is_finite(x)) arf_zero(z); else arf_nan(z); } else if (arf_is_nan(x) || arf_is_nan(y)) arf_nan(z); else if (arf_sgn(x) == arf_sgn(y)) arf_pos_inf(z); else arf_neg_inf(z); } arb-2.8.1/arf/mul_via_mpfr.c000066400000000000000000000050031264125401100156540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_mul_via_mpfr(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn, zn, val; mp_srcptr xptr, yptr; mp_ptr tmp, zptr; mpfr_t xf, yf, zf; int ret; ARF_MUL_TMP_DECL if (arf_is_special(x) || arf_is_special(y)) { arf_mul_special(z, x, y); return 0; } ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); prec = FLINT_MIN((xn + yn) * FLINT_BITS, prec); zn = (prec + FLINT_BITS - 1) / FLINT_BITS; ARF_MUL_TMP_ALLOC(tmp, zn) zf->_mpfr_d = tmp; zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = ARF_SGNBIT(x) ? -1 : 1; xf->_mpfr_exp = 0; if (x == y) { ret = mpfr_sqr(zf, xf, arf_rnd_to_mpfr(rnd)); } else { yf->_mpfr_d = (mp_ptr) yptr; yf->_mpfr_prec = yn * FLINT_BITS; yf->_mpfr_sign = ARF_SGNBIT(y) ? -1 : 1; yf->_mpfr_exp = 0; ret = mpfr_mul(zf, xf, yf, arf_rnd_to_mpfr(rnd)); } ret = (ret != 0); _fmpz_add2_fast(ARF_EXPREF(z), ARF_EXPREF(x), ARF_EXPREF(y), zf->_mpfr_exp); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); ARF_XSIZE(z) |= (zf->_mpfr_sign < 0); ARF_MUL_TMP_FREE(tmp, zn) return ret; } arb-2.8.1/arf/neg_round.c000066400000000000000000000033361264125401100151630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_neg_round(arf_t y, const arf_t x, slong prec, arf_rnd_t rnd) { if (arf_is_special(x)) { arf_neg(y, x); return 0; } else { int inexact; slong fix; mp_size_t xn; mp_srcptr xptr; if (y == x) { ARF_NEG(y); return arf_set_round(y, y, prec, rnd); } else { ARF_GET_MPN_READONLY(xptr, xn, x); inexact = _arf_set_round_mpn(y, &fix, xptr, xn, !ARF_SGNBIT(x), prec, rnd); _fmpz_add_fast(ARF_EXPREF(y), ARF_EXPREF(x), fix); return inexact; } } } arb-2.8.1/arf/print.c000066400000000000000000000042021264125401100143300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_print(const arf_t x) { if (arf_is_normal(x)) { fmpz_t man, exp; fmpz_init(man); fmpz_init(exp); arf_get_fmpz_2exp(man, exp, x); flint_printf("("); fmpz_print(man); flint_printf(" * 2^"); fmpz_print(exp); flint_printf(")"); fmpz_clear(man); fmpz_clear(exp); } else { if (arf_is_zero(x)) flint_printf("(0)"); else if (arf_is_pos_inf(x)) flint_printf("(+inf)"); else if (arf_is_neg_inf(x)) flint_printf("(-inf)"); else flint_printf("(nan)"); } } void arf_printd(const arf_t x, slong d) { if (arf_is_finite(x) && (ARF_EXP(x) <= MPFR_EMIN_MIN + 1 || ARF_EXP(x) >= MPFR_EMAX_MAX - 1)) { arf_print(x); } else { mpfr_t t; mpfr_init2(t, d * 3.33 + 10); mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); arf_get_mpfr(t, x, MPFR_RNDN); mpfr_printf("%.*Rg", FLINT_MAX(d, 1), t); mpfr_clear(t); } } arb-2.8.1/arf/randtest.c000066400000000000000000000040541264125401100150250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_randtest(arf_t x, flint_rand_t state, slong bits, slong mag_bits) { fmpz_t t; fmpz_init(t); fmpz_randtest(t, state, bits); arf_set_fmpz(x, t); if (!arf_is_zero(x)) fmpz_randtest(ARF_EXPREF(x), state, mag_bits); fmpz_clear(t); } void arf_randtest_not_zero(arf_t x, flint_rand_t state, slong bits, slong mag_bits) { fmpz_t t; fmpz_init(t); fmpz_randtest_not_zero(t, state, bits); arf_set_fmpz(x, t); fmpz_randtest(ARF_EXPREF(x), state, mag_bits); fmpz_clear(t); } void arf_randtest_special(arf_t x, flint_rand_t state, slong bits, slong mag_bits) { switch (n_randint(state, 32)) { case 0: arf_zero(x); break; case 1: arf_pos_inf(x); break; case 2: arf_neg_inf(x); break; case 3: arf_nan(x); break; default: arf_randtest_not_zero(x, state, bits, mag_bits); } } arb-2.8.1/arf/root.c000066400000000000000000000051621264125401100141650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_root(arf_ptr z, arf_srcptr x, ulong k, slong prec, arf_rnd_t rnd) { mp_size_t xn, zn, val; mp_srcptr xptr; mp_ptr tmp, zptr; mpfr_t xf, zf; fmpz_t q, r; int inexact; if (k == 0) { arf_nan(z); return 0; } if (k == 1) return arf_set_round(z, x, prec, rnd); if (k == 2) return arf_sqrt(z, x, prec, rnd); if (arf_is_special(x)) { if (arf_is_neg_inf(x)) arf_nan(z); else arf_set(z, x); return 0; } if (ARF_SGNBIT(x)) { arf_nan(z); return 0; } fmpz_init(q); fmpz_init(r); /* x = m * 2^e where e = qk + r */ /* x^(1/k) = (m * 2^(qk+r))^(1/k) */ /* x^(1/k) = (m * 2^r)^(1/k) * 2^q */ fmpz_set_ui(r, k); fmpz_fdiv_qr(q, r, ARF_EXPREF(x), r); ARF_GET_MPN_READONLY(xptr, xn, x); zn = (prec + FLINT_BITS - 1) / FLINT_BITS; zf->_mpfr_d = tmp = flint_malloc(zn * sizeof(mp_limb_t)); zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = 1; xf->_mpfr_exp = fmpz_get_ui(r); inexact = mpfr_root(zf, xf, k, arf_rnd_to_mpfr(rnd)); inexact = (inexact != 0); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); fmpz_add_si(ARF_EXPREF(z), q, zf->_mpfr_exp); flint_free(tmp); fmpz_clear(q); fmpz_clear(r); return inexact; } arb-2.8.1/arf/rsqrt.c000066400000000000000000000052271264125401100143570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_rsqrt(arf_ptr z, arf_srcptr x, slong prec, arf_rnd_t rnd) { mp_size_t xn, zn, val; mp_srcptr xptr; mp_ptr tmp, zptr; mpfr_t xf, zf; int inexact, odd_exp; ARF_MUL_TMP_DECL if (arf_is_special(x)) { if (arf_is_zero(x)) arf_pos_inf(z); else if (arf_is_pos_inf(x)) arf_zero(z); else arf_nan(z); return 0; } if (ARF_SGNBIT(x)) { arf_nan(z); return 0; } if (ARF_IS_POW2(x) && fmpz_is_odd(ARF_EXPREF(x))) { arf_set(z, x); fmpz_neg(ARF_EXPREF(z), ARF_EXPREF(z)); fmpz_cdiv_q_2exp(ARF_EXPREF(z), ARF_EXPREF(z), 1); fmpz_add_ui(ARF_EXPREF(z), ARF_EXPREF(z), 1); return 0; } ARF_GET_MPN_READONLY(xptr, xn, x); odd_exp = fmpz_is_odd(ARF_EXPREF(x)) ? 1 : 0; zn = (prec + FLINT_BITS - 1) / FLINT_BITS; ARF_MUL_TMP_ALLOC(tmp, zn) zf->_mpfr_d = tmp; zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = 1; xf->_mpfr_exp = odd_exp; inexact = mpfr_rec_sqrt(zf, xf, arf_rnd_to_mpfr(rnd)); inexact = (inexact != 0); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); fmpz_fdiv_q_2exp(ARF_EXPREF(z), ARF_EXPREF(x), 1); fmpz_neg(ARF_EXPREF(z), ARF_EXPREF(z)); fmpz_add_si(ARF_EXPREF(z), ARF_EXPREF(z), zf->_mpfr_exp); ARF_MUL_TMP_FREE(tmp, zn) return inexact; } arb-2.8.1/arf/set_d.c000066400000000000000000000040601264125401100142740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "double_extras.h" void arf_set_d(arf_t x, double v) { #if FLINT_BITS == 64 mp_limb_t h, sign, exp, frac; slong real_exp, real_man; union { double uf; mp_limb_t ul; } u; u.uf = v; h = u.ul; sign = h >> 63; exp = (h << 1) >> 53; frac = (h << 12) >> 12; if (exp == 0 && frac == 0) { arf_zero(x); } else if (exp == 0x7ff) { if (frac == 0) { if (sign) arf_neg_inf(x); else arf_pos_inf(x); } else { arf_nan(x); } } else { real_exp = exp - 1023 - 52; frac |= (UWORD(1) << 52); real_man = sign ? (-frac) : frac; arf_set_si_2exp_si(x, real_man, real_exp); } #else mpfr_t t; mp_limb_t tmp[2]; t->_mpfr_prec = 53; t->_mpfr_sign = 1; t->_mpfr_exp = 0; t->_mpfr_d = tmp; mpfr_set_d(t, v, MPFR_RNDD); arf_set_mpfr(x, t); #endif } arb-2.8.1/arf/set_fmpr.c000066400000000000000000000030141264125401100150130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_set_fmpr(arf_t y, const fmpr_t x) { if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) arf_zero(y); else if (fmpr_is_pos_inf(x)) arf_pos_inf(y); else if (fmpr_is_neg_inf(x)) arf_neg_inf(y); else arf_nan(y); } else { arf_set_fmpz(y, fmpr_manref(x)); fmpz_add_inline(ARF_EXPREF(y), ARF_EXPREF(y), fmpr_expref(x)); } } arb-2.8.1/arf/set_mpfr.c000066400000000000000000000031501264125401100150140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_set_mpfr(arf_t x, const mpfr_t y) { if (!mpfr_regular_p(y)) { if (mpfr_zero_p(y)) arf_zero(x); else if (mpfr_inf_p(y) && mpfr_sgn(y) > 0) arf_pos_inf(x); else if (mpfr_inf_p(y) && mpfr_sgn(y) < 0) arf_neg_inf(x); else arf_nan(x); } else { mp_size_t n = (y->_mpfr_prec + FLINT_BITS - 1) / FLINT_BITS; arf_set_mpn(x, y->_mpfr_d, n, y->_mpfr_sign < 0); fmpz_set_si(ARF_EXPREF(x), y->_mpfr_exp); } } arb-2.8.1/arf/set_mpn.c000066400000000000000000000035451264125401100146520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void arf_set_mpn(arf_t y, mp_srcptr x, mp_size_t xn, int sgnbit) { unsigned int leading; mp_size_t yn, xn1; mp_ptr yptr; mp_limb_t bot; xn1 = xn; while (x[0] == 0) { x++; xn--; } count_leading_zeros(leading, x[xn - 1]); bot = x[0]; /* This works when leading == 0, since x[0] != 0. */ yn = xn - ((bot << leading) == 0); ARF_GET_MPN_WRITE(yptr, yn, y); ARF_XSIZE(y) |= sgnbit; if (leading == 0) { flint_mpn_copyi(yptr, x, xn); } else if (xn == yn) { mpn_lshift(yptr, x, yn, leading); } else { mpn_lshift(yptr, x + 1, yn, leading); yptr[0] |= (bot >> (FLINT_BITS - leading)); } fmpz_set_ui(ARF_EXPREF(y), xn1 * FLINT_BITS - leading); } arb-2.8.1/arf/set_round.c000066400000000000000000000045641264125401100152110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_set_round(arf_t y, const arf_t x, slong prec, arf_rnd_t rnd) { if (arf_is_special(x)) { arf_set(y, x); return 0; } else { int inexact; slong fix; mp_size_t xn; mp_srcptr xptr; if (y == x) { mp_ptr xtmp; TMP_INIT; ARF_GET_MPN_READONLY(xptr, xn, x); /* exact */ if (xn * FLINT_BITS <= prec) return 0; if ((xn - 1) * FLINT_BITS < prec) { /* exact */ if ((xptr[0] << (prec - (xn-1) * FLINT_BITS)) == 0) return 0; } /* inexact */ TMP_START; xtmp = TMP_ALLOC(xn * sizeof(mp_limb_t)); flint_mpn_copyi(xtmp, xptr, xn); inexact = _arf_set_round_mpn(y, &fix, xtmp, xn, ARF_SGNBIT(x), prec, rnd); _fmpz_add_fast(ARF_EXPREF(y), ARF_EXPREF(x), fix); TMP_END; return inexact; } else { ARF_GET_MPN_READONLY(xptr, xn, x); inexact = _arf_set_round_mpn(y, &fix, xptr, xn, ARF_SGNBIT(x), prec, rnd); _fmpz_add_fast(ARF_EXPREF(y), ARF_EXPREF(x), fix); return inexact; } } } arb-2.8.1/arf/set_round_mpn.c000066400000000000000000000107761264125401100160650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" void _arf_set_mpn_roundup_power_two(arf_t y, int sgnbit) { /* The exponent has already been set, so just increment it. */ fmpz_add_ui(ARF_EXPREF(y), ARF_EXPREF(y), 1); ARF_DEMOTE(y); ARF_NOPTR_D(y)[0] = LIMB_TOP; ARF_XSIZE(y) = ARF_MAKE_XSIZE(1, sgnbit); } int _arf_set_round_mpn(arf_t y, slong * exp_shift, mp_srcptr x, mp_size_t xn, int sgnbit, slong prec, arf_rnd_t rnd) { unsigned int leading; mp_bitcnt_t exp, bc, val, val_bits; mp_size_t yn, val_limbs; mp_ptr yptr; mp_limb_t t; int increment, inexact; /* Compute the total bit length of x. */ count_leading_zeros(leading, x[xn - 1]); exp = xn * FLINT_BITS - leading; /* Set exponent. */ *exp_shift = -(slong) leading; /* Find first nonzero bit. */ val_limbs = 0; while (x[val_limbs] == 0) val_limbs++; count_trailing_zeros(val_bits, x[val_limbs]); val = val_limbs * FLINT_BITS + val_bits; if (exp - val <= prec) { inexact = 0; increment = 0; } else { inexact = 1; increment = arf_rounds_up(rnd, sgnbit); /* Limb and bit of the truncation point. */ val_limbs = (exp - prec) / FLINT_BITS; val_bits = (exp - prec) % FLINT_BITS; if (!increment) { /* Find first nonzero bit from the truncation point. */ t = x[val_limbs] & (LIMB_ONES << val_bits); while (t == 0) { val_limbs++; t = x[val_limbs]; } count_trailing_zeros(val_bits, t); val = val_limbs * FLINT_BITS + val_bits; } else { /* Find first zero bit from the truncation point */ t = (~x[val_limbs]) & (LIMB_ONES << val_bits); while (t == 0) { val_limbs++; if (val_limbs < xn) t = ~x[val_limbs]; else /* The array is all ones up to the highest limb. */ { val_bits = 0; goto END_SCAN1; } } count_trailing_zeros(val_bits, t); END_SCAN1: val = val_limbs * FLINT_BITS + val_bits; /* Overflow to next power of two (unlikely). */ if (val == exp) { exp_shift[0]++; ARF_DEMOTE(y); ARF_NOPTR_D(y)[0] = LIMB_TOP; ARF_XSIZE(y) = ARF_MAKE_XSIZE(1, sgnbit); return 1; } } } /* Now copy the result to destination. */ x += val_limbs; xn -= val_limbs; bc = exp - val; yn = (bc + FLINT_BITS - 1) / FLINT_BITS; ARF_GET_MPN_WRITE(yptr, yn, y); ARF_XSIZE(y) |= sgnbit; if (leading == 0) { flint_mpn_copyi(yptr, x, xn); } else if (xn == yn) { mpn_lshift(yptr, x, yn, leading); } else { mpn_lshift(yptr, x + 1, yn, leading); yptr[0] |= (x[0] >> (FLINT_BITS - leading)); } if (increment) { /* Mask off bits from the last limb. */ yptr[0] &= LIMB_ONES << (yn * FLINT_BITS - bc); /* Increment (no carry propagation). */ yptr[0] += LIMB_ONE << (yn * FLINT_BITS - bc); } else if (inexact && prec < yn * FLINT_BITS) { /* Mask off bits from the last limb. */ yptr[0] &= LIMB_ONES << (yn * FLINT_BITS - prec); } return inexact; } arb-2.8.1/arf/set_round_ui.c000066400000000000000000000064411264125401100157020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" /* Top-aligns the nonzero limb v and rounds it to prec bit. */ #define ARF_NORMALISE_ROUND_LIMB(inexact, exp, v, \ sgnbit, prec, rnd) \ do { \ count_leading_zeros(exp, v); \ v <<= exp; \ exp = FLINT_BITS - exp; \ if (prec >= exp) \ { \ inexact = 0; \ } \ else \ { \ mp_limb_t __t = v; \ v = MASK_LIMB(v, FLINT_BITS - prec); \ inexact = (__t != v); \ if (inexact && arf_rounds_up(rnd, sgnbit)) \ { \ v += (LIMB_ONE << (FLINT_BITS - prec)); \ if (v == 0) \ { \ v = LIMB_TOP; \ exp++; \ } \ } \ } \ } \ while (0) int _arf_set_round_ui(arf_t x, ulong v, int sgnbit, slong prec, arf_rnd_t rnd) { if (v == 0) { arf_zero(x); return 0; } else { int exp, inexact; ARF_NORMALISE_ROUND_LIMB(inexact, exp, v, sgnbit, prec, rnd); _fmpz_demote(ARF_EXPREF(x)); ARF_EXP(x) = exp; ARF_DEMOTE(x); ARF_XSIZE(x) = ARF_MAKE_XSIZE(1, sgnbit); ARF_NOPTR_D(x)[0] = v; return inexact; } } arb-2.8.1/arf/set_round_uiui.c000066400000000000000000000132051264125401100162340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" /* Top-aligns the nonzero limb v and rounds it to prec bit. */ #define ARF_NORMALISE_ROUND_LIMB(inexact, exp, v, \ sgnbit, prec, rnd) \ do { \ count_leading_zeros(exp, v); \ v <<= exp; \ exp = FLINT_BITS - exp; \ if (prec >= exp) \ { \ inexact = 0; \ } \ else \ { \ mp_limb_t __t = v; \ v = MASK_LIMB(v, FLINT_BITS - prec); \ inexact = (__t != v); \ if (inexact && arf_rounds_up(rnd, sgnbit)) \ { \ v += (LIMB_ONE << (FLINT_BITS - prec)); \ if (v == 0) \ { \ v = LIMB_TOP; \ exp++; \ } \ } \ } \ } \ while (0) int _arf_set_round_uiui(arf_t z, slong * fix, mp_limb_t hi, mp_limb_t lo, int sgnbit, slong prec, arf_rnd_t rnd) { int leading, trailing, bc, inexact, zn, up, exp; if (hi == 0) { ARF_NORMALISE_ROUND_LIMB(inexact, exp, lo, sgnbit, prec, rnd); leading = 2 * FLINT_BITS - exp; zn = 1; } else if (lo == 0) { ARF_NORMALISE_ROUND_LIMB(inexact, exp, hi, sgnbit, prec, rnd); leading = FLINT_BITS - exp; lo = hi; zn = 1; } else { count_leading_zeros(leading, hi); count_trailing_zeros(trailing, lo); bc = 2 * FLINT_BITS - leading - trailing; if (bc <= prec) { inexact = 0; zn = 2; if (leading != 0) { if (bc <= FLINT_BITS) { lo = (hi << leading) | (lo >> (FLINT_BITS - leading)); zn = 1; } else { hi = (hi << leading) | (lo >> (FLINT_BITS - leading)); lo = (lo << leading); } } } else { inexact = 1; up = arf_rounds_up(rnd, sgnbit); if (prec <= FLINT_BITS) { zn = 1; if (leading == 0) lo = hi; else lo = (hi << leading) | (lo >> (FLINT_BITS - leading)); lo = lo & (LIMB_ONES << (FLINT_BITS - prec)); if (up) { mp_limb_t t, ovf; t = lo + (LIMB_ONE << (FLINT_BITS - prec)); ovf = (t == 0); leading -= ovf; lo = (t >> ovf) | (ovf << (FLINT_BITS - 1)); } } else { zn = 2; if (leading != 0) { hi = (hi << leading) | (lo >> (FLINT_BITS - leading)); lo = (lo << leading); } lo = lo & (LIMB_ONES << (2 * FLINT_BITS - prec)); if (up) { add_ssaaaa(hi, lo, hi, lo, 0, (LIMB_ONE << (2 * FLINT_BITS - prec))); } if (lo == 0) { if (hi == 0) { leading -= 1; lo = LIMB_TOP; } else { lo = hi; } zn = 1; } } } } *fix = -leading; ARF_DEMOTE(z); ARF_XSIZE(z) = ARF_MAKE_XSIZE(zn, sgnbit); ARF_NOPTR_D(z)[0] = lo; ARF_NOPTR_D(z)[1] = hi; return inexact; } arb-2.8.1/arf/sqrt.c000066400000000000000000000055131264125401100141730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_sqrt(arf_ptr z, arf_srcptr x, slong prec, arf_rnd_t rnd) { mp_size_t xn, zn, val; mp_srcptr xptr; mp_ptr tmp, zptr; mpfr_t xf, zf; int inexact, odd_exp; ARF_MUL_TMP_DECL if (arf_is_special(x)) { if (arf_is_neg_inf(x)) arf_nan(z); else arf_set(z, x); return 0; } if (ARF_SGNBIT(x)) { arf_nan(z); return 0; } if (ARF_IS_POW2(x) && fmpz_is_odd(ARF_EXPREF(x))) { arf_set(z, x); fmpz_cdiv_q_2exp(ARF_EXPREF(z), ARF_EXPREF(z), 1); return 0; } ARF_GET_MPN_READONLY(xptr, xn, x); odd_exp = fmpz_is_odd(ARF_EXPREF(x)) ? 1 : 0; zn = (prec + FLINT_BITS - 1) / FLINT_BITS; ARF_MUL_TMP_ALLOC(tmp, zn) zf->_mpfr_d = tmp; zf->_mpfr_prec = prec; zf->_mpfr_sign = 1; zf->_mpfr_exp = 0; xf->_mpfr_d = (mp_ptr) xptr; xf->_mpfr_prec = xn * FLINT_BITS; xf->_mpfr_sign = 1; xf->_mpfr_exp = odd_exp; inexact = mpfr_sqrt(zf, xf, arf_rnd_to_mpfr(rnd)); inexact = (inexact != 0); val = 0; while (tmp[val] == 0) val++; ARF_GET_MPN_WRITE(zptr, zn - val, z); flint_mpn_copyi(zptr, tmp + val, zn - val); fmpz_fdiv_q_2exp(ARF_EXPREF(z), ARF_EXPREF(x), 1); fmpz_add_si(ARF_EXPREF(z), ARF_EXPREF(z), zf->_mpfr_exp); ARF_MUL_TMP_FREE(tmp, zn) return inexact; } int arf_sqrt_ui(arf_t z, ulong x, slong prec, arf_rnd_t rnd) { arf_t t; arf_init_set_ui(t, x); /* no need to free */ return arf_sqrt(z, t, prec, rnd); } int arf_sqrt_fmpz(arf_t z, const fmpz_t x, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_set_fmpz(t, x); inexact = arf_sqrt(z, t, prec, rnd); arf_clear(t); return inexact; } arb-2.8.1/arf/sub.c000066400000000000000000000132021264125401100137650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_sub_special(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { if (arf_is_zero(x)) { if (arf_is_zero(y)) { arf_zero(z); return 0; } else return arf_neg_round(z, y, prec, rnd); } else if (arf_is_zero(y)) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_nan(x) || arf_is_nan(y) || (arf_is_pos_inf(x) && arf_is_pos_inf(y)) || (arf_is_neg_inf(x) && arf_is_neg_inf(y))) { arf_nan(z); return 0; } else if (arf_is_special(x)) { arf_set(z, x); return 0; } else { arf_neg(z, y); return 0; } } int arf_sub(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; slong shift; if (arf_is_special(x) || arf_is_special(y)) { return arf_sub_special(z, x, y, prec, rnd); } shift = _fmpz_sub_small(ARF_EXPREF(x), ARF_EXPREF(y)); ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); if (shift >= 0) return _arf_add_mpn(z, xptr, xn, ARF_SGNBIT(x), ARF_EXPREF(x), yptr, yn, ARF_SGNBIT(y) ^ 1, shift, prec, rnd); else return _arf_add_mpn(z, yptr, yn, ARF_SGNBIT(y) ^ 1, ARF_EXPREF(y), xptr, xn, ARF_SGNBIT(x), -shift, prec, rnd); } int arf_sub_si(arf_ptr z, arf_srcptr x, slong y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; mp_limb_t ytmp; int xsgnbit, ysgnbit; fmpz yexp; slong shift; if (y == 0) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_special(x)) { if (arf_is_zero(x)) { arf_set_si(z, y); return arf_neg_round(z, z, prec, rnd); } else { arf_set(z, x); return 0; } } ysgnbit = (y < 0); if (ysgnbit) ytmp = -y; else ytmp = y; yptr = &ytmp; yn = 1; yexp = FLINT_BITS; ysgnbit ^= 1; shift = _fmpz_sub_small(ARF_EXPREF(x), &yexp); xsgnbit = ARF_SGNBIT(x); ARF_GET_MPN_READONLY(xptr, xn, x); if (shift >= 0) return _arf_add_mpn(z, xptr, xn, xsgnbit, ARF_EXPREF(x), yptr, yn, ysgnbit, shift, prec, rnd); else return _arf_add_mpn(z, yptr, yn, ysgnbit, &yexp, xptr, xn, xsgnbit, -shift, prec, rnd); } int arf_sub_ui(arf_ptr z, arf_srcptr x, ulong y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; mp_limb_t ytmp; int xsgnbit, ysgnbit; fmpz yexp; slong shift; if (y == 0) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_special(x)) { if (arf_is_zero(x)) { arf_set_ui(z, y); return arf_neg_round(z, z, prec, rnd); } else { arf_set(z, x); return 0; } } ysgnbit = 1; ytmp = y; yptr = &ytmp; yn = 1; yexp = FLINT_BITS; shift = _fmpz_sub_small(ARF_EXPREF(x), &yexp); xsgnbit = ARF_SGNBIT(x); ARF_GET_MPN_READONLY(xptr, xn, x); if (shift >= 0) return _arf_add_mpn(z, xptr, xn, xsgnbit, ARF_EXPREF(x), yptr, yn, ysgnbit, shift, prec, rnd); else return _arf_add_mpn(z, yptr, yn, ysgnbit, &yexp, xptr, xn, xsgnbit, -shift, prec, rnd); } int arf_sub_fmpz(arf_ptr z, arf_srcptr x, const fmpz_t y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn; mp_srcptr xptr, yptr; mp_limb_t ytmp; int xsgnbit, ysgnbit; fmpz yexp; slong shift; if (fmpz_is_zero(y)) { return arf_set_round(z, x, prec, rnd); } else if (arf_is_special(x)) { if (arf_is_zero(x)) { arf_set_fmpz(z, y); return arf_neg_round(z, z, prec, rnd); } else { arf_set(z, x); return 0; } } FMPZ_GET_MPN_READONLY(ysgnbit, yn, yptr, ytmp, *y) yexp = yn * FLINT_BITS; shift = _fmpz_sub_small(ARF_EXPREF(x), &yexp); ysgnbit ^= 1; xsgnbit = ARF_SGNBIT(x); ARF_GET_MPN_READONLY(xptr, xn, x); if (shift >= 0) return _arf_add_mpn(z, xptr, xn, xsgnbit, ARF_EXPREF(x), yptr, yn, ysgnbit, shift, prec, rnd); else return _arf_add_mpn(z, yptr, yn, ysgnbit, &yexp, xptr, xn, xsgnbit, -shift, prec, rnd); } arb-2.8.1/arf/submul.c000066400000000000000000000110341264125401100145040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_submul(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn, zn, tn, alloc; mp_srcptr xptr, yptr, zptr; mp_ptr tptr, tptr2; fmpz_t texp; slong shift; int tsgnbit, inexact; ARF_MUL_TMP_DECL if (arf_is_special(x) || arf_is_special(y) || arf_is_special(z)) { if (arf_is_zero(z)) { return arf_neg_mul(z, x, y, prec, rnd); } else if (arf_is_finite(x) && arf_is_finite(y)) { return arf_set_round(z, z, prec, rnd); } else { /* todo: speed up */ arf_t t; arf_init(t); arf_mul(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_sub(z, z, t, prec, rnd); arf_clear(t); return inexact; } } tsgnbit = ARF_SGNBIT(x) ^ ARF_SGNBIT(y) ^ 1; ARF_GET_MPN_READONLY(xptr, xn, x); ARF_GET_MPN_READONLY(yptr, yn, y); ARF_GET_MPN_READONLY(zptr, zn, z); fmpz_init(texp); _fmpz_add2_fast(texp, ARF_EXPREF(x), ARF_EXPREF(y), 0); shift = _fmpz_sub_small(ARF_EXPREF(z), texp); alloc = tn = xn + yn; ARF_MUL_TMP_ALLOC(tptr2, alloc) tptr = tptr2; ARF_MPN_MUL(tptr, xptr, xn, yptr, yn); tn -= (tptr[0] == 0); tptr += (tptr[0] == 0); if (shift >= 0) inexact = _arf_add_mpn(z, zptr, zn, ARF_SGNBIT(z), ARF_EXPREF(z), tptr, tn, tsgnbit, shift, prec, rnd); else inexact = _arf_add_mpn(z, tptr, tn, tsgnbit, texp, zptr, zn, ARF_SGNBIT(z), -shift, prec, rnd); ARF_MUL_TMP_FREE(tptr2, alloc) fmpz_clear(texp); return inexact; } int arf_submul_mpz(arf_ptr z, arf_srcptr x, const mpz_t y, slong prec, arf_rnd_t rnd) { mp_size_t xn, yn, zn, tn, alloc; mp_srcptr xptr, yptr, zptr; mp_ptr tptr, tptr2; fmpz_t texp, yexp; slong shift; int tsgnbit, ysgnbit, inexact; ARF_MUL_TMP_DECL yn = FLINT_ABS(y->_mp_size); if (arf_is_special(x) || yn == 0 || arf_is_special(z)) { if (arf_is_zero(z)) { /* TODO: make more efficient */ arf_mul_mpz(z, x, y, ARF_PREC_EXACT, rnd); return arf_neg_round(z, z, prec, rnd); } else if (arf_is_finite(x)) { return arf_set_round(z, z, prec, rnd); } else { /* todo: speed up */ arf_t t; arf_init(t); arf_mul_mpz(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_sub(z, z, t, prec, rnd); arf_clear(t); return inexact; } } ARF_GET_MPN_READONLY(xptr, xn, x); yptr = y->_mp_d; ysgnbit = (y->_mp_size > 0); *yexp = yn * FLINT_BITS; ARF_GET_MPN_READONLY(zptr, zn, z); fmpz_init(texp); tsgnbit = ARF_SGNBIT(x) ^ ysgnbit; alloc = tn = xn + yn; ARF_MUL_TMP_ALLOC(tptr2, alloc) tptr = tptr2; ARF_MPN_MUL(tptr, xptr, xn, yptr, yn); shift = (tptr[tn - 1] == 0) * FLINT_BITS; tn -= (tptr[tn - 1] == 0); _fmpz_add2_fast(texp, ARF_EXPREF(x), yexp, -shift); shift = _fmpz_sub_small(ARF_EXPREF(z), texp); if (shift >= 0) inexact = _arf_add_mpn(z, zptr, zn, ARF_SGNBIT(z), ARF_EXPREF(z), tptr, tn, tsgnbit, shift, prec, rnd); else inexact = _arf_add_mpn(z, tptr, tn, tsgnbit, texp, zptr, zn, ARF_SGNBIT(z), -shift, prec, rnd); ARF_MUL_TMP_FREE(tptr2, alloc) fmpz_clear(texp); return inexact; } arb-2.8.1/arf/sum.c000066400000000000000000000121251264125401100140030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int _arf_are_close(const arf_t x, const arf_t y, slong prec) { fmpz_t xb, yb; fmpz_t delta; int result; fmpz_init(xb); fmpz_init(yb); fmpz_init(delta); arf_bot(xb, x); arf_bot(yb, y); if (fmpz_cmp(ARF_EXPREF(x), ARF_EXPREF(y)) >= 0) fmpz_sub(delta, xb, ARF_EXPREF(y)); else fmpz_sub(delta, yb, ARF_EXPREF(x)); fmpz_sub_ui(delta, delta, 64); result = (fmpz_cmp_ui(delta, prec) < 0); fmpz_clear(xb); fmpz_clear(yb); fmpz_clear(delta); return result; } int _arf_add_eps(arf_t s, const arf_t x, int sgn, slong prec, arf_rnd_t rnd) { arf_t t; slong bits; bits = arf_bits(x); if (bits == 0) { flint_printf("_arf_add_eps\n"); abort(); } bits = FLINT_MAX(bits, prec) + 10; arf_init(t); arf_set_si(t, sgn); arf_mul_2exp_fmpz(t, t, ARF_EXPREF(x)); arf_mul_2exp_si(t, t, -bits); arf_add(s, x, t, prec, rnd); arf_clear(t); return 1; } int arf_sum(arf_t s, arf_srcptr terms, slong len, slong prec, arf_rnd_t rnd) { arf_ptr blocks; slong i, j, used; int have_merged, res; /* first check if the result is inf or nan */ { int have_pos_inf = 0; int have_neg_inf = 0; for (i = 0; i < len; i++) { if (arf_is_pos_inf(terms + i)) { if (have_neg_inf) { arf_nan(s); return 0; } have_pos_inf = 1; } else if (arf_is_neg_inf(terms + i)) { if (have_pos_inf) { arf_nan(s); return 0; } have_neg_inf = 1; } else if (arf_is_nan(terms + i)) { arf_nan(s); return 0; } } if (have_pos_inf) { arf_pos_inf(s); return 0; } if (have_neg_inf) { arf_neg_inf(s); return 0; } } blocks = flint_malloc(sizeof(arf_struct) * len); for (i = 0; i < len; i++) arf_init(blocks + i); /* put all terms into blocks */ used = 0; for (i = 0; i < len; i++) { if (!arf_is_zero(terms + i)) { arf_set(blocks + used, terms + i); used++; } } /* merge blocks until all are well separated */ have_merged = 1; while (used >= 2 && have_merged) { have_merged = 0; for (i = 0; i < used && !have_merged; i++) { for (j = i + 1; j < used && !have_merged; j++) { if (_arf_are_close(blocks + i, blocks + j, prec)) { arf_add(blocks + i, blocks + i, blocks + j, ARF_PREC_EXACT, ARF_RND_DOWN); /* remove the merged block */ arf_swap(blocks + j, blocks + used - 1); used--; /* remove the updated block if the sum is zero */ if (arf_is_zero(blocks + i)) { arf_swap(blocks + i, blocks + used - 1); used--; } have_merged = 1; } } } } if (used == 0) { arf_zero(s); res = 0; } else if (used == 1) { res = arf_set_round(s, blocks + 0, prec, rnd); } else { /* find the two largest blocks */ for (i = 1; i < used; i++) if (arf_cmpabs(blocks + 0, blocks + i) < 0) arf_swap(blocks + 0, blocks + i); for (i = 2; i < used; i++) if (arf_cmpabs(blocks + 1, blocks + i) < 0) arf_swap(blocks + 1, blocks + i); res = _arf_add_eps(s, blocks + 0, arf_sgn(blocks + 1), prec, rnd); } for (i = 0; i < len; i++) arf_clear(blocks + i); flint_free(blocks); return res; } arb-2.8.1/arf/test/000077500000000000000000000000001264125401100140115ustar00rootroot00000000000000arb-2.8.1/arf/test/t-abs_bound_le_2exp_fmpz.c000066400000000000000000000044221264125401100210260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("abs_bound_le_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y; fmpz_t b; int cmp1, cmp2; arf_init(x); arf_init(y); fmpz_init(b); arf_randtest_not_zero(x, state, 2 + n_randint(state, 1000), 100); arf_abs_bound_le_2exp_fmpz(b, x); arf_one(y); arf_mul_2exp_fmpz(y, y, b); cmp1 = (arf_cmpabs(x, y) <= 0); arf_mul_2exp_si(y, y, -1); cmp2 = (arf_cmpabs(y, x) < 0); arf_mul_2exp_si(y, y, 1); if (!cmp1 || !cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } arf_clear(x); arf_clear(y); fmpz_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-abs_bound_lt_2exp_fmpz.c000066400000000000000000000044221264125401100210450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("abs_bound_lt_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y; fmpz_t b; int cmp1, cmp2; arf_init(x); arf_init(y); fmpz_init(b); arf_randtest_not_zero(x, state, 2 + n_randint(state, 1000), 100); arf_abs_bound_lt_2exp_fmpz(b, x); arf_one(y); arf_mul_2exp_fmpz(y, y, b); cmp1 = (arf_cmpabs(x, y) < 0); arf_mul_2exp_si(y, y, -1); cmp2 = (arf_cmpabs(y, x) <= 0); arf_mul_2exp_si(y, y, 1); if (!cmp1 || !cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } arf_clear(x); arf_clear(y); fmpz_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-abs_bound_lt_2exp_si.c000066400000000000000000000055471264125401100205150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("abs_bound_lt_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x; fmpz_t b; slong c; arf_init(x); fmpz_init(b); if (iter < 5) { arf_set_ui_2exp_si(x, 1, LONG_MIN + 2); arf_mul_2exp_si(x, x, -iter); } else if (iter < 10) { arf_set_ui_2exp_si(x, 1, WORD_MAX - 2); arf_mul_2exp_si(x, x, iter - 5); } else { arf_randtest_special(x, state, 2 + n_randint(state, 1000), 100); } arf_abs_bound_lt_2exp_fmpz(b, x); c = arf_abs_bound_lt_2exp_si(x); if (c == -ARF_PREC_EXACT) { if (!(arf_is_zero(x) || fmpz_cmp_si(b, -ARF_PREC_EXACT) <= 0)) { flint_printf("FAIL (small/zero)\n\n"); abort(); } } else if (c == ARF_PREC_EXACT) { if (!(arf_is_inf(x) || arf_is_nan(x) || fmpz_cmp_si(b, ARF_PREC_EXACT) >= 0)) { flint_printf("FAIL (large/inf/nan)\n\n"); abort(); } } else { if (fmpz_cmp_si(b, c) != 0) { flint_printf("FAIL (normal)\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("c = %wd\n\n", c); abort(); } } arf_clear(x); fmpz_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-add.c000066400000000000000000000142751264125401100151570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_add_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { fmpr_t a, b; slong r; fmpr_init(a); fmpr_init(b); arf_get_fmpr(a, x); arf_get_fmpr(b, y); r = fmpr_add(a, a, b, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); fmpr_clear(b); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(y)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_add(z, x, y, prec, rnd); r2 = arf_add_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = arf_add(z, x, x, prec, rnd); r2 = arf_add_naive(v, x, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = arf_add_naive(v, x, x, prec, rnd); r1 = arf_add(x, x, x, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = arf_add_naive(v, x, y, prec, rnd); r1 = arf_add(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_add_naive(v, x, y, prec, rnd); r1 = arf_add(x, y, x, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-add_fmpz.c000066400000000000000000000077641264125401100162200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_add_fmpz_naive(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz(t, y); r = arf_add(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("add_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; fmpz_t y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); fmpz_init(y); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); fmpz_randtest(y, state, 2000); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_add_fmpz(z, x, y, prec, rnd); r2 = arf_add_fmpz_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_add_fmpz_naive(v, x, y, prec, rnd); r1 = arf_add_fmpz(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); fmpz_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-add_fmpz_2exp.c000066400000000000000000000104651264125401100171460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_add_fmpz_2exp_naive(arf_t z, const arf_t x, const fmpz_t y, const fmpz_t e, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz_2exp(t, y, e); r = arf_add(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("add_fmpz_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; fmpz_t y, e; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); fmpz_init(y); fmpz_init(e); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); fmpz_randtest(y, state, 2000); fmpz_randtest(e, state, 10); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_add_fmpz_2exp(z, x, y, e, prec, rnd); r2 = arf_add_fmpz_2exp_naive(v, x, y, e, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("e = "); fmpz_print(e); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_add_fmpz_2exp_naive(v, x, y, e, prec, rnd); r1 = arf_add_fmpz_2exp(x, x, y, e, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("e = "); fmpz_print(e); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); fmpz_clear(y); fmpz_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-add_si.c000066400000000000000000000077241264125401100156530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "long_extras.h" int arf_add_si_naive(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_si(t, y); r = arf_add(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("add_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; slong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); y = z_randtest(state); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_add_si(z, x, y, prec, rnd); r2 = arf_add_si_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_add_si_naive(v, x, y, prec, rnd); r1 = arf_add_si(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-add_ui.c000066400000000000000000000077251264125401100156560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "ulong_extras.h" int arf_add_ui_naive(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_ui(t, y); r = arf_add(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("add_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; ulong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); y = n_randtest(state); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_add_ui(z, x, y, prec, rnd); r2 = arf_add_ui_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_add_ui_naive(v, x, y, prec, rnd); r1 = arf_add_ui(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-addmul.c000066400000000000000000000143051264125401100156670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_addmul_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_add(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("addmul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, y, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(y)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_addmul(z, x, y, prec, rnd); r2 = arf_addmul_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = arf_addmul(z, x, x, prec, rnd); r2 = arf_addmul_naive(v, x, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = arf_addmul_naive(v, v, v, prec, rnd); r1 = arf_addmul(z, z, z, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = arf_addmul_naive(v, v, y, prec, rnd); r1 = arf_addmul(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_addmul_naive(v, x, v, prec, rnd); r1 = arf_addmul(z, x, z, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-addmul_fmpz.c000066400000000000000000000103211264125401100167150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_addmul_fmpz_naive(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul_fmpz(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_add(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("addmul_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; fmpz_t y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); fmpz_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); fmpz_randtest(y, state, 2000); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_addmul_fmpz(z, x, y, prec, rnd); r2 = arf_addmul_fmpz_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_debug(z); flint_printf("\n\n"); flint_printf("v = "); arf_debug(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_addmul_fmpz_naive(v, v, y, prec, rnd); r1 = arf_addmul_fmpz(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); fmpz_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-addmul_si.c000066400000000000000000000102151264125401100163560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "long_extras.h" int arf_addmul_si_naive(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul_si(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_add(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("addmul_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; slong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); y = z_randtest(state); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_addmul_si(z, x, y, prec, rnd); r2 = arf_addmul_si_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = %wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_debug(z); flint_printf("\n\n"); flint_printf("v = "); arf_debug(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_addmul_si_naive(v, v, y, prec, rnd); r1 = arf_addmul_si(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = %wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-addmul_ui.c000066400000000000000000000101641264125401100163630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_addmul_ui_naive(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul_ui(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_add(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("addmul_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; ulong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); y = n_randtest(state); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_addmul_ui(z, x, y, prec, rnd); r2 = arf_addmul_ui_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = %wu", y); flint_printf("\n\n"); flint_printf("z = "); arf_debug(z); flint_printf("\n\n"); flint_printf("v = "); arf_debug(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_addmul_ui_naive(v, v, y, prec, rnd); r1 = arf_addmul_ui(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = %wu", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-ceil.c000066400000000000000000000056421264125401100153410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("ceil...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y; int result; arf_init(x); arf_init(y); arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); arf_ceil(y, x); result = 1; if (arf_is_int(x) || !arf_is_finite(x)) { result = arf_equal(y, x); } else if (!arf_is_int(y)) { result = 0; } else if (arf_cmp(y, x) <= 0) { result = 0; } else { arf_t s, t[3]; /* check x - ceil(x) + 1 > 0 */ arf_init(s); arf_init(t[0]); arf_init(t[1]); arf_init(t[2]); arf_set(t[0], x); arf_neg(t[1], y); arf_one(t[2]); arf_sum(s, (arf_ptr) t, 3, 32, ARF_RND_DOWN); result = arf_sgn(s) > 0; arf_clear(s); arf_clear(t[0]); arf_clear(t[1]); arf_clear(t[2]); } if (!result) { flint_printf("FAIL!\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); abort(); } arf_ceil(x, x); if (!arf_equal(x, y)) { flint_printf("FAIL (aliasing)!\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-cmp.c000066400000000000000000000072411264125401100152010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("cmp...."); fflush(stdout); flint_randinit(state); /* compare with fmpz */ { arf_t x, y; fmpz_t X, Y; arf_init(x); arf_init(y); fmpz_init(X); fmpz_init(Y); for (iter = 0; iter < 100000; iter++) { int cmp1, cmp2; fmpz_randtest(X, state, 1 + n_randint(state, 1000)); switch (n_randint(state, 8)) { case 0: fmpz_neg(Y, X); break; case 1: fmpz_set(Y, X); break; default: fmpz_randtest(Y, state, 1 + n_randint(state, 1000)); } arf_set_fmpz(x, X); arf_set_fmpz(y, Y); cmp1 = arf_cmp(x, y); cmp2 = fmpz_cmp(X, Y); cmp2 = (cmp2 > 0) - (cmp2 < 0); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_debug(x); flint_printf("\n\n"); flint_printf("y = "); arf_debug(y); flint_printf("\n\n"); flint_printf("X = "); fmpz_print(X); flint_printf("\n\n"); flint_printf("Y = "); fmpz_print(Y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } } arf_clear(x); arf_clear(y); fmpz_clear(X); fmpz_clear(Y); } /* compare with mpfr */ for (iter = 0; iter < 100000; iter++) { slong bits; arf_t x, y; mpfr_t X, Y; int cmp1, cmp2; bits = 2 + n_randint(state, 200); arf_init(x); arf_init(y); mpfr_init2(X, bits); mpfr_init2(Y, bits); arf_randtest_special(x, state, bits, 10); arf_randtest_special(y, state, bits, 10); arf_get_mpfr(X, x, MPFR_RNDN); arf_get_mpfr(Y, y, MPFR_RNDN); cmp1 = arf_cmp(x, y); cmp2 = mpfr_cmp(X, Y); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } arf_clear(x); arf_clear(y); mpfr_clear(X); mpfr_clear(Y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-cmp_2exp_si.c000066400000000000000000000042211264125401100166250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("cmp_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits, e; arf_t x, y; int cmp1, cmp2; bits = 2 + n_randint(state, 1000); e = n_randtest(state); arf_init(x); arf_init(y); if (iter % 10 == 0) arf_set_ui_2exp_si(x, 1, e); else arf_randtest_special(x, state, bits, 100); arf_set_ui_2exp_si(y, 1, e); cmp1 = arf_cmp(x, y); cmp2 = arf_cmp_2exp_si(x, e); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } arf_clear(x); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-cmpabs.c000066400000000000000000000073641264125401100156750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("cmpabs...."); fflush(stdout); flint_randinit(state); /* compare with fmpz */ { arf_t x, y; fmpz_t X, Y; arf_init(x); arf_init(y); fmpz_init(X); fmpz_init(Y); for (iter = 0; iter < 100000; iter++) { int cmp1, cmp2; fmpz_randtest(X, state, 1 + n_randint(state, 1000)); switch (n_randint(state, 8)) { case 0: fmpz_neg(Y, X); break; case 1: fmpz_set(Y, X); break; default: fmpz_randtest(Y, state, 1 + n_randint(state, 1000)); } arf_set_fmpz(x, X); arf_set_fmpz(y, Y); cmp1 = arf_cmpabs(x, y); cmp2 = fmpz_cmpabs(X, Y); cmp2 = (cmp2 > 0) - (cmp2 < 0); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_debug(x); flint_printf("\n\n"); flint_printf("y = "); arf_debug(y); flint_printf("\n\n"); flint_printf("X = "); fmpz_print(X); flint_printf("\n\n"); flint_printf("Y = "); fmpz_print(Y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } } arf_clear(x); arf_clear(y); fmpz_clear(X); fmpz_clear(Y); } /* compare with mpfr */ for (iter = 0; iter < 100000; iter++) { slong bits; arf_t x, y; mpfr_t X, Y; int cmp1, cmp2; bits = 2 + n_randint(state, 200); arf_init(x); arf_init(y); mpfr_init2(X, bits); mpfr_init2(Y, bits); arf_randtest_special(x, state, bits, 10); arf_randtest_special(y, state, bits, 10); arf_get_mpfr(X, x, MPFR_RNDN); arf_get_mpfr(Y, y, MPFR_RNDN); mpfr_abs(X, X, MPFR_RNDN); mpfr_abs(Y, Y, MPFR_RNDN); cmp1 = arf_cmpabs(x, y); cmp2 = mpfr_cmp(X, Y); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } arf_clear(x); arf_clear(y); mpfr_clear(X); mpfr_clear(Y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-cmpabs_2exp_si.c000066400000000000000000000042321264125401100173150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("cmpabs_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits, e; arf_t x, y; int cmp1, cmp2; bits = 2 + n_randint(state, 1000); e = n_randtest(state); arf_init(x); arf_init(y); if (iter % 10 == 0) arf_set_ui_2exp_si(x, 1, e); else arf_randtest_special(x, state, bits, 100); arf_set_ui_2exp_si(y, 1, e); cmp1 = arf_cmpabs(x, y); cmp2 = arf_cmpabs_2exp_si(x, e); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } arf_clear(x); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-complex_mul.c000066400000000000000000000170711264125401100167500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter, iter2; flint_rand_t state; flint_printf("complex_mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t e1, f1, e2, f2, a, b, c, d; slong prec, r1, r2; arf_rnd_t rnd; arf_init(a); arf_init(b); arf_init(c); arf_init(d); arf_init(e1); arf_init(f1); arf_init(e2); arf_init(f2); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(a, state, 3000, 100); arf_randtest_special(b, state, 3000, 100); arf_randtest_special(c, state, 3000, 100); arf_randtest_special(d, state, 3000, 100); prec = 2 + n_randint(state, 3000); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_complex_mul(e1, f1, a, b, c, d, prec, rnd); r2 = arf_complex_mul_fallback(e2, f2, a, b, c, d, prec, rnd); if (!arf_equal(e1, e2) || !arf_equal(f1, f2) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("c = "); arf_print(c); flint_printf("\n\n"); flint_printf("d = "); arf_print(d); flint_printf("\n\n"); flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n"); flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n"); flint_printf("e2 = "); arf_print(e2); flint_printf("\n\n"); flint_printf("f2 = "); arf_print(f2); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: arf_set(c, a); arf_set(d, b); r1 = arf_complex_mul(e1, f1, a, b, a, b, prec, rnd); r2 = arf_complex_mul_fallback(e2, f2, a, b, c, d, prec, rnd); if (!arf_equal(e1, e2) || !arf_equal(f1, f2) || r1 != r2) { flint_printf("FAIL! (aliasing 1)\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("c = "); arf_print(c); flint_printf("\n\n"); flint_printf("d = "); arf_print(d); flint_printf("\n\n"); flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n"); flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n"); flint_printf("e2 = "); arf_print(e2); flint_printf("\n\n"); flint_printf("f2 = "); arf_print(f2); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r1 = arf_complex_mul_fallback(e1, f1, a, b, a, b, prec, rnd); r2 = arf_complex_mul(a, b, a, b, a, b, prec, rnd); if (!arf_equal(e1, a) || !arf_equal(f1, b) || r1 != r2) { flint_printf("FAIL! (aliasing 2)\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n"); flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r1 = arf_complex_mul_fallback(e1, f1, a, b, c, d, prec, rnd); r2 = arf_complex_mul(a, b, a, b, c, d, prec, rnd); if (!arf_equal(e1, a) || !arf_equal(f1, b) || r1 != r2) { flint_printf("FAIL! (aliasing 3)\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("c = "); arf_print(c); flint_printf("\n\n"); flint_printf("d = "); arf_print(d); flint_printf("\n\n"); flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n"); flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r1 = arf_complex_mul_fallback(e1, f1, a, b, c, d, prec, rnd); r2 = arf_complex_mul(c, d, a, b, c, d, prec, rnd); if (!arf_equal(e1, c) || !arf_equal(f1, d) || r1 != r2) { flint_printf("FAIL! (aliasing 4)\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("c = "); arf_print(c); flint_printf("\n\n"); flint_printf("d = "); arf_print(d); flint_printf("\n\n"); flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n"); flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(a); arf_clear(b); arf_clear(c); arf_clear(d); arf_clear(e1); arf_clear(f1); arf_clear(e2); arf_clear(f2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-complex_sqr.c000066400000000000000000000100701264125401100167500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter, iter2; flint_rand_t state; flint_printf("complex_sqr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t e1, f1, e2, f2, a, b; slong prec, r1, r2; arf_rnd_t rnd; arf_init(a); arf_init(b); arf_init(e1); arf_init(f1); arf_init(e2); arf_init(f2); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(a, state, 3000, 100); arf_randtest_special(b, state, 3000, 100); prec = 2 + n_randint(state, 3000); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_complex_sqr(e1, f1, a, b, prec, rnd); r2 = arf_complex_mul_fallback(e2, f2, a, b, a, b, prec, rnd); if (!arf_equal(e1, e2) || !arf_equal(f1, f2) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n"); flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n"); flint_printf("e2 = "); arf_print(e2); flint_printf("\n\n"); flint_printf("f2 = "); arf_print(f2); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r1 = arf_complex_mul_fallback(e1, f1, a, b, a, b, prec, rnd); r2 = arf_complex_sqr(a, b, a, b, prec, rnd); if (!arf_equal(e1, a) || !arf_equal(f1, b) || r1 != r2) { flint_printf("FAIL! (aliasing)\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("e1 = "); arf_print(e1); flint_printf("\n\n"); flint_printf("f1 = "); arf_print(f1); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(a); arf_clear(b); arf_clear(e1); arf_clear(f1); arf_clear(e2); arf_clear(f2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-div.c000066400000000000000000000141451264125401100152050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_div_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { fmpr_t a, b; slong r; fmpr_init(a); fmpr_init(b); arf_get_fmpr(a, x); arf_get_fmpr(b, y); r = fmpr_div(a, a, b, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); fmpr_clear(b); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("div...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); prec = 2 + n_randint(state, 2000); if (n_randint(state, 20) == 0) arf_mul(x, x, y, 2 + n_randint(state, 3000), ARF_RND_FLOOR); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_div(z, x, y, prec, rnd); r2 = arf_div_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = arf_div(z, x, x, prec, rnd); r2 = arf_div_naive(v, x, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = arf_div_naive(v, x, x, prec, rnd); r1 = arf_div(x, x, x, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = arf_div_naive(v, x, y, prec, rnd); r1 = arf_div(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_div_naive(v, y, x, prec, rnd); r1 = arf_div(x, y, x, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-floor.c000066400000000000000000000056461264125401100155520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("floor...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y; int result; arf_init(x); arf_init(y); arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); arf_floor(y, x); result = 1; if (arf_is_int(x) || !arf_is_finite(x)) { result = arf_equal(y, x); } else if (!arf_is_int(y)) { result = 0; } else if (arf_cmp(y, x) >= 0) { result = 0; } else { arf_t s, t[3]; /* check floor(x) - x + 1 > 0 */ arf_init(s); arf_init(t[0]); arf_init(t[1]); arf_init(t[2]); arf_set(t[0], y); arf_neg(t[1], x); arf_one(t[2]); arf_sum(s, (arf_ptr) t, 3, 32, ARF_RND_DOWN); result = arf_sgn(s) > 0; arf_clear(s); arf_clear(t[0]); arf_clear(t[1]); arf_clear(t[2]); } if (!result) { flint_printf("FAIL!\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); abort(); } arf_floor(x, x); if (!arf_equal(x, y)) { flint_printf("FAIL (aliasing)!\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-get_d.c000066400000000000000000000110651264125401100155030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("get_d...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip */ for (iter = 0; iter < 100000; iter++) { arf_t x, z; double y; arf_rnd_t rnd; arf_init(x); arf_init(z); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; case 3: rnd = ARF_RND_CEIL; break; default: rnd = ARF_RND_NEAR; break; } arf_randtest_special(x, state, 53, 8); y = arf_get_d(x, rnd); arf_set_d(z, y); if (!arf_equal(x, z)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = %.17g\n\n", y); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); } /* test rounding */ for (iter = 0; iter < 100000; iter++) { arf_t x, z, w; arf_rnd_t rnd; double y; arf_init(x); arf_init(z); arf_init(w); arf_randtest_special(x, state, 300, 8); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } y = arf_get_d(x, rnd); arf_set_d(w, y); arf_set_round(z, x, 53, rnd); if (!arf_equal(w, z)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = %.17g\n\n", y); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("w = "); arf_print(w); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); arf_clear(w); } /* compare with mpfr */ for (iter = 0; iter < 100000; iter++) { arf_t x, r1, r2; arf_rnd_t rnd; mpfr_t t; double d1, d2; arf_init(x); arf_init(r1); arf_init(r2); mpfr_init2(t, 300); arf_randtest_special(x, state, 300, 20); arf_get_mpfr(t, x, MPFR_RNDD); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; case 3: rnd = ARF_RND_CEIL; break; default: rnd = ARF_RND_NEAR; break; } d1 = arf_get_d(x, rnd); d2 = mpfr_get_d(t, rnd_to_mpfr(rnd)); arf_set_d(r1, d1); arf_set_d(r2, d2); if (!arf_equal(r1, r2)) { flint_printf("FAIL:\n\n"); flint_printf("rnd = %i\n\n", rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("d1 = %.17g\n\n", d1); flint_printf("d2 = %.17g\n\n", d2); flint_printf("r1 = "); arf_print(r1); flint_printf("\n\n"); flint_printf("r2 = "); arf_print(r2); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(r1); arf_clear(r2); mpfr_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-get_fmpz.c000066400000000000000000000056201264125401100162340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("get_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; arf_t x; mpfr_t y; fmpz_t z, z2; mpz_t w; bits = 2 + n_randint(state, 1000); arf_init(x); mpfr_init2(y, bits); fmpz_init(z); fmpz_init(z2); mpz_init(w); arf_randtest(x, state, bits, 10); arf_get_mpfr(y, x, MPFR_RNDN); switch (n_randint(state, 5)) { case 0: arf_get_fmpz(z, x, ARF_RND_FLOOR); mpfr_get_z(w, y, MPFR_RNDD); break; case 1: arf_get_fmpz(z, x, ARF_RND_CEIL); mpfr_get_z(w, y, MPFR_RNDU); break; case 2: arf_get_fmpz(z, x, ARF_RND_DOWN); mpfr_get_z(w, y, MPFR_RNDZ); break; case 3: arf_get_fmpz(z, x, ARF_RND_UP); mpfr_get_z(w, y, MPFR_RNDA); break; default: arf_get_fmpz(z, x, ARF_RND_NEAR); mpfr_get_z(w, y, MPFR_RNDN); break; } fmpz_set_mpz(z2, w); if (!fmpz_equal(z, z2)) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpz_print(z); flint_printf("\n\n"); flint_printf("z2 = "); fmpz_print(z2); flint_printf("\n\n"); abort(); } arf_clear(x); mpfr_clear(y); fmpz_clear(z); fmpz_clear(z2); mpz_clear(w); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-get_mpfr.c000066400000000000000000000037421264125401100162270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("get_mpfr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; arf_t x, z; mpfr_t y; bits = 2 + n_randint(state, 200); arf_init(x); arf_init(z); mpfr_init2(y, bits); arf_randtest_special(x, state, bits, 10); arf_get_mpfr(y, x, MPFR_RNDN); arf_set_mpfr(z, y); if (!arf_equal(x, z)) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); mpfr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-mul.c000066400000000000000000000141051264125401100152140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_mul_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { fmpr_t a, b; slong r; fmpr_init(a); fmpr_init(b); arf_get_fmpr(a, x); arf_get_fmpr(b, y); r = fmpr_mul_naive(a, a, b, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); fmpr_clear(b); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); prec = 2 + n_randint(state, 2000); if (n_randint(state, 50) == 0) prec = ARF_PREC_EXACT; switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_mul(z, x, y, prec, rnd); r2 = arf_mul_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = arf_mul(z, x, x, prec, rnd); r2 = arf_mul_naive(v, x, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = arf_mul_naive(v, x, x, prec, rnd); r1 = arf_mul(x, x, x, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = arf_mul_naive(v, x, y, prec, rnd); r1 = arf_mul(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_mul_naive(v, x, y, prec, rnd); r1 = arf_mul(x, y, x, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-mul_fmpz.c000066400000000000000000000076621264125401100162620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_mul_fmpz_naive(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz(t, y); r = arf_mul(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; fmpz_t y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); fmpz_init(y); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); fmpz_randtest(y, state, 2000); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10)) prec = ARF_PREC_EXACT; switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_mul_fmpz(z, x, y, prec, rnd); r2 = arf_mul_fmpz_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_mul_fmpz_naive(v, x, y, prec, rnd); r1 = arf_mul_fmpz(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); fmpz_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-mul_si.c000066400000000000000000000076271264125401100157220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "long_extras.h" int arf_mul_si_naive(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_si(t, y); r = arf_mul(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; slong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); y = z_randtest(state); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0) prec = ARF_PREC_EXACT; switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_mul_si(z, x, y, prec, rnd); r2 = arf_mul_si_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_mul_si_naive(v, x, y, prec, rnd); r1 = arf_mul_si(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-mul_ui.c000066400000000000000000000076301264125401100157160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "ulong_extras.h" int arf_mul_ui_naive(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_ui(t, y); r = arf_mul(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; ulong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); y = n_randtest(state); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0) prec = ARF_PREC_EXACT; switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_mul_ui(z, x, y, prec, rnd); r2 = arf_mul_ui_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_mul_ui_naive(v, x, y, prec, rnd); r1 = arf_mul_ui(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-mul_via_mpfr.c000066400000000000000000000141731264125401100171040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_mul_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { fmpr_t a, b; slong r; fmpr_init(a); fmpr_init(b); arf_get_fmpr(a, x); arf_get_fmpr(b, y); r = fmpr_mul_naive(a, a, b, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); fmpr_clear(b); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul_via_mpfr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); prec = 2 + n_randint(state, 2000); if (n_randint(state, 50) == 0) prec = ARF_PREC_EXACT; switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_mul_via_mpfr(z, x, y, prec, rnd); r2 = arf_mul_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = arf_mul_via_mpfr(z, x, x, prec, rnd); r2 = arf_mul_naive(v, x, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = arf_mul_naive(v, x, x, prec, rnd); r1 = arf_mul_via_mpfr(x, x, x, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = arf_mul_naive(v, x, y, prec, rnd); r1 = arf_mul_via_mpfr(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_mul_naive(v, x, y, prec, rnd); r1 = arf_mul_via_mpfr(x, y, x, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-root.c000066400000000000000000000076251264125401100154130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_root_naive(arf_t z, const arf_t x, ulong k, slong prec, arf_rnd_t rnd) { fmpr_t a; slong r; fmpr_init(a); arf_get_fmpr(a, x); r = fmpr_root(a, a, k, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("root...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; slong prec, r1, r2; ulong k; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 10; iter2++) { arf_randtest_special(x, state, 2000, 100); prec = 2 + n_randint(state, 2000); k = n_randint(state, 50); if (n_randint(state, 20) == 0) arf_mul(x, x, x, prec, ARF_RND_DOWN); else if (n_randint(state, 20) == 0) arf_mul(x, x, x, prec, ARF_RND_UP); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_root(z, x, k, prec, rnd); r2 = arf_root_naive(v, x, k, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("k = %wu, prec = %wd, rnd = %d\n\n", k, prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_root_naive(v, x, k, prec, rnd); r1 = arf_root(x, x, k, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("k = %wu, prec = %wd, rnd = %d\n\n", k, prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-rsqrt.c000066400000000000000000000071611264125401100155760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_rsqrt_naive(arf_t z, const arf_t x, slong prec, arf_rnd_t rnd) { fmpr_t a; slong r; fmpr_init(a); arf_get_fmpr(a, x); r = fmpr_rsqrt(a, a, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("rsqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_rsqrt(z, x, prec, rnd); r2 = arf_rsqrt_naive(v, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_rsqrt_naive(v, x, prec, rnd); r1 = arf_rsqrt(x, x, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-set_fmpq.c000066400000000000000000000042711264125401100162400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("set_fmpq...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip R -> Q -> R */ for (iter = 0; iter < 100000; iter++) { slong bits, res; arf_t x, z; fmpq_t y; bits = 2 + n_randint(state, 200); arf_init(x); arf_init(z); fmpq_init(y); arf_randtest(x, state, bits, 10); arf_randtest(z, state, bits, 10); arf_get_fmpq(y, x); res = arf_set_fmpq(z, y, bits, ARF_RND_DOWN); if (!arf_equal(x, z) || res != 0) { flint_printf("FAIL\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); fmpq_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-set_fmpr.c000066400000000000000000000061371264125401100162440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("set_fmpr...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip R -> Q -> R */ for (iter = 0; iter < 100000; iter++) { slong bits; arf_t x, z; fmpr_t y; bits = 2 + n_randint(state, 1000); arf_init(x); arf_init(z); fmpr_init(y); arf_randtest_special(x, state, bits, 1 + n_randint(state, 100)); arf_randtest_special(z, state, bits, 1 + n_randint(state, 100)); arf_get_fmpr(y, x); arf_set_fmpr(z, y); if (!arf_equal(x, z)) { flint_printf("FAIL\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); fmpr_clear(y); } /* test exact roundtrip Q -> R -> Q */ for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, z; arf_t y; bits = 2 + n_randint(state, 1000); fmpr_init(x); fmpr_init(z); arf_init(y); fmpr_randtest_special(x, state, bits, 1 + n_randint(state, 100)); fmpr_randtest_special(z, state, bits, 1 + n_randint(state, 100)); arf_set_fmpr(y, x); arf_get_fmpr(z, y); if (!fmpr_equal(x, z)) { flint_printf("FAIL (2)\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-set_fmpz_2exp.c000066400000000000000000000045071264125401100172110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("set_fmpz_2exp...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip R -> Q -> R */ for (iter = 0; iter < 100000; iter++) { slong bits; arf_t x, z; fmpz_t y, e; bits = 2 + n_randint(state, 200); arf_init(x); arf_init(z); fmpz_init(y); fmpz_init(e); arf_randtest(x, state, bits, 1 + n_randint(state, 100)); arf_randtest(z, state, bits, 1 + n_randint(state, 100)); arf_get_fmpz_2exp(y, e, x); arf_set_fmpz_2exp(z, y, e); if (!arf_equal(x, z)) { flint_printf("FAIL\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("e = "); fmpz_print(e); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); fmpz_clear(y); fmpz_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-set_round.c000066400000000000000000000114521264125401100164230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("set_round...."); fflush(stdout); flint_randinit(state); { arf_t x, y, z; arf_init(x); arf_init(y); arf_init(z); for (iter = 0; iter < 100000; iter++) { slong bits1, bits2; int ret1, ret2; mpfr_t g1, g2; fmpz_t e; arf_rnd_t rnd; bits1 = 1 + n_randint(state, 1000); bits2 = 2 + n_randint(state, 1000); if (n_randint(state, 100) == 0) bits2 = ARF_PREC_EXACT; switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } fmpz_init(e); mpfr_init2(g1, FLINT_MAX(2, bits1)); mpfr_init2(g2, FLINT_MIN(bits2, 10000)); if (n_randint(state, 100) == 0) { arf_clear(x); arf_clear(y); arf_clear(z); arf_init(x); arf_init(y); arf_init(z); } /* dirty output variables */ if (n_randint(state, 2)) { arf_randtest_special(y, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); arf_randtest_special(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); } arf_randtest_special(x, state, bits1, 1 + n_randint(state, 10)); arf_get_mpfr(g1, x, MPFR_RNDD); /* exact */ /* test large exponents */ if (n_randint(state, 4) == 0) fmpz_randtest(e, state, 1 + n_randint(state, 100)); if (!arf_is_special(x)) fmpz_add(ARF_EXPREF(x), ARF_EXPREF(x), e); ret1 = arf_set_round(y, x, bits2, rnd); ret2 = mpfr_set(g2, g1, arf_rnd_to_mpfr(rnd)); arf_set_mpfr(z, g2); if (!arf_is_special(y)) fmpz_sub(ARF_EXPREF(y), ARF_EXPREF(y), e); if (!arf_equal(y, z) || ((ret1 == ARF_RESULT_EXACT) != (ret2 == 0))) { flint_printf("FAIL\n\n"); flint_printf("bits1: %wd\n", bits1); flint_printf("bits2: %wd\n", bits2); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("ret1 = %d, ret2 = %d\n\n", ret1, ret2); abort(); } if (!arf_is_special(x)) fmpz_add(ARF_EXPREF(x), ARF_EXPREF(x), e); ret1 = arf_set_round(y, x, bits2, rnd); arf_set(z, x); ret2 = arf_set_round(z, z, bits2, rnd); if (!arf_equal(y, z) || ret1 != ret2) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("bits1: %wd\n", bits1); flint_printf("bits2: %wd\n", bits2); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("ret1 = %d, ret2 = %d\n\n", ret1, ret2); abort(); } mpfr_clear(g1); mpfr_clear(g2); fmpz_clear(e); } arf_clear(x); arf_clear(y); arf_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-set_round_fmpz.c000066400000000000000000000071761264125401100174670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("set_round_fmpz...."); fflush(stdout); flint_randinit(state); { arf_t x, y; arf_init(x); arf_init(y); for (iter = 0; iter < 100000; iter++) { slong bits1, bits2; int ret1, ret2; fmpz_t a; mpz_t b; mpfr_t g; arf_rnd_t rnd; bits1 = 1 + n_randint(state, 1000); bits2 = 2 + n_randint(state, 1000); if (n_randint(state, 100) == 0) bits2 = ARF_PREC_EXACT; fmpz_init(a); mpz_init(b); mpfr_init2(g, FLINT_MIN(bits2, 10000)); if (n_randint(state, 100) == 0) { arf_clear(x); arf_clear(y); arf_init(x); arf_init(y); } /* dirty output variables */ if (n_randint(state, 2)) { arf_randtest_special(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); arf_randtest_special(y, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); } fmpz_randtest(a, state, bits1); fmpz_get_mpz(b, a); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } ret1 = arf_set_round_fmpz(x, a, bits2, rnd); ret2 = mpfr_set_z(g, b, arf_rnd_to_mpfr(rnd)); arf_set_mpfr(y, g); arf_equal(x, y); if (!arf_equal(x, y) || ((ret1 == ARF_RESULT_EXACT) != (ret2 == 0))) { flint_printf("FAIL\n\n"); flint_printf("bits1: %wd\n", bits1); flint_printf("bits2: %wd\n", bits2); flint_printf("a = "); fmpz_print(a); flint_printf("\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("ret1 = %d, ret2 = %d\n\n", ret1, ret2); abort(); } fmpz_clear(a); mpz_clear(b); mpfr_clear(g); } arf_clear(x); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-set_round_mpz.c000066400000000000000000000071741264125401100173170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("set_round_mpz...."); fflush(stdout); flint_randinit(state); { arf_t x, y; arf_init(x); arf_init(y); for (iter = 0; iter < 100000; iter++) { slong bits1, bits2; int ret1, ret2; fmpz_t a; mpz_t b; mpfr_t g; arf_rnd_t rnd; bits1 = 1 + n_randint(state, 1000); bits2 = 2 + n_randint(state, 1000); if (n_randint(state, 100) == 0) bits2 = ARF_PREC_EXACT; fmpz_init(a); mpz_init(b); mpfr_init2(g, FLINT_MIN(bits2, 10000)); if (n_randint(state, 100) == 0) { arf_clear(x); arf_clear(y); arf_init(x); arf_init(y); } /* dirty output variables */ if (n_randint(state, 2)) { arf_randtest_special(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); arf_randtest_special(y, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); } fmpz_randtest(a, state, bits1); fmpz_get_mpz(b, a); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } ret1 = arf_set_round_mpz(x, b, bits2, rnd); ret2 = mpfr_set_z(g, b, arf_rnd_to_mpfr(rnd)); arf_set_mpfr(y, g); arf_equal(x, y); if (!arf_equal(x, y) || ((ret1 == ARF_RESULT_EXACT) != (ret2 == 0))) { flint_printf("FAIL\n\n"); flint_printf("bits1: %wd\n", bits1); flint_printf("bits2: %wd\n", bits2); flint_printf("a = "); fmpz_print(a); flint_printf("\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("ret1 = %d, ret2 = %d\n\n", ret1, ret2); abort(); } fmpz_clear(a); mpz_clear(b); mpfr_clear(g); } arf_clear(x); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-set_round_uiui.c000066400000000000000000000062351264125401100174610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("set_round_uiui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000000; iter++) { arf_t x, y; slong prec, fix1, fix2; int ret1, ret2, sgnbit; mp_limb_t t[2]; arf_rnd_t rnd; prec = 2 + n_randint(state, 1000); arf_init(x); arf_init(y); arf_randtest_special(x, state, 1 + n_randint(state, 200), 1 + n_randint(state, 100)); arf_randtest_special(y, state, 1 + n_randint(state, 200), 1 + n_randint(state, 100)); do { t[0] = n_randtest(state); t[1] = n_randtest(state); } while (t[0] == 0 && t[1] == 0); sgnbit = n_randint(state, 2); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } if (t[1] != 0) { ret1 = _arf_set_round_mpn(x, &fix1, t, 2, sgnbit, prec, rnd); fmpz_set_si(ARF_EXPREF(x), 2 * FLINT_BITS + fix1); } else { ret1 = _arf_set_round_mpn(x, &fix1, t, 1, sgnbit, prec, rnd); fmpz_set_si(ARF_EXPREF(x), FLINT_BITS + fix1); } ret2 = _arf_set_round_uiui(y, &fix2, t[1], t[0], sgnbit, prec, rnd); fmpz_set_si(ARF_EXPREF(y), 2 * FLINT_BITS + fix2); if (!arf_equal(x, y) || (ret1 != ret2)) { flint_printf("FAIL\n\n"); flint_printf("prec = %wd", prec); flint_printf("\n\n"); flint_printf("hi = %wu, lo = %wu\n\n", t[1], t[0]); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("ret1 = %d, ret2 = %d\n\n", ret1, ret2); abort(); } arf_clear(x); arf_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-sqrt.c000066400000000000000000000074601264125401100154160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_sqrt_naive(arf_t z, const arf_t x, slong prec, arf_rnd_t rnd) { fmpr_t a; slong r; fmpr_init(a); arf_get_fmpr(a, x); r = fmpr_sqrt(a, a, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("sqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); prec = 2 + n_randint(state, 2000); if (n_randint(state, 20) == 0) arf_mul(x, x, x, prec, ARF_RND_DOWN); else if (n_randint(state, 20) == 0) arf_mul(x, x, x, prec, ARF_RND_UP); switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_sqrt(z, x, prec, rnd); r2 = arf_sqrt_naive(v, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_sqrt_naive(v, x, prec, rnd); r1 = arf_sqrt(x, x, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-sub.c000066400000000000000000000142751264125401100152200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_sub_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { fmpr_t a, b; slong r; fmpr_init(a); fmpr_init(b); arf_get_fmpr(a, x); arf_get_fmpr(b, y); r = fmpr_sub(a, a, b, prec, rnd); arf_set_fmpr(z, a); fmpr_clear(a); fmpr_clear(b); return (r == FMPR_RESULT_EXACT) ? 0 : 1; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("sub...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, y, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(y)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_sub(z, x, y, prec, rnd); r2 = arf_sub_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = arf_sub(z, x, x, prec, rnd); r2 = arf_sub_naive(v, x, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = arf_sub_naive(v, x, x, prec, rnd); r1 = arf_sub(x, x, x, prec, rnd); if (!arf_equal(v, x) || r1 != r2) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = arf_sub_naive(v, x, y, prec, rnd); r1 = arf_sub(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_sub_naive(v, y, x, prec, rnd); r1 = arf_sub(x, y, x, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-sub_fmpz.c000066400000000000000000000077641264125401100162610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_sub_fmpz_naive(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz(t, y); r = arf_sub(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("sub_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; fmpz_t y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); fmpz_init(y); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); fmpz_randtest(y, state, 2000); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_sub_fmpz(z, x, y, prec, rnd); r2 = arf_sub_fmpz_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_sub_fmpz_naive(v, x, y, prec, rnd); r1 = arf_sub_fmpz(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); fmpz_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-sub_si.c000066400000000000000000000077241264125401100157140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "long_extras.h" int arf_sub_si_naive(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_si(t, y); r = arf_sub(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("sub_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; slong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); y = z_randtest(state); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_sub_si(z, x, y, prec, rnd); r2 = arf_sub_si_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_sub_si_naive(v, x, y, prec, rnd); r1 = arf_sub_si(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-sub_ui.c000066400000000000000000000077251264125401100157170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "ulong_extras.h" int arf_sub_ui_naive(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_ui(t, y); r = arf_sub(z, x, t, prec, rnd); arf_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("sub_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arf_t x, z, v; ulong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 10); y = n_randtest(state); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_sub_ui(z, x, y, prec, rnd); r2 = arf_sub_ui_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_sub_ui_naive(v, x, y, prec, rnd); r1 = arf_sub_ui(x, x, y, prec, rnd); if (!arf_equal(x, v) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); flint_printf("%wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-submul.c000066400000000000000000000143051264125401100157300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_submul_naive(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_sub(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("submul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, y, z, v; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); arf_randtest_special(y, state, 2000, 100); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(y)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = arf_submul(z, x, y, prec, rnd); r2 = arf_submul_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = arf_submul(z, x, x, prec, rnd); r2 = arf_submul_naive(v, x, x, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = arf_submul_naive(v, v, v, prec, rnd); r1 = arf_submul(z, z, z, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = arf_submul_naive(v, v, y, prec, rnd); r1 = arf_submul(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_submul_naive(v, x, v, prec, rnd); r1 = arf_submul(z, x, z, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-submul_fmpz.c000066400000000000000000000103211264125401100167560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_submul_fmpz_naive(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul_fmpz(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_sub(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("submul_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; fmpz_t y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); fmpz_init(y); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); fmpz_randtest(y, state, 2000); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_submul_fmpz(z, x, y, prec, rnd); r2 = arf_submul_fmpz_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_debug(z); flint_printf("\n\n"); flint_printf("v = "); arf_debug(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_submul_fmpz_naive(v, v, y, prec, rnd); r1 = arf_submul_fmpz(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); fmpz_clear(y); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-submul_si.c000066400000000000000000000102151264125401100164170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" #include "long_extras.h" int arf_submul_si_naive(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul_si(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_sub(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("submul_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; slong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); y = z_randtest(state); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_submul_si(z, x, y, prec, rnd); r2 = arf_submul_si_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = %wd", y); flint_printf("\n\n"); flint_printf("z = "); arf_debug(z); flint_printf("\n\n"); flint_printf("v = "); arf_debug(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_submul_si_naive(v, v, y, prec, rnd); r1 = arf_submul_si(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = %wd", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-submul_ui.c000066400000000000000000000101641264125401100164240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "arf.h" int arf_submul_ui_naive(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) { arf_t t; int inexact; arf_init(t); arf_mul_ui(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); inexact = arf_sub(z, z, t, prec, rnd); arf_clear(t); return inexact; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("submul_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { arf_t x, z, v; ulong y; slong prec, r1, r2; arf_rnd_t rnd; arf_init(x); arf_init(z); arf_init(v); for (iter2 = 0; iter2 < 100; iter2++) { arf_randtest_special(x, state, 2000, 100); y = n_randtest(state); arf_randtest_special(z, state, 2000, 100); arf_set(v, z); prec = 2 + n_randint(state, 2000); if (n_randint(state, 10) == 0 && fmpz_bits(ARF_EXPREF(x)) < 10 && fmpz_bits(ARF_EXPREF(z)) < 10) { prec = ARF_PREC_EXACT; } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = arf_submul_ui(z, x, y, prec, rnd); r2 = arf_submul_ui_naive(v, x, y, prec, rnd); if (!arf_equal(z, v) || r1 != r2) { flint_printf("FAIL!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = %wu", y); flint_printf("\n\n"); flint_printf("z = "); arf_debug(z); flint_printf("\n\n"); flint_printf("v = "); arf_debug(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = arf_submul_ui_naive(v, v, y, prec, rnd); r1 = arf_submul_ui(z, z, y, prec, rnd); if (!arf_equal(v, z) || r1 != r2) { flint_printf("FAIL (aliasing)!\n"); flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd); flint_printf("y = %wu", y); flint_printf("\n\n"); flint_printf("v = "); arf_print(v); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } arf_clear(x); arf_clear(z); arf_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/arf/test/t-sum.c000066400000000000000000000103251264125401100152230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "arf.h" int main() { slong iter; flint_rand_t state; flint_printf("sum...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000000; iter++) { slong i, len, prec, bits, expbits; int res1, res2; arf_t s1, s2, s3, err; mag_t err_bound; arf_struct terms[20]; arf_rnd_t rnd; len = n_randint(state, 20); bits = 2 + n_randint(state, 1000); prec = 2 + n_randint(state, 1000); expbits = n_randint(state, 14); arf_init(s1); arf_init(s2); arf_init(s3); arf_init(err); mag_init(err_bound); for (i = 0; i < len; i++) { arf_init(terms + i); arf_randtest_special(terms + i, state, bits, expbits); } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } res1 = arf_sum(s1, terms, len, prec, rnd); arf_zero(s2); for (i = 0; i < len; i++) arf_add(s2, s2, terms + i, ARF_PREC_EXACT, ARF_RND_DOWN); res2 = arf_set_round(s3, s2, prec, rnd); if (!arf_equal(s1, s3) || res1 != res2) { flint_printf("FAIL (%wd)\n\n", iter); flint_printf("prec = %wd\n\n", prec); for (i = 0; i < len; i++) { flint_printf("terms[%wd] = ", i); arf_print(terms + i); flint_printf("\n\n"); } flint_printf("s1 = "); arf_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); arf_print(s2); flint_printf("\n\n"); flint_printf("s3 = "); arf_print(s3); flint_printf("\n\n"); flint_printf("res1 = %d, res2 = %d\n\n", res1, res2); abort(); } arf_sub(err, s1, s2, ARF_PREC_EXACT, ARF_RND_DOWN); arf_abs(err, err); if (res1) arf_mag_set_ulp(err_bound, s1, prec); else mag_zero(err_bound); if (arf_cmpabs_mag(err, err_bound) > 0) { flint_printf("FAIL (error bound)!\n"); flint_printf("prec = %wd\n\n", prec); for (i = 0; i < len; i++) { flint_printf("terms[%wd] = ", i); arf_print(terms + i); flint_printf("\n\n"); } flint_printf("s1 = "); arf_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); arf_print(s2); flint_printf("\n\n"); flint_printf("s3 = "); arf_print(s3); flint_printf("\n\n"); flint_printf("error: "); arf_print(err); flint_printf("\n\n"); flint_printf("error bound: "); mag_print(err_bound); flint_printf("\n\n"); flint_printf("res1 = %d, res2 = %d\n\n", res1, res2); abort(); } arf_clear(s1); arf_clear(s2); arf_clear(s3); arf_clear(err); mag_clear(err_bound); for (i = 0; i < len; i++) arf_clear(terms + i); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/bernoulli.h000066400000000000000000000067671264125401100144460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef BERNOULLI_H #define BERNOULLI_H #include #include "flint.h" #include "fmpz.h" #include "fmpz_vec.h" #include "fmpq.h" #include "arith.h" #include "fmprb.h" #include "arb.h" #ifdef __cplusplus extern "C" { #endif extern slong TLS_PREFIX bernoulli_cache_num; extern TLS_PREFIX fmpq * bernoulli_cache; void bernoulli_cache_compute(slong n); /* Crude bound for the bits in d(n) = denom(B_n). By von Staudt-Clausen, d(n) = prod_{p-1 | n} p <= prod_{k | n} 2k <= n^{sigma_0(n)}. We get a more accurate estimate taking the square root of this. Further, at least for sufficiently large n, sigma_0(n) < exp(1.066 log(n) / log(log(n))). */ static __inline__ slong bernoulli_denom_size(slong n) { return 0.5 * 1.4427 * log(n) * pow(n, 1.066 / log(log(n))); } static __inline__ slong bernoulli_zeta_terms(ulong s, slong prec) { slong N; N = pow(2.0, (prec + 1.0) / (s - 1.0)); N += ((N % 2) == 0); return N; } static __inline__ slong bernoulli_power_prec(slong i, ulong s1, slong wp) { slong p = wp - s1 * log(i) * 1.44269504088896341; return FLINT_MAX(p, 10); } /* we should technically add O(log(n)) guard bits, but this is unnecessary in practice since the denominator estimate is quite a bit larger than the true denominators */ static __inline__ slong bernoulli_global_prec(ulong nmax) { return arith_bernoulli_number_size(nmax) + bernoulli_denom_size(nmax); } /* avoid potential numerical problems for very small n */ #define BERNOULLI_REV_MIN 32 typedef struct { slong alloc; slong prec; slong max_power; fmpz * powers; fmpz_t pow_error; arb_t prefactor; arb_t two_pi_squared; ulong n; } bernoulli_rev_struct; typedef bernoulli_rev_struct bernoulli_rev_t[1]; void bernoulli_rev_init(bernoulli_rev_t iter, ulong nmax); void bernoulli_rev_next(fmpz_t numer, fmpz_t denom, bernoulli_rev_t iter); void bernoulli_rev_clear(bernoulli_rev_t iter); #define BERNOULLI_ENSURE_CACHED(n) \ do { \ slong __n = (n); \ if (__n >= bernoulli_cache_num) \ bernoulli_cache_compute(__n + 1); \ } while (0); \ slong bernoulli_bound_2exp_si(ulong n); void bernoulli_fmprb_ui_zeta(fmprb_t b, ulong n, slong prec); void bernoulli_fmprb_ui(fmprb_t b, ulong n, slong prec); void _bernoulli_fmpq_ui_zeta(fmpz_t num, fmpz_t den, ulong n); void _bernoulli_fmpq_ui(fmpz_t num, fmpz_t den, ulong n); void bernoulli_fmpq_ui(fmpq_t b, ulong n); #ifdef __cplusplus } #endif #endif arb-2.8.1/bernoulli/000077500000000000000000000000001264125401100142555ustar00rootroot00000000000000arb-2.8.1/bernoulli/bound_2exp_si.c000066400000000000000000000076341264125401100171730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" const short bernoulli_bound_tab[256] = { 1, -2, -4, -5, -4, -3, -1, 1, 3, 6, 10, 13, 17, 21, 25, 30, 34, 39, 44, 49, 55, 60, 66, 71, 77, 83, 89, 95, 102, 108, 115, 121, 128, 135, 141, 148, 155, 162, 170, 177, 184, 192, 199, 207, 214, 222, 230, 237, 245, 253, 261, 269, 277, 285, 294, 302, 310, 318, 327, 335, 344, 352, 361, 370, 378, 387, 396, 405, 413, 422, 431, 440, 449, 458, 467, 477, 486, 495, 504, 514, 523, 532, 542, 551, 561, 570, 580, 589, 599, 608, 618, 628, 638, 647, 657, 667, 677, 687, 697, 707, 717, 727, 737, 747, 757, 767, 777, 787, 797, 808, 818, 828, 838, 849, 859, 870, 880, 890, 901, 911, 922, 932, 943, 953, 964, 975, 985, 996, 1007, 1017, 1028, 1039, 1050, 1061, 1071, 1082, 1093, 1104, 1115, 1126, 1137, 1148, 1159, 1170, 1181, 1192, 1203, 1214, 1225, 1236, 1247, 1258, 1270, 1281, 1292, 1303, 1315, 1326, 1337, 1349, 1360, 1371, 1383, 1394, 1405, 1417, 1428, 1440, 1451, 1463, 1474, 1486, 1497, 1509, 1520, 1532, 1544, 1555, 1567, 1579, 1590, 1602, 1614, 1625, 1637, 1649, 1661, 1672, 1684, 1696, 1708, 1720, 1732, 1743, 1755, 1767, 1779, 1791, 1803, 1815, 1827, 1839, 1851, 1863, 1875, 1887, 1899, 1911, 1923, 1935, 1948, 1960, 1972, 1984, 1996, 2008, 2021, 2033, 2045, 2057, 2070, 2082, 2094, 2106, 2119, 2131, 2143, 2156, 2168, 2180, 2193, 2205, 2218, 2230, 2243, 2255, 2267, 2280, 2292, 2305, 2317, 2330, 2342, 2355, 2368, 2380, 2393, 2405, 2418, 2430, 2443, 2456, 2468, 2481, 2494, 2506, }; #define LOG_PREC 6 /* table of ceil(log(n,2) * M - log_prec * M) for n from M to 2M inclusive where M = 2^LOG_PREC */ const unsigned char log_tab[] = { 0, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55, 55, 56, 57, 58, 59, 59, 60, 61, 62, 62, 63, 64, 64 }; slong bernoulli_bound_2exp_si(ulong n) { if (n % 2) { if (n == 1) return -WORD(1); else return LONG_MIN; } else if (n < 512) { return bernoulli_bound_tab[n / 2]; } else { /* |B_n| < 4 * n! / (2*pi)^n < 4 * (n+1)^(n+1) e^(-n) / (2*pi)^n */ mp_limb_t l, u, hi, lo; int b, shift; b = FLINT_BIT_COUNT(n + 1); shift = b - (LOG_PREC + 1); /* (n+1) * log_2(n+1) */ u = n + 1; l = log_tab[((u >> shift) + 1) - (1 << LOG_PREC)]; l += (LOG_PREC << LOG_PREC); umul_ppmm(hi, lo, l, u); if (hi || n > (UWORD(1) << (FLINT_BITS - 6))) { flint_printf("bernoulli_bound_2exp_si: n too large\n"); abort(); } l = (lo >> LOG_PREC) + 1; l += shift * u; /* log_2(2*pi*e) > 131 / 32 */ return l + 2 - (131 * n) / 32; } } arb-2.8.1/bernoulli/cache_compute.c000066400000000000000000000044751264125401100172320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" TLS_PREFIX slong bernoulli_cache_num = 0; TLS_PREFIX fmpq * bernoulli_cache = NULL; void bernoulli_cleanup(void) { slong i; for (i = 0; i < bernoulli_cache_num; i++) fmpq_clear(bernoulli_cache + i); flint_free(bernoulli_cache); bernoulli_cache = NULL; bernoulli_cache_num = 0; } void bernoulli_cache_compute(slong n) { if (bernoulli_cache_num < n) { slong i, new_num; bernoulli_rev_t iter; if (bernoulli_cache_num == 0) { flint_register_cleanup_function(bernoulli_cleanup); } new_num = FLINT_MAX(bernoulli_cache_num + 128, n); bernoulli_cache = flint_realloc(bernoulli_cache, new_num * sizeof(fmpq)); for (i = bernoulli_cache_num; i < new_num; i++) fmpq_init(bernoulli_cache + i); i = new_num - 1; i -= (i % 2); bernoulli_rev_init(iter, i); for ( ; i >= bernoulli_cache_num; i -= 2) { bernoulli_rev_next(fmpq_numref(bernoulli_cache + i), fmpq_denref(bernoulli_cache + i), iter); } bernoulli_rev_clear(iter); if (new_num > 1) fmpq_set_si(bernoulli_cache + 1, -1, 2); bernoulli_cache_num = new_num; } } arb-2.8.1/bernoulli/fmpq_ui.c000066400000000000000000000027521264125401100160670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" void _bernoulli_fmpq_ui(fmpz_t num, fmpz_t den, ulong n) { if (n < (ulong) bernoulli_cache_num) { fmpz_set(num, fmpq_numref(bernoulli_cache + n)); fmpz_set(den, fmpq_denref(bernoulli_cache + n)); } else { _bernoulli_fmpq_ui_zeta(num, den, n); } } void bernoulli_fmpq_ui(fmpq_t b, ulong n) { _bernoulli_fmpq_ui(fmpq_numref(b), fmpq_denref(b), n); } arb-2.8.1/bernoulli/fmpq_ui_zeta.c000066400000000000000000000034721264125401100171120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" #include "arb.h" void _bernoulli_fmpq_ui_zeta(fmpz_t num, fmpz_t den, ulong n) { slong prec; arb_t t; arith_bernoulli_number_denom(den, n); if (n % 2) { fmpz_set_si(num, -(n == 1)); return; } if (n < BERNOULLI_SMALL_NUMER_LIMIT) { fmpz_set_si(num, _bernoulli_numer_small[n / 2]); return; } arb_init(t); for (prec = arith_bernoulli_number_size(n) + fmpz_bits(den) + 2; ; prec += 20) { arb_bernoulli_ui_zeta(t, n, prec); arb_mul_fmpz(t, t, den, prec); if (arb_get_unique_fmpz(num, t)) break; flint_printf("warning: %wd insufficient precision for Bernoulli number %wu\n", prec, n); } arb_clear(t); } arb-2.8.1/bernoulli/rev_clear.c000066400000000000000000000025301264125401100163630ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" void bernoulli_rev_clear(bernoulli_rev_t iter) { if (iter->alloc != 0) { _fmpz_vec_clear(iter->powers, iter->alloc); fmpz_clear(iter->pow_error); arb_clear(iter->prefactor); arb_clear(iter->two_pi_squared); } } arb-2.8.1/bernoulli/rev_init.c000066400000000000000000000053101264125401100162370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" void bernoulli_rev_init(bernoulli_rev_t iter, ulong nmax) { slong j; fmpz_t t; arb_t x; arf_t u; int round1, round2; slong wp; nmax -= (nmax % 2); iter->n = nmax; iter->alloc = 0; if (nmax < BERNOULLI_REV_MIN) return; iter->prec = wp = bernoulli_global_prec(nmax); iter->max_power = bernoulli_zeta_terms(nmax, iter->prec); iter->alloc = iter->max_power + 1; iter->powers = _fmpz_vec_init(iter->alloc); fmpz_init(iter->pow_error); arb_init(iter->prefactor); arb_init(iter->two_pi_squared); arb_init(x); fmpz_init(t); arf_init(u); /* precompute powers */ for (j = 3; j <= iter->max_power; j += 2) { arb_ui_pow_ui(x, j, nmax, bernoulli_power_prec(j, nmax, wp)); arb_inv(x, x, bernoulli_power_prec(j, nmax, wp)); round1 = arf_get_fmpz_fixed_si(t, arb_midref(x), -wp); fmpz_set(iter->powers + j, t); /* error: the radius, plus two roundings */ arf_set_mag(u, arb_radref(x)); round2 = arf_get_fmpz_fixed_si(t, u, -wp); fmpz_add_ui(t, t, (round1 != 0) + (round2 != 0)); if (fmpz_cmp(iter->pow_error, t) < 0) fmpz_set(iter->pow_error, t); } /* precompute (2pi)^2 and 2*(n!)/(2pi)^n */ arb_fac_ui(iter->prefactor, nmax, wp); arb_mul_2exp_si(iter->prefactor, iter->prefactor, 1); arb_const_pi(x, wp); arb_mul_2exp_si(x, x, 1); arb_mul(iter->two_pi_squared, x, x, wp); arb_pow_ui(x, iter->two_pi_squared, nmax / 2, wp); arb_div(iter->prefactor, iter->prefactor, x, wp); fmpz_clear(t); arb_clear(x); arf_clear(u); } arb-2.8.1/bernoulli/rev_next.c000066400000000000000000000107111264125401100162530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "bernoulli.h" static __inline__ void mag_ui_div(mag_t z, ulong c, const mag_t x) { mag_t t; mag_init(t); mag_set_ui(t, c); mag_div(z, t, x); mag_clear(t); } void bernoulli_rev_next(fmpz_t numer, fmpz_t denom, bernoulli_rev_t iter) { ulong n; slong j, wp; fmpz_t sum; mag_t err; arb_t z, h; n = iter->n; wp = iter->prec; if (n < BERNOULLI_REV_MIN) { _arith_bernoulli_number(numer, denom, n); if (n != 0) iter->n -= 2; return; } fmpz_init(sum); mag_init(err); arb_init(z); arb_init(h); /* add all odd powers */ fmpz_zero(sum); for (j = iter->max_power; j >= 3; j -= 2) fmpz_add(sum, sum, iter->powers + j); arb_set_fmpz(z, sum); /* bound numerical error from the powers */ fmpz_mul_ui(sum, iter->pow_error, iter->max_power / 2); mag_set_fmpz(err, sum); mag_add(arb_radref(z), arb_radref(z), err); arb_mul_2exp_si(z, z, -wp); arb_add_ui(z, z, 1, wp); /* add truncation error: sum_{k > N} 1/k^n <= 1/N^(i-1) */ mag_set_ui_lower(err, iter->max_power); mag_pow_ui_lower(err, err, n - 1); mag_ui_div(err, 1, err); mag_add(arb_radref(z), arb_radref(z), err); /* convert zeta to Bernoulli number */ arb_div_2expm1_ui(h, z, n, wp); arb_add(z, z, h, wp); arb_mul(z, z, iter->prefactor, wp); arith_bernoulli_number_denom(denom, n); arb_mul_fmpz(z, z, denom, wp); if (n % 4 == 0) arb_neg(z, z); /* flint_printf("%wd: ", n); arb_printd(z, 5); flint_printf("\n"); */ if (!arb_get_unique_fmpz(numer, z)) { flint_printf("warning: insufficient precision for B_%wd\n", n); _bernoulli_fmpq_ui(numer, denom, n); } /* update prefactor */ if (n > 0) { arb_mul(iter->prefactor, iter->prefactor, iter->two_pi_squared, wp); arb_div_ui(iter->prefactor, iter->prefactor, n, wp); arb_div_ui(iter->prefactor, iter->prefactor, n - 1, wp); } /* update powers */ for (j = 3; j <= iter->max_power; j += 2) fmpz_mul2_uiui(iter->powers + j, iter->powers + j, j, j); /* bound error after update */ fmpz_mul2_uiui(iter->pow_error, iter->pow_error, iter->max_power, iter->max_power); /* readjust precision */ if (n % 64 == 0 && n > BERNOULLI_REV_MIN) { slong new_prec, new_max; new_prec = bernoulli_global_prec(n); new_max = bernoulli_zeta_terms(n, new_prec); if (new_prec < iter->prec && new_max <= iter->max_power) { /* change precision of the powers */ for (j = 3; j <= new_max; j += 2) fmpz_tdiv_q_2exp(iter->powers + j, iter->powers + j, iter->prec - new_prec); /* the error also changes precision */ fmpz_cdiv_q_2exp(iter->pow_error, iter->pow_error, iter->prec - new_prec); /* contribution of rounding error when changing the precision of the powers */ fmpz_add_ui(iter->pow_error, iter->pow_error, 1); /* speed improvement (could be skipped with better multiplication) */ arb_set_round(iter->two_pi_squared, iter->two_pi_squared, new_prec); iter->max_power = new_max; iter->prec = new_prec; } } iter->n -= 2; fmpz_clear(sum); mag_clear(err); arb_clear(z); arb_clear(h); } arb-2.8.1/bernoulli/test/000077500000000000000000000000001264125401100152345ustar00rootroot00000000000000arb-2.8.1/bernoulli/test/t-bound_2exp_si.c000066400000000000000000000045471264125401100204130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include #include #include "bernoulli.h" double log2bern_approx(double n) { return 1 + ((n+0.5)*log(n) - n - (n-0.5)*log(2*3.14159265358979323)) * (1. / log(2)); } int main() { slong i, bound; double a, b; fmpq_t q; fmpr_t t; flint_printf("bound_2exp_si...."); fflush(stdout); fmpq_init(q); fmpr_init(t); for (i = 0; i < 1000; i++) { arith_bernoulli_number(q, i); bound = bernoulli_bound_2exp_si(i); fmpr_set_round_fmpz(t, fmpq_numref(q), 32, FMPR_RND_UP); fmpr_div_fmpz(t, t, fmpq_denref(q), 32, FMPR_RND_UP); if (fmpr_cmpabs_2exp_si(t, bound) > 0) { flint_printf("FAIL: %wd\n", i); fmpr_print(t); flint_printf("\n\n"); flint_printf("%wd\n", bound); flint_printf("\n\n"); abort(); } } fmpq_clear(q); fmpr_clear(t); for (i = 100; i < 4000000; i += 1) { i += (i & 1); a = bernoulli_bound_2exp_si(i); b = log2bern_approx(i); if (a < b || a > 1.01 * b) { flint_printf("FAIL: %wd\n", i); flint_printf("%wd: %f %f %f\n", i, a, b, (float) a / b); abort(); } } flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/bernoulli/test/t-fmpq_ui.c000066400000000000000000000045261264125401100173100ustar00rootroot00000000000000/*============================================================================= This file is part of FLINT. FLINT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. FLINT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011, 2013 Fredrik Johansson ******************************************************************************/ #include #include #include "fmpz_vec.h" #include "arith.h" #include "bernoulli.h" int main() { fmpz * num1; fmpz * den1; fmpz_t num2; fmpz_t den2; slong n, N; flint_printf("fmpq_ui...."); fflush(stdout); N = 4000; num1 = _fmpz_vec_init(N); den1 = _fmpz_vec_init(N); fmpz_init(num2); fmpz_init(den2); _arith_bernoulli_number_vec_multi_mod(num1, den1, N); for (n = 0; n < N; n++) { _bernoulli_fmpq_ui(num2, den2, n); if (!fmpz_equal(num1 + n, num2)) { flint_printf("FAIL: n = %wd, numerator\n", n); flint_printf("vec: "); fmpz_print(num1 + n); flint_printf("\n"); flint_printf("single: "); fmpz_print(num2); flint_printf("\n"); abort(); } if (!fmpz_equal(den1 + n, den2)) { flint_printf("FAIL: n = %wd, denominator\n", n); flint_printf("vec: "); fmpz_print(den1 + n); flint_printf("\n"); flint_printf("single: "); fmpz_print(den2); flint_printf("\n"); abort(); } } _fmpz_vec_clear(num1, N); _fmpz_vec_clear(den1, N); fmpz_clear(num2); fmpz_clear(den2); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/bernoulli/test/t-rev.c000066400000000000000000000061161264125401100164410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include #include "bernoulli.h" #include "ulong_extras.h" #include "nmod_poly.h" #include "nmod_vec.h" int main() { flint_rand_t state; slong nmax, n, bound, count; mp_limb_t p, pinv, m1, m2; nmod_poly_t A; flint_printf("rev...."); fflush(stdout); flint_randinit(state); bound = 100000; p = n_nextprime(UWORD(1) << (FLINT_BITS - 1), 0); pinv = n_preinvert_limb(p); nmod_poly_init(A, p); nmod_poly_set_coeff_ui(A, 1, 1); nmod_poly_exp_series(A, A, bound); nmod_poly_shift_right(A, A, 1); nmod_poly_inv_series(A, A, bound); m1 = 1; for (n = 0; n < A->length; n++) { A->coeffs[n] = n_mulmod2_preinv(A->coeffs[n], m1, p, pinv); m1 = n_mulmod2_preinv(m1, n + 1, p, pinv); } for (nmax = 0; nmax < bound; nmax = 1.5 * nmax + 2) { fmpz_t numer, denom; bernoulli_rev_t iter; fmpz_init(numer); fmpz_init(denom); nmax += (nmax % 2); bernoulli_rev_init(iter, nmax); if (nmax < 8000) count = 4000; else count = 100; /* flint_printf("nmax = %wd, count = %wd\n", nmax, count); */ for (n = nmax; n >= 0 && count > 0; n -= 2, count--) { bernoulli_rev_next(numer, denom, iter); m1 = fmpz_fdiv_ui(numer, p); m2 = fmpz_fdiv_ui(denom, p); m2 = n_invmod(m2, p); m1 = n_mulmod2_preinv(m1, m2, p, pinv); m2 = nmod_poly_get_coeff_ui(A, n); if (m1 != m2) { flint_printf("FAIL:\n"); flint_printf("nmax = %wd, n = %wd\n", nmax, n); flint_printf("m1 = %wu mod %wu\n", m1, p); flint_printf("m2 = %wu mod %wu\n", m2, p); abort(); } } bernoulli_rev_clear(iter); fmpz_clear(numer); fmpz_clear(denom); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/configure000077500000000000000000000413051264125401100141740ustar00rootroot00000000000000#!/bin/sh # (C) 2007, Robert Bradshaw, William Hart, William Stein, Michael Abshoff # (C) 2011, William Hart # (C) 2012, William Hart, Jean-Pierre Flori, Thomas DuBuisson # (C) 2012, Jan Engelhardt # soname version # # arb => soname # 2.7.0 => 0.0.0 ARB_MAJOR=1 ARB_MINOR=1 ARB_PATCH=1 PREFIX="/usr/local" GMP_DIR="/usr/local" MPFR_DIR="/usr/local" FLINT_DIR="/usr/local" NTL_DIR="/usr/local" GC_DIR="/usr/local" BLAS_DIR="/usr/local" WANT_NTL=0 WANT_BLAS=0 SHARED=1 STATIC=1 TLS=1 PTHREAD=1 REENTRANT=0 WANT_GC=0 WANT_TLS=0 WANT_CXX=0 ASSERT=0 BUILD= EXTENSIONS= EXT_MODS= EXTRA_BUILD= usage() { echo "Usage: ./configure " echo " where may be" echo " -h display usage information" echo " where may be:" echo " --prefix= Specify path to installation location (default: /usr/local)" echo " --with-mpir= Specify location of MPIR (default: /usr/local)" echo " --with-gmp= Specify location of GMP (default: /usr/local)" echo " --with-mpfr= Specify location of MPFR (default: /usr/local)" echo " --with-flint= Specify location of FLINT (default: /usr/local)" echo " --with-blas[=] Use BLAS and specify its location (default: /usr/local)" echo " --without-blas Do not use BLAS (default)" echo " --with-ntl[=] Build NTL interface and specify its location (default: /usr/local)" echo " --without-ntl Do not build NTL interface (default)" echo " --extensions= Specify location of extension modules" echo " --build=arch-os Specify architecture/OS combination rather than use values from uname -m/-s" echo " --enable-shared Build a shared library (default)" echo " --disable-shared Do not build a shared library" echo " --enable-static Build a static library (default)" echo " --disable-static Do not build a static library" echo " --single Faster [non-reentrant if tls or pthread not used] version of library (default)" echo " --reentrant Build fully reentrant [with or without tls, with pthread] version of library" echo " --with-gc= GC safe build with path to gc" echo " --enable-pthread Use pthread (default)" echo " --disable-pthread Do not use pthread" echo " --enable-tls Use thread-local storage (default)" echo " --disable-tls Do not use thread-local storage" echo " --enable-assert Enable use of asserts (use for debug builds only)" echo " --disable-assert Disable use of asserts (default)" echo " --enable-cxx Enable C++ wrapper tests" echo " --disable-cxx Disable C++ wrapper tests (default)" echo " CC= Use the C compiler with the given name (default: gcc)" echo " CXX= Use the C++ compiler with the given name (default: g++)" echo " AR= Use the AR library builder with the given name (default: ar)" echo " CFLAGS= Pass the given flags to the compiler" echo " ABI=[32|64] Tell the compiler to use given ABI (default: empty)" } absolute_path(){ dirlist="$1" retval="" for dir in $dirlist; do case $dir in /*) dir=$dir;; *) dir=$PWD/$dir;; esac retval=$retval" "$dir done echo $retval } while [ "$1" != "" ]; do PARAM=`echo $1 | sed 's/=.*//'` VALUE=`echo $1 | sed 's/[^=]*//; s/=//'` case "$PARAM" in -h|--help) usage exit 0 ;; --with-mpir|--with-gmp) GMP_DIR=$(absolute_path "$VALUE") ;; --with-mpfr) MPFR_DIR=$(absolute_path "$VALUE") ;; --with-flint) FLINT_DIR=$(absolute_path "$VALUE") ;; --with-ntl) WANT_NTL=1 if [ ! -z "$VALUE" ]; then NTL_DIR=$(absolute_path "$VALUE") fi ;; --without-ntl) WANT_NTL=0 ;; --with-blas) WANT_BLAS=1 if [ ! -z "$VALUE" ]; then BLAS_DIR=$(absolute_path "$VALUE") fi ;; --without-blas) WANT_BLAS=0 ;; --extensions) EXTENSIONS=$(absolute_path "$VALUE") ;; --build) BUILD="$VALUE" ;; --prefix) PREFIX=$VALUE ;; --enable-shared) SHARED=1 ;; --disable-shared) SHARED=0 ;; --enable-static) STATIC=1 ;; --disable-static) STATIC=0 ;; --single) REENTRANT=0 ;; --reentrant) REENTRANT=1 ;; --with-gc) WANT_GC=1 if [ ! -z "$VALUE" ]; then GC_DIR="$VALUE" fi ;; --enable-pthread) PTHREAD=1 ;; --disable-pthread) PTHREAD=0 ;; --enable-tls) TLS=1 WANT_TLS=1;; --disable-tls) TLS=0 ;; --enable-assert) ASSERT=1 ;; --disable-assert) ASSERT=0 ;; --enable-cxx) WANT_CXX=1 ;; --disable-cxx) WANT_CXX=0 ;; AR) AR="$VALUE" ;; CC) CC="$VALUE" ;; CXX) CXX="$VALUE" ;; CFLAGS) CFLAGS="$VALUE" ;; ABI) ABI="$VALUE" ;; *) usage exit 1 ;; esac shift done #find dependencies LIBS="m" if [ -d "${GMP_DIR}/lib" ]; then GMP_LIB_DIR="${GMP_DIR}/lib" GMP_INC_DIR="${GMP_DIR}/include" elif [ -d "${GMP_DIR}/lib64" ]; then GMP_LIB_DIR="${GMP_DIR}/lib64" GMP_INC_DIR="${GMP_DIR}/include" elif [ -d "${GMP_DIR}/.libs" ]; then GMP_LIB_DIR="${GMP_DIR}/.libs" GMP_INC_DIR="${GMP_DIR}" else echo "Invalid GMP directory" exit 1 fi LIB_DIRS="${LIB_DIRS} ${GMP_LIB_DIR}" INC_DIRS="${INC_DIRS} ${GMP_INC_DIR}" LIBS="${LIBS} gmp" if [ -d "${MPFR_DIR}/lib" ]; then MPFR_LIB_DIR="${MPFR_DIR}/lib" MPFR_INC_DIR="${MPFR_DIR}/include" elif [ -d "${MPFR_DIR}/lib64" ]; then MPFR_LIB_DIR="${MPFR_DIR}/lib64" MPFR_INC_DIR="${MPFR_DIR}/include" elif [ -d "${MPFR_DIR}/.libs" ]; then MPFR_LIB_DIR="${MPFR_DIR}/.libs" MPFR_INC_DIR="${MPFR_DIR}" elif [ -d "${MPFR_DIR}/src/.libs" ]; then MPFR_LIB_DIR="${MPFR_DIR}/src/.libs" MPFR_INC_DIR="${MPFR_DIR}/src" else echo "Invalid MPFR directory" exit 1 fi LIB_DIRS="${LIB_DIRS} ${MPFR_LIB_DIR}" INC_DIRS="${INC_DIRS} ${MPFR_INC_DIR}" LIBS="${LIBS} mpfr" if [ -d "${FLINT_DIR}/lib" ]; then FLINT_LIB_DIR="${FLINT_DIR}/lib" FLINT_INC_DIR="${FLINT_DIR}/include" elif [ -d "${FLINT_DIR}/lib64" ]; then FLINT_LIB_DIR="${FLINT_DIR}/lib64" FLINT_INC_DIR="${FLINT_DIR}/include" elif [ -d "${FLINT_DIR}/.libs" ]; then FLINT_LIB_DIR="${FLINT_DIR}/.libs" FLINT_INC_DIR="${FLINT_DIR}" elif [ -d "${FLINT_DIR}" ]; then FLINT_LIB_DIR="${FLINT_DIR}" FLINT_INC_DIR="${FLINT_DIR}" else echo "Invalid FLINT directory" exit 1 fi if [ -d "${FLINT_INC_DIR}/flint" ]; then FLINT_INC_DIR="${FLINT_INC_DIR}/flint" fi LIB_DIRS="${LIB_DIRS} ${FLINT_LIB_DIR}" INC_DIRS="${INC_DIRS} ${FLINT_INC_DIR}" LIBS="${LIBS} flint" #configure extra libraries if [ "$WANT_NTL" = "1" ]; then if [ -d "${NTL_DIR}/lib" ]; then NTL_LIB_DIR="${NTL_DIR}/lib" NTL_INC_DIR="${NTL_DIR}/include" elif [ -d "${NTL_DIR}/lib64" ]; then NTL_LIB_DIR="${NTL_DIR}/lib64" NTL_INC_DIR="${NTL_DIR}/include" else echo "Invalid NTL directory" exit 1 fi EXTRA_INC_DIRS="${EXTRA_INC_DIRS} ${NTL_INC_DIR}" EXTRA_LIB_DIRS="${EXTRA_LIB_DIRS} ${NTL_LIB_DIR}" EXTRA_LIBS="${EXTRA_LIBS} ntl" fi if [ "$WANT_BLAS" = "1" ]; then if [ -d "${BLAS_DIR}" ]; then BLAS_LIB_DIR="${BLAS_DIR}" BLAS_INC_DIR="${BLAS_DIR}" else echo "Invalid BLAS directory" exit 1 fi EXTRA_INC_DIRS="${EXTRA_INC_DIRS} ${BLAS_INC_DIR}" EXTRA_LIB_DIRS="${EXTRA_LIB_DIRS} ${BLAS_LIB_DIR}" EXTRA_LIBS="${EXTRA_LIBS} openblas" fi CONFIG_BLAS="#define HAVE_BLAS ${WANT_BLAS}" if [ "$WANT_GC" = "1" ]; then if [ -d "${GC_DIR}" ]; then GC_LIB_DIR="${GC_DIR}/lib" GC_INC_DIR="${GC_DIR}/include" else echo "Invalid GC directory" exit 1 fi EXTRA_INC_DIRS="${EXTRA_INC_DIRS} ${GC_INC_DIR}" EXTRA_LIB_DIRS="${EXTRA_LIB_DIRS} ${GC_LIB_DIR}" EXTRA_LIBS="${EXTRA_LIBS} gc" fi CONFIG_GC="#define HAVE_GC ${WANT_GC}" # defaults for CC, CXX and AR if [ -z "$CC" ]; then CC=gcc fi if [ -z "$CXX" ]; then CXX=g++ fi if [ -z "$AR" ]; then AR=ar fi # Architecture handler KERNEL=`uname` if [ -z "$BUILD" ]; then ARCH=`uname -m` if [ "$(uname | cut -d_ -f1)" = "MINGW32" ]; then if [ "$ABI" = "64" ]; then OS="MINGW64" else OS="MINGW32" fi elif [ "$(uname | cut -d_ -f1)" = "CYGWIN" ]; then if [ "$ARCH" = "x86_64" ]; then if [ "$ABI" = "32" ]; then OS="CYGWIN32" else OS="CYGWIN64" ABI="64" fi else OS="CYGWIN32" fi else OS=`uname -s` fi else ARCH=`echo "$BUILD" | cut -d- -f1` OS=`echo "$BUILD" | cut -d- -f2` fi case "$ARCH" in x86_64 | amd64) MACHINE="x86_64";; x86 | i*86 | pc) MACHINE="x86";; ia64) MACHINE="ia64";; sparc | sun4*) MACHINE="sparc";; sparc64) MACHINE="sparc64";; ppc64 | powerpc64) MACHINE="ppc64";; ppc | powerpc | [P|p]ower*) MACHINE="ppc";; *) MACHINE="unknown";; esac #ABI flag if [ "$ABI" = "32" ]; then ABI_FLAG="-m32" case "$MACHINE" in x86_64) MACHINE="x86";; sparc64) MACHINE="sparc";; ppc64) MACHINE="ppc";; *) ;; esac elif [ "$ABI" = "64" ]; then ABI_FLAG="-m64" if [ "$MACHINE" = "sparc" ]; then MACHINE="sparc64" fi if [ "$MACHINE" = "x86" ]; then MACHINE="x86_64" fi fi if [ "$MACHINE" = "sparc" ] || [ "$MACHINE" = "sparc64" ]; then if [ "$CC" = "gcc" ]; then CC="gcc -mno-relax" fi fi echo "Configuring...${MACHINE}-${OS}" #name for ARB shared library ARB_SOLIB=0 if [ -z "$ARB_LIB" ]; then case "$OS" in Darwin) ARB_LIBNAME="libarb.dylib" ARB_LIB="libarb-$ARB_MAJOR.$ARB_MINOR.$ARB_PATCH.dylib" EXTRA_SHARED_FLAGS="-install_name $PREFIX/lib/$ARB_LIB -compatibility_version $ARB_MAJOR.$ARB_MINOR -current_version $ARB_MAJOR.$ARB_MINOR.$ARB_PATCH";; CYGWIN* | MINGW*) ARB_LIBNAME="libarb.dll" ARB_LIB="libarb-$ARB_MAJOR.dll" EXTRA_SHARED_FLAGS="-static-libgcc -shared -Wl,--export-all-symbols -Wl,-soname,libarb-$ARB_MAJOR.dll.$ARB_MINOR.$ARB_PATCH";; *) ARB_LIBNAME="libarb.so" ARB_LIB="libarb.so.$ARB_MAJOR.$ARB_MINOR.$ARB_PATCH" EXTRA_SHARED_FLAGS="-Wl,-soname,libarb.so.$ARB_MAJOR" ARB_SOLIB=1;; esac fi # sometimes LDCONFIG is not to be found in the path. Look at some common places. case "$OS" in MINGW*|CYGWIN*|Darwin) LDCONFIG="true";; *) if [ -z "$LDCONFIG" ]; then LDCONFIG="true" if [ "$ARB_SOLIB" = "1" ]; then if command -v ldconfig > /dev/null; then LDCONFIG="ldconfig" elif [ -x /sbin/ldconfig ]; then LDCONFIG="/sbin/ldconfig" fi fi fi;; esac #extension for executables if [ -z "$EXEEXT" ]; then case "$OS" in CYGWIN* | MINGW*) EXEEXT=".exe";; *) EXEEXT="";; esac fi #don't build both shared and static lib on MinGW and Cygwin case "$OS" in CYGWIN* | MINGW*) if [ "$STATIC" = "1" ] && [ "$SHARED" = "1" ]; then echo "Building both static and shared versions of MPIR/GMP on $OS is currently" echo "unsupported, and so is it for MPFR, FLINT and ARB." echo "You should pass --disable-shared or --disable-static to configure" echo "depending on the versions of MPIR/GMP, MPFR and FLINT you built." exit 1 fi ;; *) ;; esac #test for popcnt flag and set needed CFLAGS mkdir -p build rm -f build/test-popcnt > /dev/null 2>&1 MSG="Testing __builtin_popcountl..." printf "%s" "$MSG" echo "int main(int argc, char ** argv) { #if defined(_WIN64) return __builtin_popcountll(argc) == 100; #else return __builtin_popcountl(argc) == 100; #endif }" > build/test-popcnt.c $CC build/test-popcnt.c -o ./build/test-popcnt > /dev/null 2>&1 if [ $? -eq 0 ]; then printf "%s\n" "yes" CONFIG_POPCNT_INTRINSICS="#define POPCNT_INTRINSICS" if [ "$MACHINE" = "x86_64" ]; then MSG="Testing native popcount..." printf "%s" "$MSG" touch build/test-popcnt.c rm build/test-popcnt $CC -mpopcnt build/test-popcnt.c -o ./build/test-popcnt > /dev/null 2>&1 build/test-popcnt > /dev/null 2>&1 if [ $? -eq 0 ]; then printf "%s\n" "yes" POPCNT_FLAG="-mpopcnt" else printf "%s\n" "no" fi rm -f build/test-popcnt{,.c} #in case -mpopcnt is not available, the test program will use an illegal #instruction and that will print out something on stderr when the if #construction is exited, whence the following "2> /dev/null" fi 2> /dev/null else rm -f build/test-popcnt.c printf "%s\n" "no" fi #defaults for CFLAGS if [ -z "$CFLAGS" ]; then if [ "$OS" = "MINGW64" ]; then CFLAGS="-O2 -funroll-loops -g $POPCNT_FLAG $ABI_FLAG" elif [ "$OS" = "CYGWIN64" ]; then CFLAGS="-O2 -funroll-loops -g -D _WIN64 $POPCNT_FLAG $ABI_FLAG" else CFLAGS="-ansi -pedantic -Wall -O2 -funroll-loops -g $POPCNT_FLAG $ABI_FLAG" fi fi #this is needed on PPC G5 and does not hurt on other OS Xes if [ "$KERNEL" = Darwin ]; then CFLAGS="-fno-common $CFLAGS" fi #PIC flag if [ -z "$PIC_FLAG" ]; then case "$OS" in CYGWIN* | MINGW*) ;; *) PIC_FLAG="-fPIC";; esac fi #test support for thread-local storage CONFIG_TLS="#define HAVE_TLS 0" if [ "$TLS" = "1" ]; then mkdir -p build rm -f build/test-tls > /dev/null 2>&1 MSG="Testing __thread..." printf "%s" "$MSG" echo "__thread int x = 42; int main(int argc, char ** argv) { return x != 42; }" > build/test-tls.c $CC build/test-tls.c -o ./build/test-tls > /dev/null 2>&1 if [ $? -eq 0 ]; then build/test-tls > /dev/null 2>&1 if [ $? -eq 0 ]; then printf "%s\n" "yes" CONFIG_TLS="#define HAVE_TLS 1" else printf "%s\n" "no" fi rm -f build/test-tls{,.c} else rm -f build/test-tls.c printf "%s\n" "no" #build-tls can segfault on systems where tls is not available fi 2> /dev/null fi #pthread configuration CONFIG_PTHREAD="#define HAVE_PTHREAD ${PTHREAD}" #pocess external modules EXTRA_INC_DIRS="${EXTRA_INC_DIRS} ${EXTENSIONS}" #include paths INCS="-I\$(CURDIR)" for INC_DIR in ${INC_DIRS} ${EXTRA_INC_DIRS}; do INCS="${INCS} -I${INC_DIR}" done #library paths LLIBS="-L\$(CURDIR)" for LIB_DIR in ${LIB_DIRS} ${EXTRA_LIB_DIRS}; do LLIBS="${LLIBS} -L${LIB_DIR}" done #linker params if [ "$PTHREAD" = "1" ]; then lLIBS2="-lpthread ${lLIBS2}" fi for LIB in ${EXTRA_LIBS} ${LIBS}; do lLIBS2="-l${LIB} ${lLIBS2}" done lLIBS="-larb $lLIBS2" LIBS2="$LLIBS $lLIBS2" LIBS="$LLIBS $lLIBS" #paths for dynamic linker case "$OS" in CYGWIN* | MINGW*) DLPATH="PATH";; Darwin) DLPATH="DYLD_LIBRARY_PATH";; sparc) DLPATH="LD_LIBRARY_PATH32";; sparc64) DLPATH="LD_LIBRARY_PATH64";; *) DLPATH="LD_LIBRARY_PATH";; esac DLPATH_ADD="\$(CURDIR)" for LIB_DIR in ${LIB_DIRS} ${EXTRA_LIB_DIRS}; do DLPATH_ADD="${DLPATH_ADD}:${LIB_DIR}" done #cxx if [ "$WANT_CXX" = "1" ]; then EXTRA_BUILD="$EXTRA_BUILD arbxx" fi #write out Makefile echo "# This file is autogenerated by ./configure -- do not edit!" > Makefile echo "" >> Makefile echo "SHELL=/bin/sh" >> Makefile echo "" >> Makefile echo "ARB_STATIC=$STATIC" >> Makefile echo "ARB_SHARED=$SHARED" >> Makefile echo "ARB_LIB=$ARB_LIB" >> Makefile echo "ARB_LIBNAME=$ARB_LIBNAME" >> Makefile echo "ARB_SOLIB=$ARB_SOLIB" >> Makefile echo "EXEEXT=$EXEEXT" >> Makefile echo "PREFIX=$PREFIX" >> Makefile echo "" >> Makefile echo "WANT_NTL=$WANT_NTL" >> Makefile echo "" >> Makefile echo "INCS=$INCS" >> Makefile echo "LIBS=$LIBS" >> Makefile echo "LIBS2=$LIBS2" >> Makefile echo "" >> Makefile echo "CC=$CC" >> Makefile echo "CXX=$CXX" >> Makefile echo "AR=$AR" >> Makefile echo "LDCONFIG=$LDCONFIG" >> Makefile echo "" >> Makefile echo "CFLAGS=$CFLAGS" >> Makefile echo "ABI_FLAG=$ABI_FLAG" >> Makefile echo "PIC_FLAG=$PIC_FLAG" >> Makefile echo "EXTRA_SHARED_FLAGS=$EXTRA_SHARED_FLAGS" >> Makefile echo "" >> Makefile echo "DLPATH=$DLPATH" >> Makefile echo "DLPATH_ADD=$DLPATH_ADD" >> Makefile echo "EXTENSIONS=$EXTENSIONS" >> Makefile echo "EXTRA_BUILD_DIRS=$EXTRA_BUILD" >> Makefile echo "" >> Makefile cat Makefile.in >> Makefile echo "ARB was successfully configured." arb-2.8.1/doc/000077500000000000000000000000001264125401100130275ustar00rootroot00000000000000arb-2.8.1/doc/Makefile000066400000000000000000000126711264125401100144760ustar00rootroot00000000000000# Makefile for Sphinx documentation # # You can set these variables from the command line. SPHINXOPTS = SPHINXBUILD = sphinx-build PAPER = BUILDDIR = build # Internal variables. 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The Texinfo files are in $(BUILDDIR)/texinfo." @echo "Run \`make' in that directory to run these through makeinfo" \ "(use \`make info' here to do that automatically)." info: $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo @echo "Running Texinfo files through makeinfo..." make -C $(BUILDDIR)/texinfo info @echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo." gettext: $(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale @echo @echo "Build finished. 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¶dzÉíÝ@òiTh+!†’|4æI»Î—÷é(2ìMòÔˆÉ>ªÅm$w”&…$I16f ž_«¿‰äáål^µ– $·±è}Ƽ HòÉ$£q Bh„ŽäW ÂÑ?E.“fÑËß<ØÊm²°' gg]à×YÊ,AdhWRtp"€‰B..S{âKó‹ 5ÏrH "C‡£'rIÌ0¹ˆi`5€Œ œs%}‘¡SÏ-Œ4büÀ|›‰³l°¹T¾¯¸Àc–qT2K®È¥‘mô¾'ðïÏðr©{—hvÎQÒª ívjU(ÅÅ‘ADAAd‘ADAAd„6¢V"èP< àbïw‹D"‚ ‚ ‚ B§ÆÿMÆè1n\k¨IEND®B`‚arb-2.8.1/doc/source/_static/arbwhite.svg000066400000000000000000000111511264125401100203020ustar00rootroot00000000000000 image/svg+xml ζ(s) arb-2.8.1/doc/source/acb.rst000066400000000000000000001011131264125401100156030ustar00rootroot00000000000000.. _acb: **acb.h** -- complex numbers =============================================================================== An :type:`acb_t` represents a complex number with error bounds. An :type:`acb_t` consists of a pair of real number balls of type :type:`arb_struct`, representing the real and imaginary part with separate error bounds. An :type:`acb_t` thus represents a rectangle `[m_1-r_1, m_1+r_1] + [m_2-r_2, m_2+r_2] i` in the complex plane. This is used instead of a disk or square representation (consisting of a complex floating-point midpoint with a single radius), since it allows implementing many operations more conveniently by splitting into ball operations on the real and imaginary parts. It also allows tracking when complex numbers have an exact (for example exactly zero) real part and an inexact imaginary part, or vice versa. The interface for the :type:`acb_t` type is slightly less developed than that for the :type:`arb_t` type. In many cases, the user can easily perform missing operations by directly manipulating the real and imaginary parts. Types, macros and constants ------------------------------------------------------------------------------- .. type:: acb_struct .. type:: acb_t An *acb_struct* consists of a pair of *arb_struct*:s. An *acb_t* is defined as an array of length one of type *acb_struct*, permitting an *acb_t* to be passed by reference. .. type:: acb_ptr Alias for ``acb_struct *``, used for vectors of numbers. .. type:: acb_srcptr Alias for ``const acb_struct *``, used for vectors of numbers when passed as constant input to functions. .. macro:: acb_realref(x) Macro returning a pointer to the real part of *x* as an *arb_t*. .. macro:: acb_imagref(x) Macro returning a pointer to the imaginary part of *x* as an *arb_t*. Memory management ------------------------------------------------------------------------------- .. function:: void acb_init(acb_t x) Initializes the variable *x* for use, and sets its value to zero. .. function:: void acb_clear(acb_t x) Clears the variable *x*, freeing or recycling its allocated memory. .. function:: acb_ptr _acb_vec_init(slong n) Returns a pointer to an array of *n* initialized *acb_struct*:s. .. function:: void _acb_vec_clear(acb_ptr v, slong n) Clears an array of *n* initialized *acb_struct*:s. Basic manipulation ------------------------------------------------------------------------------- .. function:: int acb_is_zero(const acb_t z) Returns nonzero iff *z* is zero. .. function:: int acb_is_one(const acb_t z) Returns nonzero iff *z* is exactly 1. .. function:: int acb_is_finite(const acb_t z) Returns nonzero iff *z* certainly is finite. .. function:: int acb_is_exact(const acb_t z) Returns nonzero iff *z* is exact. .. function:: int acb_is_int(const acb_t z) Returns nonzero iff *z* is an exact integer. .. function:: void acb_zero(acb_t z) .. function:: void acb_one(acb_t z) .. function:: void acb_onei(acb_t z) Sets *z* respectively to 0, 1, `i = \sqrt{-1}`. .. function:: void acb_set(acb_t z, const acb_t x) .. function:: void acb_set_ui(acb_t z, slong x) .. function:: void acb_set_si(acb_t z, slong x) .. function:: void acb_set_d(acb_t z, double x) .. function:: void acb_set_fmpz(acb_t z, const fmpz_t x) .. function:: void acb_set_arb(acb_t z, const arb_t c) Sets *z* to the value of *x*. .. function:: void acb_set_si_si(acb_t z, slong x, slong y) .. function:: void acb_set_d_d(acb_t z, double x, double y) .. function:: void acb_set_fmpz_fmpz(acb_t z, const fmpz_t x, const fmpz_t y) .. function:: void acb_set_arb_arb(acb_t z, const arb_t x, const arb_t y) Sets the real and imaginary part of *z* to the values *x* and *y* respectively .. function:: void acb_set_fmpq(acb_t z, const fmpq_t x, slong prec) .. function:: void acb_set_round(acb_t z, const acb_t x, slong prec) .. function:: void acb_set_round_fmpz(acb_t z, const fmpz_t x, slong prec) .. function:: void acb_set_round_arb(acb_t z, const arb_t x, slong prec) Sets *z* to *x*, rounded to *prec* bits. .. function:: void acb_swap(acb_t z, acb_t x) Swaps *z* and *x* efficiently. .. function:: void acb_add_error_mag(acb_t x, const mag_t err) Adds *err* to the error bounds of both the real and imaginary parts of *x*, modifying *x* in-place. Input and output ------------------------------------------------------------------------------- .. function:: void acb_print(const acb_t x) Prints the internal representation of *x*. .. function:: void acb_printd(const acb_t z, slong digits) Prints *x* in decimal. The printed value of the radius is not adjusted to compensate for the fact that the binary-to-decimal conversion of both the midpoint and the radius introduces additional error. Random number generation ------------------------------------------------------------------------------- .. function:: void acb_randtest(acb_t z, flint_rand_t state, slong prec, slong mag_bits) Generates a random complex number by generating separate random real and imaginary parts. .. function:: void acb_randtest_special(acb_t z, flint_rand_t state, slong prec, slong mag_bits) Generates a random complex number by generating separate random real and imaginary parts. Also generates NaNs and infinities. .. function:: void acb_randtest_precise(acb_t z, flint_rand_t state, slong prec, slong mag_bits) Generates a random complex number with precise real and imaginary parts. .. function:: void acb_randtest_param(acb_t z, flint_rand_t state, slong prec, slong mag_bits) Generates a random complex number, with very high probability of generating integers and half-integers. Precision and comparisons ------------------------------------------------------------------------------- .. function:: int acb_equal(const acb_t x, const acb_t y) Returns nonzero iff *x* and *y* are identical as sets, i.e. if the real and imaginary parts are equal as balls. Note that this is not the same thing as testing whether both *x* and *y* certainly represent the same complex number, unless either *x* or *y* is exact (and neither contains NaN). To test whether both operands *might* represent the same mathematical quantity, use :func:`acb_overlaps` or :func:`acb_contains`, depending on the circumstance. .. function:: int acb_eq(const acb_t x, const acb_t y) Returns nonzero iff *x* and *y* are certainly equal, as determined by testing that :func:`arb_eq` holds for both the real and imaginary parts. .. function:: int acb_ne(const acb_t x, const acb_t y) Returns nonzero iff *x* and *y* are certainly not equal, as determined by testing that :func:`arb_ne` holds for either the real or imaginary parts. .. function:: int acb_overlaps(const acb_t x, const acb_t y) Returns nonzero iff *x* and *y* have some point in common. .. function:: void acb_get_abs_ubound_arf(arf_t u, const acb_t z, slong prec) Sets *u* to an upper bound for the absolute value of *z*, computed using a working precision of *prec* bits. .. function:: void acb_get_abs_lbound_arf(arf_t u, const acb_t z, slong prec) Sets *u* to a lower bound for the absolute value of *z*, computed using a working precision of *prec* bits. .. function:: void acb_get_rad_ubound_arf(arf_t u, const acb_t z, slong prec) Sets *u* to an upper bound for the error radius of *z* (the value is currently not computed tightly). .. function:: void acb_get_mag(mag_t u, const acb_t x) Sets *u* to an upper bound for the absolute value of *x*. .. function:: void acb_get_mag_lower(mag_t u, const acb_t x) Sets *u* to a lower bound for the absolute value of *x*. .. function:: int acb_contains_fmpq(const acb_t x, const fmpq_t y) .. function:: int acb_contains_fmpz(const acb_t x, const fmpz_t y) .. function:: int acb_contains(const acb_t x, const acb_t y) Returns nonzero iff *y* is contained in *x*. .. function:: int acb_contains_zero(const acb_t x) Returns nonzero iff zero is contained in *x*. .. function:: int acb_contains_int(const acb_t x) Returns nonzero iff the complex interval represented by *x* contains an integer. .. function:: slong acb_rel_error_bits(const acb_t x) Returns the effective relative error of *x* measured in bits. This is computed as if calling :func:`arb_rel_error_bits` on the real ball whose midpoint is the larger out of the real and imaginary midpoints of *x*, and whose radius is the larger out of the real and imaginary radiuses of *x*. .. function:: slong acb_rel_accuracy_bits(const acb_t x) Returns the effective relative accuracy of *x* measured in bits, equal to the negative of the return value from :func:`acb_rel_error_bits`. .. function:: slong acb_bits(const acb_t x) Returns the maximum of *arb_bits* applied to the real and imaginary parts of *x*, i.e. the minimum precision sufficient to represent *x* exactly. .. function:: void acb_indeterminate(acb_t x) Sets *x* to `[\operatorname{NaN} \pm \infty] + [\operatorname{NaN} \pm \infty]i`, representing an indeterminate result. .. function:: void acb_trim(acb_t y, const acb_t x) Sets *y* to a a copy of *x* with both the real and imaginary parts trimmed (see :func:`arb_trim`). .. function:: int acb_is_real(const acb_t x) Returns nonzero iff the imaginary part of *x* is zero. It does not test whether the real part of *x* also is finite. .. function:: int acb_get_unique_fmpz(fmpz_t z, const acb_t x) If *x* contains a unique integer, sets *z* to that value and returns nonzero. Otherwise (if *x* represents no integers or more than one integer), returns zero. Complex parts ------------------------------------------------------------------------------- .. function:: void acb_get_real(arb_t re, const acb_t z) Sets *re* to the real part of *z*. .. function:: void acb_get_imag(arb_t im, const acb_t z) Sets *im* to the imaginary part of *z*. .. function:: void acb_arg(arb_t r, const acb_t z, slong prec) Sets *r* to a real interval containing the complex argument (phase) of *z*. We define the complex argument have a discontinuity on `(-\infty,0]`, with the special value `\operatorname{arg}(0) = 0`, and `\operatorname{arg}(a+0i) = \pi` for `a < 0`. Equivalently, if `z = a+bi`, the argument is given by `\operatorname{atan2}(b,a)` (see :func:`arb_atan2`). .. function:: void acb_abs(arb_t r, const acb_t z, slong prec) Sets *r* to the absolute value of *z*. Arithmetic ------------------------------------------------------------------------------- .. function:: void acb_neg(acb_t z, const acb_t x) Sets *z* to the negation of *x*. .. function:: void acb_conj(acb_t z, const acb_t x) Sets *z* to the complex conjugate of *x*. .. function:: void acb_add_ui(acb_t z, const acb_t x, ulong y, slong prec) .. function:: void acb_add_si(acb_t z, const acb_t x, slong y, slong prec) .. function:: void acb_add_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) .. function:: void acb_add_arb(acb_t z, const acb_t x, const arb_t y, slong prec) .. function:: void acb_add(acb_t z, const acb_t x, const acb_t y, slong prec) Sets *z* to the sum of *x* and *y*. .. function:: void acb_sub_ui(acb_t z, const acb_t x, ulong y, slong prec) .. function:: void acb_sub_si(acb_t z, const acb_t x, slong y, slong prec) .. function:: void acb_sub_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) .. function:: void acb_sub_arb(acb_t z, const acb_t x, const arb_t y, slong prec) .. function:: void acb_sub(acb_t z, const acb_t x, const acb_t y, slong prec) Sets *z* to the difference of *x* and *y*. .. function:: void acb_mul_onei(acb_t z, const acb_t x) Sets *z* to *x* multiplied by the imaginary unit. .. function:: void acb_div_onei(acb_t z, const acb_t x) Sets *z* to *x* divided by the imaginary unit. .. function:: void acb_mul_ui(acb_t z, const acb_t x, ulong y, slong prec) .. function:: void acb_mul_si(acb_t z, const acb_t x, slong y, slong prec) .. function:: void acb_mul_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) .. function:: void acb_mul_arb(acb_t z, const acb_t x, const arb_t y, slong prec) Sets *z* to the product of *x* and *y*. .. function:: void acb_mul(acb_t z, const acb_t x, const acb_t y, slong prec) Sets *z* to the product of *x* and *y*. If at least one part of *x* or *y* is zero, the operations is reduced to two real multiplications. If *x* and *y* are the same pointers, they are assumed to represent the same mathematical quantity and the squaring formula is used. .. function:: void acb_mul_2exp_si(acb_t z, const acb_t x, slong e) .. function:: void acb_mul_2exp_fmpz(acb_t z, const acb_t x, const fmpz_t e) Sets *z* to *x* multiplied by `2^e`, without rounding. .. function:: void acb_cube(acb_t z, const acb_t x, slong prec) Sets *z* to *x* cubed, computed efficiently using two real squarings, two real multiplications, and scalar operations. .. function:: void acb_addmul(acb_t z, const acb_t x, const acb_t y, slong prec) .. function:: void acb_addmul_ui(acb_t z, const acb_t x, ulong y, slong prec) .. function:: void acb_addmul_si(acb_t z, const acb_t x, slong y, slong prec) .. function:: void acb_addmul_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) .. function:: void acb_addmul_arb(acb_t z, const acb_t x, const arb_t y, slong prec) Sets *z* to *z* plus the product of *x* and *y*. .. function:: void acb_submul(acb_t z, const acb_t x, const acb_t y, slong prec) .. function:: void acb_submul_ui(acb_t z, const acb_t x, ulong y, slong prec) .. function:: void acb_submul_si(acb_t z, const acb_t x, slong y, slong prec) .. function:: void acb_submul_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) .. function:: void acb_submul_arb(acb_t z, const acb_t x, const arb_t y, slong prec) Sets *z* to *z* minus the product of *x* and *y*. .. function:: void acb_inv(acb_t z, const acb_t x, slong prec) Sets *z* to the multiplicative inverse of *x*. .. function:: void acb_div_ui(acb_t z, const acb_t x, ulong y, slong prec) .. function:: void acb_div_si(acb_t z, const acb_t x, slong y, slong prec) .. function:: void acb_div_fmpz(acb_t z, const acb_t x, const fmpz_t y, slong prec) .. function:: void acb_div_arb(acb_t z, const acb_t x, const arb_t y, slong prec) .. function:: void acb_div(acb_t z, const acb_t x, const acb_t y, slong prec) Sets *z* to the quotient of *x* and *y*. Mathematical constants ------------------------------------------------------------------------------- .. function:: void acb_const_pi(acb_t y, slong prec) Sets *y* to the constant `\pi`. Powers and roots ------------------------------------------------------------------------------- .. function:: void acb_sqrt(acb_t r, const acb_t z, slong prec) Sets *r* to the square root of *z*. If either the real or imaginary part is exactly zero, only a single real square root is needed. Generally, we use the formula `\sqrt{a+bi} = u/2 + ib/u, u = \sqrt{2(|a+bi|+a)}`, requiring two real square root extractions. .. function:: void acb_rsqrt(acb_t r, const acb_t z, slong prec) Sets *r* to the reciprocal square root of *z*. If either the real or imaginary part is exactly zero, only a single real reciprocal square root is needed. Generally, we use the formula `1/\sqrt{a+bi} = ((a+r) - bi)/v, r = |a+bi|, v = \sqrt{r |a+bi+r|^2}`, requiring one real square root and one real reciprocal square root. .. function:: void acb_quadratic_roots_fmpz(acb_t r1, acb_t r2, const fmpz_t a, const fmpz_t b, const fmpz_t c, slong prec) Sets *r1* and *r2* to the roots of the quadratic polynomial `ax^2 + bx + c`. Requires that *a* is nonzero. This function is implemented so that both roots are computed accurately even when direct use of the quadratic formula would lose accuracy. .. function:: void acb_root_ui(acb_t r, const acb_t z, ulong k, slong prec) Sets *r* to the principal *k*-th root of *z*. .. function:: void acb_pow_fmpz(acb_t y, const acb_t b, const fmpz_t e, slong prec) .. function:: void acb_pow_ui(acb_t y, const acb_t b, ulong e, slong prec) .. function:: void acb_pow_si(acb_t y, const acb_t b, slong e, slong prec) Sets `y = b^e` using binary exponentiation (with an initial division if `e < 0`). Note that these functions can get slow if the exponent is extremely large (in such cases :func:`acb_pow` may be superior). .. function:: void acb_pow_arb(acb_t z, const acb_t x, const arb_t y, slong prec) .. function:: void acb_pow(acb_t z, const acb_t x, const acb_t y, slong prec) Sets `z = x^y`, computed using binary exponentiation if `y` if a small exact integer, as `z = (x^{1/2})^{2y}` if `y` is a small exact half-integer, and generally as `z = \exp(y \log x)`. Exponentials and logarithms ------------------------------------------------------------------------------- .. function:: void acb_exp(acb_t y, const acb_t z, slong prec) Sets *y* to the exponential function of *z*, computed as `\exp(a+bi) = \exp(a) \left( \cos(b) + \sin(b) i \right)`. .. function:: void acb_exp_pi_i(acb_t y, const acb_t z, slong prec) Sets *y* to `\exp(\pi i z)`. .. function:: void acb_exp_invexp(acb_t s, acb_t t, const acb_t z, slong prec) Sets `v = \exp(z)` and `w = \exp(-z)`. .. function:: void acb_log(acb_t y, const acb_t z, slong prec) Sets *y* to the principal branch of the natural logarithm of *z*, computed as `\log(a+bi) = \frac{1}{2} \log(a^2 + b^2) + i \operatorname{arg}(a+bi)`. .. function:: void acb_log1p(acb_t z, const acb_t x, slong prec) Sets `z = \log(1+x)`, computed accurately when `x \approx 0`. Trigonometric functions ------------------------------------------------------------------------------- .. function:: void acb_sin(acb_t s, const acb_t z, slong prec) .. function:: void acb_cos(acb_t c, const acb_t z, slong prec) .. function:: void acb_sin_cos(acb_t s, acb_t c, const acb_t z, slong prec) Sets `s = \sin(z)`, `c = \cos(z)`, evaluated as `\sin(a+bi) = \sin(a)\cosh(b) + i \cos(a)\sinh(b)`, `\cos(a+bi) = \cos(a)\cosh(b) - i \sin(a)\sinh(b)`. .. function:: void acb_tan(acb_t s, const acb_t z, slong prec) Sets `s = \tan(z) = \sin(z) / \cos(z)`. For large imaginary parts, the function is evaluated in a numerically stable way as `\pm i` plus a decreasing exponential factor. .. function:: void acb_cot(acb_t s, const acb_t z, slong prec) Sets `s = \cot(z) = \cos(z) / \sin(z)`. For large imaginary parts, the function is evaluated in a numerically stable way as `\pm i` plus a decreasing exponential factor. .. function:: void acb_sin_pi(acb_t s, const acb_t z, slong prec) .. function:: void acb_cos_pi(acb_t s, const acb_t z, slong prec) .. function:: void acb_sin_cos_pi(acb_t s, acb_t c, const acb_t z, slong prec) Sets `s = \sin(\pi z)`, `c = \cos(\pi z)`, evaluating the trigonometric factors of the real and imaginary part accurately via :func:`arb_sin_cos_pi`. .. function:: void acb_tan_pi(acb_t s, const acb_t z, slong prec) Sets `s = \tan(\pi z)`. Uses the same algorithm as :func:`acb_tan`, but evaluates the sine and cosine accurately via :func:`arb_sin_cos_pi`. .. function:: void acb_cot_pi(acb_t s, const acb_t z, slong prec) Sets `s = \cot(\pi z)`. Uses the same algorithm as :func:`acb_cot`, but evaluates the sine and cosine accurately via :func:`arb_sin_cos_pi`. Inverse trigonometric functions ------------------------------------------------------------------------------- .. function:: void acb_asin(acb_t res, const acb_t z, slong prec) Sets *res* to `\operatorname{asin}(z) = -i \log(iz + \sqrt{1-z^2})`. .. function:: void acb_acos(acb_t res, const acb_t z, slong prec) Sets *res* to `\operatorname{acos}(z) = \tfrac{1}{2} \pi - \operatorname{asin}(z)`. .. function:: void acb_atan(acb_t res, const acb_t z, slong prec) Sets *res* to `\operatorname{atan}(z) = \tfrac{1}{2} i (\log(1-iz)-\log(1+iz))`. Hyperbolic functions ------------------------------------------------------------------------------- .. function:: void acb_sinh(acb_t s, const acb_t z, slong prec) .. function:: void acb_cosh(acb_t c, const acb_t z, slong prec) .. function:: void acb_sinh_cosh(acb_t s, acb_t c, const acb_t z, slong prec) .. function:: void acb_tanh(acb_t s, const acb_t z, slong prec) .. function:: void acb_coth(acb_t s, const acb_t z, slong prec) Respectively computes `\sinh(z) = -i\sin(iz)`, `\cosh(z) = \cos(iz)`, `\tanh(z) = -i\tan(iz)`, `\coth(z) = i\cot(iz)`. Inverse hyperbolic functions ------------------------------------------------------------------------------- .. function:: void acb_asinh(acb_t res, const acb_t z, slong prec) Sets *res* to `\operatorname{asinh}(z) = -i \operatorname{asin}(iz)`. .. function:: void acb_acosh(acb_t res, const acb_t z, slong prec) Sets *res* to `\operatorname{acosh}(z) = \log(z + \sqrt{z+1} \sqrt{z-1})`. .. function:: void acb_atanh(acb_t res, const acb_t z, slong prec) Sets *res* to `\operatorname{atanh}(z) = -i \operatorname{atan}(iz)`. Rising factorials ------------------------------------------------------------------------------- .. function:: void acb_rising_ui_bs(acb_t z, const acb_t x, ulong n, slong prec) .. function:: void acb_rising_ui_rs(acb_t z, const acb_t x, ulong n, ulong step, slong prec) .. function:: void acb_rising_ui_rec(acb_t z, const acb_t x, ulong n, slong prec) .. function:: void acb_rising_ui(acb_t z, const acb_t x, ulong n, slong prec) .. function:: void acb_rising(acb_t z, const acb_t x, const acb_t n, slong prec) Computes the rising factorial `z = x (x+1) (x+2) \cdots (x+n-1)`. The *bs* version uses binary splitting. The *rs* version uses rectangular splitting. The *rec* version uses either *bs* or *rs* depending on the input. The default version uses the gamma function unless *n* is a small integer. The *rs* version takes an optional *step* parameter for tuning purposes (to use the default step length, pass zero). .. function :: void acb_rising2_ui_bs(acb_t u, acb_t v, const acb_t x, ulong n, slong prec) .. function :: void acb_rising2_ui_rs(acb_t u, acb_t v, const acb_t x, ulong n, ulong step, slong prec) .. function :: void acb_rising2_ui(acb_t u, acb_t v, const acb_t x, ulong n, slong prec) Letting `u(x) = x (x+1) (x+2) \cdots (x+n-1)`, simultaneously compute `u(x)` and `v(x) = u'(x)`, respectively using binary splitting, rectangular splitting (with optional nonzero step length *step* to override the default choice), and an automatic algorithm choice. .. function :: void acb_rising_ui_get_mag(mag_t bound, const acb_t x, ulong n) Computes an upper bound for the absolute value of the rising factorial `z = x (x+1) (x+2) \cdots (x+n-1)`. Not currently optimized for large *n*. Gamma function ------------------------------------------------------------------------------- .. function:: void acb_gamma(acb_t y, const acb_t x, slong prec) Computes the gamma function `y = \Gamma(x)`. .. function:: void acb_rgamma(acb_t y, const acb_t x, slong prec) Computes the reciprocal gamma function `y = 1/\Gamma(x)`, avoiding division by zero at the poles of the gamma function. .. function:: void acb_lgamma(acb_t y, const acb_t x, slong prec) Computes the logarithmic gamma function `y = \log \Gamma(x)`. The branch cut of the logarithmic gamma function is placed on the negative half-axis, which means that `\log \Gamma(z) + \log z = \log \Gamma(z+1)` holds for all `z`, whereas `\log \Gamma(z) \ne \log(\Gamma(z))` in general. In the left half plane, the reflection formula with correct branch structure is evaluated via :func:`acb_log_sin_pi`. .. function:: void acb_digamma(acb_t y, const acb_t x, slong prec) Computes the digamma function `y = \psi(x) = (\log \Gamma(x))' = \Gamma'(x) / \Gamma(x)`. .. function:: void acb_log_sin_pi(acb_t res, const acb_t z, slong prec) Computes the logarithmic sine function defined by .. math :: S(z) = \log(\pi) - \log \Gamma(z) + \log \Gamma(1-z) which is equal to .. math :: S(z) = \int_{1/2}^z \pi \cot(\pi t) dt where the path of integration goes through the upper half plane if `0 < \arg(z) \le \pi` and through the lower half plane if `-\pi < \arg(z) \le 0`. Equivalently, .. math :: S(z) = \log(\sin(\pi(z-n))) \mp n \pi i, \quad n = \lfloor \operatorname{re}(z) \rfloor where the negative sign is taken if `0 < \arg(z) \le \pi` and the positive sign is taken otherwise (if the interval `\arg(z)` does not certainly satisfy either condition, the union of both cases is computed). After subtracting *n*, we have `0 \le \operatorname{re}(z) < 1`. In this strip, we use use `S(z) = \log(\sin(\pi(z)))` if the imaginary part of *z* is small. Otherwise, we use `S(z) = i \pi (z-1/2) + \log((1+e^{-2i\pi z})/2)` in the lower half-plane and the conjugated expression in the upper half-plane to avoid exponent overflow. The function is evaluated at the midpoint and the propagated error is computed from `S'(z)` to get a continuous change when `z` is non-real and `n` spans more than one possible integer value. .. function:: void acb_polygamma(acb_t z, const acb_t s, const acb_t z, slong prec) Sets *res* to the value of the generalized polygamma function `\psi(s,z)`. If *s* is a nonnegative order, this is simply the *s*-order derivative of the digamma function. If `s = 0`, this function simply calls the digamma function internally. For integers `s \ge 1`, it calls the Hurwitz zeta function. Note that for small integers `s \ge 1`, it can be faster to use :func:`acb_poly_digamma_series` and read off the coefficients. The generalization to other values of *s* is due to Espinosa and Moll [EM2004]_: .. math :: \psi(s,z) = \frac{\zeta'(s+1,z) + (\gamma + \psi(-s)) \zeta(s+1,z)}{\Gamma(-s)} .. function:: void acb_barnes_g(acb_t res, const acb_t z, slong prec) .. function:: void acb_log_barnes_g(acb_t res, const acb_t z, slong prec) Computes Barnes *G*-function or the logarithmic Barnes *G*-function, respectively. The logarithmic version has branch cuts on the negative real axis and is continuous elsewhere in the complex plane, in analogy with the logarithmic gamma function. The functional equation .. math :: \log G(z+1) = \log \Gamma(z) + \log G(z). holds for all *z*. For small integers, we directly use the recurrence relation `G(z+1) = \Gamma(z) G(z)` together with the initial value `G(1) = 1`. For general *z*, we use the formula .. math :: \log G(z) = (z-1) \log \Gamma(z) - \zeta'(-1,z) + \zeta'(-1). Zeta function ------------------------------------------------------------------------------- .. function:: void acb_zeta(acb_t z, const acb_t s, slong prec) Sets *z* to the value of the Riemann zeta function `\zeta(s)`. Note: for computing derivatives with respect to `s`, use :func:`acb_poly_zeta_series` or related methods. .. function:: void acb_hurwitz_zeta(acb_t z, const acb_t s, const acb_t a, slong prec) Sets *z* to the value of the Hurwitz zeta function `\zeta(s, a)`. Note: for computing derivatives with respect to `s`, use :func:`acb_poly_zeta_series` or related methods. Polylogarithms ------------------------------------------------------------------------------- .. function:: void acb_polylog(acb_t w, const acb_t s, const acb_t z, slong prec) .. function:: void acb_polylog_si(acb_t w, slong s, const acb_t z, slong prec) Sets *w* to the polylogarithm `\operatorname{Li}_s(z)`. Arithmetic-geometric mean ------------------------------------------------------------------------------- .. function:: void acb_agm1(acb_t m, const acb_t z, slong prec) Sets *m* to the arithmetic-geometric mean `M(z) = \operatorname{agm}(1,z)`, defined such that the function is continuous in the complex plane except for a branch cut along the negative half axis (where it is continuous from above). This corresponds to always choosing an "optimal" branch for the square root in the arithmetic-geometric mean iteration. .. function:: void acb_agm1_cpx(acb_ptr m, const acb_t z, slong len, slong prec) Sets the coefficients in the array *m* to the power series expansion of the arithmetic-geometric mean at the point *z* truncated to length *len*, i.e. `M(z+x) \in \mathbb{C}[[x]]`. Other special functions ------------------------------------------------------------------------------- .. function:: void acb_chebyshev_t_ui(acb_t a, ulong n, const acb_t x, slong prec) .. function:: void acb_chebyshev_u_ui(acb_t a, ulong n, const acb_t x, slong prec) Evaluates the Chebyshev polynomial of the first kind `a = T_n(x)` or the Chebyshev polynomial of the second kind `a = U_n(x)`. .. function:: void acb_chebyshev_t2_ui(acb_t a, acb_t b, ulong n, const acb_t x, slong prec) .. function:: void acb_chebyshev_u2_ui(acb_t a, acb_t b, ulong n, const acb_t x, slong prec) Simultaneously evaluates `a = T_n(x), b = T_{n-1}(x)` or `a = U_n(x), b = U_{n-1}(x)`. Aliasing between *a*, *b* and *x* is not permitted. Vector functions ------------------------------------------------------------------------------- .. function:: void _acb_vec_zero(acb_ptr A, slong n) Sets all entries in *vec* to zero. .. function:: int _acb_vec_is_zero(acb_srcptr vec, slong len) Returns nonzero iff all entries in *x* are zero. .. function:: int _acb_vec_is_real(acb_srcptr v, slong len) Returns nonzero iff all entries in *x* have zero imaginary part. .. function:: void _acb_vec_set(acb_ptr res, acb_srcptr vec, slong len) Sets *res* to a copy of *vec*. .. function:: void _acb_vec_set_round(acb_ptr res, acb_srcptr vec, slong len, slong prec) Sets *res* to a copy of *vec*, rounding each entry to *prec* bits. .. function:: void _acb_vec_neg(acb_ptr res, acb_srcptr vec, slong len) .. function:: void _acb_vec_add(acb_ptr res, acb_srcptr vec1, acb_srcptr vec2, slong len, slong prec) .. function:: void _acb_vec_sub(acb_ptr res, acb_srcptr vec1, acb_srcptr vec2, slong len, slong prec) .. function:: void _acb_vec_scalar_submul(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) .. function:: void _acb_vec_scalar_addmul(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) .. function:: void _acb_vec_scalar_mul(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) .. function:: void _acb_vec_scalar_mul_ui(acb_ptr res, acb_srcptr vec, slong len, ulong c, slong prec) .. function:: void _acb_vec_scalar_mul_2exp_si(acb_ptr res, acb_srcptr vec, slong len, slong c) .. function:: void _acb_vec_scalar_mul_onei(acb_ptr res, acb_srcptr vec, slong len) .. function:: void _acb_vec_scalar_div_ui(acb_ptr res, acb_srcptr vec, slong len, ulong c, slong prec) .. function:: void _acb_vec_scalar_div(acb_ptr res, acb_srcptr vec, slong len, const acb_t c, slong prec) .. function:: void _acb_vec_scalar_mul_arb(acb_ptr res, acb_srcptr vec, slong len, const arb_t c, slong prec) .. function:: void _acb_vec_scalar_div_arb(acb_ptr res, acb_srcptr vec, slong len, const arb_t c, slong prec) .. function:: void _acb_vec_scalar_mul_fmpz(acb_ptr res, acb_srcptr vec, slong len, const fmpz_t c, slong prec) .. function:: void _acb_vec_scalar_div_fmpz(acb_ptr res, acb_srcptr vec, slong len, const fmpz_t c, slong prec) Performs the respective scalar operation elementwise. .. function:: slong _acb_vec_bits(acb_srcptr vec, slong len) Returns the maximum of :func:`arb_bits` for all entries in *vec*. .. function:: void _acb_vec_set_powers(acb_ptr xs, const acb_t x, slong len, slong prec) Sets *xs* to the powers `1, x, x^2, \ldots, x^{len-1}`. .. function:: void _acb_vec_add_error_arf_vec(acb_ptr res, arf_srcptr err, slong len) .. function:: void _acb_vec_add_error_mag_vec(acb_ptr res, mag_srcptr err, slong len) Adds the magnitude of each entry in *err* to the radius of the corresponding entry in *res*. .. function:: void _acb_vec_indeterminate(acb_ptr vec, slong len) Applies :func:`acb_indeterminate` elementwise. .. function:: void _acb_vec_trim(acb_ptr res, acb_srcptr vec, slong len) Applies :func:`acb_trim` elementwise. .. function:: int _acb_vec_get_unique_fmpz_vec(fmpz * res, acb_srcptr vec, slong len) Calls :func:`acb_get_unique_fmpz` elementwise and returns nonzero if all entries can be rounded uniquely to integers. If any entry in *vec* cannot be rounded uniquely to an integer, returns zero. .. function:: void _acb_vec_sort_pretty(acb_ptr vec, slong len) Sorts the vector of complex numbers based on the real and imaginary parts. This is intended to reveal structure when printing a set of complex numbers, not to apply an order relation in a rigorous way. arb-2.8.1/doc/source/acb_calc.rst000066400000000000000000000107311264125401100165720ustar00rootroot00000000000000.. _acb-calc: **acb_calc.h** -- calculus with complex-valued functions =============================================================================== This module provides functions for operations of calculus over the complex numbers (intended to include root-finding, integration, and so on). Types, macros and constants ------------------------------------------------------------------------------- .. type:: acb_calc_func_t Typedef for a pointer to a function with signature:: int func(acb_ptr out, const acb_t inp, void * param, slong order, slong prec) implementing a univariate complex function `f(x)`. When called, *func* should write to *out* the first *order* coefficients in the Taylor series expansion of `f(x)` at the point *inp*, evaluated at a precision of *prec* bits. The *param* argument may be used to pass through additional parameters to the function. The return value is reserved for future use as an error code. It can be assumed that *out* and *inp* are not aliased and that *order* is positive. Bounds ------------------------------------------------------------------------------- .. function:: void acb_calc_cauchy_bound(arb_t bound, acb_calc_func_t func, void * param, const acb_t x, const arb_t radius, slong maxdepth, slong prec) Sets *bound* to a ball containing the value of the integral .. math :: C(x,r) = \frac{1}{2 \pi r} \oint_{|z-x| = r} |f(z)| dz = \int_0^1 |f(x+re^{2\pi i t})| dt where *f* is specified by (*func*, *param*) and *r* is given by *radius*. The integral is computed using a simple step sum. The integration range is subdivided until the order of magnitude of *b* can be determined (i.e. its error bound is smaller than its midpoint), or until the step length has been cut in half *maxdepth* times. This function is currently implemented completely naively, and repeatedly subdivides the whole integration range instead of performing adaptive subdivisions. Integration ------------------------------------------------------------------------------- .. function:: int acb_calc_integrate_taylor(acb_t res, acb_calc_func_t func, void * param, const acb_t a, const acb_t b, const arf_t inner_radius, const arf_t outer_radius, slong accuracy_goal, slong prec) Computes the integral .. math :: I = \int_a^b f(t) dt where *f* is specified by (*func*, *param*), following a straight-line path between the complex numbers *a* and *b* which both must be finite. The integral is approximated by piecewise centered Taylor polynomials. Rigorous truncation error bounds are calculated using the Cauchy integral formula. More precisely, if the Taylor series of *f* centered at the point *m* is `f(m+x) = \sum_{n=0}^{\infty} a_n x^n`, then .. math :: \int f(m+x) = \left( \sum_{n=0}^{N-1} a_n \frac{x^{n+1}}{n+1} \right) + \left( \sum_{n=N}^{\infty} a_n \frac{x^{n+1}}{n+1} \right). For sufficiently small *x*, the second series converges and its absolute value is bounded by .. math :: \sum_{n=N}^{\infty} \frac{C(m,R)}{R^n} \frac{|x|^{n+1}}{N+1} = \frac{C(m,R) R x}{(R-x)(N+1)} \left( \frac{x}{R} \right)^N. It is required that any singularities of *f* are isolated from the path of integration by a distance strictly greater than the positive value *outer_radius* (which is the integration radius used for the Cauchy bound). Taylor series step lengths are chosen so as not to exceed *inner_radius*, which must be strictly smaller than *outer_radius* for convergence. A smaller *inner_radius* gives more rapid convergence of each Taylor series but means that more series might have to be used. A reasonable choice might be to set *inner_radius* to half the value of *outer_radius*, giving roughly one accurate bit per term. The truncation point of each Taylor series is chosen so that the absolute truncation error is roughly `2^{-p}` where *p* is given by *accuracy_goal* (in the future, this might change to a relative accuracy). Arithmetic operations and function evaluations are performed at a precision of *prec* bits. Note that due to accumulation of numerical errors, both values may have to be set higher (and the endpoints may have to be computed more accurately) to achieve a desired accuracy. This function chooses the evaluation points uniformly rather than implementing adaptive subdivision. arb-2.8.1/doc/source/acb_hypgeom.rst000066400000000000000000001153541264125401100173470ustar00rootroot00000000000000.. _acb-hypgeom: **acb_hypgeom.h** -- hypergeometric functions in the complex numbers ================================================================================== The generalized hypergeometric function is formally defined by .. math :: {}_pF_q(a_1,\ldots,a_p;b_1,\ldots,b_q;z) = \sum_{k=0}^\infty \frac{(a_1)_k\dots(a_p)_k}{(b_1)_k\dots(b_q)_k} \frac {z^k} {k!}. It can be interpreted using analytic continuation or regularization when the sum does not converge. In a looser sense, we understand "hypergeometric functions" to be linear combinations of generalized hypergeometric functions with prefactors that are products of exponentials, powers, and gamma functions. Convergent series ------------------------------------------------------------------------------- In this section, we define .. math :: T(k) = \frac{\prod_{i=0}^{p-1} (a_i)_k}{\prod_{i=0}^{q-1} (b_i)_k} z^k and .. math :: {}_pH_{q}(a_0,\ldots,a_{p-1}; b_0 \ldots b_{q-1}; z) = {}_{p+1}F_{q}(a_0,\ldots,a_{p-1},1; b_0 \ldots b_{q-1}; z) = \sum_{k=0}^{\infty} T(k) For the conventional generalized hypergeometric function `{}_pF_{q}`, compute `{}_pH_{q+1}` with the explicit parameter `b_q = 1`, or remove a 1 from the `a_i` parameters if there is one. .. function:: void acb_hypgeom_pfq_bound_factor(mag_t C, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, ulong n) Computes a factor *C* such that .. math :: \left|\sum_{k=n}^{\infty} T(k)\right| \le C |T(n)|. We check that `\operatorname{Re}(b+n) > 0` for all lower parameters *b*. If this does not hold, *C* is set to infinity. Otherwise, we cancel out pairs of parameters `a` and `b` against each other. We have .. math :: \left|\frac{a+k}{b+k}\right| = \left|1 + \frac{a-b}{b+k}\right| \le 1 + \frac{|a-b|}{|b+n|} and .. math :: \left|\frac{1}{b+k}\right| \le \frac{1}{|b+n|} for all `k \ge n`. This gives us a constant *D* such that `T(k+1) \le D T(k)` for all `k \ge n`. If `D \ge 1`, we set *C* to infinity. Otherwise, we take `C = \sum_{k=0}^{\infty} D^k = (1-D)^{-1}`. As currently implemented, the bound becomes infinite when `n` is too small, even if the series converges. .. function:: slong acb_hypgeom_pfq_choose_n(acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong prec) Heuristically attempts to choose a number of terms *n* to sum of a hypergeometric series at a working precision of *prec* bits. Uses double precision arithmetic internally. As currently implemented, it can fail to produce a good result if the parameters are extremely large or extremely close to nonpositive integers. Numerical cancellation is assumed to be significant, so truncation is done when the current term is *prec* bits smaller than the largest encountered term. This function will also attempt to pick a reasonable truncation point for divergent series. .. function:: void acb_hypgeom_pfq_sum_forward(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) .. function:: void acb_hypgeom_pfq_sum_rs(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) .. function:: void acb_hypgeom_pfq_sum_bs(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) .. function:: void acb_hypgeom_pfq_sum_fme(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) .. function:: void acb_hypgeom_pfq_sum(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) Computes `s = \sum_{k=0}^{n-1} T(k)` and `t = T(n)`. Does not allow aliasing between input and output variables. We require `n \ge 0`. The *forward* version computes the sum using forward recurrence. The *bs* version computes the sum using binary splitting. The *rs* version computes the sum in reverse order using rectangular splitting. It only computes a magnitude bound for the value of *t*. The *fme* version uses fast multipoint evaluation. The default version automatically chooses an algorithm depending on the inputs. .. function:: void acb_hypgeom_pfq_sum_bs_invz(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t w, slong n, slong prec) .. function:: void acb_hypgeom_pfq_sum_invz(acb_t s, acb_t t, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, const acb_t w, slong n, slong prec) Like :func:`acb_hypgeom_pfq_sum`, but taking advantage of `w = 1/z` possibly having few bits. .. function:: void acb_hypgeom_pfq_direct(acb_t res, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec) Computes .. math :: {}_pH_{q}(z) = \sum_{k=0}^{\infty} T(k) = \sum_{k=0}^{n-1} T(k) + \varepsilon directly from the defining series, including a rigorous bound for the truncation error `\varepsilon` in the output. If `n < 0`, this function chooses a number of terms automatically using :func:`acb_hypgeom_pfq_choose_n`. .. function:: void acb_hypgeom_pfq_series_direct(acb_poly_t res, const acb_poly_struct * a, slong p, const acb_poly_struct * b, slong q, const acb_poly_t z, int regularized, slong n, slong len, slong prec) Computes `{}_pH_{q}(z)` directly using the defining series, given parameters and argument that are power series. The result is a power series of length *len*. An error bound is computed automatically as a function of the number of terms *n*. If `n < 0`, the number of terms is chosen automatically. If *regularized* is set, the regularized hypergeometric function is computed instead. Asymptotic series ------------------------------------------------------------------------------- Let `U(a,b,z)` denote the confluent hypergeometric function of the second kind with the principal branch cut, and let `U^{*} = z^a U(a,b,z)`. For all `z \ne 0` and `b \notin \mathbb{Z}` (but valid for all `b` as a limit), we have (DLMF 13.2.42) .. math :: U(a,b,z) = \frac{\Gamma(1-b)}{\Gamma(a-b+1)} M(a,b,z) + \frac{\Gamma(b-1)}{\Gamma(a)} z^{1-b} M(a-b+1,2-b,z). Moreover, for all `z \ne 0` we have .. math :: \frac{{}_1F_1(a,b,z)}{\Gamma(b)} = \frac{(-z)^{-a}}{\Gamma(b-a)} U^{*}(a,b,z) + \frac{z^{a-b} e^z}{\Gamma(a)} U^{*}(b-a,b,-z) which is equivalent to DLMF 13.2.41 (but simpler in form). We have the asymptotic expansion .. math :: U^{*}(a,b,z) \sim {}_2F_0(a, a-b+1, -1/z) where `{}_2F_0(a,b,z)` denotes a formal hypergeometric series, i.e. .. math :: U^{*}(a,b,z) = \sum_{k=0}^{n-1} \frac{(a)_k (a-b+1)_k}{k! (-z)^k} + \varepsilon_n(z). The error term `\varepsilon_n(z)` is bounded according to DLMF 13.7. A case distinction is made depending on whether `z` lies in one of three regions which we index by `R`. Our formula for the error bound increases with the value of `R`, so we can always choose the larger out of two indices if `z` lies in the union of two regions. Let `r = |b-2a|`. If `\operatorname{Re}(z) \ge r`, set `R = 1`. Otherwise, if `\operatorname{Im}(z) \ge r` or `\operatorname{Re}(z) \ge 0 \land |z| \ge r`, set `R = 2`. Otherwise, if `|z| \ge 2r`, set `R = 3`. Otherwise, the bound is infinite. If the bound is finite, we have .. math :: |\varepsilon_n(z)| \le 2 \alpha C_n \left|\frac{(a)_n (a-b+1)_n}{n! z^n} \right| \exp(2 \alpha \rho C_1 / |z|) in terms of the following auxiliary quantities .. math :: \sigma = |(b-2a)/z| C_n = \begin{cases} 1 & \text{if } R = 1 \\ \chi(n) & \text{if } R = 2 \\ (\chi(n) + \rho \nu^2 n) \nu^n & \text{if } R = 3 \end{cases} \nu = \left(\tfrac{1}{2} + \tfrac{1}{2}\sqrt{1-4\sigma^2}\right)^{-1/2} \le 1 + 2 \sigma^2 \chi(n) = \sqrt{\pi} \Gamma(\tfrac{1}{2}n+1) / \Gamma(\tfrac{1}{2} n + \tfrac{1}{2}) \sigma' = \begin{cases} \sigma & \text{if } R \ne 3 \\ \nu \sigma & \text{if } R = 3 \end{cases} \alpha = (1 - \sigma')^{-1} \rho = \tfrac{1}{2} |2a^2-2ab+b| + \sigma' (1+ \tfrac{1}{4} \sigma') (1-\sigma')^{-2} .. function:: void acb_hypgeom_u_asymp(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong n, slong prec) Sets *res* to `U^{*}(a,b,z)` computed using *n* terms of the asymptotic series, with a rigorous bound for the error included in the output. We require `n \ge 0`. .. function:: int acb_hypgeom_u_use_asymp(const acb_t z, slong prec) Heuristically determines whether the asymptotic series can be used to evaluate `U(a,b,z)` to *prec* accurate bits (assuming that *a* and *b* are small). Confluent hypergeometric functions ------------------------------------------------------------------------------- .. function:: void acb_hypgeom_u_1f1_series(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t z, slong len, slong prec) Computes `U(a,b,z)` as a power series truncated to length *len*, given `a, b, z \in \mathbb{C}[[x]]`. If `b[0] \in \mathbb{Z}`, it computes one extra derivative and removes the singularity (it is then assumed that `b[1] \ne 0`). As currently implemented, the output is indeterminate if `b` is nonexact and contains an integer. .. function:: void acb_hypgeom_u_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec) Computes `U(a,b,z)` as a sum of two convergent hypergeometric series. If `b \in \mathbb{Z}`, it computes the limit value via :func:`acb_hypgeom_u_1f1_series`. As currently implemented, the output is indeterminate if `b` is nonexact and contains an integer. .. function:: void acb_hypgeom_u(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec) Computes `U(a,b,z)` using an automatic algorithm choice. The function :func:`acb_hypgeom_u_asymp` is used if `a` or `a-b+1` is a nonpositive integer (in which case the asymptotic series terminates), or if *z* is sufficiently large. Otherwise :func:`acb_hypgeom_u_1f1` is used. .. function:: void acb_hypgeom_m_asymp(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec) .. function:: void acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec) .. function:: void acb_hypgeom_m(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec) Computes the confluent hypergeometric function `M(a,b,z) = {}_1F_1(a,b,z)`, or `\mathbf{M}(a,b,z) = \frac{1}{\Gamma(b)} {}_1F_1(a,b,z)` if *regularized* is set. .. function:: void acb_hypgeom_0f1_asymp(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec) .. function:: void acb_hypgeom_0f1_direct(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec) .. function:: void acb_hypgeom_0f1(acb_t res, const acb_t a, const acb_t z, int regularized, slong prec) Computes the confluent hypergeometric function `{}_0F_1(a,z)`, or `\frac{1}{\Gamma(a)} {}_0F_1(a,z)` if *regularized* is set, using asymptotic expansions, direct summation, or an automatic algorithm choice. The *asymp* version uses the asymptotic expansions of Bessel functions, together with the connection formulas .. math :: \frac{{}_0F_1(a,z)}{\Gamma(a)} = (-z)^{(1-a)/2} J_{a-1}(2 \sqrt{-z}) = z^{(1-a)/2} I_{a-1}(2 \sqrt{z}). The Bessel-*J* function is used in the left half-plane and the Bessel-*I* function is used in the right half-plane, to avoid loss of accuracy due to evaluating the square root on the branch cut. The error function ------------------------------------------------------------------------------- .. function:: void acb_hypgeom_erf_1f1a(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_erf_1f1b(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_erf_asymp(acb_t res, const acb_t z, slong prec, slong prec2) .. function:: void acb_hypgeom_erf(acb_t res, const acb_t z, slong prec) Computes the error function respectively using .. math :: \operatorname{erf}(z) = \frac{2z}{\sqrt{\pi}} {}_1F_1(\tfrac{1}{2}, \tfrac{3}{2}, -z^2) \operatorname{erf}(z) = \frac{2z e^{-z^2}}{\sqrt{\pi}} {}_1F_1(1, \tfrac{3}{2}, z^2) \operatorname{erf}(z) = \frac{z}{\sqrt{z^2}} \left(1 - \frac{e^{-z^2}}{\sqrt{\pi}} U(\tfrac{1}{2}, \tfrac{1}{2}, z^2)\right). and an automatic algorithm choice. The *asymp* version takes a second precision to use for the *U* term. .. function:: void acb_hypgeom_erfc(acb_t res, const acb_t z, slong prec) Computes the complementary error function `\operatorname{erfc}(z) = 1 - \operatorname{erf}(z)`. This function avoids catastrophic cancellation for large positive *z*. .. function:: void acb_hypgeom_erfi(acb_t res, const acb_t z, slong prec) Computes the imaginary error function `\operatorname{erfi}(z) = -i\operatorname{erf}(iz)`. This is a trivial wrapper of :func:`acb_hypgeom_erf`. Bessel functions ------------------------------------------------------------------------------- .. function:: void acb_hypgeom_bessel_j_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the Bessel function of the first kind via :func:`acb_hypgeom_u_asymp`. For all complex `\nu, z`, we have .. math :: J_{\nu}(z) = \frac{z^{\nu}}{2^{\nu} e^{iz} \Gamma(\nu+1)} {}_1F_1(\nu+\tfrac{1}{2}, 2\nu+1, 2iz) = A_{+} B_{+} + A_{-} B_{-} where .. math :: A_{\pm} = z^{\nu} (z^2)^{-\tfrac{1}{2}-\nu} (\mp i z)^{\tfrac{1}{2}+\nu} (2 \pi)^{-1/2} = (\pm iz)^{-1/2-\nu} z^{\nu} (2 \pi)^{-1/2} B_{\pm} = e^{\pm i z} U^{*}(\nu+\tfrac{1}{2}, 2\nu+1, \mp 2iz). Nicer representations of the factors `A_{\pm}` can be given depending conditionally on the parameters. If `\nu + \tfrac{1}{2} = n \in \mathbb{Z}`, we have `A_{\pm} = (\pm i)^{n} (2 \pi z)^{-1/2}`. And if `\operatorname{Re}(z) > 0`, we have `A_{\pm} = \exp(\mp i [(2\nu+1)/4] \pi) (2 \pi z)^{-1/2}`. .. function:: void acb_hypgeom_bessel_j_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the Bessel function of the first kind from .. math :: J_{\nu}(z) = \frac{1}{\Gamma(\nu+1)} \left(\frac{z}{2}\right)^{\nu} {}_0F_1\left(\nu+1, -\frac{z^2}{4}\right). .. function:: void acb_hypgeom_bessel_j(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the Bessel function of the first kind `J_{\nu}(z)` using an automatic algorithm choice. .. function:: void acb_hypgeom_bessel_y(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the Bessel function of the second kind `Y_{\nu}(z)` from the formula .. math :: Y_{\nu}(z) = \frac{\cos(\nu \pi) J_{\nu}(z) - J_{-\nu}(z)}{\sin(\nu \pi)} unless `\nu = n` is an integer in which case the limit value .. math :: Y_n(z) = -\frac{2}{\pi} \left( i^n K_n(iz) + \left[\log(iz)-\log(z)\right] J_n(z) \right) is computed. As currently implemented, the output is indeterminate if `\nu` is nonexact and contains an integer. .. function:: void acb_hypgeom_bessel_jy(acb_t res1, acb_t res2, const acb_t nu, const acb_t z, slong prec) Sets *res1* to `J_{\nu}(z)` and *res2* to `Y_{\nu}(z)`, computed simultaneously. From these values, the user can easily construct the Bessel functions of the third kind (Hankel functions) `H_{\nu}^{(1)}(z), H_{\nu}^{(2)}(z) = J_{\nu}(z) \pm i Y_{\nu}(z)`. .. function:: void acb_hypgeom_bessel_i_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec) .. function:: void acb_hypgeom_bessel_i_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec) .. function:: void acb_hypgeom_bessel_i(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the modified Bessel function of the first kind `I_{\nu}(z) = z^{\nu} (iz)^{-\nu} J_{\nu}(iz)` respectively using asymptotic series (see :func:`acb_hypgeom_bessel_j_asymp`), the convergent series .. math :: I_{\nu}(z) = \frac{1}{\Gamma(\nu+1)} \left(\frac{z}{2}\right)^{\nu} {}_0F_1\left(\nu+1, \frac{z^2}{4}\right), or an automatic algorithm choice. .. function:: void acb_hypgeom_bessel_k_asymp(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the modified Bessel function of the second kind via via :func:`acb_hypgeom_u_asymp`. For all `\nu` and all `z \ne 0`, we have .. math :: K_{\nu}(z) = \left(\frac{2z}{\pi}\right)^{-1/2} e^{-z} U^{*}(\nu+\tfrac{1}{2}, 2\nu+1, 2z). .. function:: void acb_hypgeom_bessel_k_0f1_series(acb_poly_t res, const acb_poly_t nu, const acb_poly_t z, slong len, slong prec) Computes the modified Bessel function of the second kind `K_{\nu}(z)` as a power series truncated to length *len*, given `\nu, z \in \mathbb{C}[[x]]`. Uses the formula .. math :: K_{\nu}(z) = \frac{1}{2} \frac{\pi}{\sin(\pi \nu)} \left[ \left(\frac{z}{2}\right)^{-\nu} {}_0{\widetilde F}_1\left(1-\nu, \frac{z^2}{4}\right) - \left(\frac{z}{2}\right)^{\nu} {}_0{\widetilde F}_1\left(1+\nu, \frac{z^2}{4}\right) \right]. If `\nu[0] \in \mathbb{Z}`, it computes one extra derivative and removes the singularity (it is then assumed that `\nu[1] \ne 0`). As currently implemented, the output is indeterminate if `\nu[0]` is nonexact and contains an integer. .. function:: void acb_hypgeom_bessel_k_0f1(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the modified Bessel function of the second kind from .. math :: K_{\nu}(z) = \frac{1}{2} \left[ \left(\frac{z}{2}\right)^{-\nu} \Gamma(\nu) {}_0F_1\left(1-\nu, \frac{z^2}{4}\right) - \left(\frac{z}{2}\right)^{\nu} \frac{\pi}{\nu \sin(\pi \nu) \Gamma(\nu)} {}_0F_1\left(\nu+1, \frac{z^2}{4}\right) \right] if `\nu \notin \mathbb{Z}`. If `\nu \in \mathbb{Z}`, it computes the limit value via :func:`acb_hypgeom_bessel_k_0f1_series`. As currently implemented, the output is indeterminate if `\nu` is nonexact and contains an integer. .. function:: void acb_hypgeom_bessel_k(acb_t res, const acb_t nu, const acb_t z, slong prec) Computes the modified Bessel function of the second kind `K_{\nu}(z)` using an automatic algorithm choice. Airy functions ------------------------------------------------------------------------------- The Airy functions are linearly independent solutions of the differential equation `y'' - zy = 0`. All solutions are entire functions. The standard solutions are denoted `\operatorname{Ai}(z), \operatorname{Bi}(z)`. For negative *z*, both functions are oscillatory. For positive *z*, the first function decreases exponentially while the second increases exponentially. The Airy functions can be expressed in terms of Bessel functions of fractional order, but this is inconvenient since such formulas only hold piecewise (due to the Stokes phenomenon). Computation of the Airy functions can also be optimized more than Bessel functions in general. We therefore provide a dedicated interface for evaluating Airy functions. The following functions optionally compute `(\operatorname{Ai}(z), \operatorname{Ai}'(z), \operatorname{Bi}(z), \operatorname{Bi}'(z))` simultaneously. Any of the four functions can be omitted by passing *NULL* for the unwanted output variables. Note that higher derivatives of the Airy functions can be computed via recurrence relations. .. function:: void acb_hypgeom_airy_direct(acb_t ai, acb_t ai_prime, acb_t bi, acb_t bi_prime, const acb_t z, slong n, slong prec) Computes the Airy functions using direct series expansions truncated at *n* terms. Error bounds are included in the output. .. function:: void acb_hypgeom_airy_asymp(acb_t ai, acb_t ai_prime, acb_t bi, acb_t bi_prime, const acb_t z, slong n, slong prec) Computes the Airy functions using asymptotic expansions truncated at *n* terms. Error bounds, based on Olver (DLMF section 9.7), are included in the output. For `\arg(z) < \pi` and `\zeta = (2/3) z^{3/2}`, we have .. math :: \operatorname{Ai}(z) = \frac{e^{-\zeta}}{2 \sqrt{\pi} z^{1/4}} \left[S_n(\zeta) + R_n(z)\right], \quad \operatorname{Ai}'(z) = -\frac{z^{1/4} e^{-\zeta}}{2 \sqrt{\pi}} \left[(S'_n(\zeta) + R'_n(z)\right] S_n(\zeta) = \sum_{k=0}^{n-1} (-1)^k \frac{u(k)}{\zeta^k}, \quad S'_n(\zeta) = \sum_{k=0}^{n-1} (-1)^k \frac{v(k)}{\zeta^k} u(k) = \frac{(1/6)_k (5/6)_k}{2^k k!}, \quad v(k) = \frac{6k+1}{1-6k} u(k). Assuming that *n* is positive, the error terms are bounded by .. math :: |R_n(z)| \le C |u(n)| |\zeta|^{-n}, \quad |R'_n(z)| \le C |v(n)| |\zeta|^{-n} where .. math :: C = \begin{cases} 2 \exp(7 / (36 |\zeta|)) & |\arg(z)| \le \pi/3 \\ 2 \chi(n) \exp(7 \pi / (72 |\zeta|)) & \pi/3 \le |\arg(z)| \le 2\pi/3 \\ 4 \chi(n) \exp(7 \pi / (36 |\operatorname{re}(\zeta)|)) |\cos(\arg(\zeta))|^{-n} & 2\pi/3 \le |\arg(z)| < \pi. \end{cases} For computing Bi when *z* is roughly in the positive half-plane, we use the connection formulas .. math :: \operatorname{Bi}(z) = -i (2 w^{+1} \operatorname{Ai}(z w^{-2}) - \operatorname{Ai}(z)) \operatorname{Bi}(z) = +i (2 w^{-1} \operatorname{Ai}(z w^{+2}) - \operatorname{Ai}(z)) where `w = \exp(\pi i/3)`. Combining roots of unity gives .. math :: \operatorname{Bi}(z) = \frac{1}{2 \sqrt{\pi} z^{1/4}} [2X + iY] \operatorname{Bi}(z) = \frac{1}{2 \sqrt{\pi} z^{1/4}} [2X - iY] X = \exp(+\zeta) [S_n(-\zeta) + R_n(z w^{\mp 2})], \quad Y = \exp(-\zeta) [S_n(\zeta) + R_n(z)] where the upper formula is valid for `-\pi/3 < \arg(z) < \pi` and the lower formula is valid for `-\pi < \arg(z) < \pi/3`. We proceed analogously for the derivative of Bi. In the negative half-plane, we use the connection formulas .. math :: \operatorname{Ai}(z) = e^{+\pi i/3} \operatorname{Ai}(z_1) + e^{-\pi i/3} \operatorname{Ai}(z_2) \operatorname{Bi}(z) = e^{-\pi i/6} \operatorname{Ai}(z_1) + e^{+\pi i/6} \operatorname{Ai}(z_2) where `z_1 = -z e^{+\pi i/3}`, `z_2 = -z e^{-\pi i/3}`. Provided that `|\arg(-z)| < 2 \pi / 3`, we have `|\arg(z_1)|, |\arg(z_2)| < \pi`, and thus the asymptotic expansion for Ai can be used. As before, we collect roots of unity to obtain .. math :: \operatorname{Ai}(z) = A_1 [S_n(i \zeta) + R_n(z_1)] + A_2 [S_n(-i \zeta) + R_n(z_2)] \operatorname{Bi}(z) = A_3 [S_n(i \zeta) + R_n(z_1)] + A_4 [S_n(-i \zeta) + R_n(z_2)] where `\zeta = (2/3) (-z)^{3/2}` and .. math :: A_1 = \frac{\exp(-i (\zeta - \pi/4))}{2 \sqrt{\pi} (-z)^{1/4}}, \quad A_2 = \frac{\exp(+i (\zeta - \pi/4))}{2 \sqrt{\pi} (-z)^{1/4}}, \quad A_3 = -i A_1, \quad A_4 = +i A_2. The differentiated formulas are analogous. .. function:: void acb_hypgeom_airy_bound(mag_t ai, mag_t aip, mag_t bi, mag_t bip, const acb_t z) Computes bounds for the Airy functions using first-order asymptotic expansions together with error bounds. This function uses some shortcuts to make it slightly faster than calling :func:`acb_hypgeom_airy_asymp` with `n = 1`. .. function:: void acb_hypgeom_airy(acb_t ai, acb_t ai_prime, acb_t bi, acb_t bi_prime, const acb_t z, slong prec) Computes Airy functions using an automatic algorithm choice. We use :func:`acb_hypgeom_airy_asymp` whenever this gives full accuracy and :func:`acb_hypgeom_airy_direct` otherwise. In the latter case, we first use double precision arithmetic to determine an accurate estimate of the working precision needed to compute the Airy functions accurately for given *z*. This estimate is obtained by comparing the leading-order asymptotic estimate of the Airy functions with the magnitude of the largest term in the power series. The estimate is generic in the sense that it does not take into account vanishing near the roots of the functions. We subsequently evaluate the power series at the midpoint of *z* and bound the propagated error using derivatives. Derivatives are bounded using :func:`acb_hypgeom_airy_bound`. Incomplete gamma functions ------------------------------------------------------------------------------- .. function:: void acb_hypgeom_gamma_upper_asymp(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) .. function:: void acb_hypgeom_gamma_upper_1f1a(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) .. function:: void acb_hypgeom_gamma_upper_1f1b(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) .. function:: void acb_hypgeom_gamma_upper_singular(acb_t res, slong s, const acb_t z, int modified, slong prec) .. function:: void acb_hypgeom_gamma_upper(acb_t res, const acb_t s, const acb_t z, int modified, slong prec) Computes the upper incomplete gamma function respectively using .. math :: \Gamma(s,z) = e^{-z} U(1-s,1-s,z) \Gamma(s,z) = \Gamma(s) - \frac{z^s}{s} {}_1F_1(s, s+1, -z) \Gamma(s,z) = \Gamma(s) - \frac{z^s e^{-z}}{s} {}_1F_1(1, s+1, z) \Gamma(s,z) = \frac{(-1)^n}{n!} (\psi(n+1) - \log(z)) + \frac{(-1)^n}{(n+1)!} z \, {}_2F_2(1,1,2,2+n,-z) - z^{-n} \sum_{k=0}^{n-1} \frac{(-z)^k}{(k-n) k!}, \quad n = -s \in \mathbb{Z}_{\ge 0} and an automatic algorithm choice. The automatic version also handles other special input such as `z = 0` and `s = 1, 2, 3`. The *singular* version evaluates the finite sum directly and therefore assumes that *s* is not too large. If *modified* is set, computes the exponential integral `z^{-s} \Gamma(s,z) = E_{1-s}(z)` instead. Exponential and trigonometric integrals ------------------------------------------------------------------------------- The branch cut conventions of the following functions match Mathematica. .. function:: void acb_hypgeom_expint(acb_t res, const acb_t s, const acb_t z, slong prec) Computes the generalized exponential integral `E_s(z)`. This is a trivial wrapper of :func:`acb_hypgeom_gamma_upper`. .. function:: void acb_hypgeom_ei_asymp(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_ei_2f2(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_ei(acb_t res, const acb_t z, slong prec) Computes the exponential integral `\operatorname{Ei}(z)`, respectively using .. math :: \operatorname{Ei}(z) = -e^z U(1,1,-z) - \log(-z) + \frac{1}{2} \left(\log(z) - \log\left(\frac{1}{z}\right) \right) \operatorname{Ei}(z) = z {}_2F_2(1, 1; 2, 2; z) + \gamma + \frac{1}{2} \left(\log(z) - \log\left(\frac{1}{z}\right) \right) and an automatic algorithm choice. .. function:: void acb_hypgeom_si_asymp(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_si_1f2(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_si(acb_t res, const acb_t z, slong prec) Computes the sine integral `\operatorname{Si}(z)`, respectively using .. math :: \operatorname{Si}(z) = \frac{i}{2} \left[ e^{iz} U(1,1,-iz) - e^{-iz} U(1,1,iz) + \log(-iz) - \log(iz) \right] \operatorname{Si}(z) = z {}_1F_2(\tfrac{1}{2}; \tfrac{3}{2}, \tfrac{3}{2}; -\tfrac{z^2}{4}) and an automatic algorithm choice. .. function:: void acb_hypgeom_ci_asymp(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_ci_2f3(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_ci(acb_t res, const acb_t z, slong prec) Computes the cosine integral `\operatorname{Ci}(z)`, respectively using .. math :: \operatorname{Ci}(z) = \log(z) - \frac{1}{2} \left[ e^{iz} U(1,1,-iz) + e^{-iz} U(1,1,iz) + \log(-iz) + \log(iz) \right] \operatorname{Ci}(z) = -\tfrac{z^2}{4} {}_2F_3(1, 1; 2, 2, \tfrac{3}{2}; -\tfrac{z^2}{4}) + \log(z) + \gamma and an automatic algorithm choice. .. function:: void acb_hypgeom_shi(acb_t res, const acb_t z, slong prec) Computes the hyperbolic sine integral `\operatorname{Shi}(z) = -i \operatorname{Si}(iz)`. This is a trivial wrapper of :func:`acb_hypgeom_si`. .. function:: void acb_hypgeom_chi_asymp(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_chi_2f3(acb_t res, const acb_t z, slong prec) .. function:: void acb_hypgeom_chi(acb_t res, const acb_t z, slong prec) Computes the hyperbolic cosine integral `\operatorname{Chi}(z)`, respectively using .. math :: \operatorname{Chi}(z) = -\frac{1}{2} \left[ e^{z} U(1,1,-z) + e^{-z} U(1,1,z) + \log(-z) - \log(z) \right] \operatorname{Chi}(z) = \tfrac{z^2}{4} {}_2F_3(1, 1; 2, 2, \tfrac{3}{2}; \tfrac{z^2}{4}) + \log(z) + \gamma and an automatic algorithm choice. .. function:: void acb_hypgeom_li(acb_t res, const acb_t z, int offset, slong prec) If *offset* is zero, computes the logarithmic integral `\operatorname{li}(z) = \operatorname{Ei}(\log(z))`. If *offset* is nonzero, computes the offset logarithmic integral `\operatorname{Li}(z) = \operatorname{li}(z) - \operatorname{li}(2)`. Gauss hypergeometric function ------------------------------------------------------------------------------- The following methods compute the Gauss hypergeometric function .. math :: F(z) = {}_2F_1(a,b,c,z) = \sum_{k=0}^{\infty} \frac{(a)_k (b)_k}{(c)_k} \frac{z^k}{k!} or the regularized version `\operatorname{\mathbf{F}}(z) = \operatorname{\mathbf{F}}(a,b,c,z) = {}_2F_1(a,b,c,z) / \Gamma(c)` if the flag *regularized* is set. .. function:: void acb_hypgeom_2f1_continuation(acb_t res0, acb_t res1, const acb_t a, const acb_t b, const acb_t c, const acb_t z0, const acb_t z1, const acb_t f0, const acb_t f1, slong prec) Given `F(z_0), F'(z_0)` in *f0*, *f1*, sets *res0* and *res1* to `F(z_1), F'(z_1)` by integrating the hypergeometric differential equation along a straight-line path. The evaluation points should be well-isolated from the singular points 0 and 1. .. function:: void acb_hypgeom_2f1_series_direct(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t c, const acb_poly_t z, int regularized, slong len, slong prec) Computes `F(z)` of the given power series truncated to length *len*, using direct summation of the hypergeometric series. .. function:: void acb_hypgeom_2f1_direct(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec) Computes `F(z)` using direct summation of the hypergeometric series. .. function:: void acb_hypgeom_2f1_transform(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, int which, slong prec) .. function:: void acb_hypgeom_2f1_transform_limit(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, int which, slong prec) Computes `F(z)` using an argument transformation determined by the flag *which*. Legal values are 1 for `z/(z-1)`, 2 for `1/z`, 3 for `1/(1-z)`, 4 for `1-z`, and 5 for `1-1/z`. The *limit* version assumes that *which* is not 1. If *which* is 2 or 3, it assumes that `b-a` represents an exact integer. If *which* is 4 or 5, it assumes that `c-a-b` represents an exact integer. In these cases, it computes the correct limit value. .. function:: void acb_hypgeom_2f1_corner(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec) Computes `F(z)` near the corner cases `\exp(\pm \pi i \sqrt{3})` by analytic continuation. .. function:: int acb_hypgeom_2f1_choose(const acb_t z) Chooses a method to compute the function based on the location of *z* in the complex plane. If the return value is 0, direct summation should be used. If the return value is 1 to 5, the transformation with this index in :func:`acb_hypgeom_2f1_transform` should be used. If the return value is 6, the corner case algorithm should be used. .. function:: void acb_hypgeom_2f1(acb_t res, const acb_t a, const acb_t b, const acb_t c, const acb_t z, int regularized, slong prec) Computes `F(z)` (or `\operatorname{\mathbf{F}}(z)` if *regularized* is set) using an automatic algorithm choice. Orthogonal polynomials and functions ------------------------------------------------------------------------------- .. function:: void acb_hypgeom_chebyshev_t(acb_t res, const acb_t n, const acb_t z, slong prec) .. function:: void acb_hypgeom_chebyshev_u(acb_t res, const acb_t n, const acb_t z, slong prec) Computes the Chebyshev polynomial (or Chebyshev function) of first or second kind .. math :: T_n(z) = {}_2F_1\left(-n,n,\frac{1}{2},\frac{1-z}{2}\right) U_n(z) = (n+1) {}_2F_1\left(-n,n+2,\frac{3}{2},\frac{1-z}{2}\right). The hypergeometric series definitions are only used for computation near the point 1. In general, trigonometric representations are used. For word-size integer *n*, :func:`acb_chebyshev_t_ui` and :func:`acb_chebyshev_u_ui` are called. .. function:: void acb_hypgeom_jacobi_p(acb_t res, const acb_t n, const acb_t a, const acb_t b, const acb_t z, slong prec) Computes the Jacobi polynomial (or Jacobi function) .. math :: P_n^{(a,b)}(z)=\frac{(a+1)_n}{\Gamma(n+1)} {}_2F_1\left(-n,n+a+b+1,a+1,\frac{1-z}{2}\right). For nonnegative integer *n*, this is a polynomial in *a*, *b* and *z*, even when the parameters are such that the hypergeometric series is undefined. In such cases, the polynomial is evaluated using direct methods. .. function:: void acb_hypgeom_gegenbauer_c(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec) Computes the Gegenbauer polynomial (or Gegenbauer function) .. math :: C_n^{m}(z)=\frac{(2m)_n}{\Gamma(n+1)} {}_2F_1\left(-n,2m+n,m+\frac{1}{2},\frac{1-z}{2}\right). For nonnegative integer *n*, this is a polynomial in *m* and *z*, even when the parameters are such that the hypergeometric series is undefined. In such cases, the polynomial is evaluated using direct methods. .. function:: void acb_hypgeom_laguerre_l(acb_t res, const acb_t n, const acb_t m, const acb_t z, slong prec) Computes the Laguerre polynomial (or Laguerre function) .. math :: L_n^{m}(z)=\frac{(m+1)_n}{\Gamma(n+1)} {}_1F_1\left(-n,m+1,z\right). For nonnegative integer *n*, this is a polynomial in *m* and *z*, even when the parameters are such that the hypergeometric series is undefined. In such cases, the polynomial is evaluated using direct methods. There are at least two incompatible ways to define the Laguerre function when *n* is a negative integer. One possibility when `m = 0` is to define `L_{-n}^0(z) = e^z L_{n-1}^0(-z)`. Another possibility is to cover this case with the recurrence relation `L_{n-1}^m(z) + L_n^{m-1}(z) = L_n^m(z)`. Currently, we leave this case undefined (returning indeterminate). .. function:: void acb_hypgeom_hermite_h(acb_t res, const acb_t n, const acb_t z, slong prec) Computes the Hermite polynomial (or Hermite function) .. math :: H_n(z) = 2^n \sqrt{\pi} \left( \frac{1}{\Gamma((1-n)/2)} {}_1F_1\left(-\frac{n}{2},\frac{1}{2},z^2\right) - \frac{2z}{\Gamma(-n/2)} {}_1F_1\left(\frac{1-n}{2},\frac{3}{2},z^2\right)\right). .. function:: void acb_hypgeom_legendre_p(acb_t res, const acb_t n, const acb_t m, const acb_t z, int type, slong prec) Sets *res* to the associated Legendre function of the first kind evaluated for degree *n*, order *m*, and argument *z*. When *m* is zero, this reduces to the Legendre polynomial `P_n(z)`. Many different branch cut conventions appear in the literature. If *type* is 0, the version .. math :: P_n^m(z) = \frac{(1+z)^{m/2}}{(1-z)^{m/2}} \mathbf{F}\left(-n, n+1, 1-m, \frac{1-z}{2}\right) is computed, and if *type* is 1, the alternative version .. math :: {\mathcal P}_n^m(z) = \frac{(z+1)^{m/2}}{(z-1)^{m/2}} \mathbf{F}\left(-n, n+1, 1-m, \frac{1-z}{2}\right). is computed. Type 0 and type 1 respectively correspond to type 2 and type 3 in *Mathematica* and *mpmath*. .. function:: void acb_hypgeom_legendre_q(acb_t res, const acb_t n, const acb_t m, const acb_t z, int type, slong prec) Sets *res* to the associated Legendre function of the second kind evaluated for degree *n*, order *m*, and argument *z*. When *m* is zero, this reduces to the Legendre function `Q_n(z)`. Many different branch cut conventions appear in the literature. If *type* is 0, the version .. math :: Q_n^m(z) = \frac{\pi}{2 \sin(\pi m)} \left( \cos(\pi m) P_n^m(z) - \frac{\Gamma(1+m+n)}{\Gamma(1-m+n)} P_n^{-m}(z)\right) is computed, and if *type* is 1, the alternative version .. math :: \mathcal{Q}_n^m(z) = \frac{\pi}{2 \sin(\pi m)} e^{\pi i m} \left( \mathcal{P}_n^m(z) - \frac{\Gamma(1+m+n)}{\Gamma(1-m+n)} \mathcal{P}_n^{-m}(z)\right) is computed. Type 0 and type 1 respectively correspond to type 2 and type 3 in *Mathematica* and *mpmath*. When *m* is an integer, either expression is interpreted as a limit. We make use of the connection formulas [WQ3a]_, [WQ3b]_ and [WQ3c]_ to allow computing the function even in the limiting case. (The formula [WQ3d]_ would be useful, but is incorrect in the lower half plane.) .. [WQ3a] http://functions.wolfram.com/07.11.26.0033.01 .. [WQ3b] http://functions.wolfram.com/07.12.27.0014.01 .. [WQ3c] http://functions.wolfram.com/07.12.26.0003.01 .. [WQ3d] http://functions.wolfram.com/07.12.26.0088.01 .. function:: void acb_hypgeom_legendre_p_uiui_rec(acb_t res, ulong n, ulong m, const acb_t z, slong prec) For nonnegative integer *n* and *m*, uses recurrence relations to evaluate `(1-z^2)^{-m/2} P_n^m(z)` which is a polynomial in *z*. .. function:: void acb_hypgeom_spherical_y(acb_t res, slong n, slong m, const acb_t theta, const acb_t phi, slong prec) Computes the spherical harmonic of degree *n*, order *m*, latitude angle *theta*, and longitude angle *phi*, normalized such that .. math :: Y_n^m(\theta, \phi) = \sqrt{\frac{2n+1}{4\pi} \frac{(n-m)!}{(n+m)!}} e^{im\phi} P_n^m(\cos(\theta)). The definition is extended to negative *m* and *n* by symmetry. This function is a polynomial in `\cos(\theta)` and `\sin(\theta)`. We evaluate it using :func:`acb_hypgeom_legendre_p_uiui_rec`. arb-2.8.1/doc/source/acb_mat.rst000066400000000000000000000274351264125401100164620ustar00rootroot00000000000000.. _acb-mat: **acb_mat.h** -- matrices over the complex numbers =============================================================================== An :type:`acb_mat_t` represents a dense matrix over the complex numbers, implemented as an array of entries of type :type:`acb_struct`. The dimension (number of rows and columns) of a matrix is fixed at initialization, and the user must ensure that inputs and outputs to an operation have compatible dimensions. The number of rows or columns in a matrix can be zero. Types, macros and constants ------------------------------------------------------------------------------- .. type:: acb_mat_struct .. type:: acb_mat_t Contains a pointer to a flat array of the entries (entries), an array of pointers to the start of each row (rows), and the number of rows (r) and columns (c). An *acb_mat_t* is defined as an array of length one of type *acb_mat_struct*, permitting an *acb_mat_t* to be passed by reference. .. macro:: acb_mat_entry(mat, i, j) Macro giving a pointer to the entry at row *i* and column *j*. .. macro:: acb_mat_nrows(mat) Returns the number of rows of the matrix. .. macro:: acb_mat_ncols(mat) Returns the number of columns of the matrix. Memory management ------------------------------------------------------------------------------- .. function:: void acb_mat_init(acb_mat_t mat, slong r, slong c) Initializes the matrix, setting it to the zero matrix with *r* rows and *c* columns. .. function:: void acb_mat_clear(acb_mat_t mat) Clears the matrix, deallocating all entries. Conversions ------------------------------------------------------------------------------- .. function:: void acb_mat_set(acb_mat_t dest, const acb_mat_t src) .. function:: void acb_mat_set_fmpz_mat(acb_mat_t dest, const fmpz_mat_t src) .. function:: void acb_mat_set_round_fmpz_mat(acb_mat_t dest, const fmpz_mat_t src, slong prec) .. function:: void acb_mat_set_fmpq_mat(acb_mat_t dest, const fmpq_mat_t src, slong prec) .. function:: void acb_mat_set_arb_mat(acb_mat_t dest, const arb_mat_t src) .. function:: void acb_mat_set_round_arb_mat(acb_mat_t dest, const arb_mat_t src, slong prec) Sets *dest* to *src*. The operands must have identical dimensions. Random generation ------------------------------------------------------------------------------- .. function:: void acb_mat_randtest(acb_mat_t mat, flint_rand_t state, slong prec, slong mag_bits) Sets *mat* to a random matrix with up to *prec* bits of precision and with exponents of width up to *mag_bits*. Input and output ------------------------------------------------------------------------------- .. function:: void acb_mat_printd(const acb_mat_t mat, slong digits) Prints each entry in the matrix with the specified number of decimal digits. Comparisons ------------------------------------------------------------------------------- .. function:: int acb_mat_equal(const acb_mat_t mat1, const acb_mat_t mat2) Returns nonzero iff the matrices have the same dimensions and identical entries. .. function:: int acb_mat_overlaps(const acb_mat_t mat1, const acb_mat_t mat2) Returns nonzero iff the matrices have the same dimensions and each entry in *mat1* overlaps with the corresponding entry in *mat2*. .. function:: int acb_mat_contains(const acb_mat_t mat1, const acb_mat_t mat2) .. function:: int acb_mat_contains_fmpz_mat(const acb_mat_t mat1, const fmpz_mat_t mat2) .. function:: int acb_mat_contains_fmpq_mat(const acb_mat_t mat1, const fmpq_mat_t mat2) Returns nonzero iff the matrices have the same dimensions and each entry in *mat2* is contained in the corresponding entry in *mat1*. .. function:: int acb_mat_eq(const acb_mat_t mat1, const acb_mat_t mat2) Returns nonzero iff *mat1* and *mat2* certainly represent the same matrix. .. function:: int acb_mat_ne(const acb_mat_t mat1, const acb_mat_t mat2) Returns nonzero iff *mat1* and *mat2* certainly do not represent the same matrix. .. function:: int acb_mat_is_real(const acb_mat_t mat) Returns nonzero iff all entries in *mat* have zero imaginary part. Special matrices ------------------------------------------------------------------------------- .. function:: void acb_mat_zero(acb_mat_t mat) Sets all entries in mat to zero. .. function:: void acb_mat_one(acb_mat_t mat) Sets the entries on the main diagonal to ones, and all other entries to zero. Transpose ------------------------------------------------------------------------------- .. function:: void acb_mat_transpose(acb_mat_t dest, const acb_mat_t src) Sets *dest* to the exact transpose *src*. The operands must have compatible dimensions. Aliasing is allowed. Norms ------------------------------------------------------------------------------- .. function:: void acb_mat_bound_inf_norm(mag_t b, const acb_mat_t A) Sets *b* to an upper bound for the infinity norm (i.e. the largest absolute value row sum) of *A*. Arithmetic ------------------------------------------------------------------------------- .. function:: void acb_mat_neg(acb_mat_t dest, const acb_mat_t src) Sets *dest* to the exact negation of *src*. The operands must have the same dimensions. .. function:: void acb_mat_add(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec) Sets res to the sum of *mat1* and *mat2*. The operands must have the same dimensions. .. function:: void acb_mat_sub(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec) Sets *res* to the difference of *mat1* and *mat2*. The operands must have the same dimensions. .. function:: void acb_mat_mul(acb_mat_t res, const acb_mat_t mat1, const acb_mat_t mat2, slong prec) Sets *res* to the matrix product of *mat1* and *mat2*. The operands must have compatible dimensions for matrix multiplication. .. function:: void acb_mat_sqr(acb_mat_t res, const acb_mat_t mat, slong prec) Sets *res* to the matrix square of *mat*. The operands must both be square with the same dimensions. .. function:: void acb_mat_pow_ui(acb_mat_t res, const acb_mat_t mat, ulong exp, slong prec) Sets *res* to *mat* raised to the power *exp*. Requires that *mat* is a square matrix. Scalar arithmetic ------------------------------------------------------------------------------- .. function:: void acb_mat_scalar_mul_2exp_si(acb_mat_t B, const acb_mat_t A, slong c) Sets *B* to *A* multiplied by `2^c`. .. function:: void acb_mat_scalar_addmul_si(acb_mat_t B, const acb_mat_t A, slong c, slong prec) .. function:: void acb_mat_scalar_addmul_fmpz(acb_mat_t B, const acb_mat_t A, const fmpz_t c, slong prec) .. function:: void acb_mat_scalar_addmul_arb(acb_mat_t B, const acb_mat_t A, const arb_t c, slong prec) .. function:: void acb_mat_scalar_addmul_acb(acb_mat_t B, const acb_mat_t A, const acb_t c, slong prec) Sets *B* to `B + A \times c`. .. function:: void acb_mat_scalar_mul_si(acb_mat_t B, const acb_mat_t A, slong c, slong prec) .. function:: void acb_mat_scalar_mul_fmpz(acb_mat_t B, const acb_mat_t A, const fmpz_t c, slong prec) .. function:: void acb_mat_scalar_mul_arb(acb_mat_t B, const acb_mat_t A, const arb_t c, slong prec) .. function:: void acb_mat_scalar_mul_acb(acb_mat_t B, const acb_mat_t A, const acb_t c, slong prec) Sets *B* to `A \times c`. .. function:: void acb_mat_scalar_div_si(acb_mat_t B, const acb_mat_t A, slong c, slong prec) .. function:: void acb_mat_scalar_div_fmpz(acb_mat_t B, const acb_mat_t A, const fmpz_t c, slong prec) .. function:: void acb_mat_scalar_div_arb(acb_mat_t B, const acb_mat_t A, const arb_t c, slong prec) .. function:: void acb_mat_scalar_div_acb(acb_mat_t B, const acb_mat_t A, const acb_t c, slong prec) Sets *B* to `A / c`. Gaussian elimination and solving ------------------------------------------------------------------------------- .. function:: int acb_mat_lu(slong * perm, acb_mat_t LU, const acb_mat_t A, slong prec) Given an `n \times n` matrix `A`, computes an LU decomposition `PLU = A` using Gaussian elimination with partial pivoting. The input and output matrices can be the same, performing the decomposition in-place. Entry `i` in the permutation vector perm is set to the row index in the input matrix corresponding to row `i` in the output matrix. The algorithm succeeds and returns nonzero if it can find `n` invertible (i.e. not containing zero) pivot entries. This guarantees that the matrix is invertible. The algorithm fails and returns zero, leaving the entries in `P` and `LU` undefined, if it cannot find `n` invertible pivot elements. In this case, either the matrix is singular, the input matrix was computed to insufficient precision, or the LU decomposition was attempted at insufficient precision. .. function:: void acb_mat_solve_lu_precomp(acb_mat_t X, const slong * perm, const acb_mat_t LU, const acb_mat_t B, slong prec) Solves `AX = B` given the precomputed nonsingular LU decomposition `A = PLU`. The matrices `X` and `B` are allowed to be aliased with each other, but `X` is not allowed to be aliased with `LU`. .. function:: int acb_mat_solve(acb_mat_t X, const acb_mat_t A, const acb_mat_t B, slong prec) Solves `AX = B` where `A` is a nonsingular `n \times n` matrix and `X` and `B` are `n \times m` matrices, using LU decomposition. If `m > 0` and `A` cannot be inverted numerically (indicating either that `A` is singular or that the precision is insufficient), the values in the output matrix are left undefined and zero is returned. A nonzero return value guarantees that `A` is invertible and that the exact solution matrix is contained in the output. .. function:: int acb_mat_inv(acb_mat_t X, const acb_mat_t A, slong prec) Sets `X = A^{-1}` where `A` is a square matrix, computed by solving the system `AX = I`. If `A` cannot be inverted numerically (indicating either that `A` is singular or that the precision is insufficient), the values in the output matrix are left undefined and zero is returned. A nonzero return value guarantees that the matrix is invertible and that the exact inverse is contained in the output. .. function:: void acb_mat_det(acb_t det, const acb_mat_t A, slong prec) Computes the determinant of the matrix, using Gaussian elimination with partial pivoting. If at some point an invertible pivot element cannot be found, the elimination is stopped and the magnitude of the determinant of the remaining submatrix is bounded using Hadamard's inequality. Characteristic polynomial ------------------------------------------------------------------------------- .. function:: void _acb_mat_charpoly(acb_ptr cp, const acb_mat_t mat, slong prec) .. function:: void acb_mat_charpoly(acb_poly_t cp, const acb_mat_t mat, slong prec) Sets *cp* to the characteristic polynomial of *mat* which must be a square matrix. If the matrix has *n* rows, the underscore method requires space for `n + 1` output coefficients. Employs a division-free algorithm using `O(n^4)` operations. Special functions ------------------------------------------------------------------------------- .. function:: void acb_mat_exp(acb_mat_t B, const acb_mat_t A, slong prec) Sets *B* to the exponential of the matrix *A*, defined by the Taylor series .. math :: \exp(A) = \sum_{k=0}^{\infty} \frac{A^k}{k!}. The function is evaluated as `\exp(A/2^r)^{2^r}`, where `r` is chosen to give rapid convergence of the Taylor series. The series is evaluated using rectangular splitting. Error bounds are computed as for :func:`arb_mat_exp`. .. function:: void acb_mat_trace(acb_t trace, const acb_mat_t mat, slong prec) Sets *trace* to the trace of the matrix, i.e. the sum of entries on the main diagonal of *mat*. The matrix is required to be square. arb-2.8.1/doc/source/acb_modular.rst000066400000000000000000000560531264125401100173420ustar00rootroot00000000000000.. _acb-modular: **acb_modular.h** -- modular forms in the complex numbers =============================================================================== This module provides methods for numerical evaluation of modular forms, Jacobi theta functions, and elliptic functions. In the context of this module, *tau* or `\tau` always denotes an element of the complex upper half-plane `\mathbb{H} = \{z \in \mathbb{C} : \operatorname{Im}(z) > 0\}`. We also often use the variable `q`, variously defined as `q = e^{2 \pi i \tau}` (usually in relation to modular forms) or `q = e^{\pi i \tau}` (usually in relation to theta functions) and satisfying `|q| < 1`. We will clarify the local meaning of `q` every time such a quantity appears as a function of `\tau`. As usual, the numerical functions in this module compute strict error bounds: if *tau* is represented by an :type:`acb_t` whose content overlaps with the real line (or lies in the lower half-plane), and *tau* is passed to a function defined only on `\mathbb{H}`, then the output will have an infinite radius. The analogous behavior holds for functions requiring `|q| < 1`. The modular group ------------------------------------------------------------------------------- .. type:: psl2z_struct .. type:: psl2z_t Represents an element of the modular group `\text{PSL}(2, \mathbb{Z})`, namely an integer matrix .. math :: \begin{pmatrix} a & b \\ c & d \end{pmatrix} with `ad-bc = 1`, and with signs canonicalized such that `c \ge 0`, and `d > 0` if `c = 0`. The struct members *a*, *b*, *c*, *d* are of type *fmpz*. .. function:: void psl2z_init(psl2z_t g) Initializes *g* and set it to the identity element. .. function:: void psl2z_clear(psl2z_t g) Clears *g*. .. function:: void psl2z_swap(psl2z_t f, psl2z_t g) Swaps *f* and *g* efficiently. .. function:: void psl2z_set(psl2z_t f, const psl2z_t g) Sets *f* to a copy of *g*. .. function:: void psl2z_one(psl2z_t g) Sets *g* to the identity element. .. function:: int psl2z_is_one(const psl2z_t g) Returns nonzero iff *g* is the identity element. .. function:: void psl2z_print(const psl2z_t g) Prints *g* to standard output. .. function:: int psl2z_equal(const psl2z_t f, const psl2z_t g) Returns nonzero iff *f* and *g* are equal. .. function:: void psl2z_mul(psl2z_t h, const psl2z_t f, const psl2z_t g) Sets *h* to the product of *f* and *g*, namely the matrix product with the signs canonicalized. .. function:: void psl2z_inv(psl2z_t h, const psl2z_t g) Sets *h* to the inverse of *g*. .. function:: int psl2z_is_correct(const psl2z_t g) Returns nonzero iff *g* contains correct data, i.e. satisfying `ad-bc = 1`, `c \ge 0`, and `d > 0` if `c = 0`. .. function:: void psl2z_randtest(psl2z_t g, flint_rand_t state, slong bits) Sets *g* to a random element of `\text{PSL}(2, \mathbb{Z})` with entries of bit length at most *bits* (or 1, if *bits* is not positive). We first generate *a* and *d*, compute their Bezout coefficients, divide by the GCD, and then correct the signs. Modular transformations ------------------------------------------------------------------------------- .. function:: void acb_modular_transform(acb_t w, const psl2z_t g, const acb_t z, slong prec) Applies the modular transformation *g* to the complex number *z*, evaluating .. math :: w = g z = \frac{az+b}{cz+d}. .. function:: void acb_modular_fundamental_domain_approx_d(psl2z_t g, double x, double y, double one_minus_eps) .. function:: void acb_modular_fundamental_domain_approx_arf(psl2z_t g, const arf_t x, const arf_t y, const arf_t one_minus_eps, slong prec) Attempts to determine a modular transformation *g* that maps the complex number `x+yi` to the fundamental domain or just slightly outside the fundamental domain, where the target tolerance (not a strict bound) is specified by *one_minus_eps*. The inputs are assumed to be finite numbers, with *y* positive. Uses floating-point iteration, repeatedly applying either the transformation `z \gets z + b` or `z \gets -1/z`. The iteration is terminated if `|x| \le 1/2` and `x^2 + y^2 \ge 1 - \varepsilon` where `1 - \varepsilon` is passed as *one_minus_eps*. It is also terminated if too many steps have been taken without convergence, or if the numbers end up too large or too small for the working precision. The algorithm can fail to produce a satisfactory transformation. The output *g* is always set to *some* correct modular transformation, but it is up to the user to verify a posteriori that *g* maps `x+yi` close enough to the fundamental domain. .. function:: void acb_modular_fundamental_domain_approx(acb_t w, psl2z_t g, const acb_t z, const arf_t one_minus_eps, slong prec) Attempts to determine a modular transformation *g* that maps the complex number `z` to the fundamental domain or just slightly outside the fundamental domain, where the target tolerance (not a strict bound) is specified by *one_minus_eps*. It also computes the transformed value `w = gz`. This function first tries to use :func:`acb_modular_fundamental_domain_approx_d` and checks if the result is acceptable. If this fails, it calls :func:`acb_modular_fundamental_domain_approx_arf` with higher precision. Finally, `w = gz` is evaluated by a single application of *g*. The algorithm can fail to produce a satisfactory transformation. The output *g* is always set to *some* correct modular transformation, but it is up to the user to verify a posteriori that `w` is close enough to the fundamental domain. .. function:: int acb_modular_is_in_fundamental_domain(const acb_t z, const arf_t tol, slong prec) Returns nonzero if it is certainly true that `|z| \ge 1 - \varepsilon` and `|\operatorname{Re}(z)| \le 1/2 + \varepsilon` where `\varepsilon` is specified by *tol*. Returns zero if this is false or cannot be determined. Addition sequences ------------------------------------------------------------------------------- .. function:: void acb_modular_fill_addseq(slong * tab, slong len) Builds a near-optimal addition sequence for a sequence of integers which is assumed to be reasonably dense. As input, the caller should set each entry in *tab* to `-1` if that index is to be part of the addition sequence, and to 0 otherwise. On output, entry *i* in *tab* will either be zero (if the number is not part of the sequence), or a value *j* such that both *j* and `i - j` are also marked. The first two entries in *tab* are ignored (the number 1 is always assumed to be part of the sequence). Jacobi theta functions ------------------------------------------------------------------------------- Unfortunately, there are many inconsistent notational variations for Jacobi theta functions in the literature. Unless otherwise noted, we use the functions .. math :: \theta_1(z,\tau) = -i \sum_{n=-\infty}^{\infty} (-1)^n \exp(\pi i [(n + 1/2)^2 \tau + (2n + 1) z]) = 2 q_{1/4} \sum_{n=0}^{\infty} (-1)^n q^{n(n+1)} \sin((2n+1) \pi z) \theta_2(z,\tau) = \sum_{n=-\infty}^{\infty} \exp(\pi i [(n + 1/2)^2 \tau + (2n + 1) z]) = 2 q_{1/4} \sum_{n=0}^{\infty} q^{n(n+1)} \cos((2n+1) \pi z) \theta_3(z,\tau) = \sum_{n=-\infty}^{\infty} \exp(\pi i [n^2 \tau + 2n z]) = 1 + 2 \sum_{n=1}^{\infty} q^{n^2} \cos(2n \pi z) \theta_4(z,\tau) = \sum_{n=-\infty}^{\infty} (-1)^n \exp(\pi i [n^2 \tau + 2n z]) = 1 + 2 \sum_{n=1}^{\infty} (-1)^n q^{n^2} \cos(2n \pi z) where `q = \exp(\pi i \tau)` and `q_{1/4} = \exp(\pi i \tau / 4)`. Note that many authors write `q_{1/4}` as `q^{1/4}`, but the principal fourth root `(q)^{1/4} = \exp(\frac{1}{4} \log q)` differs from `q_{1/4}` in general and some formulas are only correct if one reads "`q^{1/4} = \exp(\pi i \tau / 4)`". To avoid confusion, we only write `q^k` when `k` is an integer. .. function:: void acb_modular_theta_transform(int * R, int * S, int * C, const psl2z_t g) We wish to write a theta function with quasiperiod `\tau` in terms of a theta function with quasiperiod `\tau' = g \tau`, given some `g = (a, b; c, d) \in \text{PSL}(2, \mathbb{Z})`. For `i = 0, 1, 2, 3`, this function computes integers `R_i` and `S_i` (*R* and *S* should be arrays of length 4) and `C \in \{0, 1\}` such that .. math :: \theta_{1+i}(z,\tau) = \exp(\pi i R_i / 4) \cdot A \cdot B \cdot \theta_{1+S_i}(z',\tau') where `z' = z, A = B = 1` if `C = 0`, and .. math :: z' = \frac{-z}{c \tau + d}, \quad A = \sqrt{\frac{i}{c \tau + d}}, \quad B = \exp\left(-\pi i c \frac{z^2}{c \tau + d}\right) if `C = 1`. Note that `A` is well-defined with the principal branch of the square root since `A^2 = i/(c \tau + d)` lies in the right half-plane. Firstly, if `c = 0`, we have `\theta_i(z, \tau) = \exp(-\pi i b / 4) \theta_i(z, \tau+b)` for `i = 1, 2`, whereas `\theta_3` and `\theta_4` remain unchanged when `b` is even and swap places with each other when `b` is odd. In this case we set `C = 0`. For an arbitrary `g` with `c > 0`, we set `C = 1`. The general transformations are given by Rademacher [Rad1973]_. We need the function `\theta_{m,n}(z,\tau)` defined for `m, n \in \mathbb{Z}` by (beware of the typos in [Rad1973]_) .. math :: \theta_{0,0}(z,\tau) = \theta_3(z,\tau), \quad \theta_{0,1}(z,\tau) = \theta_4(z,\tau) \theta_{1,0}(z,\tau) = \theta_2(z,\tau), \quad \theta_{1,1}(z,\tau) = i \theta_1(z,\tau) \theta_{m+2,n}(z,\tau) = (-1)^n \theta_{m,n}(z,\tau) \theta_{m,n+2}(z,\tau) = \theta_{m,n}(z,\tau). Then we may write .. math :: \theta_1(z,\tau) = \varepsilon_1 A B \theta_1(z', \tau') \theta_2(z,\tau) = \varepsilon_2 A B \theta_{1-c,1+a}(z', \tau') \theta_3(z,\tau) = \varepsilon_3 A B \theta_{1+d-c,1-b+a}(z', \tau') \theta_4(z,\tau) = \varepsilon_4 A B \theta_{1+d,1-b}(z', \tau') where `\varepsilon_i` is an 8th root of unity. Specifically, if we denote the 24th root of unity in the transformation formula of the Dedekind eta function by `\varepsilon(a,b,c,d) = \exp(\pi i R(a,b,c,d) / 12)` (see :func:`acb_modular_epsilon_arg`), then: .. math :: \varepsilon_1(a,b,c,d) = \exp(\pi i [R(-d,b,c,-a) + 1] / 4) \varepsilon_2(a,b,c,d) = \exp(\pi i [-R(a,b,c,d) + (5+(2-c)a)] / 4) \varepsilon_3(a,b,c,d) = \exp(\pi i [-R(a,b,c,d) + (4+(c-d-2)(b-a))] / 4) \varepsilon_4(a,b,c,d) = \exp(\pi i [-R(a,b,c,d) + (3-(2+d)b)] / 4) These formulas are easily derived from the formulas in [Rad1973]_ (Rademacher has the transformed/untransformed variables exchanged, and his "`\varepsilon`" differs from ours by a constant offset in the phase). .. function:: void acb_modular_addseq_theta(slong * exponents, slong * aindex, slong * bindex, slong num) Constructs an addition sequence for the first *num* squares and triangular numbers interleaved (excluding zero), i.e. 1, 2, 4, 6, 9, 12, 16, 20, 25, 30 etc. .. function:: void acb_modular_theta_sum(acb_ptr theta1, acb_ptr theta2, acb_ptr theta3, acb_ptr theta4, const acb_t w, int w_is_unit, const acb_t q, slong len, slong prec) Simultaneously computes the first *len* coefficients of each of the formal power series .. math :: \theta_1(z+x,\tau) / q_{1/4} \in \mathbb{C}[[x]] \theta_2(z+x,\tau) / q_{1/4} \in \mathbb{C}[[x]] \theta_3(z+x,\tau) \in \mathbb{C}[[x]] \theta_4(z+x,\tau) \in \mathbb{C}[[x]] given `w = \exp(\pi i z)` and `q = \exp(\pi i \tau)`, by summing a finite truncation of the respective theta function series. In particular, with *len* equal to 1, computes the respective value of the theta function at the point *z*. We require *len* to be positive. If *w_is_unit* is nonzero, *w* is assumed to lie on the unit circle, i.e. *z* is assumed to be real. Note that the factor `q_{1/4}` is removed from `\theta_1` and `\theta_2`. To get the true theta function values, the user has to multiply this factor back. This convention avoids unnecessary computations, since the user can compute `q_{1/4} = \exp(\pi i \tau / 4)` followed by `q = (q_{1/4})^4`, and in many cases when computing products or quotients of theta functions, the factor `q_{1/4}` can be eliminated entirely. This function is intended for `|q| \ll 1`. It can be called with any `q`, but will return useless intervals if convergence is not rapid. For general evaluation of theta functions, the user should only call this function after applying a suitable modular transformation. We consider the sums together, alternatingly updating `(\theta_1, \theta_2)` or `(\theta_3, \theta_4)`. For `k = 0, 1, 2, \ldots`, the powers of `q` are `\lfloor (k+2)^2 / 4 \rfloor = 1, 2, 4, 6, 9` etc. and the powers of `w` are `\pm (k+2) = \pm 2, \pm 3, \pm 4, \ldots` etc. The scheme is illustrated by the following table: .. math :: \begin{array}{llll} & \theta_1, \theta_2 & q^0 & (w^1 \pm w^{-1}) \\ k = 0 & \theta_3, \theta_4 & q^1 & (w^2 \pm w^{-2}) \\ k = 1 & \theta_1, \theta_2 & q^2 & (w^3 \pm w^{-3}) \\ k = 2 & \theta_3, \theta_4 & q^4 & (w^4 \pm w^{-4}) \\ k = 3 & \theta_1, \theta_2 & q^6 & (w^5 \pm w^{-5}) \\ k = 4 & \theta_3, \theta_4 & q^9 & (w^6 \pm w^{-6}) \\ k = 5 & \theta_1, \theta_2 & q^{12} & (w^7 \pm w^{-7}) \\ \end{array} For some integer `N \ge 1`, the summation is stopped just before term `k = N`. Let `Q = |q|`, `W = \max(|w|,|w^{-1}|)`, `E = \lfloor (N+2)^2 / 4 \rfloor` and `F = \lfloor (N+1)/2 \rfloor + 1`. The error of the zeroth derivative can be bounded as .. math :: 2 Q^E W^{N+2} \left[ 1 + Q^F W + Q^{2F} W^2 + \ldots \right] = \frac{2 Q^E W^{N+2}}{1 - Q^F W} provided that the denominator is positive (otherwise we set the error bound to infinity). When *len* is greater than 1, consider the derivative of order *r*. The term of index *k* and order *r* picks up a factor of magnitude `(k+2)^r` from differentiation of `w^{k+2}` (it also picks up a factor `\pi^r`, but we omit this until we rescale the coefficients at the end of the computation). Thus we have the error bound .. math :: 2 Q^E W^{N+2} (N+2)^r \left[ 1 + Q^F W \frac{(N+3)^r}{(N+2)^r} + Q^{2F} W^2 \frac{(N+4)^r}{(N+2)^r} + \ldots \right] which by the inequality `(1 + m/(N+2))^r \le \exp(mr/(N+2))` can be bounded as .. math :: \frac{2 Q^E W^{N+2} (N+2)^r}{1 - Q^F W \exp(r/(N+2))}, again valid when the denominator is positive. To actually evaluate the series, we write the even cosine terms as `w^{2n} + w^{-2n}`, the odd cosine terms as `w (w^{2n} + w^{-2n-2})`, and the sine terms as `w (w^{2n} - w^{-2n-2})`. This way we only need even powers of `w` and `w^{-1}`. The implementation is not yet optimized for real `z`, in which case further work can be saved. This function does not permit aliasing between input and output arguments. .. function:: void acb_modular_theta_const_sum_basecase(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec) .. function:: void acb_modular_theta_const_sum_rs(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong N, slong prec) Computes the truncated theta constant sums `\theta_2 = \sum_{k(k+1) < N} q^{k(k+1)}`, `\theta_3 = \sum_{k^2 < N} q^{k^2}`, `\theta_4 = \sum_{k^2 < N} (-1)^k q^{k^2}`. The *basecase* version uses a minimal addition sequence. The *rs* version uses rectangular splitting. .. function:: void acb_modular_theta_const_sum(acb_t theta2, acb_t theta3, acb_t theta4, const acb_t q, slong prec) Computes the respective theta constants by direct summation (without applying modular transformations). This function selects an appropriate *N*, calls either :func:`acb_modular_theta_const_sum_basecase` or :func:`acb_modular_theta_const_sum_rs` or depending on *N*, and adds a bound for the truncation error. .. function:: void acb_modular_theta_notransform(acb_t theta1, acb_t theta2, acb_t theta3, acb_t theta4, const acb_t z, const acb_t tau, slong prec) Evaluates the Jacobi theta functions `\theta_i(z,\tau)`, `i = 1, 2, 3, 4` simultaneously. This function does not move `\tau` to the fundamental domain. This is generally worse than :func:`acb_modular_theta`, but can be slightly better for moderate input. .. function:: void acb_modular_theta(acb_t theta1, acb_t theta2, acb_t theta3, acb_t theta4, const acb_t z, const acb_t tau, slong prec) Evaluates the Jacobi theta functions `\theta_i(z,\tau)`, `i = 1, 2, 3, 4` simultaneously. This function moves `\tau` to the fundamental domain before calling :func:`acb_modular_theta_sum`. The Dedekind eta function ------------------------------------------------------------------------------- .. function:: void acb_modular_addseq_eta(slong * exponents, slong * aindex, slong * bindex, slong num) Constructs an addition sequence for the first *num* generalized pentagonal numbers (excluding zero), i.e. 1, 2, 5, 7, 12, 15, 22, 26, 35, 40 etc. .. function:: void acb_modular_eta_sum(acb_t eta, const acb_t q, slong prec) Evaluates the Dedekind eta function without the leading 24th root, i.e. .. math :: \exp(-\pi i \tau/12) \eta(\tau) = \sum_{n=-\infty}^{\infty} (-1)^n q^{(3n^2-n)/2} given `q = \exp(2 \pi i \tau)`, by summing the defining series. This function is intended for `|q| \ll 1`. It can be called with any `q`, but will return useless intervals if convergence is not rapid. For general evaluation of the eta function, the user should only call this function after applying a suitable modular transformation. .. function:: int acb_modular_epsilon_arg(const psl2z_t g) Given `g = (a, b; c, d)`, computes an integer `R` such that `\varepsilon(a,b,c,d) = \exp(\pi i R / 12)` is the 24th root of unity in the transformation formula for the Dedekind eta function, .. math :: \eta\left(\frac{a\tau+b}{c\tau+d}\right) = \varepsilon (a,b,c,d) \sqrt{c\tau+d} \eta(\tau). .. function:: void acb_modular_eta(acb_t r, const acb_t tau, slong prec) Computes the Dedekind eta function `\eta(\tau)` given `\tau` in the upper half-plane. This function applies the functional equation to move `\tau` to the fundamental domain before calling :func:`acb_modular_eta_sum`. Modular forms ------------------------------------------------------------------------------- .. function:: void acb_modular_j(acb_t r, const acb_t tau, slong prec) Computes Klein's j-invariant `j(\tau)` given `\tau` in the upper half-plane. The function is normalized so that `j(i) = 1728`. We first move `\tau` to the fundamental domain, which does not change the value of the function. Then we use the formula `j(\tau) = 32 (\theta_2^8+\theta_3^8+\theta_4^8)^3 / (\theta_2 \theta_3 \theta_4)^8` where `\theta_i = \theta_i(0,\tau)`. .. function:: void acb_modular_lambda(acb_t r, const acb_t tau, slong prec) Computes the lambda function `\lambda(\tau) = \theta_2^4(0,\tau) / \theta_3^4(0,\tau)`, which is invariant under modular transformations `(a, b; c, d)` where `a, d` are odd and `b, c` are even. .. function:: void acb_modular_delta(acb_t r, const acb_t tau, slong prec) Computes the modular discriminant `\Delta(\tau) = \eta(\tau)^{24}`, which transforms as .. math :: \Delta\left(\frac{a\tau+b}{c\tau+d}\right) = (c\tau+d)^{12} \Delta(\tau). The modular discriminant is sometimes defined with an extra factor `(2\pi)^{12}`, which we omit in this implementation. .. function:: void acb_modular_eisenstein(acb_ptr r, const acb_t tau, slong len, slong prec) Computes simultaneously the first *len* entries in the sequence of Eisenstein series `G_4(\tau), G_6(\tau), G_8(\tau), \ldots`, defined by .. math :: G_{2k}(\tau) = \sum_{m^2 + n^2 \ne 0} \frac{1}{(m+n\tau )^{2k}} and satisfying .. math :: G_{2k} \left(\frac{a\tau+b}{c\tau+d}\right) = (c\tau+d)^{2k} G_{2k}(\tau). We first evaluate `G_4(\tau)` and `G_6(\tau)` on the fundamental domain using theta functions, and then compute the Eisenstein series of higher index using a recurrence relation. Elliptic functions ------------------------------------------------------------------------------- .. function:: void acb_modular_elliptic_p(acb_t wp, const acb_t z, const acb_t tau, slong prec) Computes Weierstrass's elliptic function .. math :: \wp(z, \tau) = \frac{1}{z^2} + \sum_{n^2+m^2 \ne 0} \left[ \frac{1}{(z+m+n\tau)^2} - \frac{1}{(m+n\tau)^2} \right] which satisfies `\wp(z, \tau) = \wp(z + 1, \tau) = \wp(z + \tau, \tau)`. To evaluate the function efficiently, we use the formula .. math :: \wp(z, \tau) = \pi^2 \theta_2^2(0,\tau) \theta_3^2(0,\tau) \frac{\theta_4^2(z,\tau)}{\theta_1^2(z,\tau)} - \frac{\pi^2}{3} \left[ \theta_3^4(0,\tau) + \theta_3^4(0,\tau)\right]. .. function:: void acb_modular_elliptic_p_zpx(acb_ptr wp, const acb_t z, const acb_t tau, slong len, slong prec) Computes the formal power series `\wp(z + x, \tau) \in \mathbb{C}[[x]]`, truncated to length *len*. In particular, with *len* = 2, simultaneously computes `\wp(z, \tau), \wp'(z, \tau)` which together generate the field of elliptic functions with periods 1 and `\tau`. Elliptic integrals ------------------------------------------------------------------------------- .. function:: void acb_modular_elliptic_k(acb_t w, const acb_t m, slong prec) Computes the complete elliptic integral of the first kind `K(m)`, using the arithmetic-geometric mean: `K(m) = \pi / (2 M(\sqrt{1-m}))`. .. function:: void acb_modular_elliptic_k_cpx(acb_ptr w, const acb_t m, slong len, slong prec) Sets the coefficients in the array *w* to the power series expansion of the complete elliptic integral of the first kind at the point *m* truncated to length *len*, i.e. `K(m+x) \in \mathbb{C}[[x]]`. .. function:: void acb_modular_elliptic_e(acb_t w, const acb_t m, slong prec) Computes the complete elliptic integral of the second kind `E(m)`, which is given by `E(m) = (1-m)(2m K'(m) + K(m))` (where the prime denotes a derivative, not a complementary integral). Class polynomials ------------------------------------------------------------------------------- .. function:: void acb_modular_hilbert_class_poly(fmpz_poly_t res, slong D) Sets *res* to the Hilbert class polynomial of discriminant *D*, defined as .. math :: H_D(x) = \prod_{(a,b,c)} \left(x - j\left(\frac{-b+\sqrt{D}}{2a}\right)\right) where `(a,b,c)` ranges over the primitive reduced positive definite binary quadratic forms of discriminant `b^2 - 4ac = D`. The Hilbert class polynomial is only defined if `D < 0` and *D* is congruent to 0 or 1 mod 4. If some other value of *D* is passed as input, *res* is set to the zero polynomial. arb-2.8.1/doc/source/acb_poly.rst000066400000000000000000001376241264125401100166660ustar00rootroot00000000000000.. _acb-poly: **acb_poly.h** -- polynomials over the complex numbers =============================================================================== An :type:`acb_poly_t` represents a polynomial over the complex numbers, implemented as an array of coefficients of type :type:`acb_struct`. Most functions are provided in two versions: an underscore method which operates directly on pre-allocated arrays of coefficients and generally has some restrictions (such as requiring the lengths to be nonzero and not supporting aliasing of the input and output arrays), and a non-underscore method which performs automatic memory management and handles degenerate cases. Types, macros and constants ------------------------------------------------------------------------------- .. type:: acb_poly_struct .. type:: acb_poly_t Contains a pointer to an array of coefficients (coeffs), the used length (length), and the allocated size of the array (alloc). An *acb_poly_t* is defined as an array of length one of type *acb_poly_struct*, permitting an *acb_poly_t* to be passed by reference. Memory management ------------------------------------------------------------------------------- .. function:: void acb_poly_init(acb_poly_t poly) Initializes the polynomial for use, setting it to the zero polynomial. .. function:: void acb_poly_clear(acb_poly_t poly) Clears the polynomial, deallocating all coefficients and the coefficient array. .. function:: void acb_poly_fit_length(acb_poly_t poly, slong len) Makes sures that the coefficient array of the polynomial contains at least *len* initialized coefficients. .. function:: void _acb_poly_set_length(acb_poly_t poly, slong len) Directly changes the length of the polynomial, without allocating or deallocating coefficients. The value shold not exceed the allocation length. .. function:: void _acb_poly_normalise(acb_poly_t poly) Strips any trailing coefficients which are identical to zero. .. function:: void acb_poly_swap(acb_poly_t poly1, acb_poly_t poly2) Swaps *poly1* and *poly2* efficiently. Basic properties and manipulation ------------------------------------------------------------------------------- .. function:: slong acb_poly_length(const acb_poly_t poly) Returns the length of *poly*, i.e. zero if *poly* is identically zero, and otherwise one more than the index of the highest term that is not identically zero. .. function:: slong acb_poly_degree(const acb_poly_t poly) Returns the degree of *poly*, defined as one less than its length. Note that if one or several leading coefficients are balls containing zero, this value can be larger than the true degree of the exact polynomial represented by *poly*, so the return value of this function is effectively an upper bound. .. function:: void acb_poly_zero(acb_poly_t poly) Sets *poly* to the zero polynomial. .. function:: void acb_poly_one(acb_poly_t poly) Sets *poly* to the constant polynomial 1. .. function:: void acb_poly_set(acb_poly_t dest, const acb_poly_t src) Sets *dest* to a copy of *src*. .. function:: void acb_poly_set_round(acb_poly_t dest, const acb_poly_t src, slong prec) Sets *dest* to a copy of *src*, rounded to *prec* bits. .. function:: void acb_poly_set_coeff_si(acb_poly_t poly, slong n, slong c) .. function:: void acb_poly_set_coeff_acb(acb_poly_t poly, slong n, const acb_t c) Sets the coefficient with index *n* in *poly* to the value *c*. We require that *n* is nonnegative. .. function:: void acb_poly_get_coeff_acb(acb_t v, const acb_poly_t poly, slong n) Sets *v* to the value of the coefficient with index *n* in *poly*. We require that *n* is nonnegative. .. macro:: acb_poly_get_coeff_ptr(poly, n) Given `n \ge 0`, returns a pointer to coefficient *n* of *poly*, or *NULL* if *n* exceeds the length of *poly*. .. function:: void _acb_poly_shift_right(acb_ptr res, acb_srcptr poly, slong len, slong n) .. function:: void acb_poly_shift_right(acb_poly_t res, const acb_poly_t poly, slong n) Sets *res* to *poly* divided by `x^n`, throwing away the lower coefficients. We require that *n* is nonnegative. .. function:: void _acb_poly_shift_left(acb_ptr res, acb_srcptr poly, slong len, slong n) .. function:: void acb_poly_shift_left(acb_poly_t res, const acb_poly_t poly, slong n) Sets *res* to *poly* multiplied by `x^n`. We require that *n* is nonnegative. .. function:: void acb_poly_truncate(acb_poly_t poly, slong n) Truncates *poly* to have length at most *n*, i.e. degree strictly smaller than *n*. Input and output ------------------------------------------------------------------------------- .. function:: void acb_poly_printd(const acb_poly_t poly, slong digits) Prints the polynomial as an array of coefficients, printing each coefficient using *arb_printd*. Random generation ------------------------------------------------------------------------------- .. function:: void acb_poly_randtest(acb_poly_t poly, flint_rand_t state, slong len, slong prec, slong mag_bits) Creates a random polynomial with length at most *len*. Comparisons ------------------------------------------------------------------------------- .. function:: int acb_poly_equal(const acb_poly_t A, const acb_poly_t B) Returns nonzero iff *A* and *B* are identical as interval polynomials. .. function:: int acb_poly_contains(const acb_poly_t poly1, const acb_poly_t poly2) .. function:: int acb_poly_contains_fmpz_poly(const acb_poly_t poly1, const fmpz_poly_t poly2) .. function:: int acb_poly_contains_fmpq_poly(const acb_poly_t poly1, const fmpq_poly_t poly2) Returns nonzero iff *poly2* is contained in *poly1*. .. function:: int _acb_poly_overlaps(acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2) .. function:: int acb_poly_overlaps(const acb_poly_t poly1, const acb_poly_t poly2) Returns nonzero iff *poly1* overlaps with *poly2*. The underscore function requires that *len1* ist at least as large as *len2*. .. function:: int acb_poly_get_unique_fmpz_poly(fmpz_poly_t z, const acb_poly_t x) If *x* contains a unique integer polynomial, sets *z* to that value and returns nonzero. Otherwise (if *x* represents no integers or more than one integer), returns zero, possibly partially modifying *z*. .. function:: int acb_poly_is_real(const acb_poly_t poly) Returns nonzero iff all coefficients in *poly* have zero imaginary part. Conversions ------------------------------------------------------------------------------- .. function:: void acb_poly_set_fmpz_poly(acb_poly_t poly, const fmpz_poly_t re, slong prec) .. function:: void acb_poly_set2_fmpz_poly(acb_poly_t poly, const fmpz_poly_t re, const fmpz_poly_t im, slong prec) .. function:: void acb_poly_set_arb_poly(acb_poly_t poly, const arb_poly_t re) .. function:: void acb_poly_set2_arb_poly(acb_poly_t poly, const arb_poly_t re, const arb_poly_t im) .. function:: void acb_poly_set_fmpq_poly(acb_poly_t poly, const fmpq_poly_t re, slong prec) .. function:: void acb_poly_set2_fmpq_poly(acb_poly_t poly, const fmpq_poly_t re, const fmpq_poly_t im, slong prec) Sets *poly* to the given real part *re* plus the imaginary part *im*, both rounded to *prec* bits. .. function:: void acb_poly_set_acb(acb_poly_t poly, slong src) .. function:: void acb_poly_set_si(acb_poly_t poly, slong src) Sets *poly* to *src*. Bounds ------------------------------------------------------------------------------- .. function:: void _acb_poly_majorant(arb_ptr res, acb_srcptr poly, slong len, slong prec) .. function:: void acb_poly_majorant(arb_poly_t res, const acb_poly_t poly, slong prec) Sets *res* to an exact real polynomial whose coefficients are upper bounds for the absolute values of the coefficients in *poly*, rounded to *prec* bits. Arithmetic ------------------------------------------------------------------------------- .. function:: void _acb_poly_add(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) Sets *{C, max(lenA, lenB)}* to the sum of *{A, lenA}* and *{B, lenB}*. Allows aliasing of the input and output operands. .. function:: void acb_poly_add(acb_poly_t C, const acb_poly_t A, const acb_poly_t B, slong prec) .. function:: void acb_poly_add_si(acb_poly_t C, const acb_poly_t A, slong B, slong prec) Sets *C* to the sum of *A* and *B*. .. function:: void _acb_poly_sub(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) Sets *{C, max(lenA, lenB)}* to the difference of *{A, lenA}* and *{B, lenB}*. Allows aliasing of the input and output operands. .. function:: void acb_poly_sub(acb_poly_t C, const acb_poly_t A, const acb_poly_t B, slong prec) Sets *C* to the difference of *A* and *B*. .. function:: void acb_poly_neg(acb_poly_t C, const acb_poly_t A) Sets *C* to the negation of *A*. .. function:: void acb_poly_scalar_mul_2exp_si(acb_poly_t C, const acb_poly_t A, slong c) Sets *C* to *A* multiplied by `2^c`. .. function:: void _acb_poly_mullow_classical(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong n, slong prec) .. function:: void _acb_poly_mullow_transpose(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong n, slong prec) .. function:: void _acb_poly_mullow_transpose_gauss(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong n, slong prec) .. function:: void _acb_poly_mullow(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong n, slong prec) Sets *{C, n}* to the product of *{A, lenA}* and *{B, lenB}*, truncated to length *n*. The output is not allowed to be aliased with either of the inputs. We require `\mathrm{lenA} \ge \mathrm{lenB} > 0`, `n > 0`, `\mathrm{lenA} + \mathrm{lenB} - 1 \ge n`. The *classical* version uses a plain loop. The *transpose* version evaluates the product using four real polynomial multiplications (via :func:`_arb_poly_mullow`). The *transpose_gauss* version evaluates the product using three real polynomial multiplications. This is almost always faster than *transpose*, but has worse numerical stability when the coefficients vary in magnitude. The default function :func:`_acb_poly_mullow` automatically switches been *classical* and *transpose* multiplication. If the input pointers are identical (and the lengths are the same), they are assumed to represent the same polynomial, and its square is computed. .. function:: void acb_poly_mullow_classical(acb_poly_t C, const acb_poly_t A, const acb_poly_t B, slong n, slong prec) .. function:: void acb_poly_mullow_transpose(acb_poly_t C, const acb_poly_t A, const acb_poly_t B, slong n, slong prec) .. function:: void acb_poly_mullow_transpose_gauss(acb_poly_t C, const acb_poly_t A, const acb_poly_t B, slong n, slong prec) .. function:: void acb_poly_mullow(acb_poly_t C, const acb_poly_t A, const acb_poly_t B, slong n, slong prec) Sets *C* to the product of *A* and *B*, truncated to length *n*. If the same variable is passed for *A* and *B*, sets *C* to the square of *A* truncated to length *n*. .. function:: void _acb_poly_mul(acb_ptr C, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) Sets *{C, lenA + lenB - 1}* to the product of *{A, lenA}* and *{B, lenB}*. The output is not allowed to be aliased with either of the inputs. We require `\mathrm{lenA} \ge \mathrm{lenB} > 0`. This function is implemented as a simple wrapper for :func:`_acb_poly_mullow`. If the input pointers are identical (and the lengths are the same), they are assumed to represent the same polynomial, and its square is computed. .. function:: void acb_poly_mul(acb_poly_t C, const acb_poly_t A1, const acb_poly_t B2, slong prec) Sets *C* to the product of *A* and *B*. If the same variable is passed for *A* and *B*, sets *C* to the square of *A*. .. function:: void _acb_poly_inv_series(acb_ptr Qinv, acb_srcptr Q, slong Qlen, slong len, slong prec) Sets *{Qinv, len}* to the power series inverse of *{Q, Qlen}*. Uses Newton iteration. .. function:: void acb_poly_inv_series(acb_poly_t Qinv, const acb_poly_t Q, slong n, slong prec) Sets *Qinv* to the power series inverse of *Q*. .. function:: void _acb_poly_div_series(acb_ptr Q, acb_srcptr A, slong Alen, acb_srcptr B, slong Blen, slong n, slong prec) Sets *{Q, n}* to the power series quotient of *{A, Alen}* by *{B, Blen}*. Uses Newton iteration followed by multiplication. .. function:: void acb_poly_div_series(acb_poly_t Q, const acb_poly_t A, const acb_poly_t B, slong n, slong prec) Sets *Q* to the power series quotient *A* divided by *B*, truncated to length *n*. .. function:: void _acb_poly_div(acb_ptr Q, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) .. function:: void _acb_poly_rem(acb_ptr R, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) .. function:: void _acb_poly_divrem(acb_ptr Q, acb_ptr R, acb_srcptr A, slong lenA, acb_srcptr B, slong lenB, slong prec) .. function:: void acb_poly_divrem(acb_poly_t Q, acb_poly_t R, const acb_poly_t A, const acb_poly_t B, slong prec) Performs polynomial division with remainder, computing a quotient `Q` and a remainder `R` such that `A = BQ + R`. The implementation reverses the inputs and performs power series division. If the leading coefficient of `B` contains zero (or if `B` is identically zero), returns 0 indicating failure without modifying the outputs. Otherwise returns nonzero. .. function:: void _acb_poly_div_root(acb_ptr Q, acb_t R, acb_srcptr A, slong len, const acb_t c, slong prec) Divides `A` by the polynomial `x - c`, computing the quotient `Q` as well as the remainder `R = f(c)`. Composition ------------------------------------------------------------------------------- .. function:: void _acb_poly_compose_horner(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) .. function:: void acb_poly_compose_horner(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) .. function:: void _acb_poly_compose_divconquer(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) .. function:: void acb_poly_compose_divconquer(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) .. function:: void _acb_poly_compose(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong prec) .. function:: void acb_poly_compose(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong prec) Sets *res* to the composition `h(x) = f(g(x))` where `f` is given by *poly1* and `g` is given by *poly2*, respectively using Horner's rule, divide-and-conquer, and an automatic choice between the two algorithms. The underscore methods do not support aliasing of the output with either input polynomial. .. function:: void _acb_poly_compose_series_horner(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) .. function:: void acb_poly_compose_series_horner(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) .. function:: void _acb_poly_compose_series_brent_kung(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) .. function:: void acb_poly_compose_series_brent_kung(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) .. function:: void _acb_poly_compose_series(acb_ptr res, acb_srcptr poly1, slong len1, acb_srcptr poly2, slong len2, slong n, slong prec) .. function:: void acb_poly_compose_series(acb_poly_t res, const acb_poly_t poly1, const acb_poly_t poly2, slong n, slong prec) Sets *res* to the power series composition `h(x) = f(g(x))` truncated to order `O(x^n)` where `f` is given by *poly1* and `g` is given by *poly2*, respectively using Horner's rule, the Brent-Kung baby step-giant step algorithm, and an automatic choice between the two algorithms. We require that the constant term in `g(x)` is exactly zero. The underscore methods do not support aliasing of the output with either input polynomial. .. function:: void _acb_poly_revert_series_lagrange(acb_ptr h, acb_srcptr f, slong flen, slong n, slong prec) .. function:: void acb_poly_revert_series_lagrange(acb_poly_t h, const acb_poly_t f, slong n, slong prec) .. function:: void _acb_poly_revert_series_newton(acb_ptr h, acb_srcptr f, slong flen, slong n, slong prec) .. function:: void acb_poly_revert_series_newton(acb_poly_t h, const acb_poly_t f, slong n, slong prec) .. function:: void _acb_poly_revert_series_lagrange_fast(acb_ptr h, acb_srcptr f, slong flen, slong n, slong prec) .. function:: void acb_poly_revert_series_lagrange_fast(acb_poly_t h, const acb_poly_t f, slong n, slong prec) .. function:: void _acb_poly_revert_series(acb_ptr h, acb_srcptr f, slong flen, slong n, slong prec) .. function:: void acb_poly_revert_series(acb_poly_t h, const acb_poly_t f, slong n, slong prec) Sets `h` to the power series reversion of `f`, i.e. the expansion of the compositional inverse function `f^{-1}(x)`, truncated to order `O(x^n)`, using respectively Lagrange inversion, Newton iteration, fast Lagrange inversion, and a default algorithm choice. We require that the constant term in `f` is exactly zero and that the linear term is nonzero. The underscore methods assume that *flen* is at least 2, and do not support aliasing. Evaluation ------------------------------------------------------------------------------- .. function:: void _acb_poly_evaluate_horner(acb_t y, acb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void acb_poly_evaluate_horner(acb_t y, const acb_poly_t f, const acb_t x, slong prec) .. function:: void _acb_poly_evaluate_rectangular(acb_t y, acb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void acb_poly_evaluate_rectangular(acb_t y, const acb_poly_t f, const acb_t x, slong prec) .. function:: void _acb_poly_evaluate(acb_t y, acb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void acb_poly_evaluate(acb_t y, const acb_poly_t f, const acb_t x, slong prec) Sets `y = f(x)`, evaluated respectively using Horner's rule, rectangular splitting, and an automatic algorithm choice. .. function:: void _acb_poly_evaluate2_horner(acb_t y, acb_t z, acb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void acb_poly_evaluate2_horner(acb_t y, acb_t z, const acb_poly_t f, const acb_t x, slong prec) .. function:: void _acb_poly_evaluate2_rectangular(acb_t y, acb_t z, acb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void acb_poly_evaluate2_rectangular(acb_t y, acb_t z, const acb_poly_t f, const acb_t x, slong prec) .. function:: void _acb_poly_evaluate2(acb_t y, acb_t z, acb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void acb_poly_evaluate2(acb_t y, acb_t z, const acb_poly_t f, const acb_t x, slong prec) Sets `y = f(x), z = f'(x)`, evaluated respectively using Horner's rule, rectangular splitting, and an automatic algorithm choice. When Horner's rule is used, the only advantage of evaluating the function and its derivative simultaneously is that one does not have to generate the derivative polynomial explicitly. With the rectangular splitting algorithm, the powers can be reused, making simultaneous evaluation slightly faster. Product trees ------------------------------------------------------------------------------- .. function:: void _acb_poly_product_roots(acb_ptr poly, acb_srcptr xs, slong n, slong prec) .. function:: void acb_poly_product_roots(acb_poly_t poly, acb_srcptr xs, slong n, slong prec) Generates the polynomial `(x-x_0)(x-x_1)\cdots(x-x_{n-1})`. .. function:: acb_ptr * _acb_poly_tree_alloc(slong len) Returns an initialized data structured capable of representing a remainder tree (product tree) of *len* roots. .. function:: void _acb_poly_tree_free(acb_ptr * tree, slong len) Deallocates a tree structure as allocated using *_acb_poly_tree_alloc*. .. function:: void _acb_poly_tree_build(acb_ptr * tree, acb_srcptr roots, slong len, slong prec) Constructs a product tree from a given array of *len* roots. The tree structure must be pre-allocated to the specified length using :func:`_acb_poly_tree_alloc`. Multipoint evaluation ------------------------------------------------------------------------------- .. function:: void _acb_poly_evaluate_vec_iter(acb_ptr ys, acb_srcptr poly, slong plen, acb_srcptr xs, slong n, slong prec) .. function:: void acb_poly_evaluate_vec_iter(acb_ptr ys, const acb_poly_t poly, acb_srcptr xs, slong n, slong prec) Evaluates the polynomial simultaneously at *n* given points, calling :func:`_acb_poly_evaluate` repeatedly. .. function:: void _acb_poly_evaluate_vec_fast_precomp(acb_ptr vs, acb_srcptr poly, slong plen, acb_ptr * tree, slong len, slong prec) .. function:: void _acb_poly_evaluate_vec_fast(acb_ptr ys, acb_srcptr poly, slong plen, acb_srcptr xs, slong n, slong prec) .. function:: void acb_poly_evaluate_vec_fast(acb_ptr ys, const acb_poly_t poly, acb_srcptr xs, slong n, slong prec) Evaluates the polynomial simultaneously at *n* given points, using fast multipoint evaluation. Interpolation ------------------------------------------------------------------------------- .. function:: void _acb_poly_interpolate_newton(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) .. function:: void acb_poly_interpolate_newton(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) Recovers the unique polynomial of length at most *n* that interpolates the given *x* and *y* values. This implementation first interpolates in the Newton basis and then converts back to the monomial basis. .. function:: void _acb_poly_interpolate_barycentric(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) .. function:: void acb_poly_interpolate_barycentric(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) Recovers the unique polynomial of length at most *n* that interpolates the given *x* and *y* values. This implementation uses the barycentric form of Lagrange interpolation. .. function:: void _acb_poly_interpolation_weights(acb_ptr w, acb_ptr * tree, slong len, slong prec) .. function:: void _acb_poly_interpolate_fast_precomp(acb_ptr poly, acb_srcptr ys, acb_ptr * tree, acb_srcptr weights, slong len, slong prec) .. function:: void _acb_poly_interpolate_fast(acb_ptr poly, acb_srcptr xs, acb_srcptr ys, slong len, slong prec) .. function:: void acb_poly_interpolate_fast(acb_poly_t poly, acb_srcptr xs, acb_srcptr ys, slong n, slong prec) Recovers the unique polynomial of length at most *n* that interpolates the given *x* and *y* values, using fast Lagrange interpolation. The precomp function takes a precomputed product tree over the *x* values and a vector of interpolation weights as additional inputs. Differentiation ------------------------------------------------------------------------------- .. function:: void _acb_poly_derivative(acb_ptr res, acb_srcptr poly, slong len, slong prec) Sets *{res, len - 1}* to the derivative of *{poly, len}*. Allows aliasing of the input and output. .. function:: void acb_poly_derivative(acb_poly_t res, const acb_poly_t poly, slong prec) Sets *res* to the derivative of *poly*. .. function:: void _acb_poly_integral(acb_ptr res, acb_srcptr poly, slong len, slong prec) Sets *{res, len}* to the integral of *{poly, len - 1}*. Allows aliasing of the input and output. .. function:: void acb_poly_integral(acb_poly_t res, const acb_poly_t poly, slong prec) Sets *res* to the integral of *poly*. Elementary functions ------------------------------------------------------------------------------- .. function:: void _acb_poly_pow_ui_trunc_binexp(acb_ptr res, acb_srcptr f, slong flen, ulong exp, slong len, slong prec) Sets *{res, len}* to *{f, flen}* raised to the power *exp*, truncated to length *len*. Requires that *len* is no longer than the length of the power as computed without truncation (i.e. no zero-padding is performed). Does not support aliasing of the input and output, and requires that *flen* and *len* are positive. Uses binary expontiation. .. function:: void acb_poly_pow_ui_trunc_binexp(acb_poly_t res, const acb_poly_t poly, ulong exp, slong len, slong prec) Sets *res* to *poly* raised to the power *exp*, truncated to length *len*. Uses binary exponentiation. .. function:: void _acb_poly_pow_ui(acb_ptr res, acb_srcptr f, slong flen, ulong exp, slong prec) Sets *res* to *{f, flen}* raised to the power *exp*. Does not support aliasing of the input and output, and requires that *flen* is positive. .. function:: void acb_poly_pow_ui(acb_poly_t res, const acb_poly_t poly, ulong exp, slong prec) Sets *res* to *poly* raised to the power *exp*. .. function:: void _acb_poly_pow_series(acb_ptr h, acb_srcptr f, slong flen, acb_srcptr g, slong glen, slong len, slong prec) Sets *{h, len}* to the power series `f(x)^{g(x)} = \exp(g(x) \log f(x))` truncated to length *len*. This function detects special cases such as *g* being an exact small integer or `\pm 1/2`, and computes such powers more efficiently. This function does not support aliasing of the output with either of the input operands. It requires that all lengths are positive, and assumes that *flen* and *glen* do not exceed *len*. .. function:: void acb_poly_pow_series(acb_poly_t h, const acb_poly_t f, const acb_poly_t g, slong len, slong prec) Sets *h* to the power series `f(x)^{g(x)} = \exp(g(x) \log f(x))` truncated to length *len*. This function detects special cases such as *g* being an exact small integer or `\pm 1/2`, and computes such powers more efficiently. .. function:: void _acb_poly_pow_acb_series(acb_ptr h, acb_srcptr f, slong flen, const acb_t g, slong len, slong prec) Sets *{h, len}* to the power series `f(x)^g = \exp(g \log f(x))` truncated to length *len*. This function detects special cases such as *g* being an exact small integer or `\pm 1/2`, and computes such powers more efficiently. This function does not support aliasing of the output with either of the input operands. It requires that all lengths are positive, and assumes that *flen* does not exceed *len*. .. function:: void acb_poly_pow_acb_series(acb_poly_t h, const acb_poly_t f, const acb_t g, slong len, slong prec) Sets *h* to the power series `f(x)^g = \exp(g \log f(x))` truncated to length *len*. .. function:: void _acb_poly_sqrt_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_sqrt_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) Sets *g* to the power series square root of *h*, truncated to length *n*. Uses division-free Newton iteration for the reciprocal square root, followed by a multiplication. The underscore method does not support aliasing of the input and output arrays. It requires that *hlen* and *n* are greater than zero. .. function:: void _acb_poly_rsqrt_series(acb_ptr g, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_rsqrt_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) Sets *g* to the reciprocal power series square root of *h*, truncated to length *n*. Uses division-free Newton iteration. The underscore method does not support aliasing of the input and output arrays. It requires that *hlen* and *n* are greater than zero. .. function:: void _acb_poly_log_series(acb_ptr res, acb_srcptr f, slong flen, slong n, slong prec) .. function:: void acb_poly_log_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec) Sets *res* to the power series logarithm of *f*, truncated to length *n*. Uses the formula `\log(f(x)) = \int f'(x) / f(x) dx`, adding the logarithm of the constant term in *f* as the constant of integration. The underscore method supports aliasing of the input and output arrays. It requires that *flen* and *n* are greater than zero. .. function:: void _acb_poly_atan_series(acb_ptr res, acb_srcptr f, slong flen, slong n, slong prec) .. function:: void acb_poly_atan_series(acb_poly_t res, const acb_poly_t f, slong n, slong prec) Sets *res* the power series inverse tangent of *f*, truncated to length *n*. Uses the formula .. math :: \tan^{-1}(f(x)) = \int f'(x) / (1+f(x)^2) dx, adding the function of the constant term in *f* as the constant of integration. The underscore method supports aliasing of the input and output arrays. It requires that *flen* and *n* are greater than zero. .. function:: void _acb_poly_exp_series_basecase(acb_ptr f, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_exp_series_basecase(acb_poly_t f, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_exp_series(acb_ptr f, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_exp_series(acb_poly_t f, const acb_poly_t h, slong n, slong prec) Sets `f` to the power series exponential of `h`, truncated to length `n`. The basecase version uses a simple recurrence for the coefficients, requiring `O(nm)` operations where `m` is the length of `h`. The main implementation uses Newton iteration, starting from a small number of terms given by the basecase algorithm. The complexity is `O(M(n))`. Redundant operations in the Newton iteration are avoided by using the scheme described in [HZ2004]_. The underscore methods support aliasing and allow the input to be shorter than the output, but require the lengths to be nonzero. .. function:: void _acb_poly_sin_cos_series_basecase(acb_ptr s, acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec, int times_pi) .. function:: void acb_poly_sin_cos_series_basecase(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec, int times_pi) .. function:: void _acb_poly_sin_cos_series_tangent(acb_ptr s, acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec, int times_pi) .. function:: void acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec, int times_pi) .. function:: void _acb_poly_sin_cos_series(acb_ptr s, acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_sin_cos_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec) Sets *s* and *c* to the power series sine and cosine of *h*, computed simultaneously. The *basecase* version uses a simple recurrence for the coefficients, requiring `O(nm)` operations where `m` is the length of `h`. The *tangent* version uses the tangent half-angle formulas to compute the sine and cosine via :func:`_acb_poly_tan_series`. This requires `O(M(n))` operations. When `h = h_0 + h_1` where the constant term `h_0` is nonzero, the evaluation is done as `\sin(h_0 + h_1) = \cos(h_0) \sin(h_1) + \sin(h_0) \cos(h_1)`, `\cos(h_0 + h_1) = \cos(h_0) \cos(h_1) - \sin(h_0) \sin(h_1)`, to improve accuracy and avoid dividing by zero at the poles of the tangent function. The default version automatically selects between the *basecase* and *tangent* algorithms depending on the input. The *basecase* and *tangent* versions take a flag *times_pi* specifying that the input is to be multiplied by `\pi`. The underscore methods support aliasing and require the lengths to be nonzero. .. function:: void _acb_poly_sin_series(acb_ptr s, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_sin_series(acb_poly_t s, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_cos_series(acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_cos_series(acb_poly_t c, const acb_poly_t h, slong n, slong prec) Respectively evaluates the power series sine or cosine. These functions simply wrap :func:`_acb_poly_sin_cos_series`. The underscore methods support aliasing and require the lengths to be nonzero. .. function:: void _acb_poly_tan_series(acb_ptr g, acb_srcptr h, slong hlen, slong len, slong prec) .. function:: void acb_poly_tan_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec) Sets *g* to the power series tangent of *h*. For small *n* takes the quotient of the sine and cosine as computed using the basecase algorithm. For large *n*, uses Newton iteration to invert the inverse tangent series. The complexity is `O(M(n))`. The underscore version does not support aliasing, and requires the lengths to be nonzero. .. function:: void _acb_poly_sin_cos_pi_series(acb_ptr s, acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_sin_pi_series(acb_ptr s, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_sin_pi_series(acb_poly_t s, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_cos_pi_series(acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_cos_pi_series(acb_poly_t c, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_cot_pi_series(acb_ptr c, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_cot_pi_series(acb_poly_t c, const acb_poly_t h, slong n, slong prec) Compute the respective trigonometric functions of the input multiplied by `\pi`. Gamma function ------------------------------------------------------------------------------- .. function:: void _acb_poly_gamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_gamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_rgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_rgamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_lgamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_lgamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec) .. function:: void _acb_poly_digamma_series(acb_ptr res, acb_srcptr h, slong hlen, slong n, slong prec) .. function:: void acb_poly_digamma_series(acb_poly_t res, const acb_poly_t h, slong n, slong prec) Sets *res* to the series expansion of `\Gamma(h(x))`, `1/\Gamma(h(x))`, or `\log \Gamma(h(x))`, `\psi(h(x))`, truncated to length *n*. These functions first generate the Taylor series at the constant term of *h*, and then call :func:`_acb_poly_compose_series`. The Taylor coefficients are generated using Stirling's series. The underscore methods support aliasing of the input and output arrays, and require that *hlen* and *n* are greater than zero. .. function:: void _acb_poly_rising_ui_series(acb_ptr res, acb_srcptr f, slong flen, ulong r, slong trunc, slong prec) .. function:: void acb_poly_rising_ui_series(acb_poly_t res, const acb_poly_t f, ulong r, slong trunc, slong prec) Sets *res* to the rising factorial `(f) (f+1) (f+2) \cdots (f+r-1)`, truncated to length *trunc*. The underscore method assumes that *flen*, *r* and *trunc* are at least 1, and does not support aliasing. Uses binary splitting. Power sums ------------------------------------------------------------------------------- .. function:: void _acb_poly_powsum_series_naive(acb_ptr z, const acb_t s, const acb_t a, const acb_t q, slong n, slong len, slong prec) .. function:: void _acb_poly_powsum_series_naive_threaded(acb_ptr z, const acb_t s, const acb_t a, const acb_t q, slong n, slong len, slong prec) Computes .. math :: z = S(s,a,n) = \sum_{k=0}^{n-1} \frac{q^k}{(k+a)^{s+t}} as a power series in `t` truncated to length *len*. This function evaluates the sum naively term by term. The *threaded* version splits the computation over the number of threads returned by *flint_get_num_threads()*. .. function:: void _acb_poly_powsum_one_series_sieved(acb_ptr z, const acb_t s, slong n, slong len, slong prec) Computes .. math :: z = S(s,1,n) \sum_{k=1}^n \frac{1}{k^{s+t}} as a power series in `t` truncated to length *len*. This function stores a table of powers that have already been calculated, computing `(ij)^r` as `i^r j^r` whenever `k = ij` is composite. As a further optimization, it groups all even `k` and evaluates the sum as a polynomial in `2^{-(s+t)}`. This scheme requires about `n / \log n` powers, `n / 2` multiplications, and temporary storage of `n / 6` power series. Due to the extra power series multiplications, it is only faster than the naive algorithm when *len* is small. Zeta function ------------------------------------------------------------------------------- .. function:: void _acb_poly_zeta_em_choose_param(mag_t bound, ulong * N, ulong * M, const acb_t s, const acb_t a, slong d, slong target, slong prec) Chooses *N* and *M* for Euler-Maclaurin summation of the Hurwitz zeta function, using a default algorithm. .. function:: void _acb_poly_zeta_em_bound1(mag_t bound, const acb_t s, const acb_t a, slong N, slong M, slong d, slong wp) .. function:: void _acb_poly_zeta_em_bound(arb_ptr vec, const acb_t s, const acb_t a, ulong N, ulong M, slong d, slong wp) Compute bounds for Euler-Maclaurin evaluation of the Hurwitz zeta function or its power series, using the formulas in [Joh2013]_. .. function:: void _acb_poly_zeta_em_tail_naive(acb_ptr z, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong len, slong prec) .. function:: void _acb_poly_zeta_em_tail_bsplit(acb_ptr z, const acb_t s, const acb_t Na, acb_srcptr Nasx, slong M, slong len, slong prec) Evaluates the tail in the Euler-Maclaurin sum for the Hurwitz zeta function, respectively using the naive recurrence and binary splitting. .. function:: void _acb_poly_zeta_em_sum(acb_ptr z, const acb_t s, const acb_t a, int deflate, ulong N, ulong M, slong d, slong prec) Evaluates the truncated Euler-Maclaurin sum of order `N, M` for the length-*d* truncated Taylor series of the Hurwitz zeta function `\zeta(s,a)` at `s`, using a working precision of *prec* bits. With `a = 1`, this gives the usual Riemann zeta function. If *deflate* is nonzero, `\zeta(s,a) - 1/(s-1)` is evaluated (which permits series expansion at `s = 1`). .. function:: void _acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate, slong d, slong prec) Computes the series expansion of `\zeta(s+x,a)` (or `\zeta(s+x,a) - 1/(s+x-1)` if *deflate* is nonzero) to order *d*. This function wraps :func:`_acb_poly_zeta_em_sum`, automatically choosing default values for `N, M` using :func:`_acb_poly_zeta_em_choose_param` to target an absolute truncation error of `2^{-\operatorname{prec}}`. .. function:: void _acb_poly_zeta_series(acb_ptr res, acb_srcptr h, slong hlen, const acb_t a, int deflate, slong len, slong prec) .. function:: void acb_poly_zeta_series(acb_poly_t res, const acb_poly_t f, const acb_t a, int deflate, slong n, slong prec) Sets *res* to the Hurwitz zeta function `\zeta(s,a)` where `s` a power series and `a` is a constant, truncated to length *n*. To evaluate the usual Riemann zeta function, set `a = 1`. If *deflate* is nonzero, evaluates `\zeta(s,a) + 1/(1-s)`, which is well-defined as a limit when the constant term of `s` is 1. In particular, expanding `\zeta(s,a) + 1/(1-s)` with `s = 1+x` gives the Stieltjes constants .. math :: \sum_{k=0}^{n-1} \frac{(-1)^k}{k!} \gamma_k(a) x^k`. If `a = 1`, this implementation uses the reflection formula if the midpoint of the constant term of `s` is negative. Other special functions ------------------------------------------------------------------------------- .. function:: void _acb_poly_polylog_cpx_small(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec) .. function:: void _acb_poly_polylog_cpx_zeta(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec) .. function:: void _acb_poly_polylog_cpx(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec) Sets *w* to the Taylor series with respect to *x* of the polylogarithm `\operatorname{Li}_{s+x}(z)`, where *s* and *z* are given complex constants. The output is computed to length *len* which must be positive. Aliasing between *w* and *s* or *z* is not permitted. The *small* version uses the standard power series expansion with respect to *z*, convergent when `|z| < 1`. The *zeta* version evaluates the polylogarithm as a sum of two Hurwitz zeta functions. The default version automatically delegates to the *small* version when *z* is close to zero, and the *zeta* version otherwise. For further details, see :ref:`algorithms_polylogarithms`. .. function:: void _acb_poly_polylog_series(acb_ptr w, acb_srcptr s, slong slen, const acb_t z, slong len, slong prec) .. function:: void acb_poly_polylog_series(acb_poly_t w, const acb_poly_t s, const acb_t z, slong len, slong prec) Sets *w* to the polylogarithm `\operatorname{Li}_{s}(z)` where *s* is a given power series, truncating the output to length *len*. The underscore method requires all lengths to be positive and supports aliasing between all inputs and outputs. .. function:: void _acb_poly_erf_series(acb_ptr res, acb_srcptr z, slong zlen, slong n, slong prec) .. function:: void acb_poly_erf_series(acb_poly_t res, const acb_poly_t z, slong n, slong prec) Sets *res* to the error function of the power series *z*, truncated to length *n*. .. function:: void _acb_poly_upper_gamma_series(acb_ptr res, acb_t s, acb_srcptr z, slong zlen, slong n, slong prec) .. function:: void acb_poly_upper_gamma_series(acb_poly_t res, const acb_t s, const acb_poly_t z, slong n, slong prec) Sets *res* to the upper incomplete gamma function `\Gamma(s,z)` where *s* is a constant and *z* is a power series, truncated to length *n*. .. function:: void _acb_poly_agm1_series(acb_ptr res, acb_srcptr z, slong zlen, slong len, slong prec) .. function:: void acb_poly_agm1_series(acb_poly_t res, const acb_poly_t z, slong n, slong prec) Sets *res* to the arithmetic-geometric mean of 1 and the power series *z*, truncated to length *n*. .. function:: void _acb_poly_elliptic_k_series(acb_ptr res, acb_srcptr z, slong zlen, slong len, slong prec) .. function:: void acb_poly_elliptic_k_series(acb_poly_t res, const acb_poly_t z, slong n, slong prec) Sets *res* to the complete elliptic integral of the first kind of the power series *z*, truncated to length *n*. .. function:: void _acb_poly_elliptic_p_series(acb_ptr res, acb_srcptr z, slong zlen, const acb_t tau, slong len, slong prec) .. function:: void acb_poly_elliptic_p_series(acb_poly_t res, const acb_poly_t z, const acb_t tau, slong n, slong prec) Sets *res* to the Weierstrass elliptic function of the power series *z*, with periods 1 and *tau*, truncated to length *n*. Root-finding ------------------------------------------------------------------------------- .. function:: void _acb_poly_root_bound_fujiwara(mag_t bound, acb_srcptr poly, slong len) .. function:: void acb_poly_root_bound_fujiwara(mag_t bound, acb_poly_t poly) Sets *bound* to an upper bound for the magnitude of all the complex roots of *poly*. Uses Fujiwara's bound .. math :: 2 \max \left\{\left|\frac{a_{n-1}}{a_n}\right|, \left|\frac{a_{n-2}}{a_n}\right|^{1/2}, \cdots, \left|\frac{a_1}{a_n}\right|^{1/(n-1)}, \left|\frac{a_0}{2a_n}\right|^{1/n} \right\} where `a_0, \ldots, a_n` are the coefficients of *poly*. .. function:: void _acb_poly_root_inclusion(acb_t r, const acb_t m, acb_srcptr poly, acb_srcptr polyder, slong len, slong prec) Given any complex number `m`, and a nonconstant polynomial `f` and its derivative `f'`, sets *r* to a complex interval centered on `m` that is guaranteed to contain at least one root of `f`. Such an interval is obtained by taking a ball of radius `|f(m)/f'(m)| n` where `n` is the degree of `f`. Proof: assume that the distance to the nearest root exceeds `r = |f(m)/f'(m)| n`. Then .. math :: \left|\frac{f'(m)}{f(m)}\right| = \left|\sum_i \frac{1}{m-\zeta_i}\right| \le \sum_i \frac{1}{|m-\zeta_i|} < \frac{n}{r} = \left|\frac{f'(m)}{f(m)}\right| which is a contradiction (see [Kob2010]_). .. function:: slong _acb_poly_validate_roots(acb_ptr roots, acb_srcptr poly, slong len, slong prec) Given a list of approximate roots of the input polynomial, this function sets a rigorous bounding interval for each root, and determines which roots are isolated from all the other roots. It then rearranges the list of roots so that the isolated roots are at the front of the list, and returns the count of isolated roots. If the return value equals the degree of the polynomial, then all roots have been found. If the return value is smaller, all the remaining output intervals are guaranteed to contain roots, but it is possible that not all of the polynomial's roots are contained among them. .. function:: void _acb_poly_refine_roots_durand_kerner(acb_ptr roots, acb_srcptr poly, slong len, slong prec) Refines the given roots simultaneously using a single iteration of the Durand-Kerner method. The radius of each root is set to an approximation of the correction, giving a rough estimate of its error (not a rigorous bound). .. function:: slong _acb_poly_find_roots(acb_ptr roots, acb_srcptr poly, acb_srcptr initial, slong len, slong maxiter, slong prec) .. function:: slong acb_poly_find_roots(acb_ptr roots, const acb_poly_t poly, acb_srcptr initial, slong maxiter, slong prec) Attempts to compute all the roots of the given nonzero polynomial *poly* using a working precision of *prec* bits. If *n* denotes the degree of *poly*, the function writes *n* approximate roots with rigorous error bounds to the preallocated array *roots*, and returns the number of roots that are isolated. If the return value equals the degree of the polynomial, then all roots have been found. If the return value is smaller, all the output intervals are guaranteed to contain roots, but it is possible that not all of the polynomial's roots are contained among them. The roots are computed numerically by performing several steps with the Durand-Kerner method and terminating if the estimated accuracy of the roots approaches the working precision or if the number of steps exceeds *maxiter*, which can be set to zero in order to use a default value. Finally, the approximate roots are validated rigorously. Initial values for the iteration can be provided as the array *initial*. If *initial* is set to *NULL*, default values `(0.4+0.9i)^k` are used. The polynomial is assumed to be squarefree. If there are repeated roots, the iteration is likely to find them (with low numerical accuracy), but the error bounds will not converge as the precision increases. .. function:: int _acb_poly_validate_real_roots(acb_srcptr roots, acb_srcptr poly, slong len, slong prec) .. function:: int acb_poly_validate_real_roots(acb_srcptr roots, const acb_poly_t poly, slong prec) Given a strictly real polynomial *poly* (of length *len*) and isolating intervals for all its complex roots, determines if all the real roots are separated from the non-real roots. If this function returns nonzero, every root enclosure that touches the real axis (as tested by applying :func:`arb_contains_zero` to the imaginary part) corresponds to a real root (its imaginary part can be set to zero), and every other root enclosure corresponds to a non-real root (with known sign for the imaginary part). If this function returns zero, then the signs of the imaginary parts are not known for certain, based on the accuracy of the inputs and the working precision *prec*. arb-2.8.1/doc/source/arb.rst000066400000000000000000001654571264125401100156470ustar00rootroot00000000000000.. _arb: **arb.h** -- real numbers represented as floating-point balls =============================================================================== An :type:`arb_t` represents a ball over the real numbers, that is, an interval `[m \pm r] \equiv [m-r, m+r]` where the midpoint `m` and the radius `r` are (extended) real numbers and `r` is nonnegative (possibly infinite). The result of an (approximate) operation done on :type:`arb_t` variables is a ball which contains the result of the (mathematically exact) operation applied to any choice of points in the input balls. In general, the output ball is not the smallest possible. The precision parameter passed to each function roughly indicates the precision to which calculations on the midpoint are carried out (operations on the radius are always done using a fixed, small precision.) For arithmetic operations, the precision parameter currently simply specifies the precision of the corresponding :type:`arf_t` operation. In the future, the arithmetic might be made faster by incorporating sloppy rounding (typically equivalent to a loss of 1-2 bits of effective working precision) when the result is known to be inexact (while still propagating errors rigorously, of course). Arithmetic operations done on exact input with exactly representable output are always guaranteed to produce exact output. For more complex operations, the precision parameter indicates a minimum working precision (algorithms might allocate extra internal precision to attempt to produce an output accurate to the requested number of bits, especially when the required precision can be estimated easily, but this is not generally required). If the precision is increased and the inputs either are exact or are computed with increased accuracy as well, the output should converge proportionally, absent any bugs. The general intended strategy for using ball arithmetic is to add a few guard bits, and then repeat the calculation as necessary with an exponentially increasing number of guard bits (Ziv's strategy) until the result is exact enough for one's purposes (typically the first attempt will be successful). The following balls with an infinite or NaN component are permitted, and may be returned as output from functions. * The ball `[+\infty \pm c]`, where `c` is finite, represents the point at positive infinity. Such a ball can always be replaced by `[+\infty \pm 0]` while preserving mathematical correctness (this is currently not done automatically by the library). * The ball `[-\infty \pm c]`, where `c` is finite, represents the point at negative infinity. Such a ball can always be replaced by `[-\infty \pm 0]` while preserving mathematical correctness (this is currently not done automatically by the library). * The ball `[c \pm \infty]`, where `c` is finite or infinite, represents the whole extended real line `[-\infty,+\infty]`. Such a ball can always be replaced by `[0 \pm \infty]` while preserving mathematical correctness (this is currently not done automatically by the library). Note that there is no way to represent a half-infinite interval such as `[0,\infty]`. * The ball `[\operatorname{NaN} \pm c]`, where `c` is finite or infinite, represents an indeterminate value (the value could be any extended real number, or it could represent a function being evaluated outside its domain of definition, for example where the result would be complex). Such an indeterminate ball can always be replaced by `[\operatorname{NaN} \pm \infty]` while preserving mathematical correctness (this is currently not done automatically by the library). The :type:`arb_t` type is almost identical semantically to the legacy :type:`fmprb_t` type, but uses a more efficient internal representation. Whereas the midpoint and radius of an :type:`fmprb_t` both have the same type, the :type:`arb_t` type uses an :type:`arf_t` for the midpoint and a :type:`mag_t` for the radius. Code designed to manipulate the radius of an :type:`fmprb_t` directly can be ported to the :type:`arb_t` type by writing the radius to a temporary :type:`arf_t` variable, manipulating that variable, and then converting back to the :type:`mag_t` radius. Alternatively, :type:`mag_t` methods can be used directly where available. Types, macros and constants ------------------------------------------------------------------------------- .. type:: arb_struct .. type:: arb_t An :type:`arb_struct` consists of an :type:`arf_struct` (the midpoint) and a :type:`mag_struct` (the radius). An :type:`arb_t` is defined as an array of length one of type :type:`arb_struct`, permitting an :type:`arb_t` to be passed by reference. .. type:: arb_ptr Alias for ``arb_struct *``, used for vectors of numbers. .. type:: arb_srcptr Alias for ``const arb_struct *``, used for vectors of numbers when passed as constant input to functions. .. macro:: arb_midref(x) Macro returning a pointer to the midpoint of *x* as an :type:`arf_t`. .. macro:: arb_radref(x) Macro returning a pointer to the radius of *x* as a :type:`mag_t`. Memory management ------------------------------------------------------------------------------- .. function:: void arb_init(arb_t x) Initializes the variable *x* for use. Its midpoint and radius are both set to zero. .. function:: void arb_clear(arb_t x) Clears the variable *x*, freeing or recycling its allocated memory. .. function:: arb_ptr _arb_vec_init(slong n) Returns a pointer to an array of *n* initialized :type:`arb_struct` entries. .. function:: void _arb_vec_clear(arb_ptr v, slong n) Clears an array of *n* initialized :type:`arb_struct` entries. .. function:: void arb_swap(arb_t x, arb_t y) Swaps *x* and *y* efficiently. Assignment and rounding ------------------------------------------------------------------------------- .. function:: void arb_set_fmprb(arb_t y, const fmprb_t x) .. function:: void arb_get_fmprb(fmprb_t y, const arb_t x) .. function:: void arb_set(arb_t y, const arb_t x) .. function:: void arb_set_arf(arb_t y, const arf_t x) .. function:: void arb_set_si(arb_t y, slong x) .. function:: void arb_set_ui(arb_t y, ulong x) .. function:: void arb_set_d(arb_t y, double x) .. function:: void arb_set_fmpz(arb_t y, const fmpz_t x) Sets *y* to the value of *x* without rounding. .. function:: void arb_set_fmpz_2exp(arb_t y, const fmpz_t x, const fmpz_t e) Sets *y* to `x \cdot 2^e`. .. function:: void arb_set_round(arb_t y, const arb_t x, slong prec) .. function:: void arb_set_round_fmpz(arb_t y, const fmpz_t x, slong prec) Sets *y* to the value of *x*, rounded to *prec* bits. .. function:: void arb_set_round_fmpz_2exp(arb_t y, const fmpz_t x, const fmpz_t e, slong prec) Sets *y* to `x \cdot 2^e`, rounded to *prec* bits. .. function:: void arb_set_fmpq(arb_t y, const fmpq_t x, slong prec) Sets *y* to the rational number *x*, rounded to *prec* bits. .. function:: int arb_set_str(arb_t res, const char * inp, slong prec) Sets *res* to the value specified by the human-readable string *inp*. The input may be a decimal floating-point literal, such as "25", "0.001", "7e+141" or "-31.4159e-1", and may also consist of two such literals separated by the symbol "+/-" and optionally enclosed in brackets, e.g. "[3.25 +/- 0.0001]", or simply "[+/- 10]" with an implicit zero midpoint. The output is rounded to *prec* bits, and if the binary-to-decimal conversion is inexact, the resulting error is added to the radius. The symbols "inf" and "nan" are recognized (a nan midpoint results in an indeterminate interval, with infinite radius). Returns 0 if successful and nonzero if unsuccessful. If unsuccessful, the result is set to an indeterminate interval. .. function:: char * arb_get_str(const arb_t x, slong n, ulong flags) Returns a nice human-readable representation of *x*, with at most *n* digits of the midpoint printed. With default flags, the output can be parsed back with :func:`arb_set_str`, and this is guaranteed to produce an interval containing the original interval *x*. By default, the output is rounded so that the value given for the midpoint is correct up to 1 ulp (unit in the last decimal place). If *ARB_STR_MORE* is added to *flags*, more (possibly incorrect) digits may be printed. If *ARB_STR_NO_RADIUS* is added to *flags*, the radius is not included in the output if at least 1 digit of the midpoint can be printed. By adding a multiple *m* of *ARB_STR_CONDENSE* to *flags*, strings of more than three times *m* consecutive digits are condensed, only printing the leading and trailing *m* digits along with brackets indicating the number of digits omitted (useful when computing values to extremely high precision). Assignment of special values ------------------------------------------------------------------------------- .. function:: void arb_zero(arb_t x) Sets *x* to zero. .. function:: void arb_one(arb_t f) Sets *x* to the exact integer 1. .. function:: void arb_pos_inf(arb_t x) Sets *x* to positive infinity, with a zero radius. .. function:: void arb_neg_inf(arb_t x) Sets *x* to negative infinity, with a zero radius. .. function:: void arb_zero_pm_inf(arb_t x) Sets *x* to `[0 \pm \infty]`, representing the whole extended real line. .. function:: void arb_indeterminate(arb_t x) Sets *x* to `[\operatorname{NaN} \pm \infty]`, representing an indeterminate result. Input and output ------------------------------------------------------------------------------- .. function:: void arb_print(const arb_t x) Prints the internal representation of *x*. .. function:: void arb_printd(const arb_t x, slong digits) Prints *x* in decimal. The printed value of the radius is not adjusted to compensate for the fact that the binary-to-decimal conversion of both the midpoint and the radius introduces additional error. .. function:: void arb_printn(const arb_t x, slong digits, ulong flags) Prints a nice decimal representation of *x*. By default, the output is guaranteed to be correct to within one unit in the last digit. An error bound is also printed explicitly. See :func:`arb_get_str` for details. Random number generation ------------------------------------------------------------------------------- .. function:: void arb_randtest(arb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random ball. The midpoint and radius will both be finite. .. function:: void arb_randtest_exact(arb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random number with zero radius. .. function:: void arb_randtest_precise(arb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random number with radius around `2^{-\text{prec}}` the magnitude of the midpoint. .. function:: void arb_randtest_wide(arb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random number with midpoint and radius chosen independently, possibly giving a very large interval. .. function:: void arb_randtest_special(arb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random interval, possibly having NaN or an infinity as the midpoint and possibly having an infinite radius. .. function:: void arb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const arb_t x, slong bits) Sets *q* to a random rational number from the interval represented by *x*. A denominator is chosen by multiplying the binary denominator of *x* by a random integer up to *bits* bits. The outcome is undefined if the midpoint or radius of *x* is non-finite, or if the exponent of the midpoint or radius is so large or small that representing the endpoints as exact rational numbers would cause overflows. Radius and interval operations ------------------------------------------------------------------------------- .. function:: void arb_get_mid_arb(arb_t m, const arb_t x) Sets *m* to the midpoint of *x*. .. function:: void arb_get_rad_arb(arb_t r, const arb_t x) Sets *m* to the radius of *x*. .. function:: void arb_add_error_arf(arb_t x, const arf_t err) .. function:: void arb_add_error_mag(arb_t x, const mag_t err) .. function:: void arb_add_error(arb_t x, const arb_t err) Adds the absolute value of *err* to the radius of *x* (the operation is done in-place). .. function:: void arb_add_error_2exp_si(arb_t x, slong e) .. function:: void arb_add_error_2exp_fmpz(arb_t x, const fmpz_t e) Adds `2^e` to the radius of *x*. .. function:: void arb_union(arb_t z, const arb_t x, const arb_t y, slong prec) Sets *z* to a ball containing both *x* and *y*. .. function:: void arb_get_abs_ubound_arf(arf_t u, const arb_t x, slong prec) Sets *u* to the upper bound for the absolute value of *x*, rounded up to *prec* bits. If *x* contains NaN, the result is NaN. .. function:: void arb_get_abs_lbound_arf(arf_t u, const arb_t x, slong prec) Sets *u* to the lower bound for the absolute value of *x*, rounded down to *prec* bits. If *x* contains NaN, the result is NaN. .. function:: void arb_get_mag(mag_t z, const arb_t x) Sets *z* to an upper bound for the absolute value of *x*. If *x* contains NaN, the result is positive infinity. .. function:: void arb_get_mag_lower(mag_t z, const arb_t x) Sets *z* to a lower bound for the absolute value of *x*. If *x* contains NaN, the result is zero. .. function:: void arb_get_mag_lower_nonnegative(mag_t z, const arb_t x) Sets *z* to a lower bound for the signed value of *x*, or zero if *x* overlaps with the negative half-axis. If *x* contains NaN, the result is zero. .. function:: void arb_get_interval_fmpz_2exp(fmpz_t a, fmpz_t b, fmpz_t exp, const arb_t x) Computes the exact interval represented by *x*, in the form of an integer interval multiplied by a power of two, i.e. `x = [a, b] \times 2^{\text{exp}}`. The outcome is undefined if the midpoint or radius of *x* is non-finite, or if the difference in magnitude between the midpoint and radius is so large that representing the endpoints exactly would cause overflows. .. function:: void arb_set_interval_arf(arb_t x, const arf_t a, const arf_t b, slong prec) .. function:: void arb_set_interval_mpfr(arb_t x, const mpfr_t a, const mpfr_t b, slong prec) Sets *x* to a ball containing the interval `[a, b]`. We require that `a \le b`. .. function:: void arb_get_interval_arf(arf_t a, arf_t b, const arb_t x, slong prec) .. function:: void arb_get_interval_mpfr(mpfr_t a, mpfr_t b, const arb_t x) Constructs an interval `[a, b]` containing the ball *x*. The MPFR version uses the precision of the output variables. .. function:: slong arb_rel_error_bits(const arb_t x) Returns the effective relative error of *x* measured in bits, defined as the difference between the position of the top bit in the radius and the top bit in the midpoint, plus one. The result is clamped between plus/minus *ARF_PREC_EXACT*. .. function:: slong arb_rel_accuracy_bits(const arb_t x) Returns the effective relative accuracy of *x* measured in bits, equal to the negative of the return value from :func:`arb_rel_error_bits`. .. function:: slong arb_bits(const arb_t x) Returns the number of bits needed to represent the absolute value of the mantissa of the midpoint of *x*, i.e. the minimum precision sufficient to represent *x* exactly. Returns 0 if the midpoint of *x* is a special value. .. function:: void arb_trim(arb_t y, const arb_t x) Sets *y* to a trimmed copy of *x*: rounds *x* to a number of bits equal to the accuracy of *x* (as indicated by its radius), plus a few guard bits. The resulting ball is guaranteed to contain *x*, but is more economical if *x* has less than full accuracy. .. function:: int arb_get_unique_fmpz(fmpz_t z, const arb_t x) If *x* contains a unique integer, sets *z* to that value and returns nonzero. Otherwise (if *x* represents no integers or more than one integer), returns zero. .. function:: void arb_floor(arb_t y, const arb_t x, slong prec) .. function:: void arb_ceil(arb_t y, const arb_t x, slong prec) Sets *y* to a ball containing `\lfloor x \rfloor` and `\lceil x \rceil` respectively, with the midpoint of *y* rounded to at most *prec* bits. .. function:: void arb_get_fmpz_mid_rad_10exp(fmpz_t mid, fmpz_t rad, fmpz_t exp, const arb_t x, slong n) Assuming that *x* is finite and not exactly zero, computes integers *mid*, *rad*, *exp* such that `x \in [m-r, m+r] \times 10^e` and such that the larger out of *mid* and *rad* has at least *n* digits plus a few guard digits. If *x* is infinite or exactly zero, the outputs are all set to zero. Comparisons ------------------------------------------------------------------------------- .. function:: int arb_is_zero(const arb_t x) Returns nonzero iff the midpoint and radius of *x* are both zero. .. function:: int arb_is_nonzero(const arb_t x) Returns nonzero iff zero is not contained in the interval represented by *x*. .. function:: int arb_is_one(const arb_t f) Returns nonzero iff *x* is exactly 1. .. function:: int arb_is_finite(const arb_t x) Returns nonzero iff the midpoint and radius of *x* are both finite floating-point numbers, i.e. not infinities or NaN. .. function:: int arb_is_exact(const arb_t x) Returns nonzero iff the radius of *x* is zero. .. function:: int arb_is_int(const arb_t x) Returns nonzero iff *x* is an exact integer. .. function:: int arb_equal(const arb_t x, const arb_t y) Returns nonzero iff *x* and *y* are equal as balls, i.e. have both the same midpoint and radius. Note that this is not the same thing as testing whether both *x* and *y* certainly represent the same real number, unless either *x* or *y* is exact (and neither contains NaN). To test whether both operands *might* represent the same mathematical quantity, use :func:`arb_overlaps` or :func:`arb_contains`, depending on the circumstance. .. function:: int arb_is_positive(const arb_t x) .. function:: int arb_is_nonnegative(const arb_t x) .. function:: int arb_is_negative(const arb_t x) .. function:: int arb_is_nonpositive(const arb_t x) Returns nonzero iff all points *p* in the interval represented by *x* satisfy, respectively, `p > 0`, `p \ge 0`, `p < 0`, `p \le 0`. If *x* contains NaN, returns zero. .. function:: int arb_overlaps(const arb_t x, const arb_t y) Returns nonzero iff *x* and *y* have some point in common. If either *x* or *y* contains NaN, this function always returns nonzero (as a NaN could be anything, it could in particular contain any number that is included in the other operand). .. function:: int arb_contains_arf(const arb_t x, const arf_t y) .. function:: int arb_contains_fmpq(const arb_t x, const fmpq_t y) .. function:: int arb_contains_fmpz(const arb_t x, const fmpz_t y) .. function:: int arb_contains_si(const arb_t x, slong y) .. function:: int arb_contains_mpfr(const arb_t x, const mpfr_t y) .. function:: int arb_contains(const arb_t x, const arb_t y) Returns nonzero iff the given number (or ball) *y* is contained in the interval represented by *x*. If *x* is contains NaN, this function always returns nonzero (as it could represent anything, and in particular could represent all the points included in *y*). If *y* contains NaN and *x* does not, it always returns zero. .. function:: int arb_contains_int(const arb_t x) Returns nonzero iff the interval represented by *x* contains an integer. .. function:: int arb_contains_zero(const arb_t x) .. function:: int arb_contains_negative(const arb_t x) .. function:: int arb_contains_nonpositive(const arb_t x) .. function:: int arb_contains_positive(const arb_t x) .. function:: int arb_contains_nonnegative(const arb_t x) Returns nonzero iff there is any point *p* in the interval represented by *x* satisfying, respectively, `p = 0`, `p < 0`, `p \le 0`, `p > 0`, `p \ge 0`. If *x* contains NaN, returns nonzero. .. function:: int arb_eq(const arb_t x, const arb_t y) .. function:: int arb_ne(const arb_t x, const arb_t y) .. function:: int arb_lt(const arb_t x, const arb_t y) .. function:: int arb_le(const arb_t x, const arb_t y) .. function:: int arb_gt(const arb_t x, const arb_t y) .. function:: int arb_ge(const arb_t x, const arb_t y) Respectively performs the comparison `x = y`, `x \ne y`, `x < y`, `x \le y`, `x > y`, `x \ge y` in a mathematically meaningful way. If the comparison `t \, (\operatorname{op}) \, u` holds for all `t \in x` and all `u \in y`, returns 1. Otherwise, returns 0. The balls *x* and *y* are viewed as subintervals of the extended real line. Note that balls that are formally different can compare as equal under this definition: for example, `[-\infty \pm 3] = [-\infty \pm 0]`. Also `[-\infty] \le [\infty \pm \infty]`. The output is always 0 if either input has NaN as midpoint. Arithmetic ------------------------------------------------------------------------------- .. function:: void arb_neg(arb_t y, const arb_t x) .. function:: void arb_neg_round(arb_t y, const arb_t x, slong prec) Sets *y* to the negation of *x*. .. function:: void arb_abs(arb_t y, const arb_t x) Sets *y* to the absolute value of *x*. No attempt is made to improve the interval represented by *x* if it contains zero. .. function:: void arb_add(arb_t z, const arb_t x, const arb_t y, slong prec) .. function:: void arb_add_arf(arb_t z, const arb_t x, const arf_t y, slong prec) .. function:: void arb_add_ui(arb_t z, const arb_t x, ulong y, slong prec) .. function:: void arb_add_si(arb_t z, const arb_t x, slong y, slong prec) .. function:: void arb_add_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) Sets `z = x + y`, rounded to *prec* bits. The precision can be *ARF_PREC_EXACT* provided that the result fits in memory. .. function:: void arb_add_fmpz_2exp(arb_t z, const arb_t x, const fmpz_t m, const fmpz_t e, slong prec) Sets `z = x + m \cdot 2^e`, rounded to *prec* bits. The precision can be *ARF_PREC_EXACT* provided that the result fits in memory. .. function:: void arb_sub(arb_t z, const arb_t x, const arb_t y, slong prec) .. function:: void arb_sub_arf(arb_t z, const arb_t x, const arf_t y, slong prec) .. function:: void arb_sub_ui(arb_t z, const arb_t x, ulong y, slong prec) .. function:: void arb_sub_si(arb_t z, const arb_t x, slong y, slong prec) .. function:: void arb_sub_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) Sets `z = x - y`, rounded to *prec* bits. The precision can be *ARF_PREC_EXACT* provided that the result fits in memory. .. function:: void arb_mul(arb_t z, const arb_t x, const arb_t y, slong prec) .. function:: void arb_mul_arf(arb_t z, const arb_t x, const arf_t y, slong prec) .. function:: void arb_mul_si(arb_t z, const arb_t x, slong y, slong prec) .. function:: void arb_mul_ui(arb_t z, const arb_t x, ulong y, slong prec) .. function:: void arb_mul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) Sets `z = x \cdot y`, rounded to *prec* bits. The precision can be *ARF_PREC_EXACT* provided that the result fits in memory. .. function:: void arb_mul_2exp_si(arb_t y, const arb_t x, slong e) .. function:: void arb_mul_2exp_fmpz(arb_t y, const arb_t x, const fmpz_t e) Sets *y* to *x* multiplied by `2^e`. .. function:: void arb_addmul(arb_t z, const arb_t x, const arb_t y, slong prec) .. function:: void arb_addmul_arf(arb_t z, const arb_t x, const arf_t y, slong prec) .. function:: void arb_addmul_si(arb_t z, const arb_t x, slong y, slong prec) .. function:: void arb_addmul_ui(arb_t z, const arb_t x, ulong y, slong prec) .. function:: void arb_addmul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) Sets `z = z + x \cdot y`, rounded to prec bits. The precision can be *ARF_PREC_EXACT* provided that the result fits in memory. .. function:: void arb_submul(arb_t z, const arb_t x, const arb_t y, slong prec) .. function:: void arb_submul_arf(arb_t z, const arb_t x, const arf_t y, slong prec) .. function:: void arb_submul_si(arb_t z, const arb_t x, slong y, slong prec) .. function:: void arb_submul_ui(arb_t z, const arb_t x, ulong y, slong prec) .. function:: void arb_submul_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) Sets `z = z - x \cdot y`, rounded to prec bits. The precision can be *ARF_PREC_EXACT* provided that the result fits in memory. .. function:: void arb_inv(arb_t y, const arb_t x, slong prec) Sets *z* to `1 / x`. .. function:: void arb_div(arb_t z, const arb_t x, const arb_t y, slong prec) .. function:: void arb_div_arf(arb_t z, const arb_t x, const arf_t y, slong prec) .. function:: void arb_div_si(arb_t z, const arb_t x, slong y, slong prec) .. function:: void arb_div_ui(arb_t z, const arb_t x, ulong y, slong prec) .. function:: void arb_div_fmpz(arb_t z, const arb_t x, const fmpz_t y, slong prec) .. function:: void arb_fmpz_div_fmpz(arb_t z, const fmpz_t x, const fmpz_t y, slong prec) .. function:: void arb_ui_div(arb_t z, ulong x, const arb_t y, slong prec) Sets `z = x / y`, rounded to *prec* bits. If *y* contains zero, *z* is set to `0 \pm \infty`. Otherwise, error propagation uses the rule .. math :: \left| \frac{x}{y} - \frac{x+\xi_1 a}{y+\xi_2 b} \right| = \left|\frac{x \xi_2 b - y \xi_1 a}{y (y+\xi_2 b)}\right| \le \frac{|xb|+|ya|}{|y| (|y|-b)} where `-1 \le \xi_1, \xi_2 \le 1`, and where the triangle inequality has been applied to the numerator and the reverse triangle inequality has been applied to the denominator. .. function:: void arb_div_2expm1_ui(arb_t z, const arb_t x, ulong n, slong prec) Sets `z = x / (2^n - 1)`, rounded to *prec* bits. Powers and roots ------------------------------------------------------------------------------- .. function:: void arb_sqrt(arb_t z, const arb_t x, slong prec) .. function:: void arb_sqrt_arf(arb_t z, const arf_t x, slong prec) .. function:: void arb_sqrt_fmpz(arb_t z, const fmpz_t x, slong prec) .. function:: void arb_sqrt_ui(arb_t z, ulong x, slong prec) Sets *z* to the square root of *x*, rounded to *prec* bits. If `x = m \pm x` where `m \ge r \ge 0`, the propagated error is bounded by `\sqrt{m} - \sqrt{m-r} = \sqrt{m} (1 - \sqrt{1 - r/m}) \le \sqrt{m} (r/m + (r/m)^2)/2`. .. function:: void arb_sqrtpos(arb_t z, const arb_t x, slong prec) Sets *z* to the square root of *x*, assuming that *x* represents a nonnegative number (i.e. discarding any negative numbers in the input interval). .. function:: void arb_hypot(arb_t z, const arb_t x, const arb_t y, slong prec) Sets *z* to `\sqrt{x^2 + y^2}`. .. function:: void arb_rsqrt(arb_t z, const arb_t x, slong prec) .. function:: void arb_rsqrt_ui(arb_t z, ulong x, slong prec) Sets *z* to the reciprocal square root of *x*, rounded to *prec* bits. At high precision, this is faster than computing a square root. .. function:: void arb_sqrt1pm1(arb_t z, const arb_t x, slong prec) Sets `z = \sqrt{1+x}-1`, computed accurately when `x \approx 0`. .. function:: void arb_root_ui(arb_t z, const arb_t x, ulong k, slong prec) Sets *z* to the *k*-th root of *x*, rounded to *prec* bits. This function selects between different algorithms. For large *k*, it evaluates `\exp(\log(x)/k)`. For small *k*, it uses :func:`arf_root` at the midpoint and computes a propagated error bound as follows: if input interval is `[m-r, m+r]` with `r \le m`, the error is largest at `m-r` where it satisfies .. math :: m^{1/k} - (m-r)^{1/k} = m^{1/k} [1 - (1-r/m)^{1/k}] = m^{1/k} [1 - \exp(\log(1-r/m)/k)] \le m^{1/k} \min(1, -\log(1-r/m)/k) = m^{1/k} \min(1, \log(1+r/(m-r))/k). This is evaluated using :func:`mag_log1p`. .. function:: void arb_root(arb_t z, const arb_t x, ulong k, slong prec) Alias for :func:`arb_root_ui`, provided for backwards compatibility. .. function:: void arb_pow_fmpz_binexp(arb_t y, const arb_t b, const fmpz_t e, slong prec) .. function:: void arb_pow_fmpz(arb_t y, const arb_t b, const fmpz_t e, slong prec) .. function:: void arb_pow_ui(arb_t y, const arb_t b, ulong e, slong prec) .. function:: void arb_ui_pow_ui(arb_t y, ulong b, ulong e, slong prec) .. function:: void arb_si_pow_ui(arb_t y, slong b, ulong e, slong prec) Sets `y = b^e` using binary exponentiation (with an initial division if `e < 0`). Provided that *b* and *e* are small enough and the exponent is positive, the exact power can be computed by setting the precision to *ARF_PREC_EXACT*. Note that these functions can get slow if the exponent is extremely large (in such cases :func:`arb_pow` may be superior). .. function:: void arb_pow_fmpq(arb_t y, const arb_t x, const fmpq_t a, slong prec) Sets `y = b^e`, computed as `y = (b^{1/q})^p` if the denominator of `e = p/q` is small, and generally as `y = \exp(e \log b)`. Note that this function can get slow if the exponent is extremely large (in such cases :func:`arb_pow` may be superior). .. function:: void arb_pow(arb_t z, const arb_t x, const arb_t y, slong prec) Sets `z = x^y`, computed using binary exponentiation if `y` if a small exact integer, as `z = (x^{1/2})^{2y}` if `y` is a small exact half-integer, and generally as `z = \exp(y \log x)`. Exponentials and logarithms ------------------------------------------------------------------------------- .. function:: void arb_log_ui(arb_t z, ulong x, slong prec) .. function:: void arb_log_fmpz(arb_t z, const fmpz_t x, slong prec) .. function:: void arb_log_arf(arb_t z, const arf_t x, slong prec) .. function:: void arb_log(arb_t z, const arb_t x, slong prec) Sets `z = \log(x)`. At low to medium precision (up to about 4096 bits), :func:`arb_log_arf` uses table-based argument reduction and fast Taylor series evaluation via :func:`_arb_atan_taylor_rs`. At high precision, it falls back to MPFR. The function :func:`arb_log` simply calls :func:`arb_log_arf` with the midpoint as input, and separately adds the propagated error. .. function:: void arb_log_ui_from_prev(arb_t log_k1, ulong k1, arb_t log_k0, ulong k0, slong prec) Computes `\log(k_1)`, given `\log(k_0)` where `k_0 < k_1`. At high precision, this function uses the formula `\log(k_1) = \log(k_0) + 2 \operatorname{atanh}((k_1-k_0)/(k_1+k_0))`, evaluating the inverse hyperbolic tangent using binary splitting (for best efficiency, `k_0` should be large and `k_1 - k_0` should be small). Otherwise, it ignores `\log(k_0)` and evaluates the logarithm the usual way. .. function:: void arb_log1p(arb_t z, const arb_t x, slong prec) Sets `z = \log(1+x)`, computed accurately when `x \approx 0`. .. function:: void arb_exp(arb_t z, const arb_t x, slong prec) Sets `z = \exp(x)`. Error propagation is done using the following rule: assuming `x = m \pm r`, the error is largest at `m + r`, and we have `\exp(m+r) - \exp(m) = \exp(m) (\exp(r)-1) \le r \exp(m+r)`. .. function:: void arb_expm1(arb_t z, const arb_t x, slong prec) Sets `z = \exp(x)-1`, computed accurately when `x \approx 0`. .. function:: void arb_exp_invexp(arb_t z, arb_t w, const arb_t x, slong prec) Sets `z = \exp(x)` and `w = \exp(-x)`. The second exponential is computed from the first using a division, but propagated error bounds are computed separately. Trigonometric functions ------------------------------------------------------------------------------- .. function:: void arb_sin(arb_t s, const arb_t x, slong prec) .. function:: void arb_cos(arb_t c, const arb_t x, slong prec) .. function:: void arb_sin_cos(arb_t s, arb_t c, const arb_t x, slong prec) Sets `s = \sin(x)`, `c = \cos(x)`. Error propagation uses the rule `|\sin(m \pm r) - \sin(m)| \le \min(r,2)`. .. function:: void arb_sin_pi(arb_t s, const arb_t x, slong prec) .. function:: void arb_cos_pi(arb_t c, const arb_t x, slong prec) .. function:: void arb_sin_cos_pi(arb_t s, arb_t c, const arb_t x, slong prec) Sets `s = \sin(\pi x)`, `c = \cos(\pi x)`. .. function:: void arb_tan(arb_t y, const arb_t x, slong prec) Sets `y = \tan(x) = \sin(x) / \cos(y)`. .. function:: void arb_cot(arb_t y, const arb_t x, slong prec) Sets `y = \cot(x) = \cos(x) / \sin(y)`. .. function:: void arb_sin_cos_pi_fmpq(arb_t s, arb_t c, const fmpq_t x, slong prec) .. function:: void arb_sin_pi_fmpq(arb_t s, const fmpq_t x, slong prec) .. function:: void arb_cos_pi_fmpq(arb_t c, const fmpq_t x, slong prec) Sets `s = \sin(\pi x)`, `c = \cos(\pi x)` where `x` is a rational number (whose numerator and denominator are assumed to be reduced). We first use trigonometric symmetries to reduce the argument to the octant `[0, 1/4]`. Then we either multiply by a numerical approximation of `\pi` and evaluate the trigonometric function the usual way, or we use algebraic methods, depending on which is estimated to be faster. Since the argument has been reduced to the first octant, the first of these two methods gives full accuracy even if the original argument is close to some root other the origin. .. function:: void arb_tan_pi(arb_t y, const arb_t x, slong prec) Sets `y = \tan(\pi x)`. .. function:: void arb_cot_pi(arb_t y, const arb_t x, slong prec) Sets `y = \cot(\pi x)`. .. function:: void arb_sinc(arb_t z, const arb_t x, slong prec) Sets `z = \operatorname{sinc}(x) = \sin(x) / x`. Inverse trigonometric functions ------------------------------------------------------------------------------- .. function:: void arb_atan_arf(arb_t z, const arf_t x, slong prec) .. function:: void arb_atan(arb_t z, const arb_t x, slong prec) Sets `z = \operatorname{atan}(x)`. At low to medium precision (up to about 4096 bits), :func:`arb_atan_arf` uses table-based argument reduction and fast Taylor series evaluation via :func:`_arb_atan_taylor_rs`. At high precision, it falls back to MPFR. The function :func:`arb_atan` simply calls :func:`arb_atan_arf` with the midpoint as input, and separately adds the propagated error. The function :func:`arb_atan_arf` uses lookup tables if possible, and otherwise falls back to :func:`arb_atan_arf_bb`. .. function:: void arb_atan2(arb_t z, const arb_t b, const arb_t a, slong prec) Sets *r* to an the argument (phase) of the complex number `a + bi`, with the branch cut discontinuity on `(-\infty,0]`. We define `\operatorname{atan2}(0,0) = 0`, and for `a < 0`, `\operatorname{atan2}(0,a) = \pi`. .. function:: void arb_asin(arb_t z, const arb_t x, slong prec) Sets `z = \operatorname{asin}(x) = \operatorname{atan}(x / \sqrt{1-x^2})`. If `x` is not contained in the domain `[-1,1]`, the result is an indeterminate interval. .. function:: void arb_acos(arb_t z, const arb_t x, slong prec) Sets `z = \operatorname{acos}(x) = \pi/2 - \operatorname{asin}(x)`. If `x` is not contained in the domain `[-1,1]`, the result is an indeterminate interval. Hyperbolic functions ------------------------------------------------------------------------------- .. function:: void arb_sinh(arb_t s, const arb_t x, slong prec) .. function:: void arb_cosh(arb_t c, const arb_t x, slong prec) .. function:: void arb_sinh_cosh(arb_t s, arb_t c, const arb_t x, slong prec) Sets `s = \sinh(x)`, `c = \cosh(x)`. If the midpoint of `x` is close to zero and the hyperbolic sine is to be computed, evaluates `(e^{2x}\pm1) / (2e^x)` via :func:`arb_expm1` to avoid loss of accuracy. Otherwise evaluates `(e^x \pm e^{-x}) / 2`. .. function:: void arb_tanh(arb_t y, const arb_t x, slong prec) Sets `y = \tanh(x) = \sinh(x) / \cosh(x)`, evaluated via :func:`arb_expm1` as `\tanh(x) = (e^{2x} - 1) / (e^{2x} + 1)` if `|x|` is small, and as `\tanh(\pm x) = 1 - 2 e^{\mp 2x} / (1 + e^{\mp 2x})` if `|x|` is large. .. function:: void arb_coth(arb_t y, const arb_t x, slong prec) Sets `y = \coth(x) = \cosh(x) / \sinh(x)`, evaluated using the same strategy as :func:`arb_tanh`. Inverse hyperbolic functions ------------------------------------------------------------------------------- .. function:: void arb_atanh(arb_t z, const arb_t x, slong prec) Sets `z = \operatorname{atanh}(x)`. .. function:: void arb_asinh(arb_t z, const arb_t x, slong prec) Sets `z = \operatorname{asinh}(x)`. .. function:: void arb_acosh(arb_t z, const arb_t x, slong prec) Sets `z = \operatorname{acosh}(x)`. If `x < 1`, the result is an indeterminate interval. Constants ------------------------------------------------------------------------------- The following functions cache the computed values to speed up repeated calls at the same or lower precision. For further implementation details, see :ref:`algorithms_constants`. .. function:: void arb_const_pi(arb_t z, slong prec) Computes `\pi`. .. function:: void arb_const_sqrt_pi(arb_t z, slong prec) Computes `\sqrt{\pi}`. .. function:: void arb_const_log_sqrt2pi(arb_t z, slong prec) Computes `\log \sqrt{2 \pi}`. .. function:: void arb_const_log2(arb_t z, slong prec) Computes `\log(2)`. .. function:: void arb_const_log10(arb_t z, slong prec) Computes `\log(10)`. .. function:: void arb_const_euler(arb_t z, slong prec) Computes Euler's constant `\gamma = \lim_{k \rightarrow \infty} (H_k - \log k)` where `H_k = 1 + 1/2 + \ldots + 1/k`. .. function:: void arb_const_catalan(arb_t z, slong prec) Computes Catalan's constant `C = \sum_{n=0}^{\infty} (-1)^n / (2n+1)^2`. .. function:: void arb_const_e(arb_t z, slong prec) Computes `e = \exp(1)`. .. function:: void arb_const_khinchin(arb_t z, slong prec) Computes Khinchin's constant `K_0`. .. function:: void arb_const_glaisher(arb_t z, slong prec) Computes the Glaisher-Kinkelin constant `A = \exp(1/12 - \zeta'(-1))`. .. function:: void arb_const_apery(arb_t z, slong prec) Computes Apery's constant `\zeta(3)`. Gamma function and factorials ------------------------------------------------------------------------------- .. function:: void arb_rising_ui_bs(arb_t z, const arb_t x, ulong n, slong prec) .. function:: void arb_rising_ui_rs(arb_t z, const arb_t x, ulong n, ulong step, slong prec) .. function:: void arb_rising_ui_rec(arb_t z, const arb_t x, ulong n, slong prec) .. function:: void arb_rising_ui(arb_t z, const arb_t x, ulong n, slong prec) .. function:: void arb_rising(arb_t z, const arb_t x, const arb_t n, slong prec) Computes the rising factorial `z = x (x+1) (x+2) \cdots (x+n-1)`. The *bs* version uses binary splitting. The *rs* version uses rectangular splitting. The *rec* version uses either *bs* or *rs* depending on the input. The default version uses the gamma function unless *n* is a small integer. The *rs* version takes an optional *step* parameter for tuning purposes (to use the default step length, pass zero). .. function:: void arb_rising_fmpq_ui(arb_t z, const fmpq_t x, ulong n, slong prec) Computes the rising factorial `z = x (x+1) (x+2) \cdots (x+n-1)` using binary splitting. If the denominator or numerator of *x* is large compared to *prec*, it is more efficient to convert *x* to an approximation and use :func:`arb_rising_ui`. .. function :: void arb_rising2_ui_bs(arb_t u, arb_t v, const arb_t x, ulong n, slong prec) .. function :: void arb_rising2_ui_rs(arb_t u, arb_t v, const arb_t x, ulong n, ulong step, slong prec) .. function :: void arb_rising2_ui(arb_t u, arb_t v, const arb_t x, ulong n, slong prec) Letting `u(x) = x (x+1) (x+2) \cdots (x+n-1)`, simultaneously compute `u(x)` and `v(x) = u'(x)`, respectively using binary splitting, rectangular splitting (with optional nonzero step length *step* to override the default choice), and an automatic algorithm choice. .. function:: void arb_fac_ui(arb_t z, ulong n, slong prec) Computes the factorial `z = n!` via the gamma function. .. function:: void arb_doublefac_ui(arb_t z, ulong n, slong prec) Computes the double factorial `z = n!!` via the gamma function. .. function:: void arb_bin_ui(arb_t z, const arb_t n, ulong k, slong prec) .. function:: void arb_bin_uiui(arb_t z, ulong n, ulong k, slong prec) Computes the binomial coefficient `z = {n \choose k}`, via the rising factorial as `{n \choose k} = (n-k+1)_k / k!`. .. function:: void arb_gamma(arb_t z, const arb_t x, slong prec) .. function:: void arb_gamma_fmpq(arb_t z, const fmpq_t x, slong prec) .. function:: void arb_gamma_fmpz(arb_t z, const fmpz_t x, slong prec) Computes the gamma function `z = \Gamma(x)`. .. function:: void arb_lgamma(arb_t z, const arb_t x, slong prec) Computes the logarithmic gamma function `z = \log \Gamma(x)`. The complex branch structure is assumed, so if `x \le 0`, the result is an indeterminate interval. .. function:: void arb_rgamma(arb_t z, const arb_t x, slong prec) Computes the reciprocal gamma function `z = 1/\Gamma(x)`, avoiding division by zero at the poles of the gamma function. .. function:: void arb_digamma(arb_t y, const arb_t x, slong prec) Computes the digamma function `z = \psi(x) = (\log \Gamma(x))' = \Gamma'(x) / \Gamma(x)`. Zeta function ------------------------------------------------------------------------------- .. function:: void arb_zeta_ui_vec_borwein(arb_ptr z, ulong start, slong num, ulong step, slong prec) Evaluates `\zeta(s)` at `\mathrm{num}` consecutive integers *s* beginning with *start* and proceeding in increments of *step*. Uses Borwein's formula ([Bor2000]_, [GS2003]_), implemented to support fast multi-evaluation (but also works well for a single *s*). Requires `\mathrm{start} \ge 2`. For efficiency, the largest *s* should be at most about as large as *prec*. Arguments approaching *LONG_MAX* will cause overflows. One should therefore only use this function for *s* up to about *prec*, and then switch to the Euler product. The algorithm for single *s* is basically identical to the one used in MPFR (see [MPFR2012]_ for a detailed description). In particular, we evaluate the sum backwards to avoid storing more than one `d_k` coefficient, and use integer arithmetic throughout since it is convenient and the terms turn out to be slightly larger than `2^\mathrm{prec}`. The only numerical error in the main loop comes from the division by `k^s`, which adds less than 1 unit of error per term. For fast multi-evaluation, we repeatedly divide by `k^{\mathrm{step}}`. Each division reduces the input error and adds at most 1 unit of additional rounding error, so by induction, the error per term is always smaller than 2 units. .. function:: void arb_zeta_ui_asymp(arb_t x, ulong s, slong prec) Assuming `s \ge 2`, approximates `\zeta(s)` by `1 + 2^{-s}` along with a correct error bound. We use the following bounds: for `s > b`, `\zeta(s) - 1 < 2^{-b}`, and generally, `\zeta(s) - (1 + 2^{-s}) < 2^{2-\lfloor 3 s/2 \rfloor}`. .. function:: void arb_zeta_ui_euler_product(arb_t z, ulong s, slong prec) Computes `\zeta(s)` using the Euler product. This is fast only if *s* is large compared to the precision. Writing `P(a,b) = \prod_{a \le p \le b} (1 - p^{-s})`, we have `1/\zeta(s) = P(a,M) P(M+1,\infty)`. To bound the error caused by truncating the product at `M`, we write `P(M+1,\infty) = 1 - \epsilon(s,M)`. Since `0 < P(a,M) \le 1`, the absolute error for `\zeta(s)` is bounded by `\epsilon(s,M)`. According to the analysis in [Fil1992]_, it holds for all `s \ge 6` and `M \ge 1` that `1/P(M+1,\infty) - 1 \le f(s,M) \equiv 2 M^{1-s} / (s/2 - 1)`. Thus, we have `1/(1-\epsilon(s,M)) - 1 \le f(s,M)`, and expanding the geometric series allows us to conclude that `\epsilon(M) \le f(s,M)`. .. function:: void arb_zeta_ui_bernoulli(arb_t x, ulong s, slong prec) Computes `\zeta(s)` for even *s* via the corresponding Bernoulli number. .. function:: void arb_zeta_ui_borwein_bsplit(arb_t x, ulong s, slong prec) Computes `\zeta(s)` for arbitrary `s \ge 2` using a binary splitting implementation of Borwein's algorithm. This has quasilinear complexity with respect to the precision (assuming that `s` is fixed). .. function:: void arb_zeta_ui_vec(arb_ptr x, ulong start, slong num, slong prec) .. function:: void arb_zeta_ui_vec_even(arb_ptr x, ulong start, slong num, slong prec) .. function:: void arb_zeta_ui_vec_odd(arb_ptr x, ulong start, slong num, slong prec) Computes `\zeta(s)` at *num* consecutive integers (respectively *num* even or *num* odd integers) beginning with `s = \mathrm{start} \ge 2`, automatically choosing an appropriate algorithm. .. function:: void arb_zeta_ui(arb_t x, ulong s, slong prec) Computes `\zeta(s)` for nonnegative integer `s \ne 1`, automatically choosing an appropriate algorithm. This function is intended for numerical evaluation of isolated zeta values; for multi-evaluation, the vector versions are more efficient. .. function:: void arb_zeta(arb_t z, const arb_t s, slong prec) Sets *z* to the value of the Riemann zeta function `\zeta(s)`. For computing derivatives with respect to `s`, use :func:`arb_poly_zeta_series`. .. function:: void arb_hurwitz_zeta(arb_t z, const arb_t s, const arb_t a, slong prec) Sets *z* to the value of the Hurwitz zeta function `\zeta(s,a)`. For computing derivatives with respect to `s`, use :func:`arb_poly_zeta_series`. Bernoulli numbers ------------------------------------------------------------------------------- .. function:: void arb_bernoulli_ui(arb_t b, ulong n, slong prec) Sets `b` to the numerical value of the Bernoulli number `B_n` accurate to *prec* bits, computed by a division of the exact fraction if `B_n` is in the global cache or the exact numerator roughly is larger than *prec* bits, and using :func:`arb_bernoulli_ui_zeta` otherwise. This function reads `B_n` from the global cache if the number is already cached, but does not automatically extend the cache by itself. .. function:: void arb_bernoulli_ui_zeta(arb_t b, ulong n, slong prec) Sets `b` to the numerical value of `B_n` accurate to *prec* bits, computed using the formula `B_{2n} = (-1)^{n+1} 2 (2n)! \zeta(2n) / (2 \pi)^n`. To avoid potential infinite recursion, we explicitly call the Euler product implementation of the zeta function. We therefore assume that the precision is small enough and `n` large enough for the Euler product to converge rapidly (otherwise this function will effectively hang). .. function:: void arb_power_sum_vec(arb_ptr res, const arb_t a, const arb_t b, slong len, slong prec) For *n* from 0 to *len* - 1, sets entry *n* in the output vector *res* to .. math :: S_n(a,b) = \frac{1}{n+1}\left(B_{n+1}(b) - B_{n+1}(a)\right) where `B_n(x)` is a Bernoulli polynomial. If *a* and *b* are integers and `b \ge a`, this is equivalent to .. math :: S_n(a,b) = \sum_{k=a}^{b-1} k^n. The computation uses the generating function for Bernoulli polynomials. Polylogarithms ------------------------------------------------------------------------------- .. function:: void arb_polylog(arb_t w, const arb_t s, const arb_t z, slong prec) .. function:: void arb_polylog_si(arb_t w, slong s, const arb_t z, slong prec) Sets *w* to the polylogarithm `\operatorname{Li}_s(z)`. Other special functions ------------------------------------------------------------------------------- .. function:: void arb_fib_fmpz(arb_t z, const fmpz_t n, slong prec) .. function:: void arb_fib_ui(arb_t z, ulong n, slong prec) Computes the Fibonacci number `F_n`. Uses the binary squaring algorithm described in [Tak2000]_. Provided that *n* is small enough, an exact Fibonacci number can be computed by setting the precision to *ARF_PREC_EXACT*. .. function:: void arb_agm(arb_t z, const arb_t x, const arb_t y, slong prec) Sets *z* to the arithmetic-geometric mean of *x* and *y*. .. function:: void arb_chebyshev_t_ui(arb_t a, ulong n, const arb_t x, slong prec) .. function:: void arb_chebyshev_u_ui(arb_t a, ulong n, const arb_t x, slong prec) Evaluates the Chebyshev polynomial of the first kind `a = T_n(x)` or the Chebyshev polynomial of the second kind `a = U_n(x)`. .. function:: void arb_chebyshev_t2_ui(arb_t a, arb_t b, ulong n, const arb_t x, slong prec) .. function:: void arb_chebyshev_u2_ui(arb_t a, arb_t b, ulong n, const arb_t x, slong prec) Simultaneously evaluates `a = T_n(x), b = T_{n-1}(x)` or `a = U_n(x), b = U_{n-1}(x)`. Aliasing between *a*, *b* and *x* is not permitted. .. function:: void arb_bell_sum_bsplit(arb_t res, const fmpz_t n, const fmpz_t a, const fmpz_t b, const fmpz_t mmag, slong prec) .. function:: void arb_bell_sum_taylor(arb_t res, const fmpz_t n, const fmpz_t a, const fmpz_t b, const fmpz_t mmag, slong prec) Helper functions for Bell numbers, evaluating the sum `\sum_{k=a}^{b-1} k^n / k!`. If *mmag* is non-NULL, it may be used to indicate that the target error tolerance should be `2^{mmag - prec}`. .. function:: void arb_bell_fmpz(arb_t res, const fmpz_t n, slong prec) .. function:: void arb_bell_ui(arb_t res, ulong n, slong prec) Sets *res* to the Bell number `B_n`. If the number is too large to fit exactly in *prec* bits, a numerical approximation is computed efficiently. Internals for computing elementary functions ------------------------------------------------------------------------------- .. function:: void _arb_atan_taylor_naive(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int alternating) .. function:: void _arb_atan_taylor_rs(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int alternating) Computes an approximation of `y = \sum_{k=0}^{N-1} x^{2k+1} / (2k+1)` (if *alternating* is 0) or `y = \sum_{k=0}^{N-1} (-1)^k x^{2k+1} / (2k+1)` (if *alternating* is 1). Used internally for computing arctangents and logarithms. The *naive* version uses the forward recurrence, and the *rs* version uses a division-avoiding rectangular splitting scheme. Requires `N \le 255`, `0 \le x \le 1/16`, and *xn* positive. The input *x* and output *y* are fixed-point numbers with *xn* fractional limbs. A bound for the ulp error is written to *error*. .. function:: void _arb_exp_taylor_naive(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N) .. function:: void _arb_exp_taylor_rs(mp_ptr y, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N) Computes an approximation of `y = \sum_{k=0}^{N-1} x^k / k!`. Used internally for computing exponentials. The *naive* version uses the forward recurrence, and the *rs* version uses a division-avoiding rectangular splitting scheme. Requires `N \le 287`, `0 \le x \le 1/16`, and *xn* positive. The input *x* is a fixed-point number with *xn* fractional limbs, and the output *y* is a fixed-point number with *xn* fractional limbs plus one extra limb for the integer part of the result. A bound for the ulp error is written to *error*. .. function:: void _arb_sin_cos_taylor_naive(mp_ptr ysin, mp_ptr ycos, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N) .. function:: void _arb_sin_cos_taylor_rs(mp_ptr ysin, mp_ptr ycos, mp_limb_t * error, mp_srcptr x, mp_size_t xn, ulong N, int sinonly, int alternating) Computes approximations of `y_s = \sum_{k=0}^{N-1} (-1)^k x^{2k+1} / (2k+1)!` and `y_c = \sum_{k=0}^{N-1} (-1)^k x^{2k} / (2k)!`. Used internally for computing sines and cosines. The *naive* version uses the forward recurrence, and the *rs* version uses a division-avoiding rectangular splitting scheme. Requires `N \le 143`, `0 \le x \le 1/16`, and *xn* positive. The input *x* and outputs *ysin*, *ycos* are fixed-point numbers with *xn* fractional limbs. A bound for the ulp error is written to *error*. If *sinonly* is 1, only the sine is computed; if *sinonly* is 0 both the sine and cosine are computed. To compute sin and cos, *alternating* should be 1. If *alternating* is 0, the hyperbolic sine is computed (this is currently only intended to be used together with *sinonly*). .. function:: int _arb_get_mpn_fixed_mod_log2(mp_ptr w, fmpz_t q, mp_limb_t * error, const arf_t x, mp_size_t wn) Attempts to write `w = x - q \log(2)` with `0 \le w < \log(2)`, where *w* is a fixed-point number with *wn* limbs and ulp error *error*. Returns success. .. function:: int _arb_get_mpn_fixed_mod_pi4(mp_ptr w, fmpz_t q, int * octant, mp_limb_t * error, const arf_t x, mp_size_t wn) Attempts to write `w = |x| - q \pi/4` with `0 \le w < \pi/4`, where *w* is a fixed-point number with *wn* limbs and ulp error *error*. Returns success. The value of *q* mod 8 is written to *octant*. The output variable *q* can be NULL, in which case the full value of *q* is not stored. .. function:: slong _arb_exp_taylor_bound(slong mag, slong prec) Returns *n* such that `\left|\sum_{k=n}^{\infty} x^k / k!\right| \le 2^{-\mathrm{prec}}`, assuming `|x| \le 2^{\mathrm{mag}} \le 1/4`. .. function:: void arb_exp_arf_bb(arb_t z, const arf_t x, slong prec, int m1) Computes the exponential function using the bit-burst algorithm. If *m1* is nonzero, the exponential function minus one is computed accurately. Aborts if *x* is extremely small or large (where another algorithm should be used). For large *x*, repeated halving is used. In fact, we always do argument reduction until `|x|` is smaller than about `2^{-d}` where `d \approx 16` to speed up convergence. If `|x| \approx 2^m`, we thus need about `m+d` squarings. Computing `\log(2)` costs roughly 100-200 multiplications, so is not usually worth the effort at very high precision. However, this function could be improved by using `\log(2)` based reduction at precision low enough that the value can be assumed to be cached. .. function:: void _arb_exp_sum_bs_simple(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) .. function:: void _arb_exp_sum_bs_powtab(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) Computes *T*, *Q* and *Qexp* such that `T / (Q 2^{\text{Qexp}}) = \sum_{k=1}^N (x/2^r)^k/k!` using binary splitting. Note that the sum is taken to *N* inclusive and omits the constant term. The *powtab* version precomputes a table of powers of *x*, resulting in slightly higher memory usage but better speed. For best efficiency, *N* should have many trailing zero bits. .. function:: void _arb_atan_sum_bs_simple(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) .. function:: void _arb_atan_sum_bs_powtab(fmpz_t T, fmpz_t Q, mp_bitcnt_t * Qexp, const fmpz_t x, mp_bitcnt_t r, slong N) Computes *T*, *Q* and *Qexp* such that `T / (Q 2^{\text{Qexp}}) = \sum_{k=1}^N (-1)^k (x/2^r)^{2k} / (2k+1)` using binary splitting. Note that the sum is taken to *N* inclusive, omits the linear term, and requires a final multiplication by `(x/2^r)` to give the true series for atan. The *powtab* version precomputes a table of powers of *x*, resulting in slightly higher memory usage but better speed. For best efficiency, *N* should have many trailing zero bits. .. function:: void arb_atan_arf_bb(arb_t z, const arf_t x, slong prec) Computes the arctangent of *x*. Initially, the argument-halving formula .. math :: \operatorname{atan}(x) = 2 \operatorname{atan}\left(\frac{x}{1+\sqrt{1+x^2}}\right) is applied up to 8 times to get a small argument. Then a version of the bit-burst algorithm is used. The functional equation .. math :: \operatorname{atan}(x) = \operatorname{atan}(p/q) + \operatorname{atan}(w), \quad w = \frac{qx-p}{px+q}, \quad p = \lfloor qx \rfloor is applied repeatedly instead of integrating a differential equation for the arctangent, as this appears to be more efficient. Vector functions ------------------------------------------------------------------------------- .. function:: void _arb_vec_zero(arb_ptr vec, slong n) Sets all entries in *vec* to zero. .. function:: int _arb_vec_is_zero(arb_srcptr vec, slong len) Returns nonzero iff all entries in *x* are zero. .. function:: int _arb_vec_is_finite(arb_srcptr x, slong len) Returns nonzero iff all entries in *x* certainly are finite. .. function:: void _arb_vec_set(arb_ptr res, arb_srcptr vec, slong len) Sets *res* to a copy of *vec*. .. function:: void _arb_vec_set_round(arb_ptr res, arb_srcptr vec, slong len, slong prec) Sets *res* to a copy of *vec*, rounding each entry to *prec* bits. .. function:: void _arb_vec_swap(arb_ptr vec1, arb_ptr vec2, slong len) Swaps the entries of *vec1* and *vec2*. .. function:: void _arb_vec_neg(arb_ptr B, arb_srcptr A, slong n) .. function:: void _arb_vec_sub(arb_ptr C, arb_srcptr A, arb_srcptr B, slong n, slong prec) .. function:: void _arb_vec_add(arb_ptr C, arb_srcptr A, arb_srcptr B, slong n, slong prec) .. function:: void _arb_vec_scalar_mul(arb_ptr res, arb_srcptr vec, slong len, const arb_t c, slong prec) .. function:: void _arb_vec_scalar_div(arb_ptr res, arb_srcptr vec, slong len, const arb_t c, slong prec) .. function:: void _arb_vec_scalar_mul_fmpz(arb_ptr res, arb_srcptr vec, slong len, const fmpz_t c, slong prec) .. function:: void _arb_vec_scalar_mul_2exp_si(arb_ptr res, arb_srcptr src, slong len, slong c) .. function:: void _arb_vec_scalar_addmul(arb_ptr res, arb_srcptr vec, slong len, const arb_t c, slong prec) Performs the respective scalar operation elementwise. .. function:: void _arb_vec_dot(arb_t res, arb_srcptr vec1, arb_srcptr vec2, slong len2, slong prec) Sets *res* to the dot product of *vec1* and *vec2*. .. function:: void _arb_vec_norm(arb_t res, arb_srcptr vec, slong len, slong prec) Sets *res* to the dot product of *vec* with itself. .. function:: void _arb_vec_get_mag(mag_t bound, arb_srcptr vec, slong len, slong prec) Sets *bound* to an upper bound for the entries in *vec*. .. function:: slong _arb_vec_bits(arb_srcptr x, slong len) Returns the maximum of :func:`arb_bits` for all entries in *vec*. .. function:: void _arb_vec_set_powers(arb_ptr xs, const arb_t x, slong len, slong prec) Sets *xs* to the powers `1, x, x^2, \ldots, x^{len-1}`. .. function:: void _arb_vec_add_error_arf_vec(arb_ptr res, arf_srcptr err, slong len) .. function:: void _arb_vec_add_error_mag_vec(arb_ptr res, mag_srcptr err, slong len) Adds the magnitude of each entry in *err* to the radius of the corresponding entry in *res*. .. function:: void _arb_vec_indeterminate(arb_ptr vec, slong len) Applies :func:`arb_indeterminate` elementwise. .. function:: void _arb_vec_trim(arb_ptr res, arb_srcptr vec, slong len) Applies :func:`arb_trim` elementwise. .. function:: int _arb_vec_get_unique_fmpz_vec(fmpz * res, arb_srcptr vec, slong len) Calls :func:`arb_get_unique_fmpz` elementwise and returns nonzero if all entries can be rounded uniquely to integers. If any entry in *vec* cannot be rounded uniquely to an integer, returns zero. arb-2.8.1/doc/source/arb_calc.rst000066400000000000000000000242531264125401100166150ustar00rootroot00000000000000.. _arb-calc: **arb_calc.h** -- calculus with real-valued functions =============================================================================== This module provides functions for operations of calculus over the real numbers (intended to include root-finding, optimization, integration, and so on). It is planned that the module will include two types of algorithms: * Interval algorithms that give provably correct results. An example would be numerical integration on an interval by dividing the interval into small balls and evaluating the function on each ball, giving rigorous upper and lower bounds. * Conventional numerical algorithms that use heuristics to estimate the accuracy of a result, without guaranteeing that it is correct. An example would be numerical integration based on pointwise evaluation, where the error is estimated by comparing the results with two different sets of evaluation points. Ball arithmetic then still tracks the accuracy of the function evaluations. Any algorithms of the second kind will be clearly marked as such. Types, macros and constants ------------------------------------------------------------------------------- .. type:: arb_calc_func_t Typedef for a pointer to a function with signature:: int func(arb_ptr out, const arb_t inp, void * param, slong order, slong prec) implementing a univariate real function `f(x)`. When called, *func* should write to *out* the first *order* coefficients in the Taylor series expansion of `f(x)` at the point *inp*, evaluated at a precision of *prec* bits. The *param* argument may be used to pass through additional parameters to the function. The return value is reserved for future use as an error code. It can be assumed that *out* and *inp* are not aliased and that *order* is positive. .. macro:: ARB_CALC_SUCCESS Return value indicating that an operation is successful. .. macro:: ARB_CALC_IMPRECISE_INPUT Return value indicating that the input to a function probably needs to be computed more accurately. .. macro:: ARB_CALC_NO_CONVERGENCE Return value indicating that an algorithm has failed to convergence, possibly due to the problem not having a solution, the algorithm not being applicable, or the precision being insufficient Debugging ------------------------------------------------------------------------------- .. var:: int arb_calc_verbose If set, enables printing information about the calculation to standard output. Subdivision-based root finding ------------------------------------------------------------------------------- .. type:: arf_interval_struct .. type:: arf_interval_t An :type:`arf_interval_struct` consists of a pair of :type:`arf_struct`, representing an interval used for subdivision-based root-finding. An :type:`arf_interval_t` is defined as an array of length one of type :type:`arf_interval_struct`, permitting an :type:`arf_interval_t` to be passed by reference. .. type:: arf_interval_ptr Alias for ``arf_interval_struct *``, used for vectors of intervals. .. type:: arf_interval_srcptr Alias for ``const arf_interval_struct *``, used for vectors of intervals. .. function:: void arf_interval_init(arf_interval_t v) .. function:: void arf_interval_clear(arf_interval_t v) .. function:: arf_interval_ptr _arf_interval_vec_init(slong n) .. function:: void _arf_interval_vec_clear(arf_interval_ptr v, slong n) .. function:: void arf_interval_set(arf_interval_t v, const arf_interval_t u) .. function:: void arf_interval_swap(arf_interval_t v, arf_interval_t u) .. function:: void arf_interval_get_arb(arb_t x, const arf_interval_t v, slong prec) .. function:: void arf_interval_printd(const arf_interval_t v, slong n) Helper functions for endpoint-based intervals. .. function:: slong arb_calc_isolate_roots(arf_interval_ptr * found, int ** flags, arb_calc_func_t func, void * param, const arf_interval_t interval, slong maxdepth, slong maxeval, slong maxfound, slong prec) Rigorously isolates single roots of a real analytic function on the interior of an interval. This routine writes an array of *n* interesting subintervals of *interval* to *found* and corresponding flags to *flags*, returning the integer *n*. The output has the following properties: * The function has no roots on *interval* outside of the output subintervals. * Subintervals are sorted in increasing order (with no overlap except possibly starting and ending with the same point). * Subintervals with a flag of 1 contain exactly one (single) root. * Subintervals with any other flag may or may not contain roots. If no flags other than 1 occur, all roots of the function on *interval* have been isolated. If there are output subintervals on which the existence or nonexistence of roots could not be determined, the user may attempt further searches on those subintervals (possibly with increased precision and/or increased bounds for the breaking criteria). Note that roots of multiplicity higher than one and roots located exactly at endpoints cannot be isolated by the algorithm. The following breaking criteria are implemented: * At most *maxdepth* recursive subdivisions are attempted. The smallest details that can be distinguished are therefore about `2^{-\text{maxdepth}}` times the width of *interval*. A typical, reasonable value might be between 20 and 50. * If the total number of tested subintervals exceeds *maxeval*, the algorithm is terminated and any untested subintervals are added to the output. The total number of calls to *func* is thereby restricted to a small multiple of *maxeval* (the actual count can be slightly higher depending on implementation details). A typical, reasonable value might be between 100 and 100000. * The algorithm terminates if *maxfound* roots have been isolated. In particular, setting *maxfound* to 1 can be used to locate just one root of the function even if there are numerous roots. To try to find all roots, *LONG_MAX* may be passed. The argument *prec* denotes the precision used to evaluate the function. It is possibly also used for some other arithmetic operations performed internally by the algorithm. Note that it probably does not make sense for *maxdepth* to exceed *prec*. Warning: it is assumed that subdivision points of *interval* can be represented exactly as floating-point numbers in memory. Do not pass `1 \pm 2^{-10^{100}}` as input. .. function:: int arb_calc_refine_root_bisect(arf_interval_t r, arb_calc_func_t func, void * param, const arf_interval_t start, slong iter, slong prec) Given an interval *start* known to contain a single root of *func*, refines it using *iter* bisection steps. The algorithm can return a failure code if the sign of the function at an evaluation point is ambiguous. The output *r* is set to a valid isolating interval (possibly just *start*) even if the algorithm fails. Newton-based root finding ------------------------------------------------------------------------------- .. function:: void arb_calc_newton_conv_factor(arf_t conv_factor, arb_calc_func_t func, void * param, const arb_t conv_region, slong prec) Given an interval `I` specified by *conv_region*, evaluates a bound for `C = \sup_{t,u \in I} \frac{1}{2} |f''(t)| / |f'(u)|`, where `f` is the function specified by *func* and *param*. The bound is obtained by evaluating `f'(I)` and `f''(I)` directly. If `f` is ill-conditioned, `I` may need to be extremely precise in order to get an effective, finite bound for *C*. .. function:: int arb_calc_newton_step(arb_t xnew, arb_calc_func_t func, void * param, const arb_t x, const arb_t conv_region, const arf_t conv_factor, slong prec) Performs a single step with an interval version of Newton's method. The input consists of the function `f` specified by *func* and *param*, a ball `x = [m-r, m+r]` known to contain a single root of `f`, a ball `I` (*conv_region*) containing `x` with an associated bound (*conv_factor*) for `C = \sup_{t,u \in I} \frac{1}{2} |f''(t)| / |f'(u)|`, and a working precision *prec*. The Newton update consists of setting `x' = [m'-r', m'+r']` where `m' = m - f(m) / f'(m)` and `r' = C r^2`. The expression `m - f(m) / f'(m)` is evaluated using ball arithmetic at a working precision of *prec* bits, and the rounding error during this evaluation is accounted for in the output. We now check that `x' \in I` and `r' < r`. If both conditions are satisfied, we set *xnew* to `x'` and return *ARB_CALC_SUCCESS*. If either condition fails, we set *xnew* to `x` and return *ARB_CALC_NO_CONVERGENCE*, indicating that no progress is made. .. function:: int arb_calc_refine_root_newton(arb_t r, arb_calc_func_t func, void * param, const arb_t start, const arb_t conv_region, const arf_t conv_factor, slong eval_extra_prec, slong prec) Refines a precise estimate of a single root of a function to high precision by performing several Newton steps, using nearly optimally chosen doubling precision steps. The inputs are defined as for *arb_calc_newton_step*, except for the precision parameters: *prec* is the target accuracy and *eval_extra_prec* is the estimated number of guard bits that need to be added to evaluate the function accurately close to the root (for example, if the function is a polynomial with large coefficients of alternating signs and Horner's rule is used to evaluate it, the extra precision should typically be approximately the bit size of the coefficients). This function returns *ARB_CALC_SUCCESS* if all attempted Newton steps are successful (note that this does not guarantee that the computed root is accurate to *prec* bits, which has to be verified by the user), only that it is more accurate than the starting ball. On failure, *ARB_CALC_IMPRECISE_INPUT* or *ARB_CALC_NO_CONVERGENCE* may be returned. In this case, *r* is set to a ball for the root which is valid but likely does have full accuracy (it can possibly just be equal to the starting ball). arb-2.8.1/doc/source/arb_mat.rst000066400000000000000000000302161264125401100164700ustar00rootroot00000000000000.. _arb-mat: **arb_mat.h** -- matrices over the real numbers =============================================================================== An :type:`arb_mat_t` represents a dense matrix over the real numbers, implemented as an array of entries of type :type:`arb_struct`. The dimension (number of rows and columns) of a matrix is fixed at initialization, and the user must ensure that inputs and outputs to an operation have compatible dimensions. The number of rows or columns in a matrix can be zero. Types, macros and constants ------------------------------------------------------------------------------- .. type:: arb_mat_struct .. type:: arb_mat_t Contains a pointer to a flat array of the entries (entries), an array of pointers to the start of each row (rows), and the number of rows (r) and columns (c). An *arb_mat_t* is defined as an array of length one of type *arb_mat_struct*, permitting an *arb_mat_t* to be passed by reference. .. macro:: arb_mat_entry(mat, i, j) Macro giving a pointer to the entry at row *i* and column *j*. .. macro:: arb_mat_nrows(mat) Returns the number of rows of the matrix. .. macro:: arb_mat_ncols(mat) Returns the number of columns of the matrix. Memory management ------------------------------------------------------------------------------- .. function:: void arb_mat_init(arb_mat_t mat, slong r, slong c) Initializes the matrix, setting it to the zero matrix with *r* rows and *c* columns. .. function:: void arb_mat_clear(arb_mat_t mat) Clears the matrix, deallocating all entries. Conversions ------------------------------------------------------------------------------- .. function:: void arb_mat_set(arb_mat_t dest, const arb_mat_t src) .. function:: void arb_mat_set_fmpz_mat(arb_mat_t dest, const fmpz_mat_t src) .. function:: void arb_mat_set_round_fmpz_mat(arb_mat_t dest, const fmpz_mat_t src, slong prec) .. function:: void arb_mat_set_fmpq_mat(arb_mat_t dest, const fmpq_mat_t src, slong prec) Sets *dest* to *src*. The operands must have identical dimensions. Random generation ------------------------------------------------------------------------------- .. function:: void arb_mat_randtest(arb_mat_t mat, flint_rand_t state, slong prec, slong mag_bits) Sets *mat* to a random matrix with up to *prec* bits of precision and with exponents of width up to *mag_bits*. Input and output ------------------------------------------------------------------------------- .. function:: void arb_mat_printd(const arb_mat_t mat, slong digits) Prints each entry in the matrix with the specified number of decimal digits. Comparisons ------------------------------------------------------------------------------- .. function:: int arb_mat_equal(const arb_mat_t mat1, const arb_mat_t mat2) Returns nonzero iff the matrices have the same dimensions and identical entries. .. function:: int arb_mat_overlaps(const arb_mat_t mat1, const arb_mat_t mat2) Returns nonzero iff the matrices have the same dimensions and each entry in *mat1* overlaps with the corresponding entry in *mat2*. .. function:: int arb_mat_contains(const arb_mat_t mat1, const arb_mat_t mat2) .. function:: int arb_mat_contains_fmpz_mat(const arb_mat_t mat1, const fmpz_mat_t mat2) .. function:: int arb_mat_contains_fmpq_mat(const arb_mat_t mat1, const fmpq_mat_t mat2) Returns nonzero iff the matrices have the same dimensions and each entry in *mat2* is contained in the corresponding entry in *mat1*. .. function:: int arb_mat_eq(const arb_mat_t mat1, const arb_mat_t mat2) Returns nonzero iff *mat1* and *mat2* certainly represent the same matrix. .. function:: int arb_mat_ne(const arb_mat_t mat1, const arb_mat_t mat2) Returns nonzero iff *mat1* and *mat2* certainly do not represent the same matrix. Special matrices ------------------------------------------------------------------------------- .. function:: void arb_mat_zero(arb_mat_t mat) Sets all entries in mat to zero. .. function:: void arb_mat_one(arb_mat_t mat) Sets the entries on the main diagonal to ones, and all other entries to zero. Transpose ------------------------------------------------------------------------------- .. function:: void arb_mat_transpose(arb_mat_t dest, const arb_mat_t src) Sets *dest* to the exact transpose *src*. The operands must have compatible dimensions. Aliasing is allowed. Norms ------------------------------------------------------------------------------- .. function:: void arb_mat_bound_inf_norm(mag_t b, const arb_mat_t A) Sets *b* to an upper bound for the infinity norm (i.e. the largest absolute value row sum) of *A*. Arithmetic ------------------------------------------------------------------------------- .. function:: void arb_mat_neg(arb_mat_t dest, const arb_mat_t src) Sets *dest* to the exact negation of *src*. The operands must have the same dimensions. .. function:: void arb_mat_add(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec) Sets res to the sum of *mat1* and *mat2*. The operands must have the same dimensions. .. function:: void arb_mat_sub(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec) Sets *res* to the difference of *mat1* and *mat2*. The operands must have the same dimensions. .. function:: void arb_mat_mul_classical(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec) .. function:: void arb_mat_mul_threaded(arb_mat_t C, const arb_mat_t A, const arb_mat_t B, slong prec) .. function:: void arb_mat_mul(arb_mat_t res, const arb_mat_t mat1, const arb_mat_t mat2, slong prec) Sets *res* to the matrix product of *mat1* and *mat2*. The operands must have compatible dimensions for matrix multiplication. The *threaded* version splits the computation over the number of threads returned by *flint_get_num_threads()*. The default version automatically calls the *threaded* version if the matrices are sufficiently large and more than one thread can be used. .. function:: void arb_mat_sqr_classical(arb_mat_t B, const arb_mat_t A, slong prec) .. function:: void arb_mat_sqr(arb_mat_t res, const arb_mat_t mat, slong prec) Sets *res* to the matrix square of *mat*. The operands must both be square with the same dimensions. .. function:: void arb_mat_pow_ui(arb_mat_t res, const arb_mat_t mat, ulong exp, slong prec) Sets *res* to *mat* raised to the power *exp*. Requires that *mat* is a square matrix. Scalar arithmetic ------------------------------------------------------------------------------- .. function:: void arb_mat_scalar_mul_2exp_si(arb_mat_t B, const arb_mat_t A, slong c) Sets *B* to *A* multiplied by `2^c`. .. function:: void arb_mat_scalar_addmul_si(arb_mat_t B, const arb_mat_t A, slong c, slong prec) .. function:: void arb_mat_scalar_addmul_fmpz(arb_mat_t B, const arb_mat_t A, const fmpz_t c, slong prec) .. function:: void arb_mat_scalar_addmul_arb(arb_mat_t B, const arb_mat_t A, const arb_t c, slong prec) Sets *B* to `B + A \times c`. .. function:: void arb_mat_scalar_mul_si(arb_mat_t B, const arb_mat_t A, slong c, slong prec) .. function:: void arb_mat_scalar_mul_fmpz(arb_mat_t B, const arb_mat_t A, const fmpz_t c, slong prec) .. function:: void arb_mat_scalar_mul_arb(arb_mat_t B, const arb_mat_t A, const arb_t c, slong prec) Sets *B* to `A \times c`. .. function:: void arb_mat_scalar_div_si(arb_mat_t B, const arb_mat_t A, slong c, slong prec) .. function:: void arb_mat_scalar_div_fmpz(arb_mat_t B, const arb_mat_t A, const fmpz_t c, slong prec) .. function:: void arb_mat_scalar_div_arb(arb_mat_t B, const arb_mat_t A, const arb_t c, slong prec) Sets *B* to `A / c`. Gaussian elimination and solving ------------------------------------------------------------------------------- .. function:: int arb_mat_lu(slong * perm, arb_mat_t LU, const arb_mat_t A, slong prec) Given an `n \times n` matrix `A`, computes an LU decomposition `PLU = A` using Gaussian elimination with partial pivoting. The input and output matrices can be the same, performing the decomposition in-place. Entry `i` in the permutation vector perm is set to the row index in the input matrix corresponding to row `i` in the output matrix. The algorithm succeeds and returns nonzero if it can find `n` invertible (i.e. not containing zero) pivot entries. This guarantees that the matrix is invertible. The algorithm fails and returns zero, leaving the entries in `P` and `LU` undefined, if it cannot find `n` invertible pivot elements. In this case, either the matrix is singular, the input matrix was computed to insufficient precision, or the LU decomposition was attempted at insufficient precision. .. function:: void arb_mat_solve_lu_precomp(arb_mat_t X, const slong * perm, const arb_mat_t LU, const arb_mat_t B, slong prec) Solves `AX = B` given the precomputed nonsingular LU decomposition `A = PLU`. The matrices `X` and `B` are allowed to be aliased with each other, but `X` is not allowed to be aliased with `LU`. .. function:: int arb_mat_solve(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec) Solves `AX = B` where `A` is a nonsingular `n \times n` matrix and `X` and `B` are `n \times m` matrices, using LU decomposition. If `m > 0` and `A` cannot be inverted numerically (indicating either that `A` is singular or that the precision is insufficient), the values in the output matrix are left undefined and zero is returned. A nonzero return value guarantees that `A` is invertible and that the exact solution matrix is contained in the output. .. function:: int arb_mat_inv(arb_mat_t X, const arb_mat_t A, slong prec) Sets `X = A^{-1}` where `A` is a square matrix, computed by solving the system `AX = I`. If `A` cannot be inverted numerically (indicating either that `A` is singular or that the precision is insufficient), the values in the output matrix are left undefined and zero is returned. A nonzero return value guarantees that the matrix is invertible and that the exact inverse is contained in the output. .. function:: void arb_mat_det(arb_t det, const arb_mat_t A, slong prec) Computes the determinant of the matrix, using Gaussian elimination with partial pivoting. If at some point an invertible pivot element cannot be found, the elimination is stopped and the magnitude of the determinant of the remaining submatrix is bounded using Hadamard's inequality. Characteristic polynomial ------------------------------------------------------------------------------- .. function:: void _arb_mat_charpoly(arb_ptr cp, const arb_mat_t mat, slong prec) .. function:: void arb_mat_charpoly(arb_poly_t cp, const arb_mat_t mat, slong prec) Sets *cp* to the characteristic polynomial of *mat* which must be a square matrix. If the matrix has *n* rows, the underscore method requires space for `n + 1` output coefficients. Employs a division-free algorithm using `O(n^4)` operations. Special functions ------------------------------------------------------------------------------- .. function:: void arb_mat_exp(arb_mat_t B, const arb_mat_t A, slong prec) Sets *B* to the exponential of the matrix *A*, defined by the Taylor series .. math :: \exp(A) = \sum_{k=0}^{\infty} \frac{A^k}{k!}. The function is evaluated as `\exp(A/2^r)^{2^r}`, where `r` is chosen to give rapid convergence. The series is evaluated using rectangular splitting. The elementwise error when truncating the Taylor series after *N* terms is bounded by the error in the infinity norm, for which we have .. math :: \left\|\exp(2^{-r}A) - \sum_{k=0}^{N-1} \frac{\left(2^{-r} A\right)^k}{k!} \right\|_{\infty} = \left\|\sum_{k=N}^{\infty} \frac{\left(2^{-r} A\right)^k}{k!}\right\|_{\infty} \le \sum_{k=N}^{\infty} \frac{(2^{-r} \|A\|_{\infty})^k}{k!}. We bound the sum on the right using :func:`mag_exp_tail`. .. function:: void arb_mat_trace(arb_t trace, const arb_mat_t mat, slong prec) Sets *trace* to the trace of the matrix, i.e. the sum of entries on the main diagonal of *mat*. The matrix is required to be square. arb-2.8.1/doc/source/arb_poly.rst000066400000000000000000001337231264125401100167010ustar00rootroot00000000000000.. _arb-poly: **arb_poly.h** -- polynomials over the real numbers =============================================================================== An :type:`arb_poly_t` represents a polynomial over the real numbers, implemented as an array of coefficients of type :type:`arb_struct`. Most functions are provided in two versions: an underscore method which operates directly on pre-allocated arrays of coefficients and generally has some restrictions (such as requiring the lengths to be nonzero and not supporting aliasing of the input and output arrays), and a non-underscore method which performs automatic memory management and handles degenerate cases. Types, macros and constants ------------------------------------------------------------------------------- .. type:: arb_poly_struct .. type:: arb_poly_t Contains a pointer to an array of coefficients (coeffs), the used length (length), and the allocated size of the array (alloc). An *arb_poly_t* is defined as an array of length one of type *arb_poly_struct*, permitting an *arb_poly_t* to be passed by reference. Memory management ------------------------------------------------------------------------------- .. function:: void arb_poly_init(arb_poly_t poly) Initializes the polynomial for use, setting it to the zero polynomial. .. function:: void arb_poly_clear(arb_poly_t poly) Clears the polynomial, deallocating all coefficients and the coefficient array. .. function:: void arb_poly_fit_length(arb_poly_t poly, slong len) Makes sures that the coefficient array of the polynomial contains at least *len* initialized coefficients. .. function:: void _arb_poly_set_length(arb_poly_t poly, slong len) Directly changes the length of the polynomial, without allocating or deallocating coefficients. The value shold not exceed the allocation length. .. function:: void _arb_poly_normalise(arb_poly_t poly) Strips any trailing coefficients which are identical to zero. Basic manipulation ------------------------------------------------------------------------------- .. function:: void arb_poly_zero(arb_poly_t poly) .. function:: void arb_poly_one(arb_poly_t poly) Sets *poly* to the constant 0 respectively 1. .. function:: void arb_poly_set(arb_poly_t dest, const arb_poly_t src) Sets *dest* to a copy of *src*. .. function:: void arb_poly_set_round(arb_poly_t dest, const arb_poly_t src, slong prec) Sets *dest* to a copy of *src*, rounded to *prec* bits. .. function:: void arb_poly_set_coeff_si(arb_poly_t poly, slong n, slong c) .. function:: void arb_poly_set_coeff_arb(arb_poly_t poly, slong n, const arb_t c) Sets the coefficient with index *n* in *poly* to the value *c*. We require that *n* is nonnegative. .. function:: void arb_poly_get_coeff_arb(arb_t v, const arb_poly_t poly, slong n) Sets *v* to the value of the coefficient with index *n* in *poly*. We require that *n* is nonnegative. .. macro:: arb_poly_get_coeff_ptr(poly, n) Given `n \ge 0`, returns a pointer to coefficient *n* of *poly*, or *NULL* if *n* exceeds the length of *poly*. .. function:: void _arb_poly_shift_right(arb_ptr res, arb_srcptr poly, slong len, slong n) .. function:: void arb_poly_shift_right(arb_poly_t res, const arb_poly_t poly, slong n) Sets *res* to *poly* divided by `x^n`, throwing away the lower coefficients. We require that *n* is nonnegative. .. function:: void _arb_poly_shift_left(arb_ptr res, arb_srcptr poly, slong len, slong n) .. function:: void arb_poly_shift_left(arb_poly_t res, const arb_poly_t poly, slong n) Sets *res* to *poly* multiplied by `x^n`. We require that *n* is nonnegative. .. function:: void arb_poly_truncate(arb_poly_t poly, slong n) Truncates *poly* to have length at most *n*, i.e. degree strictly smaller than *n*. .. function:: slong arb_poly_length(const arb_poly_t poly) Returns the length of *poly*, i.e. zero if *poly* is identically zero, and otherwise one more than the index of the highest term that is not identically zero. .. function:: slong arb_poly_degree(const arb_poly_t poly) Returns the degree of *poly*, defined as one less than its length. Note that if one or several leading coefficients are balls containing zero, this value can be larger than the true degree of the exact polynomial represented by *poly*, so the return value of this function is effectively an upper bound. Conversions ------------------------------------------------------------------------------- .. function:: void arb_poly_set_fmpz_poly(arb_poly_t poly, const fmpz_poly_t src, slong prec) .. function:: void arb_poly_set_fmpq_poly(arb_poly_t poly, const fmpq_poly_t src, slong prec) .. function:: void arb_poly_set_si(arb_poly_t poly, slong src) Sets *poly* to *src*, rounding the coefficients to *prec* bits. Input and output ------------------------------------------------------------------------------- .. function:: void arb_poly_printd(const arb_poly_t poly, slong digits) Prints the polynomial as an array of coefficients, printing each coefficient using *arb_printd*. Random generation ------------------------------------------------------------------------------- .. function:: void arb_poly_randtest(arb_poly_t poly, flint_rand_t state, slong len, slong prec, slong mag_bits) Creates a random polynomial with length at most *len*. Comparisons ------------------------------------------------------------------------------- .. function:: int arb_poly_contains(const arb_poly_t poly1, const arb_poly_t poly2) .. function:: int arb_poly_contains_fmpz_poly(const arb_poly_t poly1, const fmpz_poly_t poly2) .. function:: int arb_poly_contains_fmpq_poly(const arb_poly_t poly1, const fmpq_poly_t poly2) Returns nonzero iff *poly1* contains *poly2*. .. function:: int arb_poly_equal(const arb_poly_t A, const arb_poly_t B) Returns nonzero iff *A* and *B* are equal as polynomial balls, i.e. all coefficients have equal midpoint and radius. .. function:: int _arb_poly_overlaps(arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2) .. function:: int arb_poly_overlaps(const arb_poly_t poly1, const arb_poly_t poly2) Returns nonzero iff *poly1* overlaps with *poly2*. The underscore function requires that *len1* ist at least as large as *len2*. .. function:: int arb_poly_get_unique_fmpz_poly(fmpz_poly_t z, const arb_poly_t x) If *x* contains a unique integer polynomial, sets *z* to that value and returns nonzero. Otherwise (if *x* represents no integers or more than one integer), returns zero, possibly partially modifying *z*. Bounds ------------------------------------------------------------------------------- .. function:: void _arb_poly_majorant(arb_ptr res, arb_srcptr poly, slong len, slong prec) .. function:: void arb_poly_majorant(arb_poly_t res, const arb_poly_t poly, slong prec) Sets *res* to an exact real polynomial whose coefficients are upper bounds for the absolute values of the coefficients in *poly*, rounded to *prec* bits. Arithmetic ------------------------------------------------------------------------------- .. function:: void _arb_poly_add(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) Sets *{C, max(lenA, lenB)}* to the sum of *{A, lenA}* and *{B, lenB}*. Allows aliasing of the input and output operands. .. function:: void arb_poly_add(arb_poly_t C, const arb_poly_t A, const arb_poly_t B, slong prec) .. function:: void arb_poly_add_si(arb_poly_t C, const arb_poly_t A, slong B, slong prec) Sets *C* to the sum of *A* and *B*. .. function:: void _arb_poly_sub(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) Sets *{C, max(lenA, lenB)}* to the difference of *{A, lenA}* and *{B, lenB}*. Allows aliasing of the input and output operands. .. function:: void arb_poly_sub(arb_poly_t C, const arb_poly_t A, const arb_poly_t B, slong prec) Sets *C* to the difference of *A* and *B*. .. function:: void arb_poly_neg(arb_poly_t C, const arb_poly_t A) Sets *C* to the negation of *A*. .. function:: void arb_poly_scalar_mul_2exp_si(arb_poly_t C, const arb_poly_t A, slong c) Sets *C* to *A* multiplied by `2^c`. .. function:: void _arb_poly_mullow_classical(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong n, slong prec) .. function:: void _arb_poly_mullow_block(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong n, slong prec) .. function:: void _arb_poly_mullow(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong n, slong prec) Sets *{C, n}* to the product of *{A, lenA}* and *{B, lenB}*, truncated to length *n*. The output is not allowed to be aliased with either of the inputs. We require `\mathrm{lenA} \ge \mathrm{lenB} > 0`, `n > 0`, `\mathrm{lenA} + \mathrm{lenB} - 1 \ge n`. The *classical* version uses a plain loop. This has good numerical stability but gets slow for large *n*. The *block* version decomposes the product into several subproducts which are computed exactly over the integers. It first attempts to find an integer `c` such that `A(2^c x)` and `B(2^c x)` have slowly varying coefficients, to reduce the number of blocks. The scaling factor `c` is chosen in a quick, heuristic way by picking the first and last nonzero terms in each polynomial. If the indices in `A` are `a_2, a_1` and the log-2 magnitudes are `e_2, e_1`, and the indices in `B` are `b_2, b_1` with corresponding magnitudes `f_2, f_1`, then we compute `c` as the weighted arithmetic mean of the slopes, rounded to the nearest integer: .. math :: c = \left\lfloor \frac{(e_2 - e_1) + (f_2 + f_1)}{(a_2 - a_1) + (b_2 - b_1)} + \frac{1}{2} \right \rfloor. This strategy is used because it is simple. It is not optimal in all cases, but will typically give good performance when multiplying two power series with a similar decay rate. The default algorithm chooses the *classical* algorithm for short polynomials and the *block* algorithm for slong polynomials. If the input pointers are identical (and the lengths are the same), they are assumed to represent the same polynomial, and its square is computed. .. function:: void arb_poly_mullow_classical(arb_poly_t C, const arb_poly_t A, const arb_poly_t B, slong n, slong prec) .. function:: void arb_poly_mullow_ztrunc(arb_poly_t C, const arb_poly_t A, const arb_poly_t B, slong n, slong prec) .. function:: void arb_poly_mullow_block(arb_poly_t C, const arb_poly_t A, const arb_poly_t B, slong n, slong prec) .. function:: void arb_poly_mullow(arb_poly_t C, const arb_poly_t A, const arb_poly_t B, slong n, slong prec) Sets *C* to the product of *A* and *B*, truncated to length *n*. If the same variable is passed for *A* and *B*, sets *C* to the square of *A* truncated to length *n*. .. function:: void _arb_poly_mul(arb_ptr C, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) Sets *{C, lenA + lenB - 1}* to the product of *{A, lenA}* and *{B, lenB}*. The output is not allowed to be aliased with either of the inputs. We require `\mathrm{lenA} \ge \mathrm{lenB} > 0`. This function is implemented as a simple wrapper for :func:`_arb_poly_mullow`. If the input pointers are identical (and the lengths are the same), they are assumed to represent the same polynomial, and its square is computed. .. function:: void arb_poly_mul(arb_poly_t C, const arb_poly_t A, const arb_poly_t B, slong prec) Sets *C* to the product of *A* and *B*. If the same variable is passed for *A* and *B*, sets *C* to the square of *A*. .. function:: void _arb_poly_inv_series(arb_ptr Q, arb_srcptr A, slong Alen, slong len, slong prec) Sets *{Q, len}* to the power series inverse of *{A, Alen}*. Uses Newton iteration. .. function:: void arb_poly_inv_series(arb_poly_t Q, const arb_poly_t A, slong n, slong prec) Sets *Q* to the power series inverse of *A*, truncated to length *n*. .. function:: void _arb_poly_div_series(arb_ptr Q, arb_srcptr A, slong Alen, arb_srcptr B, slong Blen, slong n, slong prec) Sets *{Q, n}* to the power series quotient of *{A, Alen}* by *{B, Blen}*. Uses Newton iteration followed by multiplication. .. function:: void arb_poly_div_series(arb_poly_t Q, const arb_poly_t A, const arb_poly_t B, slong n, slong prec) Sets *Q* to the power series quotient *A* divided by *B*, truncated to length *n*. .. function:: void _arb_poly_div(arb_ptr Q, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) .. function:: void _arb_poly_rem(arb_ptr R, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) .. function:: void _arb_poly_divrem(arb_ptr Q, arb_ptr R, arb_srcptr A, slong lenA, arb_srcptr B, slong lenB, slong prec) .. function:: int arb_poly_divrem(arb_poly_t Q, arb_poly_t R, const arb_poly_t A, const arb_poly_t B, slong prec) Performs polynomial division with remainder, computing a quotient `Q` and a remainder `R` such that `A = BQ + R`. The implementation reverses the inputs and performs power series division. If the leading coefficient of `B` contains zero (or if `B` is identically zero), returns 0 indicating failure without modifying the outputs. Otherwise returns nonzero. .. function:: void _arb_poly_div_root(arb_ptr Q, arb_t R, arb_srcptr A, slong len, const arb_t c, slong prec) Divides `A` by the polynomial `x - c`, computing the quotient `Q` as well as the remainder `R = f(c)`. Composition ------------------------------------------------------------------------------- .. function:: void _arb_poly_compose_horner(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) .. function:: void arb_poly_compose_horner(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) .. function:: void _arb_poly_compose_divconquer(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) .. function:: void arb_poly_compose_divconquer(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) .. function:: void _arb_poly_compose(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong prec) .. function:: void arb_poly_compose(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong prec) Sets *res* to the composition `h(x) = f(g(x))` where `f` is given by *poly1* and `g` is given by *poly2*, respectively using Horner's rule, divide-and-conquer, and an automatic choice between the two algorithms. The underscore methods do not support aliasing of the output with either input polynomial. .. function:: void _arb_poly_compose_series_horner(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) .. function:: void arb_poly_compose_series_horner(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) .. function:: void _arb_poly_compose_series_brent_kung(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) .. function:: void arb_poly_compose_series_brent_kung(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) .. function:: void _arb_poly_compose_series(arb_ptr res, arb_srcptr poly1, slong len1, arb_srcptr poly2, slong len2, slong n, slong prec) .. function:: void arb_poly_compose_series(arb_poly_t res, const arb_poly_t poly1, const arb_poly_t poly2, slong n, slong prec) Sets *res* to the power series composition `h(x) = f(g(x))` truncated to order `O(x^n)` where `f` is given by *poly1* and `g` is given by *poly2*, respectively using Horner's rule, the Brent-Kung baby step-giant step algorithm, and an automatic choice between the two algorithms. We require that the constant term in `g(x)` is exactly zero. The underscore methods do not support aliasing of the output with either input polynomial. .. function:: void _arb_poly_revert_series_lagrange(arb_ptr h, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_revert_series_lagrange(arb_poly_t h, const arb_poly_t f, slong n, slong prec) .. function:: void _arb_poly_revert_series_newton(arb_ptr h, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_revert_series_newton(arb_poly_t h, const arb_poly_t f, slong n, slong prec) .. function:: void _arb_poly_revert_series_lagrange_fast(arb_ptr h, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_revert_series_lagrange_fast(arb_poly_t h, const arb_poly_t f, slong n, slong prec) .. function:: void _arb_poly_revert_series(arb_ptr h, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_revert_series(arb_poly_t h, const arb_poly_t f, slong n, slong prec) Sets `h` to the power series reversion of `f`, i.e. the expansion of the compositional inverse function `f^{-1}(x)`, truncated to order `O(x^n)`, using respectively Lagrange inversion, Newton iteration, fast Lagrange inversion, and a default algorithm choice. We require that the constant term in `f` is exactly zero and that the linear term is nonzero. The underscore methods assume that *flen* is at least 2, and do not support aliasing. Evaluation ------------------------------------------------------------------------------- .. function:: void _arb_poly_evaluate_horner(arb_t y, arb_srcptr f, slong len, const arb_t x, slong prec) .. function:: void arb_poly_evaluate_horner(arb_t y, const arb_poly_t f, const arb_t x, slong prec) .. function:: void _arb_poly_evaluate_rectangular(arb_t y, arb_srcptr f, slong len, const arb_t x, slong prec) .. function:: void arb_poly_evaluate_rectangular(arb_t y, const arb_poly_t f, const arb_t x, slong prec) .. function:: void _arb_poly_evaluate(arb_t y, arb_srcptr f, slong len, const arb_t x, slong prec) .. function:: void arb_poly_evaluate(arb_t y, const arb_poly_t f, const arb_t x, slong prec) Sets `y = f(x)`, evaluated respectively using Horner's rule, rectangular splitting, and an automatic algorithm choice. .. function:: void _arb_poly_evaluate_acb_horner(acb_t y, arb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void arb_poly_evaluate_acb_horner(acb_t y, const arb_poly_t f, const acb_t x, slong prec) .. function:: void _arb_poly_evaluate_acb_rectangular(acb_t y, arb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void arb_poly_evaluate_acb_rectangular(acb_t y, const arb_poly_t f, const acb_t x, slong prec) .. function:: void _arb_poly_evaluate_acb(acb_t y, arb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void arb_poly_evaluate_acb(acb_t y, const arb_poly_t f, const acb_t x, slong prec) Sets `y = f(x)` where `x` is a complex number, evaluating the polynomial respectively using Horner's rule, rectangular splitting, and an automatic algorithm choice. .. function:: void _arb_poly_evaluate2_horner(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec) .. function:: void arb_poly_evaluate2_horner(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec) .. function:: void _arb_poly_evaluate2_rectangular(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec) .. function:: void arb_poly_evaluate2_rectangular(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec) .. function:: void _arb_poly_evaluate2(arb_t y, arb_t z, arb_srcptr f, slong len, const arb_t x, slong prec) .. function:: void arb_poly_evaluate2(arb_t y, arb_t z, const arb_poly_t f, const arb_t x, slong prec) Sets `y = f(x), z = f'(x)`, evaluated respectively using Horner's rule, rectangular splitting, and an automatic algorithm choice. When Horner's rule is used, the only advantage of evaluating the function and its derivative simultaneously is that one does not have to generate the derivative polynomial explicitly. With the rectangular splitting algorithm, the powers can be reused, making simultaneous evaluation slightly faster. .. function:: void _arb_poly_evaluate2_acb_horner(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void arb_poly_evaluate2_acb_horner(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec) .. function:: void _arb_poly_evaluate2_acb_rectangular(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void arb_poly_evaluate2_acb_rectangular(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec) .. function:: void _arb_poly_evaluate2_acb(acb_t y, acb_t z, arb_srcptr f, slong len, const acb_t x, slong prec) .. function:: void arb_poly_evaluate2_acb(acb_t y, acb_t z, const arb_poly_t f, const acb_t x, slong prec) Sets `y = f(x), z = f'(x)`, evaluated respectively using Horner's rule, rectangular splitting, and an automatic algorithm choice. Product trees ------------------------------------------------------------------------------- .. function:: void _arb_poly_product_roots(arb_ptr poly, arb_srcptr xs, slong n, slong prec) .. function:: void arb_poly_product_roots(arb_poly_t poly, arb_srcptr xs, slong n, slong prec) Generates the polynomial `(x-x_0)(x-x_1)\cdots(x-x_{n-1})`. .. function:: arb_ptr * _arb_poly_tree_alloc(slong len) Returns an initialized data structured capable of representing a remainder tree (product tree) of *len* roots. .. function:: void _arb_poly_tree_free(arb_ptr * tree, slong len) Deallocates a tree structure as allocated using *_arb_poly_tree_alloc*. .. function:: void _arb_poly_tree_build(arb_ptr * tree, arb_srcptr roots, slong len, slong prec) Constructs a product tree from a given array of *len* roots. The tree structure must be pre-allocated to the specified length using :func:`_arb_poly_tree_alloc`. Multipoint evaluation ------------------------------------------------------------------------------- .. function:: void _arb_poly_evaluate_vec_iter(arb_ptr ys, arb_srcptr poly, slong plen, arb_srcptr xs, slong n, slong prec) .. function:: void arb_poly_evaluate_vec_iter(arb_ptr ys, const arb_poly_t poly, arb_srcptr xs, slong n, slong prec) Evaluates the polynomial simultaneously at *n* given points, calling :func:`_arb_poly_evaluate` repeatedly. .. function:: void _arb_poly_evaluate_vec_fast_precomp(arb_ptr vs, arb_srcptr poly, slong plen, arb_ptr * tree, slong len, slong prec) .. function:: void _arb_poly_evaluate_vec_fast(arb_ptr ys, arb_srcptr poly, slong plen, arb_srcptr xs, slong n, slong prec) .. function:: void arb_poly_evaluate_vec_fast(arb_ptr ys, const arb_poly_t poly, arb_srcptr xs, slong n, slong prec) Evaluates the polynomial simultaneously at *n* given points, using fast multipoint evaluation. Interpolation ------------------------------------------------------------------------------- .. function:: void _arb_poly_interpolate_newton(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) .. function:: void arb_poly_interpolate_newton(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) Recovers the unique polynomial of length at most *n* that interpolates the given *x* and *y* values. This implementation first interpolates in the Newton basis and then converts back to the monomial basis. .. function:: void _arb_poly_interpolate_barycentric(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) .. function:: void arb_poly_interpolate_barycentric(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) Recovers the unique polynomial of length at most *n* that interpolates the given *x* and *y* values. This implementation uses the barycentric form of Lagrange interpolation. .. function:: void _arb_poly_interpolation_weights(arb_ptr w, arb_ptr * tree, slong len, slong prec) .. function:: void _arb_poly_interpolate_fast_precomp(arb_ptr poly, arb_srcptr ys, arb_ptr * tree, arb_srcptr weights, slong len, slong prec) .. function:: void _arb_poly_interpolate_fast(arb_ptr poly, arb_srcptr xs, arb_srcptr ys, slong len, slong prec) .. function:: void arb_poly_interpolate_fast(arb_poly_t poly, arb_srcptr xs, arb_srcptr ys, slong n, slong prec) Recovers the unique polynomial of length at most *n* that interpolates the given *x* and *y* values, using fast Lagrange interpolation. The precomp function takes a precomputed product tree over the *x* values and a vector of interpolation weights as additional inputs. Differentiation ------------------------------------------------------------------------------- .. function:: void _arb_poly_derivative(arb_ptr res, arb_srcptr poly, slong len, slong prec) Sets *{res, len - 1}* to the derivative of *{poly, len}*. Allows aliasing of the input and output. .. function:: void arb_poly_derivative(arb_poly_t res, const arb_poly_t poly, slong prec) Sets *res* to the derivative of *poly*. .. function:: void _arb_poly_integral(arb_ptr res, arb_srcptr poly, slong len, slong prec) Sets *{res, len}* to the integral of *{poly, len - 1}*. Allows aliasing of the input and output. .. function:: void arb_poly_integral(arb_poly_t res, const arb_poly_t poly, slong prec) Sets *res* to the integral of *poly*. Transforms ------------------------------------------------------------------------------- .. function:: void _arb_poly_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec) .. function:: void arb_poly_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec) Computes the Borel transform of the input polynomial, mapping `\sum_k a_k x^k` to `\sum_k (a_k / k!) x^k`. The underscore method allows aliasing. .. function:: void _arb_poly_inv_borel_transform(arb_ptr res, arb_srcptr poly, slong len, slong prec) .. function:: void arb_poly_inv_borel_transform(arb_poly_t res, const arb_poly_t poly, slong prec) Computes the inverse Borel transform of the input polynomial, mapping `\sum_k a_k x^k` to `\sum_k a_k k! x^k`. The underscore method allows aliasing. .. function:: void _arb_poly_binomial_transform_basecase(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec) .. function:: void arb_poly_binomial_transform_basecase(arb_poly_t b, const arb_poly_t a, slong len, slong prec) .. function:: void _arb_poly_binomial_transform_convolution(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec) .. function:: void arb_poly_binomial_transform_convolution(arb_poly_t b, const arb_poly_t a, slong len, slong prec) .. function:: void _arb_poly_binomial_transform(arb_ptr b, arb_srcptr a, slong alen, slong len, slong prec) .. function:: void arb_poly_binomial_transform(arb_poly_t b, const arb_poly_t a, slong len, slong prec) Computes the binomial transform of the input polynomial, truncating the output to length *len*. The binomial transform maps the coefficients `a_k` in the input polynomial to the coefficients `b_k` in the output polynomial via `b_n = \sum_{k=0}^n (-1)^k {n \choose k} a_k`. The binomial transform is equivalent to the power series composition `f(x) \to (1-x)^{-1} f(x/(x-1))`, and is its own inverse. The *basecase* version evaluates coefficients one by one from the definition, generating the binomial coefficients by a recurrence relation. The *convolution* version uses the identity `T(f(x)) = B^{-1}(e^x B(f(-x)))` where `T` denotes the binomial transform operator and `B` denotes the Borel transform operator. This only costs a single polynomial multiplication, plus some scalar operations. The default version automatically chooses an algorithm. The underscore methods do not support aliasing, and assume that the lengths are nonzero. Powers and elementary functions ------------------------------------------------------------------------------- .. function:: void _arb_poly_pow_ui_trunc_binexp(arb_ptr res, arb_srcptr f, slong flen, ulong exp, slong len, slong prec) Sets *{res, len}* to *{f, flen}* raised to the power *exp*, truncated to length *len*. Requires that *len* is no longer than the length of the power as computed without truncation (i.e. no zero-padding is performed). Does not support aliasing of the input and output, and requires that *flen* and *len* are positive. Uses binary expontiation. .. function:: void arb_poly_pow_ui_trunc_binexp(arb_poly_t res, const arb_poly_t poly, ulong exp, slong len, slong prec) Sets *res* to *poly* raised to the power *exp*, truncated to length *len*. Uses binary exponentiation. .. function:: void _arb_poly_pow_ui(arb_ptr res, arb_srcptr f, slong flen, ulong exp, slong prec) Sets *res* to *{f, flen}* raised to the power *exp*. Does not support aliasing of the input and output, and requires that *flen* is positive. .. function:: void arb_poly_pow_ui(arb_poly_t res, const arb_poly_t poly, ulong exp, slong prec) Sets *res* to *poly* raised to the power *exp*. .. function:: void _arb_poly_pow_series(arb_ptr h, arb_srcptr f, slong flen, arb_srcptr g, slong glen, slong len, slong prec) Sets *{h, len}* to the power series `f(x)^{g(x)} = \exp(g(x) \log f(x))` truncated to length *len*. This function detects special cases such as *g* being an exact small integer or `\pm 1/2`, and computes such powers more efficiently. This function does not support aliasing of the output with either of the input operands. It requires that all lengths are positive, and assumes that *flen* and *glen* do not exceed *len*. .. function:: void arb_poly_pow_series(arb_poly_t h, const arb_poly_t f, const arb_poly_t g, slong len, slong prec) Sets *h* to the power series `f(x)^{g(x)} = \exp(g(x) \log f(x))` truncated to length *len*. This function detects special cases such as *g* being an exact small integer or `\pm 1/2`, and computes such powers more efficiently. .. function:: void _arb_poly_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec) Sets *{h, len}* to the power series `f(x)^g = \exp(g \log f(x))` truncated to length *len*. This function detects special cases such as *g* being an exact small integer or `\pm 1/2`, and computes such powers more efficiently. This function does not support aliasing of the output with either of the input operands. It requires that all lengths are positive, and assumes that *flen* does not exceed *len*. .. function:: void arb_poly_pow_arb_series(arb_poly_t h, const arb_poly_t f, const arb_t g, slong len, slong prec) Sets *h* to the power series `f(x)^g = \exp(g \log f(x))` truncated to length *len*. .. function:: void _arb_poly_sqrt_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_sqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) Sets *g* to the power series square root of *h*, truncated to length *n*. Uses division-free Newton iteration for the reciprocal square root, followed by a multiplication. The underscore method does not support aliasing of the input and output arrays. It requires that *hlen* and *n* are greater than zero. .. function:: void _arb_poly_rsqrt_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_rsqrt_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) Sets *g* to the reciprocal power series square root of *h*, truncated to length *n*. Uses division-free Newton iteration. The underscore method does not support aliasing of the input and output arrays. It requires that *hlen* and *n* are greater than zero. .. function:: void _arb_poly_log_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_log_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) Sets *res* to the power series logarithm of *f*, truncated to length *n*. Uses the formula `\log(f(x)) = \int f'(x) / f(x) dx`, adding the logarithm of the constant term in *f* as the constant of integration. The underscore method supports aliasing of the input and output arrays. It requires that *flen* and *n* are greater than zero. .. function:: void _arb_poly_atan_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_atan_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) .. function:: void _arb_poly_asin_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_asin_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) .. function:: void _arb_poly_acos_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec) .. function:: void arb_poly_acos_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec) Sets *res* respectively to the power series inverse tangent, inverse sine and inverse cosine of *f*, truncated to length *n*. Uses the formulas .. math :: \tan^{-1}(f(x)) = \int f'(x) / (1+f(x)^2) dx, \sin^{-1}(f(x)) = \int f'(x) / (1-f(x)^2)^{1/2} dx, \cos^{-1}(f(x)) = -\int f'(x) / (1-f(x)^2)^{1/2} dx, adding the inverse function of the constant term in *f* as the constant of integration. The underscore methods supports aliasing of the input and output arrays. They require that *flen* and *n* are greater than zero. .. function:: void _arb_poly_exp_series_basecase(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_exp_series_basecase(arb_poly_t f, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_exp_series(arb_ptr f, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_exp_series(arb_poly_t f, const arb_poly_t h, slong n, slong prec) Sets `f` to the power series exponential of `h`, truncated to length `n`. The basecase version uses a simple recurrence for the coefficients, requiring `O(nm)` operations where `m` is the length of `h`. The main implementation uses Newton iteration, starting from a small number of terms given by the basecase algorithm. The complexity is `O(M(n))`. Redundant operations in the Newton iteration are avoided by using the scheme described in [HZ2004]_. The underscore methods support aliasing and allow the input to be shorter than the output, but require the lengths to be nonzero. .. function:: void _arb_poly_sin_cos_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec, int times_pi) .. function:: void arb_poly_sin_cos_series_basecase(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec, int times_pi) .. function:: void _arb_poly_sin_cos_series_tangent(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec, int times_pi) .. function:: void arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec, int times_pi) .. function:: void _arb_poly_sin_cos_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_sin_cos_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec) Sets *s* and *c* to the power series sine and cosine of *h*, computed simultaneously. The *basecase* version uses a simple recurrence for the coefficients, requiring `O(nm)` operations where `m` is the length of `h`. The *tangent* version uses the tangent half-angle formulas to compute the sine and cosine via :func:`_arb_poly_tan_series`. This requires `O(M(n))` operations. When `h = h_0 + h_1` where the constant term `h_0` is nonzero, the evaluation is done as `\sin(h_0 + h_1) = \cos(h_0) \sin(h_1) + \sin(h_0) \cos(h_1)`, `\cos(h_0 + h_1) = \cos(h_0) \cos(h_1) - \sin(h_0) \sin(h_1)`, to improve accuracy and avoid dividing by zero at the poles of the tangent function. The default version automatically selects between the *basecase* and *tangent* algorithms depending on the input. The *basecase* and *tangent* versions take a flag *times_pi* specifying that the input is to be multiplied by `\pi`. The underscore methods support aliasing and require the lengths to be nonzero. .. function:: void _arb_poly_sin_series(arb_ptr s, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_sin_series(arb_poly_t s, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_cos_series(arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_cos_series(arb_poly_t c, const arb_poly_t h, slong n, slong prec) Respectively evaluates the power series sine or cosine. These functions simply wrap :func:`_arb_poly_sin_cos_series`. The underscore methods support aliasing and require the lengths to be nonzero. .. function:: void _arb_poly_tan_series(arb_ptr g, arb_srcptr h, slong hlen, slong len, slong prec) .. function:: void arb_poly_tan_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec) Sets *g* to the power series tangent of *h*. For small *n* takes the quotient of the sine and cosine as computed using the basecase algorithm. For large *n*, uses Newton iteration to invert the inverse tangent series. The complexity is `O(M(n))`. The underscore version does not support aliasing, and requires the lengths to be nonzero. .. function:: void _arb_poly_sin_cos_pi_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_sin_cos_pi_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_sin_pi_series(arb_ptr s, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_sin_pi_series(arb_poly_t s, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_cos_pi_series(arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_cos_pi_series(arb_poly_t c, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_cot_pi_series(arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_cot_pi_series(arb_poly_t c, const arb_poly_t h, slong n, slong prec) Compute the respective trigonometric functions of the input multiplied by `\pi`. Gamma function and factorials ------------------------------------------------------------------------------- .. function:: void _arb_poly_gamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_gamma_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_rgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_rgamma_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_lgamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_lgamma_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec) .. function:: void _arb_poly_digamma_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_digamma_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec) Sets *res* to the series expansion of `\Gamma(h(x))`, `1/\Gamma(h(x))`, or `\log \Gamma(h(x))`, `\psi(h(x))`, truncated to length *n*. These functions first generate the Taylor series at the constant term of *h*, and then call :func:`_arb_poly_compose_series`. The Taylor coefficients are generated using the Riemann zeta function if the constant term of *h* is a small integer, and with Stirling's series otherwise. The underscore methods support aliasing of the input and output arrays, and require that *hlen* and *n* are greater than zero. .. function:: void _arb_poly_rising_ui_series(arb_ptr res, arb_srcptr f, slong flen, ulong r, slong trunc, slong prec) .. function:: void arb_poly_rising_ui_series(arb_poly_t res, const arb_poly_t f, ulong r, slong trunc, slong prec) Sets *res* to the rising factorial `(f) (f+1) (f+2) \cdots (f+r-1)`, truncated to length *trunc*. The underscore method assumes that *flen*, *r* and *trunc* are at least 1, and does not support aliasing. Uses binary splitting. Zeta function ------------------------------------------------------------------------------- .. function:: void arb_poly_zeta_series(arb_poly_t res, const arb_poly_t s, const arb_t a, int deflate, slong n, slong prec) Sets *res* to the Hurwitz zeta function `\zeta(s,a)` where `s` a power series and `a` is a constant, truncated to length *n*. To evaluate the usual Riemann zeta function, set `a = 1`. If *deflate* is nonzero, evaluates `\zeta(s,a) + 1/(1-s)`, which is well-defined as a limit when the constant term of `s` is 1. In particular, expanding `\zeta(s,a) + 1/(1-s)` with `s = 1+x` gives the Stieltjes constants .. math :: \sum_{k=0}^{n-1} \frac{(-1)^k}{k!} \gamma_k(a) x^k. If `a = 1`, this implementation uses the reflection formula if the midpoint of the constant term of `s` is negative. .. function:: void _arb_poly_riemann_siegel_theta_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_riemann_siegel_theta_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec) Sets *res* to the series expansion of the Riemann-Siegel theta function .. math :: \theta(h) = \arg \left(\Gamma\left(\frac{2ih+1}{4}\right)\right) - \frac{\log \pi}{2} h where the argument of the gamma function is chosen continuously as the imaginary part of the log gamma function. The underscore method does not support aliasing of the input and output arrays, and requires that the lengths are greater than zero. .. function:: void _arb_poly_riemann_siegel_z_series(arb_ptr res, arb_srcptr h, slong hlen, slong n, slong prec) .. function:: void arb_poly_riemann_siegel_z_series(arb_poly_t res, const arb_poly_t h, slong n, slong prec) Sets *res* to the series expansion of the Riemann-Siegel Z-function .. math :: Z(h) = e^{i\theta(h)} \zeta(1/2+ih). The zeros of the Z-function on the real line precisely correspond to the imaginary parts of the zeros of the Riemann zeta function on the critical line. The underscore method supports aliasing of the input and output arrays, and requires that the lengths are greater than zero. Root-finding ------------------------------------------------------------------------------- .. function:: void _arb_poly_root_bound_fujiwara(mag_t bound, arb_srcptr poly, slong len) .. function:: void arb_poly_root_bound_fujiwara(mag_t bound, arb_poly_t poly) Sets *bound* to an upper bound for the magnitude of all the complex roots of *poly*. Uses Fujiwara's bound .. math :: 2 \max \left\{\left|\frac{a_{n-1}}{a_n}\right|, \left|\frac{a_{n-2}}{a_n}\right|^{1/2}, \cdots, \left|\frac{a_1}{a_n}\right|^{1/(n-1)}, \left|\frac{a_0}{2a_n}\right|^{1/n} \right\} where `a_0, \ldots, a_n` are the coefficients of *poly*. .. function:: void _arb_poly_newton_convergence_factor(arf_t convergence_factor, arb_srcptr poly, slong len, const arb_t convergence_interval, slong prec) Given an interval `I` specified by *convergence_interval*, evaluates a bound for `C = \sup_{t,u \in I} \frac{1}{2} |f''(t)| / |f'(u)|`, where `f` is the polynomial defined by the coefficients *{poly, len}*. The bound is obtained by evaluating `f'(I)` and `f''(I)` directly. If `f` has large coefficients, `I` must be extremely precise in order to get a finite factor. .. function:: int _arb_poly_newton_step(arb_t xnew, arb_srcptr poly, slong len, const arb_t x, const arb_t convergence_interval, const arf_t convergence_factor, slong prec) Performs a single step with Newton's method. The input consists of the polynomial `f` specified by the coefficients *{poly, len}*, an interval `x = [m-r, m+r]` known to contain a single root of `f`, an interval `I` (*convergence_interval*) containing `x` with an associated bound (*convergence_factor*) for `C = \sup_{t,u \in I} \frac{1}{2} |f''(t)| / |f'(u)|`, and a working precision *prec*. The Newton update consists of setting `x' = [m'-r', m'+r']` where `m' = m - f(m) / f'(m)` and `r' = C r^2`. The expression `m - f(m) / f'(m)` is evaluated using ball arithmetic at a working precision of *prec* bits, and the rounding error during this evaluation is accounted for in the output. We now check that `x' \in I` and `m' < m`. If both conditions are satisfied, we set *xnew* to `x'` and return nonzero. If either condition fails, we set *xnew* to `x` and return zero, indicating that no progress was made. .. function:: void _arb_poly_newton_refine_root(arb_t r, arb_srcptr poly, slong len, const arb_t start, const arb_t convergence_interval, const arf_t convergence_factor, slong eval_extra_prec, slong prec) Refines a precise estimate of a polynomial root to high precision by performing several Newton steps, using nearly optimally chosen doubling precision steps. The inputs are defined as for *_arb_poly_newton_step*, except for the precision parameters: *prec* is the target accuracy and *eval_extra_prec* is the estimated number of guard bits that need to be added to evaluate the polynomial accurately close to the root (typically, if the polynomial has large coefficients of alternating signs, this needs to be approximately the bit size of the coefficients). Other special polynomials ------------------------------------------------------------------------------- .. function:: void _arb_poly_swinnerton_dyer_ui(arb_ptr poly, ulong n, slong trunc, slong prec) .. function:: void arb_poly_swinnerton_dyer_ui(arb_poly_t poly, ulong n, slong prec) Computes the Swinnerton-Dyer polynomial `S_n`, which has degree `2^n` and is the rational minimal polynomial of the sum of the square roots of the first *n* prime numbers. If *prec* is set to zero, a precision is chosen automatically such that :func:`arb_poly_get_unique_fmpz_poly` should be successful. Otherwise a working precision of *prec* bits is used. The underscore version accepts an additional *trunc* parameter. Even when computing a truncated polynomial, the array *poly* must have room for `2^n + 1` coefficients, used as temporary space. arb-2.8.1/doc/source/arf.rst000066400000000000000000000607341264125401100156430ustar00rootroot00000000000000.. _arf: **arf.h** -- arbitrary-precision floating-point numbers =============================================================================== A variable of type :type:`arf_t` holds an arbitrary-precision binary floating-point number, i.e. a rational number of the form `x \times 2^y` where `x, y \in \mathbb{Z}` and `x` is odd; or one of the special values zero, plus infinity, minus infinity, or NaN (not-a-number). The *exponent* of a finite and nonzero floating-point number can be defined in different ways: for example, as the component *y* above, or as the unique integer *e* such that `x \times 2^y = m \times 2^e` where `1/2 \le |m| < 1`. The internal representation of an :type:`arf_t` stores the exponent in the latter format. The conventions for special values largely follow those of the IEEE floating-point standard. At the moment, there is no support for negative zero, unsigned infinity, or a NaN with a payload, though some of these might be added in the future. Except where otherwise noted, the output of an operation is the floating-point number obtained by taking the inputs as exact numbers, in principle carrying out the operation exactly, and rounding the resulting real number to the nearest representable floating-point number whose mantissa has at most the specified number of bits, in the specified direction of rounding. Some operations are always or optionally done exactly. The :type:`arf_t` type is almost identical semantically to the legacy :type:`fmpr_t` type, but uses a more efficient internal representation. The most significant differences that the user has to be aware of are: * The mantissa is no longer represented as a FLINT :type:`fmpz`, and the internal exponent points to the top of the binary expansion of the mantissa instead of of the bottom. Code designed to manipulate components of an :type:`fmpr_t` directly can be ported to the :type:`arf_t` type by making use of :func:`arf_get_fmpz_2exp` and :func:`arf_set_fmpz_2exp`. * Some :type:`arf_t` functions return an :type:`int` indicating whether a result is inexact, whereas the corresponding :type:`fmpr_t` functions return an :type:`slong` encoding the relative exponent of the error. Types, macros and constants ------------------------------------------------------------------------------- .. type:: arf_struct .. type:: arf_t An :type:`arf_struct` contains four words: an :type:`fmpz` exponent (*exp*), a *size* field tracking the number of limbs used (one bit of this field is also used for the sign of the number), and two more words. The last two words hold the value directly if there are at most two limbs, and otherwise contain one *alloc* field (tracking the total number of allocated limbs, not all of which might be used) and a pointer to the actual limbs. Thus, up to 128 bits on a 64-bit machine and 64 bits on a 32-bit machine, no space outside of the :type:`arf_struct` is used. An :type:`arf_t` is defined as an array of length one of type :type:`arf_struct`, permitting an :type:`arf_t` to be passed by reference. .. type:: arf_rnd_t Specifies the rounding mode for the result of an approximate operation. .. macro:: ARF_RND_DOWN Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards zero. .. macro:: ARF_RND_UP Specifies that the result of an operation should be rounded to the nearest representable number in the direction away from zero. .. macro:: ARF_RND_FLOOR Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards minus infinity. .. macro:: ARF_RND_CEIL Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards plus infinity. .. macro:: ARF_RND_NEAR Specifies that the result of an operation should be rounded to the nearest representable number, rounding to an odd mantissa if there is a tie between two values. *Warning*: this rounding mode is currently not implemented (except for a few conversions functions where this stated explicitly). .. macro:: ARF_PREC_EXACT If passed as the precision parameter to a function, indicates that no rounding is to be performed. This must only be used when it is known that the result of the operation can be represented exactly and fits in memory (the typical use case is working with small integer values). Note that, for example, adding two numbers whose exponents are far apart can easily produce an exact result that is far too large to store in memory. Memory management ------------------------------------------------------------------------------- .. function:: void arf_init(arf_t x) Initializes the variable *x* for use. Its value is set to zero. .. function:: void arf_clear(arf_t x) Clears the variable *x*, freeing or recycling its allocated memory. Special values ------------------------------------------------------------------------------- .. function:: void arf_zero(arf_t x) .. function:: void arf_one(arf_t x) .. function:: void arf_pos_inf(arf_t x) .. function:: void arf_neg_inf(arf_t x) .. function:: void arf_nan(arf_t x) Sets *x* respectively to 0, 1, `+\infty`, `-\infty`, NaN. .. function:: int arf_is_zero(const arf_t x) .. function:: int arf_is_one(const arf_t x) .. function:: int arf_is_pos_inf(const arf_t x) .. function:: int arf_is_neg_inf(const arf_t x) .. function:: int arf_is_nan(const arf_t x) Returns nonzero iff *x* respectively equals 0, 1, `+\infty`, `-\infty`, NaN. .. function:: int arf_is_inf(const arf_t x) Returns nonzero iff *x* equals either `+\infty` or `-\infty`. .. function:: int arf_is_normal(const arf_t x) Returns nonzero iff *x* is a finite, nonzero floating-point value, i.e. not one of the special values 0, `+\infty`, `-\infty`, NaN. .. function:: int arf_is_special(const arf_t x) Returns nonzero iff *x* is one of the special values 0, `+\infty`, `-\infty`, NaN, i.e. not a finite, nonzero floating-point value. .. function:: int arf_is_finite(arf_t x) Returns nonzero iff *x* is a finite floating-point value, i.e. not one of the values `+\infty`, `-\infty`, NaN. (Note that this is not equivalent to the negation of :func:`arf_is_inf`.) Assignment, rounding and conversions ------------------------------------------------------------------------------- .. function:: void arf_set(arf_t y, const arf_t x) .. function:: void arf_set_mpz(arf_t y, const mpz_t x) .. function:: void arf_set_fmpz(arf_t y, const fmpz_t x) .. function:: void arf_set_ui(arf_t y, ulong x) .. function:: void arf_set_si(arf_t y, slong x) .. function:: void arf_set_mpfr(arf_t y, const mpfr_t x) .. function:: void arf_set_fmpr(arf_t y, const fmpr_t x) .. function:: void arf_set_d(arf_t y, double x) Sets *y* exactly to *x*. .. function:: void arf_swap(arf_t y, arf_t x) Swaps *y* and *x* efficiently. .. function:: void arf_init_set_ui(arf_t y, ulong x) .. function:: void arf_init_set_si(arf_t y, slong x) Initialises *y* and sets it to *x* in a single operation. .. function:: int arf_set_round(arf_t y, const arf_t x, slong prec, arf_rnd_t rnd) .. function:: int arf_set_round_si(arf_t x, slong v, slong prec, arf_rnd_t rnd) .. function:: int arf_set_round_ui(arf_t x, ulong v, slong prec, arf_rnd_t rnd) .. function:: int arf_set_round_mpz(arf_t y, const mpz_t x, slong prec, arf_rnd_t rnd) .. function:: int arf_set_round_fmpz(arf_t y, const fmpz_t x, slong prec, arf_rnd_t rnd) Sets *y* to *x*, rounded to *prec* bits in the direction specified by *rnd*. .. function:: void arf_set_si_2exp_si(arf_t y, slong m, slong e) .. function:: void arf_set_ui_2exp_si(arf_t y, ulong m, slong e) .. function:: void arf_set_fmpz_2exp(arf_t y, const fmpz_t m, const fmpz_t e) Sets *y* to `m \times 2^e`. .. function:: int arf_set_round_fmpz_2exp(arf_t y, const fmpz_t x, const fmpz_t e, slong prec, arf_rnd_t rnd) Sets *y* to `x \times 2^e`, rounded to *prec* bits in the direction specified by *rnd*. .. function:: void arf_get_fmpz_2exp(fmpz_t m, fmpz_t e, const arf_t x) Sets *m* and *e* to the unique integers such that `x = m \times 2^e` and *m* is odd, provided that *x* is a nonzero finite fraction. If *x* is zero, both *m* and *e* are set to zero. If *x* is infinite or NaN, the result is undefined. .. function:: double arf_get_d(const arf_t x, arf_rnd_t rnd) Returns *x* rounded to a double in the direction specified by *rnd*. This method supports rounding to nearest with *ARF_RND_NEAR*. It also rounds correctly when overflowing or underflowing the double exponent range (this was not the case in an earlier version). .. function:: void arf_get_fmpr(fmpr_t y, const arf_t x) Sets *y* exactly to *x*. .. function:: int arf_get_mpfr(mpfr_t y, const arf_t x, mpfr_rnd_t rnd) Sets the MPFR variable *y* to the value of *x*. If the precision of *x* is too small to allow *y* to be represented exactly, it is rounded in the specified MPFR rounding mode. The return value (-1, 0 or 1) indicates the direction of rounding, following the convention of the MPFR library. .. function:: void arf_get_fmpz(fmpz_t z, const arf_t x, arf_rnd_t rnd) Sets *z* to *x* rounded to the nearest integer in the direction specified by *rnd*. If rnd is *ARF_RND_NEAR*, rounds to the nearest even integer in case of a tie. Aborts if *x* is infinite, NaN or if the exponent is unreasonably large. .. function:: slong arf_get_si(const arf_t x, arf_rnd_t rnd) Returns *x* rounded to the nearest integer in the direction specified by *rnd*. If *rnd* is *ARF_RND_NEAR*, rounds to the nearest even integer in case of a tie. Aborts if *x* is infinite, NaN, or the value is too large to fit in a slong. .. function:: int arf_get_fmpz_fixed_fmpz(fmpz_t y, const arf_t x, const fmpz_t e) .. function:: int arf_get_fmpz_fixed_si(fmpz_t y, const arf_t x, slong e) Converts *x* to a mantissa with predetermined exponent, i.e. computes an integer *y* such that `y \times 2^e \approx x`, truncating if necessary. Returns 0 if exact and 1 if truncation occurred. .. function:: void arf_floor(arf_t y, const arf_t x) .. function:: void arf_ceil(arf_t y, const arf_t x) Sets *y* to `\lfloor x \rfloor` and `\lceil x \rceil` respectively. The result is always represented exactly, requiring no more bits to store than the input. To round the result to a floating-point number with a lower precision, call :func:`arf_set_round` afterwards. Comparisons and bounds ------------------------------------------------------------------------------- .. function:: int arf_equal(const arf_t x, const arf_t y) .. function:: int arf_equal_si(const arf_t x, slong y) Returns nonzero iff *x* and *y* are exactly equal. This function does not treat NaN specially, i.e. NaN compares as equal to itself. .. function:: int arf_cmp(const arf_t x, const arf_t y) Returns negative, zero, or positive, depending on whether *x* is respectively smaller, equal, or greater compared to *y*. Comparison with NaN is undefined. .. function:: int arf_cmpabs(const arf_t x, const arf_t y) .. function:: int arf_cmpabs_ui(const arf_t x, ulong y) .. function:: int arf_cmpabs_mag(const arf_t x, const mag_t y) Compares the absolute values of *x* and *y*. .. function:: int arf_cmp_2exp_si(const arf_t x, slong e) .. function:: int arf_cmpabs_2exp_si(const arf_t x, slong e) Compares *x* (respectively its absolute value) with `2^e`. .. function:: int arf_sgn(const arf_t x) Returns `-1`, `0` or `+1` according to the sign of *x*. The sign of NaN is undefined. .. function:: void arf_min(arf_t z, const arf_t a, const arf_t b) .. function:: void arf_max(arf_t z, const arf_t a, const arf_t b) Sets *z* respectively to the minimum and the maximum of *a* and *b*. .. function:: slong arf_bits(const arf_t x) Returns the number of bits needed to represent the absolute value of the mantissa of *x*, i.e. the minimum precision sufficient to represent *x* exactly. Returns 0 if *x* is a special value. .. function:: int arf_is_int(const arf_t x) Returns nonzero iff *x* is integer-valued. .. function:: int arf_is_int_2exp_si(const arf_t x, slong e) Returns nonzero iff *x* equals `n 2^e` for some integer *n*. .. function:: void arf_abs_bound_lt_2exp_fmpz(fmpz_t b, const arf_t x) Sets *b* to the smallest integer such that `|x| < 2^b`. If *x* is zero, infinity or NaN, the result is undefined. .. function:: void arf_abs_bound_le_2exp_fmpz(fmpz_t b, const arf_t x) Sets *b* to the smallest integer such that `|x| \le 2^b`. If *x* is zero, infinity or NaN, the result is undefined. .. function:: slong arf_abs_bound_lt_2exp_si(const arf_t x) Returns the smallest integer *b* such that `|x| < 2^b`, clamping the result to lie between -*ARF_PREC_EXACT* and *ARF_PREC_EXACT* inclusive. If *x* is zero, -*ARF_PREC_EXACT* is returned, and if *x* is infinity or NaN, *ARF_PREC_EXACT* is returned. Magnitude functions ------------------------------------------------------------------------------- .. function:: void arf_get_mag(mag_t y, const arf_t x) Sets *y* to an upper bound for the absolute value of *x*. .. function:: void arf_get_mag_lower(mag_t y, const arf_t x) Sets *y* to a lower bound for the absolute value of *x*. .. function:: void arf_set_mag(arf_t y, const mag_t x) Sets *y* to *x*. .. function:: void mag_init_set_arf(mag_t y, const arf_t x) Initializes *y* and sets it to an upper bound for *x*. .. function:: void mag_fast_init_set_arf(mag_t y, const arf_t x) Initializes *y* and sets it to an upper bound for *x*. Assumes that the exponent of *y* is small. .. function:: void arf_mag_set_ulp(mag_t z, const arf_t y, slong prec) Sets *z* to the magnitude of the unit in the last place (ulp) of *y* at precision *prec*. .. function:: void arf_mag_add_ulp(mag_t z, const mag_t x, const arf_t y, slong prec) Sets *z* to an upper bound for the sum of *x* and the magnitude of the unit in the last place (ulp) of *y* at precision *prec*. .. function:: void arf_mag_fast_add_ulp(mag_t z, const mag_t x, const arf_t y, slong prec) Sets *z* to an upper bound for the sum of *x* and the magnitude of the unit in the last place (ulp) of *y* at precision *prec*. Assumes that all exponents are small. Shallow assignment ------------------------------------------------------------------------------- .. function:: void arf_init_set_shallow(arf_t z, const arf_t x) .. function:: void arf_init_set_mag_shallow(arf_t z, const mag_t x) Initializes *z* to a shallow copy of *x*. A shallow copy just involves copying struct data (no heap allocation is performed). The target variable *z* may not be cleared or modified in any way (it can only be used as constant input to functions), and may not be used after *x* has been cleared. Moreover, after *x* has been assigned shallowly to *z*, no modification of *x* is permitted as slong as *z* is in use. .. function:: void arf_init_neg_shallow(arf_t z, const arf_t x) .. function:: void arf_init_neg_mag_shallow(arf_t z, const mag_t x) Initializes *z* shallowly to the negation of *x*. Random number generation ------------------------------------------------------------------------------- .. function:: void arf_randtest(arf_t x, flint_rand_t state, slong bits, slong mag_bits) Generates a finite random number whose mantissa has precision at most *bits* and whose exponent has at most *mag_bits* bits. The values are distributed non-uniformly: special bit patterns are generated with high probability in order to allow the test code to exercise corner cases. .. function:: void arf_randtest_not_zero(arf_t x, flint_rand_t state, slong bits, slong mag_bits) Identical to :func:`arf_randtest`, except that zero is never produced as an output. .. function:: void arf_randtest_special(arf_t x, flint_rand_t state, slong bits, slong mag_bits) Indentical to :func:`arf_randtest`, except that the output occasionally is set to an infinity or NaN. Input and output ------------------------------------------------------------------------------- .. function:: void arf_debug(const arf_t x) Prints information about the internal representation of *x*. .. function:: void arf_print(const arf_t x) Prints *x* as an integer mantissa and exponent. .. function:: void arf_printd(const arf_t y, slong d) Prints *x* as a decimal floating-point number, rounding to *d* digits. This function is currently implemented using MPFR, and does not support large exponents. Addition and multiplication ------------------------------------------------------------------------------- .. function:: void arf_abs(arf_t y, const arf_t x) Sets *y* to the absolute value of *x*. .. function:: void arf_neg(arf_t y, const arf_t x) Sets `y = -x` exactly. .. function:: int arf_neg_round(arf_t y, const arf_t x, slong prec, arf_rnd_t rnd) Sets `y = -x`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. .. function:: void arf_mul_2exp_si(arf_t y, const arf_t x, slong e) .. function:: void arf_mul_2exp_fmpz(arf_t y, const arf_t x, const fmpz_t e) Sets `y = x 2^e` exactly. .. function:: int arf_mul(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_mul_ui(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) .. function:: int arf_mul_si(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) .. function:: int arf_mul_mpz(arf_t z, const arf_t x, const mpz_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_mul_fmpz(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) Sets `z = x \times y`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. .. function:: int arf_add(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_add_si(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) .. function:: int arf_add_ui(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) .. function:: int arf_add_fmpz(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) Sets `z = x + y`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. .. function:: int arf_add_fmpz_2exp(arf_t z, const arf_t x, const fmpz_t y, const fmpz_t e, slong prec, arf_rnd_t rnd) Sets `z = x + y 2^e`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. .. function:: int arf_sub(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_sub_si(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) .. function:: int arf_sub_ui(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) .. function:: int arf_sub_fmpz(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) Sets `z = x - y`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. .. function:: int arf_addmul(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_addmul_ui(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) .. function:: int arf_addmul_si(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) .. function:: int arf_addmul_mpz(arf_t z, const arf_t x, const mpz_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_addmul_fmpz(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) Sets `z = z + x \times y`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. .. function:: int arf_submul(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_submul_ui(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) .. function:: int arf_submul_si(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) .. function:: int arf_submul_mpz(arf_t z, const arf_t x, const mpz_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_submul_fmpz(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) Sets `z = z - x \times y`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. Summation ------------------------------------------------------------------------------- .. function:: int arf_sum(arf_t s, arf_srcptr terms, slong len, slong prec, arf_rnd_t rnd) Sets *s* to the sum of the array *terms* of length *len*, rounded to *prec* bits in the direction specified by *rnd*. The sum is computed as if done without any intermediate rounding error, with only a single rounding applied to the final result. Unlike repeated calls to :func:`arf_add` with infinite precision, this function does not overflow if the magnitudes of the terms are far apart. Warning: this function is implemented naively, and the running time is quadratic with respect to *len* in the worst case. Division ------------------------------------------------------------------------------- .. function:: int arf_div(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_div_ui(arf_t z, const arf_t x, ulong y, slong prec, arf_rnd_t rnd) .. function:: int arf_ui_div(arf_t z, ulong x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_div_si(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) .. function:: int arf_si_div(arf_t z, slong x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_div_fmpz(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_fmpz_div(arf_t z, const fmpz_t x, const arf_t y, slong prec, arf_rnd_t rnd) .. function:: int arf_fmpz_div_fmpz(arf_t z, const fmpz_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) Sets `z = x / y`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. The result is NaN if *y* is zero. Square roots ------------------------------------------------------------------------------- .. function:: int arf_sqrt(arf_t z, const arf_t x, slong prec, arf_rnd_t rnd) .. function:: int arf_sqrt_ui(arf_t z, ulong x, slong prec, arf_rnd_t rnd) .. function:: int arf_sqrt_fmpz(arf_t z, const fmpz_t x, slong prec, arf_rnd_t rnd) Sets `z = \sqrt{x}`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. The result is NaN if *x* is negative. .. function:: int arf_rsqrt(arf_t z, const arf_t x, slong prec, arf_rnd_t rnd) Sets `z = 1/\sqrt{x}`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. The result is NaN if *x* is negative, and `+\infty` if *x* is zero. .. function:: int arf_root(arf_t z, const arf_t x, ulong k, slong prec, arf_rnd_t rnd) Sets `z = x^{1/k}`, rounded to *prec* bits in the direction specified by *rnd*, returning nonzero iff the operation is inexact. The result is NaN if *x* is negative. Warning: this function is a wrapper around the MPFR root function. It gets slow and uses much memory for large *k*. Complex arithmetic ------------------------------------------------------------------------------- .. function:: int arf_complex_mul(arf_t e, arf_t f, const arf_t a, const arf_t b, const arf_t c, const arf_t d, slong prec, arf_rnd_t rnd) .. function:: int arf_complex_mul_fallback(arf_t e, arf_t f, const arf_t a, const arf_t b, const arf_t c, const arf_t d, slong prec, arf_rnd_t rnd) Computes the complex product `e + fi = (a + bi)(c + di)`, rounding both `e` and `f` correctly to *prec* bits in the direction specified by *rnd*. The first bit in the return code indicates inexactness of `e`, and the second bit indicates inexactness of `f`. If any of the components *a*, *b*, *c*, *d* is zero, two real multiplications and no additions are done. This convention is used even if any other part contains an infinity or NaN, and the behavior with infinite/NaN input is defined accordingly. The *fallback* version is implemented naively, for testing purposes. No squaring optimization is implemented. .. function:: int arf_complex_sqr(arf_t e, arf_t f, const arf_t a, const arf_t b, slong prec, arf_rnd_t rnd) Computes the complex square `e + fi = (a + bi)^2`. This function has identical semantics to :func:`arf_complex_mul` (with `c = a, b = d`), but is faster. arb-2.8.1/doc/source/bernoulli.rst000066400000000000000000000111061264125401100170530ustar00rootroot00000000000000.. _bernoulli: **bernoulli.h** -- support for Bernoulli numbers =============================================================================== This module provides helper functions for exact or approximate calculation of the Bernoulli numbers, which are defined by the exponential generating function .. math :: \frac{x}{e^x-1} = \sum_{n=0}^{\infty} B_n \frac{x^n}{n!}. Efficient algorithms are implemented for both multi-evaluation and calculation of isolated Bernoulli numbers. A global (or thread-local) cache is also provided, to support fast repeated evaluation of various special functions that depend on the Bernoulli numbers (including the gamma function and the Riemann zeta function). Generation of Bernoulli numbers -------------------------------------------------------------------------------- .. type:: bernoulli_rev_t An iterator object for generating a range of even-indexed Bernoulli numbers exactly in reverse order, i.e. computing the exact fractions `B_n, B_{n-2}, B_{n-4}, \ldots, B_0`. The Bernoulli numbers are generated from scratch, i.e. no caching is performed. The Bernoulli numbers are computed by direct summation of the zeta series. This is made fast by storing a table of powers (as done by Bloemen et al. http://remcobloemen.nl/2009/11/even-faster-zeta-calculation.html). As an optimization, we only include the odd powers, and use fixed-point arithmetic. The reverse iteration order is preferred for performance reasons, as the powers can be updated using multiplications instead of divisions, and we avoid having to periodically recompute terms to higher precision. To generate Bernoulli numbers in the forward direction without having to store all of them, one can split the desired range into smaller blocks and compute each block with a single reverse pass. .. function:: void bernoulli_rev_init(bernoulli_rev_t iter, ulong n) Initializes the iterator *iter*. The first Bernoulli number to be generated by calling :func:`bernoulli_rev_next` is `B_n`. It is assumed that `n` is even. .. function:: void bernoulli_rev_next(fmpz_t numer, fmpz_t denom, bernoulli_rev_t iter) Sets *numer* and *denom* to the exact, reduced numerator and denominator of the Bernoulli number `B_k` and advances the state of *iter* so that the next invocation generates `B_{k-2}`. .. function:: void bernoulli_rev_clear(bernoulli_rev_t iter) Frees all memory allocated internally by *iter*. Caching ------------------------------------------------------------------------------- .. var:: slong bernoulli_cache_num .. var:: fmpq * bernoulli_cache Cache of Bernoulli numbers. Uses thread-local storage if enabled in FLINT. .. function:: void bernoulli_cache_compute(slong n) Makes sure that the Bernoulli numbers up to at least `B_{n-1}` are cached. Calling :func:`flint_cleanup()` frees the cache. Bounding ------------------------------------------------------------------------------- .. function:: slong bernoulli_bound_2exp_si(ulong n) Returns an integer `b` such that `|B_n| \le 2^b`. Uses a lookup table for small `n`, and for larger `n` uses the inequality `|B_n| < 4 n! / (2 \pi)^n < 4 (n+1)^{n+1} e^{-n} / (2 \pi)^n`. Uses integer arithmetic throughout, with the bound for the logarithm being looked up from a table. If `|B_n| = 0`, returns *LONG_MIN*. Otherwise, the returned exponent `b` is never more than one percent larger than the true magnitude. This function is intended for use when `n` small enough that one might comfortably compute `B_n` exactly. It aborts if `n` is so large that internal overflow occurs. .. function:: void _bernoulli_fmpq_ui_zeta(fmpz_t num, fmpz_t den, ulong n) Sets *num* and *den* to the reduced numerator and denominator of the Bernoulli number `B_n`. This function computes the denominator `d` using von Staudt-Clausen theorem, numerically approximates `B_n` using :func:`arb_bernoulli_ui_zeta`, and then rounds `d B_n` to the correct numerator. If the working precision is insufficient to determine the numerator, the function prints a warning message and retries with increased precision (this should not be expected to happen). .. function:: void _bernoulli_fmpq_ui(fmpz_t num, fmpz_t den, ulong n) .. function:: void bernoulli_fmpq_ui(fmpq_t b, ulong n) Computes the Bernoulli number `B_n` as an exact fraction, for an isolated integer `n`. This function reads `B_n` from the global cache if the number is already cached, but does not automatically extend the cache by itself. arb-2.8.1/doc/source/conf.py000066400000000000000000000176031264125401100156350ustar00rootroot00000000000000# -*- coding: utf-8 -*- # # Arb documentation build configuration file, created by # sphinx-quickstart on Thu Oct 11 09:33:44 2012. # # This file is execfile()d with the current directory set to its containing dir. # # Note that not all possible configuration values are present in this # autogenerated file. # # All configuration values have a default; values that are commented out # serve to show the default. import sys, os # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. #sys.path.insert(0, os.path.abspath('.')) # -- General configuration ----------------------------------------------------- # If your documentation needs a minimal Sphinx version, state it here. #needs_sphinx = '1.0' # Add any Sphinx extension module names here, as strings. They can be extensions # coming with Sphinx (named 'sphinx.ext.*') or your custom ones. extensions = ['sphinx.ext.mathjax'] # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] # The suffix of source filenames. source_suffix = '.rst' # The encoding of source files. #source_encoding = 'utf-8-sig' # The master toctree document. master_doc = 'index' # General information about the project. project = u'Arb' copyright = u'2012-2014, Fredrik Johansson' # The version info for the project you're documenting, acts as replacement for # |version| and |release|, also used in various other places throughout the # built documents. # # The short X.Y version. for _line in open("../../arb/version.c").readlines(): if _line.startswith("const char * arb_version"): _i1 = _line.find('"') _i2 = _line.find('"', _i1 + 1) version = _line[_i1+1:_i2] release = version # The language for content autogenerated by Sphinx. Refer to documentation # for a list of supported languages. #language = None # There are two options for replacing |today|: either, you set today to some # non-false value, then it is used: #today = '' # Else, today_fmt is used as the format for a strftime call. #today_fmt = '%B %d, %Y' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. exclude_patterns = [] # The reST default role (used for this markup: `text`) to use for all documents. default_role = 'math' latex_preamble = r""" \usepackage{amsmath,amssymb} \setcounter{tocdepth}{2} """ primary_domain = 'c' # If true, '()' will be appended to :func: etc. cross-reference text. #add_function_parentheses = True # If true, the current module name will be prepended to all description # unit titles (such as .. function::). #add_module_names = True # If true, sectionauthor and moduleauthor directives will be shown in the # output. They are ignored by default. #show_authors = False # The name of the Pygments (syntax highlighting) style to use. pygments_style = 'sphinx' # A list of ignored prefixes for module index sorting. #modindex_common_prefix = [] # -- Options for HTML output --------------------------------------------------- # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. html_theme = 'default' #html_theme = 'pyramid' # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. html_theme_options = {'sidebarwidth' : 300} # Add any paths that contain custom themes here, relative to this directory. #html_theme_path = [] # The name for this set of Sphinx documents. If None, it defaults to # " v documentation". #html_title = None # A shorter title for the navigation bar. Default is the same as html_title. #html_short_title = None # The name of an image file (relative to this directory) to place at the top # of the sidebar. html_logo = "_static/arbwhite.png" # The name of an image file (within the static path) to use as favicon of the # docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 # pixels large. html_favicon = "_static/arb.ico" # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". html_static_path = ['_static'] # If not '', a 'Last updated on:' timestamp is inserted at every page bottom, # using the given strftime format. #html_last_updated_fmt = '%b %d, %Y' # If true, SmartyPants will be used to convert quotes and dashes to # typographically correct entities. #html_use_smartypants = True # Custom sidebar templates, maps document names to template names. #html_sidebars = {} # Additional templates that should be rendered to pages, maps page names to # template names. #html_additional_pages = {} # If false, no module index is generated. #html_domain_indices = True # If false, no index is generated. #html_use_index = True # If true, the index is split into individual pages for each letter. #html_split_index = False # If true, links to the reST sources are added to the pages. #html_show_sourcelink = True # If true, "Created using Sphinx" is shown in the HTML footer. Default is True. #html_show_sphinx = True # If true, "(C) Copyright ..." is shown in the HTML footer. Default is True. #html_show_copyright = True # If true, an OpenSearch description file will be output, and all pages will # contain a tag referring to it. The value of this option must be the # base URL from which the finished HTML is served. #html_use_opensearch = '' # This is the file name suffix for HTML files (e.g. ".xhtml"). #html_file_suffix = None # Output file base name for HTML help builder. htmlhelp_basename = 'Arbdoc' # -- Options for LaTeX output -------------------------------------------------- latex_elements = { # The paper size ('letterpaper' or 'a4paper'). #'papersize': 'letterpaper', # The font size ('10pt', '11pt' or '12pt'). #'pointsize': '10pt', # Additional stuff for the LaTeX preamble. #'preamble': '', } # Grouping the document tree into LaTeX files. List of tuples # (source start file, target name, title, author, documentclass [howto/manual]). latex_documents = [ ('index', 'Arb.tex', u'Arb Documentation', u'Fredrik Johansson', 'manual'), ] # The name of an image file (relative to this directory) to place at the top of # the title page. latex_logo = "_static/arbtext.pdf" # For "manual" documents, if this is true, then toplevel headings are parts, # not chapters. #latex_use_parts = False # If true, show page references after internal links. #latex_show_pagerefs = False # If true, show URL addresses after external links. #latex_show_urls = False # Documents to append as an appendix to all manuals. #latex_appendices = [] # If false, no module index is generated. #latex_domain_indices = True # -- Options for manual page output -------------------------------------------- # One entry per manual page. List of tuples # (source start file, name, description, authors, manual section). man_pages = [ ('index', 'arb', u'Arb Documentation', [u'Fredrik Johansson'], 1) ] # If true, show URL addresses after external links. #man_show_urls = False # -- Options for Texinfo output ------------------------------------------------ # Grouping the document tree into Texinfo files. List of tuples # (source start file, target name, title, author, # dir menu entry, description, category) texinfo_documents = [ ('index', 'Arb', u'Arb Documentation', u'Fredrik Johansson', 'Arb', 'One line description of project.', 'Miscellaneous'), ] # Documents to append as an appendix to all manuals. #texinfo_appendices = [] # If false, no module index is generated. #texinfo_domain_indices = True # How to display URL addresses: 'footnote', 'no', or 'inline'. #texinfo_show_urls = 'footnote' arb-2.8.1/doc/source/constants.rst000066400000000000000000000077641264125401100171130ustar00rootroot00000000000000.. _algorithms_constants: Algorithms for mathematical constants =============================================================================== Most mathematical constants are evaluated using the generic hypergeometric summation code. Pi ------------------------------------------------------------------------------- `\pi` is computed using the Chudnovsky series .. math :: \frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}} which is hypergeometric and adds roughly 14 digits per term. Methods based on the arithmetic-geometric mean seem to be slower by a factor three in practice. A small trick is to compute `1/\sqrt{640320}` instead of `\sqrt{640320}` at the end. Logarithms of integers ------------------------------------------------------------------------------- We use the formulas .. math :: \log(2) = \frac{3}{4} \sum_{k=0}^{\infty} \frac{(-1)^k (k!)^2}{2^k (2k+1)!} \log(10) = 46 \operatorname{atanh}(1/31) + 34 \operatorname{atanh}(1/49) + 20 \operatorname{atanh}(1/161) Euler's constant ------------------------------------------------------------------------------- Euler's constant `\gamma` is computed using the Brent-McMillan formula ([BM1980]_, [MPFR2012]_) .. math :: \gamma = \frac{S_0(2n) - K_0(2n)}{I_0(2n)} - \log(n) in which `n` is a free parameter and .. math :: S_0(x) = \sum_{k=0}^{\infty} \frac{H_k}{(k!)^2} \left(\frac{x}{2}\right)^{2k}, \quad I_0(x) = \sum_{k=0}^{\infty} \frac{1}{(k!)^2} \left(\frac{x}{2}\right)^{2k} 2x I_0(x) K_0(x) \sim \sum_{k=0}^{\infty} \frac{[(2k)!]^3}{(k!)^4 8^{2k} x^{2k}}. All series are evaluated using binary splitting. The first two series are evaluated simultaneously, with the summation taken up to `k = N - 1` inclusive where `N \ge \alpha n + 1` and `\alpha \approx 4.9706257595442318644` satisfies `\alpha (\log \alpha - 1) = 3`. The third series is taken up to `k = 2n-1` inclusive. With these parameters, it is shown in [BJ2013]_ that the error is bounded by `24e^{-8n}`. Catalan's constant ------------------------------------------------------------------------------- Catalan's constant is computed using the hypergeometric series .. math :: C = \sum_{k=0}^{\infty} \frac{(-1)^k 4^{4 k+1} \left(40 k^2+56 k+19\right) [(k+1)!]^2 [(2k+2)!]^3}{(k+1)^3 (2 k+1) [(4k+4)!]^2} Khinchin's constant ------------------------------------------------------------------------------- Khinchin's constant `K_0` is computed using the formula .. math :: \log K_0 = \frac{1}{\log 2} \left[ \sum_{k=2}^{N-1} \log \left(\frac{k-1}{k} \right) \log \left(\frac{k+1}{k} \right) + \sum_{n=1}^\infty \frac {\zeta (2n,N)}{n} \sum_{k=1}^{2n-1} \frac{(-1)^{k+1}}{k} \right] where `N \ge 2` is a free parameter that can be used for tuning [BBC1997]_. If the infinite series is truncated after `n = M`, the remainder is smaller in absolute value than .. math :: \sum_{n=M+1}^{\infty} \zeta(2n, N) = \sum_{n=M+1}^{\infty} \sum_{k=0}^{\infty} (k+N)^{-2n} \le \sum_{n=M+1}^{\infty} \left( N^{-2n} + \int_0^{\infty} (t+N)^{-2n} dt \right) = \sum_{n=M+1}^{\infty} \frac{1}{N^{2n}} \left(1 + \frac{N}{2n-1}\right) \le \sum_{n=M+1}^{\infty} \frac{N+1}{N^{2n}} = \frac{1}{N^{2M} (N-1)} \le \frac{1}{N^{2M}}. Thus, for an error of at most `2^{-p}` in the series, it is sufficient to choose `M \ge p / (2 \log_2 N)`. Glaisher's constant ------------------------------------------------------------------------------- Glaisher's constant `A = \exp(1/12 - \zeta'(-1))` is computed directly from this formula. We don't use the reflection formula for the zeta function, as the arithmetic in Euler-Maclaurin summation is faster at `s = -1` than at `s = 2`. Apery's constant ------------------------------------------------------------------------------- Apery's constant `\zeta(3)` is computed using the hypergeometric series .. math :: \zeta(3) = \frac{1}{64} \sum_{k=0}^\infty (-1)^k (205k^2 + 250k + 77) \frac{(k!)^{10}}{[(2k+1)!]^5}. arb-2.8.1/doc/source/credits.rst000066400000000000000000000225111264125401100165170ustar00rootroot00000000000000.. _credits: Credits and references =============================================================================== Arb is licensed GNU General Public License version 2, or any later version. Fredrik Johansson is the main author. The project was started in 2012 as a numerical extension of FLINT, and the initial design was heavily based on FLINT 2.0 (with particular credit to Bill Hart and Sebastian Pancratz). From 2012 to July 2014, Fredrik's work on Arb was supported by Austrian Science Fund FWF Grant Y464-N18 (Fast Computer Algebra for Special Functions). During that period, he was a PhD student (and briefly a postdoc) at RISC, Johannes Kepler University, Linz, supervised by Manuel Kauers. From September 2014 to October 2015, Fredrik was a postdoc in the LFANT project-team at INRIA Bordeaux and Institut de Mathématiques de Bordeaux, headed by Andreas Enge. During that period, Fredrik's work on Arb was supported by ERC Starting Grant ANTICS 278537 (Algorithmic Number Theory in Computer Science) http://cordis.europa.eu/project/rcn/101288_en.html Since October 2015, Fredrik is a CR2 researcher in the LFANT team, funded by INRIA. Contributors ------------------------------------------------------------------------------- Several people have contributed patches, bug reports, or substantial feedback. This list is probably incomplete. * Bill Hart - build system, Windows 64 support, design of FLINT * Sebastian Pancratz - divide-and-conquer polynomial composition algorithm (taken from FLINT) * The MPFR development team - Arb includes two-limb multiplication code taken from MPFR * Jonathan Bober - C++ compatibility fixes * Yuri Matiyasevich - feedback about the zeta function and root-finding code * Abhinav Baid - dot product and norm functions * OndÅ™ej ÄŒertík - bug reports, feedback * Andrew Booker - bug reports, feedback * Francesco Biscani - C++ compatibility fixes, feedback * Clemens Heuberger - work on Arb interface in Sage, feedback * Marc Mezzarobba - work on Arb interface in Sage, bug reports, feedback * Pascal Molin - feedback * Ricky Farr - convenience functions, feedback * Marcello Seri - fix for static builds on OS X * Tommy Hofmann - matrix transpose, comparison, other utility methods, Julia interface * Alexander Kobel - documentation and code cleanup patches * Hrvoje Abraham - patches for MinGW compatibility * Julien Puydt - soname versioning support * Alex Griffing - sinc function, matrix trace, improved matrix squaring, miscellaneous patches * Jeroen Demeyer - patch for major bug on PPC64 Software ------------------------------------------------------------------------------- The following software has been helpful in the development of Arb. * GMP (Torbjörn Granlund and others), http://gmplib.org * MPIR (Brian Gladman, Jason Moxham, William Hart and others), http://mpir.org * MPFR (Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, Philippe Théveny, Paul Zimmermann and others), http://mpfr.org * FLINT (William Hart, Sebastian Pancratz, Andy Novocin, Fredrik Johansson, David Harvey and others), http://flintlib.org * Sage (William Stein and others), http://sagemath.org * Pari/GP (The Pari group), http://pari.math.u-bordeaux.fr/ * SymPy (OndÅ™ej ÄŒertík, Aaron Meurer and others), http://sympy.org * mpmath (Fredrik Johansson and others), http://mpmath.org * Mathematica (Wolfram Research), http://www.wolfram.com/mathematica * HolonomicFunctions (Christoph Koutschan), http://www.risc.jku.at/research/combinat/software/HolonomicFunctions/ * Sphinx (George Brandl and others), http://sphinx.pocoo.org * CM (Andreas Enge), http://www.multiprecision.org/index.php?prog=cm Citing Arb ------------------------------------------------------------------------------- If you wish to cite Arb in a scientific paper, the following reference can be used (you may also cite the manual or the website directly): \F. Johansson. "Arb: a C library for ball arithmetic", *ACM Communications in Computer Algebra*, 47(4):166-169, 2013. In BibTeX format:: @article{Johansson2013arb, title={{A}rb: a {C} library for ball arithmetic}, author={F. Johansson}, journal={ACM Communications in Computer Algebra}, volume={47}, number={4}, pages={166--169}, year={2013}, publisher={ACM} } Bibliography ------------------------------------------------------------------------------- .. [Arn2010] \J. Arndt, *Matters Computational*, Springer (2010), http://www.jjj.de/fxt/#fxtbook .. [BBC1997] \D. H. Bailey, J. M. Borwein and R. E. Crandall, "On the Khintchine constant", Mathematics of Computation 66 (1997) 417-431 .. [BBC2000] \J. Borwein, D. M. Bradley and R. E. Crandall, "Computational strategies for the Riemann zeta function", Journal of Computational and Applied Mathematics 121 (2000) 247-296 .. [BZ1992]_ \J. Borwein and I. Zucker, "Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind", IMA Journal of Numerical Analysis 12 (1992) 519-526 .. [Bor1987]_ \P. Borwein, "Reduced complexity evaluation of hypergeometric functions", Journal of Approximation Theory 50:3 (1987) .. [Bor2000] \P. Borwein, "An Efficient Algorithm for the Riemann Zeta Function", Constructive experimental and nonlinear analysis, CMS Conference Proc. 27 (2000) 29-34, http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P155.pdf .. [BM1980] \R. P. Brent and E. M. McMillan, "Some new algorithms for high-precision computation of Euler's constant", Mathematics of Computation 34 (1980) 305-312. .. [Bre1978] \R. P. Brent, "A Fortran multiple-precision arithmetic package", ACM Transactions on Mathematical Software, 4(1):57–70, March 1978. .. [Bre2010] \R. P. Brent, "Ramanujan and Euler's Constant", http://wwwmaths.anu.edu.au/~brent/pd/Euler_CARMA_10.pdf .. [BJ2013] \R. P. Brent and F. Johansson, "A bound for the error term in the Brent-McMillan algorithm", preprint (2013), http://arxiv.org/abs/1312.0039 .. [BZ2011] \R. P. Brent and P. Zimmermann, *Modern Computer Arithmetic*, Cambridge University Press (2011), http://www.loria.fr/~zimmerma/mca/pub226.html .. [CP2005] \R. Crandall and C. Pomerance, *Prime Numbers: A Computational Perspective*, second edition, Springer (2005). .. [EM2004] \O. Espinosa and V. Moll, "A generalized polygamma function", Integral Transforms and Special Functions (2004), 101-115. .. [Fil1992] \S. Fillebrown, "Faster Computation of Bernoulli Numbers", Journal of Algorithms 13 (1992) 431-445 .. [GG2003] \J. von zur Gathen and J. Gerhard, *Modern Computer Algebra*, second edition, Cambridge University Press (2003) .. [GS2003] \X. Gourdon and P. Sebah, "Numerical evaluation of the Riemann Zeta-function" (2003), http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf .. [HZ2004] \G. Hanrot and P. Zimmermann, "Newton Iteration Revisited" (2004), http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz .. [Hoe2009] \J. van der Hoeven, "Ball arithmetic", Technical Report, HAL 00432152 (2009), http://www.texmacs.org/joris/ball/ball-abs.html .. [Joh2012] \F. Johansson, "Efficient implementation of the Hardy-Ramanujan-Rademacher formula", LMS Journal of Computation and Mathematics, Volume 15 (2012), 341-359, http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8710297 .. [Joh2013] \F. Johansson, "Rigorous high-precision computation of the Hurwitz zeta function and its derivatives", Numerical Algorithms, http://arxiv.org/abs/1309.2877 http://dx.doi.org/10.1007/s11075-014-9893-1 .. [Joh2014a] \F. Johansson, *Fast and rigorous computation of special functions to high precision*, PhD thesis, RISC, Johannes Kepler University, Linz, 2014. http://fredrikj.net/thesis/ .. [Joh2014b] \F. Johansson, "Evaluating parametric holonomic sequences using rectangular splitting", ISSAC 2014, 256-263. http://dx.doi.org/10.1145/2608628.2608629 .. [Joh2014c] \F. Johansson, "Efficient implementation of elementary functions in the medium-precision range", http://arxiv.org/abs/1410.7176 .. [Kar1998] \E. A. Karatsuba, "Fast evaluation of the Hurwitz zeta function and Dirichlet L-series", Problems of Information Transmission 34:4 (1998), 342-353, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ppi&paperid=425&option_lang=eng .. [Kob2010] \A. Kobel, "Certified Complex Numerical Root Finding", Seminar on Computational Geometry and Geometric Computing (2010), http://www.mpi-inf.mpg.de/departments/d1/teaching/ss10/Seminar_CGGC/Slides/02_Kobel_NRS.pdf .. [MPFR2012] The MPFR team, "MPFR Algorithms" (2012), http://www.mpfr.org/algo.html .. [NIST2012] National Institute of Standards and Technology, *Digital Library of Mathematical Functions* (2012), http://dlmf.nist.gov/ .. [Olv1997] \F. Olver, *Asymptotics and special functions*, AKP Classics, AK Peters Ltd., Wellesley, MA, 1997. Reprint of the 1974 original. .. [Rad1973] \H. Rademacher, *Topics in analytic number theory*, Springer, 1973. .. [PS1973] \M. S. Paterson and L. J. Stockmeyer, "On the number of nonscalar multiplications necessary to evaluate polynomials", SIAM J. Comput (1973) .. [Smi2001] \D. M. Smith, "Algorithm: Fortran 90 Software for Floating-Point Multiple Precision Arithmetic, Gamma and Related Functions", Transactions on Mathematical Software 27 (2001) 377-387, http://myweb.lmu.edu/dmsmith/toms2001.pdf .. [Tak2000] \D. Takahashi, "A fast algorithm for computing large Fibonacci numbers", Information Processing Letters 75 (2000) 243-246, http://www.ii.uni.wroc.pl/~lorys/IPL/article75-6-1.pdf arb-2.8.1/doc/source/examples.rst000066400000000000000000000415711264125401100167070ustar00rootroot00000000000000.. _examples: Example programs =============================================================================== The *examples* directory (https://github.com/fredrik-johansson/arb/tree/master/examples) contains several complete C programs, which are documented below. Running:: make examples will compile the programs and place the binaries in ``build/examples``. pi.c ------------------------------------------------------------------------------- This program computes `\pi` to an accuracy of roughly *n* decimal digits by calling the :func:`arb_const_pi` function with a working precision of roughly `n \log_2(10)` bits. Sample output, computing `\pi` to one million digits:: > build/examples/pi 1000000 computing pi with a precision of 3321933 bits... cpu/wall(s): 0.58 0.586 virt/peak/res/peak(MB): 28.24 36.84 8.86 15.56 [3.14159265358979323846{...999959 digits...}42209010610577945815 +/- 3e-1000000] The program prints an interval guaranteed to contain `\pi`, and where all displayed digits are correct up to an error of plus or minus one unit in the last place (see :func:`arb_printn`). By default, only the first and last few digits are printed. Pass 0 as a second argument to print all digits (or pass *m* to print *m* + 1 leading and *m* trailing digits, as above with the default *m* = 20). hilbert_matrix.c ------------------------------------------------------------------------------- Given an input integer *n*, this program accurately computes the determinant of the *n* by *n* Hilbert matrix. Hilbert matrices are notoriously ill-conditioned: although the entries are close to unit magnitude, the determinant `h_n` decreases superexponentially (nearly as `1/4^{n^2}`) as a function of *n*. This program automatically doubles the working precision until the ball computed for `h_n` by :func:`arb_mat_det` does not contain zero. Sample output:: > build/examples/hilbert_matrix 200 prec=20: 0 +/- 5.5777e-330 prec=40: 0 +/- 2.5785e-542 prec=80: 0 +/- 8.1169e-926 prec=160: 0 +/- 2.8538e-1924 prec=320: 0 +/- 6.3868e-4129 prec=640: 0 +/- 1.7529e-8826 prec=1280: 0 +/- 1.8545e-17758 prec=2560: 2.955454297e-23924 +/- 6.4586e-24044 success! cpu/wall(s): 9.06 9.095 virt/peak/res/peak(MB): 55.52 55.52 35.50 35.50 keiper_li.c ------------------------------------------------------------------------------- Given an input integer *n*, this program rigorously computes numerical values of the Keiper-Li coefficients `\lambda_0, \ldots, \lambda_n`. The Keiper-Li coefficients have the property that `\lambda_n > 0` for all `n > 0` if and only if the Riemann hypothesis is true. This program was used for the record computations described in [Joh2013]_ (the paper describes the algorithm in some more detail). The program takes the following parameters:: keiper_li n [-prec prec] [-threads num_threads] [-out out_file] The program prints the first and last few coefficients. It can optionally write all the computed data to a file. The working precision defaults to a value that should give all the coefficients to a few digits of accuracy, but can optionally be set higher (or lower). On a multicore system, using several threads results in faster execution. Sample output:: > build/examples/keiper_li 1000 -threads 2 zeta: cpu/wall(s): 0.4 0.244 virt/peak/res/peak(MB): 167.98 294.69 5.09 7.43 log: cpu/wall(s): 0.03 0.038 gamma: cpu/wall(s): 0.02 0.016 binomial transform: cpu/wall(s): 0.01 0.018 0: -0.69314718055994530941723212145817656807550013436026 +/- 6.5389e-347 1: 0.023095708966121033814310247906495291621932127152051 +/- 2.0924e-345 2: 0.046172867614023335192864243096033943387066108314123 +/- 1.674e-344 3: 0.0692129735181082679304973488726010689942120263932 +/- 5.0219e-344 4: 0.092197619873060409647627872409439018065541673490213 +/- 2.0089e-343 5: 0.11510854289223549048622128109857276671349132303596 +/- 1.0044e-342 6: 0.13792766871372988290416713700341666356138966078654 +/- 6.0264e-342 7: 0.16063715965299421294040287257385366292282442046163 +/- 2.1092e-341 8: 0.18321945964338257908193931774721859848998098273432 +/- 8.4368e-341 9: 0.20565733870917046170289387421343304741236553410044 +/- 7.5931e-340 10: 0.22793393631931577436930340573684453380748385942738 +/- 7.5931e-339 991: 2.3196617961613367928373899656994682562101430813341 +/- 2.461e-11 992: 2.3203766239254884035349896518332550233162909717288 +/- 9.5363e-11 993: 2.321092061239733282811659116333262802034375592414 +/- 1.8495e-10 994: 2.3218073540188462110258826121503870112747188888893 +/- 3.5907e-10 995: 2.3225217392815185726928702951225314023773358152533 +/- 6.978e-10 996: 2.3232344485814623873333223609413703912358283071281 +/- 1.3574e-09 997: 2.3239447114886014522889542667580382034526509232475 +/- 2.6433e-09 998: 2.3246517591032700808344143240352605148856869322209 +/- 5.1524e-09 999: 2.3253548275861382119812576052060526988544993162101 +/- 1.0053e-08 1000: 2.3260531616864664574065046940832238158044982041872 +/- 3.927e-08 virt/peak/res/peak(MB): 170.18 294.69 7.51 7.51 real_roots.c ------------------------------------------------------------------------------- This program isolates the roots of a function on the interval `(a,b)` (where *a* and *b* are input as double-precision literals) using the routines in the :ref:`arb_calc ` module. The program takes the following arguments:: real_roots function a b [-refine d] [-verbose] [-maxdepth n] [-maxeval n] [-maxfound n] [-prec n] The following functions (specified by an integer code) are implemented: * 0 - `Z(x)` (Riemann-Siegel Z-function) * 1 - `\sin(x)` * 2 - `\sin(x^2)` * 3 - `\sin(1/x)` * 4 - `\operatorname{Ai}(x)` (Airy function) * 5 - `\operatorname{Ai}'(x)` (Airy function) * 6 - `\operatorname{Bi}(x)` (Airy function) * 7 - `\operatorname{Bi}'(x)` (Airy function) The following options are available: * ``-refine d``: If provided, after isolating the roots, attempt to refine the roots to *d* digits of accuracy using a few bisection steps followed by Newton's method with adaptive precision, and then print them. * ``-verbose``: Print more information. * ``-maxdepth n``: Stop searching after *n* recursive subdivisions. * ``-maxeval n``: Stop searching after approximately *n* function evaluations (the actual number evaluations will be a small multiple of this). * ``-maxfound n``: Stop searching after having found *n* isolated roots. * ``-prec n``: Working precision to use for the root isolation. With *function* 0, the program isolates roots of the Riemann zeta function on the critical line, and guarantees that no roots are missed (there are more efficient ways to do this, but it is a nice example):: > build/examples/real_roots 0 0.0 50.0 -verbose interval: [0, 50] maxdepth = 30, maxeval = 100000, maxfound = 100000, low_prec = 30 found isolated root in: [14.111328125, 14.16015625] found isolated root in: [20.99609375, 21.044921875] found isolated root in: [25, 25.048828125] found isolated root in: [30.419921875, 30.4443359375] found isolated root in: [32.91015625, 32.958984375] found isolated root in: [37.548828125, 37.59765625] found isolated root in: [40.91796875, 40.966796875] found isolated root in: [43.310546875, 43.3349609375] found isolated root in: [47.998046875, 48.0224609375] found isolated root in: [49.755859375, 49.7802734375] --------------------------------------------------------------- Found roots: 10 Subintervals possibly containing undetected roots: 0 Function evaluations: 3058 cpu/wall(s): 0.202 0.202 virt/peak/res/peak(MB): 26.12 26.14 2.76 2.76 Find just one root and refine it to approximately 75 digits:: > build/examples/real_roots 0 0.0 50.0 -maxfound 1 -refine 75 interval: [0, 50] maxdepth = 30, maxeval = 100000, maxfound = 1, low_prec = 30 refined root (0/8): [14.134725141734693790457251983562470270784257115699243175685567460149963429809 +/- 2.57e-76] --------------------------------------------------------------- Found roots: 1 Subintervals possibly containing undetected roots: 7 Function evaluations: 761 cpu/wall(s): 0.055 0.056 virt/peak/res/peak(MB): 26.12 26.14 2.75 2.75 Find the first few roots of an Airy function and refine them to 50 digits each:: > build/examples/real_roots 4 -10 0 -refine 50 interval: [-10, 0] maxdepth = 30, maxeval = 100000, maxfound = 100000, low_prec = 30 refined root (0/6): [-9.022650853340980380158190839880089256524677535156083 +/- 4.85e-52] refined root (1/6): [-7.944133587120853123138280555798268532140674396972215 +/- 1.92e-52] refined root (2/6): [-6.786708090071758998780246384496176966053882477393494 +/- 3.84e-52] refined root (3/6): [-5.520559828095551059129855512931293573797214280617525 +/- 1.05e-52] refined root (4/6): [-4.087949444130970616636988701457391060224764699108530 +/- 2.46e-52] refined root (5/6): [-2.338107410459767038489197252446735440638540145672388 +/- 1.48e-52] --------------------------------------------------------------- Found roots: 6 Subintervals possibly containing undetected roots: 0 Function evaluations: 200 cpu/wall(s): 0.003 0.003 virt/peak/res/peak(MB): 26.12 26.14 2.24 2.24 Find roots of `\sin(x^2)` on `(0,100)`. The algorithm cannot isolate the root at `x = 0` (it is at the endpoint of the interval, and in any case a root of multiplicity higher than one). The failure is reported:: > build/examples/real_roots 2 0 100 interval: [0, 100] maxdepth = 30, maxeval = 100000, maxfound = 100000, low_prec = 30 --------------------------------------------------------------- Found roots: 3183 Subintervals possibly containing undetected roots: 1 Function evaluations: 34058 cpu/wall(s): 0.032 0.032 virt/peak/res/peak(MB): 26.32 26.37 2.04 2.04 This does not miss any roots:: > build/examples/real_roots 2 1 100 interval: [1, 100] maxdepth = 30, maxeval = 100000, maxfound = 100000, low_prec = 30 --------------------------------------------------------------- Found roots: 3183 Subintervals possibly containing undetected roots: 0 Function evaluations: 34039 cpu/wall(s): 0.023 0.023 virt/peak/res/peak(MB): 26.32 26.37 2.01 2.01 Looking for roots of `\sin(1/x)` on `(0,1)`, the algorithm finds many roots, but will never find all of them since there are infinitely many:: > build/examples/real_roots 3 0.0 1.0 interval: [0, 1] maxdepth = 30, maxeval = 100000, maxfound = 100000, low_prec = 30 --------------------------------------------------------------- Found roots: 10198 Subintervals possibly containing undetected roots: 24695 Function evaluations: 202587 cpu/wall(s): 0.171 0.171 virt/peak/res/peak(MB): 28.39 30.38 4.05 4.05 Remark: the program always computes rigorous containing intervals for the roots, but the accuracy after refinement could be less than *d* digits. poly_roots.c ------------------------------------------------------------------------------- This program finds the complex roots of an integer polynomial by calling :func:`acb_poly_find_roots` with increasing precision until the roots certainly have been isolated. The program takes the following arguments:: poly_roots [-refine d] [-print d] Isolates all the complex roots of a polynomial with integer coefficients. For convergence, the input polynomial is required to be squarefree. If -refine d is passed, the roots are refined to an absolute tolerance better than 10^(-d). By default, the roots are only computed to sufficient accuracy to isolate them. The refinement is not currently done efficiently. If -print d is passed, the computed roots are printed to d decimals. By default, the roots are not printed. The polynomial can be specified by passing the following as : a Easy polynomial 1 + 2x + ... + (n+1)x^n t Chebyshev polynomial T_n u Chebyshev polynomial U_n p Legendre polynomial P_n c Cyclotomic polynomial Phi_n s Swinnerton-Dyer polynomial S_n b Bernoulli polynomial B_n w Wilkinson polynomial W_n e Taylor series of exp(x) truncated to degree n m The Mignotte-like polynomial x^n + (100x+1)^m, n > m c0 c1 ... cn c0 + c1 x + ... + cn x^n where all c:s are specified integers This finds the roots of the Wilkinson polynomial with roots at the positive integers 1, 2, ..., 100:: > build/examples/poly_roots -print 15 w 100 prec=53: 0 isolated roots | cpu/wall(s): 0.42 0.426 prec=106: 0 isolated roots | cpu/wall(s): 1.37 1.368 prec=212: 0 isolated roots | cpu/wall(s): 1.48 1.485 prec=424: 100 isolated roots | cpu/wall(s): 0.61 0.611 done! (1 + 1.7285178043492e-125j) +/- (7.2e-122, 7.2e-122j) (2 + 5.1605530263601e-122j) +/- (3.77e-118, 3.77e-118j) (3 + -2.58115555871665e-118j) +/- (5.72e-115, 5.72e-115j) (4 + 1.02141628524271e-115j) +/- (4.38e-112, 4.38e-112j) (5 + 1.61326834094948e-113j) +/- (2.6e-109, 2.6e-109j) ... (95 + 4.15294196875447e-62j) +/- (6.66e-59, 6.66e-59j) (96 + 3.54502401922667e-64j) +/- (7.37e-60, 7.37e-60j) (97 + -1.67755595325625e-65j) +/- (6.4e-61, 6.4e-61j) (98 + 2.04638822325299e-65j) +/- (4e-62, 4e-62j) (99 + -2.73425468028238e-66j) +/- (1.71e-63, 1.71e-63j) (100 + -1.00950111302288e-68j) +/- (3.24e-65, 3.24e-65j) cpu/wall(s): 3.88 3.893 This finds the roots of a Bernoulli polynomial which has both real and complex roots. Note that the program does not attempt to determine that the imaginary parts of the real roots really are zero (this could be done by verifying sign changes):: > build/examples/poly_roots -refine 100 -print 20 b 16 prec=53: 16 isolated roots | cpu/wall(s): 0 0.007 prec=106: 16 isolated roots | cpu/wall(s): 0 0.004 prec=212: 16 isolated roots | cpu/wall(s): 0 0.004 prec=424: 16 isolated roots | cpu/wall(s): 0 0.004 done! (-0.94308706466055783383 + -5.512272663168484603e-128j) +/- (2.2e-125, 2.2e-125j) (-0.75534059252067985752 + 1.937401283040249068e-128j) +/- (1.09e-125, 1.09e-125j) (-0.24999757119077421009 + -4.5347924422246038692e-130j) +/- (3.6e-127, 3.6e-127j) (0.24999757152512726002 + 4.2191300761823281708e-129j) +/- (4.98e-127, 4.98e-127j) (0.75000242847487273998 + 9.0360649917413170142e-128j) +/- (8.88e-126, 8.88e-126j) (1.2499975711907742101 + 7.8804123808107088267e-127j) +/- (2.66e-124, 2.66e-124j) (1.7553405925206798575 + 5.432465269253967768e-126j) +/- (6.23e-123, 6.23e-123j) (1.9430870646605578338 + 3.3035377342500953239e-125j) +/- (7.05e-123, 7.05e-123j) (-0.99509334829256233279 + 0.44547958157103608805j) +/- (5.5e-125, 5.5e-125j) (-0.99509334829256233279 + -0.44547958157103608805j) +/- (5.46e-125, 5.46e-125j) (1.9950933482925623328 + 0.44547958157103608805j) +/- (1.44e-122, 1.44e-122j) (1.9950933482925623328 + -0.44547958157103608805j) +/- (1.43e-122, 1.43e-122j) (-0.92177327714429290564 + -1.0954360955079385542j) +/- (9.31e-125, 9.31e-125j) (-0.92177327714429290564 + 1.0954360955079385542j) +/- (1.02e-124, 1.02e-124j) (1.9217732771442929056 + 1.0954360955079385542j) +/- (9.15e-123, 9.15e-123j) (1.9217732771442929056 + -1.0954360955079385542j) +/- (8.12e-123, 8.12e-123j) cpu/wall(s): 0.02 0.02 complex_plot.c ------------------------------------------------------------------------------- This program plots one of the predefined functions over a complex interval `[x_a, x_b] + [y_a, y_b]i` using domain coloring, at a resolution of *xn* times *yn* pixels. The program takes the parameters:: complex_plot [-range xa xb ya yb] [-size xn yn] Defaults parameters are `[-10,10] + [-10,10]i` and *xn* = *yn* = 512. The output is written to ``arbplot.ppm``. If you have ImageMagick, run ``convert arbplot.ppm arbplot.png`` to get a PNG. Function codes ```` are: * ``gamma`` - Gamma function * ``digamma`` - Digamma function * ``lgamma`` - Logarithmic gamma function * ``zeta`` - Riemann zeta function * ``erf`` - Error function * ``ai`` - Airy function Ai * ``bi`` - Airy function Bi * ``besselj`` - Bessel function `J_0` * ``bessely`` - Bessel function `Y_0` * ``besseli`` - Bessel function `I_0` * ``besselk`` - Bessel function `K_0` * ``modj`` - Modular j-function * ``modeta`` - Dedekind eta function * ``barnesg`` - Barnes G-function * ``agm`` - Arithmetic geometric mean The function is just sampled at point values; no attempt is made to resolve small features by adaptive subsampling. For example, the following plots the Riemann zeta function around a portion of the critical strip with imaginary part between 100 and 140:: > build/examples/complex_plot zeta -range -10 10 100 140 -size 256 512 arb-2.8.1/doc/source/fmpr.rst000066400000000000000000000603151264125401100160320ustar00rootroot00000000000000.. _fmpr: **fmpr.h** -- arbitrary-precision floating-point numbers =============================================================================== This type is now obsolete: use :type:`arf_t` instead. A variable of type :type:`fmpr_t` holds an arbitrary-precision binary floating-point number, i.e. a rational number of the form `x \times 2^y` where `x, y \in \mathbb{Z}` and `x` is odd; or one of the special values zero, plus infinity, minus infinity, or NaN (not-a-number). The component `x` is called the *mantissa*, and `y` is called the *exponent*. Note that this is just one among many possible conventions: the mantissa (alternatively *significand*) is sometimes viewed as a fraction in the interval `[1/2, 1)`, with the exponent pointing to the position above the top bit rather than the position of the bottom bit, and with a separate sign. The conventions for special values largely follow those of the IEEE floating-point standard. At the moment, there is no support for negative zero, unsigned infinity, or a NaN with a payload, though some these might be added in the future. An *fmpr* number is exact and has no inherent "accuracy". We use the term *precision* to denote either the target precision of an operation, or the bit size of a mantissa (which in general is unrelated to the "accuracy" of the number: for example, the floating-point value 1 has a precision of 1 bit in this sense and is simultaneously an infinitely accurate approximation of the integer 1 and a 2-bit accurate approximation of `\sqrt 2 = 1.011010100\ldots_2`). Except where otherwise noted, the output of an operation is the floating-point number obtained by taking the inputs as exact numbers, in principle carrying out the operation exactly, and rounding the resulting real number to the nearest representable floating-point number whose mantissa has at most the specified number of bits, in the specified direction of rounding. Some operations are always or optionally done exactly. Types, macros and constants ------------------------------------------------------------------------------- .. type:: fmpr_struct An *fmpr_struct* holds a mantissa and an exponent. If the mantissa and exponent are sufficiently small, their values are stored as immediate values in the *fmpr_struct*; large values are represented by pointers to heap-allocated arbitrary-precision integers. Currently, both the mantissa and exponent are implemented using the FLINT *fmpz* type. Special values are currently encoded by the mantissa being set to zero. .. type:: fmpr_t An *fmpr_t* is defined as an array of length one of type *fmpr_struct*, permitting an *fmpr_t* to be passed by reference. .. type:: fmpr_rnd_t Specifies the rounding mode for the result of an approximate operation. .. macro:: FMPR_RND_DOWN Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards zero. .. macro:: FMPR_RND_UP Specifies that the result of an operation should be rounded to the nearest representable number in the direction away from zero. .. macro:: FMPR_RND_FLOOR Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards minus infinity. .. macro:: FMPR_RND_CEIL Specifies that the result of an operation should be rounded to the nearest representable number in the direction towards plus infinity. .. macro:: FMPR_RND_NEAR Specifies that the result of an operation should be rounded to the nearest representable number, rounding to an odd mantissa if there is a tie between two values. *Warning*: this rounding mode is currently not implemented (except for a few conversions functions where this stated explicitly). .. macro:: FMPR_PREC_EXACT If passed as the precision parameter to a function, indicates that no rounding is to be performed. This must only be used when it is known that the result of the operation can be represented exactly and fits in memory (the typical use case is working small integer values). Note that, for example, adding two numbers whose exponents are far apart can easily produce an exact result that is far too large to store in memory. Memory management ------------------------------------------------------------------------------- .. function:: void fmpr_init(fmpr_t x) Initializes the variable *x* for use. Its value is set to zero. .. function:: void fmpr_clear(fmpr_t x) Clears the variable *x*, freeing or recycling its allocated memory. Special values ------------------------------------------------------------------------------- .. function:: void fmpr_zero(fmpr_t x) .. function:: void fmpr_one(fmpr_t x) .. function:: void fmpr_pos_inf(fmpr_t x) .. function:: void fmpr_neg_inf(fmpr_t x) .. function:: void fmpr_nan(fmpr_t x) Sets *x* respectively to 0, 1, `+\infty`, `-\infty`, NaN. .. function:: int fmpr_is_zero(const fmpr_t x) .. function:: int fmpr_is_one(const fmpr_t x) .. function:: int fmpr_is_pos_inf(const fmpr_t x) .. function:: int fmpr_is_neg_inf(const fmpr_t x) .. function:: int fmpr_is_nan(const fmpr_t x) Returns nonzero iff *x* respectively equals 0, 1, `+\infty`, `-\infty`, NaN. .. function:: int fmpr_is_inf(const fmpr_t x) Returns nonzero iff *x* equals either `+\infty` or `-\infty`. .. function:: int fmpr_is_normal(const fmpr_t x) Returns nonzero iff *x* is a finite, nonzero floating-point value, i.e. not one of the special values 0, `+\infty`, `-\infty`, NaN. .. function:: int fmpr_is_special(const fmpr_t x) Returns nonzero iff *x* is one of the special values 0, `+\infty`, `-\infty`, NaN, i.e. not a finite, nonzero floating-point value. .. function:: int fmpr_is_finite(fmpr_t x) Returns nonzero iff *x* is a finite floating-point value, i.e. not one of the values `+\infty`, `-\infty`, NaN. (Note that this is not equivalent to the negation of :func:`fmpr_is_inf`.) Assignment, rounding and conversions ------------------------------------------------------------------------------- .. function:: slong _fmpr_normalise(fmpz_t man, fmpz_t exp, slong prec, fmpr_rnd_t rnd) Rounds the mantissa and exponent in-place. .. function:: void fmpr_set(fmpr_t y, const fmpr_t x) Sets *y* to a copy of *x*. .. function:: void fmpr_swap(fmpr_t x, fmpr_t y) Swaps *x* and *y* efficiently. .. function:: slong fmpr_set_round(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_set_round_fmpz(fmpr_t x, const fmpz_t x, slong prec, fmpr_rnd_t rnd) Sets *y* to a copy of *x* rounded in the direction specified by rnd to the number of bits specified by prec. .. function:: slong _fmpr_set_round_mpn(slong * shift, fmpz_t man, mp_srcptr x, mp_size_t xn, int negative, slong prec, fmpr_rnd_t rnd) Given an integer represented by a pointer *x* to a raw array of *xn* limbs (negated if *negative* is nonzero), sets *man* to the corresponding floating-point mantissa rounded to *prec* bits in direction *rnd*, sets *shift* to the exponent, and returns the error bound. We require that *xn* is positive and that the leading limb of *x* is nonzero. .. function:: slong fmpr_set_round_ui_2exp_fmpz(fmpr_t z, mp_limb_t lo, const fmpz_t exp, int negative, slong prec, fmpr_rnd_t rnd) Sets *z* to the unsigned integer *lo* times two to the power *exp*, negating the value if *negative* is nonzero, and rounding the result to *prec* bits in direction *rnd*. .. function:: slong fmpr_set_round_uiui_2exp_fmpz(fmpr_t z, mp_limb_t hi, mp_limb_t lo, const fmpz_t exp, int negative, slong prec, fmpr_rnd_t rnd) Sets *z* to the unsigned two-limb integer *{hi, lo}* times two to the power *exp*, negating the value if *negative* is nonzero, and rounding the result to *prec* bits in direction *rnd*. .. function:: void fmpr_set_error_result(fmpr_t err, const fmpr_t result, slong rret) Given the return value *rret* and output variable *result* from a function performing a rounding (e.g. *fmpr_set_round* or *fmpr_add*), sets *err* to a bound for the absolute error. .. function:: void fmpr_add_error_result(fmpr_t err, const fmpr_t err_in, const fmpr_t result, slong rret, slong prec, fmpr_rnd_t rnd) Like *fmpr_set_error_result*, but adds *err_in* to the error. .. function:: void fmpr_ulp(fmpr_t u, const fmpr_t x, slong prec) Sets *u* to the floating-point unit in the last place (ulp) of *x*. The ulp is defined as in the MPFR documentation and satisfies `2^{-n} |x| < u \le 2^{-n+1} |x|` for any finite nonzero *x*. If *x* is a special value, *u* is set to the absolute value of *x*. .. function:: int fmpr_check_ulp(const fmpr_t x, slong r, slong prec) Assume that *r* is the return code and *x* is the floating-point result from a single floating-point rounding. Then this function returns nonzero iff *x* and *r* define an error of exactly 0 or 1 ulp. In other words, this function checks that :func:`fmpr_set_error_result` gives exactly 0 or 1 ulp as expected. .. function:: int fmpr_get_mpfr(mpfr_t x, const fmpr_t y, mpfr_rnd_t rnd) Sets the MPFR variable *x* to the value of *y*. If the precision of *x* is too small to allow *y* to be represented exactly, it is rounded in the specified MPFR rounding mode. The return value indicates the direction of rounding, following the standard convention of the MPFR library. .. function:: void fmpr_set_mpfr(fmpr_t x, const mpfr_t y) Sets *x* to the exact value of the MPFR variable *y*. .. function:: double fmpr_get_d(const fmpr_t x, fmpr_rnd_t rnd) Returns *x* rounded to a *double* in the direction specified by *rnd*. .. function:: void fmpr_set_d(fmpr_t x, double v) Sets *x* the the exact value of the argument *v* of type *double*. .. function:: void fmpr_set_ui(fmpr_t x, ulong c) .. function:: void fmpr_set_si(fmpr_t x, slong c) .. function:: void fmpr_set_fmpz(fmpr_t x, const fmpz_t c) Sets *x* exactly to the integer *c*. .. function:: void fmpr_get_fmpz(fmpz_t z, const fmpr_t x, fmpr_rnd_t rnd) Sets *z* to *x* rounded to the nearest integer in the direction specified by *rnd*. If *rnd* is *FMPR_RND_NEAR*, rounds to the nearest even integer in case of a tie. Aborts if *x* is infinite, NaN or if the exponent is unreasonably large. .. function:: slong fmpr_get_si(const fmpr_t x, fmpr_rnd_t rnd) Returns *x* rounded to the nearest integer in the direction specified by *rnd*. If *rnd* is *FMPR_RND_NEAR*, rounds to the nearest even integer in case of a tie. Aborts if *x* is infinite, NaN, or the value is too large to fit in an *slong*. .. function:: void fmpr_get_fmpq(fmpq_t y, const fmpr_t x) Sets *y* to the exact value of *x*. The result is undefined if *x* is not a finite fraction. .. function:: slong fmpr_set_fmpq(fmpr_t x, const fmpq_t y, slong prec, fmpr_rnd_t rnd) Sets *x* to the value of *y*, rounded according to *prec* and *rnd*. .. function:: void fmpr_set_fmpz_2exp(fmpr_t x, const fmpz_t man, const fmpz_t exp) .. function:: void fmpr_set_si_2exp_si(fmpr_t x, slong man, slong exp) .. function:: void fmpr_set_ui_2exp_si(fmpr_t x, ulong man, slong exp) Sets *x* to `\mathrm{man} \times 2^{\mathrm{exp}}`. .. function:: slong fmpr_set_round_fmpz_2exp(fmpr_t x, const fmpz_t man, const fmpz_t exp, slong prec, fmpr_rnd_t rnd) Sets *x* to `\mathrm{man} \times 2^{\mathrm{exp}}`, rounded according to *prec* and *rnd*. .. function:: void fmpr_get_fmpz_2exp(fmpz_t man, fmpz_t exp, const fmpr_t x) Sets *man* and *exp* to the unique integers such that `x = \mathrm{man} \times 2^{\mathrm{exp}}` and *man* is odd, provided that *x* is a nonzero finite fraction. If *x* is zero, both *man* and *exp* are set to zero. If *x* is infinite or NaN, the result is undefined. .. function:: int fmpr_get_fmpz_fixed_fmpz(fmpz_t y, const fmpr_t x, const fmpz_t e) .. function:: int fmpr_get_fmpz_fixed_si(fmpz_t y, const fmpr_t x, slong e) Converts *x* to a mantissa with predetermined exponent, i.e. computes an integer *y* such that `y \times 2^e \approx x`, truncating if necessary. Returns 0 if exact and 1 if truncation occurred. Comparisons ------------------------------------------------------------------------------- .. function:: int fmpr_equal(const fmpr_t x, const fmpr_t y) Returns nonzero iff *x* and *y* are exactly equal. This function does not treat NaN specially, i.e. NaN compares as equal to itself. .. function:: int fmpr_cmp(const fmpr_t x, const fmpr_t y) Returns negative, zero, or positive, depending on whether *x* is respectively smaller, equal, or greater compared to *y*. Comparison with NaN is undefined. .. function:: int fmpr_cmpabs(const fmpr_t x, const fmpr_t y) .. function:: int fmpr_cmpabs_ui(const fmpr_t x, ulong y) Compares the absolute values of *x* and *y*. .. function:: int fmpr_cmp_2exp_si(const fmpr_t x, slong e) .. function:: int fmpr_cmpabs_2exp_si(const fmpr_t x, slong e) Compares *x* (respectively its absolute value) with `2^e`. .. function:: int fmpr_sgn(const fmpr_t x) Returns `-1`, `0` or `+1` according to the sign of *x*. The sign of NaN is undefined. .. function:: void fmpr_min(fmpr_t z, const fmpr_t a, const fmpr_t b) .. function:: void fmpr_max(fmpr_t z, const fmpr_t a, const fmpr_t b) Sets *z* respectively to the minimum and the maximum of *a* and *b*. .. function:: slong fmpr_bits(const fmpr_t x) Returns the number of bits needed to represent the absolute value of the mantissa of *x*, i.e. the minimum precision sufficient to represent *x* exactly. Returns 0 if *x* is a special value. .. function:: int fmpr_is_int(const fmpr_t x) Returns nonzero iff *x* is integer-valued. .. function:: int fmpr_is_int_2exp_si(const fmpr_t x, slong e) Returns nonzero iff *x* equals `n 2^e` for some integer *n*. .. function:: void fmpr_abs_bound_le_2exp_fmpz(fmpz_t b, const fmpr_t x) Sets *b* to the smallest integer such that `|x| \le 2^b`. If *x* is zero, infinity or NaN, the result is undefined. .. function:: void fmpr_abs_bound_lt_2exp_fmpz(fmpz_t b, const fmpr_t x) Sets *b* to the smallest integer such that `|x| < 2^b`. If *x* is zero, infinity or NaN, the result is undefined. .. function:: slong fmpr_abs_bound_lt_2exp_si(const fmpr_t x) Returns the smallest integer *b* such that `|x| < 2^b`, clamping the result to lie between -*FMPR_PREC_EXACT* and *FMPR_PREC_EXACT* inclusive. If *x* is zero, -*FMPR_PREC_EXACT* is returned, and if *x* is infinity or NaN, *FMPR_PREC_EXACT* is returned. Random number generation ------------------------------------------------------------------------------- .. function:: void fmpr_randtest(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits) Generates a finite random number whose mantissa has precision at most *bits* and whose exponent has at most *mag_bits* bits. The values are distributed non-uniformly: special bit patterns are generated with high probability in order to allow the test code to exercise corner cases. .. function:: void fmpr_randtest_not_zero(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits) Identical to *fmpr_randtest*, except that zero is never produced as an output. .. function:: void fmpr_randtest_special(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits) Indentical to *fmpr_randtest*, except that the output occasionally is set to an infinity or NaN. Input and output ------------------------------------------------------------------------------- .. function:: void fmpr_print(const fmpr_t x) Prints the mantissa and exponent of *x* as integers, precisely showing the internal representation. .. function:: void fmpr_printd(const fmpr_t x, slong digits) Prints *x* as a decimal floating-point number, rounding to the specified number of digits. This function is currently implemented using MPFR, and does not support large exponents. Arithmetic ------------------------------------------------------------------------------- .. function:: void fmpr_neg(fmpr_t y, const fmpr_t x) Sets *y* to the negation of *x*. .. function:: slong fmpr_neg_round(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) Sets *y* to the negation of *x*, rounding the result. .. function:: void fmpr_abs(fmpr_t y, const fmpr_t x) Sets *y* to the absolute value of *x*. .. function:: slong fmpr_add(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_add_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_add_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_add_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) Sets `z = x + y`, rounded according to *prec* and *rnd*. The precision can be *FMPR_PREC_EXACT* to perform an exact addition, provided that the result fits in memory. .. function:: slong _fmpr_add_eps(fmpr_t z, const fmpr_t x, int sign, slong prec, fmpr_rnd_t rnd) Sets *z* to the value that results by adding an infinitesimal quantity of the given sign to *x*, and rounding. The result is undefined if *x* is zero. .. function:: slong fmpr_sub(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_sub_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_sub_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_sub_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) Sets `z = x - y`, rounded according to *prec* and *rnd*. The precision can be *FMPR_PREC_EXACT* to perform an exact addition, provided that the result fits in memory. .. function:: slong fmpr_sum(fmpr_t s, const fmpr_struct * terms, slong len, slong prec, fmpr_rnd_t rnd) Sets *s* to the sum of the array *terms* of length *len*, rounded to *prec* bits in the direction *rnd*. The sum is computed as if done without any intermediate rounding error, with only a single rounding applied to the final result. Unlike repeated calls to *fmpr_add*, this function does not overflow if the magnitudes of the terms are far apart. Warning: this function is implemented naively, and the running time is quadratic with respect to *len* in the worst case. .. function:: slong fmpr_mul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_mul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_mul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_mul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) Sets `z = x \times y`, rounded according to prec and rnd. The precision can be *FMPR_PREC_EXACT* to perform an exact multiplication, provided that the result fits in memory. .. function:: void fmpr_mul_2exp_si(fmpr_t y, const fmpr_t x, slong e) .. function:: void fmpr_mul_2exp_fmpz(fmpr_t y, const fmpr_t x, const fmpz_t e) Sets *y* to *x* multiplied by `2^e` without rounding. .. function:: slong fmpr_div(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_div_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_ui_div(fmpr_t z, ulong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_div_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_si_div(fmpr_t z, slong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_div_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_fmpz_div(fmpr_t z, const fmpz_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_fmpz_div_fmpz(fmpr_t z, const fmpz_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) Sets `z = x / y`, rounded according to *prec* and *rnd*. If *y* is zero, *z* is set to NaN. .. function:: void fmpr_divappr_abs_ubound(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec) Sets `z` to an upper bound for `|x| / |y|`, computed to a precision of approximately *prec* bits. The error can be a few ulp. .. function:: slong fmpr_addmul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_addmul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_addmul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_addmul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) Sets `z = z + x \times y`, rounded according to *prec* and *rnd*. The intermediate multiplication is always performed without roundoff. The precision can be *FMPR_PREC_EXACT* to perform an exact addition, provided that the result fits in memory. .. function:: slong fmpr_submul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_submul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_submul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_submul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) Sets `z = z - x \times y`, rounded according to *prec* and *rnd*. The intermediate multiplication is always performed without roundoff. The precision can be *FMPR_PREC_EXACT* to perform an exact subtraction, provided that the result fits in memory. .. function:: slong fmpr_sqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_sqrt_ui(fmpr_t z, ulong x, slong prec, fmpr_rnd_t rnd) .. function:: slong fmpr_sqrt_fmpz(fmpr_t z, const fmpz_t x, slong prec, fmpr_rnd_t rnd) Sets *z* to the square root of *x*, rounded according to *prec* and *rnd*. The result is NaN if *x* is negative. .. function:: slong fmpr_rsqrt(fmpr_t z, const fmpr_t x, slong prec, fmpr_rnd_t rnd) Sets *z* to the reciprocal square root of *x*, rounded according to *prec* and *rnd*. The result is NaN if *x* is negative. At high precision, this is faster than computing a square root. .. function:: slong fmpr_root(fmpr_t z, const fmpr_t x, ulong k, slong prec, fmpr_rnd_t rnd) Sets *z* to the *k*-th root of *x*, rounded to *prec* bits in the direction *rnd*. Warning: this function wraps MPFR, and is currently only fast for small *k*. .. function:: void fmpr_pow_sloppy_fmpz(fmpr_t y, const fmpr_t b, const fmpz_t e, slong prec, fmpr_rnd_t rnd) .. function:: void fmpr_pow_sloppy_ui(fmpr_t y, const fmpr_t b, ulong e, slong prec, fmpr_rnd_t rnd) .. function:: void fmpr_pow_sloppy_si(fmpr_t y, const fmpr_t b, slong e, slong prec, fmpr_rnd_t rnd) Sets `y = b^e`, computed using without guaranteeing correct (optimal) rounding, but guaranteeing that the result is a correct upper or lower bound if the rounding is directional. Currently requires `b \ge 0`. Special functions ------------------------------------------------------------------------------- .. function:: slong fmpr_log(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) Sets *y* to `\log(x)`, rounded according to *prec* and *rnd*. The result is NaN if *x* is negative. This function is currently implemented using MPFR and does not support large exponents. .. function:: slong fmpr_log1p(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) Sets *y* to `\log(1+x)`, rounded according to *prec* and *rnd*. This function computes an accurate value when *x* is small. The result is NaN if `1+x` is negative. This function is currently implemented using MPFR and does not support large exponents. .. function:: slong fmpr_exp(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) Sets *y* to `\exp(x)`, rounded according to *prec* and *rnd*. This function is currently implemented using MPFR and does not support large exponents. .. function:: slong fmpr_expm1(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) Sets *y* to `\exp(x)-1`, rounded according to *prec* and *rnd*. This function computes an accurate value when *x* is small. This function is currently implemented using MPFR and does not support large exponents. arb-2.8.1/doc/source/fmprb.rst000066400000000000000000000437301264125401100161760ustar00rootroot00000000000000.. _fmprb: **fmprb.h** -- real numbers represented as floating-point balls =============================================================================== This type is now obsolete: use :type:`arb_t` instead. An :type:`fmprb_t` represents a ball over the real numbers. Types, macros and constants ------------------------------------------------------------------------------- .. type:: fmprb_struct .. type:: fmprb_t An *fmprb_struct* consists of a pair of *fmpr_struct*:s. An *fmprb_t* is defined as an array of length one of type *fmprb_struct*, permitting an *fmprb_t* to be passed by reference. .. type:: fmprb_ptr Alias for ``fmprb_struct *``, used for vectors of numbers. .. type:: fmprb_srcptr Alias for ``const fmprb_struct *``, used for vectors of numbers when passed as constant input to functions. .. macro:: FMPRB_RAD_PREC The precision used for operations on the radius. This is small enough to fit in a single word, currently 30 bits. .. macro:: fmprb_midref(x) Macro returning a pointer to the midpoint of *x* as an *fmpr_t*. .. macro:: fmprb_radref(x) Macro returning a pointer to the radius of *x* as an *fmpr_t*. Memory management ------------------------------------------------------------------------------- .. function:: void fmprb_init(fmprb_t x) Initializes the variable *x* for use. Its midpoint and radius are both set to zero. .. function:: void fmprb_clear(fmprb_t x) Clears the variable *x*, freeing or recycling its allocated memory. .. function:: fmprb_ptr _fmprb_vec_init(slong n) Returns a pointer to an array of *n* initialized *fmprb_struct*:s. .. function:: void _fmprb_vec_clear(fmprb_ptr v, slong n) Clears an array of *n* initialized *fmprb_struct*:s. Assignment and rounding ------------------------------------------------------------------------------- .. function:: void fmprb_set(fmprb_t y, const fmprb_t x) Sets *y* to a copy of *x*. .. function:: void fmprb_set_round(fmprb_t y, const fmprb_t x, slong prec) Sets *y* to a copy of *x*, rounded to *prec* bits. .. function:: void fmprb_set_fmpr(fmprb_t y, const fmpr_t x) .. function:: void fmprb_set_si(fmprb_t y, slong x) .. function:: void fmprb_set_ui(fmprb_t y, ulong x) .. function:: void fmprb_set_fmpz(fmprb_t y, const fmpz_t x) Sets *y* exactly to *x*. .. function:: void fmprb_set_fmpq(fmprb_t y, const fmpq_t x, slong prec) Sets *y* to the rational number *x*, rounded to *prec* bits. .. function:: void fmprb_set_fmpz_2exp(fmprb_t x, const fmpz_t y, const fmpz_t exp) Sets *x* to *y* multiplied by 2 raised to the power *exp*. .. function:: void fmprb_set_round_fmpz_2exp(fmprb_t y, const fmpz_t x, const fmpz_t exp, slong prec) Sets *x* to *y* multiplied by 2 raised to the power *exp*, rounding the result to *prec* bits. Assignment of special values ------------------------------------------------------------------------------- .. function:: void fmprb_zero(fmprb_t x) Sets *x* to zero. .. function:: void fmprb_one(fmprb_t x) Sets *x* to the exact integer 1. .. function:: void fmprb_pos_inf(fmprb_t x) Sets *x* to positive infinity, with a zero radius. .. function:: void fmprb_neg_inf(fmprb_t x) Sets *x* to negative infinity, with a zero radius. .. function:: void fmprb_zero_pm_inf(fmprb_t x) Sets *x* to `[0 \pm \infty]`, representing the whole extended real line. .. function:: void fmprb_indeterminate(fmprb_t x) Sets *x* to `[\operatorname{NaN} \pm \infty]`, representing an indeterminate result. Input and output ------------------------------------------------------------------------------- .. function:: void fmprb_print(const fmprb_t x) Prints the internal representation of *x*. .. function:: void fmprb_printd(const fmprb_t x, slong digits) Prints *x* in decimal. The printed value of the radius is not adjusted to compensate for the fact that the binary-to-decimal conversion of both the midpoint and the radius introduces additional error. Random number generation ------------------------------------------------------------------------------- .. function:: void fmprb_randtest(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random ball. The midpoint and radius will both be finite. .. function:: void fmprb_randtest_exact(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random number with zero radius. .. function:: void fmprb_randtest_precise(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random number with radius at most `2^{-\mathrm{prec}}` the magnitude of the midpoint. .. function:: void fmprb_randtest_wide(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random number with midpoint and radius chosen independently, possibly giving a very large interval. .. function:: void fmprb_randtest_special(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) Generates a random interval, possibly having NaN or an infinity as the midpoint and possibly having an infinite radius. .. function:: void fmprb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const fmprb_t x, slong bits) Sets *q* to a random rational number from the interval represented by *x*. A denominator is chosen by multiplying the binary denominator of *x* by a random integer up to *bits* bits. The outcome is undefined if the midpoint or radius of *x* is non-finite, or if the exponent of the midpoint or radius is so large or small that representing the endpoints as exact rational numbers would cause overflows. Radius and interval operations ------------------------------------------------------------------------------- .. function:: void fmprb_add_error_fmpr(fmprb_t x, const fmpr_t err) Adds *err*, which is assumed to be nonnegative, to the radius of *x*. .. function:: void fmprb_add_error_2exp_si(fmprb_t x, slong e) .. function:: void fmprb_add_error_2exp_fmpz(fmprb_t x, const fmpz_t e) Adds `2^e` to the radius of *x*. .. function:: void fmprb_add_error(fmprb_t x, const fmprb_t err) Adds the supremum of *err*, which is assumed to be nonnegative, to the radius of *x*. .. function:: void fmprb_union(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) Sets *z* to a ball containing both *x* and *y*. .. function:: void fmprb_get_abs_ubound_fmpr(fmpr_t u, const fmprb_t x, slong prec) Sets *u* to the upper bound of the absolute value of *x*, rounded up to *prec* bits. If *x* contains NaN, the result is NaN. .. function:: void fmprb_get_abs_lbound_fmpr(fmpr_t u, const fmprb_t x, slong prec) Sets *u* to the lower bound of the absolute value of *x*, rounded down to *prec* bits. If *x* contains NaN, the result is NaN. .. function:: void fmprb_get_interval_fmpz_2exp(fmpz_t a, fmpz_t b, fmpz_t exp, const fmprb_t x) Computes the exact interval represented by *x*, in the form of an integer interval multiplied by a power of two, i.e. `x = [a, b] \times 2^{\mathrm{exp}}`. The outcome is undefined if the midpoint or radius of *x* is non-finite, or if the difference in magnitude between the midpoint and radius is so large that representing the endpoints exactly would cause overflows. .. function:: void fmprb_set_interval_fmpr(fmprb_t x, const fmpr_t a, const fmpr_t b, slong prec) Sets *x* to a ball containing the interval `[a, b]`. We require that `a \le b`. .. function:: slong fmprb_rel_error_bits(const fmprb_t x) Returns the effective relative error of *x* measured in bits, defined as the difference between the position of the top bit in the radius and the top bit in the midpoint, plus one. The result is clamped between plus/minus *FMPR_PREC_EXACT*. .. function:: slong fmprb_rel_accuracy_bits(const fmprb_t x) Returns the effective relative accuracy of *x* measured in bits, equal to the negative of the return value from *fmprb_rel_error_bits*. .. function:: slong fmprb_bits(const fmprb_t x) Returns the number of bits needed to represent the absolute value of the mantissa of the midpoint of *x*, i.e. the minimum precision sufficient to represent *x* exactly. Returns 0 if the midpoint of *x* is a special value. .. function:: void fmprb_trim(fmprb_t y, const fmprb_t x) Sets *y* to a trimmed copy of *x*: rounds *x* to a number of bits equal to the accuracy of *x* (as indicated by its radius), plus a few guard bits. The resulting ball is guaranteed to contain *x*, but is more economical if *x* has less than full accuracy. .. function:: int fmprb_get_unique_fmpz(fmpz_t z, const fmprb_t x) If *x* contains a unique integer, sets *z* to that value and returns nonzero. Otherwise (if *x* represents no integers or more than one integer), returns zero. Comparisons ------------------------------------------------------------------------------- .. function:: int fmprb_is_zero(const fmprb_t x) Returns nonzero iff the midpoint and radius of *x* are both zero. .. function:: int fmprb_is_nonzero(const fmprb_t x) Returns nonzero iff zero is not contained in the interval represented by *x*. .. function:: int fmprb_is_one(const fmprb_t x) Returns nonzero iff *x* is exactly 1. .. function:: int fmprb_is_finite(fmprb_t x) Returns nonzero iff the midpoint and radius of *x* are both finite floating-point numbers, i.e. not infinities or NaN. .. function:: int fmprb_is_exact(const fmprb_t x) Returns nonzero iff the radius of *x* is zero. .. function:: int fmprb_is_int(const fmprb_t x) Returns nonzero iff *x* is an exact integer. .. function:: int fmprb_equal(const fmprb_t x, const fmprb_t y) Returns nonzero iff *x* and *y* are equal as balls, i.e. have both the same midpoint and radius. Note that this is not the same thing as testing whether both *x* and *y* certainly represent the same real number, unless either *x* or *y* is exact (and neither contains NaN). To test whether both operands *might* represent the same mathematical quantity, use :func:`fmprb_overlaps` or :func:`fmprb_contains`, depending on the circumstance. .. function:: int fmprb_is_positive(const fmprb_t x) .. function:: int fmprb_is_nonnegative(const fmprb_t x) .. function:: int fmprb_is_negative(const fmprb_t x) .. function:: int fmprb_is_nonpositive(const fmprb_t x) Returns nonzero iff all points *p* in the interval represented by *x* satisfy, respectively, `p > 0`, `p \ge 0`, `p < 0`, `p \le 0`. If *x* contains NaN, returns zero. .. function:: int fmprb_overlaps(const fmprb_t x, const fmprb_t y) Returns nonzero iff *x* and *y* have some point in common. If either *x* or *y* contains NaN, this function always returns nonzero (as a NaN could be anything, it could in particular contain any number that is included in the other operand). .. function:: int fmprb_contains_fmpr(const fmprb_t x, const fmpr_t y) .. function:: int fmprb_contains_fmpq(const fmprb_t x, const fmpq_t y) .. function:: int fmprb_contains_fmpz(const fmprb_t x, const fmpz_t y) .. function:: int fmprb_contains_si(const fmprb_t x, slong y) .. function:: int fmprb_contains_mpfr(const fmprb_t x, const mpfr_t y) .. function:: int fmprb_contains_zero(const fmprb_t x) .. function:: int fmprb_contains(const fmprb_t x, const fmprb_t y) Returns nonzero iff the given number (or ball) *y* is contained in the interval represented by *x*. If *x* is contains NaN, this function always returns nonzero (as it could represent anything, and in particular could represent all the points included in *y*). If *y* contains NaN and *x* does not, it always returns zero. .. function:: int fmprb_contains_negative(const fmprb_t x) .. function:: int fmprb_contains_nonpositive(const fmprb_t x) .. function:: int fmprb_contains_positive(const fmprb_t x) .. function:: int fmprb_contains_nonnegative(const fmprb_t x) Returns nonzero iff there is any point *p* in the interval represented by *x* satisfying, respectively, `p < 0`, `p \le 0`, `p > 0`, `p \ge 0`. If *x* contains NaN, returns nonzero. Arithmetic ------------------------------------------------------------------------------- .. function:: void fmprb_neg(fmprb_t y, const fmprb_t x) Sets *y* to the negation of *x*. .. function:: void fmprb_abs(fmprb_t y, const fmprb_t x) Sets *y* to the absolute value of *x*. No attempt is made to improve the interval represented by *x* if it contains zero. .. function:: void fmprb_add(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) .. function:: void fmprb_add_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) .. function:: void fmprb_add_si(fmprb_t z, const fmprb_t x, slong y, slong prec) .. function:: void fmprb_add_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) .. function:: void fmprb_add_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec) Sets `z = x + y`, rounded to *prec* bits. The precision can be *FMPR_PREC_EXACT* provided that the result fits in memory. .. function:: void fmprb_sub(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) .. function:: void fmprb_sub_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) .. function:: void fmprb_sub_si(fmprb_t z, const fmprb_t x, slong y, slong prec) .. function:: void fmprb_sub_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) Sets `z = x - y`, rounded to *prec* bits. The precision can be *FMPR_PREC_EXACT* provided that the result fits in memory. .. function:: void fmprb_mul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) .. function:: void fmprb_mul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) .. function:: void fmprb_mul_si(fmprb_t z, const fmprb_t x, slong y, slong prec) .. function:: void fmprb_mul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) Sets `z = x \times y`, rounded to *prec* bits. The precision can be *FMPR_PREC_EXACT* provided that the result fits in memory. .. function:: void fmprb_mul_2exp_si(fmprb_t y, const fmprb_t x, slong e) .. function:: void fmprb_mul_2exp_fmpz(fmprb_t y, const fmprb_t x, const fmpz_t e) Sets *y* to *x* multiplied by `2^e`. .. function:: void fmprb_inv(fmprb_t z, const fmprb_t x, slong prec) Sets *z* to the multiplicative inverse of *x*. .. function:: void fmprb_div(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) .. function:: void fmprb_div_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) .. function:: void fmprb_div_si(fmprb_t z, const fmprb_t x, slong y, slong prec) .. function:: void fmprb_div_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) .. function:: void fmprb_div_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec) .. function:: void fmprb_fmpz_div_fmpz(fmprb_t y, const fmpz_t num, const fmpz_t den, slong prec) .. function:: void fmprb_ui_div(fmprb_t z, ulong x, const fmprb_t y, slong prec) Sets `z = x / y`, rounded to *prec* bits. If *y* contains zero, *z* is set to `0 \pm \infty`. Otherwise, error propagation uses the rule .. math :: \left| \frac{x}{y} - \frac{x+\xi_1 a}{y+\xi_2 b} \right| = \left|\frac{x \xi_2 b - y \xi_1 a}{y (y+\xi_2 b)}\right| \le \frac{|xb|+|ya|}{|y| (|y|-b)} where `-1 \le \xi_1, \xi_2 \le 1`, and where the triangle inequality has been applied to the numerator and the reverse triangle inequality has been applied to the denominator. .. function:: void fmprb_addmul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) .. function:: void fmprb_addmul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) .. function:: void fmprb_addmul_si(fmprb_t z, const fmprb_t x, slong y, slong prec) .. function:: void fmprb_addmul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) Sets `z = z + x \times y`, rounded to prec bits. The precision can be *FMPR_PREC_EXACT* provided that the result fits in memory. .. function:: void fmprb_submul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) .. function:: void fmprb_submul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) .. function:: void fmprb_submul_si(fmprb_t z, const fmprb_t x, slong y, slong prec) .. function:: void fmprb_submul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) Sets `z = z - x \times y`, rounded to *prec* bits. The precision can be *FMPR_PREC_EXACT* provided that the result fits in memory. Powers and roots ------------------------------------------------------------------------------- .. function:: void fmprb_sqrt(fmprb_t z, const fmprb_t x, slong prec) .. function:: void fmprb_sqrt_ui(fmprb_t z, ulong x, slong prec) .. function:: void fmprb_sqrt_fmpz(fmprb_t z, const fmpz_t x, slong prec) Sets *z* to the square root of *x*, rounded to *prec* bits. Error propagation is done using the following rule: assuming `m > r \ge 0`, the error is largest at `m - r`, and we have `\sqrt{m} - \sqrt{m-r} \le r / (2 \sqrt{m-r})`. .. function:: void fmprb_sqrtpos(fmprb_t z, const fmprb_t x, slong prec) Sets *z* to the square root of *x*, assuming that *x* represents a nonnegative number (i.e. discarding any negative numbers in the input interval), and producing an output interval not containing any negative numbers (unless the radius is infinite). .. function:: void fmprb_hypot(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) Sets *z* to `\sqrt{x^2 + y^2}`. .. function:: void fmprb_rsqrt(fmprb_t z, const fmprb_t x, slong prec) .. function:: void fmprb_rsqrt_ui(fmprb_t z, ulong x, slong prec) Sets *z* to the reciprocal square root of *x*, rounded to *prec* bits. At high precision, this is faster than computing a square root. .. function:: void fmprb_root(fmprb_t z, const fmprb_t x, ulong k, slong prec) Sets *z* to the *k*-th root of *x*, rounded to *prec* bits. As currently implemented, this function is only fast for small fixed *k*. For large *k* it is better to use :func:`fmprb_pow_fmpq` or :func:`fmprb_pow`. .. function:: void fmprb_agm(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) Sets *z* to the arithmetic-geometric mean of *x* and *y*. arb-2.8.1/doc/source/gamma.rst000066400000000000000000000064251264125401100161520ustar00rootroot00000000000000.. _algorithms_gamma: Algorithms for gamma functions =============================================================================== The Stirling series ------------------------------------------------------------------------------- In general, the gamma function is computed via the Stirling series .. math :: \log \Gamma(z) = \left(z-\frac{1}{2}\right)\log z - z + \frac{\ln {2 \pi}}{2} + \sum_{k=1}^{n-1} \frac{B_{2k}}{2k(2k-1)z^{2k-1}} + R(n,z) where ([Olv1997]_ pp. 293-295) the remainder term is exactly .. math :: R_n(z) = \int_0^{\infty} \frac{B_{2n} - {\tilde B}_{2n}(x)}{2n(x+z)^{2n}} dx. To evaluate the gamma function of a power series argument, we substitute `z \to z + t \in \mathbb{C}[[t]]`. Using the bound for `|x+z|` given by [Olv1997]_ and the fact that the numerator of the integrand is bounded in absolute value by `2 |B_{2n}|`, the remainder can be shown to satisfy the bound .. math :: |[t^k] R_n(z+t)| \le 2 |B_{2n}| \frac{\Gamma(2n+k-1)}{\Gamma(k+1) \Gamma(2n+1)} \; |z| \; (b / |z|)^{2n+k} where `b = 1/\cos(\operatorname{arg}(z)/2)`. Note that by trigonometric identities, assuming that `z = x+yi`, we have `b = \sqrt{1 + t^2}` where .. math :: t = \frac{y}{\sqrt{x^2 + y^2} + x} = \frac{\sqrt{x^2 + y^2} - x}{y}. To use the Stirling series at `p`-bit precision, we select parameters `r`, `n` such that the remainder `R(n,z)` approximately is bounded by `2^{-p}`. If `|z|` is too small for the Stirling series to give sufficient accuracy directly, we first translate to `z + r` using the formula `\Gamma(z) = \Gamma(z+r) / (z (z+1) (z+2) \cdots (z+r-1))`. To obtain a remainder smaller than `2^{-p}`, we must choose an `r` such that, in the real case, `z + r > \beta p`, where `\beta > \log(2) / (2 \pi) \approx 0.11`. In practice, a slightly larger factor `\beta \approx 0.2` more closely balances `n` and `r`. A much larger `\beta` (e.g. `\beta = 1`) could be used to reduce the number of Bernoulli numbers that have to be precomputed, at the expense of slower repeated evaluation. Rational arguments ------------------------------------------------------------------------------- We use efficient methods to compute `y = \Gamma(p/q)` where `q` is one of `1, 2, 3, 4, 6` and `p` is a small integer. The cases `\Gamma(1) = 1` and `\Gamma(1/2) = \sqrt \pi` are trivial. We reduce all remaining cases to `\Gamma(1/3)` or `\Gamma(1/4)` using the following relations: .. math :: \Gamma(2/3) = \frac{2 \pi}{3^{1/2} \Gamma(1/3)}, \quad \quad \Gamma(3/4) = \frac{2^{1/2} \pi}{\Gamma(1/4)}, \Gamma(1/6) = \frac{\Gamma(1/3)^2}{(\pi/3)^{1/2} 2^{1/3}}, \quad \quad \Gamma(5/6) = \frac{2 \pi (\pi/3)^{1/2} 2^{1/3}}{\Gamma(1/3)^2}. We compute `\Gamma(1/3)` and `\Gamma(1/4)` rapidly to high precision using .. math :: \Gamma(1/3) = \left( \frac{12 \pi^4}{\sqrt{10}} \sum_{k=0}^{\infty} \frac{(6k)!(-1)^k}{(k!)^3 (3k)! 3^k 160^{3k}} \right)^{1/6}, \quad \quad \Gamma(1/4) = \sqrt{\frac{(2\pi)^{3/2}}{\operatorname{agm}(1, \sqrt 2)}}. An alternative formula which could be used for `\Gamma(1/3)` is .. math :: \Gamma(1/3) = \frac{2^{4/9} \pi^{2/3}}{3^{1/12} \left( \operatorname{agm}\left(1,\frac{1}{2} \sqrt{2+\sqrt{3}}\right)\right)^{1/3}}, but this appears to be slightly slower in practice. arb-2.8.1/doc/source/history.rst000066400000000000000000000674301264125401100165740ustar00rootroot00000000000000.. _history: History and changes =============================================================================== For more details, view the commit log in the git repository https://github.com/fredrik-johansson/arb * 2015-12-31 - version 2.8.1 * Fixed 32-bit test failure for the Laguerre function. * Made the Laguerre function indeterminate at negative integer orders, to be consistent with the test code. * 2015-12-29 - version 2.8.0 * Compatibility and build system * Windows64 support (contributed by Bill Hart). * Fixed a bug that broke basic arithmetic on targets where FLINT uses fallback code instead of assembly code, such as PPC64 (contributed by Jeroen Demeyer). * Fixed configure to use EXTRA_SHARED_FLAGS/LDFLAGS, and other build system fixes (contributed by Tommy Hofmann, Bill Hart). * Added soname versioning (contributed by Julien Puydt). * Fixed test code on MinGW (contributed by Hrvoje Abraham). * Miscellaneous fixes to simplify interfacing Arb from Julia. * Arithmetic and elementary functions * Fixed arf_get_d to handle underflow/overflow correctly and to support round-to-nearest. * Added more complex inverse hyperbolic functions (acb_asin, acb_acos, acb_asinh, acb_acosh, acb_atanh). * Added arb_contains_int and acb_contains_int for testing whether an interval contains any integer. * Added acb_quadratic_roots_fmpz. * Improved arb_sinh to use a more accurate formula for x < 0. * Added sinc function (arb_sinc) (contributed by Alex Griffing). * Fixed bug in arb_exp affecting convergence for huge input. * Faster implementation of arb_div_2expm1_ui. * Added mag_root, mag_geom_series. * Improved and added test code for arb_add_error functions. * Changed arb_pow and acb_pow to make pow(0,positive) = 0 instead of nan. * Improved acb_sqrt to return finite output for finite input straddling the branch cut. * Improved arb_set_interval_arf so that [inf,inf] = inf instead of an infinite interval. * Added computation of Bell numbers (arb_bell_fmpz). * Added arb_power_sum_vec for computing power sums using Bernoulli numbers. * Added computation of the Fujiwara root bound for acb_poly. * Added code to identify all the real roots of a real polynomial (acb_poly_validate_real_roots). * Added several convenient assignment functions, including arb_set_d, acb_set_d, acb_set_d_d, acb_set_fmpz_fmpz (contributed by Ricky Farr). * Added many accessor functions (_arb/acb_vec_entry_ptr, arb_get_mid/rad_arb, acb_real/imag_ptr, arb_mid/rad_ptr, acb_get_real/imag). * Added missing functions acb_add_si, acb_sub_si. * Renamed arb_root to arb_root_ui (keeping alias) and added acb_root_ui. * Special functions * Implemented the Gauss hypergeometric function 2F1 and its regularized version. * Fixed two bugs in acb_hypgeom_pfq_series_direct discovered while implementing 2F1. In rare cases, these could lead to incorrect values for functions depending on parameter derivatives of hypergeometric series. * The first bug involved incorrect handling of negative integer parameters. The bug only affected 2F1 and higher functions; it did not affect correctness of any previously implemented functions that relied on acb_hypgeom_pfq_series_direct (such as Bessel Y and K functions of integer order). * The second bug involved a too small bound being computed for the sum of a geometric series. The geometric series bound is nearly tight for 2F1, and the incorrect version caused immediate test failures for that function. Theoretically, this bug affected correctness of some previously-implemented functions that relied on acb_hypgeom_pfq_series_direct (such as Bessel Y and K functions of integer order), but since the geometric bound is not as tight in those cases, those functions were still reliable in practice (no failing test case has been found). * Implemented Airy functions and their derivatives (acb_hypgeom_airy). * Implemented the confluent hypergeometric function 0F1 (acb_hypgeom_0f1). * Implemented associated Legendre functions P and Q. * Implemented Chebyshev, Jacobi, Gegenbauer, Laguerre, Hermite functions. * Implemented spherical harmonics. * Added function for computing Bessel J and Y functions simultaneously. * Added rising factorials for non-integer n (arb_rising, acb_rising). * Made rising factorials use gamma function for large integer n. * Faster algorithm for theta constants and Dedekind eta function at very high precision. * Fixed erf to give finite values instead of +/-inf for big imaginary input. * Improved acb_zeta (and arb_zeta) to automatically use fast code for integer zeta values. * Added double factorial (arb_doublefac_ui). * Added code for generating Hilbert class polynomials (acb_modular_hilbert_class_poly). * Matrices * Added faster matrix squaring (arb/acb_mat_sqr) (contributed by Alex Griffing). * Added matrix trace (arb/acb_mat_trace) (contributed by Alex Griffing). * Added arb/acb_mat_set_round_fmpz_mat, acb_mat_set(_round)_arb_mat (contributed by Tommy Hofmann). * Added arb/acb_mat_transpose (contributed by Tommy Hofmann). * Added comparison methods arb/acb_mat_eq/ne (contributed by Tommy Hofmann). * Other * Added complex_plot example program. * Added Airy functions to real_roots example program. * Other minor patches were contributed by Alexander Kobel, Marc Mezzarobba, Julien Puydt. * Removed obsolete file config.h. * 2015-07-14 - version 2.7.0 * hypergeometric functions * implemented Bessel I and Y functions (acb_hypgeom_bessel_i, acb_hypgeom_bessel_y) * fixed bug in Bessel K function giving the wrong branch for negative real arguments * added code for evaluating complex hypergeometric series binary splitting * added code for evaluating complex hypergeometric series using fast multipoint evaluation * gamma related functions * implemented the Barnes G-function and its continuous logarithm (acb_barnes_g, acb_log_barnes_g) * implemented the generalized polygamma function (acb_polygamma) * implemented the reflection formula for the logarithmic gamma function (acb_lgamma, acb_poly_lgamma_series) * implemented the digamma function of power series (arb_poly_digamma_series, acb_poly_digamma_series) * improved acb_poly_zeta_series to produce exact zero imaginary parts in most cases when the result should be real-valued * made the real logarithmic gamma function (arb_lgamma, arb_poly_lgamma_series) abort more quickly for negative input * elementary functions * added arb_exp_expinv and acb_exp_expinv functions for simultaneously computing exp(x), exp(-x) * improved acb_tan, acb_tan_pi, acb_cot and acb_cot_pi for input with large imaginary parts * added complex hyperbolic functions (acb_sinh, acb_cosh, acb_sinh_cosh, acb_tanh, acb_coth) * added acb_log_sin_pi for computing the logarithmic sine function without branch cuts away from the real line * added arb_poly_cot_pi_series, acb_poly_cot_pi_series * added arf_root and improved speed of arb_root * tuned algorithm selection in arb_pow_fmpq * other * added documentation for arb and acb vector functions * 2015-04-19 - version 2.6.0 * special functions * added the Bessel K function * added the confluent hypergeometric functions M and U * added exponential, trigonometric and logarithmic integrals ei, si, shi, ci, chi, li * added the complete elliptic integral of the second kind E * added support for computing hypergeometric functions with power series as parameters * fixed special cases in Bessel J function returning useless output * fix precision of zeta function accidentally being capped at 7000 digits (bug in 2.5) * special-cased real input in the gamma functions for complex types * fixed exp of huge numbers outputting unnecessarily useless intervals * fixed broken code in erf that sometimes gave useless output * made selection of number of terms in hypergeometric series more robust * polynomials and power series * added sin_pi, cos_pi and sin_cos_pi for real and complex power series * speeded up series reciprocal and division for length = 2 * added add_si methods for polynomials * made inv_series and div_series with zero input produce indeterminates instead of aborting * added arb_poly_majorant, acb_poly_majorant * basic functions * added comparison methods arb_eq, arb_ne, arb_lt, arb_le, arb_gt, arb_ge, acb_eq, acb_ne * added acb_rel_accuracy_bits and improved the real version * fixed precision of constants like pi behaving more nondeterministically than necessary * fixed arf_get_mag_lower(nan) to output 0 instead of inf * other * removed call to fmpq_dedekind_sum which only exists in the git version of flint * fixed a test code bug that could cause crashes on some systems * added fix for static build on OS X (thanks Marcello Seri) * miscellaneous corrections to the documentation * 2015-01-28 - version 2.5.0 * string conversion * added arb_set_str * added arb_get_str and arb_printn for pretty-printed rigorous decimal output * added helper functions for binary to decimal conversion * core arithmetic * improved speed of division when using GMP instead of MPIR * improved complex division with a small denominator * removed a little bit of overhead for complex squaring * special functions * faster code for atan at very high precision, used instead of mpfr_atan * optimized elementary functions slightly for small input * added modified error functions erfc and erfi * added the generalized exponential integral * added the upper incomplete gamma function * implemented the complete elliptic integral of the first kind * implemented the arithmetic-geometric mean of complex numbers * optimized arb_digamma for small integers * made mag_log_ui, mag_binpow_uiui and mag_polylog_tail proper functions * added pow, agm, erf, elliptic_k, elliptic_p as functions of complex power series * added incomplete gamma function of complex power series * improved code for bounding complex rising factorials (the old code could potentially have given wrong results in degenerate cases) * added arb_sqrt1pm1, arb_atanh, arb_asinh, arb_atanh * added arb_log1p, acb_log1p, acb_atan * added arb_hurwitz_zeta * improved parameter selection in the Hurwitz zeta function to try to avoid stalling when given enormous input * optimized sqrt and rsqrt of power series when given a binomial as input * made arb_bernoulli_ui(2^64-2) not crash * fixed rgamma of negative integers returning indeterminate * polynomials and matrices * added characteristic polynomial computation for real and complex matrices * added polynomial set_round methods * added is_real methods for more types * added more get_unique_fmpz methods * added code for generating Swinnerton-Dyer polynomials * improved error bounding in det() and exp() of complex matrices to recognize when the result is real-valued * changed polynomial divrem to return success/fail instead of aborting on divide by zero * miscellaneous * added logo to documentation * made inlined functions build as part of the library * silenced a clang warning * made _acb_vec_sort_pretty a library function * 2014-11-15 - version 2.4.0 * arithmetic and core functions * made evaluation of sin, cos and exp at medium precision faster using the sqrt trick * optimized arb_sinh and arb_sinh_cosh * optimized complex division with a small denominator * optimized cubing of complex numbers * added floor and ceil functions for the arf and arb types * added acb_poly powering functions * added acb_exp_pi_i * added functions for evaluation of Chebyshev polynomials * fixed arb_div to output nan for input containing nan * added a module acb_hypgeom for hypergeometric functions * evaluation of the generalized hypergeometric function in convergent cases * evaluation of confluent hypergeometric functions using asymptotic expansions * the Bessel function of the first kind for complex input * the error function for complex input * added a module acb_modular for modular forms and elliptic functions * support for working with modular transformations * mapping a point to the fundamental domain * evaluation of Jacobi theta functions and their series expansions * the Dedekind eta function * the j-invariant and the modular lambda and delta function * Eisenstein series * the Weierstrass elliptic function and its series expansion * miscellaneous * fixed mag_print printing a too large exponent * fixed printd methods to use a fallback instead of aborting when printing numbers too large for MPFR * added version number string (arb_version) * various additions to the documentation * 2014-09-25 - version 2.3.0 * removed most of the legacy (Arb 1.x) modules * updated build scripts, hopefully fixing various issues * new implementations of arb_sin, arb_cos, arb_sin_cos, arb_atan, arb_log, arb_exp, arb_expm1, much faster up to a few thousand bits * ported the bit-burst code for high-precision exponentials to the arb type * speeded up arb_log_ui_from_prev * added mag_exp, mag_expm1, mag_exp_tail, mag_pow_fmpz * improved various mag functions * added arb_get/set_interval_mpfr, arb_get_interval_arf, and improved arb_set_interval_arf * improved arf_get_fmpz * prettier printing of complex numbers with negative imaginary part * changed some frequently-used functions from inline to non-inline to reduce code size * 2014-08-01 - version 2.2.0 * added functions for computing polylogarithms and order expansions of polylogarithms, with support for real and complex s, z * added a missing cast affecting C++ compatibility * generalized powsum functions to allow a geometric factor * improved powsum functions slightly when the exponent is an integer * faster arb_log_ui_from_prev * added mag_sqrt and mag_rsqrt functions * fixed various minor bugs and added missing tests and documentation entries * 2014-06-20 - version 2.1.0 * ported most of the remaining functions to the new arb/acb types, including: * elementary functions (log, atan, etc.) * hypergeometric series summation * the gamma function * the Riemann zeta function and related functions * Bernoulli numbers * the partition function * the calculus modules (rigorous real root isolation, rigorous numerical integration of complex-valued functions) * example programs * added several missing utility functions to the arf and mag modules * 2014-05-27 - version 2.0.0 * new modules mag, arf, arb, arb_poly, arb_mat, acb, acb_poly, acb_mat for higher-performance ball arithmetic * poly_roots2 and hilbert_matrix2 example programs * vector dot product and norm functions (contributed by Abhinav Baid) * 2014-05-03 - version 1.1.0 * faster and more accurate error bounds for polynomial multiplication (error bounds are now always as good as with classical multiplication, and multiplying high-degree polynomials with approximately equal coefficients now has proper quasilinear complexity) * faster and much less memory-hungry exponentials at very high precision * improved the partition function to support n bigger than a single word, and enabled the possibility to use two threads for the computation * fixed a bug in floating-point arithmetic that caused a too small bound for the rounding error to be reported when the result of an inexact operation was rounded up to a power of two (this bug did not affect the correctness of ball arithmetic, because operations on ball midpoints always round down) * minor optimizations to floating-point arithmetic * improved argument reduction of the digamma function and short series expansions of the rising factorial * removed the holonomic module for now, as it did not really do anything very useful * 2013-12-21 - version 1.0.0 * new example programs directory * poly_roots example program * real_roots example program * pi_digits example program * hilbert_matrix example program * keiper_li example program * new fmprb_calc module for calculus with real functions * bisection-based root isolation * asymptotically fast Newton root refinement * new fmpcb_calc module for calculus with complex functions * numerical integration using Taylor series * scalar functions * simplified fmprb_const_euler using published error bound * added fmprb_inv * fmprb_trim, fmpcb_trim * added fmpcb_rsqrt (complex reciprocal square root) * fixed bug in fmprb_sqrtpos with nonfinite input * slightly improved fmprb powering code * added various functions for bounding fmprs by powers of two * added fmpr_is_int * polynomials and power series * implemented scaling to speed up blockwise multiplication * slightly faster basecase power series exponentials * improved sin/cos/tan/exp for short power series * added complex sqrt_series, rsqrt_series * implemented the Riemann-Siegel Z and theta functions for real power series * added fmprb_poly_pow_series, fmprb_poly_pow_ui and related methods * fmprb/fmpcb_poly_contains_fmpz_poly * faster composition by monomials * implemented Borel transform and binomial transform for real power series * matrices * implemented matrix exponentials * multithreaded fmprb_mat_mul * added matrix infinity norm functions * added some more matrix-scalar functions * added matrix contains and overlaps methods * zeta function evaluation * multithreaded power sum evaluation * faster parameter selection when computing many derivatives * implemented binary splitting to speed up computing many derivatives * miscellaneous * corrections for C++ compatibility (contributed by Jonathan Bober) * several minor bugfixes and test code enhancements * 2013-08-07 - version 0.7 * floating-point and ball functions * documented, added test code, and fixed bugs for various operations involving a ball containing an infinity or NaN * added reciprocal square root functions (fmpr_rsqrt, fmprb_rsqrt) based on mpfr_rec_sqrt * faster high-precision division by not computing an explicit remainder * slightly faster computation of pi by using new reciprocal square root and division code * added an fmpr function for approximate division to speed up certain radius operations * added fmpr_set_d for conversion from double * allow use of doubles to optionally compute the partition function faster but without an error bound * bypass mpfr overflow when computing the exponential function to extremely high precision (approximately 1 billion digits) * made fmprb_exp faster for large numbers at extremely high precision by skipping the log(2) removal * made fmpcb_lgamma faster at high precision by speeding up the argument reduction branch computation * added fmprb_asin, fmprb_acos * added various other utility functions to the fmprb module * added a function for computing the Glaisher constant * optimized evaluation of the Riemann zeta function at high precision * polynomials and power series * made squaring of polynomials faster than generic multiplication * implemented power series reversion (various algorithms) for the fmprb_poly type * added many fmprb_poly utility functions (shifting, truncating, setting/getting coefficients, etc.) * improved power series division when either operand is short * improved power series logarithm when the input is short * improved power series exponential to use the basecase algorithm for short input regardless of the output size * added power series square root and reciprocal square root * added atan, tan, sin, cos, sin_cos, asin, acos fmprb_poly power series functions * added Newton iteration macros to simplify various functions * added gamma functions of real and complex power series ([fmprb/fmpcb]_poly_[gamma/rgamma/lgamma]_series) * added wrappers for computing the Hurwitz zeta function of a power series ([fmprb/fmpcb]_poly_zeta_series) * implemented sieving and other optimizations to improve performance for evaluating the zeta function of a short power series * improved power series composition when the inner series is linear * added many fmpcb_poly versions of nearly all fmprb_poly functions * improved speed and stability of series composition/reversion by balancing the power table exponents * other * added support for freeing all cached data by calling flint_cleanup() * introduced fmprb_ptr, fmprb_srcptr, fmpcb_ptr, fmpcb_srcptr typedefs for cleaner function signatures * various bug fixes and general cleanup * 2013-05-31 - version 0.6 * made fast polynomial multiplication over the reals numerically stable by using a blockwise algorithm * disabled default use of the Gauss formula for multiplication of complex polynomials, to improve numerical stability * added division and remainder for complex polynomials * added fast multipoint evaluation and interpolation for complex polynomials * added missing fmprb_poly_sub and fmpcb_poly_sub functions * faster exponentials (fmprb_exp and dependent functions) at low precision, using precomputation * rewrote fmpr_add and fmpr_sub using mpn level code, improving efficiency at low precision * ported the partition function implementation from flint (using ball arithmetic in all steps of the calculation to guarantee correctness) * ported algorithm for computing the cosine minimal polynomial from flint (using ball arithmetic to guarantee correctness) * support using gmp instead of mpir * only use thread-local storage when enabled in flint * slightly faster error bounding for the zeta function * added some other helper functions * 2013-03-28 - version 0.5 * arithmetic and elementary functions * added fmpr_get_fmpz, fmpr_get_si * fixed accuracy problem with fmprb_div_2expm1 * special-cased squaring of complex numbers * added various fmpcb convenience functions (addmul_ui, etc) * optimized fmpr_cmp_2exp_si and fmpr_cmpabs_2exp_si, and added test code for comparison functions * added fmprb_atan2, also fixing a bug in fmpcb_arg * added fmprb_sin_pi, cos_pi, sin_cos_pi etc. * added fmprb_sin_pi_fmpq (etc.) using algebraic methods for fast evaluation of roots of unity * faster fmprb_poly_evaluate and evaluate_fmpcb using rectangular splitting * added fmprb_poly_evaluate2, evaluate2_fmpcb for simultaneously evaluating the derivative * added fmprb_poly root polishing code using near-optimal Newton steps (experimental) * added fmpr_root, fmprb_root (currently based on MPFR) * added fmpr_min, fmpr_max * added fmprb_set_interval_fmpr, fmprb_union * added fmpr_bits, fmprb_bits, fmpcb_bits for obtaining the mantissa width * added fmprb_hypot * added complex square roots * improved fmprb_log to slightly improve speed, and properly support huge arguments * fixed exp, cosh, sinh to work with huge arguments * added fmprb_expm1 * fixed sin, cos, atan to work with huge arguments * improved fmprb_pow and fmpcb_pow, including automatic detection of small integer and half-integer exponents * added many more elementary functions: fmprb_tan/cot/tanh/coth, fmpcb_tan/cot, and pi versions * added fmprb const_e, const_log2, const_log10, const_catalan * fixed ball containment/overlap checking to work operate efficiently and correctly with huge exponents * strengthened test code for many core operations * special functions * reorganized zeta function related code * faster evaluation of the Riemann zeta function via sieving * documented and improved efficiency of the zeta constant binary splitting code * calculate error bound in Borwein's algorithm with fmprs instead of using doubles * optimized divisions in zeta evaluation via the Euler product * use functional equation for Riemann zeta function of a negative argument * compute single Bernoulli numbers using ball arithmetic instead of relying on the floating-point code in flint * initial code for evaluating the gamma function using its Taylor series * much faster rising factorials at high precision, using difference polynomials * much faster gamma function at high precision * added complex gamma function, log gamma function, and other versions * added fmprb_agm (real arithmetic-geometric mean) * added fmprb_gamma_fmpq, supporting rapid computation of gamma(p/q) for q = 1,2,3,4,6 * added real and complex digamma function * fixed unnecessary recomputation of Bernoulli numbers * optimized computation of Euler's constant, and added proper error bounds * avoid reliance on doubles in the hypergeometric series tail bound * cleaned up factorials and binomials, computing factorials via gamma * other * added an fmpz_extras module to collect various internal fmpz helper functions * fixed detection of flint header files * fixed various other small bugs * 2013-01-26 - version 0.4 * much faster fmpr_mul, fmprb_mul and set_round, resulting in general speed improvements * code for computing the complex Hurwitz zeta function with derivatives * fixed and documented error bounds for hypergeometric series * better algorithm for series evaluation of the gamma function at a rational point * much faster generation of Bernoulli numbers * complex log, exp, pow, trigonometric functions (currently based on MPFR) * complex nth roots via Newton iteration * added code for arithmetic on fmpcb_polys * code for computing Khinchin's constant * code for rising factorials of polynomials or power series * faster sin_cos * better div_2expm1 * many other new helper functions * improved thread safety * more test code for core operations * 2012-11-07 - version 0.3 * converted documentation to sphinx * new module fmpcb for ball interval arithmetic over the complex numbers * conversions, utility functions and arithmetic operations * new module fmpcb_mat for matrices over the complex numbers * conversions, utility functions and arithmetic operations * multiplication, LU decomposition, solving, inverse and determinant * new module fmpcb_poly for polynomials over the complex numbers * root isolation for complex polynomials * new module fmpz_holonomic for functions/sequences defined by linear differential/difference equations with polynomial coefficients * functions for creating various special sequences and functions * some closure properties for sequences * Taylor series expansion for differential equations * computing the nth entry of a sequence using binary splitting * computing the nth entry mod p using fast multipoint evaluation * generic binary splitting code with automatic error bounding is now used for evaluating hypergeometric series * matrix powering * various other helper functions * 2012-09-29 - version 0.2 * code for computing the gamma function (Karatsuba, Stirling's series) * rising factorials * fast exp_series using Newton iteration * improved multiplication of small polynomials by using classical multiplication * implemented error propagation for square roots * polynomial division (Newton-based) * polynomial evaluation (Horner) and composition (divide-and-conquer) * product trees, fast multipoint evaluation and interpolation (various algorithms) * power series composition (Horner, Brent-Kung) * added the fmprb_mat module for matrices of balls of real numbers * matrix multiplication * interval-aware LU decomposition, solving, inverse and determinant * many helper functions and small bugfixes * 2012-09-14 - version 0.1 * 2012-08-05 - began simplified rewrite * 2012-04-05 - experimental ball and polynomial code arb-2.8.1/doc/source/hypgeom.rst000066400000000000000000000162431264125401100165370ustar00rootroot00000000000000.. _hypgeom: **hypgeom.h** -- support for hypergeometric series =============================================================================== This module provides functions for high-precision evaluation of series of the form .. math :: \sum_{k=0}^{n-1} \frac{A(k)}{B(k)} \prod_{j=1}^k \frac{P(k)}{Q(k)} z^k where `A, B, P, Q` are polynomials. The present version only supports `A, B, P, Q \in \mathbb{Z}[k]` (represented using the FLINT *fmpz_poly_t* type). This module also provides functions for high-precision evaluation of infinite series (`n \to \infty`), with automatic, rigorous error bounding. Note that we can standardize to `A = B = 1` by setting `\tilde P(k) = P(k) A(k) B(k-1), \tilde Q(k) = Q(k) A(k-1) B(k)`. However, separating out `A` and `B` is convenient and improves efficiency during evaluation. Strategy for error bounding ------------------------------------------------------------------------------- We wish to evaluate `S(z) = \sum_{k=0}^{\infty} T(k) z^k` where `T(k)` satisfies `T(0) = 1` and .. math :: T(k) = R(k) T(k-1) = \left( \frac{P(k)}{Q(k)} \right) T(k-1) for given polynomials .. math :: P(k) = a_p k^p + a_{p-1} k^{p-1} + \ldots a_0 Q(k) = b_q k^q + b_{q-1} k^{q-1} + \ldots b_0. For convergence, we require `p < q`, or `p = q` with `|z| |a_p| < |b_q|`. We also assume that `P(k)` and `Q(k)` have no roots among the positive integers (if there are positive integer roots, the sum is either finite or undefined). With these conditions satisfied, our goal is to find a parameter `n \ge 0` such that .. math :: \left\lvert \sum_{k=n}^{\infty} T(k) z^k \right\rvert \le 2^{-d}. We can rewrite the hypergeometric term ratio as .. math :: z R(k) = z \frac{P(k)}{Q(k)} = z \left( \frac{a_p}{b_q} \right) \frac{1}{k^{q-p}} F(k) where .. math :: F(k) = \frac{ 1 + \tilde a_{1} / k + \tilde a_{2} / k^2 + \ldots + \tilde a_q / k^p }{ 1 + \tilde b_{1} / k + \tilde b_{2} / k^2 + \ldots + \tilde b_q / k^q } = 1 + O(1/k) and where `\tilde a_i = a_{p-i} / a_p`, `\tilde b_i = b_{q-i} / b_q`. Next, we define .. math :: C = \max_{1 \le i \le p} |\tilde a_i|^{(1/i)}, \quad D = \max_{1 \le i \le q} |\tilde b_i|^{(1/i)}. Now, if `k > C`, the magnitude of the numerator of `F(k)` is bounded from above by .. math :: 1 + \sum_{i=1}^p \left(\frac{C}{k}\right)^i \le 1 + \frac{C}{k-C} and if `k > 2D`, the magnitude of the denominator of `F(k)` is bounded from below by .. math :: 1 - \sum_{i=1}^q \left(\frac{D}{k}\right)^i \ge 1 + \frac{D}{D-k}. Putting the inequalities together gives the following bound, valid for `k > K = \max(C, 2D)`: .. math :: |F(k)| \le \frac{k (k-D)}{(k-C)(k-2D)} = \left(1 + \frac{C}{k-C} \right) \left(1 + \frac{D}{k-2D} \right). Let `r = q-p` and `\tilde z = |z a_p / b_q|`. Assuming `k > \max(C, 2D, {\tilde z}^{1/r})`, we have .. math :: |z R(k)| \le G(k) = \frac{\tilde z F(k)}{k^r} where `G(k)` is monotonically decreasing. Now we just need to find an `n` such that `G(n) < 1` and for which `|T(n)| / (1 - G(n)) \le 2^{-d}`. This can be done by computing a floating-point guess for `n` then trying successively larger values. This strategy leaves room for some improvement. For example, if `\tilde b_1` is positive and large, the bound `B` becomes very pessimistic (a larger positive `\tilde b_1` causes faster convergence, not slower convergence). Types, macros and constants ------------------------------------------------------------------------------- .. type:: hypgeom_struct .. type:: hypgeom_t Stores polynomials *A*, *B*, *P*, *Q* and precomputed bounds, representing a fixed hypergeometric series. Memory management ------------------------------------------------------------------------------- .. function:: void hypgeom_init(hypgeom_t hyp) .. function:: void hypgeom_clear(hypgeom_t hyp) Error bounding ------------------------------------------------------------------------------- .. function:: slong hypgeom_estimate_terms(const mag_t z, int r, slong d) Computes an approximation of the largest `n` such that `|z|^n/(n!)^r = 2^{-d}`, giving a first-order estimate of the number of terms needed to approximate the sum of a hypergeometric series of weight `r \ge 0` and argument `z` to an absolute precision of `d \ge 0` bits. If `r = 0`, the direct solution of the equation is given by `n = (\log(1-z) - d \log 2) / \log z`. If `r > 0`, using `\log n! \approx n \log n - n` gives an equation that can be solved in terms of the Lambert *W*-function as `n = (d \log 2) / (r\,W\!(t))` where `t = (d \log 2) / (e r z^{1/r})`. The evaluation is done using double precision arithmetic. The function aborts if the computed value of `n` is greater than or equal to LONG_MAX / 2. .. function:: slong hypgeom_bound(mag_t error, int r, slong C, slong D, slong K, const mag_t TK, const mag_t z, slong prec) Computes a truncation parameter sufficient to achieve *prec* bits of absolute accuracy, according to the strategy described above. The input consists of `r`, `C`, `D`, `K`, precomputed bound for `T(K)`, and `\tilde z = z (a_p / b_q)`, such that for `k > K`, the hypergeometric term ratio is bounded by .. math :: \frac{\tilde z}{k^r} \frac{k(k-D)}{(k-C)(k-2D)}. Given this information, we compute a `\varepsilon` and an integer `n` such that `\left| \sum_{k=n}^{\infty} T(k) \right| \le \varepsilon \le 2^{-\mathrm{prec}}`. The output variable *error* is set to the value of `\varepsilon`, and `n` is returned. .. function:: void hypgeom_precompute(hypgeom_t hyp) Precomputes the bounds data `C`, `D`, `K` and an upper bound for `T(K)`. Summation ------------------------------------------------------------------------------- .. function:: void fmprb_hypgeom_sum(fmprb_t P, fmprb_t Q, const hypgeom_t hyp, const slong n, slong prec) Computes `P, Q` such that `P / Q = \sum_{k=0}^{n-1} T(k)` where `T(k)` is defined by *hyp*, using binary splitting and a working precision of *prec* bits. .. function:: void fmprb_hypgeom_infsum(fmprb_t P, fmprb_t Q, hypgeom_t hyp, slong tol, slong prec) Computes `P, Q` such that `P / Q = \sum_{k=0}^{\infty} T(k)` where `T(k)` is defined by *hyp*, using binary splitting and working precision of *prec* bits. The number of terms is chosen automatically to bound the truncation error by at most `2^{-\mathrm{tol}}`. The bound for the truncation error is included in the output as part of *P*. .. function:: void arb_hypgeom_sum(arb_t P, arb_t Q, const hypgeom_t hyp, const slong n, slong prec) Computes `P, Q` such that `P / Q = \sum_{k=0}^{n-1} T(k)` where `T(k)` is defined by *hyp*, using binary splitting and a working precision of *prec* bits. .. function:: void arb_hypgeom_infsum(arb_t P, arb_t Q, hypgeom_t hyp, slong tol, slong prec) Computes `P, Q` such that `P / Q = \sum_{k=0}^{\infty} T(k)` where `T(k)` is defined by *hyp*, using binary splitting and working precision of *prec* bits. The number of terms is chosen automatically to bound the truncation error by at most `2^{-\mathrm{tol}}`. The bound for the truncation error is included in the output as part of *P*. arb-2.8.1/doc/source/index.rst000066400000000000000000000041271264125401100161740ustar00rootroot00000000000000Welcome to Arb's documentation! =============================== .. only:: latex Introduction :::::::::::: Arb is a C library for arbitrary-precision floating-point ball arithmetic, developed by `Fredrik Johansson `_ (fredrik.johansson@gmail.com). It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many transcendental functions. All is done with automatic, rigorous error bounds. The git repository is https://github.com/fredrik-johansson/arb/ The documentation website is http://fredrikj.net/arb/ .. only:: html .. image:: _static/arbtext.png Arb is a C library for arbitrary-precision floating-point ball arithmetic, developed by `Fredrik Johansson `_ (fredrik.johansson@gmail.com). It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many transcendental functions. All is done with automatic, rigorous error bounds. The git repository is https://github.com/fredrik-johansson/arb/ The documentation website is http://fredrikj.net/arb/ A `PDF version `_ of this documentation is available. General information :::::::::::::::::::: .. toctree:: :maxdepth: 1 overview.rst setup.rst issues.rst history.rst examples.rst Module documentation (Arb 2.x types) :::::::::::::::::::::::::::::::::::: .. toctree:: :maxdepth: 1 mag.rst arf.rst arb.rst arb_poly.rst arb_mat.rst arb_calc.rst acb.rst acb_poly.rst acb_mat.rst acb_calc.rst acb_hypgeom.rst acb_modular.rst bernoulli.rst hypgeom.rst partitions.rst Algorithms and proofs :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: .. toctree:: :maxdepth: 1 constants.rst gamma.rst polylogarithms.rst Module documentation (Arb 1.x types) :::::::::::::::::::::::::::::::::::: .. toctree:: :maxdepth: 1 fmpr.rst fmprb.rst Credits and references :::::::::::::::::::::::: .. toctree:: :maxdepth: 2 credits.rst arb-2.8.1/doc/source/issues.rst000066400000000000000000000225661264125401100164070ustar00rootroot00000000000000.. _issues: Potential issues =============================================================================== Interface changes ------------------------------------------------------------------------------- Most of the core API should be stable at this point, and significant compatibility-breaking changes will be specified in the release notes. In general, Arb does not distinguish between "private" and "public" parts of the API. The implementation is meant to be transparent by design. All methods are intended to be fully documented and tested (exceptions to this are mainly due to lack of time on part of the author). The user should use common sense to determine whether a function is concerned with implementation details, making it likely to change as the implementation changes in the future. The interface of :func:`arb_add` is probably not going to change in the next version, but :func:`_arb_get_mpn_fixed_mod_pi4` just might. Correctness ------------------------------------------------------------------------------- Except where otherwise specified, Arb is designed to produce provably correct error bounds. The code has been written carefully, and the library is extensively tested. However, like any complex mathematical software, Arb is virtually certain to contains bugs, so the usual precautions are advised: * Perform sanity checks on the output (check known mathematical relations; recompute to another precision and compare) * Compare against other mathematical software * Read the source code to verify that it does what it is supposed to do All bug reports are highly welcome! Aliasing ------------------------------------------------------------------------------- As a rule, Arb allows aliasing of operands. For example, in the function call ``arb_add(z, x, y, prec)``, which performs `z \gets x + y`, any two (or all three) of the variables *x*, *y* and *z* are allowed to be the same. Exceptions to this rule are documented explicitly. The general rule that input and output variables can be aliased with each other only applies to variables *of the same type* (ignoring *const* qualifiers on input variables -- a special case is that :type:`arb_srcptr` is considered the *const* version of :type:`arb_ptr`). This is a natural extension of the so-called *strict aliasing rule* in C. For example, in :func:`arb_poly_evaluate` which evaluates `y = f(x)` for a polynomial *f*, the output variable *y* is not allowed to be a pointer to one of the coefficients of *f* (but aliasing between *x* and *y* or between *x* and the coefficients of *f* is allowed). This also applies to :func:`_arb_poly_evaluate`: for the purposes of aliasing, :type:`arb_srcptr` (the type of the coefficient array within *f*) and :type:`arb_t` (the type of *x*) are *not* considered to be the same type, and therefore must not be aliased with each other, even though an :type:`arb_ptr`/:type:`arb_srcptr` variable pointing to a length 1 array would otherwise be interchangeable with an :type:`arb_t`/*const* :type:`arb_t`. Moreover, in functions that allow aliasing between an input array and an output array, the arrays must either be identical or completely disjoint, never partially overlapping. There are natural exceptions to these aliasing restrictions, which may used internally without being documented explicitly. However, third party code should avoid relying on such exceptions. An important caveat applies to **aliasing of input variables**. Identical pointers are understood to give permission for **algebraic simplification**. This assumption is made to improve performance. For example, the call ``arb_mul(z, x, x, prec)`` sets *z* to a ball enclosing the set .. math :: \{ t^2 \,:\, t \in x \} and not the (generally larger) set .. math :: \{ t u \,:\, t \in x, u \in x \}. If the user knows that two values *x* and *y* both lie in the interval `[-1,1]` and wants to compute an enclosure for `f(x,y)`, then it would be a mistake to create an :type:`arb_t` variable *x* enclosing `[-1,1]` and reusing the same variable for *y*, calling `f(x,x)`. Instead, the user has to create a distinct variable *y* also enclosing `[-1,1]`. Algebraic simplification is not guaranteed to occur. For example, ``arb_add(z, x, x, prec)`` and ``arb_sub(z, x, x, prec)`` currently do not implement this optimization. It is better to use ``arb_mul_2exp_si(z, x, 1)`` and ``arb_zero(z)``, respectively. Integer overflow ------------------------------------------------------------------------------- Machine-size integers are used for precisions, sizes of integers in bits, lengths of polynomials, and similar quantities that relate to sizes in memory. Very few checks are performed to verify that such quantities do not overflow. Precisions and lengths exceeding a small fraction of *LONG_MAX*, say `2^{24} \sim 10^7` on 32-bit systems, should be regarded as resulting in undefined behavior. On 64-bit systems this should generally not be an issue, since most calculations will exhaust the available memory (or the user's patience waiting for the computation to complete) long before running into integer overflows. However, the user needs to be wary of unintentionally passing input parameters of order *LONG_MAX* or negative parameters where positive parameters are expected, for example due to a runaway loop that repeatedly increases the precision. This caveat does not apply to exponents of floating-point numbers, which are represented as arbitrary-precision integers, nor to integers used as numerical scalars (e.g. :func:`arb_mul_si`). However, it still applies to conversions and operations where the result is requested exactly and sizes become an issue. For example, trying to convert the floating-point number `2^{2^{100}}` to an integer could result in anything from a silent wrong value to thrashing followed by a crash, and it is the user's responsibility not to attempt such a thing. Thread safety and caches ------------------------------------------------------------------------------- Arb should be fully threadsafe, provided that both MPFR and FLINT have been built in threadsafe mode. Use ``flint_set_num_threads()`` to set the number of threads that Arb is allowed to use internally for single computations (this is currently only exploited by a handful of operations). Please note that thread safety is only tested minimally, and extra caution when developing multithreaded code is therefore recommended. Arb may cache some data (such as the value of `\pi` and Bernoulli numbers) to speed up various computations. In threadsafe mode, caches use thread-local storage. There is currently no way to save memory and avoid recomputation by having several threads share the same cache. Caches can be freed by calling the ``flint_cleanup()`` function. To avoid memory leaks, the user should call ``flint_cleanup()`` when exiting a thread. It is also recommended to call ``flint_cleanup()`` when exiting the main program (this should result in a clean output when running `Valgrind `_, and can help catching memory issues). There does not seem to be an obvious way to make sure that ``flint_cleanup()`` is called when exiting a thread using OpenMP. A possible solution to this problem is to use OpenMP sections, or to use C++ and create a thread-local object whose destructor invokes ``flint_cleanup()``. Use of hardware floating-point arithmetic ------------------------------------------------------------------------------- Arb uses hardware floating-point arithmetic (the ``double`` type in C) in two different ways. Firstly, ``double`` arithmetic as well as transcendental ``libm`` functions (such as ``exp``, ``log``) are used to select parameters heuristically in various algorithms. Such heuristic use of approximate arithmetic does not affect correctness: when any error bounds depend on the parameters, the error bounds are evaluated separately using rigorous methods. At worst, flaws in the floating-point arithmetic on a particular machine could cause an algorithm to become inefficient due to inefficient parameters being selected. Secondly, ``double`` arithmetic is used internally for some rigorous error bound calculations. To guarantee correctness, we make the following assumptions. With the stated exceptions, these should hold on all commonly used platforms. * A ``double`` uses the standard IEEE 754 format (with a 53-bit significand, 11-bit exponent, encoding of infinities and NaNs, etc.) * We assume that the compiler does not perform "unsafe" floating-point optimizations, such as reordering of operations. Unsafe optimizations are disabled by default in most modern C compilers, including GCC and Clang. The exception appears to be the Intel C++ compiler, which does some unsafe optimizations by default. These must be disabled by the user. * We do not assume that floating-point operations are correctly rounded (a counterexample is the x87 FPU), or that rounding is done in any particular direction (the rounding mode may have been changed by the user). We assume that any floating-point operation is done with at most 1.1 ulp error. * We do not assume that underflow or overflow behaves in a particular way (we only use doubles that fit in the regular exponent range, or explicit infinities). * We do not use transcendental ``libm`` functions, since these can have errors of several ulps, and there is unfortunately no way to get guaranteed bounds. However, we do use functions such as ``ldexp`` and ``sqrt``, which we assume to be correctly implemented. arb-2.8.1/doc/source/mag.rst000066400000000000000000000266751264125401100156450ustar00rootroot00000000000000.. _mag: **mag.h** -- fixed-precision unsigned floating-point numbers for bounds =============================================================================== The :type:`mag_t` type is an unsigned floating-point type with a fixed-precision mantissa (30 bits) and an arbitrary-precision exponent (represented as an :type:`fmpz_t`), suited for representing and rigorously manipulating magnitude bounds efficiently. Operations always produce a strict upper or lower bound, but for performance reasons, no attempt is made to compute the best possible bound (in general, a result may a few ulps larger/smaller than the optimal value). The special values zero and positive infinity are supported (but not NaN). Applications requiring more flexibility (such as correct rounding, or higher precision) should use the :type:`arf_t` type instead. Types, macros and constants ------------------------------------------------------------------------------- .. type:: mag_struct A :type:`mag_struct` holds a mantissa and an exponent. Special values are encoded by the mantissa being set to zero. .. type:: mag_t A :type:`mag_t` is defined as an array of length one of type :type:`mag_struct`, permitting a :type:`mag_t` to be passed by reference. Memory management ------------------------------------------------------------------------------- .. function:: void mag_init(mag_t x) Initializes the variable *x* for use. Its value is set to zero. .. function:: void mag_clear(mag_t x) Clears the variable *x*, freeing or recycling its allocated memory. .. function:: void mag_init_set(mag_t x, const mag_t y) Initializes *x* and sets it to the value of *y*. .. function:: void mag_swap(mag_t x, mag_t y) Swaps *x* and *y* efficiently. .. function:: void mag_set(mag_t x, const mag_t y) Sets *x* to the value of *y*. .. function:: mag_ptr _mag_vec_init(slong n) Allocates a vector of length *n*. All entries are set to zero. .. function:: void _mag_vec_clear(mag_ptr v, slong n) Clears a vector of length *n*. Special values ------------------------------------------------------------------------------- .. function:: void mag_zero(mag_t x) Sets *x* to zero. .. function:: void mag_one(mag_t x) Sets *x* to one. .. function:: void mag_inf(mag_t x) Sets *x* to positive infinity. .. function:: int mag_is_special(const mag_t x) Returns nonzero iff *x* is zero or positive infinity. .. function:: int mag_is_zero(const mag_t x) Returns nonzero iff *x* is zero. .. function:: int mag_is_inf(const mag_t x) Returns nonzero iff *x* is positive infinity. .. function:: int mag_is_finite(const mag_t x) Returns nonzero iff *x* is not positive infinity (since there is no NaN value, this function is exactly the negation of :func:`mag_is_inf`). Comparisons ------------------------------------------------------------------------------- .. function:: int mag_equal(const mag_t x, const mag_t y) Returns nonzero iff *x* and *y* have the same value. .. function:: int mag_cmp(const mag_t x, const mag_t y) Returns negative, zero, or positive, depending on whether *x* is smaller, equal, or larger than *y*. .. function:: int mag_cmp_2exp_si(const mag_t x, slong y) Returns negative, zero, or positive, depending on whether *x* is smaller, equal, or larger than `2^y`. .. function:: void mag_min(mag_t z, const mag_t x, const mag_t y) .. function:: void mag_max(mag_t z, const mag_t x, const mag_t y) Sets *z* respectively to the smaller or the larger of *x* and *y*. Input and output ------------------------------------------------------------------------------- .. function:: void mag_print(const mag_t x) Prints *x* to standard output. Random generation ------------------------------------------------------------------------------- .. function:: void mag_randtest(mag_t x, flint_rand_t state, slong expbits) Sets *x* to a random finite value, with an exponent up to *expbits* bits large. .. function:: void mag_randtest_special(mag_t x, flint_rand_t state, slong expbits) Like :func:`mag_randtest`, but also sometimes sets *x* to infinity. Conversions ------------------------------------------------------------------------------- .. function:: void mag_set_d(mag_t y, double x) .. function:: void mag_set_fmpr(mag_t y, const fmpr_t x) .. function:: void mag_set_ui(mag_t y, ulong x) .. function:: void mag_set_fmpz(mag_t y, const fmpz_t x) Sets *y* to an upper bound for `|x|`. .. function:: void mag_set_d_2exp_fmpz(mag_t z, double x, const fmpz_t y) .. function:: void mag_set_fmpz_2exp_fmpz(mag_t z, const fmpz_t x, const fmpz_t y) .. function:: void mag_set_ui_2exp_si(mag_t z, ulong x, slong y) Sets *z* to an upper bound for `|x| \times 2^y`. .. function:: void mag_get_fmpr(fmpr_t y, const mag_t x) Sets *y* exactly to *x*. .. function:: void mag_get_fmpq(fmpq_t y, const mag_t x) Sets *y* exactly to *x*. Assumes that no overflow occurs. .. function:: void mag_set_ui_lower(mag_t z, ulong x) .. function:: void mag_set_fmpz_lower(mag_t z, const fmpz_t x) Sets *y* to a lower bound for `|x|`. .. function:: void mag_set_fmpz_2exp_fmpz_lower(mag_t z, const fmpz_t x, const fmpz_t y) Sets *z* to a lower bound for `|x| \times 2^y`. Arithmetic ------------------------------------------------------------------------------- .. function:: void mag_mul_2exp_si(mag_t z, const mag_t x, slong y) .. function:: void mag_mul_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t y) Sets *z* to `x \times 2^y`. This operation is exact. .. function:: void mag_mul(mag_t z, const mag_t x, const mag_t y) .. function:: void mag_mul_ui(mag_t z, const mag_t x, ulong y) .. function:: void mag_mul_fmpz(mag_t z, const mag_t x, const fmpz_t y) Sets *z* to an upper bound for `xy`. .. function:: void mag_add(mag_t z, const mag_t x, const mag_t y) Sets *z* to an upper bound for `x + y`. .. function:: void mag_addmul(mag_t z, const mag_t x, const mag_t y) Sets *z* to an upper bound for `z + xy`. .. function:: void mag_add_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t e) Sets *z* to an upper bound for `x + 2^e`. .. function:: void mag_div(mag_t z, const mag_t x, const mag_t y) .. function:: void mag_div_ui(mag_t z, const mag_t x, ulong y) .. function:: void mag_div_fmpz(mag_t z, const mag_t x, const fmpz_t y) Sets *z* to an upper bound for `x / y`. .. function:: void mag_mul_lower(mag_t z, const mag_t x, const mag_t y) .. function:: void mag_mul_ui_lower(mag_t z, const mag_t x, ulong y) .. function:: void mag_mul_fmpz_lower(mag_t z, const mag_t x, const fmpz_t y) Sets *z* to a lower bound for `xy`. .. function:: void mag_add_lower(mag_t z, const mag_t x, const mag_t y) Sets *z* to a lower bound for `x + y`. .. function:: void mag_sub_lower(mag_t z, const mag_t x, const mag_t y) Sets *z* to a lower bound for `\max(x-y, 0)`. Fast, unsafe arithmetic ------------------------------------------------------------------------------- The following methods assume that all inputs are finite and that all exponents (in all inputs as well as the final result) fit as *fmpz* inline values. They also assume that the output variables do not have promoted exponents, as they will be overwritten directly (thus leaking memory). .. function:: void mag_fast_init_set(mag_t x, const mag_t y) Initialises *x* and sets it to the value of *y*. .. function:: void mag_fast_zero(mag_t x) Sets *x* to zero. .. function:: int mag_fast_is_zero(const mag_t x) Returns nonzero iff *x* to zero. .. function:: void mag_fast_mul(mag_t z, const mag_t x, const mag_t y) Sets *z* to an upper bound for `xy`. .. function:: void mag_fast_addmul(mag_t z, const mag_t x, const mag_t y) Sets *z* to an upper bound for `z + xy`. .. function:: void mag_fast_add_2exp_si(mag_t z, const mag_t x, slong e) Sets *z* to an upper bound for `x + 2^e`. .. function:: void mag_fast_mul_2exp_si(mag_t z, const mag_t x, slong e) Sets *z* to an upper bound for `x 2^e`. Powers and logarithms ------------------------------------------------------------------------------- .. function:: void mag_pow_ui(mag_t z, const mag_t x, ulong e) .. function:: void mag_pow_fmpz(mag_t z, const mag_t x, const fmpz_t e) Sets *z* to an upper bound for `x^e`. Requires `e \ge 0`. .. function:: void mag_pow_ui_lower(mag_t z, const mag_t x, ulong e) Sets *z* to a lower bound for `x^e`. .. function:: void mag_sqrt(mag_t z, const mag_t x) Sets *z* to an upper bound for `\sqrt{x}`. .. function:: void mag_rsqrt(mag_t z, const mag_t x) Sets *z* to an upper bound for `1/\sqrt{x}`. .. function:: void mag_hypot(mag_t z, const mag_t x, const mag_t y) Sets *z* to an upper bound for `\sqrt{x^2 + y^2}`. .. function:: void mag_root(mag_t z, const mag_t x, ulong n) Sets *z* to an upper bound for `x^{1/n}`. We evaluate `\exp(\log(1+2^{kn}x)/n) 2^{-k}`, where *k* is chosen so that `2^{kn}x \approx 2^{30}`. .. function:: void mag_log1p(mag_t z, const mag_t x) Sets *z* to an upper bound for `\log(1+x)`. The bound is computed accurately for small *x*. .. function:: void mag_log_ui(mag_t z, ulong n) Sets *z* to an upper bound for `\log(n)`. .. function:: void mag_exp(mag_t z, const mag_t x) Sets *z* to an upper bound for `\exp(x)`. .. function:: void mag_expm1(mag_t z, const mag_t x) Sets *z* to an upper bound for `\exp(x) - 1`. The bound is computed accurately for small *x*. .. function:: void mag_exp_tail(mag_t z, const mag_t x, ulong N) Sets *z* to an upper bound for `\sum_{k=N}^{\infty} x^k / k!`. .. function:: void mag_binpow_uiui(mag_t z, ulong m, ulong n) Sets *z* to an upper bound for `(1 + 1/m)^n`. .. function:: void mag_geom_series(mag_t res, const mag_t x, ulong N) Sets *res* to an upper bound for `\sum_{k=N}^{\infty} x^k`. Special functions ------------------------------------------------------------------------------- .. function:: void mag_fac_ui(mag_t z, ulong n) Sets *z* to an upper bound for `n!`. .. function:: void mag_rfac_ui(mag_t z, ulong n) Sets *z* to an upper bound for `1/n!`. .. function:: void mag_bernoulli_div_fac_ui(mag_t z, ulong n) Sets *z* to an upper bound for `|B_n| / n!` where `B_n` denotes a Bernoulli number. .. function:: void mag_polylog_tail(mag_t u, const mag_t z, slong s, ulong d, ulong N) Sets *u* to an upper bound for .. math :: \sum_{k=N}^{\infty} \frac{z^k \log^d(k)}{k^s}. Note: in applications where `s` in this formula may be real or complex, the user can simply substitute any convenient integer `s'` such that `s' \le \operatorname{Re}(s)`. Denote the terms by `T(k)`. We pick a nonincreasing function `U(k)` such that .. math :: \frac{T(k+1)}{T(k)} = z \left(\frac{k}{k+1}\right)^s \left( \frac{\log(k+1)}{\log(k)} \right)^d \le U(k). Then, as soon as `U(N) < 1`, .. math :: \sum_{k=N}^{\infty} T(k) \le T(N) \sum_{k=0}^{\infty} U(N)^k = \frac{T(N)}{1 - U(N)}. In particular, we take .. math :: U(k) = z \; B(k, \max(0, -s)) \; B(k \log(k), d) where `B(m,n) = (1 + 1/m)^n`. This follows from the bounds .. math :: \left(\frac{k}{k+1}\right)^{s} \le \begin{cases} 1 & \text{if } s \ge 0 \\ (1 + 1/k)^{-s} & \text{if } s < 0. \end{cases} and .. math :: \left( \frac{\log(k+1)}{\log(k)} \right)^d \le \left(1 + \frac{1}{k \log(k)}\right)^d. arb-2.8.1/doc/source/overview.rst000066400000000000000000000065361264125401100167410ustar00rootroot00000000000000.. _overview: Feature overview =============================================================================== Ball arithmetic, also known as mid-rad interval arithmetic, is an extension of floating-point arithmetic in which an error bound is attached to each variable. This allows doing rigorous computations over the real numbers, while avoiding the overhead of traditional (inf-sup) interval arithmetic at high precision, and eliminating much of the need for time-consuming and bug-prone manual error analysis associated with standard floating-point arithmetic. (See for example [Hoe2009]_.) Other implementations of ball arithmetic include `iRRAM `_ and `Mathemagix `_. In contrast to those systems, Arb is more focused on low-level arithmetic and computation of transcendental functions needed for number theory. Arb also differs in some technical aspects of the implementation. Arb 2.x contains: * A module (:ref:`arf `) for correctly rounded arbitrary-precision floating-point arithmetic. Arb's floating-point numbers have a few special features, such as arbitrary-size exponents (useful for combinatorics and asymptotics) and dynamic allocation (facilitating implementation of hybrid integer/floating-point and mixed-precision algorithms). * A module (:ref:`mag `) for representing magnitudes (error bounds) more efficiently than with an arbitrary-precision floating-point type. * A module (:ref:`arb `) for real ball arithmetic, where a ball is implemented as an *arf* midpoint and a *mag* radius. * A module (:ref:`acb `) for complex numbers in rectangular form, represented as pairs real balls. * Functions for fast high-precision evaluation of various mathematical constants and special functions, implemented using ball arithmetic with rigorous error bounds. * Modules (:ref:`arb_poly `, :ref:`acb_poly `) for polynomials or power series over the real and complex numbers, implemented using balls as coefficients, with asymptotically fast polynomial multiplication and many other operations. * Modules (:ref:`arb_mat `, :ref:`acb_mat `) for matrices over the real and complex numbers, implemented using balls as coefficients. At the moment, only rudimentary linear algebra operations are provided. Arb 1.x used a different set of numerical base types (*fmpr*, *fmprb* and *fmpcb*). These types had a slightly simpler internal representation, but generally had worse performance. Almost all methods for the Arb 1.x types have now been ported to faster equivalents for the Arb 2.x types. The last version to include both the Arb 1.x and Arb 2.x types and methods was Arb 2.2. As of Arb 2.3, only a small set of *fmpr* and *fmprb* methods are left for fallback and testing purposes. Planned features include more transcendental functions and more extensive polynomial and matrix functionality, as well as further optimizations. Arb uses `GMP `_ / `MPIR `_ and `FLINT `_ for the underlying integer arithmetic and other functions. The code conventions borrow from FLINT, and the project might get merged back into FLINT when the code stabilizes in the future. Arb also uses `MPFR `_ for testing purposes and for evaluation of some functions. arb-2.8.1/doc/source/partitions.rst000066400000000000000000000064231264125401100172620ustar00rootroot00000000000000.. _partitions: **partitions.h** -- computation of the partition function =============================================================================== This module implements the asymptotically fast algorithm for evaluating the integer partition function `p(n)` described in [Joh2012]_. The idea is to evaluate a truncation of the Hardy-Ramanujan-Rademacher series using tight precision estimates, and symbolically factoring the occurring exponential sums. An implementation based on floating-point arithmetic can also be found in FLINT. That version relies on some numerical subroutines that have not been proved correct. The implementation provided here uses ball arithmetic throughout to guarantee a correct error bound for the numerical approximation of `p(n)`. Optionally, hardware double arithmetic can be used for low-precision terms. This gives a significant speedup for small (e.g. `n < 10^6`). .. function:: void partitions_rademacher_bound(arf_t b, const fmpz_t n, ulong N) Sets `b` to an upper bound for .. math :: M(n,N) = \frac{44 \pi^2}{225 \sqrt 3} N^{-1/2} + \frac{\pi \sqrt{2}}{75} \left( \frac{N}{n-1} \right)^{1/2} \sinh\left(\frac{\pi}{N} \sqrt{\frac{2n}{3}}\right). This formula gives an upper bound for the truncation error in the Hardy-Ramanujan-Rademacher formula when the series is taken up to the term `t(n,N)` inclusive. .. function:: partitions_hrr_sum_arb(arb_t x, const fmpz_t n, slong N0, slong N, int use_doubles) Evaluates the partial sum `\sum_{k=N_0}^N t(n,k)` of the Hardy-Ramanujan-Rademacher series. If *use_doubles* is nonzero, doubles and the system's standard library math functions are used to evaluate the smallest terms. This significantly speeds up evaluation for small `n` (e.g. `n < 10^6`), and gives a small speed improvement for larger `n`, but the result is not guaranteed to be correct. In practice, the error is estimated very conservatively, and unless the system's standard library is broken, use of doubles can be considered safe. Setting *use_doubles* to zero gives a fully guaranteed bound. .. function:: void partitions_fmpz_fmpz(fmpz_t p, const fmpz_t n, int use_doubles) Computes the partition function `p(n)` using the Hardy-Ramanujan-Rademacher formula. This function computes a numerical ball containing `p(n)` and verifies that the ball contains a unique integer. If *n* is sufficiently large and a number of threads greater than 1 has been selected with :func:`flint_set_num_threads()`, the computation time will be reduced by using two threads. See :func:`partitions_hrr_sum_arb` for an explanation of the *use_doubles* option. .. function:: void partitions_fmpz_ui(fmpz_t p, ulong n) Computes the partition function `p(n)` using the Hardy-Ramanujan-Rademacher formula. This function computes a numerical ball containing `p(n)` and verifies that the ball contains a unique integer. .. function:: void partitions_fmpz_ui_using_doubles(fmpz_t p, ulong n) Computes the partition function `p(n)`, enabling the use of doubles internally. This significantly speeds up evaluation for small `n` (e.g. `n < 10^6`), but the error bounds are not certified (see remarks for :func:`partitions_hrr_sum_arb`). arb-2.8.1/doc/source/polylogarithms.rst000066400000000000000000000062301264125401100201370ustar00rootroot00000000000000.. _algorithms_polylogarithms: Algorithms for polylogarithms =============================================================================== The polylogarithm is defined for `s, z \in \mathbb{C}` with `|z| < 1` by .. math :: \operatorname{Li}_s(z) = \sum_{k=1}^{\infty} \frac{z^k}{k^s} and for `|z| \ge 1` by analytic continuation, except for the singular point `z = 1`. Computation for small z ------------------------------------------------------------------------------- The power sum converges rapidly when `|z| \ll 1`. To compute the series expansion with respect to `s`, we substitute `s \to s + x \in \mathbb{C}[[x]]` and obtain .. math :: \operatorname{Li}_{s+x}(z) = \sum_{d=0}^{\infty} x^d \frac{(-1)^d}{d!} \sum_{k=1}^{\infty} T(k) where .. math :: T(k) = \frac{z^k \log^d(k)}{k^s}. The remainder term `\left| \sum_{k=N}^{\infty} T(k) \right|` is bounded via :func:`mag_polylog_tail`. Expansion for general z ------------------------------------------------------------------------------- For general complex `s, z`, we write the polylogarithm as a sum of two Hurwitz zeta functions .. math :: \operatorname{Li}_s(z) = \frac{\Gamma(v)}{(2\pi)^v} \left[ i^v \zeta \left(v, \frac{1}{2} + \frac{\log(-z)}{2\pi i}\right) + i^{-v} \zeta \left(v, \frac{1}{2} - \frac{\log(-z)}{2\pi i}\right) \right] in which `s = 1-v`. With the principal branch of `\log(-z)`, we obtain the conventional analytic continuation of the polylogarithm with a branch cut on `z \in (1,+\infty)`. To compute the series expansion with respect to `v`, we substitute `v \to v + x \in \mathbb{C}[[x]]` in this formula (at the end of the computation, we map `x \to -x` to obtain the power series for `\operatorname{Li}_{s+x}(z)`). The right hand side becomes .. math :: \Gamma(v+x) [E_1 Z_1 + E_2 Z_2] where `E_1 = (i/(2 \pi))^{v+x}`, `Z_1 = \zeta(v+x,\ldots)`, `E_2 = (1/(2 \pi i))^{v+x}`, `Z_2 = \zeta(v+x,\ldots)`. When `v = 1`, the `Z_1` and `Z_2` terms become Laurent series with a leading `1/x` term. In this case, we compute the deflated series `\tilde Z_1, \tilde Z_2 = \zeta(x,\ldots) - 1/x`. Then .. math :: E_1 Z_1 + E_2 Z_2 = (E_1 + E_2)/x + E_1 \tilde Z_1 + E_2 \tilde Z_2. Note that `(E_1 + E_2) / x` is a power series, since the constant term in `E_1 + E_2` is zero when `v = 1`. So we simply compute one extra derivative of both `E_1` and `E_2`, and shift them one step. When `v = 0, -1, -2, \ldots`, the `\Gamma(v+x)` prefactor has a pole. In this case, we proceed analogously and formally multiply `x \, \Gamma(v+x)` with `[E_1 Z_1 + E_2 Z_2] / x`. Note that the formal cancellation only works when the order `s` (or `v`) is an exact integer: it is not currently possible to use this method when `s` is a small ball containing any of `0, 1, 2, \ldots` (then the result becomes indeterminate). The Hurwitz zeta method becomes inefficient when `|z| \to 0` (it gives an indeterminate result when `z = 0`). This is not a problem since we just use the defining series for the polylogarithm in that region. It also becomes inefficient when `|z| \to \infty`, for which an asymptotic expansion would better. arb-2.8.1/doc/source/setup.rst000066400000000000000000000066201264125401100162250ustar00rootroot00000000000000.. _setup: Setup =============================================================================== Download ------------------------------------------------------------------------------- Tarballs of released versions can be downloaded from https://github.com/fredrik-johansson/arb/releases Alternatively, you can simply install Arb from a git checkout of https://github.com/fredrik-johansson/arb/. The master branch is generally safe to use (the test suite should pass at all times), and recommended for keeping up with the latest changes. Dependencies ------------------------------------------------------------------------------- Arb has the following dependencies: * Either MPIR (http://www.mpir.org) 2.6.0 or later, or GMP (http://www.gmplib.org) 5.1.0 or later. If MPIR is used instead of GMP, it must be compiled with the ``--enable-gmpcompat`` option. * MPFR (http://www.mpfr.org) 3.0.0 or later. * FLINT (http://www.flintlib.org) version 2.4 or later. You may also use a git checkout of https://github.com/fredrik-johansson/flint2 Installation as part of FLINT ------------------------------------------------------------------------------- With a sufficiently new version of FLINT, Arb can be compiled as a FLINT extension package. Simply put the Arb source directory somewhere, say ``/path/to/arb``. Then go to the FLINT source directory and build FLINT using:: ./configure --extensions=/path/to/arb make make check (optional) make install This is convenient, as Arb does not need to be configured or linked separately. Arb becomes part of the compiled FLINT library, and the Arb header files will be installed along with the other FLINT header files. Standalone installation ------------------------------------------------------------------------------- To compile, test and install Arb from source as a standalone library, first install FLINT. Then go to the Arb source directory and run:: ./configure make make check (optional) make install If GMP/MPIR, MPFR or FLINT is installed in some other location than the default path ``/usr/local``, pass ``--with-gmp=...``, ``--with-mpfr=...`` or ``--with-flint=...`` with the correct path to configure (type ``./configure --help`` to show more options). Running code ------------------------------------------------------------------------------- Here is an example program to get started using Arb: .. code-block:: c #include "arb.h" int main() { arb_t x; arb_init(x); arb_const_pi(x, 50 * 3.33); arb_printn(x, 50, 0); flint_printf("\n"); flint_printf("Computed with arb-%s\n", arb_version); arb_clear(x); } Compile it with:: gcc -larb test.c or (if Arb is built as part of FLINT):: gcc -lflint test.c If the Arb/FLINT header and library files are not in a standard location (``/usr/local`` on most systems), you may also have to pass options such as:: -I/path/to/arb -I/path/to/flint -L/path/to/flint -L/path/to/arb to ``gcc``. Finally, to run the program, make sure that the linker can find the FLINT (and Arb) libraries. If they are installed in a nonstandard location, you can for example add this path to the ``LD_LIBRARY_PATH`` environment variable. The output of the example program should be something like the following:: [3.1415926535897932384626433832795028841971693993751 +/- 6.28e-50] Computed with arb-2.4.0 arb-2.8.1/doc/source/verify_taylor.py000066400000000000000000000172621264125401100176070ustar00rootroot00000000000000from gmpy import mpq, lcm, denom, numer, fac def atan_coefficients(NN, bits): ps = [] qs = [] temp = [] Q = 1 for k in range(2*NN+50): p = 1 q = 2*k+1 if lcm(Q, q) < 2**bits: temp.append(mpq(p,q)) Q = lcm(Q, q) else: for a in temp: ps.append(int(a * Q)) qs.append(int(Q)) Q = q temp = [mpq(p,q)] return ps[:NN], qs[:NN] def exp_coefficients(M, bits): N = 2*M+50 Qs = [fac(k) for k in range(N)] prevstop = 0 for k in range(N): if Qs[k] >= 2**bits-1: q = Qs[k-1] for i in range(k, N): Qs[i] //= q for i in range(prevstop, k): Qs[i] = q prevstop = k Ps = Qs[:] fact = 1 for k in range(1, N): assert Qs[k] < 2**bits-1 if Qs[k] == Qs[k-1]: fact *= k else: fact = k Ps[k] //= fact return map(int, Ps)[:N], map(int, Qs)[:N] class FixedPointBound(object): def __init__(self, bits, mid, rad): self.bits = bits self.mid = mpq(mid) self.rad = mpq(rad) # rad is in ulp def add(self, other): if isinstance(other, FixedPointBound): mid = self.mid + other.mid rad = self.rad + other.rad else: assert other == int(other) and other >= 0 mid = self.mid + int(other) rad = self.rad return FixedPointBound(self.bits, mid, rad) def mul(self, other): if isinstance(other, FixedPointBound): MAX_ULP = mpq(1, 2**self.bits) mid = self.mid * other.mid rad = 0 rad += self.rad * other.mid # ulp rad += self.mid * other.rad # ulp rad += self.rad * other.rad * MAX_ULP # ulp rad += 1 # ulp rounding else: assert other == int(other) and other >= 0 mid = self.mid * int(other) rad = self.rad * int(other) return FixedPointBound(self.bits, mid, rad) def div(self, other): assert other == int(other) and other >= 0 mid = self.mid / mpq(other) rad = self.rad / mpq(other) + 1 return FixedPointBound(self.bits, mid, rad) def addmul(self, other, c): assert c == int(c) and c >= 0 c = abs(int(c)) mid = self.mid + other.mid * c rad = self.rad + other.rad * c return FixedPointBound(self.bits, mid, rad) def check_overflow_0(self): # check that self fits 0 integral limbs MAX_ULP = mpq(1, 2**self.bits) assert self.mid + self.rad * MAX_ULP < 1 - MAX_ULP def check_overflow_1(self): # check that self fits 1 integral limb MAX_ULP = mpq(1, 2**self.bits) assert self.mid + self.rad * MAX_ULP < 2**self.bits - MAX_ULP def check_le_int(self, c): # check that |self| <= c MAX_ULP = mpq(1, 2**self.bits) assert self.mid + self.rad * MAX_ULP <= c def verify_atan(N, PS, QS, bits): X = FixedPointBound(bits, mpq(1,16), 0) S = FixedPointBound(bits, 0, 0) m = 2 while m * m < N: m += 2 T = [None] * (m+1) T[1] = X.mul(X) T[2] = T[1].mul(T[1]) for k in range(4, m + 1, 2): T[k-1] = T[k//2].mul(T[k//2-1]) T[k] = T[k//2].mul(T[k//2]) for k in range(N-1, -1, -1): c, d, e = PS[k], QS[k], QS[k+1] if d != e and k < N-1: # if alternating, adding e must give a nonnegative number S.check_le_int(e) # adding e must not overflow S.add(e).check_overflow_1() S = S.mul(d).div(e) # if alternating, adding d must not overflow S.add(d).check_overflow_1() if k % m == 0: # if alternating, adding c must give a nonnegative number S.check_le_int(c) S = S.add(c) S.check_overflow_1() if k != 0: S = S.mul(T[m]) S.check_overflow_1() else: S = S.addmul(T[k % m], c) S.check_overflow_1() S = S.div(mpq(QS[0])) S = S.mul(X) S.check_overflow_0() print N, float(S.mid), float(S.rad) assert S.rad <= 2 def verify_exp(N, PS, QS, bits): X = FixedPointBound(bits, mpq(1,16), 0) S = FixedPointBound(bits, 0, 0) m = 2 while m * m < N: m += 2 T = [None] * (m+1) T[1] = X T[2] = T[1].mul(T[1]) for k in range(4, m + 1, 2): T[k-1] = T[k//2].mul(T[k//2-1]) T[k] = T[k//2].mul(T[k//2]) for k in range(N-1, -1, -1): c, d, e = PS[k], QS[k], QS[k+1] if d != e and k < N-1: # if alternating, adding e must give a nonnegative number S.check_le_int(e) # adding e must not overflow S.add(e).check_overflow_1() S = S.div(e) # if alternating, adding 1 must not overflow S.add(1).check_overflow_1() if k % m == 0: # if alternating, adding c must give a nonnegative number S.check_le_int(c) S = S.add(c) S.check_overflow_1() if k != 0: S = S.mul(T[m]) S.check_overflow_1() else: S = S.addmul(T[k % m], c) S.check_overflow_1() S = S.div(mpq(QS[0])) S.check_overflow_1() print N, float(S.mid), float(S.rad) assert S.rad <= 2 def verify_sin_cos(N, PS, QS, bits): X = FixedPointBound(bits, mpq(1,16), 0) m = 2 while m * m < N: m += 2 T = [None] * (m+1) T[1] = X.mul(X) T[2] = T[1].mul(T[1]) for k in range(4, m + 1, 2): T[k-1] = T[k//2].mul(T[k//2-1]) T[k] = T[k//2].mul(T[k//2]) for cosorsin in range(2): S = FixedPointBound(bits, 0, 0) for k in range(N-1, -1, -1): c, d, e = PS[2*k+cosorsin], QS[2*k+cosorsin], QS[2*k+cosorsin+2] if d != e and k < N-1: # if alternating, adding e must give a nonnegative number S.check_le_int(e) # adding e must not overflow S.add(e).check_overflow_1() S = S.div(e) # if alternating, adding 1 must not overflow S.add(1).check_overflow_1() if k % m == 0: # if alternating, adding c must give a nonnegative number S.check_le_int(c) S = S.add(c) S.check_overflow_1() if k != 0: S = S.mul(T[m]) S.check_overflow_1() else: S = S.addmul(T[k % m], c) S.check_overflow_1() if cosorsin == 0: S = S.div(mpq(QS[0])) S.check_overflow_1() # note: top limb must actually be 0 or 1; # but this follows by S.rad <= 2 print N, float(S.mid), float(S.rad) assert S.rad <= 2 else: S = S.div(mpq(QS[0])) S.check_overflow_1() S = S.mul(X) S.check_overflow_0() print N, float(S.mid), float(S.rad) assert S.rad <= 2 for bits in [32, 64]: PS, QS = exp_coefficients(300, bits) for N in range(300): verify_sin_cos(N, PS, QS, bits) for bits in [32, 64]: PS, QS = exp_coefficients(300, bits) for N in range(300): verify_exp(N, PS, QS, bits) for bits in [32, 64]: PS, QS = atan_coefficients(300, bits) for N in range(300): verify_atan(N, PS, QS, bits) arb-2.8.1/examples/000077500000000000000000000000001264125401100141005ustar00rootroot00000000000000arb-2.8.1/examples/complex_plot.c000066400000000000000000000205141264125401100167530ustar00rootroot00000000000000/* This file is public domain. Author: Fredrik Johansson. */ #include #include "acb.h" #include "acb_hypgeom.h" #include "acb_modular.h" #include "profiler.h" /* HLS algorithm from python's colorsys module */ static double vv(double m1, double m2, double hue) { hue = hue - floor(hue); if (hue < 1/6.) return m1 + (m2-m1)*hue*6.0; if (hue < 0.5) return m2; if (hue < 2/3.) return m1 + (m2-m1)*(2/3.-hue)*6.0; return m1; } static void hls_to_rgb(double *R, double *G, double *B, double h, double l, double s) { double m1, m2; if (s == 0.0) { *R = *G = *B = l; return; } if (l <= 0.5) m2 = l * (1.0+s); else m2 = l+s-(l*s); m1 = 2.0*l - m2; *R = vv(m1, m2, h + 1/3.); *G = vv(m1, m2, h); *B = vv(m1, m2, h - 1/3.); } #define PI 3.1415926535898 void color_function(double * R, double * G, double * B, const acb_t z) { double H, L, S; slong prec; arb_t t, u; if (!acb_is_finite(z) || acb_rel_accuracy_bits(z) < 4) { *R = *G = *B = 0.5; return; } arb_init(t); arb_init(u); prec = 32; arf_set_round(arb_midref(t), arb_midref(acb_realref(z)), prec, ARF_RND_DOWN); arf_set_round(arb_midref(u), arb_midref(acb_imagref(z)), prec, ARF_RND_DOWN); arb_atan2(t, u, t, prec); H = arf_get_d(arb_midref(t), ARF_RND_DOWN); H = (H + PI) / (2 * PI) + 0.5; H = H - floor(H); acb_abs(t, z, prec); if (arf_cmpabs_2exp_si(arb_midref(t), 200) > 0) { L = 1.0; } else if (arf_cmpabs_2exp_si(arb_midref(t), -200) < 0) { L = 0.0; } else { L = arf_get_d(arb_midref(t), ARF_RND_DOWN); L = 1.0 - 1.0/(1.0 + pow(L, 0.2)); } S = 0.8; hls_to_rgb(R, G, B, H, L, S); arb_clear(t); arb_clear(u); } typedef void (*func_ptr)(acb_t, const acb_t, slong); void ai(acb_t res, const acb_t z, slong prec) { acb_hypgeom_airy(res, NULL, NULL, NULL, z, prec); } void bi(acb_t res, const acb_t z, slong prec) { acb_hypgeom_airy(NULL, NULL, res, NULL, z, prec); } void besselj(acb_t res, const acb_t z, slong prec) { acb_t nu; acb_init(nu); acb_hypgeom_bessel_j(res, nu, z, prec); acb_clear(nu); } void bessely(acb_t res, const acb_t z, slong prec) { acb_t nu; acb_init(nu); acb_hypgeom_bessel_y(res, nu, z, prec); acb_clear(nu); } void besseli(acb_t res, const acb_t z, slong prec) { acb_t nu; acb_init(nu); acb_hypgeom_bessel_i(res, nu, z, prec); acb_clear(nu); } void besselk(acb_t res, const acb_t z, slong prec) { acb_t nu; acb_init(nu); acb_hypgeom_bessel_k(res, nu, z, prec); acb_clear(nu); } /* this function looks better when scaled */ void modj(acb_t res, const acb_t z, slong prec) { acb_modular_j(res, z, prec); acb_div_ui(res, res, 1728, prec); } int main(int argc, char *argv[]) { slong x, y, xnum, ynum, prec, i; double R, G, B, dxa, dxb, dya, dyb; FILE * fp; arf_t xa, xb, ya, yb; acb_t z, w; func_ptr func; if (argc < 2) { printf("complex_plot [-range xa xb ya yb] [-size xn yn] \n\n"); printf("Plots one of the predefined functions on [xa,xb] + [ya,yb]i\n"); printf("using domain coloring, at a resolution of xn by yn pixels.\n\n"); printf("Defaults parameters are [-10,10] + [-10,10]i and xn = yn = 512.\n\n"); printf("The output is written to arbplot.ppm. If you have ImageMagick,\n"); printf("run [convert arbplot.ppm arbplot.png] to get a PNG.\n\n"); printf("Function codes are:\n"); printf(" gamma - Gamma function\n"); printf(" digamma - Digamma function\n"); printf(" lgamma - Logarithmic gamma function\n"); printf(" zeta - Riemann zeta function\n"); printf(" erf - Error function\n"); printf(" ai - Airy function Ai\n"); printf(" bi - Airy function Bi\n"); printf(" besselj - Bessel function J_0\n"); printf(" bessely - Bessel function Y_0\n"); printf(" besseli - Bessel function I_0\n"); printf(" besselk - Bessel function K_0\n"); printf(" modj - Modular j-function\n"); printf(" modeta - Dedekind eta function\n"); printf(" barnesg - Barnes G-function\n"); printf(" agm - Arithmetic geometric mean\n\n"); return 1; } xnum = 512; ynum = 512; dxa = dya = -10; dxb = dyb = 10; func = acb_gamma; for (i = 1; i < argc; i++) { if (!strcmp(argv[i], "-size")) { xnum = atol(argv[i+1]); ynum = atol(argv[i+2]); i += 2; } else if (!strcmp(argv[i], "-range")) { dxa = atof(argv[i+1]); dxb = atof(argv[i+2]); dya = atof(argv[i+3]); dyb = atof(argv[i+4]); i += 4; } else if (!strcmp(argv[i], "gamma")) { func = acb_gamma; } else if (!strcmp(argv[i], "digamma")) { func = acb_digamma; } else if (!strcmp(argv[i], "lgamma")) { func = acb_lgamma; } else if (!strcmp(argv[i], "zeta")) { func = acb_zeta; } else if (!strcmp(argv[i], "erf")) { func = acb_hypgeom_erf; } else if (!strcmp(argv[i], "ai")) { func = ai; } else if (!strcmp(argv[i], "bi")) { func = bi; } else if (!strcmp(argv[i], "besselj")) { func = besselj; } else if (!strcmp(argv[i], "bessely")) { func = bessely; } else if (!strcmp(argv[i], "besseli")) { func = besseli; } else if (!strcmp(argv[i], "besselk")) { func = besselk; } else if (!strcmp(argv[i], "modj")) { func = modj; } else if (!strcmp(argv[i], "modeta")) { func = acb_modular_eta; } else if (!strcmp(argv[i], "barnesg")) { func = acb_barnes_g; } else if (!strcmp(argv[i], "agm")) { func = acb_agm1; } else { printf("unknown option: %s\n", argv[i]); return 1; } } acb_init(z); acb_init(w); arf_init(xa); arf_init(xb); arf_init(ya); arf_init(yb); arf_set_d(xa, dxa); arf_set_d(xb, dxb); arf_set_d(ya, dya); arf_set_d(yb, dyb); fp = fopen("arbplot.ppm", "w"); fprintf(fp, "P6\n%ld %ld 255\n", xnum, ynum); TIMEIT_ONCE_START for (y = ynum - 1; y >= 0; y--) { if (y % (ynum / 16) == 0) printf("row %ld\n", y); for (x = 0; x < xnum; x++) { for (prec = 30; prec < 500; prec *= 2) { arf_sub(arb_midref(acb_imagref(z)), yb, ya, prec, ARF_RND_DOWN); arf_mul_ui(arb_midref(acb_imagref(z)), arb_midref(acb_imagref(z)), y, prec, ARF_RND_DOWN); arf_div_ui(arb_midref(acb_imagref(z)), arb_midref(acb_imagref(z)), ynum - 1, prec, ARF_RND_DOWN); arf_add(arb_midref(acb_imagref(z)), arb_midref(acb_imagref(z)), ya, prec, ARF_RND_DOWN); arf_sub(arb_midref(acb_realref(z)), xb, xa, prec, ARF_RND_DOWN); arf_mul_ui(arb_midref(acb_realref(z)), arb_midref(acb_realref(z)), x, prec, ARF_RND_DOWN); arf_div_ui(arb_midref(acb_realref(z)), arb_midref(acb_realref(z)), xnum - 1, prec, ARF_RND_DOWN); arf_add(arb_midref(acb_realref(z)), arb_midref(acb_realref(z)), xa, prec, ARF_RND_DOWN); func(w, z, prec); if (acb_rel_accuracy_bits(w) > 4) break; } color_function(&R, &G, &B, w); fputc(FLINT_MIN(255, floor(R * 255)), fp); fputc(FLINT_MIN(255, floor(G * 255)), fp); fputc(FLINT_MIN(255, floor(B * 255)), fp); } } TIMEIT_ONCE_STOP fclose(fp); arf_clear(xa); arf_clear(xb); arf_clear(ya); arf_clear(yb); acb_clear(z); acb_clear(w); flint_cleanup(); return 0; } arb-2.8.1/examples/hilbert_matrix.c000066400000000000000000000021351264125401100172620ustar00rootroot00000000000000/* This file is public domain. Author: Fredrik Johansson. */ #include "arb_mat.h" #include "profiler.h" int main(int argc, char *argv[]) { arb_mat_t A; arb_t det; slong i, j, prec, n; if (argc < 2) { flint_printf("usage: build/examples/hilbert_matrix n\n"); return 1; } n = atol(argv[1]); arb_mat_init(A, n, n); arb_init(det); TIMEIT_ONCE_START for (prec = 20; ; prec *= 2) { for (i = 0; i < n; i++) { for (j = 0; j < n; j++) { arb_set_ui(arb_mat_entry(A, i, j), 1), arb_div_ui(arb_mat_entry(A, i, j), arb_mat_entry(A, i, j), i + j + 1, prec); } } flint_printf("prec=%wd: ", prec); arb_mat_det(det, A, prec); arb_printd(det, 10); flint_printf("\n"); if (!arb_contains_zero(det)) { flint_printf("success!\n"); break; } } TIMEIT_ONCE_STOP SHOW_MEMORY_USAGE arb_mat_clear(A); arb_clear(det); flint_cleanup(); return 0; } arb-2.8.1/examples/integrals.c000066400000000000000000000100241264125401100162310ustar00rootroot00000000000000/* This file is public domain. Author: Fredrik Johansson. */ #include "acb_calc.h" #include "profiler.h" int sinx(acb_ptr out, const acb_t inp, void * params, slong order, slong prec) { int xlen = FLINT_MIN(2, order); acb_set(out, inp); if (xlen > 1) acb_one(out + 1); _acb_poly_sin_series(out, out, xlen, order, prec); return 0; } int elliptic(acb_ptr out, const acb_t inp, void * params, slong order, slong prec) { acb_ptr t; t = _acb_vec_init(order); acb_set(t, inp); if (order > 1) acb_one(t + 1); _acb_poly_sin_series(t, t, FLINT_MIN(2, order), order, prec); _acb_poly_mullow(out, t, order, t, order, order, prec); _acb_vec_scalar_mul_2exp_si(t, out, order, -1); acb_sub_ui(t, t, 1, prec); _acb_vec_neg(t, t, order); _acb_poly_rsqrt_series(out, t, order, order, prec); _acb_vec_clear(t, order); return 0; } int bessel(acb_ptr out, const acb_t inp, void * params, slong order, slong prec) { acb_ptr t; acb_t z; ulong n; t = _acb_vec_init(order); acb_init(z); acb_set(t, inp); if (order > 1) acb_one(t + 1); n = 10; arb_set_si(acb_realref(z), 20); arb_set_si(acb_imagref(z), 10); /* z sin(t) */ _acb_poly_sin_series(out, t, FLINT_MIN(2, order), order, prec); _acb_vec_scalar_mul(out, out, order, z, prec); /* t n */ _acb_vec_scalar_mul_ui(t, t, FLINT_MIN(2, order), n, prec); _acb_poly_sub(out, t, FLINT_MIN(2, order), out, order, prec); _acb_poly_cos_series(out, out, order, order, prec); _acb_vec_clear(t, order); acb_clear(z); return 0; } int main(int argc, char *argv[]) { acb_t r, s, a, b; arf_t inr, outr; slong digits, prec; if (argc < 2) { flint_printf("integrals d\n"); flint_printf("compute integrals using d decimal digits of precision\n"); return 1; } acb_init(r); acb_init(s); acb_init(a); acb_init(b); arf_init(inr); arf_init(outr); arb_calc_verbose = 0; digits = atol(argv[1]); prec = digits * 3.32193; flint_printf("Digits: %wd\n", digits); flint_printf("----------------------------------------------------------------\n"); flint_printf("Integral of sin(t) from 0 to 100.\n"); arf_set_d(inr, 0.125); arf_set_d(outr, 1.0); TIMEIT_ONCE_START acb_set_si(a, 0); acb_set_si(b, 100); acb_calc_integrate_taylor(r, sinx, NULL, a, b, inr, outr, prec, 1.1 * prec); flint_printf("RESULT:\n"); acb_printd(r, digits); flint_printf("\n"); TIMEIT_ONCE_STOP flint_printf("----------------------------------------------------------------\n"); flint_printf("Elliptic integral F(phi, m) = integral of 1/sqrt(1 - m*sin(t)^2)\n"); flint_printf("from 0 to phi, with phi = 6+6i, m = 1/2. Integration path\n"); flint_printf("0 -> 6 -> 6+6i.\n"); arf_set_d(inr, 0.2); arf_set_d(outr, 0.5); TIMEIT_ONCE_START acb_set_si(a, 0); acb_set_si(b, 6); acb_calc_integrate_taylor(r, elliptic, NULL, a, b, inr, outr, prec, 1.1 * prec); acb_set_si(a, 6); arb_set_si(acb_realref(b), 6); arb_set_si(acb_imagref(b), 6); acb_calc_integrate_taylor(s, elliptic, NULL, a, b, inr, outr, prec, 1.1 * prec); acb_add(r, r, s, prec); flint_printf("RESULT:\n"); acb_printd(r, digits); flint_printf("\n"); TIMEIT_ONCE_STOP flint_printf("----------------------------------------------------------------\n"); flint_printf("Bessel function J_n(z) = (1/pi) * integral of cos(t*n - z*sin(t))\n"); flint_printf("from 0 to pi. With n = 10, z = 20 + 10i.\n"); arf_set_d(inr, 0.1); arf_set_d(outr, 0.5); TIMEIT_ONCE_START acb_set_si(a, 0); acb_const_pi(b, 3 * prec); acb_calc_integrate_taylor(r, bessel, NULL, a, b, inr, outr, prec, 3 * prec); acb_div(r, r, b, prec); flint_printf("RESULT:\n"); acb_printd(r, digits); flint_printf("\n"); TIMEIT_ONCE_STOP acb_clear(r); acb_clear(s); acb_clear(a); acb_clear(b); arf_clear(inr); arf_clear(outr); flint_cleanup(); return 0; } arb-2.8.1/examples/keiper_li.c000066400000000000000000000065771264125401100162260ustar00rootroot00000000000000/* This file is public domain. Author: Fredrik Johansson. */ #include #include "arb.h" #include "acb.h" #include "arb_poly.h" #include "profiler.h" void keiper_li_series(arb_ptr z, slong len, slong prec) { arb_ptr t, u, v; t = _arb_vec_init(len); u = _arb_vec_init(len); v = _arb_vec_init(len); /* -zeta(s) */ flint_printf("zeta: "); TIMEIT_ONCE_START arb_zero(t + 0); arb_one(t + 1); arb_one(u); _arb_poly_zeta_series(v, t, 2, u, 0, len, prec); _arb_vec_neg(v, v, len); TIMEIT_ONCE_STOP SHOW_MEMORY_USAGE /* logarithm */ flint_printf("log: "); TIMEIT_ONCE_START _arb_poly_log_series(t, v, len, len, prec); TIMEIT_ONCE_STOP /* add log(gamma(1+s/2)) */ flint_printf("gamma: "); TIMEIT_ONCE_START arb_one(u); arb_one(u + 1); arb_mul_2exp_si(u + 1, u + 1, -1); _arb_poly_lgamma_series(v, u, 2, len, prec); _arb_vec_add(t, t, v, len, prec); TIMEIT_ONCE_STOP /* subtract 0.5 s log(pi) */ arb_const_pi(u, prec); arb_log(u, u, prec); arb_mul_2exp_si(u, u, -1); arb_sub(t + 1, t + 1, u, prec); /* add log(1-s) */ arb_one(u); arb_set_si(u + 1, -1); _arb_poly_log_series(v, u, 2, len, prec); _arb_vec_add(t, t, v, len, prec); /* binomial transform */ flint_printf("binomial transform: "); TIMEIT_ONCE_START arb_set(z, t); _arb_vec_neg(t + 1, t + 1, len - 1); _arb_poly_binomial_transform(z + 1, t + 1, len - 1, len - 1, prec); TIMEIT_ONCE_STOP _arb_vec_clear(t, len); _arb_vec_clear(u, len); _arb_vec_clear(v, len); } int main(int argc, char *argv[]) { slong i, len, prec, num_threads; char * out_file; arb_ptr z; if (argc < 2) { flint_printf("keiper_li n [-prec prec] [-threads num_threads] [-out out_file]\n"); return 1; } len = atol(argv[1]) + 1; prec = 1.1 * len + 50; num_threads = 1; out_file = NULL; for (i = 1; i < argc; i++) { if (!strcmp(argv[i], "-prec")) prec = atol(argv[i+1]); else if (!strcmp(argv[i], "-threads")) num_threads = atol(argv[i+1]); else if (!strcmp(argv[i], "-out")) out_file = argv[i+1]; } flint_set_num_threads(num_threads); z = _arb_vec_init(len); keiper_li_series(z, len, prec); for (i = 0; i < len; i++) { if (i <= 10 || len - i <= 10) { flint_printf("%wd: ", i); arb_printd(z + i, 50); flint_printf("\n"); } } SHOW_MEMORY_USAGE if (out_file != NULL) { fmpz_t man, exp; arf_t t; FILE * fp = fopen(out_file, "w"); fmpz_init(man); fmpz_init(exp); arf_init(t); for (i = 0; i < len; i++) { arf_get_fmpz_2exp(man, exp, arb_midref(z + i)); flint_fprintf(fp, "%wd ", i); fmpz_fprint(fp, man); flint_fprintf(fp, " "); fmpz_fprint(fp, exp); flint_fprintf(fp, " "); arf_set_mag(t, arb_radref(z + i)); arf_get_fmpz_2exp(man, exp, t); fmpz_fprint(fp, man); flint_fprintf(fp, " "); fmpz_fprint(fp, exp); flint_fprintf(fp, "\n"); } fclose(fp); fmpz_clear(man); fmpz_clear(exp); arf_clear(t); } _arb_vec_clear(z, len); flint_cleanup(); return 0; } arb-2.8.1/examples/pi.c000066400000000000000000000014301264125401100146520ustar00rootroot00000000000000/* This file is public domain. Author: Fredrik Johansson. */ #include "arb.h" #include "profiler.h" int main(int argc, char *argv[]) { arb_t x; slong prec, digits, condense; if (argc < 2) { flint_printf("usage: build/examples/pi digits [condense = 20]\n"); return 1; } digits = atol(argv[1]); if (argc > 2) condense = atol(argv[2]); else condense = 20; arb_init(x); prec = digits * 3.3219280948873623 + 5; flint_printf("computing pi with a precision of %wd bits... ", prec); TIMEIT_ONCE_START arb_const_pi(x, prec); TIMEIT_ONCE_STOP SHOW_MEMORY_USAGE arb_printn(x, digits, ARB_STR_CONDENSE * condense); flint_printf("\n"); arb_clear(x); flint_cleanup(); return 0; } arb-2.8.1/examples/poly_roots.c000066400000000000000000000144761264125401100164710ustar00rootroot00000000000000/* This file is public domain. Author: Fredrik Johansson. */ #include #include "acb.h" #include "acb_poly.h" #include "arith.h" #include "profiler.h" int check_accuracy(acb_ptr vec, slong len, slong prec) { slong i; for (i = 0; i < len; i++) { if (mag_cmp_2exp_si(arb_radref(acb_realref(vec + i)), -prec) >= 0 || mag_cmp_2exp_si(arb_radref(acb_imagref(vec + i)), -prec) >= 0) return 0; } return 1; } void poly_roots(const fmpz_poly_t poly, slong initial_prec, slong target_prec, slong print_digits) { slong i, prec, deg, isolated, maxiter; acb_poly_t cpoly; acb_ptr roots; deg = poly->length - 1; acb_poly_init(cpoly); roots = _acb_vec_init(deg); for (prec = initial_prec; ; prec *= 2) { acb_poly_set_fmpz_poly(cpoly, poly, prec); maxiter = FLINT_MIN(FLINT_MAX(deg, 32), prec); TIMEIT_ONCE_START flint_printf("prec=%wd: ", prec); isolated = acb_poly_find_roots(roots, cpoly, prec == initial_prec ? NULL : roots, maxiter, prec); flint_printf("%wd isolated roots | ", isolated); TIMEIT_ONCE_STOP if (isolated == deg && check_accuracy(roots, deg, target_prec)) { flint_printf("done!\n"); break; } } if (print_digits != 0) { _acb_vec_sort_pretty(roots, deg); for (i = 0; i < deg; i++) { acb_printd(roots + i, print_digits); flint_printf("\n"); } } acb_poly_clear(cpoly); _acb_vec_clear(roots, deg); } int main(int argc, char *argv[]) { fmpz_poly_t f; fmpz_t t; slong compd, printd, i, j; if (argc < 2) { flint_printf("poly_roots2 [-refine d] [-print d] \n\n"); flint_printf("Isolates all the complex roots of a polynomial with\n"); flint_printf("integer coefficients. For convergence, the input polynomial\n"); flint_printf("is required to be squarefree.\n\n"); flint_printf("If -refine d is passed, the roots are refined to an absolute\n"); flint_printf("tolerance better than 10^(-d). By default, the roots are only\n"); flint_printf("computed to sufficient accuracy to isolate them.\n"); flint_printf("The refinement is not currently done efficiently.\n\n"); flint_printf("If -print d is passed, the computed roots are printed to\n"); flint_printf("d decimals. By default, the roots are not printed.\n\n"); flint_printf("The polynomial can be specified by passing the following as :\n\n"); flint_printf("a Easy polynomial 1 + 2x + ... + (n+1)x^n\n"); flint_printf("t Chebyshev polynomial T_n\n"); flint_printf("u Chebyshev polynomial U_n\n"); flint_printf("p Legendre polynomial P_n\n"); flint_printf("c Cyclotomic polynomial Phi_n\n"); flint_printf("s Swinnerton-Dyer polynomial S_n\n"); flint_printf("b Bernoulli polynomial B_n\n"); flint_printf("w Wilkinson polynomial W_n\n"); flint_printf("e Taylor series of exp(x) truncated to degree n\n"); flint_printf("m The Mignotte-like polynomial x^n + (100x+1)^m, n > m\n"); flint_printf("c0 c1 ... cn c0 + c1 x + ... + cn x^n where all c:s are specified integers\n"); return 1; } compd = 0; printd = 0; j = 0; fmpz_poly_init(f); fmpz_init(t); for (i = 1; i < argc; i++) { if (!strcmp(argv[i], "-refine")) { compd = atol(argv[i+1]); i++; } else if (!strcmp(argv[i], "-print")) { printd = atol(argv[i+1]); i++; } else if (!strcmp(argv[i], "a")) { slong n = atol(argv[i+1]); for (j = 0; j <= n; j++) fmpz_poly_set_coeff_ui(f, j, j+1); break; } else if (!strcmp(argv[i], "t")) { arith_chebyshev_t_polynomial(f, atol(argv[i+1])); break; } else if (!strcmp(argv[i], "u")) { arith_chebyshev_u_polynomial(f, atol(argv[i+1])); break; } else if (!strcmp(argv[i], "p")) { fmpq_poly_t g; fmpq_poly_init(g); arith_legendre_polynomial(g, atol(argv[i+1])); fmpq_poly_get_numerator(f, g); fmpq_poly_clear(g); break; } else if (!strcmp(argv[i], "c")) { arith_cyclotomic_polynomial(f, atol(argv[i+1])); break; } else if (!strcmp(argv[i], "s")) { arith_swinnerton_dyer_polynomial(f, atol(argv[i+1])); break; } else if (!strcmp(argv[i], "b")) { fmpq_poly_t g; fmpq_poly_init(g); arith_bernoulli_polynomial(g, atol(argv[i+1])); fmpq_poly_get_numerator(f, g); fmpq_poly_clear(g); break; } else if (!strcmp(argv[i], "w")) { slong n = atol(argv[i+1]); fmpz_poly_fit_length(f, n+2); arith_stirling_number_1_vec(f->coeffs, n+1, n+2); _fmpz_poly_set_length(f, n+2); fmpz_poly_shift_right(f, f, 1); break; } else if (!strcmp(argv[i], "e")) { fmpq_poly_t g; fmpq_poly_init(g); fmpq_poly_set_coeff_si(g, 0, 0); fmpq_poly_set_coeff_si(g, 1, 1); fmpq_poly_exp_series(g, g, atol(argv[i+1]) + 1); fmpq_poly_get_numerator(f, g); fmpq_poly_clear(g); break; } else if (!strcmp(argv[i], "m")) { fmpz_poly_set_coeff_ui(f, 0, 1); fmpz_poly_set_coeff_ui(f, 1, 100); fmpz_poly_pow(f, f, atol(argv[i+2])); fmpz_poly_set_coeff_ui(f, atol(argv[i+1]), 1); break; } else { fmpz_set_str(t, argv[i], 10); fmpz_poly_set_coeff_fmpz(f, j, t); j++; } } TIMEIT_ONCE_START poly_roots(f, 32, compd * 3.32193 + 2, printd); TIMEIT_ONCE_STOP fmpz_poly_clear(f); fmpz_clear(t); flint_cleanup(); return EXIT_SUCCESS; } arb-2.8.1/examples/real_roots.c000066400000000000000000000212401264125401100164140ustar00rootroot00000000000000/* This file is public domain. Author: Fredrik Johansson. */ #include #include "arb_calc.h" #include "acb_hypgeom.h" #include "profiler.h" slong eval_count = 0; int z_function(arb_ptr out, const arb_t inp, void * params, slong order, slong prec) { arb_struct x[2]; arb_init(x); arb_init(x + 1); arb_set(x, inp); arb_one(x + 1); _arb_poly_riemann_siegel_z_series(out, x, FLINT_MIN(2, order), order, prec); arb_clear(x); arb_clear(x + 1); eval_count++; return 0; } int sin_x(arb_ptr out, const arb_t inp, void * params, slong order, slong prec) { int xlen = FLINT_MIN(2, order); arb_set(out, inp); if (xlen > 1) arb_one(out + 1); _arb_poly_sin_series(out, out, xlen, order, prec); eval_count++; return 0; } int sin_x2(arb_ptr out, const arb_t inp, void * params, slong order, slong prec) { arb_ptr x; int xlen = FLINT_MIN(2, order); int ylen = FLINT_MIN(3, order); x = _arb_vec_init(xlen); arb_set(x, inp); if (xlen > 1) arb_one(x + 1); _arb_poly_mullow(out, x, xlen, x, xlen, ylen, prec); _arb_poly_sin_series(out, out, ylen, order, prec); _arb_vec_clear(x, xlen); eval_count++; return 0; } int sin_1x(arb_ptr out, const arb_t inp, void * params, slong order, slong prec) { arb_ptr x; int xlen = FLINT_MIN(2, order); x = _arb_vec_init(xlen); arb_set(x, inp); if (xlen > 1) arb_one(x + 1); _arb_poly_inv_series(out, x, xlen, order, prec); _arb_poly_sin_series(out, out, order, order, prec); _arb_vec_clear(x, xlen); eval_count++; return 0; } int airy(arb_ptr out, const arb_t inp, void * params, slong order, slong prec) { acb_t t, u; int which = ((int *) params)[0]; int xlen = FLINT_MIN(2, order); acb_init(t); acb_init(u); acb_set_arb(t, inp); if (xlen == 1) { if (which == 0) acb_hypgeom_airy(t, NULL, NULL, NULL, t, prec); else if (which == 1) acb_hypgeom_airy(NULL, t, NULL, NULL, t, prec); else if (which == 2) acb_hypgeom_airy(NULL, NULL, t, NULL, t, prec); else acb_hypgeom_airy(NULL, NULL, NULL, t, t, prec); arb_set(out, acb_realref(t)); } else { if (which == 0 || which == 1) acb_hypgeom_airy(t, u, NULL, NULL, t, prec); else acb_hypgeom_airy(NULL, NULL, t, u, t, prec); if (which == 0 || which == 2) { arb_set(out + 0, acb_realref(t)); arb_set(out + 1, acb_realref(u)); /* f''(z) = z f(z) */ if (xlen == 3) arb_mul(out + 2, out + 0, inp, prec); } else { arb_set(out + 0, acb_realref(u)); arb_mul(out + 1, acb_realref(t), inp, prec); /* f'''(z) = f(z) + z f'(z) */ if (xlen == 3) { arb_mul(out + 2, out + 0, inp, prec); arb_add(out + 2, out + 2, acb_realref(t), prec); } } } acb_clear(t); acb_clear(u); eval_count++; return 0; } int main(int argc, char *argv[]) { arf_interval_ptr blocks; arb_calc_func_t function; int * info; int params; slong digits, low_prec, high_prec, i, num, found_roots, found_unknown; slong maxdepth, maxeval, maxfound; int refine; double a, b; arf_t C; arf_interval_t t, interval; arb_t v, w, z; if (argc < 4) { flint_printf("real_roots function a b [-refine d] [-verbose] " "[-maxdepth n] [-maxeval n] [-maxfound n] [-prec n]\n"); flint_printf("available functions:\n"); flint_printf(" 0 Z(x), Riemann-Siegel Z-function\n"); flint_printf(" 1 sin(x)\n"); flint_printf(" 2 sin(x^2)\n"); flint_printf(" 3 sin(1/x)\n"); flint_printf(" 4 Ai(x), Airy function\n"); flint_printf(" 5 Ai'(x), Airy function\n"); flint_printf(" 6 Bi(x), Airy function\n"); flint_printf(" 7 Bi'(x), Airy function\n"); return 1; } params = 0; switch (atoi(argv[1])) { case 0: function = z_function; break; case 1: function = sin_x; break; case 2: function = sin_x2; break; case 3: function = sin_1x; break; case 4: function = airy; params = 0; break; case 5: function = airy; params = 1; break; case 6: function = airy; params = 2; break; case 7: function = airy; params = 3; break; default: flint_printf("require a function 0-7\n"); return 1; } a = atof(argv[2]); b = atof(argv[3]); if (a >= b) { flint_printf("require a < b!\n"); return 1; } refine = 0; digits = 0; maxdepth = 30; maxeval = 100000; maxfound = 100000; low_prec = 30; for (i = 4; i < argc; i++) { if (!strcmp(argv[i], "-refine")) { refine = 1; digits = atol(argv[i+1]); } else if (!strcmp(argv[i], "-verbose")) { arb_calc_verbose = 1; } else if (!strcmp(argv[i], "-maxdepth")) { maxdepth = atol(argv[i+1]); } else if (!strcmp(argv[i], "-maxeval")) { maxeval = atol(argv[i+1]); } else if (!strcmp(argv[i], "-maxfound")) { maxfound = atol(argv[i+1]); } else if (!strcmp(argv[i], "-prec")) { low_prec = atol(argv[i+1]); } } high_prec = digits * 3.32192809488736 + 10; found_roots = 0; found_unknown = 0; arf_init(C); arf_interval_init(t); arf_interval_init(interval); arb_init(v); arb_init(w); arb_init(z); arf_set_d(&interval->a, a); arf_set_d(&interval->b, b); flint_printf("interval: "); arf_interval_printd(interval, 15); flint_printf("\n"); flint_printf("maxdepth = %wd, maxeval = %wd, maxfound = %wd, low_prec = %wd\n", maxdepth, maxeval, maxfound, low_prec); TIMEIT_ONCE_START num = arb_calc_isolate_roots(&blocks, &info, function, ¶ms, interval, maxdepth, maxeval, maxfound, low_prec); for (i = 0; i < num; i++) { if (info[i] != 1) { if (arb_calc_verbose) { flint_printf("unable to count roots in "); arf_interval_printd(blocks + i, 15); flint_printf("\n"); } found_unknown++; continue; } found_roots++; if (!refine) continue; if (arb_calc_refine_root_bisect(t, function, ¶ms, blocks + i, 5, low_prec) != ARB_CALC_SUCCESS) { flint_printf("warning: some bisection steps failed!\n"); } if (arb_calc_verbose) { flint_printf("after bisection 1: "); arf_interval_printd(t, 15); flint_printf("\n"); } if (arb_calc_refine_root_bisect(blocks + i, function, ¶ms, t, 5, low_prec) != ARB_CALC_SUCCESS) { flint_printf("warning: some bisection steps failed!\n"); } if (arb_calc_verbose) { flint_printf("after bisection 2: "); arf_interval_printd(blocks + i, 15); flint_printf("\n"); } arf_interval_get_arb(v, t, high_prec); arb_calc_newton_conv_factor(C, function, ¶ms, v, low_prec); arf_interval_get_arb(w, blocks + i, high_prec); if (arb_calc_refine_root_newton(z, function, ¶ms, w, v, C, 10, high_prec) != ARB_CALC_SUCCESS) { flint_printf("warning: some newton steps failed!\n"); } flint_printf("refined root (%wd/%wd):\n", i, num); arb_printn(z, digits + 2, 0); flint_printf("\n\n"); } flint_printf("---------------------------------------------------------------\n"); flint_printf("Found roots: %wd\n", found_roots); flint_printf("Subintervals possibly containing undetected roots: %wd\n", found_unknown); flint_printf("Function evaluations: %wd\n", eval_count); TIMEIT_ONCE_STOP SHOW_MEMORY_USAGE for (i = 0; i < num; i++) arf_interval_clear(blocks + i); flint_free(blocks); flint_free(info); arf_interval_clear(t); arf_interval_clear(interval); arf_clear(C); arb_clear(v); arb_clear(w); arb_clear(z); flint_cleanup(); return 0; } arb-2.8.1/fmpr.h000066400000000000000000000540721264125401100134070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef FMPR_H #define FMPR_H #if defined(__MINGW64__) #include "stdint.h" #endif #include #include #include #include #include "flint.h" #include "fmpz.h" #include "fmpq.h" #include "fmpz_extras.h" #include "config.h" #ifdef HAVE_TLS #if HAVE_TLS #define TLS_PREFIX __thread #else #define TLS_PREFIX #endif #else #define TLS_PREFIX #endif #define fmpr_rnd_t int #define FMPR_RND_DOWN 0 #define FMPR_RND_UP 1 #define FMPR_RND_FLOOR 2 #define FMPR_RND_CEIL 3 #define FMPR_RND_NEAR 4 #ifdef __cplusplus extern "C" { #endif static __inline__ int rounds_up(fmpr_rnd_t rnd, int negative) { if (rnd == FMPR_RND_DOWN) return 0; if (rnd == FMPR_RND_UP) return 1; if (rnd == FMPR_RND_FLOOR) return negative; return !negative; } static __inline__ mpfr_rnd_t rnd_to_mpfr(fmpr_rnd_t rnd) { if (rnd == FMPR_RND_DOWN) return MPFR_RNDZ; else if (rnd == FMPR_RND_UP) return MPFR_RNDA; else if (rnd == FMPR_RND_FLOOR) return MPFR_RNDD; else if (rnd == FMPR_RND_CEIL) return MPFR_RNDU; else return MPFR_RNDN; } typedef struct { fmpz man; fmpz exp; } fmpr_struct; typedef fmpr_struct fmpr_t[1]; typedef fmpr_struct * fmpr_ptr; typedef const fmpr_struct * fmpr_srcptr; #define fmpr_manref(x) (&(x)->man) #define fmpr_expref(x) (&(x)->exp) static __inline__ void fmpr_init(fmpr_t x) { fmpz_init(fmpr_manref(x)); fmpz_init(fmpr_expref(x)); } static __inline__ void fmpr_clear(fmpr_t x) { fmpz_clear(fmpr_manref(x)); fmpz_clear(fmpr_expref(x)); } /* The return value encodes an error bound, or FMPR_RESULT_EXACT if exact */ #define FMPR_RESULT_EXACT WORD_MAX /* Allow 'infinite' precision for operations where a result can be computed exactly */ #define FMPR_PREC_EXACT WORD_MAX #define FMPR_PREC_ADD(prec,extra) ((prec) == FMPR_PREC_EXACT ? FMPR_PREC_EXACT : (prec) + (extra)) /* ------------------------------------------------------------------------ */ /* Special values */ /* Special values (0, +inf, -inf, NaN) are encoded using a zero mantissa. Zero is encoded with a zero exponent. */ #define FMPR_EXP_POS_INF WORD(1) #define FMPR_EXP_NEG_INF WORD(2) #define FMPR_EXP_NAN WORD(3) static __inline__ void fmpr_zero(fmpr_t x) { fmpz_zero(fmpr_manref(x)); fmpz_zero(fmpr_expref(x)); } static __inline__ int fmpr_is_zero(const fmpr_t x) { return fmpz_is_zero(fmpr_manref(x)) && fmpz_is_zero(fmpr_expref(x)); } static __inline__ int fmpr_is_special(const fmpr_t x) { return fmpz_is_zero(fmpr_manref(x)); } static __inline__ int fmpr_is_normal(const fmpr_t x) { return !fmpz_is_zero(fmpr_manref(x)); } static __inline__ int fmpr_is_inf(const fmpr_t x) { return fmpr_is_special(x) && (*fmpr_expref(x) == FMPR_EXP_POS_INF || *fmpr_expref(x) == FMPR_EXP_NEG_INF); } static __inline__ int fmpr_is_pos_inf(const fmpr_t x) { return fmpr_is_special(x) && (*fmpr_expref(x) == FMPR_EXP_POS_INF); } static __inline__ int fmpr_is_neg_inf(const fmpr_t x) { return fmpr_is_special(x) && (*fmpr_expref(x) == FMPR_EXP_NEG_INF); } static __inline__ int fmpr_is_nan(const fmpr_t x) { return fmpr_is_special(x) && (*fmpr_expref(x) == FMPR_EXP_NAN); } static __inline__ int fmpr_is_finite(const fmpr_t x) { return fmpr_is_zero(x) || !fmpr_is_special(x); } static __inline__ void fmpr_pos_inf(fmpr_t x) { fmpz_zero(fmpr_manref(x)); fmpz_set_si(fmpr_expref(x), FMPR_EXP_POS_INF); } static __inline__ void fmpr_neg_inf(fmpr_t x) { fmpz_zero(fmpr_manref(x)); fmpz_set_si(fmpr_expref(x), FMPR_EXP_NEG_INF); } static __inline__ void fmpr_nan(fmpr_t x) { fmpz_zero(fmpr_manref(x)); fmpz_set_si(fmpr_expref(x), FMPR_EXP_NAN); } static __inline__ int fmpr_is_one(const fmpr_t x) { return fmpz_is_one(fmpr_manref(x)) && fmpz_is_zero(fmpr_expref(x)); } static __inline__ void fmpr_one(fmpr_t x) { fmpz_one(fmpr_manref(x)); fmpz_zero(fmpr_expref(x)); } /* ------------------------------------------------------------------------ */ slong _fmpr_normalise_naive(fmpz_t man, fmpz_t exp, slong prec, fmpr_rnd_t rnd); static __inline__ void fmpr_set(fmpr_t y, const fmpr_t x) { if (y != x) { fmpz_set(fmpr_manref(y), fmpr_manref(x)); fmpz_set(fmpr_expref(y), fmpr_expref(x)); } } static __inline__ void fmpr_swap(fmpr_t x, fmpr_t y) { fmpz_swap(fmpr_manref(x), fmpr_manref(y)); fmpz_swap(fmpr_expref(x), fmpr_expref(y)); } slong _fmpr_set_round(fmpz_t rman, fmpz_t rexp, const fmpz_t man, const fmpz_t exp, slong prec, fmpr_rnd_t rnd); static __inline__ slong _fmpr_normalise(fmpz_t man, fmpz_t exp, slong prec, fmpr_rnd_t rnd) { if (fmpz_is_zero(man)) { fmpz_zero(man); fmpz_zero(exp); return FMPR_RESULT_EXACT; } else { return _fmpr_set_round(man, exp, man, exp, prec, rnd); } } static __inline__ slong fmpr_set_round_naive(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { fmpr_set(y, x); if (fmpr_is_special(y)) return FMPR_RESULT_EXACT; else return _fmpr_normalise(fmpr_manref(y), fmpr_expref(y), prec, rnd); } static __inline__ slong fmpr_set_round(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_special(x)) { fmpr_set(y, x); return FMPR_RESULT_EXACT; } else { return _fmpr_set_round(fmpr_manref(y), fmpr_expref(y), fmpr_manref(x), fmpr_expref(x), prec, rnd); } } static __inline__ slong fmpr_set_round_fmpz_2exp(fmpr_t y, const fmpz_t x, const fmpz_t exp, slong prec, fmpr_rnd_t rnd) { if (fmpz_is_zero(x)) { fmpr_zero(y); return FMPR_RESULT_EXACT; } else { return _fmpr_set_round(fmpr_manref(y), fmpr_expref(y), x, exp, prec, rnd); } } static __inline__ slong fmpr_set_round_fmpz(fmpr_t y, const fmpz_t x, slong prec, fmpr_rnd_t rnd) { if (fmpz_is_zero(x)) { fmpr_zero(y); return FMPR_RESULT_EXACT; } else { slong ret; fmpz_t exp; fmpz_init(exp); ret = _fmpr_set_round(fmpr_manref(y), fmpr_expref(y), x, exp, prec, rnd); fmpz_clear(exp); return ret; } } slong _fmpr_set_round_mpn(slong * shift, fmpz_t man, mp_srcptr x, mp_size_t xn, int negative, slong prec, fmpr_rnd_t rnd); slong fmpr_set_round_ui_2exp_fmpz(fmpr_t z, mp_limb_t lo, const fmpz_t exp, int negative, slong prec, fmpr_rnd_t rnd); slong fmpr_set_round_uiui_2exp_fmpz(fmpr_t z, mp_limb_t hi, mp_limb_t lo, const fmpz_t exp, int negative, slong prec, fmpr_rnd_t rnd); void fmpr_ulp(fmpr_t u, const fmpr_t x, slong prec); int fmpr_check_ulp(const fmpr_t result, slong r, slong prec); static __inline__ int fmpr_equal(const fmpr_t x, const fmpr_t y) { return fmpz_equal(fmpr_expref(x), fmpr_expref(y)) && fmpz_equal(fmpr_manref(x), fmpr_manref(y)); } static __inline__ int fmpr_sgn(const fmpr_t x) { if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) return 0; if (fmpr_is_pos_inf(x)) return 1; if (fmpr_is_neg_inf(x)) return -1; return 0; } return fmpz_sgn(fmpr_manref(x)); } int fmpr_cmp(const fmpr_t x, const fmpr_t y); int fmpr_cmpabs(const fmpr_t x, const fmpr_t y); int fmpr_cmpabs_ui(const fmpr_t x, ulong y); void fmpr_randtest(fmpr_t x, flint_rand_t state, slong bits, slong exp_bits); void fmpr_randtest_not_zero(fmpr_t x, flint_rand_t state, slong bits, slong exp_bits); void fmpr_randtest_special(fmpr_t x, flint_rand_t state, slong bits, slong exp_bits); int fmpr_get_mpfr(mpfr_t x, const fmpr_t y, mpfr_rnd_t rnd); void fmpr_set_mpfr(fmpr_t x, const mpfr_t y); double fmpr_get_d(const fmpr_t x, fmpr_rnd_t rnd); void fmpr_set_d(fmpr_t x, double v); static __inline__ void fmpr_set_ui(fmpr_t x, ulong c) { if (c == 0) { fmpr_zero(x); } else { int b; count_trailing_zeros(b, c); fmpz_set_ui(fmpr_manref(x), c >> b); fmpz_set_ui(fmpr_expref(x), b); } } static __inline__ void fmpr_set_si(fmpr_t x, slong c) { if (c == 0) { fmpr_zero(x); } else { int b; count_trailing_zeros(b, c); fmpz_set_si(fmpr_manref(x), c >> b); fmpz_set_ui(fmpr_expref(x), b); } } static __inline__ void fmpr_set_fmpz(fmpr_t x, const fmpz_t c) { if (fmpz_is_zero(c)) { fmpr_zero(x); } else { slong v = fmpz_val2(c); fmpz_tdiv_q_2exp(fmpr_manref(x), c, v); fmpz_set_ui(fmpr_expref(x), v); } } /* Arithmetic */ slong _fmpr_add_eps(fmpr_t z, const fmpr_t x, int sign, slong prec, fmpr_rnd_t rnd); slong _fmpr_add_mpn(fmpr_t z, mp_srcptr xman, mp_size_t xn, int xsign, const fmpz_t xexp, mp_srcptr yman, mp_size_t yn, int ysign, const fmpz_t yexp, slong shift, slong prec, fmpr_rnd_t rnd); static __inline__ slong _fmpr_add_1x1(fmpr_t z, mp_limb_t x, int xsign, const fmpz_t xexp, mp_limb_t y, int ysign, const fmpz_t yexp, slong shift, slong prec, slong rnd) { mp_limb_t hi, lo, t, u; int sign = ysign; t = x; u = y; (void) yexp; /* unused */ lo = u << shift; hi = (shift == 0) ? 0 : (u >> (FLINT_BITS - shift)); if (xsign == ysign) { add_ssaaaa(hi, lo, hi, lo, 0, t); } else { if (hi == 0) { if (lo >= t) { lo = lo - t; } else { lo = t - lo; sign = !sign; } } else { sub_ddmmss(hi, lo, hi, lo, 0, t); } } if (hi == 0) return fmpr_set_round_ui_2exp_fmpz(z, lo, xexp, sign, prec, rnd); else return fmpr_set_round_uiui_2exp_fmpz(z, hi, lo, xexp, sign, prec, rnd); } slong fmpr_add_naive(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong _fmpr_mul_mpn(fmpr_t z, mp_srcptr xman, mp_size_t xn, const fmpz_t xexp, mp_srcptr yman, mp_size_t yn, const fmpz_t yexp, int negative, slong prec, fmpr_rnd_t rnd); slong _fmpr_mul_1x1(fmpr_t z, mp_limb_t u, const fmpz_t xexp, mp_limb_t v, const fmpz_t yexp, int negative, slong prec, fmpr_rnd_t rnd); slong fmpr_mul_naive(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_mul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_mul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd); slong fmpr_mul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd); slong fmpr_mul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_add(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_add_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd); slong fmpr_add_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd); slong fmpr_add_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_sub(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_sub_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd); slong fmpr_sub_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd); slong fmpr_sub_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_sum(fmpr_t s, const fmpr_struct * terms, slong len, slong prec, fmpr_rnd_t rnd); slong fmpr_div(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_div_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd); slong fmpr_ui_div(fmpr_t z, ulong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_div_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd); slong fmpr_si_div(fmpr_t z, slong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_div_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_fmpz_div(fmpr_t z, const fmpz_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_fmpz_div_fmpz(fmpr_t z, const fmpz_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd); void fmpr_divappr_abs_ubound(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec); slong fmpr_addmul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_addmul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd); slong fmpr_addmul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd); slong fmpr_addmul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_submul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_submul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd); slong fmpr_submul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd); slong fmpr_submul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd); slong fmpr_sqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd); slong fmpr_sqrt_ui(fmpr_t z, ulong x, slong prec, fmpr_rnd_t rnd); slong fmpr_sqrt_fmpz(fmpr_t z, const fmpz_t x, slong prec, fmpr_rnd_t rnd); slong fmpr_rsqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd); slong fmpr_root(fmpr_t y, const fmpr_t x, ulong k, slong prec, fmpr_rnd_t rnd); slong fmpr_log(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd); slong fmpr_log1p(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd); slong fmpr_exp(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd); slong fmpr_expm1(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd); static __inline__ void fmpr_neg(fmpr_t y, const fmpr_t x) { if (fmpr_is_special(x)) { if (fmpr_is_pos_inf(x)) fmpr_neg_inf(y); else if (fmpr_is_neg_inf(x)) fmpr_pos_inf(y); else fmpr_set(y, x); } else { fmpz_neg(fmpr_manref(y), fmpr_manref(x)); fmpz_set(fmpr_expref(y), fmpr_expref(x)); } } static __inline__ slong fmpr_neg_round(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { fmpr_neg(y, x); if (fmpr_is_special(y)) return FMPR_RESULT_EXACT; else return _fmpr_normalise(fmpr_manref(y), fmpr_expref(y), prec, rnd); } static __inline__ void fmpr_abs(fmpr_t y, const fmpr_t x) { if (fmpr_sgn(x) < 0) fmpr_neg(y, x); else fmpr_set(y, x); } /* Convert return value to error bound */ static __inline__ void fmpr_set_error_result(fmpr_t err, const fmpr_t result, slong rret) { if (rret == FMPR_RESULT_EXACT) { fmpr_zero(err); } /* XXX: normally, a special value should not result from inexact arithmetic else if (fmpr_is_special(result)) { fmpr_pos_inf(err); } */ else { /* TODO: inline this */ fmpz_sub_ui(fmpr_expref(err), fmpr_expref(result), rret); fmpz_one(fmpr_manref(err)); } } static __inline__ void fmpr_add_error_result(fmpr_t err, const fmpr_t err_in, const fmpr_t result, slong rret, slong prec, fmpr_rnd_t rnd) { if (rret == FMPR_RESULT_EXACT) { fmpr_set(err, err_in); } else { fmpr_t t; fmpr_init(t); fmpr_set_error_result(t, result, rret); fmpr_add(err, err_in, t, prec, rnd); fmpr_clear(t); } } void fmpr_print(const fmpr_t x); void fmpr_printd(const fmpr_t x, slong digits); static __inline__ void fmpr_mul_2exp_si(fmpr_t y, const fmpr_t x, slong e) { if (e == 0 || fmpr_is_special(x)) { fmpr_set(y, x); } else { fmpz_set(fmpr_manref(y), fmpr_manref(x)); fmpz_add_si_inline(fmpr_expref(y), fmpr_expref(x), e); } } static __inline__ void fmpr_mul_2exp_fmpz(fmpr_t y, const fmpr_t x, const fmpz_t e) { if (e == 0 || fmpr_is_special(x)) { fmpr_set(y, x); } else { fmpz_set(fmpr_manref(y), fmpr_manref(x)); fmpz_add(fmpr_expref(y), fmpr_expref(x), e); } } void fmpr_get_fmpq(fmpq_t y, const fmpr_t x); slong fmpr_set_fmpq(fmpr_t x, const fmpq_t y, slong prec, fmpr_rnd_t rnd); void fmpr_get_fmpz(fmpz_t z, const fmpr_t x, fmpr_rnd_t rnd); slong fmpr_get_si(const fmpr_t x, fmpr_rnd_t rnd); void fmpr_set_fmpz_2exp(fmpr_t x, const fmpz_t man, const fmpz_t exp); void fmpr_get_fmpz_2exp(fmpz_t man, fmpz_t exp, const fmpr_t x); int fmpr_get_fmpz_fixed_fmpz(fmpz_t y, const fmpr_t x, const fmpz_t e); int fmpr_get_fmpz_fixed_si(fmpz_t y, const fmpr_t x, slong e); static __inline__ void fmpr_set_si_2exp_si(fmpr_t x, slong man, slong exp) { fmpr_set_si(x, man); fmpr_mul_2exp_si(x, x, exp); } static __inline__ void fmpr_set_ui_2exp_si(fmpr_t x, ulong man, slong exp) { fmpr_set_ui(x, man); fmpr_mul_2exp_si(x, x, exp); } int fmpr_cmp_2exp_si(const fmpr_t x, slong e); int fmpr_cmpabs_2exp_si(const fmpr_t x, slong e); static __inline__ void fmpr_abs_bound_le_2exp_fmpz(fmpz_t b, const fmpr_t x) { if (fmpz_is_pm1(fmpr_manref(x))) fmpz_set(b, fmpr_expref(x)); else fmpz_add_ui(b, fmpr_expref(x), fmpz_bits(fmpr_manref(x))); } static __inline__ void fmpr_abs_bound_lt_2exp_fmpz(fmpz_t b, const fmpr_t x) { fmpz_add_ui(b, fmpr_expref(x), fmpz_bits(fmpr_manref(x))); } slong fmpr_abs_bound_lt_2exp_si(const fmpr_t x); static __inline__ void fmpr_min(fmpr_t z, const fmpr_t a, const fmpr_t b) { if (fmpr_cmp(a, b) <= 0) fmpr_set(z, a); else fmpr_set(z, b); } static __inline__ void fmpr_max(fmpr_t z, const fmpr_t a, const fmpr_t b) { if (fmpr_cmp(a, b) > 0) fmpr_set(z, a); else fmpr_set(z, b); } static __inline__ slong fmpr_bits(const fmpr_t x) { if (fmpr_is_special(x)) return 0; else return fmpz_bits(fmpr_manref(x)); } static __inline__ int fmpr_is_int(const fmpr_t x) { if (fmpr_is_special(x)) return fmpr_is_zero(x); else return fmpz_sgn(fmpr_expref(x)) >= 0; } static __inline__ int fmpr_is_int_2exp_si(const fmpr_t x, slong e) { if (fmpr_is_special(x)) return fmpr_is_zero(x); else return fmpz_cmp_si(fmpr_expref(x), e) >= 0; } #define CALL_MPFR_FUNC(r, func, y, x, prec, rnd) \ do { \ mpfr_t __t, __u; \ mpfr_rnd_t __rnd; \ __rnd = rnd_to_mpfr(rnd); \ mpfr_init2(__t, 2 + fmpz_bits(fmpr_manref(x))); \ mpfr_init2(__u, FLINT_MAX(2, prec)); \ mpfr_set_emin(MPFR_EMIN_MIN); \ mpfr_set_emax(MPFR_EMAX_MAX); \ fmpr_get_mpfr(__t, x, MPFR_RNDD); \ r = func(__u, __t, __rnd); \ if (mpfr_overflow_p() || mpfr_underflow_p()) \ { \ flint_printf("exception: mpfr overflow\n"); \ abort(); \ } \ fmpr_set_mpfr(y, __u); \ if (r == 0) \ r = FMPR_RESULT_EXACT; \ else \ r = prec - fmpz_bits(fmpr_manref(y)); \ mpfr_clear(__t); \ mpfr_clear(__u); \ } while (0); #define CALL_MPFR_FUNC_K(r, func, y, x, k, prec, rnd) \ do { \ mpfr_t __t, __u; \ mpfr_rnd_t __rnd; \ __rnd = rnd_to_mpfr(rnd); \ mpfr_init2(__t, 2 + fmpz_bits(fmpr_manref(x))); \ mpfr_init2(__u, FLINT_MAX(2, prec)); \ mpfr_set_emin(MPFR_EMIN_MIN); \ mpfr_set_emax(MPFR_EMAX_MAX); \ fmpr_get_mpfr(__t, x, MPFR_RNDD); \ r = func(__u, __t, k, __rnd); \ if (mpfr_overflow_p() || mpfr_underflow_p()) \ { \ flint_printf("exception: mpfr overflow\n"); \ abort(); \ } \ fmpr_set_mpfr(y, __u); \ if (r == 0) \ r = FMPR_RESULT_EXACT; \ else \ r = prec - fmpz_bits(fmpr_manref(y)); \ mpfr_clear(__t); \ mpfr_clear(__u); \ } while (0); #define CALL_MPFR_FUNC_2X1(r1, r2, func, y1, y2, x, prec, rnd) \ do { \ mpfr_t __t, __u, __v; \ mpfr_rnd_t __rnd; \ __rnd = rnd_to_mpfr(rnd); \ mpfr_init2(__t, 2 + fmpz_bits(fmpr_manref(x))); \ mpfr_init2(__u, FLINT_MAX(2, prec)); \ mpfr_init2(__v, FLINT_MAX(2, prec)); \ mpfr_set_emin(MPFR_EMIN_MIN); \ mpfr_set_emax(MPFR_EMAX_MAX); \ fmpr_get_mpfr(__t, x, MPFR_RNDD); \ func(__u, __v, __t, __rnd); \ if (mpfr_overflow_p() || mpfr_underflow_p()) \ { \ flint_printf("exception: mpfr overflow\n"); \ abort(); \ } \ fmpr_set_mpfr(y1, __u); \ r1 = prec - fmpz_bits(fmpr_manref(y1)); \ fmpr_set_mpfr(y2, __v); \ r2 = prec - fmpz_bits(fmpr_manref(y2)); \ mpfr_clear(__t); \ mpfr_clear(__u); \ mpfr_clear(__v); \ } while (0); void fmpr_pow_sloppy_fmpz(fmpr_t y, const fmpr_t b, const fmpz_t e, slong prec, fmpr_rnd_t rnd); void fmpr_pow_sloppy_ui(fmpr_t y, const fmpr_t b, ulong e, slong prec, fmpr_rnd_t rnd); void fmpr_pow_sloppy_si(fmpr_t y, const fmpr_t b, slong e, slong prec, fmpr_rnd_t rnd); /* vector functions */ static __inline__ fmpr_ptr _fmpr_vec_init(slong n) { slong i; fmpr_ptr v = (fmpr_ptr) flint_malloc(sizeof(fmpr_struct) * n); for (i = 0; i < n; i++) fmpr_init(v + i); return v; } static __inline__ void _fmpr_vec_clear(fmpr_ptr v, slong n) { slong i; for (i = 0; i < n; i++) fmpr_clear(v + i); flint_free(v); } #ifdef __cplusplus } #endif #endif arb-2.8.1/fmpr/000077500000000000000000000000001264125401100132265ustar00rootroot00000000000000arb-2.8.1/fmpr/abs_bound_lt_2exp_si.c000066400000000000000000000033571264125401100174660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_abs_bound_lt_2exp_si(const fmpr_t x) { if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) return -FMPR_PREC_EXACT; else return FMPR_PREC_EXACT; } else { slong res; fmpz_t t; fmpz_init(t); fmpr_abs_bound_lt_2exp_fmpz(t, x); if (fmpz_fits_si(t)) res = fmpz_get_si(t); else res = fmpz_sgn(t) < 0 ? -FMPR_PREC_EXACT : FMPR_PREC_EXACT; fmpz_clear(t); if (res < -FMPR_PREC_EXACT) res = -FMPR_PREC_EXACT; if (res > FMPR_PREC_EXACT) res = FMPR_PREC_EXACT; return res; } } arb-2.8.1/fmpr/add.c000066400000000000000000000057441264125401100141340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static slong _fmpr_add_special(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_zero(x)) { if (fmpr_is_zero(y)) { fmpr_zero(z); return FMPR_RESULT_EXACT; } else return fmpr_set_round(z, y, prec, rnd); } else if (fmpr_is_zero(y)) { return fmpr_set_round(z, x, prec, rnd); } else if (fmpr_is_nan(x) || fmpr_is_nan(y) || (fmpr_is_pos_inf(x) && fmpr_is_neg_inf(y)) || (fmpr_is_neg_inf(x) && fmpr_is_pos_inf(y))) { fmpr_nan(z); return FMPR_RESULT_EXACT; } else if (fmpr_is_special(x)) { fmpr_set(z, x); return FMPR_RESULT_EXACT; } else { fmpr_set(z, y); return FMPR_RESULT_EXACT; } } slong fmpr_add(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { slong shift, xn, yn; mp_limb_t xtmp, ytmp; mp_ptr xptr, yptr; fmpz xv, yv; const fmpz * xexp; const fmpz * yexp; int xsign, ysign; if (fmpr_is_special(x) || fmpr_is_special(y)) { return _fmpr_add_special(z, x, y, prec, rnd); } shift = _fmpz_sub_small(fmpr_expref(y), fmpr_expref(x)); if (shift >= 0) { xexp = fmpr_expref(x); yexp = fmpr_expref(y); xv = *fmpr_manref(x); yv = *fmpr_manref(y); } else { xexp = fmpr_expref(y); yexp = fmpr_expref(x); xv = *fmpr_manref(y); yv = *fmpr_manref(x); shift = -shift; } FMPZ_GET_MPN_READONLY(xsign, xn, xptr, xtmp, xv) FMPZ_GET_MPN_READONLY(ysign, yn, yptr, ytmp, yv) if ((xn == 1) && (yn == 1) && (shift < FLINT_BITS)) return _fmpr_add_1x1(z, xptr[0], xsign, xexp, yptr[0], ysign, yexp, shift, prec, rnd); else return _fmpr_add_mpn(z, xptr, xn, xsign, xexp, yptr, yn, ysign, yexp, shift, prec, rnd); } arb-2.8.1/fmpr/add_eps.c000066400000000000000000000041131264125401100147700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong _fmpr_add_eps(fmpr_t z, const fmpr_t x, int sign, slong prec, fmpr_rnd_t rnd) { slong bits, shift; int xsign; xsign = fmpz_sgn(fmpr_manref(x)); if ((rnd == FMPR_RND_DOWN && xsign != sign) || (rnd == FMPR_RND_UP && xsign == sign) || (rnd == FMPR_RND_FLOOR && sign < 0) || (rnd == FMPR_RND_CEIL && sign > 0)) { bits = fmpz_bits(fmpr_manref(x)); shift = 2 + FLINT_MAX(0, prec - bits); fmpz_mul_2exp(fmpr_manref(z), fmpr_manref(x), shift); fmpz_sub_ui(fmpr_expref(z), fmpr_expref(x), shift); if (sign > 0) fmpz_add_ui(fmpr_manref(z), fmpr_manref(z), 1); else fmpz_sub_ui(fmpr_manref(z), fmpr_manref(z), 1); return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd); } else { slong ret = fmpr_set_round(z, x, prec, rnd); if (ret == FMPR_RESULT_EXACT) return prec - fmpz_bits(fmpr_manref(z)); else return ret; } } arb-2.8.1/fmpr/add_fmpz.c000066400000000000000000000024731264125401100151640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_add_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, y); r = fmpr_add(z, x, t, prec, rnd); fmpr_clear(t); return r; } arb-2.8.1/fmpr/add_mpn.c000066400000000000000000000253731264125401100150060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" #define ADD_STACK_ALLOC 40 #define ADD_TLS_ALLOC 1000 TLS_PREFIX mp_ptr __add_tmp = NULL; TLS_PREFIX slong __add_alloc = 0; void _add_tmp_cleanup(void) { flint_free(__add_tmp); __add_tmp = NULL; __add_alloc = 0; } #define ADD_TMP_ALLOC \ if (alloc <= ADD_STACK_ALLOC) \ { \ tmp = tmp_stack; \ } \ else if (alloc <= ADD_TLS_ALLOC) \ { \ if (__add_alloc < alloc) \ { \ if (__add_alloc == 0) \ { \ flint_register_cleanup_function(_add_tmp_cleanup); \ } \ __add_tmp = flint_realloc(__add_tmp, sizeof(mp_limb_t) * alloc); \ __add_alloc = alloc; \ } \ tmp = __add_tmp; \ } \ else \ { \ tmp = flint_malloc(sizeof(mp_limb_t) * alloc); \ } #define ADD_TMP_FREE \ if (alloc > ADD_TLS_ALLOC) \ flint_free(tmp); /* computes x + y * 2^shift (optionally negated) */ slong _fmpr_add_mpn(fmpr_t z, mp_srcptr xman, mp_size_t xn, int xsign, const fmpz_t xexp, mp_srcptr yman, mp_size_t yn, int ysign, const fmpz_t yexp, slong shift, slong prec, fmpr_rnd_t rnd) { slong tn, zn, alloc, ret, shift_bits, shift_limbs; int negative; mp_limb_t tmp_stack[ADD_STACK_ALLOC]; mp_limb_t cy; mp_ptr tmp, tmp2; shift_limbs = shift / FLINT_BITS; shift_bits = shift % FLINT_BITS; /* x does not overlap with y or the result -- outcome is equivalent to adding/subtracting a small number to/from y and rounding */ if (shift > xn * FLINT_BITS && prec != FMPR_PREC_EXACT && xn * FLINT_BITS + prec - (FLINT_BITS * (yn - 1)) < shift) { zn = (prec + FLINT_BITS - 1) / FLINT_BITS; zn = FLINT_MAX(zn, yn) + 2; shift_limbs = zn - yn; alloc = zn; ADD_TMP_ALLOC flint_mpn_zero(tmp, shift_limbs); flint_mpn_copyi(tmp + shift_limbs, yman, yn); if (xsign == ysign) { tmp[0] = 1; } else { mpn_sub_1(tmp, tmp, zn, 1); while (tmp[zn-1] == 0) zn--; } ret = _fmpr_set_round_mpn(&shift, fmpr_manref(z), tmp, zn, ysign, prec, rnd); shift -= shift_limbs * FLINT_BITS; fmpz_add_si_inline(fmpr_expref(z), yexp, shift); ADD_TMP_FREE return ret; } if (xsign == ysign) { negative = xsign; /* certainly no overlap between x and y * 2^shift XXXXX YYYYY |-------| shift_limbs todo: handle huge case efficiently! */ if (shift_limbs >= xn) { alloc = shift_limbs + yn + 1; ADD_TMP_ALLOC flint_mpn_copyi(tmp, xman, xn); flint_mpn_zero(tmp + xn, shift_limbs - xn); if (shift_bits == 0) { flint_mpn_copyi(tmp + shift_limbs, yman, yn); zn = shift_limbs + yn; } else { cy = mpn_lshift(tmp + shift_limbs, yman, yn, shift_bits); tmp[shift_limbs + yn] = cy; zn = shift_limbs + yn + (cy != 0); } } else /* may have overlap between x and y * 2^shift */ { slong alloc1, alloc2; alloc2 = yn + 1; /* shifted value of y */ alloc1 = FLINT_MAX(alloc2 + shift_limbs, xn) + 1; /* space for sum */ alloc = alloc1 + alloc2; ADD_TMP_ALLOC tmp2 = tmp + alloc1; flint_mpn_copyi(tmp, xman, shift_limbs); /* {t, tn} = shift of y (ignoring shift_limbs zero limbs) */ if (shift_bits == 0) { flint_mpn_copyi(tmp2, yman, yn); tn = yn; } else { cy = mpn_lshift(tmp2, yman, yn, shift_bits); tmp2[yn] = cy; tn = yn + (cy != 0); } if (tn + shift_limbs == xn) { /* XXXXXXXX TTTTT */ cy = mpn_add_n(tmp + shift_limbs, xman + shift_limbs, tmp2, tn); tmp[xn] = cy; zn = xn + (cy != 0); } else if (tn + shift_limbs < xn) { /* XXXXXXXX TTTTT */ cy = mpn_add_n(tmp + shift_limbs, xman + shift_limbs, tmp2, tn); cy = mpn_add_1(tmp + shift_limbs + tn, xman + shift_limbs + tn, xn - tn - shift_limbs, cy); tmp[xn] = cy; zn = xn + (cy != 0); } else { /* XXXXXXXX TTTTTTT */ cy = mpn_add_n(tmp + shift_limbs, xman + shift_limbs, tmp2, xn - shift_limbs); cy = mpn_add_1(tmp + xn, tmp2 + xn - shift_limbs, tn + shift_limbs - xn, cy); tmp[tn + shift_limbs] = cy; zn = tn + shift_limbs + (cy != 0); } } } else { /* certainly no overlap between x and y * 2^shift XXXXX YYYYY |-------| shift_limbs todo: handle huge case efficiently! */ if (shift_limbs >= xn) { alloc = shift_limbs + yn + 1; ADD_TMP_ALLOC mpn_neg_n(tmp, xman, xn); /* since x is nonzero, there is certainly carry (borrow) */ flint_mpn_store(tmp + xn, shift_limbs - xn, (mp_limb_t) -1); if (shift_bits == 0) { flint_mpn_copyi(tmp + shift_limbs, yman, yn); zn = shift_limbs + yn; } else { cy = mpn_lshift(tmp + shift_limbs, yman, yn, shift_bits); tmp[shift_limbs + yn] = cy; zn = shift_limbs + yn + (cy != 0); } mpn_sub_1(tmp + shift_limbs, tmp + shift_limbs, zn - shift_limbs, 1); /* y has larger absolute value, and determines the sign */ negative = ysign; } else /* may have overlap between x and y * 2^shift */ { slong alloc1, alloc2; alloc2 = yn + 1; /* shifted value of y */ alloc1 = FLINT_MAX(alloc2 + shift_limbs, xn); /* space for difference */ alloc = alloc1 + alloc2; ADD_TMP_ALLOC tmp2 = tmp + alloc1; /* {t, tn} = shift of y (ignoring shift_limbs zero limbs) */ if (shift_bits == 0) { flint_mpn_copyi(tmp2, yman, yn); tn = yn; } else { cy = mpn_lshift(tmp2, yman, yn, shift_bits); tmp2[yn] = cy; tn = yn + (cy != 0); } if (tn + shift_limbs == xn) { int comp; /* XXXXXXXX TTTTT */ comp = mpn_cmp(xman + shift_limbs, tmp2, tn); if (comp == 0) { slong i; for (i = 0; i < shift_limbs; i++) { if (xman[i] != 0) { comp = 1; break; } } /* the result is exactly zero */ if (comp == 0) { fmpr_zero(z); ret = FMPR_RESULT_EXACT; goto cleanup; } } /* x is larger */ if (comp > 0) { flint_mpn_copyi(tmp, xman, shift_limbs); mpn_sub_n(tmp + shift_limbs, xman + shift_limbs, tmp2, tn); negative = xsign; } else { mpn_sub_n(tmp + shift_limbs, tmp2, xman + shift_limbs, tn); if (shift_limbs != 0) { cy = mpn_neg_n(tmp, xman, shift_limbs); mpn_sub_1(tmp + shift_limbs, tmp + shift_limbs, tn, cy); } negative = ysign; } zn = xn; } else if (tn + shift_limbs < xn) { /* XXXXXXXX TTTTT */ flint_mpn_copyi(tmp, xman, shift_limbs); cy = mpn_sub_n(tmp + shift_limbs, xman + shift_limbs, tmp2, tn); mpn_sub_1(tmp + shift_limbs + tn, xman + shift_limbs + tn, xn - tn - shift_limbs, cy); zn = xn; negative = xsign; } else { /* XXXXXXXX TTTTTTT */ cy = mpn_sub_n(tmp + shift_limbs, tmp2, xman + shift_limbs, xn - shift_limbs); mpn_sub_1(tmp + xn, tmp2 + xn - shift_limbs, tn + shift_limbs - xn, cy); if (shift_limbs != 0) { cy = mpn_neg_n(tmp, xman, shift_limbs); mpn_sub_1(tmp + shift_limbs, tmp + shift_limbs, tn, cy); } zn = shift_limbs + tn; negative = ysign; } } /* there might have been cancellation */ while (tmp[zn-1] == 0) zn--; } ret = _fmpr_set_round_mpn(&shift, fmpr_manref(z), tmp, zn, negative, prec, rnd); fmpz_add_si_inline(fmpr_expref(z), xexp, shift); cleanup: ADD_TMP_FREE return ret; } arb-2.8.1/fmpr/add_naive.c000066400000000000000000000070151264125401100153070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static slong _fmpr_add_special(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_zero(x)) { if (fmpr_is_zero(y)) { fmpr_zero(z); return FMPR_RESULT_EXACT; } else return fmpr_set_round(z, y, prec, rnd); } else if (fmpr_is_zero(y)) { return fmpr_set_round(z, x, prec, rnd); } else if (fmpr_is_nan(x) || fmpr_is_nan(y) || (fmpr_is_pos_inf(x) && fmpr_is_neg_inf(y)) || (fmpr_is_neg_inf(x) && fmpr_is_pos_inf(y))) { fmpr_nan(z); return FMPR_RESULT_EXACT; } else if (fmpr_is_special(x)) { fmpr_set(z, x); return FMPR_RESULT_EXACT; } else { fmpr_set(z, y); return FMPR_RESULT_EXACT; } } slong fmpr_add_naive(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { slong shift, xsize, ysize; if (fmpr_is_special(x) || fmpr_is_special(y)) { return _fmpr_add_special(z, x, y, prec, rnd); } shift = _fmpz_sub_small(fmpr_expref(x), fmpr_expref(y)); if (shift == 0) { fmpz_add(fmpr_manref(z), fmpr_manref(x), fmpr_manref(y)); fmpz_set(fmpr_expref(z), fmpr_expref(x)); } else if (shift > 0) { ysize = _fmpz_size(fmpr_manref(y)) * FLINT_BITS; /* x and y do not overlap */ if (shift > ysize && prec != FMPR_PREC_EXACT) { /* y does not overlap with result */ if (ysize + prec - (slong) fmpz_bits(fmpr_manref(x)) < shift) { return _fmpr_add_eps(z, x, fmpz_sgn(fmpr_manref(y)), prec, rnd); } } fmpz_add_mul2exp(fmpr_manref(z), fmpr_manref(y), fmpr_manref(x), shift); fmpz_set(fmpr_expref(z), fmpr_expref(y)); } else { shift = -shift; xsize = _fmpz_size(fmpr_manref(x)) * FLINT_BITS; /* x and y do not overlap */ if (shift > xsize && prec != FMPR_PREC_EXACT) { /* y does not overlap with result */ if (xsize + prec - (slong) fmpz_bits(fmpr_manref(y)) < shift) { return _fmpr_add_eps(z, y, fmpz_sgn(fmpr_manref(x)), prec, rnd); } } fmpz_add_mul2exp(fmpr_manref(z), fmpr_manref(x), fmpr_manref(y), shift); fmpz_set(fmpr_expref(z), fmpr_expref(x)); } return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd); } arb-2.8.1/fmpr/add_si.c000066400000000000000000000024601264125401100146170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_add_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_si(t, y); r = fmpr_add(z, x, t, prec, rnd); fmpr_clear(t); return r; } arb-2.8.1/fmpr/add_ui.c000066400000000000000000000024601264125401100146210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_add_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, y); r = fmpr_add(z, x, t, prec, rnd); fmpr_clear(t); return r; } arb-2.8.1/fmpr/addmul.c000066400000000000000000000040161264125401100146410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_addmul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_mul(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); r = fmpr_add(z, z, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_addmul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, y); r = fmpr_addmul(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_addmul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_si(t, y); r = fmpr_addmul(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_addmul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, y); r = fmpr_addmul(z, x, t, prec, rnd); fmpr_clear(t); return r; } arb-2.8.1/fmpr/check_ulp.c000066400000000000000000000030221264125401100153240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int fmpr_check_ulp(const fmpr_t result, slong r, slong prec) { if (r == FMPR_RESULT_EXACT) { return 1; } else { fmpr_t err; fmpr_t ulp; int ok; fmpr_init(err); fmpr_init(ulp); fmpr_ulp(ulp, result, prec); fmpr_set_error_result(err, result, r); ok = fmpr_equal(err, ulp); fmpr_clear(err); fmpr_clear(ulp); return ok; } } arb-2.8.1/fmpr/cmp.c000066400000000000000000000040341264125401100141520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int fmpr_cmp(const fmpr_t x, const fmpr_t y) { int res, xsign, ysign; fmpr_t t; if (fmpr_equal(x, y)) return 0; if (fmpr_is_special(x) || fmpr_is_special(y)) { if (fmpr_is_nan(x) || fmpr_is_nan(y)) return 0; if (fmpr_is_zero(y)) return fmpr_sgn(x); if (fmpr_is_zero(x)) return -fmpr_sgn(y); if (fmpr_is_pos_inf(x)) return 1; if (fmpr_is_neg_inf(y)) return 1; return -1; } xsign = fmpr_sgn(x); ysign = fmpr_sgn(y); if (xsign != ysign) return (xsign < 0) ? -1 : 1; /* Reduces to integer comparison if bottom exponents are the same */ if (fmpz_equal(fmpr_expref(x), fmpr_expref(y))) return fmpz_cmp(fmpr_manref(x), fmpr_manref(y)) < 0 ? -1 : 1; /* TODO: compare position of top exponents to avoid subtraction */ fmpr_init(t); fmpr_sub(t, x, y, 2, FMPR_RND_DOWN); res = fmpr_sgn(t); fmpr_clear(t); return res; } arb-2.8.1/fmpr/cmp_2exp_si.c000066400000000000000000000034731264125401100156110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static __inline__ int sgn(int x) { return (x > 0) - (x < 0); } int fmpr_cmp_2exp_si(const fmpr_t x, slong e) { slong bc; int ret; fmpz_t t; if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) return -1; if (fmpr_is_pos_inf(x)) return 1; if (fmpr_is_neg_inf(x)) return -1; if (fmpr_is_nan(x)) return 0; return -1; } if (fmpz_is_one(fmpr_manref(x))) return sgn(fmpz_cmp_si(fmpr_expref(x), e)); if (fmpz_sgn(fmpr_manref(x)) < 0) return -1; bc = fmpz_bits(fmpr_manref(x)); fmpz_init(t); fmpz_add_si_inline(t, fmpr_expref(x), bc); fmpz_sub_si_inline(t, t, e); ret = (fmpz_sgn(t) <= 0) ? -1 : 1; fmpz_clear(t); return ret; } arb-2.8.1/fmpr/cmpabs.c000066400000000000000000000042541264125401100146440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int fmpr_cmpabs(const fmpr_t x, const fmpr_t y) { int res, xsign, ysign; fmpr_t t; if (fmpr_equal(x, y)) return 0; if (fmpr_is_special(x) || fmpr_is_special(y)) { if (fmpr_is_nan(x) || fmpr_is_nan(y)) return 0; if (fmpr_is_zero(x)) return -1; if (fmpr_is_zero(y)) return 1; if (fmpr_is_inf(x)) return fmpr_is_inf(y) ? 0 : 1; if (fmpr_is_inf(y)) return -1; return -1; } /* Reduces to integer comparison if bottom exponents are the same */ if (fmpz_equal(fmpr_expref(x), fmpr_expref(y))) { res = fmpz_cmpabs(fmpr_manref(x), fmpr_manref(y)); if (res != 0) res = (res < 0) ? -1 : 1; } else { /* TODO: compare position of top exponents to avoid subtraction */ xsign = fmpr_sgn(x); ysign = fmpr_sgn(y); fmpr_init(t); if (xsign == ysign) fmpr_sub(t, x, y, 2, FMPR_RND_DOWN); else fmpr_add(t, x, y, 2, FMPR_RND_DOWN); res = fmpr_sgn(t) * xsign; fmpr_clear(t); } return res; } arb-2.8.1/fmpr/cmpabs_2exp_si.c000066400000000000000000000033251264125401100162730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static __inline__ int sgn(int x) { return (x > 0) - (x < 0); } int fmpr_cmpabs_2exp_si(const fmpr_t x, slong e) { slong bc; int ret; fmpz_t t; if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) return -1; if (fmpr_is_inf(x)) return 1; if (fmpr_is_nan(x)) return 0; return -1; } if (fmpz_is_pm1(fmpr_manref(x))) return sgn(fmpz_cmp_si(fmpr_expref(x), e)); bc = fmpz_bits(fmpr_manref(x)); fmpz_init(t); fmpz_add_si_inline(t, fmpr_expref(x), bc); fmpz_sub_si_inline(t, t, e); ret = (fmpz_sgn(t) <= 0) ? -1 : 1; fmpz_clear(t); return ret; } arb-2.8.1/fmpr/cmpabs_ui.c000066400000000000000000000024101264125401100153310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int fmpr_cmpabs_ui(const fmpr_t x, ulong y) { fmpr_t t; int res; fmpr_init(t); fmpr_set_ui(t, y); res = fmpr_cmpabs(x, t); fmpr_clear(t); return res; } arb-2.8.1/fmpr/div.c000066400000000000000000000125011264125401100141530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static void _fmpr_div_special(fmpr_t z, const fmpr_t x, const fmpr_t y) { if ((fmpr_is_zero(x) && !fmpr_is_zero(y) && !fmpr_is_nan(y)) || (fmpr_is_inf(y) && !fmpr_is_special(x))) { fmpr_zero(z); } else if (fmpr_is_zero(y) || (fmpr_is_special(x) && fmpr_is_special(y)) || fmpr_is_nan(x) || fmpr_is_nan(y)) { fmpr_nan(z); } else if (fmpr_sgn(x) == fmpr_sgn(y)) fmpr_pos_inf(z); else fmpr_neg_inf(z); } static __inline__ int low_bits_are_zero(const fmpz_t u, int bits) { fmpz f = *u; mp_limb_t low; if (!COEFF_IS_MPZ(f)) low = FLINT_ABS(f); else low = COEFF_TO_PTR(f)->_mp_d[0]; return (low & ((UWORD(1) << bits) - 1)) == 0; } slong fmpr_div(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_special(x) || fmpr_is_special(y)) { _fmpr_div_special(z, x, y); return FMPR_RESULT_EXACT; } /* division by power of two <=> shift exponents */ if (fmpz_is_pm1(fmpr_manref(y))) { if (fmpz_is_one(fmpr_manref(y))) fmpz_set(fmpr_manref(z), fmpr_manref(x)); else fmpz_neg(fmpr_manref(z), fmpr_manref(x)); fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y)); return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd); } else { slong xbits, ybits, extra, extra_pad, extra_control; int negative; fmpz_t t, u; /* todo: work out exact needed shift */ xbits = fmpz_bits(fmpr_manref(x)); ybits = fmpz_bits(fmpr_manref(y)); extra = prec - xbits + ybits; extra = FLINT_MAX(extra, 0); extra_pad = 32; extra_control = 24; extra += extra_pad; fmpz_init(t); fmpz_init(u); fmpz_mul_2exp(t, fmpr_manref(x), extra); fmpz_tdiv_q(u, t, fmpr_manref(y)); if (low_bits_are_zero(u, extra_control)) { fmpz_t v; fmpz_init(v); fmpz_mul(v, u, fmpr_manref(y)); negative = fmpz_sgn(fmpr_manref(x)) != fmpz_sgn(fmpr_manref(y)); if (!fmpz_equal(t, v)) { if (negative) fmpz_sub_ui(u, u, 1); else fmpz_add_ui(u, u, 1); } fmpz_clear(v); } fmpz_swap(fmpr_manref(z), u); fmpz_clear(t); fmpz_clear(u); fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y)); fmpz_sub_ui(fmpr_expref(z), fmpr_expref(z), extra); return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd); } } slong fmpr_div_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, y); r = fmpr_div(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_ui_div(fmpr_t z, ulong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, x); r = fmpr_div(z, t, y, prec, rnd); fmpr_clear(t); return r; } slong fmpr_div_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_si(t, y); r = fmpr_div(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_si_div(fmpr_t z, slong x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_si(t, x); r = fmpr_div(z, t, y, prec, rnd); fmpr_clear(t); return r; } slong fmpr_div_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, y); r = fmpr_div(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_fmpz_div(fmpr_t z, const fmpz_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, x); r = fmpr_div(z, t, y, prec, rnd); fmpr_clear(t); return r; } slong fmpr_fmpz_div_fmpz(fmpr_t z, const fmpz_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t, u; slong r; fmpr_init(t); fmpr_init(u); fmpr_set_fmpz(t, x); fmpr_set_fmpz(u, y); r = fmpr_div(z, t, u, prec, rnd); fmpr_clear(t); fmpr_clear(u); return r; } arb-2.8.1/fmpr/divappr_abs_ubound.c000066400000000000000000000053331264125401100172440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_divappr_abs_ubound(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec) { if (fmpr_is_special(x) || fmpr_is_special(y) || fmpz_is_pm1(fmpr_manref(y))) { fmpr_div(z, x, y, prec, FMPR_RND_UP); fmpr_abs(z, z); } else { fmpz_t t, u; slong xbits, ybits, tbits, ubits, shift; xbits = fmpz_bits(fmpr_manref(x)); ybits = fmpz_bits(fmpr_manref(y)); fmpz_init(t); fmpz_init(u); ubits = FLINT_MIN(ybits, prec); tbits = prec + ubits + 1; /* upper bound for |x|, shifted */ if (xbits <= tbits) { fmpz_mul_2exp(t, fmpr_manref(x), tbits - xbits); fmpz_abs(t, t); } else if (fmpz_sgn(fmpr_manref(x)) > 0) { fmpz_cdiv_q_2exp(t, fmpr_manref(x), xbits - tbits); } else { fmpz_fdiv_q_2exp(t, fmpr_manref(x), xbits - tbits); fmpz_neg(t, t); } /* lower bound for |y|, shifted */ if (ybits <= ubits) fmpz_mul_2exp(u, fmpr_manref(y), ubits - ybits); else fmpz_tdiv_q_2exp(u, fmpr_manref(y), ybits - ubits); fmpz_abs(u, u); fmpz_cdiv_q(fmpr_manref(z), t, u); shift = (ubits - ybits) - (tbits - xbits); fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y)); if (shift >= 0) fmpz_add_ui(fmpr_expref(z), fmpr_expref(z), shift); else fmpz_sub_ui(fmpr_expref(z), fmpr_expref(z), -shift); _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, FMPR_RND_UP); fmpz_clear(t); fmpz_clear(u); } } arb-2.8.1/fmpr/exp.c000066400000000000000000000040431264125401100141670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_exp(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) fmpr_one(y); else if (fmpr_is_pos_inf(x)) fmpr_pos_inf(y); else if (fmpr_is_neg_inf(x)) fmpr_zero(y); else fmpr_nan(y); return FMPR_RESULT_EXACT; } else { slong r; CALL_MPFR_FUNC(r, mpfr_exp, y, x, prec, rnd); return r; } } slong fmpr_expm1(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) fmpr_zero(y); else if (fmpr_is_pos_inf(x)) fmpr_pos_inf(y); else if (fmpr_is_neg_inf(x)) fmpr_set_si(y, -WORD(1)); else fmpr_nan(y); return FMPR_RESULT_EXACT; } else { slong r; CALL_MPFR_FUNC(r, mpfr_expm1, y, x, prec, rnd); return r; } } arb-2.8.1/fmpr/get_d.c000066400000000000000000000027051264125401100144600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" double fmpr_get_d(const fmpr_t x, fmpr_rnd_t rnd) { double r; mpfr_rnd_t mrnd; mpfr_t t; mp_limb_t tmp[2]; if (fmpr_is_zero(x)) return 0.0; mrnd = rnd_to_mpfr(rnd); t->_mpfr_prec = 53; t->_mpfr_sign = 1; t->_mpfr_exp = 0; t->_mpfr_d = tmp; fmpr_get_mpfr(t, x, mrnd); r = mpfr_get_d(t, mrnd); return r; } arb-2.8.1/fmpr/get_fmpq.c000066400000000000000000000033331264125401100151760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_get_fmpq(fmpq_t y, const fmpr_t x) { if (fmpr_is_zero(x)) { fmpq_zero(y); } else if (fmpr_is_special(x) || COEFF_IS_MPZ(*fmpr_expref(x))) { flint_printf("exception: fmpr_get_fmpq: cannot convert to rational\n"); abort(); } else { slong exp = *fmpr_expref(x); fmpz_set_ui(fmpq_denref(y), UWORD(1)); if (exp >= 0) { fmpz_mul_2exp(fmpq_numref(y), fmpr_manref(x), exp); } else { fmpz_set(fmpq_numref(y), fmpr_manref(x)); fmpz_mul_2exp(fmpq_denref(y), fmpq_denref(y), -exp); } } } arb-2.8.1/fmpr/get_fmpz.c000066400000000000000000000067641264125401100152220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_get_fmpz(fmpz_t z, const fmpr_t x, fmpr_rnd_t rnd) { slong exp; if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) { fmpz_zero(z); } else { flint_printf("fmpr_get_fmpz: cannot convert infinity or nan to integer\n"); abort(); } } if (!COEFF_IS_MPZ(*fmpr_expref(x))) { exp = *fmpr_expref(x); } else { /* tiny */ if (fmpz_sgn(fmpr_expref(x)) < 0) { int sign = fmpz_sgn(fmpr_manref(x)); if (rnd == FMPR_RND_NEAR || rnd == FMPR_RND_DOWN || (rnd == FMPR_RND_FLOOR && sign > 0) || (rnd == FMPR_RND_CEIL && sign < 0)) fmpz_zero(z); else fmpz_set_si(z, sign); return; } else { flint_printf("fmpr_get_fmpz: number too large to convert to integer\n"); abort(); } } if (exp >= 0) { fmpz_mul_2exp(z, fmpr_manref(x), exp); } else { exp = -exp; if (rnd == FMPR_RND_NEAR) { int sign = fmpz_sgn(fmpr_manref(x)); /* half-integer -> tie, so round to even */ if (exp == 1) { fmpz_tdiv_q_2exp(z, fmpr_manref(x), 1); if (fmpz_is_odd(z)) { if (sign > 0) fmpz_add_ui(z, z, 1); else fmpz_sub_ui(z, z, 1); } } else if (fmpz_bits(fmpr_manref(x)) < exp) /* < 0.5 */ { fmpz_zero(z); } else { /* add 1/2 and round to floor */ fmpz_t t; fmpz_init(t); fmpz_one(t); fmpz_mul_2exp(t, t, exp - 1); fmpz_add(t, t, fmpr_manref(x)); fmpz_fdiv_q_2exp(z, t, exp); fmpz_clear(t); } } else if (rnd == FMPR_RND_DOWN) fmpz_tdiv_q_2exp(z, fmpr_manref(x), exp); else if (rnd == FMPR_RND_UP) fmpz_adiv_q_2exp(z, fmpr_manref(x), exp); else if (rnd == FMPR_RND_FLOOR) fmpz_fdiv_q_2exp(z, fmpr_manref(x), exp); else if (rnd == FMPR_RND_CEIL) fmpz_cdiv_q_2exp(z, fmpr_manref(x), exp); } } arb-2.8.1/fmpr/get_fmpz_2exp.c000066400000000000000000000025171264125401100161500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_get_fmpz_2exp(fmpz_t man, fmpz_t exp, const fmpr_t x) { if (fmpr_is_zero(x)) { fmpz_zero(man); fmpz_zero(exp); } else { fmpz_set(man, fmpr_manref(x)); fmpz_set(exp, fmpr_expref(x)); } } arb-2.8.1/fmpr/get_fmpz_fixed.c000066400000000000000000000033261264125401100163700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int fmpr_get_fmpz_fixed_fmpz(fmpz_t y, const fmpr_t x, const fmpz_t exp) { slong shift; if (fmpr_is_zero(x)) { fmpz_zero(y); return 0; } shift = _fmpz_sub_small(fmpr_expref(x), exp); if (shift >= 0) { fmpz_mul_2exp(y, fmpr_manref(x), shift); return 0; } else { fmpz_tdiv_q_2exp(y, fmpr_manref(x), -shift); return 1; } } int fmpr_get_fmpz_fixed_si(fmpz_t y, const fmpr_t x, slong exp) { int result; fmpz_t t; fmpz_init(t); fmpz_set_si(t, exp); result = fmpr_get_fmpz_fixed_fmpz(y, x, t); fmpz_clear(t); return result; } arb-2.8.1/fmpr/get_mpfr.c000066400000000000000000000040721264125401100152000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int fmpr_get_mpfr(mpfr_t x, const fmpr_t y, mpfr_rnd_t rnd) { int r; if (fmpr_is_special(y)) { if (fmpr_is_zero(y)) mpfr_set_zero(x, 0); else if (fmpr_is_pos_inf(y)) mpfr_set_inf(x, 1); else if (fmpr_is_neg_inf(y)) mpfr_set_inf(x, -1); else mpfr_set_nan(x); r = 0; } else if (COEFF_IS_MPZ(*fmpr_expref(y))) { flint_printf("exception: exponent too large to convert to mpfr"); abort(); } else { if (!COEFF_IS_MPZ(*fmpr_manref(y))) #if defined(__MINGW64__) r = mpfr_set_sj_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd); #else r = mpfr_set_si_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd); #endif else r = mpfr_set_z_2exp(x, COEFF_TO_PTR(*fmpr_manref(y)), *fmpr_expref(y), rnd); if (!mpfr_regular_p(x)) { flint_printf("exception: exponent too large to convert to mpfr"); abort(); } } return r; } arb-2.8.1/fmpr/get_si.c000066400000000000000000000026231264125401100146470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_get_si(const fmpr_t x, fmpr_rnd_t rnd) { fmpz_t t; slong v; fmpz_init(t); fmpr_get_fmpz(t, x, rnd); if (!fmpz_fits_si(t)) { flint_printf("fmpr_get_si: result does not fit in a signed slong\n"); abort(); } v = fmpz_get_si(t); fmpz_clear(t); return v; } arb-2.8.1/fmpr/log.c000066400000000000000000000041371264125401100141600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_log(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) fmpr_neg_inf(y); else if (fmpr_is_pos_inf(x)) fmpr_pos_inf(y); else fmpr_nan(y); return FMPR_RESULT_EXACT; } else if (fmpr_sgn(x) < 0) { fmpr_nan(y); return FMPR_RESULT_EXACT; } else if (fmpr_is_one(x)) { fmpr_zero(y); return FMPR_RESULT_EXACT; } else { slong r; CALL_MPFR_FUNC(r, mpfr_log, y, x, prec, rnd); return r; } } slong fmpr_log1p(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) fmpr_zero(y); else if (fmpr_is_pos_inf(x)) fmpr_pos_inf(y); else fmpr_nan(y); return FMPR_RESULT_EXACT; } else { slong r; CALL_MPFR_FUNC(r, mpfr_log1p, y, x, prec, rnd); return r; } } arb-2.8.1/fmpr/mul.c000066400000000000000000000051171264125401100141730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_mul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { fmpz xv, yv; if (fmpr_is_special(x) || fmpr_is_special(y)) { if (fmpr_is_zero(x) && fmpr_is_finite(y)) { fmpr_zero(z); } else if (fmpr_is_zero(y) && fmpr_is_finite(x)) { fmpr_zero(z); } else if ((fmpr_is_inf(x) && (fmpr_is_inf(y) || !fmpr_is_special(y))) || (fmpr_is_inf(y) && !fmpr_is_special(x))) { if (fmpr_sgn(x) == fmpr_sgn(y)) fmpr_pos_inf(z); else fmpr_neg_inf(z); } else { fmpr_nan(z); } return FMPR_RESULT_EXACT; } xv = *fmpr_manref(x); yv = *fmpr_manref(y); if (!COEFF_IS_MPZ(xv) && !COEFF_IS_MPZ(yv)) { return _fmpr_mul_1x1(z, FLINT_ABS(xv), fmpr_expref(x), FLINT_ABS(yv), fmpr_expref(y), (xv ^ yv) < 0, prec, rnd); } else { slong xn, yn; int xsign, ysign; mp_limb_t xtmp, ytmp; mp_ptr xptr, yptr; FMPZ_GET_MPN_READONLY(xsign, xn, xptr, xtmp, xv) FMPZ_GET_MPN_READONLY(ysign, yn, yptr, ytmp, yv) if (xn >= yn) return _fmpr_mul_mpn(z, xptr, xn, fmpr_expref(x), yptr, yn, fmpr_expref(y), xsign ^ ysign, prec, rnd); else return _fmpr_mul_mpn(z, yptr, yn, fmpr_expref(y), xptr, xn, fmpr_expref(x), ysign ^ xsign, prec, rnd); } } arb-2.8.1/fmpr/mul_1x1.c000066400000000000000000000103101264125401100146530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013, 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong _fmpr_mul_1x1(fmpr_t z, mp_limb_t u, const fmpz_t xexp, mp_limb_t v, const fmpz_t yexp, int negative, slong prec, fmpr_rnd_t rnd) { slong lead, trail, bc, shift, ret; mp_limb_t hi, lo; umul_ppmm(hi, lo, u, v); shift = 0; if (hi == 0) { /* 1 limb */ count_leading_zeros(lead, lo); bc = FLINT_BITS - lead; ret = FMPR_RESULT_EXACT; if (bc > prec) { shift += bc - prec; lo = (lo >> shift) + rounds_up(rnd, negative); count_trailing_zeros(trail, lo); lo >>= trail; shift += trail; ret = trail; /* special case: if the mantissa overflowed to the next power of two, the error bound must be multiplied by two */ ret -= (trail == prec); } if (!negative) fmpz_set_ui(fmpr_manref(z), lo); else fmpz_neg_ui(fmpr_manref(z), lo); } else { /* 2 limbs */ count_leading_zeros(lead, hi); bc = 2 * FLINT_BITS - lead; ret = FMPR_RESULT_EXACT; if (bc > prec) { shift += bc - prec; /* round */ if (shift < FLINT_BITS) { lo = (lo >> shift) | (hi << (FLINT_BITS - shift)); hi >>= shift; } else { lo = hi >> (shift - FLINT_BITS); hi = 0; } if (rounds_up(rnd, negative)) add_ssaaaa(hi, lo, hi, lo, 0, 1); /* remove trailing zeros */ if (lo == 0) { count_trailing_zeros(trail, hi); hi >>= trail; shift += FLINT_BITS + trail; ret = FLINT_BITS + trail; /* special case: if the mantissa overflowed to the next power of two, the error bound must be multiplied by two */ ret -= (FLINT_BITS + trail == prec); if (!negative) fmpz_set_ui(fmpr_manref(z), hi); else fmpz_neg_ui(fmpr_manref(z), hi); } else { count_trailing_zeros(trail, lo); if (trail != 0) { lo = (lo >> trail) | (hi << (FLINT_BITS - trail)); hi >>= trail; shift += trail; } ret = trail; /* special case: if the mantissa overflowed to the next power of two, the error bound must be multiplied by two */ ret -= (trail == prec); if (!negative) fmpz_set_uiui(fmpr_manref(z), hi, lo); else fmpz_neg_uiui(fmpr_manref(z), hi, lo); } } else { if (!negative) fmpz_set_uiui(fmpr_manref(z), hi, lo); else fmpz_neg_uiui(fmpr_manref(z), hi, lo); } } fmpz_add2_fmpz_si_inline(fmpr_expref(z), xexp, yexp, shift); return ret; } arb-2.8.1/fmpr/mul_fmpz.c000066400000000000000000000117701264125401100152310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_mul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpz xv, yv; fmpz yexp; if (fmpr_is_special(x) || fmpz_is_zero(y)) { if (fmpr_is_zero(x)) { fmpr_zero(z); } else if (fmpz_is_zero(y) && fmpr_is_finite(x)) { fmpr_zero(z); } else if (fmpr_is_inf(x) && !fmpz_is_zero(y)) { if (fmpr_sgn(x) == fmpz_sgn(y)) fmpr_pos_inf(z); else fmpr_neg_inf(z); } else { fmpr_nan(z); } return FMPR_RESULT_EXACT; } xv = *fmpr_manref(x); yv = *y; if (!COEFF_IS_MPZ(xv) && !COEFF_IS_MPZ(yv)) { mp_limb_t ytmp; unsigned int bc; ytmp = FLINT_ABS(yv); count_trailing_zeros(bc, ytmp); ytmp >>= bc; yexp = bc; return _fmpr_mul_1x1(z, FLINT_ABS(xv), fmpr_expref(x), ytmp, &yexp, (xv ^ yv) < 0, prec, rnd); } else { slong xn, yn; int xsign, ysign; mp_limb_t xtmp, ytmp; mp_ptr xptr, yptr; yexp = 0; FMPZ_GET_MPN_READONLY(xsign, xn, xptr, xtmp, xv) FMPZ_GET_MPN_READONLY(ysign, yn, yptr, ytmp, yv) if (xn >= yn) return _fmpr_mul_mpn(z, xptr, xn, fmpr_expref(x), yptr, yn, &yexp, xsign ^ ysign, prec, rnd); else return _fmpr_mul_mpn(z, yptr, yn, &yexp, xptr, xn, fmpr_expref(x), ysign ^ xsign, prec, rnd); } } slong fmpr_mul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) { fmpz xv; fmpz yexp; slong xn; int xsign, ysign; mp_limb_t xtmp, ytmp; mp_ptr xptr; if (fmpr_is_special(x) || (y == 0)) { if (fmpr_is_zero(x)) { fmpr_zero(z); } else if ((y == 0) && fmpr_is_finite(x)) { fmpr_zero(z); } else if (fmpr_is_inf(x) && (y != 0)) { if (fmpr_sgn(x) == ((y > 0) - (y < 0))) fmpr_pos_inf(z); else fmpr_neg_inf(z); } else { fmpr_nan(z); } return FMPR_RESULT_EXACT; } xv = *fmpr_manref(x); ytmp = FLINT_ABS(y); ysign = y < 0; yexp = 0; if (!COEFF_IS_MPZ(xv)) { unsigned int bc; count_trailing_zeros(bc, ytmp); ytmp >>= bc; yexp = bc; return _fmpr_mul_1x1(z, FLINT_ABS(xv), fmpr_expref(x), ytmp, &yexp, (xv < 0) ^ ysign, prec, rnd); } else { FMPZ_GET_MPN_READONLY(xsign, xn, xptr, xtmp, xv) return _fmpr_mul_mpn(z, xptr, xn, fmpr_expref(x), &ytmp, 1, &yexp, xsign ^ ysign, prec, rnd); } } slong fmpr_mul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) { fmpz xv; fmpz yexp; slong xn; int xsign; mp_limb_t xtmp, ytmp; mp_ptr xptr; if (fmpr_is_special(x) || (y == 0)) { if (fmpr_is_zero(x)) { fmpr_zero(z); } else if ((y == 0) && fmpr_is_finite(x)) { fmpr_zero(z); } else if (fmpr_is_inf(x) && (y != 0)) { if (fmpr_sgn(x) == (y != 0)) fmpr_pos_inf(z); else fmpr_neg_inf(z); } else { fmpr_nan(z); } return FMPR_RESULT_EXACT; } xv = *fmpr_manref(x); ytmp = y; yexp = 0; if (!COEFF_IS_MPZ(xv)) { unsigned int bc; count_trailing_zeros(bc, ytmp); ytmp >>= bc; yexp = bc; return _fmpr_mul_1x1(z, FLINT_ABS(xv), fmpr_expref(x), ytmp, &yexp, xv < 0, prec, rnd); } else { FMPZ_GET_MPN_READONLY(xsign, xn, xptr, xtmp, xv) return _fmpr_mul_mpn(z, xptr, xn, fmpr_expref(x), &ytmp, 1, &yexp, xsign, prec, rnd); } } arb-2.8.1/fmpr/mul_mpn.c000066400000000000000000000053141264125401100150440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013, 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" #define MUL_STACK_ALLOC 40 #define MUL_TLS_ALLOC 1000 TLS_PREFIX mp_ptr __mul_tmp = NULL; TLS_PREFIX slong __mul_alloc = 0; void _mul_tmp_cleanup(void) { flint_free(__mul_tmp); __mul_tmp = NULL; __mul_alloc = 0; } #define MUL_TMP_ALLOC \ if (alloc <= MUL_STACK_ALLOC) \ { \ tmp = tmp_stack; \ } \ else if (alloc <= MUL_TLS_ALLOC) \ { \ if (__mul_alloc < alloc) \ { \ if (__mul_alloc == 0) \ { \ flint_register_cleanup_function(_mul_tmp_cleanup); \ } \ __mul_tmp = flint_realloc(__mul_tmp, sizeof(mp_limb_t) * alloc); \ __mul_alloc = alloc; \ } \ tmp = __mul_tmp; \ } \ else \ { \ tmp = flint_malloc(sizeof(mp_limb_t) * alloc); \ } #define MUL_TMP_FREE \ if (alloc > MUL_TLS_ALLOC) \ flint_free(tmp); slong _fmpr_mul_mpn(fmpr_t z, mp_srcptr xman, mp_size_t xn, const fmpz_t xexp, mp_srcptr yman, mp_size_t yn, const fmpz_t yexp, int negative, slong prec, fmpr_rnd_t rnd) { slong zn, alloc, ret, shift; mp_limb_t tmp_stack[MUL_STACK_ALLOC]; mp_ptr tmp; zn = xn + yn; alloc = zn; MUL_TMP_ALLOC if (yn == 1) { mp_limb_t cy = mpn_mul_1(tmp, xman, xn, yman[0]); tmp[zn - 1] = cy; zn = zn - (cy == 0); } else { mpn_mul(tmp, xman, xn, yman, yn); zn = zn - (tmp[zn - 1] == 0); } ret = _fmpr_set_round_mpn(&shift, fmpr_manref(z), tmp, zn, negative, prec, rnd); fmpz_add2_fmpz_si_inline(fmpr_expref(z), xexp, yexp, shift); MUL_TMP_FREE return ret; } arb-2.8.1/fmpr/mul_naive.c000066400000000000000000000042351264125401100153550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static void _fmpr_mul_special(fmpr_t z, const fmpr_t x, const fmpr_t y) { if (fmpr_is_zero(x)) { if (!fmpr_is_special(y) || fmpr_is_zero(y)) fmpr_zero(z); else fmpr_nan(z); return; } if (fmpr_is_zero(y)) { if (!fmpr_is_special(x)) fmpr_zero(z); else fmpr_nan(z); return; } if ((fmpr_is_inf(x) && (fmpr_is_inf(y) || !fmpr_is_special(y))) || (fmpr_is_inf(y) && !fmpr_is_special(x))) { if (fmpr_sgn(x) == fmpr_sgn(y)) fmpr_pos_inf(z); else fmpr_neg_inf(z); return; } fmpr_nan(z); } slong fmpr_mul_naive(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_special(x) || fmpr_is_special(y)) { _fmpr_mul_special(z, x, y); return FMPR_RESULT_EXACT; } fmpz_mul(fmpr_manref(z), fmpr_manref(x), fmpr_manref(y)); fmpz_add(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y)); return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd); } arb-2.8.1/fmpr/normalise.c000066400000000000000000000052131264125401100153640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong _fmpr_normalise_naive(fmpz_t man, fmpz_t exp, slong prec, fmpr_rnd_t rnd) { /* TODO: this should perhaps raise an exception to avoid ambiguity */ if (fmpz_is_zero(man)) { fmpz_zero(exp); return FMPR_RESULT_EXACT; } else { slong bc, val; bc = fmpz_bits(man); val = fmpz_val2(man); if (bc - val <= prec) { if (val != 0) { fmpz_tdiv_q_2exp(man, man, val); fmpz_add_ui(exp, exp, val); } return FMPR_RESULT_EXACT; } else { slong exp_shift = bc - prec; if (rnd == FMPR_RND_NEAR) { abort(); } else if (rnd == FMPR_RND_DOWN) { fmpz_tdiv_q_2exp(man, man, exp_shift); } else if (rnd == FMPR_RND_FLOOR) { fmpz_fdiv_q_2exp(man, man, exp_shift); } else if (rnd == FMPR_RND_CEIL) { fmpz_cdiv_q_2exp(man, man, exp_shift); } else { if (fmpz_sgn(man) > 0) fmpz_cdiv_q_2exp(man, man, exp_shift); else fmpz_fdiv_q_2exp(man, man, exp_shift); } val = fmpz_val2(man); exp_shift += val; if (val != 0) fmpz_tdiv_q_2exp(man, man, val); fmpz_add_ui(exp, exp, exp_shift); return val - (val == prec); } } } arb-2.8.1/fmpr/pow_sloppy.c000066400000000000000000000047351264125401100156160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" /* TODO: correct rounding with negative b */ void fmpr_pow_sloppy_fmpz(fmpr_t y, const fmpr_t b, const fmpz_t e, slong prec, fmpr_rnd_t rnd) { slong i, wp, bits; if (fmpz_is_zero(e)) { fmpr_set_ui(y, UWORD(1)); return; } if (fmpz_sgn(e) < 0) { fmpz_t f; fmpz_init(f); fmpz_neg(f, e); fmpr_pow_sloppy_fmpz(y, b, f, prec + 2, (rnd == FMPR_RND_FLOOR || rnd == FMPR_RND_DOWN) ? FMPR_RND_UP : FMPR_RND_DOWN); fmpr_ui_div(y, UWORD(1), y, prec, rnd); fmpz_clear(f); } if (y == b) { fmpr_t t; fmpr_init(t); fmpr_set(t, b); fmpr_pow_sloppy_fmpz(y, t, e, prec, rnd); fmpr_clear(t); return; } fmpr_set(y, b); bits = fmpz_bits(e); wp = FMPR_PREC_ADD(prec, bits); for (i = bits - 2; i >= 0; i--) { fmpr_mul(y, y, y, wp, rnd); if (fmpz_tstbit(e, i)) fmpr_mul(y, y, b, wp, rnd); } } void fmpr_pow_sloppy_ui(fmpr_t y, const fmpr_t b, ulong e, slong prec, fmpr_rnd_t rnd) { fmpz_t f; fmpz_init_set_ui(f, e); fmpr_pow_sloppy_fmpz(y, b, f, prec, rnd); fmpz_clear(f); } void fmpr_pow_sloppy_si(fmpr_t y, const fmpr_t b, slong e, slong prec, fmpr_rnd_t rnd) { fmpz_t f; fmpz_init(f); fmpz_set_si(f, e); fmpr_pow_sloppy_fmpz(y, b, f, prec, rnd); fmpz_clear(f); } arb-2.8.1/fmpr/print.c000066400000000000000000000030401264125401100145230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_print(const fmpr_t x) { if (fmpr_is_normal(x)) { flint_printf("("); fmpz_print(fmpr_manref(x)); flint_printf(" * 2^"); fmpz_print(fmpr_expref(x)); flint_printf(")"); } else { if (fmpr_is_zero(x)) flint_printf("(0)"); else if (fmpr_is_pos_inf(x)) flint_printf("(+inf)"); else if (fmpr_is_neg_inf(x)) flint_printf("(-inf)"); else flint_printf("(nan)"); } } arb-2.8.1/fmpr/printd.c000066400000000000000000000025511264125401100146750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_printd(const fmpr_t x, slong digits) { mpfr_t t; mpfr_init2(t, digits * 3.33 + 10); mpfr_set_emin(MPFR_EMIN_MIN); mpfr_set_emax(MPFR_EMAX_MAX); fmpr_get_mpfr(t, x, MPFR_RNDN); mpfr_printf("%.*Rg", FLINT_MAX(digits, 1), t); mpfr_clear(t); } arb-2.8.1/fmpr/randtest.c000066400000000000000000000043141264125401100152200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_randtest(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits) { fmpz_randtest(fmpr_manref(x), state, bits); fmpz_randtest(fmpr_expref(x), state, mag_bits); fmpz_sub_ui(fmpr_expref(x), fmpr_expref(x), fmpz_bits(fmpr_manref(x))); _fmpr_normalise(fmpr_manref(x), fmpr_expref(x), bits, FMPR_RND_DOWN); } void fmpr_randtest_not_zero(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits) { fmpz_randtest_not_zero(fmpr_manref(x), state, bits); fmpz_randtest(fmpr_expref(x), state, mag_bits); fmpz_sub_ui(fmpr_expref(x), fmpr_expref(x), fmpz_bits(fmpr_manref(x))); _fmpr_normalise(fmpr_manref(x), fmpr_expref(x), bits, FMPR_RND_DOWN); } void fmpr_randtest_special(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits) { switch (n_randint(state, 32)) { case 0: fmpr_zero(x); break; case 1: fmpr_pos_inf(x); break; case 2: fmpr_neg_inf(x); break; case 3: fmpr_nan(x); break; default: fmpr_randtest_not_zero(x, state, bits, mag_bits); } } arb-2.8.1/fmpr/root.c000066400000000000000000000044021264125401100143550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_root(fmpr_t y, const fmpr_t x, ulong k, slong prec, fmpr_rnd_t rnd) { slong r; if (k == 0) { fmpr_nan(y); return FMPR_RESULT_EXACT; } else if (k == 1) { return fmpr_set_round(y, x, prec, rnd); } else if (k == 2) { return fmpr_sqrt(y, x, prec, rnd); } if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) fmpr_zero(y); else if (fmpr_is_pos_inf(x)) fmpr_pos_inf(y); else fmpr_nan(y); return FMPR_RESULT_EXACT; } if (fmpr_sgn(x) < 0) { fmpr_nan(y); return FMPR_RESULT_EXACT; } { fmpr_t t; fmpz_t a, b; fmpr_init(t); fmpz_init(a); fmpz_init(b); /* (m * 2^(aq+b))^(1/q) = (m*2^b)^(1/q) * 2^a */ fmpz_set_ui(a, k); fmpz_fdiv_qr(a, b, fmpr_expref(x), a); fmpz_set(fmpr_manref(t), fmpr_manref(x)); fmpz_set(fmpr_expref(t), b); CALL_MPFR_FUNC_K(r, mpfr_root, y, t, k, prec, rnd); fmpr_mul_2exp_fmpz(y, y, a); fmpr_clear(t); fmpz_clear(a); fmpz_clear(b); return r; } } arb-2.8.1/fmpr/rsqrt.c000066400000000000000000000042761264125401100145560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_rsqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { slong r; if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) fmpr_pos_inf(y); else if (fmpr_is_pos_inf(x)) fmpr_zero(y); else fmpr_nan(y); return FMPR_RESULT_EXACT; } if (fmpr_sgn(x) < 0) { fmpr_nan(y); return FMPR_RESULT_EXACT; } /* special case: 4^n */ if (fmpz_is_one(fmpr_manref(x)) && fmpz_is_even(fmpr_expref(x))) { r = fmpr_set_round(y, x, prec, rnd); fmpz_tdiv_q_2exp(fmpr_expref(y), fmpr_expref(y), 1); fmpz_neg(fmpr_expref(y), fmpr_expref(y)); return r; } { fmpr_t t; fmpz_t e; fmpr_init(t); fmpz_init(e); fmpz_neg(e, fmpr_expref(x)); if (fmpz_is_odd(e)) fmpz_add_ui(e, e, 1); fmpr_mul_2exp_fmpz(t, x, e); CALL_MPFR_FUNC(r, mpfr_rec_sqrt, y, t, prec, rnd); fmpz_tdiv_q_2exp(e, e, 1); fmpr_mul_2exp_fmpz(y, y, e); fmpr_clear(t); fmpz_clear(e); return r; } } arb-2.8.1/fmpr/set_d.c000066400000000000000000000040361264125401100144730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_set_d(fmpr_t x, double v) { #if FLINT_BITS == 64 mp_limb_t h, sign, exp, frac; slong real_exp, real_man; union { double uf; mp_limb_t ul; } u; u.uf = v; h = u.ul; sign = h >> 63; exp = (h << 1) >> 53; frac = (h << 12) >> 12; if (exp == 0 && frac == 0) { fmpr_zero(x); } else if (exp == 0x7ff) { if (frac == 0) { if (sign) fmpr_neg_inf(x); else fmpr_pos_inf(x); } else { fmpr_nan(x); } } else { real_exp = exp - 1023 - 52; frac |= (UWORD(1) << 52); real_man = sign ? (-frac) : frac; fmpr_set_si_2exp_si(x, real_man, real_exp); } #else mpfr_t t; mp_limb_t tmp[2]; t->_mpfr_prec = 53; t->_mpfr_sign = 1; t->_mpfr_exp = 0; t->_mpfr_d = tmp; mpfr_set_d(t, v, MPFR_RNDD); fmpr_set_mpfr(x, t); #endif } arb-2.8.1/fmpr/set_fmpq.c000066400000000000000000000031041264125401100152060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_set_fmpq(fmpr_t x, const fmpq_t y, slong prec, fmpr_rnd_t rnd) { if (fmpz_is_one(fmpq_denref(y))) { return fmpr_set_round_fmpz(x, fmpq_numref(y), prec, rnd); } else { slong res; fmpr_t t, u; fmpr_init(t); fmpr_init(u); fmpr_set_fmpz(t, fmpq_numref(y)); fmpr_set_fmpz(u, fmpq_denref(y)); res = fmpr_div(x, t, u, prec, rnd); fmpr_clear(t); fmpr_clear(u); return res; } } arb-2.8.1/fmpr/set_fmpz_2exp.c000066400000000000000000000025051264125401100161610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_set_fmpz_2exp(fmpr_t x, const fmpz_t man, const fmpz_t exp) { if (fmpz_is_zero(man)) { fmpr_zero(x); } else { fmpr_set_fmpz(x, man); fmpz_add(fmpr_expref(x), fmpr_expref(x), exp); } } arb-2.8.1/fmpr/set_mpfr.c000066400000000000000000000032051264125401100152110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_set_mpfr(fmpr_t x, const mpfr_t y) { if (!mpfr_regular_p(y)) { if (mpfr_zero_p(y)) fmpr_zero(x); else if (mpfr_inf_p(y) && mpfr_sgn(y) > 0) fmpr_pos_inf(x); else if (mpfr_inf_p(y) && mpfr_sgn(y) < 0) fmpr_neg_inf(x); else fmpr_nan(x); } else { __mpz_struct * z = _fmpz_promote(fmpr_manref(x)); fmpz_set_si(fmpr_expref(x), mpfr_get_z_2exp(z, y)); _fmpz_demote_val(fmpr_manref(x)); _fmpr_normalise(fmpr_manref(x), fmpr_expref(x), y->_mpfr_prec, FMPR_RND_DOWN); } } arb-2.8.1/fmpr/set_round.c000066400000000000000000000136511264125401100154020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" /* like mpn_scan0b, but takes an upper size */ static __inline__ mp_bitcnt_t mpn_scan0b(mp_srcptr up, mp_size_t size, mp_bitcnt_t from_bit) { mp_limb_t t; slong i, c; i = from_bit / GMP_NUMB_BITS; c = from_bit % FLINT_BITS; t = ((~up[i]) >> c) << c; while (t == 0) { i++; if (i == size) return size * FLINT_BITS; else t = ~up[i]; } count_trailing_zeros(c, t); return (i * FLINT_BITS) + c; } slong _fmpr_set_round(fmpz_t rman, fmpz_t rexp, const fmpz_t man, const fmpz_t exp, slong prec, fmpr_rnd_t rnd) { if (!COEFF_IS_MPZ(*man)) { slong lead, trail, bc, v, w, shift, ret; int negative; v = *man; count_trailing_zeros(trail, v); v >>= trail; shift = trail; ret = FMPR_RESULT_EXACT; /* may need to round */ if (prec < FLINT_BITS - 2 - trail) { if (v < 0) { negative = 1; w = -v; } else { negative = 0; w = v; } count_leading_zeros(lead, w); bc = FLINT_BITS - lead; /* round */ if (prec < bc) { w = (w >> (bc - prec)) + rounds_up(rnd, negative); shift += bc - prec; count_trailing_zeros(trail, w); w >>= trail; shift += trail; v = negative ? -w : w; ret = trail; /* special case: if w overflowed to the next power of two, the error bound must be multiplied by 2 */ ret -= (trail == prec); } } /* the input is small, so the output must be small too */ _fmpz_demote(rman); *rman = v; fmpz_add_ui_inline(rexp, exp, shift); return ret; } else { slong size, bc, val, val_bits, val_limbs, ret; int negative, increment; mp_ptr d; __mpz_struct * z = COEFF_TO_PTR(*man); size = z->_mp_size; negative = size < 0; size = FLINT_ABS(size); d = z->_mp_d; /* bit size */ count_leading_zeros(bc, d[size - 1]); bc = FLINT_BITS - bc; bc += (size - 1) * FLINT_BITS; /* quick exit */ if (bc <= prec && (d[0] & 1)) { if (rman != man) fmpz_set(rman, man); if (rexp != exp) fmpz_set(rexp, exp); return FMPR_RESULT_EXACT; } /* trailing zeros */ val_limbs = 0; while (d[val_limbs] == 0) val_limbs++; count_trailing_zeros(val_bits, d[val_limbs]); val = val_bits + (val_limbs * FLINT_BITS); /* no rounding necessary; just copy or shift to destination */ if (bc - val <= prec) { ret = FMPR_RESULT_EXACT; increment = 0; } else { /* truncation */ if (!rounds_up(rnd, negative)) { val = mpn_scan1(d, bc - prec); increment = 0; } /* round to next higher odd mantissa */ else { val = mpn_scan0b(d, size, bc - prec); /* can overflow to next power of 2 */ if (val == bc) { fmpz_set_si(rman, negative ? -1 : 1); fmpz_add_ui_inline(rexp, exp, bc); return prec - 1; } /* otherwise, incrementing will not cause overflow below */ increment = 1; } val_limbs = val / FLINT_BITS; val_bits = val % FLINT_BITS; ret = prec - (bc - val); } /* the output mantissa is a small fmpz */ if (bc - val <= FLINT_BITS - 2) { mp_limb_t h; if (val_limbs + 1 == size || val_bits == 0) h = d[val_limbs] >> val_bits; else h = (d[val_limbs] >> val_bits) | (d[val_limbs + 1] << (FLINT_BITS - val_bits)); h += increment; _fmpz_demote(rman); *rman = negative ? -h : h; } /* the output mantissa is an mpz */ else { if (rman == man) { mpz_tdiv_q_2exp(z, z, val); if (increment) z->_mp_d[0]++; } else { __mpz_struct * w = _fmpz_promote(rman); /* must reload pointer, as promoting rman could change it */ z = COEFF_TO_PTR(*man); mpz_tdiv_q_2exp(w, z, val); if (increment) w->_mp_d[0]++; } } fmpz_add_ui_inline(rexp, exp, val); return ret; } } arb-2.8.1/fmpr/set_round_mpn.c000066400000000000000000000114721264125401100162530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" /* like mpn_scan0, but takes an upper size */ static __inline__ mp_bitcnt_t mpn_scan0b(mp_srcptr up, mp_size_t size, mp_bitcnt_t from_bit) { mp_limb_t t; slong i, c; i = from_bit / GMP_NUMB_BITS; c = from_bit % FLINT_BITS; t = ((~up[i]) >> c) << c; while (t == 0) { i++; if (i == size) return size * FLINT_BITS; else t = ~up[i]; } count_trailing_zeros(c, t); return (i * FLINT_BITS) + c; } slong _fmpr_set_round_mpn(slong * shift, fmpz_t man, mp_srcptr x, mp_size_t xn, int negative, slong prec, fmpr_rnd_t rnd) { slong bc, val, val_bits, val_limbs, ret; int increment; /* compute the total bit length of x */ count_leading_zeros(bc, x[xn - 1]); bc = FLINT_BITS - bc; bc += (xn - 1) * FLINT_BITS; /* already odd */ if (x[0] & 1) { /* quick exit */ if (bc <= prec) { if (bc <= FLINT_BITS - 2) { mp_limb_t t = x[0]; _fmpz_demote(man); *man = negative ? -t : t; } else fmpz_set_mpn_large(man, x, xn, negative); *shift = 0; return FMPR_RESULT_EXACT; } else { val_limbs = val_bits = val = 0; } } else { /* trailing zero bits: val = val_limbs * FLINT_BITS + val_bits */ val_limbs = 0; while (x[val_limbs] == 0) val_limbs++; count_trailing_zeros(val_bits, x[val_limbs]); val = val_bits + (val_limbs * FLINT_BITS); } /* no rounding necessary; just copy or shift to destination */ if (bc - val <= prec) { ret = FMPR_RESULT_EXACT; increment = 0; } else { /* truncation */ if (!rounds_up(rnd, negative)) { val = mpn_scan1(x, bc - prec); increment = 0; } /* round to next higher odd mantissa */ else { val = mpn_scan0b(x, xn, bc - prec); /* can overflow to next power of 2 */ if (val == bc) { fmpz_set_si(man, negative ? -1 : 1); *shift = bc; return prec - 1; } /* otherwise, we are cutting off at a zero bit, and incrementing at that position will not cause carry propagation below */ increment = 1; } val_limbs = val / FLINT_BITS; val_bits = val % FLINT_BITS; ret = prec - (bc - val); } /* the output mantissa is a small fmpz */ if (bc - val <= FLINT_BITS - 2) { mp_limb_t h; if (val_limbs + 1 == xn || val_bits == 0) h = x[val_limbs] >> val_bits; else h = (x[val_limbs] >> val_bits) | (x[val_limbs + 1] << (FLINT_BITS - val_bits)); h += increment; _fmpz_demote(man); *man = negative ? -h : h; } /* the output mantissa is an mpz */ else { mp_ptr dest; slong res_limbs, res_alloc; __mpz_struct * zptr = _fmpz_promote(man); res_limbs = ((bc - val) + FLINT_BITS - 1) / FLINT_BITS; /* todo: only allocate the required size, not the size before shifting */ res_alloc = xn - val_limbs; if (zptr->_mp_alloc < res_alloc) mpz_realloc2(zptr, res_alloc * FLINT_BITS); dest = zptr->_mp_d; /* right shift by val */ if (val_bits == 0) flint_mpn_copyi(dest, x + val_limbs, res_limbs); else mpn_rshift(dest, x + val_limbs, xn - val_limbs, val_bits); dest[0] += increment; zptr->_mp_size = negative ? -res_limbs : res_limbs; } *shift = val; return ret; } arb-2.8.1/fmpr/set_round_ui_2exp_fmpz.c000066400000000000000000000042621264125401100200670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_set_round_ui_2exp_fmpz(fmpr_t z, mp_limb_t lo, const fmpz_t exp, int negative, slong prec, fmpr_rnd_t rnd) { slong lead, trail, bc, shift, shift2, ret; shift = 0; if ((lo & 1) == 0) { if (lo == 0) { fmpr_zero(z); return FMPR_RESULT_EXACT; } count_trailing_zeros(trail, lo); lo >>= trail; shift = trail; } count_leading_zeros(lead, lo); bc = FLINT_BITS - lead; ret = FMPR_RESULT_EXACT; if (bc > prec) { shift2 = bc - prec; lo = (lo >> shift2) + rounds_up(rnd, negative); count_trailing_zeros(trail, lo); lo >>= trail; shift += shift2; shift += trail; ret = trail; /* special case: if the mantissa overflowed to the next power of two, the error bound must be multiplied by two */ ret -= (trail == prec); } if (!negative) fmpz_set_ui(fmpr_manref(z), lo); else fmpz_neg_ui(fmpr_manref(z), lo); fmpz_add_si_inline(fmpr_expref(z), exp, shift); return ret; } arb-2.8.1/fmpr/set_round_uiui_2exp_fmpz.c000066400000000000000000000102051264125401100204170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_set_round_uiui_2exp_fmpz(fmpr_t z, mp_limb_t hi, mp_limb_t lo, const fmpz_t exp, int negative, slong prec, fmpr_rnd_t rnd) { if (hi == 0) { return fmpr_set_round_ui_2exp_fmpz(z, lo, exp, negative, prec, rnd); } else { /* 2 limbs */ slong lead, trail, bc, shift, ret; if ((lo & 1) == 0) { if (lo == 0) { shift = FLINT_BITS; ret = fmpr_set_round_ui_2exp_fmpz(z, hi, exp, negative, prec, rnd); } else { count_trailing_zeros(shift, lo); lo = (hi << (FLINT_BITS - shift)) | lo >> shift; hi = hi >> shift; ret = fmpr_set_round_uiui_2exp_fmpz(z, hi, lo, exp, negative, prec, rnd); } fmpz_add_si_inline(fmpr_expref(z), fmpr_expref(z), shift); return ret; } count_leading_zeros(lead, hi); bc = 2 * FLINT_BITS - lead; shift = 0; ret = FMPR_RESULT_EXACT; if (bc > prec) { shift = bc - prec; /* round */ if (shift < FLINT_BITS) { lo = (lo >> shift) | (hi << (FLINT_BITS - shift)); hi >>= shift; } else { lo = hi >> (shift - FLINT_BITS); hi = 0; } if (rounds_up(rnd, negative)) add_ssaaaa(hi, lo, hi, lo, 0, 1); /* remove trailing zeros */ if (lo == 0) { count_trailing_zeros(trail, hi); hi >>= trail; shift += FLINT_BITS + trail; ret = FLINT_BITS + trail; /* special case: if the mantissa overflowed to the next power of two, the error bound must be multiplied by two */ ret -= (trail + FLINT_BITS == prec); if (!negative) fmpz_set_ui(fmpr_manref(z), hi); else fmpz_neg_ui(fmpr_manref(z), hi); } else { count_trailing_zeros(trail, lo); if (trail != 0) { lo = (lo >> trail) | (hi << (FLINT_BITS - trail)); hi >>= trail; shift += trail; } ret = trail; /* special case: if the mantissa overflowed to the next power of two, the error bound must be multiplied by two */ ret -= (trail == prec); if (!negative) fmpz_set_uiui(fmpr_manref(z), hi, lo); else fmpz_neg_uiui(fmpr_manref(z), hi, lo); } } else { if (!negative) fmpz_set_uiui(fmpr_manref(z), hi, lo); else fmpz_neg_uiui(fmpr_manref(z), hi, lo); } fmpz_add_si_inline(fmpr_expref(z), exp, shift); return ret; } } arb-2.8.1/fmpr/sqrt.c000066400000000000000000000052021264125401100143620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_sqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd) { slong r; if (fmpr_is_special(x)) { if (fmpr_is_zero(x)) fmpr_zero(y); else if (fmpr_is_pos_inf(x)) fmpr_pos_inf(y); else fmpr_nan(y); return FMPR_RESULT_EXACT; } if (fmpr_sgn(x) < 0) { fmpr_nan(y); return FMPR_RESULT_EXACT; } /* special case: 4^n */ /* TODO: process all small exact square roots efficiently */ if (fmpz_is_one(fmpr_manref(x)) && fmpz_is_even(fmpr_expref(x))) { r = fmpr_set_round(y, x, prec, rnd); fmpz_tdiv_q_2exp(fmpr_expref(y), fmpr_expref(y), 1); return r; } { fmpr_t t; fmpz_t e; fmpr_init(t); fmpz_init(e); fmpz_neg(e, fmpr_expref(x)); if (fmpz_is_odd(e)) fmpz_add_ui(e, e, 1); fmpr_mul_2exp_fmpz(t, x, e); CALL_MPFR_FUNC(r, mpfr_sqrt, y, t, prec, rnd); fmpz_neg(e, e); fmpz_tdiv_q_2exp(e, e, 1); fmpr_mul_2exp_fmpz(y, y, e); fmpr_clear(t); fmpz_clear(e); return r; } } slong fmpr_sqrt_ui(fmpr_t z, ulong x, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, x); r = fmpr_sqrt(z, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_sqrt_fmpz(fmpr_t z, const fmpz_t x, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, x); r = fmpr_sqrt(z, t, prec, rnd); fmpr_clear(t); return r; } arb-2.8.1/fmpr/sub.c000066400000000000000000000071511264125401100141670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static slong _fmpr_sub_special(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { if (fmpr_is_zero(x)) { return fmpr_neg_round(z, y, prec, rnd); } else if (fmpr_is_zero(y)) { return fmpr_set_round(z, x, prec, rnd); } else if (fmpr_is_nan(x) || fmpr_is_nan(y) || (fmpr_is_pos_inf(x) && fmpr_is_pos_inf(y)) || (fmpr_is_neg_inf(x) && fmpr_is_neg_inf(y))) { fmpr_nan(z); return FMPR_RESULT_EXACT; } else if (fmpr_is_special(x)) { fmpr_set(z, x); return FMPR_RESULT_EXACT; } else { fmpr_neg(z, y); return FMPR_RESULT_EXACT; } } slong fmpr_sub(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { slong shift, xn, yn; mp_limb_t xtmp, ytmp; mp_ptr xptr, yptr; fmpz xv, yv; const fmpz * xexp; const fmpz * yexp; int xsign, ysign; if (fmpr_is_special(x) || fmpr_is_special(y)) { return _fmpr_sub_special(z, x, y, prec, rnd); } shift = _fmpz_sub_small(fmpr_expref(y), fmpr_expref(x)); if (shift >= 0) { xexp = fmpr_expref(x); yexp = fmpr_expref(y); xv = *fmpr_manref(x); yv = *fmpr_manref(y); } else { xexp = fmpr_expref(y); yexp = fmpr_expref(x); xv = *fmpr_manref(y); yv = *fmpr_manref(x); } FMPZ_GET_MPN_READONLY(xsign, xn, xptr, xtmp, xv) FMPZ_GET_MPN_READONLY(ysign, yn, yptr, ytmp, yv) if (shift >= 0) { ysign = !ysign; } else { shift = -shift; xsign = !xsign; } if ((xn == 1) && (yn == 1) && (shift < FLINT_BITS)) return _fmpr_add_1x1(z, xptr[0], xsign, xexp, yptr[0], ysign, yexp, shift, prec, rnd); else return _fmpr_add_mpn(z, xptr, xn, xsign, xexp, yptr, yn, ysign, yexp, shift, prec, rnd); } slong fmpr_sub_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, y); r = fmpr_sub(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_sub_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_si(t, y); r = fmpr_sub(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_sub_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, y); r = fmpr_sub(z, x, t, prec, rnd); fmpr_clear(t); return r; } arb-2.8.1/fmpr/submul.c000066400000000000000000000040161264125401100147020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" slong fmpr_submul(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_mul(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); r = fmpr_sub(z, z, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_submul_ui(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, y); r = fmpr_submul(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_submul_si(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_si(t, y); r = fmpr_submul(z, x, t, prec, rnd); fmpr_clear(t); return r; } slong fmpr_submul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, y); r = fmpr_submul(z, x, t, prec, rnd); fmpr_clear(t); return r; } arb-2.8.1/fmpr/sum.c000066400000000000000000000115061264125401100142010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int are_close(const fmpr_t x, const fmpr_t y, slong prec) { fmpz_t xb, yb; fmpz_t delta; int result; fmpz_init(xb); fmpz_init(yb); fmpz_init(delta); fmpz_add_ui(xb, fmpr_expref(x), fmpz_bits(fmpr_manref(x))); fmpz_add_ui(yb, fmpr_expref(y), fmpz_bits(fmpr_manref(y))); if (fmpz_cmp(xb, yb) >= 0) fmpz_sub(delta, fmpr_expref(x), yb); else fmpz_sub(delta, fmpr_expref(y), xb); fmpz_sub_ui(delta, delta, 64); result = (fmpz_cmp_ui(delta, prec) < 0); fmpz_clear(xb); fmpz_clear(yb); fmpz_clear(delta); return result; } slong fmpr_sum(fmpr_t s, const fmpr_struct * terms, slong len, slong prec, fmpr_rnd_t rnd) { fmpr_struct * blocks; slong i, j, used, res; int have_merged; /* first check if the result is inf or nan */ { int have_pos_inf = 0; int have_neg_inf = 0; for (i = 0; i < len; i++) { if (fmpr_is_pos_inf(terms + i)) { if (have_neg_inf) { fmpr_nan(s); return FMPR_RESULT_EXACT; } have_pos_inf = 1; } else if (fmpr_is_neg_inf(terms + i)) { if (have_pos_inf) { fmpr_nan(s); return FMPR_RESULT_EXACT; } have_neg_inf = 1; } else if (fmpr_is_nan(terms + i)) { fmpr_nan(s); return FMPR_RESULT_EXACT; } } if (have_pos_inf) { fmpr_pos_inf(s); return FMPR_RESULT_EXACT; } if (have_neg_inf) { fmpr_neg_inf(s); return FMPR_RESULT_EXACT; } } blocks = flint_malloc(sizeof(fmpr_struct) * len); for (i = 0; i < len; i++) fmpr_init(blocks + i); /* put all terms into blocks */ used = 0; for (i = 0; i < len; i++) { if (!fmpr_is_zero(terms + i)) { fmpr_set(blocks + used, terms + i); used++; } } /* merge blocks until all are well separated */ have_merged = 1; while (used >= 2 && have_merged) { have_merged = 0; for (i = 0; i < used && !have_merged; i++) { for (j = i + 1; j < used && !have_merged; j++) { if (are_close(blocks + i, blocks + j, prec)) { fmpr_add(blocks + i, blocks + i, blocks + j, FMPR_PREC_EXACT, FMPR_RND_DOWN); /* remove the merged block */ fmpr_swap(blocks + j, blocks + used - 1); used--; /* remove the updated block if the sum is zero */ if (fmpr_is_zero(blocks + i)) { fmpr_swap(blocks + i, blocks + used - 1); used--; } have_merged = 1; } } } } if (used == 0) { fmpr_zero(s); res = FMPR_RESULT_EXACT; } else if (used == 1) { res = fmpr_set_round(s, blocks + 0, prec, rnd); } else { /* find the two largest blocks */ for (i = 1; i < used; i++) if (fmpr_cmpabs(blocks + 0, blocks + i) < 0) fmpr_swap(blocks + 0, blocks + i); for (i = 2; i < used; i++) if (fmpr_cmpabs(blocks + 1, blocks + i) < 0) fmpr_swap(blocks + 1, blocks + i); res = _fmpr_add_eps(s, blocks + 0, fmpr_sgn(blocks + 1), prec, rnd); } for (i = 0; i < len; i++) fmpr_clear(blocks + i); flint_free(blocks); return res; } arb-2.8.1/fmpr/test/000077500000000000000000000000001264125401100142055ustar00rootroot00000000000000arb-2.8.1/fmpr/test/t-abs_bound_le_2exp_fmpz.c000066400000000000000000000044421264125401100212240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("abs_bound_le_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpr_t x, y; fmpz_t b; int cmp1, cmp2; fmpr_init(x); fmpr_init(y); fmpz_init(b); fmpr_randtest_not_zero(x, state, 2 + n_randint(state, 1000), 100); fmpr_abs_bound_le_2exp_fmpz(b, x); fmpr_one(y); fmpr_mul_2exp_fmpz(y, y, b); cmp1 = (fmpr_cmpabs(x, y) <= 0); fmpr_mul_2exp_si(y, y, -1); cmp2 = (fmpr_cmpabs(y, x) < 0); fmpr_mul_2exp_si(y, y, 1); if (!cmp1 || !cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } fmpr_clear(x); fmpr_clear(y); fmpz_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-abs_bound_lt_2exp_fmpz.c000066400000000000000000000044421264125401100212430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("abs_bound_lt_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpr_t x, y; fmpz_t b; int cmp1, cmp2; fmpr_init(x); fmpr_init(y); fmpz_init(b); fmpr_randtest_not_zero(x, state, 2 + n_randint(state, 1000), 100); fmpr_abs_bound_lt_2exp_fmpz(b, x); fmpr_one(y); fmpr_mul_2exp_fmpz(y, y, b); cmp1 = (fmpr_cmpabs(x, y) < 0); fmpr_mul_2exp_si(y, y, -1); cmp2 = (fmpr_cmpabs(y, x) <= 0); fmpr_mul_2exp_si(y, y, 1); if (!cmp1 || !cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } fmpr_clear(x); fmpr_clear(y); fmpz_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-abs_bound_lt_2exp_si.c000066400000000000000000000050671264125401100207060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("abs_bound_lt_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpr_t x; fmpz_t b; slong c; fmpr_init(x); fmpz_init(b); fmpr_randtest_special(x, state, 2 + n_randint(state, 1000), 100); fmpr_abs_bound_lt_2exp_fmpz(b, x); c = fmpr_abs_bound_lt_2exp_si(x); if (c == -FMPR_PREC_EXACT) { if (!(fmpr_is_zero(x) || fmpz_cmp_si(b, -FMPR_PREC_EXACT) <= 0)) { flint_printf("FAIL (small/zero)\n\n"); abort(); } } else if (c == FMPR_PREC_EXACT) { if (!(fmpr_is_inf(x) || fmpr_is_nan(x) || fmpz_cmp_si(b, FMPR_PREC_EXACT) >= 0)) { flint_printf("FAIL (large/inf/nan)\n\n"); abort(); } } else { if (fmpz_cmp_si(b, c) != 0) { flint_printf("FAIL (normal)\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("c = %wd\n\n", c); abort(); } } fmpr_clear(x); fmpz_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-add.c000066400000000000000000000204631264125401100153470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); /* test exact addition: (x + y) + z == x + (y + z) */ for (iter = 0; iter < 100000; iter++) { slong bits, res1, res2, res3, res4; fmpr_t x, y, z, t, u; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(t); fmpr_init(u); fmpr_randtest_special(x, state, bits, 10); fmpr_randtest_special(y, state, bits, 10); fmpr_randtest_special(z, state, bits, 10); fmpr_randtest_special(t, state, bits, 10); fmpr_randtest_special(u, state, bits, 10); res1 = fmpr_add(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); res2 = fmpr_add(t, t, z, FMPR_PREC_EXACT, FMPR_RND_DOWN); res3 = fmpr_add(u, y, z, FMPR_PREC_EXACT, FMPR_RND_DOWN); res4 = fmpr_add(u, x, u, FMPR_PREC_EXACT, FMPR_RND_DOWN); if (!fmpr_equal(t, u) || res1 != FMPR_RESULT_EXACT || res2 != FMPR_RESULT_EXACT || res3 != FMPR_RESULT_EXACT || res4 != FMPR_RESULT_EXACT) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("t = "); fmpr_print(t); flint_printf("\n\n"); flint_printf("u = "); fmpr_print(u); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(t); fmpr_clear(u); } /* compare with add_naive */ for (iter = 0; iter < 1000000; iter++) { slong prec, ret1, ret2; fmpr_t x, y, z, w; fmpr_rnd_t rnd; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(w); fmpr_randtest_special(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200)); fmpr_randtest_special(y, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200)); fmpr_randtest_special(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200)); prec = 2 + n_randint(state, 1000); if (n_randint(state, 10) == 0 && fmpz_bits(fmpr_expref(x)) < 10 && fmpz_bits(fmpr_expref(y)) < 10) prec = FMPR_PREC_EXACT; switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } ret1 = fmpr_add(z, x, y, prec, rnd); ret2 = fmpr_add_naive(w, x, y, prec, rnd); if (!fmpr_equal(z, w) || ret1 != ret2 || !fmpr_check_ulp(z, ret1, prec) || !fmpr_check_ulp(w, ret2, prec)) { flint_printf("FAIL\n\n"); flint_printf("iter %wd\n", iter); flint_printf("prec = %wd\n", prec); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); flint_printf("ret1 = %wd, ret2 = %wd\n", ret1, ret2); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(w); } /* compare rounding with mpfr */ for (iter = 0; iter < 1000000; iter++) { slong bits, res; int mpfr_res; fmpr_t x, y, z, w; mpfr_t X, Y, Z; bits = 2 + n_randint(state, 500); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 500); mpfr_init2(Y, bits + 500); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 500), 10); fmpr_randtest_special(y, state, bits + n_randint(state, 500), 10); fmpr_randtest_special(z, state, bits, 10); fmpr_get_mpfr(X, x, MPFR_RNDN); fmpr_get_mpfr(Y, y, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDZ); res = fmpr_add(z, x, y, bits, FMPR_RND_DOWN); break; case 1: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDA); res = fmpr_add(z, x, y, bits, FMPR_RND_UP); break; case 2: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDD); res = fmpr_add(z, x, y, bits, FMPR_RND_FLOOR); break; default: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDU); res = fmpr_add(z, x, y, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w) || (res == FMPR_RESULT_EXACT) != (mpfr_res == 0) || !fmpr_check_ulp(z, res, bits)) { flint_printf("FAIL\n\n"); flint_printf("iter %wd\n", iter); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); flint_printf("returned: %wd, %d\n", res, mpfr_res); abort(); } /* check error bound */ if (!fmpr_is_nan(z) && !fmpr_is_inf(z)) { fmpr_t z_exact, error_bound, true_error; fmpr_init(z_exact); fmpr_init(error_bound); fmpr_init(true_error); fmpr_set_error_result(error_bound, z, res); fmpr_add(z_exact, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_sub(true_error, z, z_exact, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_abs(true_error, true_error); if (fmpr_is_zero(error_bound) != fmpr_is_zero(true_error) || fmpr_cmp(true_error, error_bound) > 0) { flint_printf("FAIL: error bound\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z_exact = "); fmpr_print(z_exact); flint_printf("\n\n"); flint_printf("true_error = "); fmpr_print(true_error); flint_printf("\n\n"); flint_printf("error_bound = "); fmpr_print(error_bound); flint_printf("\n\n"); abort(); } fmpr_clear(z_exact); fmpr_clear(error_bound); fmpr_clear(true_error); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Y); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-add_naive.c000066400000000000000000000147661264125401100165420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("add_naive...."); fflush(stdout); flint_randinit(state); /* test exact addition: (x + y) + z == x + (y + z) */ for (iter = 0; iter < 100000; iter++) { slong bits, res1, res2, res3, res4; fmpr_t x, y, z, t, u; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(t); fmpr_init(u); fmpr_randtest_special(x, state, bits, 10); fmpr_randtest_special(y, state, bits, 10); fmpr_randtest_special(z, state, bits, 10); fmpr_randtest_special(t, state, bits, 10); fmpr_randtest_special(u, state, bits, 10); res1 = fmpr_add_naive(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); res2 = fmpr_add_naive(t, t, z, FMPR_PREC_EXACT, FMPR_RND_DOWN); res3 = fmpr_add_naive(u, y, z, FMPR_PREC_EXACT, FMPR_RND_DOWN); res4 = fmpr_add_naive(u, x, u, FMPR_PREC_EXACT, FMPR_RND_DOWN); if (!fmpr_equal(t, u) || res1 != FMPR_RESULT_EXACT || res2 != FMPR_RESULT_EXACT || res3 != FMPR_RESULT_EXACT || res4 != FMPR_RESULT_EXACT) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("t = "); fmpr_print(t); flint_printf("\n\n"); flint_printf("u = "); fmpr_print(u); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(t); fmpr_clear(u); } /* compare rounding with mpfr */ for (iter = 0; iter < 100000; iter++) { slong bits, res; int mpfr_res; fmpr_t x, y, z, w; mpfr_t X, Y, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Y, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(y, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits, 10); fmpr_get_mpfr(X, x, MPFR_RNDN); fmpr_get_mpfr(Y, y, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDZ); res = fmpr_add_naive(z, x, y, bits, FMPR_RND_DOWN); break; case 1: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDA); res = fmpr_add_naive(z, x, y, bits, FMPR_RND_UP); break; case 2: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDD); res = fmpr_add_naive(z, x, y, bits, FMPR_RND_FLOOR); break; default: mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDU); res = fmpr_add_naive(z, x, y, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w) || (res == FMPR_RESULT_EXACT) != (mpfr_res == 0) || !fmpr_check_ulp(z, res, bits)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); flint_printf("returned: %wd, %d\n", res, mpfr_res); abort(); } /* check error bound */ if (!fmpr_is_nan(z) && !fmpr_is_inf(z)) { fmpr_t z_exact, error_bound, true_error; fmpr_init(z_exact); fmpr_init(error_bound); fmpr_init(true_error); fmpr_set_error_result(error_bound, z, res); fmpr_add_naive(z_exact, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_sub(true_error, z, z_exact, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_abs(true_error, true_error); if (fmpr_is_zero(error_bound) != fmpr_is_zero(true_error) || fmpr_cmp(true_error, error_bound) > 0) { flint_printf("FAIL: error bound\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z_exact = "); fmpr_print(z_exact); flint_printf("\n\n"); flint_printf("true_error = "); fmpr_print(true_error); flint_printf("\n\n"); flint_printf("error_bound = "); fmpr_print(error_bound); flint_printf("\n\n"); abort(); } fmpr_clear(z_exact); fmpr_clear(error_bound); fmpr_clear(true_error); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Y); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-cmp.c000066400000000000000000000043571264125401100154020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("cmp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, y; mpfr_t X, Y; int cmp1, cmp2; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); mpfr_init2(X, bits); mpfr_init2(Y, bits); fmpr_randtest_special(x, state, bits, 10); fmpr_randtest_special(y, state, bits, 10); fmpr_get_mpfr(X, x, MPFR_RNDN); fmpr_get_mpfr(Y, y, MPFR_RNDN); cmp1 = fmpr_cmp(x, y); cmp2 = mpfr_cmp(X, Y); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } fmpr_clear(x); fmpr_clear(y); mpfr_clear(X); mpfr_clear(Y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-cmp_2exp_si.c000066400000000000000000000041071264125401100170240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("cmp_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits, e; fmpr_t x, y; int cmp1, cmp2; bits = 2 + n_randint(state, 1000); e = n_randtest(state); fmpr_init(x); fmpr_init(y); fmpr_randtest_special(x, state, bits, 100); fmpr_set_ui_2exp_si(y, 1, e); cmp1 = fmpr_cmp(x, y); cmp2 = fmpr_cmp_2exp_si(x, e); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } fmpr_clear(x); fmpr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-cmpabs.c000066400000000000000000000044741264125401100160700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("cmpabs...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, y; mpfr_t X, Y; int cmp1, cmp2; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); mpfr_init2(X, bits); mpfr_init2(Y, bits); fmpr_randtest_special(x, state, bits, 10); fmpr_randtest_special(y, state, bits, 10); fmpr_get_mpfr(X, x, MPFR_RNDN); fmpr_get_mpfr(Y, y, MPFR_RNDN); mpfr_abs(X, X, MPFR_RNDN); mpfr_abs(Y, Y, MPFR_RNDN); cmp1 = fmpr_cmpabs(x, y); cmp2 = mpfr_cmp(X, Y); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } fmpr_clear(x); fmpr_clear(y); mpfr_clear(X); mpfr_clear(Y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-cmpabs_2exp_si.c000066400000000000000000000041201264125401100175050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("cmpabs_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits, e; fmpr_t x, y; int cmp1, cmp2; bits = 2 + n_randint(state, 1000); e = n_randtest(state); fmpr_init(x); fmpr_init(y); fmpr_randtest_special(x, state, bits, 100); fmpr_set_ui_2exp_si(y, 1, e); cmp1 = fmpr_cmpabs(x, y); cmp2 = fmpr_cmpabs_2exp_si(x, e); if (cmp1 != cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } fmpr_clear(x); fmpr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-div.c000066400000000000000000000071411264125401100153770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("div...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits, r1, r2; fmpr_t x, y, z, w; mpfr_t X, Y, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Y, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(y, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 10); fmpr_get_mpfr(X, x, MPFR_RNDN); fmpr_get_mpfr(Y, y, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: r1 = mpfr_div(Z, X, Y, MPFR_RNDZ); r2 = fmpr_div(z, x, y, bits, FMPR_RND_DOWN); break; case 1: r1 = mpfr_div(Z, X, Y, MPFR_RNDA); r2 = fmpr_div(z, x, y, bits, FMPR_RND_UP); break; case 2: r1 = mpfr_div(Z, X, Y, MPFR_RNDD); r2 = fmpr_div(z, x, y, bits, FMPR_RND_FLOOR); break; default: r1 = mpfr_div(Z, X, Y, MPFR_RNDU); r2 = fmpr_div(z, x, y, bits, FMPR_RND_CEIL); break; } /* we use slightly different semantics for special values (?) */ if (mpfr_zero_p(Y)) mpfr_set_nan(Z); if (mpfr_inf_p(X) && mpfr_zero_p(Y)) mpfr_set_nan(Z); fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w) || ((r1 == 0) != (r2 == FMPR_RESULT_EXACT)) || !fmpr_check_ulp(z, r2, bits)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Y); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-divappr_abs_ubound.c000066400000000000000000000046241264125401100204660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("divappr_abs_ubound...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpr_t a, b, c, d; slong prec; fmpr_init(a); fmpr_init(b); fmpr_init(c); fmpr_init(d); fmpr_randtest_special(a, state, 2 + n_randint(state, 200), 100); fmpr_randtest_special(b, state, 2 + n_randint(state, 200), 100); fmpr_randtest_special(c, state, 2 + n_randint(state, 200), 100); fmpr_randtest_special(d, state, 2 + n_randint(state, 200), 100); prec = 2 + n_randint(state, 200); fmpr_div(c, a, b, prec, FMPR_RND_UP); fmpr_abs(c, c); fmpr_divappr_abs_ubound(d, a, b, prec); if (fmpr_cmp(c, d) > 0) { flint_printf("FAIL:\n"); fmpr_printd(a, prec / 3.32); flint_printf("\n"); fmpr_printd(b, prec / 3.32); flint_printf("\n"); fmpr_printd(c, prec / 3.32); flint_printf("\n"); fmpr_printd(d, prec / 3.32); flint_printf("\n"); abort(); } fmpr_clear(a); fmpr_clear(b); fmpr_clear(c); fmpr_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-exp.c000066400000000000000000000056211264125401100154120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, z, w; mpfr_t X, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 3); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 3); fmpr_get_mpfr(X, x, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_exp(Z, X, MPFR_RNDZ); fmpr_exp(z, x, bits, FMPR_RND_DOWN); break; case 1: mpfr_exp(Z, X, MPFR_RNDA); fmpr_exp(z, x, bits, FMPR_RND_UP); break; case 2: mpfr_exp(Z, X, MPFR_RNDD); fmpr_exp(z, x, bits, FMPR_RND_FLOOR); break; case 3: mpfr_exp(Z, X, MPFR_RNDU); fmpr_exp(z, x, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-expm1.c000066400000000000000000000056431264125401100156540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("expm1...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, z, w; mpfr_t X, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 3); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 3); fmpr_get_mpfr(X, x, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_expm1(Z, X, MPFR_RNDZ); fmpr_expm1(z, x, bits, FMPR_RND_DOWN); break; case 1: mpfr_expm1(Z, X, MPFR_RNDA); fmpr_expm1(z, x, bits, FMPR_RND_UP); break; case 2: mpfr_expm1(Z, X, MPFR_RNDD); fmpr_expm1(z, x, bits, FMPR_RND_FLOOR); break; case 3: mpfr_expm1(Z, X, MPFR_RNDU); fmpr_expm1(z, x, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-get_d.c000066400000000000000000000036741264125401100157060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("get_d...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip */ for (iter = 0; iter < 100000; iter++) { fmpr_t x, z; double y; fmpr_init(x); fmpr_init(z); fmpr_randtest_special(x, state, 53, 8); y = fmpr_get_d(x, FMPR_RND_DOWN); fmpr_set_d(z, y); if (!fmpr_equal(x, z)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = %.17g\n\n", y); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-get_fmpz.c000066400000000000000000000056411264125401100164330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("get_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x; mpfr_t y; fmpz_t z, z2; mpz_t w; bits = 2 + n_randint(state, 1000); fmpr_init(x); mpfr_init2(y, bits); fmpz_init(z); fmpz_init(z2); mpz_init(w); fmpr_randtest(x, state, bits, 10); fmpr_get_mpfr(y, x, MPFR_RNDN); switch (n_randint(state, 5)) { case 0: fmpr_get_fmpz(z, x, FMPR_RND_FLOOR); mpfr_get_z(w, y, MPFR_RNDD); break; case 1: fmpr_get_fmpz(z, x, FMPR_RND_CEIL); mpfr_get_z(w, y, MPFR_RNDU); break; case 2: fmpr_get_fmpz(z, x, FMPR_RND_DOWN); mpfr_get_z(w, y, MPFR_RNDZ); break; case 3: fmpr_get_fmpz(z, x, FMPR_RND_UP); mpfr_get_z(w, y, MPFR_RNDA); break; default: fmpr_get_fmpz(z, x, FMPR_RND_NEAR); mpfr_get_z(w, y, MPFR_RNDN); break; } fmpz_set_mpz(z2, w); if (!fmpz_equal(z, z2)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpz_print(z); flint_printf("\n\n"); flint_printf("z2 = "); fmpz_print(z2); flint_printf("\n\n"); abort(); } fmpr_clear(x); mpfr_clear(y); fmpz_clear(z); fmpz_clear(z2); mpz_clear(w); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-get_mpfr.c000066400000000000000000000037501264125401100164220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("get_mpfr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, z; mpfr_t y; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); mpfr_init2(y, bits); fmpr_randtest_special(x, state, bits, 10); fmpr_get_mpfr(y, x, MPFR_RNDN); fmpr_set_mpfr(z, y); if (!fmpr_equal(x, z)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); mpfr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-log.c000066400000000000000000000056231264125401100154010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("log...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, z, w; mpfr_t X, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 10); fmpr_get_mpfr(X, x, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_log(Z, X, MPFR_RNDZ); fmpr_log(z, x, bits, FMPR_RND_DOWN); break; case 1: mpfr_log(Z, X, MPFR_RNDA); fmpr_log(z, x, bits, FMPR_RND_UP); break; case 2: mpfr_log(Z, X, MPFR_RNDD); fmpr_log(z, x, bits, FMPR_RND_FLOOR); break; case 3: mpfr_log(Z, X, MPFR_RNDU); fmpr_log(z, x, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-log1p.c000066400000000000000000000056451264125401100156460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("log1p...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, z, w; mpfr_t X, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 10); fmpr_get_mpfr(X, x, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_log1p(Z, X, MPFR_RNDZ); fmpr_log1p(z, x, bits, FMPR_RND_DOWN); break; case 1: mpfr_log1p(Z, X, MPFR_RNDA); fmpr_log1p(z, x, bits, FMPR_RND_UP); break; case 2: mpfr_log1p(Z, X, MPFR_RNDD); fmpr_log1p(z, x, bits, FMPR_RND_FLOOR); break; case 3: mpfr_log1p(Z, X, MPFR_RNDU); fmpr_log1p(z, x, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-mul.c000066400000000000000000000127551264125401100154210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpr_t x, y, z, v; slong prec, r1, r2; fmpr_rnd_t rnd; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(v); for (iter2 = 0; iter2 < 100; iter2++) { fmpr_randtest_special(x, state, 2000, 200); fmpr_randtest_special(y, state, 2000, 200); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } switch (n_randint(state, 5)) { case 0: r1 = fmpr_mul(z, x, y, prec, rnd); r2 = fmpr_mul_naive(v, x, y, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 1: r1 = fmpr_mul(z, x, x, prec, rnd); r2 = fmpr_mul_naive(v, x, x, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 2: r2 = fmpr_mul_naive(v, x, x, prec, rnd); r1 = fmpr_mul(x, x, x, prec, rnd); if (!fmpr_equal(v, x) || r1 != r2 || !fmpr_check_ulp(x, r1, prec)) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; case 3: r2 = fmpr_mul_naive(v, x, y, prec, rnd); r1 = fmpr_mul(x, x, y, prec, rnd); if (!fmpr_equal(x, v) || r1 != r2 || !fmpr_check_ulp(x, r1, prec)) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: r2 = fmpr_mul_naive(v, x, y, prec, rnd); r1 = fmpr_mul(x, y, x, prec, rnd); if (!fmpr_equal(x, v) || r1 != r2 || !fmpr_check_ulp(x, r1, prec)) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-mul_fmpz.c000066400000000000000000000077251264125401100164560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" static slong fmpr_mul_fmpz_naive(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_fmpz(t, y); r = fmpr_mul(z, x, t, prec, rnd); fmpr_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { fmpr_t x, z, v; fmpz_t y; slong prec, r1, r2; fmpr_rnd_t rnd; fmpr_init(x); fmpr_init(z); fmpr_init(v); fmpz_init(y); for (iter2 = 0; iter2 < 30; iter2++) { fmpr_randtest_special(x, state, 2000, 200); fmpz_randtest(y, state, 2000); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = fmpr_mul_fmpz(z, x, y, prec, rnd); r2 = fmpr_mul_fmpz_naive(v, x, y, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: fmpr_set(v, x); fmpr_set(z, x); r1 = fmpr_mul_fmpz(z, z, y, prec, rnd); r2 = fmpr_mul_fmpz_naive(v, v, y, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } fmpr_clear(x); fmpr_clear(z); fmpr_clear(v); fmpz_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-mul_naive.c000066400000000000000000000064611264125401100166000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_naive...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, y, z, w; mpfr_t X, Y, Z; slong r; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Y, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(y, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 10); fmpr_get_mpfr(X, x, MPFR_RNDN); fmpr_get_mpfr(Y, y, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_mul(Z, X, Y, MPFR_RNDZ); r = fmpr_mul_naive(z, x, y, bits, FMPR_RND_DOWN); break; case 1: mpfr_mul(Z, X, Y, MPFR_RNDA); r = fmpr_mul_naive(z, x, y, bits, FMPR_RND_UP); break; case 2: mpfr_mul(Z, X, Y, MPFR_RNDD); r = fmpr_mul_naive(z, x, y, bits, FMPR_RND_FLOOR); break; default: mpfr_mul(Z, X, Y, MPFR_RNDU); r = fmpr_mul_naive(z, x, y, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w) || !fmpr_check_ulp(z, r, bits)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Y); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-mul_si.c000066400000000000000000000075511264125401100161120ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" #include "long_extras.h" static slong fmpr_mul_si_naive(fmpr_t z, const fmpr_t x, slong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_si(t, y); r = fmpr_mul(z, x, t, prec, rnd); fmpr_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { fmpr_t x, z, v; slong y; slong prec, r1, r2; fmpr_rnd_t rnd; fmpr_init(x); fmpr_init(z); fmpr_init(v); for (iter2 = 0; iter2 < 30; iter2++) { fmpr_randtest_special(x, state, 2000, 200); y = z_randtest(state); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = fmpr_mul_si(z, x, y, prec, rnd); r2 = fmpr_mul_si_naive(v, x, y, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = %wd\n\n", y); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: fmpr_set(v, x); fmpr_set(z, x); r1 = fmpr_mul_si(z, z, y, prec, rnd); r2 = fmpr_mul_si_naive(v, v, y, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = %wd\n\n", y); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } fmpr_clear(x); fmpr_clear(z); fmpr_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-mul_ui.c000066400000000000000000000075521264125401100161150ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" #include "ulong_extras.h" static slong fmpr_mul_ui_naive(fmpr_t z, const fmpr_t x, ulong y, slong prec, fmpr_rnd_t rnd) { fmpr_t t; slong r; fmpr_init(t); fmpr_set_ui(t, y); r = fmpr_mul(z, x, t, prec, rnd); fmpr_clear(t); return r; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 3000; iter++) { fmpr_t x, z, v; ulong y; slong prec, r1, r2; fmpr_rnd_t rnd; fmpr_init(x); fmpr_init(z); fmpr_init(v); for (iter2 = 0; iter2 < 30; iter2++) { fmpr_randtest_special(x, state, 2000, 200); y = n_randtest(state); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } switch (n_randint(state, 2)) { case 0: r1 = fmpr_mul_ui(z, x, y, prec, rnd); r2 = fmpr_mul_ui_naive(v, x, y, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = %wu\n\n", y); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; default: fmpr_set(v, x); fmpr_set(z, x); r1 = fmpr_mul_ui(z, z, y, prec, rnd); r2 = fmpr_mul_ui_naive(v, v, y, prec, rnd); if (!fmpr_equal(z, v) || r1 != r2 || !fmpr_check_ulp(z, r1, prec)) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = %wu\n\n", y); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("v = "); fmpr_print(v); flint_printf("\n\n"); flint_printf("r1 = %wd, r2 = %wd\n", r1, r2); abort(); } break; } } fmpr_clear(x); fmpr_clear(z); fmpr_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-normalise.c000066400000000000000000000067241264125401100166140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("normalise...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000000; iter++) { fmpr_t x, xcopy, y, err_bound, err; slong prec, ret1, ret2, bits, ebits; fmpr_rnd_t rnd; fmpr_init(x); fmpr_init(xcopy); fmpr_init(y); fmpr_init(err_bound); fmpr_init(err); bits = 2 + n_randint(state, 2000); ebits = 2 + n_randint(state, 200); fmpz_randtest_not_zero(fmpr_manref(x), state, bits); fmpz_randtest(fmpr_expref(x), state, ebits); fmpz_set(fmpr_manref(y), fmpr_manref(x)); fmpz_set(fmpr_expref(y), fmpr_expref(x)); fmpr_set(xcopy, x); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } prec = 2 + n_randint(state, 2000); ret1 = _fmpr_normalise(fmpr_manref(x), fmpr_expref(x), prec, rnd); ret2 = _fmpr_normalise_naive(fmpr_manref(y), fmpr_expref(y), prec, rnd); if (!fmpr_equal(x, y) || ret1 != ret2) { flint_printf("FAIL!\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("ret1 = %wd, ret2 = %wd\n", ret1, ret2); abort(); } fmpr_sub(err, x, xcopy, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_abs(err, err); fmpr_set_error_result(err_bound, x, ret1); if (fmpr_cmp(err, err_bound) > 0) { flint_printf("FAIL (error bound)!\n"); flint_printf("x (original) = "); fmpr_print(xcopy); flint_printf("\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("error: "); fmpr_print(err); flint_printf("\n\n"); flint_printf("error bound: "); fmpr_print(err_bound); flint_printf("\n\n"); flint_printf("ret = %wd\n", ret1); abort(); } fmpr_clear(x); fmpr_clear(xcopy); fmpr_clear(y); fmpr_clear(err_bound); fmpr_clear(err); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-root.c000066400000000000000000000062541264125401100156040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("root...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; ulong k; fmpr_t x, z, w; mpfr_t X, Z; bits = 2 + n_randint(state, 200); k = 1 + n_randint(state, 20); fmpr_init(x); fmpr_init(z); fmpr_init(w); mpfr_init2(X, k * (bits + 100)); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_abs(x, x); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 10); /* occasionally produce perfect powers */ if (n_randint(state, 4) == 0) fmpr_mul(x, x, x, k * bits, FMPR_RND_DOWN); fmpr_get_mpfr(X, x, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_root(Z, X, k, MPFR_RNDZ); fmpr_root(z, x, k, bits, FMPR_RND_DOWN); break; case 1: mpfr_root(Z, X, k, MPFR_RNDA); fmpr_root(z, x, k, bits, FMPR_RND_UP); break; case 2: mpfr_root(Z, X, k, MPFR_RNDD); fmpr_root(z, x, k, bits, FMPR_RND_FLOOR); break; case 3: mpfr_root(Z, X, k, MPFR_RNDU); fmpr_root(z, x, k, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd, k = %wu\n", bits, k); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-rsqrt.c000066400000000000000000000057661264125401100160030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("rsqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits, res; fmpr_t x, z, w; mpfr_t X, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpr_init(w); mpfr_init2(X, 2 * (bits + 100)); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 10); fmpr_get_mpfr(X, x, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_rec_sqrt(Z, X, MPFR_RNDZ); res = fmpr_rsqrt(z, x, bits, FMPR_RND_DOWN); break; case 1: mpfr_rec_sqrt(Z, X, MPFR_RNDA); res = fmpr_rsqrt(z, x, bits, FMPR_RND_UP); break; case 2: mpfr_rec_sqrt(Z, X, MPFR_RNDD); res = fmpr_rsqrt(z, x, bits, FMPR_RND_FLOOR); break; default: mpfr_rec_sqrt(Z, X, MPFR_RNDU); res = fmpr_rsqrt(z, x, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w) || !fmpr_check_ulp(z, res, bits)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-set_fmpq.c000066400000000000000000000043341264125401100164340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("set_fmpq...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip R -> Q -> R */ for (iter = 0; iter < 100000; iter++) { slong bits, res; fmpr_t x, z; fmpq_t y; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpq_init(y); fmpr_randtest(x, state, bits, 10); fmpr_randtest(z, state, bits, 10); fmpr_get_fmpq(y, x); res = fmpr_set_fmpq(z, y, bits, FMPR_RND_DOWN); if (!fmpr_equal(x, z) || !fmpr_check_ulp(z, res, bits)) { flint_printf("FAIL\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpq_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-set_fmpz_2exp.c000066400000000000000000000044471264125401100174100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("set_fmpz_2exp...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip R -> Q -> R */ for (iter = 0; iter < 100000; iter++) { slong bits; fmpr_t x, z; fmpz_t y, e; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpz_init(y); fmpz_init(e); fmpr_randtest(x, state, bits, 10); fmpr_randtest(z, state, bits, 10); fmpr_get_fmpz_2exp(y, e, x); fmpr_set_fmpz_2exp(z, y, e); if (!fmpr_equal(x, z)) { flint_printf("FAIL\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("e = "); fmpz_print(e); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpz_clear(y); fmpz_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-set_round_mpn.c000066400000000000000000000061751264125401100174770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("set_round_mpn...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000000; iter++) { slong prec, bits, shift, ret1, ret2; fmpz_t man, exp; fmpr_t y; mpz_t x; fmpz_t fx; fmpr_rnd_t rnd; fmpz_init(man); fmpz_init(exp); mpz_init(x); fmpz_init(fx); fmpr_init(y); bits = 1 + n_randint(state, 1000); prec = 2 + n_randint(state, 1000); if (n_randint(state, 10) == 0) prec = FMPR_PREC_EXACT; fmpz_randtest_not_zero(fx, state, bits); fmpz_get_mpz(x, fx); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } ret1 = _fmpr_set_round_mpn(&shift, man, x->_mp_d, FLINT_ABS(x->_mp_size), (x->_mp_size < 0) ? 1 : 0, prec, rnd); fmpz_set_si(exp, shift); ret2 = fmpr_set_round_fmpz(y, fx, prec, rnd); if (!fmpz_equal(fmpr_manref(y), man) || !fmpz_equal(fmpr_expref(y), exp) || ret1 != ret2 || !fmpr_check_ulp(y, ret2, prec)) { flint_printf("FAIL\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("prec: %wd\n", prec); flint_printf("x = "); fmpz_print(fx); flint_printf("\n\n"); flint_printf("man = "); fmpz_print(man); flint_printf("\n\n"); flint_printf("exp = "); fmpz_print(exp); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("ret1 = %wd, ret2 = %wd\n\n", ret1, ret2); abort(); } fmpz_clear(man); fmpz_clear(exp); mpz_clear(x); fmpz_clear(fx); fmpr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-set_round_ui_2exp_fmpz.c000066400000000000000000000061071264125401100213070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("set_round_ui_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong prec, ret1, ret2; fmpz_t man, exp; fmpr_t x, y; mp_limb_t lo; fmpr_rnd_t rnd; int negative; fmpz_init(man); fmpz_init(exp); fmpr_init(x); fmpr_init(y); prec = 2 + n_randint(state, 1000); if (n_randint(state, 10) == 0) prec = FMPR_PREC_EXACT; negative = n_randint(state, 2); lo = n_randtest(state); fmpz_randtest(exp, state, 1 + n_randint(state, 100)); if (negative) fmpz_neg_ui(man, lo); else fmpz_set_ui(man, lo); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } ret1 = fmpr_set_round_ui_2exp_fmpz(x, lo, exp, negative, prec, rnd); fmpr_set_fmpz_2exp(y, man, exp); ret2 = fmpr_set_round(y, y, prec, rnd); if (!fmpr_equal(x, y) || ret1 != ret2 || !fmpr_check_ulp(x, ret1, prec) || !fmpr_check_ulp(y, ret2, prec)) { flint_printf("FAIL\n\n"); flint_printf("prec: %wd\n", prec); flint_printf("man = "); fmpz_print(man); flint_printf("\n\n"); flint_printf("exp = "); fmpz_print(exp); flint_printf("\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("ret1 = %wd, ret2 = %wd\n\n", ret1, ret2); abort(); } fmpz_clear(man); fmpz_clear(exp); fmpr_clear(x); fmpr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-set_round_uiui_2exp_fmpz.c000066400000000000000000000062711264125401100216470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("set_round_uiui_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong prec, ret1, ret2; fmpz_t man, exp; fmpr_t x, y; mp_limb_t hi, lo; fmpr_rnd_t rnd; int negative; fmpz_init(man); fmpz_init(exp); fmpr_init(x); fmpr_init(y); prec = 2 + n_randint(state, 1000); if (n_randint(state, 10) == 0) prec = FMPR_PREC_EXACT; negative = n_randint(state, 2); hi = n_randtest(state); lo = n_randtest(state); fmpz_randtest(exp, state, 1 + n_randint(state, 100)); if (negative) fmpz_neg_uiui(man, hi, lo); else fmpz_set_uiui(man, hi, lo); switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } ret1 = fmpr_set_round_uiui_2exp_fmpz(x, hi, lo, exp, negative, prec, rnd); fmpr_set_fmpz_2exp(y, man, exp); ret2 = fmpr_set_round(y, y, prec, rnd); if (!fmpr_equal(x, y) || ret1 != ret2 || !fmpr_check_ulp(x, ret1, prec) || !fmpr_check_ulp(y, ret2, prec)) { flint_printf("FAIL\n\n"); flint_printf("prec: %wd\n", prec); flint_printf("hi = %wu, lo = %wu\n", hi, lo); flint_printf("man = "); fmpz_print(man); flint_printf("\n\n"); flint_printf("exp = "); fmpz_print(exp); flint_printf("\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("ret1 = %wd, ret2 = %wd\n\n", ret1, ret2); abort(); } fmpz_clear(man); fmpz_clear(exp); fmpr_clear(x); fmpr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-sqrt.c000066400000000000000000000061631264125401100156110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits, res; fmpr_t x, z, w; mpfr_t X, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(z); fmpr_init(w); mpfr_init2(X, 2 * (bits + 100)); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits + n_randint(state, 100), 10); /* occasionally produce perfect squares */ if (n_randint(state, 4) == 0) fmpr_mul(x, x, x, 2 * bits, FMPR_RND_DOWN); fmpr_get_mpfr(X, x, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_sqrt(Z, X, MPFR_RNDZ); res = fmpr_sqrt(z, x, bits, FMPR_RND_DOWN); break; case 1: mpfr_sqrt(Z, X, MPFR_RNDA); res = fmpr_sqrt(z, x, bits, FMPR_RND_UP); break; case 2: mpfr_sqrt(Z, X, MPFR_RNDD); res = fmpr_sqrt(z, x, bits, FMPR_RND_FLOOR); break; default: mpfr_sqrt(Z, X, MPFR_RNDU); res = fmpr_sqrt(z, x, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w) || !fmpr_check_ulp(z, res, bits)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-sub.c000066400000000000000000000146751264125401100154200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("sub...."); fflush(stdout); flint_randinit(state); /* test exact subtraction: (x - y) - z == (x - z) - y */ for (iter = 0; iter < 100000; iter++) { slong bits, res1, res2, res3, res4; fmpr_t x, y, z, t, u; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(t); fmpr_init(u); fmpr_randtest_special(x, state, bits, 10); fmpr_randtest_special(y, state, bits, 10); fmpr_randtest_special(z, state, bits, 10); fmpr_randtest_special(t, state, bits, 10); fmpr_randtest_special(u, state, bits, 10); res1 = fmpr_sub(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); res2 = fmpr_sub(t, t, z, FMPR_PREC_EXACT, FMPR_RND_DOWN); res3 = fmpr_sub(u, x, z, FMPR_PREC_EXACT, FMPR_RND_DOWN); res4 = fmpr_sub(u, u, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); if (!fmpr_equal(t, u) || res1 != FMPR_RESULT_EXACT || res2 != FMPR_RESULT_EXACT || res3 != FMPR_RESULT_EXACT || res4 != FMPR_RESULT_EXACT) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("t = "); fmpr_print(t); flint_printf("\n\n"); flint_printf("u = "); fmpr_print(u); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(t); fmpr_clear(u); } /* compare rounding with mpfr */ for (iter = 0; iter < 100000; iter++) { slong bits, res; int mpfr_res; fmpr_t x, y, z, w; mpfr_t X, Y, Z; bits = 2 + n_randint(state, 200); fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(w); mpfr_init2(X, bits + 100); mpfr_init2(Y, bits + 100); mpfr_init2(Z, bits); fmpr_randtest_special(x, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(y, state, bits + n_randint(state, 100), 10); fmpr_randtest_special(z, state, bits, 10); fmpr_get_mpfr(X, x, MPFR_RNDN); fmpr_get_mpfr(Y, y, MPFR_RNDN); switch (n_randint(state, 4)) { case 0: mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDZ); res = fmpr_sub(z, x, y, bits, FMPR_RND_DOWN); break; case 1: mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDA); res = fmpr_sub(z, x, y, bits, FMPR_RND_UP); break; case 2: mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDD); res = fmpr_sub(z, x, y, bits, FMPR_RND_FLOOR); break; default: mpfr_res = mpfr_sub(Z, X, Y, MPFR_RNDU); res = fmpr_sub(z, x, y, bits, FMPR_RND_CEIL); break; } fmpr_set_mpfr(w, Z); if (!fmpr_equal(z, w) || (res == FMPR_RESULT_EXACT) != (mpfr_res == 0) || !fmpr_check_ulp(z, res, bits)) { flint_printf("FAIL\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); flint_printf("returned: %wd, %d\n", res, mpfr_res); abort(); } /* check error bound */ if (!fmpr_is_nan(z) && !fmpr_is_inf(z)) { fmpr_t z_exact, error_bound, true_error; fmpr_init(z_exact); fmpr_init(error_bound); fmpr_init(true_error); fmpr_set_error_result(error_bound, z, res); fmpr_sub(z_exact, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_sub(true_error, z, z_exact, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_abs(true_error, true_error); if (fmpr_is_zero(error_bound) != fmpr_is_zero(true_error) || fmpr_cmp(true_error, error_bound) > 0) { flint_printf("FAIL: error bound\n\n"); flint_printf("bits = %wd\n", bits); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z_exact = "); fmpr_print(z_exact); flint_printf("\n\n"); flint_printf("true_error = "); fmpr_print(true_error); flint_printf("\n\n"); flint_printf("error_bound = "); fmpr_print(error_bound); flint_printf("\n\n"); abort(); } fmpr_clear(z_exact); fmpr_clear(error_bound); fmpr_clear(true_error); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(w); mpfr_clear(X); mpfr_clear(Y); mpfr_clear(Z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-sum.c000066400000000000000000000103641264125401100154220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("sum...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000000; iter++) { slong i, len, prec, bits, expbits, res1, res2; fmpr_t s1, s2, s3, err, err_bound; fmpr_struct terms[20]; fmpr_rnd_t rnd; len = n_randint(state, 20); bits = 2 + n_randint(state, 1000); prec = 2 + n_randint(state, 1000); expbits = n_randint(state, 14); fmpr_init(s1); fmpr_init(s2); fmpr_init(s3); fmpr_init(err); fmpr_init(err_bound); for (i = 0; i < len; i++) { fmpr_init(terms + i); fmpr_randtest_special(terms + i, state, bits, expbits); } switch (n_randint(state, 4)) { case 0: rnd = FMPR_RND_DOWN; break; case 1: rnd = FMPR_RND_UP; break; case 2: rnd = FMPR_RND_FLOOR; break; default: rnd = FMPR_RND_CEIL; break; } res1 = fmpr_sum(s1, terms, len, prec, rnd); fmpr_zero(s2); for (i = 0; i < len; i++) fmpr_add(s2, s2, terms + i, FMPR_PREC_EXACT, FMPR_RND_DOWN); res2 = fmpr_set_round(s3, s2, prec, rnd); if (!fmpr_equal(s1, s3) || res1 != res2 || !fmpr_check_ulp(s1, res1, prec) || !fmpr_check_ulp(s3, res2, prec)) { flint_printf("FAIL (%wd)\n\n", iter); flint_printf("prec = %wd\n\n", prec); for (i = 0; i < len; i++) { flint_printf("terms[%wd] = ", i); fmpr_print(terms + i); flint_printf("\n\n"); } flint_printf("s1 = "); fmpr_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); fmpr_print(s2); flint_printf("\n\n"); flint_printf("s3 = "); fmpr_print(s3); flint_printf("\n\n"); flint_printf("res1 = %wd, res2 = %wd\n\n", res1, res2); abort(); } fmpr_sub(err, s1, s2, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_abs(err, err); fmpr_set_error_result(err_bound, s1, res1); if (fmpr_cmp(err, err_bound) > 0) { flint_printf("FAIL (error bound)!\n"); flint_printf("prec = %wd\n\n", prec); for (i = 0; i < len; i++) { flint_printf("terms[%wd] = ", i); fmpr_print(terms + i); flint_printf("\n\n"); } flint_printf("s1 = "); fmpr_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); fmpr_print(s2); flint_printf("\n\n"); flint_printf("s3 = "); fmpr_print(s3); flint_printf("\n\n"); flint_printf("error: "); fmpr_print(err); flint_printf("\n\n"); flint_printf("error bound: "); fmpr_print(err_bound); flint_printf("\n\n"); flint_printf("res1 = %wd, res2 = %wd\n\n", res1, res2); abort(); } fmpr_clear(s1); fmpr_clear(s2); fmpr_clear(s3); fmpr_clear(err); fmpr_clear(err_bound); for (i = 0; i < len; i++) fmpr_clear(terms + i); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/test/t-ulp.c000066400000000000000000000045661264125401100154250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" int main() { slong iter; flint_rand_t state; flint_printf("ulp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, ulp, a, b; slong prec; fmpr_init(x); fmpr_init(ulp); fmpr_init(a); fmpr_init(b); prec = 2 + n_randint(state, 1000); fmpr_randtest_not_zero(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 100)); fmpr_ulp(ulp, x, prec); fmpr_abs(a, x); fmpr_mul_2exp_si(a, a, -prec); fmpr_abs(b, x); fmpr_mul_2exp_si(b, b, -prec+1); if (!((fmpr_cmp(a, ulp) < 0) && (fmpr_cmp(ulp, b) <= 0))) { flint_printf("FAIL!\n"); flint_printf("prec = %wd\n", prec); flint_printf("x = "); fmpr_print(x); flint_printf("\n"); flint_printf("ulp = "); fmpr_print(ulp); flint_printf("\n"); flint_printf("a = "); fmpr_print(a); flint_printf("\n"); flint_printf("b = "); fmpr_print(b); flint_printf("\n"); abort(); } fmpr_clear(x); fmpr_clear(ulp); fmpr_clear(a); fmpr_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpr/ulp.c000066400000000000000000000027131264125401100141750ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "fmpr.h" void fmpr_ulp(fmpr_t u, const fmpr_t x, slong prec) { if (fmpr_is_special(x)) { fmpr_abs(u, x); } else { fmpz_t e; fmpz_init(e); fmpz_add_ui(e, fmpr_expref(x), fmpz_bits(fmpr_manref(x))); fmpz_sub_ui(e, e, prec); fmpz_one(fmpr_manref(u)); fmpz_set(fmpr_expref(u), e); fmpz_clear(e); } } arb-2.8.1/fmprb.h000066400000000000000000000467531264125401100135600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef FMPRB_H #define FMPRB_H #include "fmpr.h" #include "fmpz_poly.h" #ifdef __cplusplus extern "C" { #endif typedef struct { fmpr_struct mid; fmpr_struct rad; } fmprb_struct; typedef fmprb_struct fmprb_t[1]; typedef fmprb_struct * fmprb_ptr; typedef const fmprb_struct * fmprb_srcptr; #define fmprb_midref(x) (&(x)->mid) #define fmprb_radref(x) (&(x)->rad) #define FMPRB_RAD_PREC 30 #define FMPRB_MIN_ADJUSTED_PREC static __inline__ void fmprb_init(fmprb_t x) { fmpr_init(fmprb_midref(x)); fmpr_init(fmprb_radref(x)); } #define FMPRB_DEBUG 0 static __inline__ void fmprb_clear(fmprb_t x) { #if FMPRB_DEBUG if (fmpr_is_nan(fmprb_radref(x)) || fmpr_sgn(fmprb_radref(x)) < 0) { flint_printf("ABORT: nan or negative radius!\n"); abort(); } #endif fmpr_clear(fmprb_midref(x)); fmpr_clear(fmprb_radref(x)); } static __inline__ fmprb_ptr _fmprb_vec_init(slong n) { slong i; fmprb_ptr v = (fmprb_ptr) flint_malloc(sizeof(fmprb_struct) * n); for (i = 0; i < n; i++) fmprb_init(v + i); return v; } static __inline__ void _fmprb_vec_clear(fmprb_ptr v, slong n) { slong i; for (i = 0; i < n; i++) fmprb_clear(v + i); flint_free(v); } static __inline__ int fmprb_is_exact(const fmprb_t x) { return fmpr_is_zero(fmprb_radref(x)); } static __inline__ int fmprb_equal(const fmprb_t x, const fmprb_t y) { return fmpr_equal(fmprb_midref(x), fmprb_midref(y)) && fmpr_equal(fmprb_radref(x), fmprb_radref(y)); } static __inline__ void fmprb_zero(fmprb_t x) { fmpr_zero(fmprb_midref(x)); fmpr_zero(fmprb_radref(x)); } static __inline__ int fmprb_is_zero(const fmprb_t x) { return fmpr_is_zero(fmprb_midref(x)) && fmpr_is_zero(fmprb_radref(x)); } static __inline__ void fmprb_pos_inf(fmprb_t x) { fmpr_pos_inf(fmprb_midref(x)); fmpr_zero(fmprb_radref(x)); } static __inline__ void fmprb_neg_inf(fmprb_t x) { fmpr_neg_inf(fmprb_midref(x)); fmpr_zero(fmprb_radref(x)); } static __inline__ void fmprb_zero_pm_inf(fmprb_t x) { fmpr_zero(fmprb_midref(x)); fmpr_pos_inf(fmprb_radref(x)); } static __inline__ void fmprb_indeterminate(fmprb_t x) { fmpr_nan(fmprb_midref(x)); fmpr_pos_inf(fmprb_radref(x)); } static __inline__ int fmprb_is_finite(const fmprb_t x) { return fmpr_is_finite(fmprb_midref(x)) && fmpr_is_finite(fmprb_radref(x)); } static __inline__ void fmprb_set(fmprb_t x, const fmprb_t y) { fmpr_set(fmprb_midref(x), fmprb_midref(y)); fmpr_set(fmprb_radref(x), fmprb_radref(y)); } void fmprb_set_round(fmprb_t z, const fmprb_t x, slong prec); void fmprb_trim(fmprb_t y, const fmprb_t x); static __inline__ void fmprb_swap(fmprb_t x, fmprb_t y) { fmprb_struct t = *x; *x = *y; *y = t; } static __inline__ void fmprb_neg(fmprb_t x, const fmprb_t y) { fmpr_neg(fmprb_midref(x), fmprb_midref(y)); fmpr_set(fmprb_radref(x), fmprb_radref(y)); } static __inline__ void fmprb_neg_round(fmprb_t x, const fmprb_t y, slong prec) { fmprb_set_round(x, y, prec); fmprb_neg(x, x); } static __inline__ void fmprb_abs(fmprb_t x, const fmprb_t y) { fmpr_abs(fmprb_midref(x), fmprb_midref(y)); fmpr_set(fmprb_radref(x), fmprb_radref(y)); } static __inline__ void fmprb_set_fmpr(fmprb_t x, const fmpr_t y) { fmpr_set(fmprb_midref(x), y); fmpr_zero(fmprb_radref(x)); } static __inline__ void fmprb_set_si(fmprb_t x, slong y) { fmpr_set_si(fmprb_midref(x), y); fmpr_zero(fmprb_radref(x)); } static __inline__ void fmprb_set_ui(fmprb_t x, ulong y) { fmpr_set_ui(fmprb_midref(x), y); fmpr_zero(fmprb_radref(x)); } static __inline__ void fmprb_set_fmpz(fmprb_t x, const fmpz_t y) { fmpr_set_fmpz(fmprb_midref(x), y); fmpr_zero(fmprb_radref(x)); } static __inline__ void fmprb_set_fmpz_2exp(fmprb_t x, const fmpz_t y, const fmpz_t exp) { fmpr_set_fmpz_2exp(fmprb_midref(x), y, exp); fmpr_zero(fmprb_radref(x)); } static __inline__ void fmprb_set_round_fmpz_2exp(fmprb_t y, const fmpz_t x, const fmpz_t exp, slong prec) { slong r = fmpr_set_round_fmpz_2exp(fmprb_midref(y), x, exp, prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(y), fmprb_midref(y), r); } static __inline__ void fmprb_set_round_fmpz(fmprb_t y, const fmpz_t x, slong prec) { slong r = fmpr_set_round_fmpz(fmprb_midref(y), x, prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(y), fmprb_midref(y), r); } static __inline__ int fmprb_is_one(const fmprb_t f) { return fmpr_is_one(fmprb_midref(f)) && fmpr_is_zero(fmprb_radref(f)); } static __inline__ void fmprb_one(fmprb_t f) { fmprb_set_ui(f, UWORD(1)); } static __inline__ void fmprb_adjust(fmprb_t x) { if (!fmprb_is_exact(x)) { /* reduce precision here */ } } void fmprb_add(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_add_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec); void fmprb_add_si(fmprb_t z, const fmprb_t x, slong y, slong prec); void fmprb_add_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec); void fmprb_add_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec); void fmprb_addmul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_addmul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec); void fmprb_addmul_si(fmprb_t z, const fmprb_t x, slong y, slong prec); void fmprb_addmul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec); void fmprb_div(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_div_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec); void fmprb_div_si(fmprb_t z, const fmprb_t x, slong y, slong prec); void fmprb_div_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec); void fmprb_div_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec); void fmprb_fmpz_div_fmpz(fmprb_t y, const fmpz_t num, const fmpz_t den, slong prec); void fmprb_ui_div(fmprb_t z, ulong x, const fmprb_t y, slong prec); static __inline__ void fmprb_inv(fmprb_t y, const fmprb_t x, slong prec) { fmprb_ui_div(y, 1, x, prec); } void fmprb_mul_fmpr_naive(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec); void fmprb_mul_main_naive(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_mul_naive(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_mul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_mul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec); void fmprb_mul_si(fmprb_t z, const fmprb_t x, slong y, slong prec); void fmprb_mul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec); void fmprb_mul_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec); void fmprb_sqrt(fmprb_t z, const fmprb_t x, slong prec); void fmprb_sqrt_ui(fmprb_t z, ulong x, slong prec); void fmprb_sqrt_fmpz(fmprb_t z, const fmpz_t x, slong prec); void fmprb_rsqrt(fmprb_t z, const fmprb_t x, slong prec); void fmprb_rsqrt_ui(fmprb_t z, ulong x, slong prec); void fmprb_sqrtpos(fmprb_t z, const fmprb_t x, slong prec); void fmprb_hypot(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_sub(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_sub_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec); void fmprb_sub_si(fmprb_t z, const fmprb_t x, slong y, slong prec); void fmprb_sub_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec); void fmprb_submul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); void fmprb_submul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec); void fmprb_submul_si(fmprb_t z, const fmprb_t x, slong y, slong prec); void fmprb_submul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec); void fmprb_root(fmprb_t z, const fmprb_t x, ulong k, slong prec); void fmprb_agm(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); static __inline__ void fmprb_print(const fmprb_t x) { fmpr_print(fmprb_midref(x)); flint_printf(" +/- "); fmpr_print(fmprb_radref(x)); } static __inline__ void fmprb_printd(const fmprb_t x, slong digits) { fmpr_printd(fmprb_midref(x), FLINT_ABS(digits)); if (digits > 0) { flint_printf(" +/- "); fmpr_printd(fmprb_radref(x), 5); } } static __inline__ void fmprb_mul_2exp_si(fmprb_t y, const fmprb_t x, slong e) { fmpr_mul_2exp_si(fmprb_midref(y), fmprb_midref(x), e); fmpr_mul_2exp_si(fmprb_radref(y), fmprb_radref(x), e); } static __inline__ void fmprb_mul_2exp_fmpz(fmprb_t y, const fmprb_t x, const fmpz_t e) { fmpr_mul_2exp_fmpz(fmprb_midref(y), fmprb_midref(x), e); fmpr_mul_2exp_fmpz(fmprb_radref(y), fmprb_radref(x), e); } static __inline__ void fmprb_set_fmpq(fmprb_t y, const fmpq_t x, slong prec) { fmprb_fmpz_div_fmpz(y, fmpq_numref(x), fmpq_denref(x), prec); } int fmprb_contains_fmpr(const fmprb_t x, const fmpr_t y); int fmprb_contains_fmpq(const fmprb_t x, const fmpq_t y); int fmprb_contains_fmpz(const fmprb_t x, const fmpz_t y); int fmprb_contains_si(const fmprb_t x, slong y); int fmprb_contains_mpfr(const fmprb_t x, const mpfr_t y); int fmprb_contains_zero(const fmprb_t x); int fmprb_overlaps(const fmprb_t x, const fmprb_t y); int fmprb_contains(const fmprb_t x, const fmprb_t y); static __inline__ int fmprb_is_int(const fmprb_t x) { return fmpr_is_zero(fmprb_radref(x)) && fmpr_is_int(fmprb_midref(x)); } static __inline__ int fmprb_is_nonzero(const fmprb_t x) { return !fmprb_contains_zero(x); } static __inline__ int fmprb_is_positive(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) > 0) && (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) < 0) && !fmpr_is_nan(fmprb_midref(x)); } static __inline__ int fmprb_is_nonnegative(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) >= 0) && (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) <= 0) && !fmpr_is_nan(fmprb_midref(x)); } static __inline__ int fmprb_is_negative(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) < 0) && (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) < 0) && !fmpr_is_nan(fmprb_midref(x)); } static __inline__ int fmprb_is_nonpositive(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) <= 0) && (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) <= 0) && !fmpr_is_nan(fmprb_midref(x)); } static __inline__ int fmprb_contains_negative(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) < 0) || (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) > 0) || fmpr_is_nan(fmprb_midref(x)); } static __inline__ int fmprb_contains_nonpositive(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) <= 0) || (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) >= 0) || fmpr_is_nan(fmprb_midref(x)); } static __inline__ int fmprb_contains_positive(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) > 0) || (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) > 0) || fmpr_is_nan(fmprb_midref(x)); } static __inline__ int fmprb_contains_nonnegative(const fmprb_t x) { return (fmpr_sgn(fmprb_midref(x)) >= 0) || (fmpr_cmpabs(fmprb_radref(x), fmprb_midref(x)) >= 0) || fmpr_is_nan(fmprb_midref(x)); } static __inline__ void fmprb_get_abs_ubound_fmpr(fmpr_t u, const fmprb_t x, slong prec) { if (fmpr_sgn(fmprb_midref(x)) < 0) fmpr_sub(u, fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_UP); else fmpr_add(u, fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_UP); fmpr_abs(u, u); } static __inline__ void fmprb_get_abs_lbound_fmpr(fmpr_t u, const fmprb_t x, slong prec) { if (fmpr_sgn(fmprb_midref(x)) > 0) { fmpr_sub(u, fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_DOWN); } else { fmpr_add(u, fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_DOWN); fmpr_neg(u, u); } if (fmpr_sgn(u) < 0) fmpr_zero(u); } void fmprb_get_interval_fmpz_2exp(fmpz_t a, fmpz_t b, fmpz_t exp, const fmprb_t x); int fmprb_get_unique_fmpz(fmpz_t z, const fmprb_t x); void fmprb_set_interval_fmpr(fmprb_t x, const fmpr_t a, const fmpr_t b, slong prec); void fmprb_union(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec); static __inline__ slong fmprb_rel_error_bits(const fmprb_t x) { fmpz_t midmag, radmag; slong result; if (fmpr_is_zero(fmprb_radref(x))) return -FMPR_PREC_EXACT; if (fmpr_is_special(fmprb_midref(x)) || fmpr_is_special(fmprb_radref(x))) return FMPR_PREC_EXACT; fmpz_init(midmag); fmpz_init(radmag); fmpr_abs_bound_lt_2exp_fmpz(midmag, fmprb_midref(x)); fmpr_abs_bound_lt_2exp_fmpz(radmag, fmprb_radref(x)); fmpz_add_ui(radmag, radmag, 1); result = _fmpz_sub_small(radmag, midmag); fmpz_clear(midmag); fmpz_clear(radmag); return result; } static __inline__ slong fmprb_rel_accuracy_bits(const fmprb_t x) { return -fmprb_rel_error_bits(x); } static __inline__ slong fmprb_bits(const fmprb_t x) { return fmpr_bits(fmprb_midref(x)); } void fmprb_add_error_fmpr(fmprb_t x, const fmpr_t err); void fmprb_add_error_2exp_si(fmprb_t x, slong err); void fmprb_add_error_2exp_fmpz(fmprb_t x, const fmpz_t err); void fmprb_add_error(fmprb_t x, const fmprb_t error); void fmprb_randtest(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits); void fmprb_randtest_exact(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits); void fmprb_randtest_wide(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits); void fmprb_randtest_precise(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits); void fmprb_randtest_special(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits); void fmprb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const fmprb_t x, slong bits); #define DEF_CACHED_CONSTANT(name, comp_func) \ TLS_PREFIX slong name ## _cached_prec = 0; \ TLS_PREFIX fmprb_t name ## _cached_value; \ void name ## _cleanup(void) \ { \ fmprb_clear(name ## _cached_value); \ name ## _cached_prec = 0; \ } \ void name(fmprb_t x, slong prec) \ { \ if (name ## _cached_prec < prec) \ { \ if (name ## _cached_prec == 0) \ { \ fmprb_init(name ## _cached_value); \ flint_register_cleanup_function(name ## _cleanup); \ } \ comp_func(name ## _cached_value, prec); \ name ## _cached_prec = prec; \ } \ fmprb_set_round(x, name ## _cached_value, prec); \ } /* vector functions */ static __inline__ void _fmprb_vec_zero(fmprb_ptr A, slong n) { slong i; for (i = 0; i < n; i++) fmprb_zero(A + i); } static __inline__ int _fmprb_vec_is_zero(fmprb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) if (!fmprb_is_zero(vec + i)) return 0; return 1; } static __inline__ void _fmprb_vec_set(fmprb_ptr res, fmprb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) fmprb_set(res + i, vec + i); } static __inline__ void _fmprb_vec_set_round(fmprb_ptr res, fmprb_srcptr vec, slong len, slong prec) { slong i; for (i = 0; i < len; i++) fmprb_set_round(res + i, vec + i, prec); } static __inline__ void _fmprb_vec_swap(fmprb_ptr res, fmprb_ptr vec, slong len) { slong i; for (i = 0; i < len; i++) fmprb_swap(res + i, vec + i); } static __inline__ void _fmprb_vec_neg(fmprb_ptr B, fmprb_srcptr A, slong n) { slong i; for (i = 0; i < n; i++) fmprb_neg(B + i, A + i); } static __inline__ void _fmprb_vec_sub(fmprb_ptr C, fmprb_srcptr A, fmprb_srcptr B, slong n, slong prec) { slong i; for (i = 0; i < n; i++) fmprb_sub(C + i, A + i, B + i, prec); } static __inline__ void _fmprb_vec_add(fmprb_ptr C, fmprb_srcptr A, fmprb_srcptr B, slong n, slong prec) { slong i; for (i = 0; i < n; i++) fmprb_add(C + i, A + i, B + i, prec); } static __inline__ void _fmprb_vec_scalar_mul(fmprb_ptr res, fmprb_srcptr vec, slong len, const fmprb_t c, slong prec) { slong i; for (i = 0; i < len; i++) fmprb_mul(res + i, vec + i, c, prec); } static __inline__ void _fmprb_vec_scalar_div(fmprb_ptr res, fmprb_srcptr vec, slong len, const fmprb_t c, slong prec) { slong i; for (i = 0; i < len; i++) fmprb_div(res + i, vec + i, c, prec); } static __inline__ void _fmprb_vec_scalar_mul_fmpz(fmprb_ptr res, fmprb_srcptr vec, slong len, const fmpz_t c, slong prec) { slong i; fmpr_t t; fmpr_init(t); fmpr_set_fmpz(t, c); for (i = 0; i < len; i++) fmprb_mul_fmpr(res + i, vec + i, t, prec); fmpr_clear(t); } static __inline__ void _fmprb_vec_scalar_mul_2exp_si(fmprb_ptr res, fmprb_srcptr src, slong len, slong c) { slong i; for (i = 0; i < len; i++) fmprb_mul_2exp_si(res + i, src + i, c); } static __inline__ void _fmprb_vec_scalar_addmul(fmprb_ptr res, fmprb_srcptr vec, slong len, const fmprb_t c, slong prec) { slong i; for (i = 0; i < len; i++) fmprb_addmul(res + i, vec + i, c, prec); } static __inline__ void _fmprb_vec_get_abs_ubound_fmpr(fmpr_t bound, fmprb_srcptr vec, slong len, slong prec) { fmpr_t t; slong i; if (len < 1) { fmpr_zero(bound); } else { fmprb_get_abs_ubound_fmpr(bound, vec, prec); fmpr_init(t); for (i = 1; i < len; i++) { fmprb_get_abs_ubound_fmpr(t, vec + i, prec); if (fmpr_cmp(t, bound) > 0) fmpr_set(bound, t); } fmpr_clear(t); } } static __inline__ slong _fmprb_vec_bits(fmprb_srcptr x, slong len) { slong i, b, c; b = 0; for (i = 0; i < len; i++) { c = fmprb_bits(x + i); b = FLINT_MAX(b, c); } return b; } static __inline__ void _fmprb_vec_set_powers(fmprb_ptr xs, const fmprb_t x, slong len, slong prec) { slong i; for (i = 0; i < len; i++) { if (i == 0) fmprb_one(xs + i); else if (i == 1) fmprb_set_round(xs + i, x, prec); else if (i % 2 == 0) fmprb_mul(xs + i, xs + i / 2, xs + i / 2, prec); else fmprb_mul(xs + i, xs + i - 1, x, prec); } } static __inline__ void _fmprb_vec_add_error_fmpr_vec(fmprb_ptr res, fmpr_srcptr err, slong len) { slong i; for (i = 0; i < len; i++) fmprb_add_error_fmpr(res + i, err + i); } static __inline__ void _fmprb_vec_indeterminate(fmprb_ptr vec, slong len) { slong i; for (i = 0; i < len; i++) { fmpr_nan(fmprb_midref(vec + i)); fmpr_pos_inf(fmprb_radref(vec + i)); } } static __inline__ void _fmprb_vec_trim(fmprb_ptr res, fmprb_srcptr vec, slong len) { slong i; for (i = 0; i < len; i++) fmprb_trim(res + i, vec + i); } #ifdef __cplusplus } #endif #endif arb-2.8.1/fmprb/000077500000000000000000000000001264125401100133705ustar00rootroot00000000000000arb-2.8.1/fmprb/add.c000066400000000000000000000043311264125401100142650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_add(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { slong r; fmpr_add(fmprb_radref(z), fmprb_radref(x), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_UP); r = fmpr_add(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), fmprb_radref(z), fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); fmprb_adjust(z); } void fmprb_add_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_ui(t, y); fmprb_add(z, x, t, prec); fmprb_clear(t); } void fmprb_add_si(fmprb_t z, const fmprb_t x, slong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_si(t, y); fmprb_add(z, x, t, prec); fmprb_clear(t); } void fmprb_add_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_fmpz(t, y); fmprb_add(z, x, t, prec); fmprb_clear(t); } void fmprb_add_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_fmpr(t, y); fmprb_add(z, x, t, prec); fmprb_clear(t); } arb-2.8.1/fmprb/add_error.c000066400000000000000000000036341264125401100155030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_add_error_fmpr(fmprb_t x, const fmpr_t err) { fmpr_add(fmprb_radref(x), fmprb_radref(x), err, FMPRB_RAD_PREC, FMPR_RND_UP); } void fmprb_add_error_2exp_si(fmprb_t x, slong err) { fmpr_t t; fmpr_init(t); fmpr_set_ui_2exp_si(t, 1, err); fmprb_add_error_fmpr(x, t); fmpr_clear(t); } void fmprb_add_error_2exp_fmpz(fmprb_t x, const fmpz_t err) { fmpr_t t; fmpr_init(t); fmpz_one(fmpr_manref(t)); fmpz_set(fmpr_expref(t), err); fmprb_add_error_fmpr(x, t); fmpr_clear(t); } void fmprb_add_error(fmprb_t x, const fmprb_t error) { fmpr_t high; fmpr_init(high); fmpr_add(high, fmprb_midref(error), fmprb_radref(error), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_add(fmprb_radref(x), fmprb_radref(x), high, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_clear(high); } arb-2.8.1/fmprb/addmul.c000066400000000000000000000035401264125401100150040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_addmul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_mul(t, x, y, prec); fmprb_add(z, z, t, prec); fmprb_clear(t); } void fmprb_addmul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_mul_ui(t, x, y, prec); fmprb_add(z, z, t, prec); fmprb_clear(t); } void fmprb_addmul_si(fmprb_t z, const fmprb_t x, slong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_mul_si(t, x, y, prec); fmprb_add(z, z, t, prec); fmprb_clear(t); } void fmprb_addmul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_mul_fmpz(t, x, y, prec); fmprb_add(z, z, t, prec); fmprb_clear(t); } arb-2.8.1/fmprb/agm.c000066400000000000000000000041071264125401100143020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_agm(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { fmprb_t t, u, v, w; if (fmprb_contains_negative(x) || fmprb_contains_negative(y)) { fmprb_indeterminate(z); return; } if (fmprb_is_zero(x) || fmprb_is_zero(y)) { fmprb_zero(z); return; } fmprb_init(t); fmprb_init(u); fmprb_init(v); fmprb_init(w); fmprb_set(t, x); fmprb_set(u, y); while (!fmprb_overlaps(t, u) && !fmprb_contains_nonpositive(t) && !fmprb_contains_nonpositive(u)) { fmprb_add(v, t, u, prec); fmprb_mul_2exp_si(v, v, -1); fmprb_mul(w, t, u, prec); fmprb_sqrt(w, w, prec); fmprb_swap(v, t); fmprb_swap(w, u); } if (!fmprb_is_finite(t) || !fmprb_is_finite(u)) { fmprb_indeterminate(z); } else { fmprb_union(z, t, u, prec); } fmprb_clear(t); fmprb_clear(u); fmprb_clear(v); fmprb_clear(w); } arb-2.8.1/fmprb/contains.c000066400000000000000000000057111264125401100153560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_contains(const fmprb_t x, const fmprb_t y) { fmpr_t t; fmpr_t u; fmpr_struct tmp[4]; int left_ok, right_ok; if (fmprb_is_exact(y)) return fmprb_contains_fmpr(x, fmprb_midref(y)); if (fmpr_is_nan(fmprb_midref(y))) return fmpr_is_nan(fmprb_midref(x)); fmpr_init(t); fmpr_init(u); /* fast check */ fmpr_sub(t, fmprb_midref(x), fmprb_radref(x), 30, FMPR_RND_CEIL); fmpr_sub(u, fmprb_midref(y), fmprb_radref(y), 30, FMPR_RND_FLOOR); left_ok = fmpr_cmp(t, u) <= 0; /* exact check */ if (!left_ok) { fmpr_init(tmp + 0); fmpr_init(tmp + 1); fmpr_init(tmp + 2); fmpr_init(tmp + 3); fmpr_set(tmp + 0, fmprb_midref(x)); fmpr_neg(tmp + 1, fmprb_radref(x)); fmpr_neg(tmp + 2, fmprb_midref(y)); fmpr_set(tmp + 3, fmprb_radref(y)); fmpr_sum(t, tmp, 4, 30, FMPR_RND_DOWN); left_ok = fmpr_sgn(t) <= 0; fmpr_clear(tmp + 0); fmpr_clear(tmp + 1); fmpr_clear(tmp + 2); fmpr_clear(tmp + 3); } /* fast check */ fmpr_add(t, fmprb_midref(x), fmprb_radref(x), 30, FMPR_RND_FLOOR); fmpr_add(u, fmprb_midref(y), fmprb_radref(y), 30, FMPR_RND_CEIL); right_ok = (fmpr_cmp(t, u) >= 0); /* exact check */ if (!right_ok) { fmpr_init(tmp + 0); fmpr_init(tmp + 1); fmpr_init(tmp + 2); fmpr_init(tmp + 3); fmpr_set(tmp + 0, fmprb_midref(x)); fmpr_set(tmp + 1, fmprb_radref(x)); fmpr_neg(tmp + 2, fmprb_midref(y)); fmpr_neg(tmp + 3, fmprb_radref(y)); fmpr_sum(t, tmp, 4, 30, FMPR_RND_DOWN); right_ok = fmpr_sgn(t) >= 0; fmpr_clear(tmp + 0); fmpr_clear(tmp + 1); fmpr_clear(tmp + 2); fmpr_clear(tmp + 3); } fmpr_clear(t); fmpr_clear(u); return left_ok && right_ok; } arb-2.8.1/fmprb/contains_fmpq.c000066400000000000000000000027521264125401100164030ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_contains_fmpq(const fmprb_t x, const fmpq_t y) { if (fmpz_is_one(fmpq_denref(y))) { return fmprb_contains_fmpz(x, fmpq_numref(y)); } else { int ans; fmprb_t t; fmprb_init(t); fmprb_mul_fmpz(t, x, fmpq_denref(y), FMPR_PREC_EXACT); ans = fmprb_contains_fmpz(t, fmpq_numref(y)); fmprb_clear(t); return ans; } } arb-2.8.1/fmprb/contains_fmpr.c000066400000000000000000000042621264125401100164020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_contains_fmpr(const fmprb_t x, const fmpr_t y) { if (fmpr_is_nan(y)) { return fmpr_is_nan(fmprb_midref(x)); } else if (fmpr_is_nan(fmprb_midref(x))) { return 1; } else if (fmprb_is_exact(x)) { return fmpr_equal(fmprb_midref(x), y); } else { fmpr_t t; fmpr_struct tmp[3]; int result; fmpr_init(t); fmpr_init(tmp + 0); fmpr_init(tmp + 1); fmpr_init(tmp + 2); /* y >= xm - xr <=> 0 >= xm - xr - y */ fmpr_set(tmp + 0, fmprb_midref(x)); fmpr_neg(tmp + 1, fmprb_radref(x)); fmpr_neg(tmp + 2, y); fmpr_sum(t, tmp, 3, 30, FMPR_RND_DOWN); result = (fmpr_sgn(t) <= 0); if (result) { /* y <= xm + xr <=> 0 <= xm + xr - y */ fmpr_neg(tmp + 1, tmp + 1); fmpr_sum(t, tmp, 3, 30, FMPR_RND_DOWN); result = (fmpr_sgn(t) >= 0); } fmpr_clear(t); fmpr_clear(tmp + 0); fmpr_clear(tmp + 1); fmpr_clear(tmp + 2); return result; } } arb-2.8.1/fmprb/contains_fmpz.c000066400000000000000000000024371264125401100164140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_contains_fmpz(const fmprb_t x, const fmpz_t y) { int ans; fmpr_t t; fmpr_init(t); fmpr_set_fmpz(t, y); ans = fmprb_contains_fmpr(x, t); fmpr_clear(t); return ans; } arb-2.8.1/fmprb/contains_mpfr.c000066400000000000000000000024371264125401100164040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_contains_mpfr(const fmprb_t x, const mpfr_t y) { int ans; fmpr_t t; fmpr_init(t); fmpr_set_mpfr(t, y); ans = fmprb_contains_fmpr(x, t); fmpr_clear(t); return ans; } arb-2.8.1/fmprb/contains_si.c000066400000000000000000000024241264125401100160470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_contains_si(const fmprb_t x, slong y) { int ans; fmpr_t t; fmpr_init(t); fmpr_set_si(t, y); ans = fmprb_contains_fmpr(x, t); fmpr_clear(t); return ans; } arb-2.8.1/fmprb/contains_zero.c000066400000000000000000000023001264125401100164040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_contains_zero(const fmprb_t x) { return fmpr_cmpabs(fmprb_midref(x), fmprb_radref(x)) <= 0; } arb-2.8.1/fmprb/div.c000066400000000000000000000116641264125401100143260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" static __inline__ void fmprb_div_zero(fmprb_t z) { fmpr_zero(fmprb_midref(z)); fmpr_pos_inf(fmprb_radref(z)); return; } void fmprb_div_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec) { slong r; if (fmpr_is_zero(y)) { fmprb_div_zero(z); } else if (fmprb_is_exact(x)) { r = fmpr_div(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r); } else if (fmpr_is_pos_inf(fmprb_radref(x))) { fmpr_div(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN); fmpr_pos_inf(fmprb_radref(z)); } else { /* (x + a) / y = x/y + a/y */ fmpr_divappr_abs_ubound(fmprb_radref(z), fmprb_radref(x), y, FMPRB_RAD_PREC); fmpr_abs(fmprb_radref(z), fmprb_radref(z)); r = fmpr_div(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), fmprb_radref(z), fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); } } void fmprb_div(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { slong r; if (fmprb_is_exact(y)) { fmprb_div_fmpr(z, x, fmprb_midref(y), prec); } else if (fmpr_is_pos_inf(fmprb_radref(x)) || fmpr_is_pos_inf(fmprb_radref(y))) { fmpr_div(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN); fmpr_pos_inf(fmprb_radref(z)); } else { fmpr_t t, u; fmpr_init(t); fmpr_init(u); /* numerator of error bound: |xb| + |ya|, rounded up */ fmpr_mul(t, fmprb_midref(x), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_abs(t, t); fmpr_mul(u, fmprb_midref(y), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_abs(u, u); fmpr_add(t, t, u, FMPRB_RAD_PREC, FMPR_RND_UP); /* denominator of error bound: |y|(|y|-b), rounded down */ if (fmpr_sgn(fmprb_midref(y)) > 0) { fmpr_sub(u, fmprb_midref(y), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_DOWN); } else { fmpr_add(u, fmprb_midref(y), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_DOWN); fmpr_neg(u, u); } if (fmpr_sgn(u) <= 0 || fmpr_is_nan(u)) { fmprb_div_zero(z); } else { fmpr_mul(u, u, fmprb_midref(y), FMPRB_RAD_PREC, FMPR_RND_DOWN); fmpr_divappr_abs_ubound(t, t, u, FMPRB_RAD_PREC); r = fmpr_div(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), t, fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); } fmpr_clear(t); fmpr_clear(u); } fmprb_adjust(z); } void fmprb_div_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) { fmpr_t t; fmpr_init(t); fmpr_set_ui(t, y); fmprb_div_fmpr(z, x, t, prec); fmpr_clear(t); } void fmprb_div_si(fmprb_t z, const fmprb_t x, slong y, slong prec) { fmpr_t t; fmpr_init(t); fmpr_set_si(t, y); fmprb_div_fmpr(z, x, t, prec); fmpr_clear(t); } void fmprb_div_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) { fmpr_t t; fmpr_init(t); fmpr_set_fmpz(t, y); fmprb_div_fmpr(z, x, t, prec); fmpr_clear(t); } void fmprb_fmpz_div_fmpz(fmprb_t y, const fmpz_t num, const fmpz_t den, slong prec) { fmpr_t p, q; slong r; fmpr_init(p); fmpr_init(q); fmpr_set_fmpz(p, num); fmpr_set_fmpz(q, den); r = fmpr_div(fmprb_midref(y), p, q, prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(y), fmprb_midref(y), r); fmpr_clear(p); fmpr_clear(q); } void fmprb_ui_div(fmprb_t z, ulong x, const fmprb_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_ui(t, x); fmprb_div(z, t, y, prec); fmprb_clear(t); } arb-2.8.1/fmprb/get_interval_fmpz_2exp.c000066400000000000000000000044171264125401100202170ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" /* Computes the exact interval represented by x, in the form of an integer interval multiplied by a power of two, i.e. x = [a, b] * 2^exp. The outcome is undefined if the midpoint or radius of x is non-finite, or if the difference in magnitude between the midpoint and radius is so large that representing the endpoints exactly would cause overflows. */ void fmprb_get_interval_fmpz_2exp(fmpz_t a, fmpz_t b, fmpz_t exp, const fmprb_t x) { if (fmprb_is_exact(x)) { fmpr_get_fmpz_2exp(a, exp, fmprb_midref(x)); fmpz_set(b, a); } else { fmpr_t t; fmpz_t exp2; slong s; fmpr_init(t); fmpz_init(exp2); fmpr_sub(t, fmprb_midref(x), fmprb_radref(x), FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_get_fmpz_2exp(a, exp, t); fmpr_add(t, fmprb_midref(x), fmprb_radref(x), FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_get_fmpz_2exp(b, exp2, t); s = _fmpz_sub_small(exp, exp2); if (s <= 0) { fmpz_mul_2exp(b, b, -s); } else { fmpz_mul_2exp(a, a, s); fmpz_set(exp, exp2); } fmpr_clear(t); fmpz_clear(exp2); } } arb-2.8.1/fmprb/get_rand_fmpq.c000066400000000000000000000070061264125401100163450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" /* Returns a random rational in x. The binary denominator of x is multiplied by den_mult to select a base denominator to choose random integers between. The outcome is undefined if the midpoint or radius of x is non-finite, or if the exponent of the midpoint or radius is so large or small that representing the endpoints as exact rational numbers would cause overflows. */ void _fmprb_get_rand_fmpq(fmpz_t num, fmpz_t den, flint_rand_t state, const fmpz_t den_mult, const fmprb_t x) { fmpz_t a, b, exp; fmpz_init(a); fmpz_init(b); fmpz_init(exp); fmprb_get_interval_fmpz_2exp(a, b, exp, x); if (COEFF_IS_MPZ(*exp)) { flint_printf("exception: fmprb_get_rand_fmpq: too large exponent\n"); abort(); } if (*exp >= 0) { fmpz_mul_2exp(a, a, *exp); fmpz_mul_2exp(b, b, *exp); } /* generate random integer in [a*den, b*den] */ fmpz_mul(a, a, den_mult); fmpz_mul(b, b, den_mult); fmpz_add_ui(b, b, UWORD(1)); fmpz_sub(b, b, a); /* return one endpoint with high probability (used for stress testing rounding) */ if (n_randint(state, 6) == 0) { if (n_randint(state, 2)) fmpz_zero(num); else fmpz_sub_ui(num, b, UWORD(1)); } else { fmpz_randtest_mod(num, state, b); } fmpz_add(num, num, a); fmpz_set(den, den_mult); if (*exp < 0) fmpz_mul_2exp(den, den, -(*exp)); fmpz_clear(a); fmpz_clear(b); fmpz_clear(exp); } /* Chooses a random rational number from the interval represented by x. A denominator is chosen by multiplying the binary denominator of x by a random integer up to size bits. The outcome is undefined if the midpoint or radius of x is non-finite, or if the exponent of the midpoint or radius is so large or small that representing the endpoints as exact rational numbers would cause overflows. */ void fmprb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const fmprb_t x, slong bits) { /* there is only one rational */ if (fmprb_is_exact(x)) { fmpr_get_fmpq(q, fmprb_midref(x)); return; } /* pick a denominator */ fmpz_randbits(fmpq_denref(q), state, n_randint(state, bits + 1)); fmpz_abs(fmpq_denref(q), fmpq_denref(q)); if (fmpz_is_zero(fmpq_denref(q))) fmpz_one(fmpq_denref(q)); _fmprb_get_rand_fmpq(fmpq_numref(q), fmpq_denref(q), state, fmpq_denref(q), x); fmpq_canonicalise(q); } arb-2.8.1/fmprb/get_unique_fmpz.c000066400000000000000000000061201264125401100167340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_get_unique_fmpz(fmpz_t z, const fmprb_t x) { if (!fmprb_is_finite(x)) { return 0; } else if (fmpr_is_zero(fmprb_radref(x))) { /* x = b*2^e, e >= 0 */ if (fmpr_is_int(fmprb_midref(x))) { if (!fmpz_fits_si(fmpr_expref(fmprb_midref(x)))) { flint_printf("fmprb_get_unique_fmpz: too large shift\n"); abort(); } fmpz_mul_2exp(z, fmpr_manref(fmprb_midref(x)), fmpz_get_si(fmpr_expref(fmprb_midref(x)))); return 1; } else { return 0; } } /* if the radius is >= 1, there are at least two integers */ else if (fmpr_cmp_2exp_si(fmprb_radref(x), 0) >= 0) { return 0; } /* there are 0 or 1 integers if the radius is < 1 */ else { /* if the midpoint is exactly an integer, it is what we want */ if (fmpr_is_int(fmprb_midref(x))) { if (!fmpz_fits_si(fmpr_expref(fmprb_midref(x)))) { flint_printf("fmprb_get_unique_fmpz: too large shift\n"); abort(); } fmpz_mul_2exp(z, fmpr_manref(fmprb_midref(x)), fmpz_get_si(fmpr_expref(fmprb_midref(x)))); return 1; } /* if the radius is tiny, it can't be an integer */ else if (!fmpz_fits_si(fmpr_expref(fmprb_radref(x)))) { return 0; } else { fmpz_t a, b, exp; int res; fmpz_init(a); fmpz_init(b); fmpz_init(exp); fmprb_get_interval_fmpz_2exp(a, b, exp, x); fmpz_cdiv_q_2exp(a, a, -fmpz_get_si(exp)); fmpz_fdiv_q_2exp(b, b, -fmpz_get_si(exp)); res = fmpz_equal(a, b); if (res) fmpz_set(z, a); fmpz_clear(a); fmpz_clear(b); fmpz_clear(exp); return res; } } } arb-2.8.1/fmprb/hypot.c000066400000000000000000000030221264125401100146740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_hypot(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { if (fmprb_is_zero(y)) { fmprb_abs(z, x); } else if (fmprb_is_zero(x)) { fmprb_abs(z, y); } else { fmprb_t t; fmprb_init(t); fmprb_mul(t, x, x, prec + 4); fmprb_mul(z, y, y, prec + 4); fmprb_add(t, t, z, prec + 4); fmprb_sqrtpos(z, t, prec); fmprb_clear(t); } } arb-2.8.1/fmprb/mul.c000066400000000000000000000154721264125401100143420ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" /* We speed up the radius operations by working with mantissas aligned to FMPRB_RAD_PREC bits (possibly one less bit after multiplying). The error is computed as x*b + y*a + a*b + r where x, b, y, a, a, b, r are floating-point numbers of the form m * 2^e and m has exactly FMPRB_RAD_PREC bits, i.e. m <= 2^FMPRB_RAD_PREC - 1. The mantissas of the products x*b, y*a, a*b are computed as m3 = floor((m1 * m2) / 2^FMPRB_RAD_PREC) + 1. One can then verify that m3 <= 2^FMPRB_RAD_PREC - 1. In the additions, we do not normalise the output mantissa. The result is largest when exponents are the same: then we have precisely m3 = m1 + m2. Thus the final mantissa is <= 4 * (2^FMPRB_RAD_PREC - 1). If FMPRB_RAD_PREC <= FLINT_BITS - 2, this precisely fits in a limb without overflow. */ #define _RAD_MUL(a, ae, b, be) \ do { \ mp_limb_t hi, lo; \ umul_ppmm(hi, lo, a, b); \ a = ((hi << (FLINT_BITS - FMPRB_RAD_PREC)) | (lo >> FMPRB_RAD_PREC)) + 1; \ fmpz_add_inline(ae, ae, be); \ } while (0); \ static __inline__ void _rad_bound(mp_limb_t * m, fmpz_t exp, const fmpr_t t) { slong e; *m = fmpz_abs_ubound_ui_2exp(&e, fmpr_manref(t), FMPRB_RAD_PREC); fmpz_add_si_inline(exp, fmpr_expref(t), e); } static __inline__ mp_limb_t _rad_add(mp_limb_t a, fmpz_t aexp, mp_limb_t b, fmpz_t bexp) { slong shift; shift = _fmpz_sub_small(aexp, bexp); if (shift == 0) { return a + b; } else if (shift > 0) { if (shift <= FMPRB_RAD_PREC) return a + (b >> shift) + 1; else return a + 1; } else { fmpz_swap(aexp, bexp); if ((-shift) <= FMPRB_RAD_PREC) return b + (a >> (-shift)) + 1; else return b + 1; } } void _fmprb_mul_main(fmpr_t z, fmpr_t c, const fmpr_t x, const fmpr_t a, const fmpr_t y, const fmpr_t b, slong prec) { mp_limb_t xm, am, ym, bm; fmpz_t xe, ae, ye, be; slong r, shift; fmpz_init(xe); fmpz_init(ae); fmpz_init(ye); fmpz_init(be); _rad_bound(&xm, xe, x); _rad_bound(&ym, ye, y); _rad_bound(&am, ae, a); _rad_bound(&bm, be, b); _RAD_MUL(xm, xe, bm, be); _RAD_MUL(ym, ye, am, ae); xm = _rad_add(xm, xe, ym, ye); _RAD_MUL(am, ae, bm, be); xm = _rad_add(xm, xe, am, ae); r = fmpr_mul(z, x, y, prec, FMPR_RND_DOWN); if (r != FMPR_RESULT_EXACT) { am = UWORD(1) << FMPRB_RAD_PREC; fmpz_add_si_inline(ae, fmpr_expref(z), -r - 2*FMPRB_RAD_PREC); xm = _rad_add(xm, xe, am, ae); } shift = FMPRB_RAD_PREC; /* make the radius mantissa odd and small */ xm += !(xm & 1); while (xm >= (UWORD(1) << FMPRB_RAD_PREC)) { xm = (xm >> 1) + 1; xm += !(xm & 1); shift++; } fmpz_set_ui(fmpr_manref(c), xm); fmpz_add_si_inline(fmpr_expref(c), xe, shift); fmpz_clear(xe); fmpz_clear(ae); fmpz_clear(ye); fmpz_clear(be); } void _fmprb_mul_fmpr_main(fmpr_t z, fmpr_t c, const fmpr_t x, const fmpr_t a, const fmpr_t y, slong prec) { mp_limb_t ym, am; fmpz_t ye, ae; slong r, shift; fmpz_init(ye); fmpz_init(ae); _rad_bound(&ym, ye, y); _rad_bound(&am, ae, a); _RAD_MUL(ym, ye, am, ae); r = fmpr_mul(z, x, y, prec, FMPR_RND_DOWN); if (r != FMPR_RESULT_EXACT) { am = UWORD(1) << FMPRB_RAD_PREC; fmpz_add_si_inline(ae, fmpr_expref(z), -r - 2*FMPRB_RAD_PREC); ym = _rad_add(ym, ye, am, ae); } shift = FMPRB_RAD_PREC; /* make the radius mantissa odd and small */ ym += !(ym & 1); while (ym >= (UWORD(1) << FMPRB_RAD_PREC)) { ym = (ym >> 1) + 1; ym += !(ym & 1); shift++; } fmpz_set_ui(fmpr_manref(c), ym); fmpz_add_si_inline(fmpr_expref(c), ye, shift); fmpz_clear(ye); fmpz_clear(ae); } void fmprb_mul_fmpr(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec) { if (fmprb_is_exact(x)) { slong r; r = fmpr_mul(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r); } else { if (fmpr_is_special(fmprb_midref(x)) || fmpr_is_special(fmprb_radref(x)) || fmpr_is_special(y)) { fmprb_mul_fmpr_naive(z, x, y, prec); } else { _fmprb_mul_fmpr_main(fmprb_midref(z), fmprb_radref(z), fmprb_midref(x), fmprb_radref(x), y, prec); } } } void fmprb_mul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { if (fmprb_is_exact(x)) { fmprb_mul_fmpr(z, y, fmprb_midref(x), prec); } else if (fmprb_is_exact(y)) { fmprb_mul_fmpr(z, x, fmprb_midref(y), prec); } else { if (fmpr_is_special(fmprb_midref(x)) || fmpr_is_special(fmprb_radref(x)) || fmpr_is_special(fmprb_midref(y)) || fmpr_is_special(fmprb_radref(y))) { fmprb_mul_main_naive(z, x, y, prec); } else { _fmprb_mul_main(fmprb_midref(z), fmprb_radref(z), fmprb_midref(x), fmprb_radref(x), fmprb_midref(y), fmprb_radref(y), prec); } } } void fmprb_mul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) { fmpr_t t; fmpr_init(t); fmpr_set_ui(t, y); fmprb_mul_fmpr(z, x, t, prec); fmpr_clear(t); } void fmprb_mul_si(fmprb_t z, const fmprb_t x, slong y, slong prec) { fmpr_t t; fmpr_init(t); fmpr_set_si(t, y); fmprb_mul_fmpr(z, x, t, prec); fmpr_clear(t); } void fmprb_mul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) { fmpr_t t; fmpr_init(t); fmpr_set_fmpz(t, y); fmprb_mul_fmpr(z, x, t, prec); fmpr_clear(t); } arb-2.8.1/fmprb/mul_naive.c000066400000000000000000000065251264125401100155230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_mul_fmpr_naive(fmprb_t z, const fmprb_t x, const fmpr_t y, slong prec) { /* (x+a) * y = x*y + y*a */ if (fmpr_is_pos_inf(fmprb_radref(x))) { fmpr_mul(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN); fmpr_pos_inf(fmprb_radref(z)); } else if (fmpr_is_zero(fmprb_radref(x))) { slong r; r = fmpr_mul(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r); } else { slong r; fmpr_mul(fmprb_radref(z), fmprb_radref(x), y, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_abs(fmprb_radref(z), fmprb_radref(z)); r = fmpr_mul(fmprb_midref(z), fmprb_midref(x), y, prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), fmprb_radref(z), fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); } } void fmprb_mul_main_naive(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { if (fmpr_is_pos_inf(fmprb_radref(x)) || fmpr_is_pos_inf(fmprb_radref(y))) { fmpr_mul(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN); fmpr_pos_inf(fmprb_radref(z)); } else { fmpr_t t, u; slong r; fmpr_init(t); fmpr_init(u); /* (x+a)*(y+b) = x*y + x*b + y*a + a*b*/ fmpr_mul(t, fmprb_midref(x), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_abs(t, t); fmpr_mul(u, fmprb_midref(y), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_abs(u, u); fmpr_add(t, t, u, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_addmul(t, fmprb_radref(x), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_UP); r = fmpr_mul(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), t, fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_clear(t); fmpr_clear(u); } } void fmprb_mul_naive(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { if (fmprb_is_exact(x)) fmprb_mul_fmpr_naive(z, y, fmprb_midref(x), prec); else if (fmprb_is_exact(y)) fmprb_mul_fmpr_naive(z, x, fmprb_midref(y), prec); else fmprb_mul_main_naive(z, x, y, prec); fmprb_adjust(z); } arb-2.8.1/fmprb/overlaps.c000066400000000000000000000040151264125401100153670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmprb_overlaps(const fmprb_t x, const fmprb_t y) { fmpr_t t; fmpr_struct u[4]; int result; if (fmpr_is_inf(fmprb_radref(x)) || fmpr_is_inf(fmprb_radref(y))) return 1; if (fmpr_equal(fmprb_midref(x), fmprb_midref(y))) return 1; fmpr_init(t); fmpr_init(u + 0); fmpr_init(u + 1); fmpr_init(u + 2); fmpr_init(u + 3); /* |xm - ym| <= xr + yr */ if (fmpr_cmp(fmprb_midref(x), fmprb_midref(y)) >= 0) { fmpr_set(u + 0, fmprb_midref(x)); fmpr_neg(u + 1, fmprb_midref(y)); } else { fmpr_neg(u + 0, fmprb_midref(x)); fmpr_set(u + 1, fmprb_midref(y)); } fmpr_neg(u + 2, fmprb_radref(x)); fmpr_neg(u + 3, fmprb_radref(y)); fmpr_sum(t, u, 4, 30, FMPR_RND_DOWN); result = fmpr_sgn(t) <= 0; fmpr_clear(t); fmpr_clear(u + 0); fmpr_clear(u + 1); fmpr_clear(u + 2); fmpr_clear(u + 3); return result; } arb-2.8.1/fmprb/randtest.c000066400000000000000000000060051264125401100153610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_randtest_exact(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) { fmpr_randtest(fmprb_midref(x), state, prec, mag_bits); fmpr_zero(fmprb_radref(x)); } void fmprb_randtest_wide(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) { fmpr_randtest(fmprb_midref(x), state, prec, mag_bits); fmpr_randtest(fmprb_radref(x), state, FMPRB_RAD_PREC, mag_bits); fmpr_abs(fmprb_radref(x), fmprb_radref(x)); } void fmprb_randtest_precise(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) { fmpr_randtest(fmprb_midref(x), state, prec, mag_bits); if (fmpr_is_zero(fmprb_midref(x)) || (n_randint(state, 8) == 0)) { fmpr_zero(fmprb_radref(x)); } else { fmpz_randtest_not_zero(fmpr_manref(fmprb_radref(x)), state, FMPRB_RAD_PREC); fmpz_abs(fmpr_manref(fmprb_radref(x)), fmpr_manref(fmprb_radref(x))); fmpz_sub_ui(fmpr_expref(fmprb_radref(x)), fmpr_expref(fmprb_midref(x)), prec + FMPRB_RAD_PREC); } } void fmprb_randtest(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) { switch (n_randint(state, 8)) { case 0: fmprb_randtest_exact(x, state, prec, mag_bits); break; case 1: fmprb_randtest_wide(x, state, prec, mag_bits); break; default: fmprb_randtest_precise(x, state, prec, mag_bits); } } void fmprb_randtest_special(fmprb_t x, flint_rand_t state, slong prec, slong mag_bits) { fmprb_randtest(x, state, prec, mag_bits); if (n_randint(state, 10) == 0) fmpr_pos_inf(fmprb_radref(x)); switch (n_randint(state, 10)) { case 0: fmpr_pos_inf(fmprb_midref(x)); break; case 1: fmpr_neg_inf(fmprb_midref(x)); break; case 2: fmpr_nan(fmprb_midref(x)); fmpr_pos_inf(fmprb_radref(x)); break; default: break; } } arb-2.8.1/fmprb/root.c000066400000000000000000000056611264125401100145270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012, 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_root(fmprb_t z, const fmprb_t x, ulong k, slong prec) { slong r; if (k == 1) { fmprb_set_round(z, x, prec); return; } if (k == 2) { fmprb_sqrt(z, x, prec); return; } if (k == -2) { fmprb_rsqrt(z, x, prec); return; } if (fmprb_contains_negative(x)) { fmprb_indeterminate(z); return; } if (fmprb_is_exact(x)) { r = fmpr_root(fmprb_midref(z), fmprb_midref(x), k, prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r); } else { fmpr_t t, u, err; fmpr_init(t); fmpr_init(u); fmpr_init(err); /* lower point */ fmpr_sub(err, fmprb_midref(x), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_DOWN); if (fmpr_is_zero(err)) { fmpr_root(err, fmprb_midref(x), k, FMPRB_RAD_PREC, FMPR_RND_UP); r = fmpr_root(fmprb_midref(z), fmprb_midref(x), k, prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), err, fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); } else { /* derivative x^(1/k) / (x k) at lower point */ fmpr_root(t, err, k, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_mul_ui(u, err, k, FMPRB_RAD_PREC, FMPR_RND_DOWN); fmpr_divappr_abs_ubound(t, t, u, FMPRB_RAD_PREC); /* multiplied by distance */ fmpr_mul(err, t, fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_UP); r = fmpr_root(fmprb_midref(z), fmprb_midref(x), k, prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), err, fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); } fmpr_clear(t); fmpr_clear(u); fmpr_clear(err); } fmprb_adjust(z); } arb-2.8.1/fmprb/rsqrt.c000066400000000000000000000045731264125401100147200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_rsqrt(fmprb_t z, const fmprb_t x, slong prec) { slong r; if (fmprb_contains_nonpositive(x)) { fmpr_nan(fmprb_midref(z)); fmpr_pos_inf(fmprb_radref(z)); return; } if (fmprb_is_exact(x)) { r = fmpr_rsqrt(fmprb_midref(z), fmprb_midref(x), prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r); } else { fmpr_t t, err; fmpr_init(t); fmpr_init(err); /* lower point */ fmpr_sub(t, fmprb_midref(x), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_DOWN); /* error bound: (1/2) t^(-3/2) * rad */ fmpr_rsqrt(err, t, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_divappr_abs_ubound(err, err, t, FMPRB_RAD_PREC); fmpr_mul(err, err, fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_mul_2exp_si(err, err, -1); r = fmpr_rsqrt(fmprb_midref(z), fmprb_midref(x), prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), err, fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_clear(t); fmpr_clear(err); } fmprb_adjust(z); } void fmprb_rsqrt_ui(fmprb_t z, ulong x, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_ui(t, x); fmprb_rsqrt(z, t, prec); fmprb_clear(t); } arb-2.8.1/fmprb/set_interval_fmpr.c000066400000000000000000000027371264125401100172700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_set_interval_fmpr(fmprb_t x, const fmpr_t a, const fmpr_t b, slong prec) { fmpr_t t; fmpr_init(t); fmprb_set_fmpr(x, a); fmprb_add_fmpr(x, x, b, prec); fmpr_sub(t, b, a, FMPRB_RAD_PREC, FMPR_RND_UP); fmprb_add_error_fmpr(x, t); if (fmpr_is_nan(fmprb_radref(x))) fmpr_pos_inf(fmprb_radref(x)); fmprb_mul_2exp_si(x, x, -1); fmpr_clear(t); } arb-2.8.1/fmprb/set_round.c000066400000000000000000000025761264125401100155500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_set_round(fmprb_t z, const fmprb_t x, slong prec) { slong r; r = fmpr_set_round(fmprb_midref(z), fmprb_midref(x), prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), fmprb_radref(x), fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); fmprb_adjust(z); } arb-2.8.1/fmprb/sqrt.c000066400000000000000000000045501264125401100145310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_sqrt(fmprb_t z, const fmprb_t x, slong prec) { slong r; if (fmprb_contains_negative(x)) { fmpr_nan(fmprb_midref(z)); fmpr_pos_inf(fmprb_radref(z)); return; } if (fmprb_is_exact(x)) { r = fmpr_sqrt(fmprb_midref(z), fmprb_midref(x), prec, FMPR_RND_DOWN); fmpr_set_error_result(fmprb_radref(z), fmprb_midref(z), r); } else { fmpr_t err; fmpr_init(err); fmpr_sub(err, fmprb_midref(x), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_DOWN); fmpr_rsqrt(err, err, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_mul(err, fmprb_radref(x), err, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_mul_2exp_si(err, err, -1); r = fmpr_sqrt(fmprb_midref(z), fmprb_midref(x), prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), err, fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_clear(err); } fmprb_adjust(z); } void fmprb_sqrt_ui(fmprb_t z, ulong x, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_ui(t, x); fmprb_sqrt(z, t, prec); fmprb_clear(t); } void fmprb_sqrt_fmpz(fmprb_t z, const fmpz_t x, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_fmpz(t, x); fmprb_sqrt(z, t, prec); fmprb_clear(t); } arb-2.8.1/fmprb/sqrtpos.c000066400000000000000000000047171264125401100152600ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" static __inline__ void fmprb_nonnegative_part(fmprb_t z, const fmprb_t x, slong prec) { if (fmprb_contains_negative(x)) { fmpr_add(fmprb_midref(z), fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_CEIL); if (fmpr_sgn(fmprb_midref(z)) <= 0) { fmpr_zero(fmprb_radref(z)); } else { fmpr_mul_2exp_si(fmprb_midref(z), fmprb_midref(z), -1); fmpr_set(fmprb_midref(z), fmprb_radref(z)); } } else { fmprb_set(z, x); } } void fmprb_sqrtpos(fmprb_t z, const fmprb_t x, slong prec) { if (!fmprb_is_finite(x)) { if (fmpr_is_zero(fmprb_radref(x)) && fmpr_is_pos_inf(fmprb_midref(x))) fmprb_pos_inf(z); else fmprb_zero_pm_inf(z); } else if (fmprb_contains_nonpositive(x)) { fmpr_t t; fmpr_init(t); fmpr_add(t, fmprb_midref(x), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_CEIL); if (fmpr_sgn(t) <= 0) { fmprb_zero(z); } else { fmpr_sqrt(t, t, FMPRB_RAD_PREC, FMPR_RND_CEIL); fmpr_mul_2exp_si(t, t, -1); fmpr_set(fmprb_midref(z), t); fmpr_set(fmprb_radref(z), t); } fmpr_clear(t); } else { fmprb_sqrt(z, x, prec); } fmprb_nonnegative_part(z, z, prec); } arb-2.8.1/fmprb/sub.c000066400000000000000000000040331264125401100143250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_sub(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { slong r; fmpr_add(fmprb_radref(z), fmprb_radref(x), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_UP); r = fmpr_sub(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN); fmpr_add_error_result(fmprb_radref(z), fmprb_radref(z), fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP); fmprb_adjust(z); } void fmprb_sub_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_ui(t, y); fmprb_sub(z, x, t, prec); fmprb_clear(t); } void fmprb_sub_si(fmprb_t z, const fmprb_t x, slong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_si(t, y); fmprb_sub(z, x, t, prec); fmprb_clear(t); } void fmprb_sub_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_set_fmpz(t, y); fmprb_sub(z, x, t, prec); fmprb_clear(t); } arb-2.8.1/fmprb/submul.c000066400000000000000000000035441264125401100150510ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_submul(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_mul(t, x, y, prec); fmprb_sub(z, z, t, prec); fmprb_clear(t); } void fmprb_submul_ui(fmprb_t z, const fmprb_t x, ulong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_mul_ui(t, x, y, prec); fmprb_sub(z, z, t, prec); fmprb_clear(t); } void fmprb_submul_si(fmprb_t z, const fmprb_t x, slong y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_sub_si(t, x, y, prec); fmprb_sub(z, z, t, prec); fmprb_clear(t); } void fmprb_submul_fmpz(fmprb_t z, const fmprb_t x, const fmpz_t y, slong prec) { fmprb_t t; fmprb_init(t); fmprb_mul_fmpz(t, x, y, prec); fmprb_sub(z, z, t, prec); fmprb_clear(t); } arb-2.8.1/fmprb/test/000077500000000000000000000000001264125401100143475ustar00rootroot00000000000000arb-2.8.1/fmprb/test/t-add.c000066400000000000000000000120101264125401100154760ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_randtest(c, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_add(c, a, b, 2 + n_randint(state, 200)); fmpq_add(z, x, y); if (!fmprb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_add(a, a, b, 2 + n_randint(state, 200)); fmpq_add(z, x, y); if (!fmprb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_add(b, a, b, 2 + n_randint(state, 200)); fmpq_add(z, x, y); if (!fmprb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-addmul.c000066400000000000000000000122221264125401100162210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("addmul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_randtest(c, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(z, state, c, 1 + n_randint(state, 200)); fmprb_addmul(c, a, b, 2 + n_randint(state, 200)); fmpq_addmul(z, x, y); if (!fmprb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, x); fmprb_addmul(a, a, b, 2 + n_randint(state, 200)); fmpq_addmul(z, x, y); if (!fmprb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, y); fmprb_addmul(b, a, b, 2 + n_randint(state, 200)); fmpq_addmul(z, x, y); if (!fmprb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-agm.c000066400000000000000000000062241264125401100155240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("agm...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t q, r; mpfr_t t, u; slong prec = 2 + n_randint(state, 200); fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(q); fmpq_init(r); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); fmprb_randtest(a, state, 1 + n_randint(state, 200), 3); fmprb_randtest(b, state, 1 + n_randint(state, 200), 3); fmprb_randtest(c, state, 1 + n_randint(state, 200), 3); fmprb_agm(c, a, b, prec); if (fmprb_equal(a, b)) { if (!fmprb_contains(c, a)) { flint_printf("FAIL: containment (identity)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); abort(); } } else { fmprb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(r, state, b, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); fmpq_get_mpfr(u, r, MPFR_RNDN); mpfr_agm(t, t, u, MPFR_RNDN); if (!fmprb_contains_mpfr(c, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); abort(); } } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(q); fmpq_clear(r); mpfr_clear(t); mpfr_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-contains.c000066400000000000000000000061001264125401100165670ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("contains...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b; fmpq_t am, ar, bm, br, t, u; int c1, c2; fmprb_init(a); fmprb_init(b); fmpq_init(am); fmpq_init(ar); fmpq_init(bm); fmpq_init(br); fmpq_init(t); fmpq_init(u); fmprb_randtest(a, state, 1 + n_randint(state, 500), 14); fmprb_randtest(b, state, 1 + n_randint(state, 500), 14); fmpr_get_fmpq(am, fmprb_midref(a)); fmpr_get_fmpq(ar, fmprb_radref(a)); fmpr_get_fmpq(bm, fmprb_midref(b)); fmpr_get_fmpq(br, fmprb_radref(b)); c1 = fmprb_contains(a, b); fmpq_sub(t, am, ar); fmpq_sub(u, bm, br); c2 = fmpq_cmp(t, u) <= 0; fmpq_add(t, am, ar); fmpq_add(u, bm, br); c2 = c2 && (fmpq_cmp(t, u) >= 0); if (c1 != c2) { flint_printf("FAIL:\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("am = "); fmpq_print(am); flint_printf("\n\n"); flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n"); flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n"); flint_printf("br = "); fmpq_print(br); flint_printf("\n\n"); flint_printf("t = "); fmpq_print(t); flint_printf("\n\n"); flint_printf("u = "); fmpq_print(u); flint_printf("\n\n"); flint_printf("c1 = %d, c2 = %d\n\n", c1, c2); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(am); fmpq_clear(ar); fmpq_clear(bm); fmpq_clear(br); fmpq_clear(t); fmpq_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-contains_fmpr.c000066400000000000000000000053571264125401100176300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("contains_fmpq...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmprb_t a; fmpr_t b; fmpq_t am, ar, bm, t; int c1, c2; fmprb_init(a); fmpr_init(b); fmpq_init(am); fmpq_init(ar); fmpq_init(bm); fmpq_init(t); fmprb_randtest(a, state, 1 + n_randint(state, 500), 14); fmpr_randtest(b, state, 1 + n_randint(state, 500), 14); fmpr_get_fmpq(am, fmprb_midref(a)); fmpr_get_fmpq(ar, fmprb_radref(a)); fmpr_get_fmpq(bm, b); c1 = fmprb_contains_fmpr(a, b); fmpq_sub(t, am, ar); c2 = fmpq_cmp(t, bm) <= 0; fmpq_add(t, am, ar); c2 = c2 && (fmpq_cmp(t, bm) >= 0); if (c1 != c2) { flint_printf("FAIL:\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpr_print(b); flint_printf("\n\n"); flint_printf("am = "); fmpq_print(am); flint_printf("\n\n"); flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n"); flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n"); flint_printf("t = "); fmpq_print(t); flint_printf("\n\n"); flint_printf("c1 = %d, c2 = %d\n\n", c1, c2); abort(); } fmprb_clear(a); fmpr_clear(b); fmpq_clear(am); fmpq_clear(ar); fmpq_clear(bm); fmpq_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-div.c000066400000000000000000000123141264125401100155370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("div...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); do { fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_randtest(c, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); } while (fmpq_is_zero(y)); fmprb_div(c, a, b, 2 + n_randint(state, 200)); fmpq_div(z, x, y); if (!fmprb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); do { fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); } while (fmpq_is_zero(y)); fmprb_div(a, a, b, 2 + n_randint(state, 200)); fmpq_div(z, x, y); if (!fmprb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); do { fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); } while (fmpq_is_zero(y)); fmprb_div(b, a, b, 2 + n_randint(state, 200)); fmpq_div(z, x, y); if (!fmprb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-get_interval_fmpz_2exp.c000066400000000000000000000047341264125401100214410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_interval_fmpz_2exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t x; fmpr_t y; fmpz_t a, b, exp; fmprb_init(x); fmpr_init(y); fmpz_init(a); fmpz_init(b); fmpz_init(exp); fmprb_randtest(x, state, 200, 10); fmprb_get_interval_fmpz_2exp(a, b, exp, x); fmpr_set_fmpz_2exp(y, a, exp); if (!fmprb_contains_fmpr(x, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("a = "); fmpz_print(a); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } fmpr_set_fmpz_2exp(y, b, exp); if (!fmprb_contains_fmpr(x, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } fmprb_clear(x); fmpr_clear(y); fmpz_clear(a); fmpz_clear(b); fmpz_clear(exp); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-get_rand_fmpq.c000066400000000000000000000036531264125401100175710ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_rand_fmpq...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t x; fmpq_t q; fmprb_init(x); fmpq_init(q); fmprb_randtest(x, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(q, state, x, 1 + n_randint(state, 200)); if (!fmprb_contains_fmpq(x, q) || !fmpq_is_canonical(q)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("q = "); fmpq_print(q); flint_printf("\n\n"); abort(); } fmprb_clear(x); fmpq_clear(q); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-get_unique_fmpz.c000066400000000000000000000076731264125401100201720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("get_unique_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t x, z; fmpz_t y, a, b, exp; int unique, unique2; fmprb_init(x); fmprb_init(z); fmpz_init(y); fmpz_init(a); fmpz_init(b); fmpz_init(exp); fmprb_randtest(x, state, 2000, 10); unique = fmprb_get_unique_fmpz(y, x); fmprb_get_interval_fmpz_2exp(a, b, exp, x); if (fmpz_sgn(exp) >= 0) { fmpz_mul_2exp(a, a, fmpz_get_si(exp)); fmpz_mul_2exp(b, b, fmpz_get_si(exp)); } else { fmpz_cdiv_q_2exp(a, a, -fmpz_get_si(exp)); fmpz_fdiv_q_2exp(b, b, -fmpz_get_si(exp)); } unique2 = fmpz_equal(a, b); if ((unique != unique2) || (unique && !fmpz_equal(y, a))) { flint_printf("FAIL:\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("unique = %d, unique2 = %d\n\n", unique, unique2); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("a = "); fmpz_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } if (unique) { fmprb_set_fmpz(z, y); fmprb_set_round(z, z, 2 + n_randint(state, 1000)); if (!fmprb_overlaps(x, z)) { flint_printf("FAIL (overlap):\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); flint_printf("z = "); fmprb_print(z); flint_printf("\n\n"); abort(); } fmpz_add_ui(b, y, 1); if (fmprb_contains_fmpz(x, b)) { flint_printf("FAIL (contains a + 1):\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); abort(); } fmpz_sub_ui(b, y, 1); if (fmprb_contains_fmpz(x, b)) { flint_printf("FAIL (contains a - 1):\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpz_print(y); flint_printf("\n\n"); abort(); } } fmprb_clear(x); fmprb_clear(z); fmpz_clear(y); fmpz_clear(a); fmpz_clear(b); fmpz_clear(exp); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-mul.c000066400000000000000000000215351264125401100155570ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int fmpr_close(const fmpr_t a, const fmpr_t b) { fmpr_t t; int res1, res2; fmpr_init(t); fmpr_mul_ui(t, b, 257, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_mul_2exp_si(t, t, -8); res1 = fmpr_cmp(a, t) <= 0; fmpr_mul_ui(t, a, 257, FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_mul_2exp_si(t, t, -8); res2 = fmpr_cmp(b, t) <= 0; fmpr_clear(t); return res1 && res2; } int main() { slong iter, iter2; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_randtest(c, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_mul(c, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!fmprb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_mul(a, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!fmprb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_mul(b, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!fmprb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* main test */ for (iter = 0; iter < 10000; iter++) { fmprb_t x, y, z, v; slong prec; fmprb_init(x); fmprb_init(y); fmprb_init(z); fmprb_init(v); for (iter2 = 0; iter2 < 100; iter2++) { fmprb_randtest_special(x, state, n_randint(state,2) ? 2000 : 200, 200); fmprb_randtest_special(y, state, n_randint(state,2) ? 2000 : 200, 200); prec = 2 + n_randint(state, 2000); switch (n_randint(state, 5)) { case 0: fmprb_mul(z, x, y, prec); fmprb_mul_naive(v, x, y, prec); if (!fmpr_equal(fmprb_midref(z), fmprb_midref(v)) || !fmpr_close(fmprb_radref(z), fmprb_radref(v))) { flint_printf("FAIL!\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); flint_printf("z = "); fmprb_print(z); flint_printf("\n\n"); flint_printf("v = "); fmprb_print(v); flint_printf("\n\n"); abort(); } break; case 1: fmprb_set(y, x); fmprb_mul(z, x, y, prec); fmprb_mul(v, x, x, prec); if (!fmprb_equal(z, v)) { flint_printf("FAIL (aliasing 1)!\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("z = "); fmprb_print(z); flint_printf("\n\n"); flint_printf("v = "); fmprb_print(v); flint_printf("\n\n"); abort(); } break; case 2: fmprb_mul(v, x, x, prec); fmprb_mul(x, x, x, prec); if (!fmprb_equal(v, x)) { flint_printf("FAIL (aliasing 2)!\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("z = "); fmprb_print(z); flint_printf("\n\n"); flint_printf("v = "); fmprb_print(v); flint_printf("\n\n"); abort(); } break; case 3: fmprb_mul(v, x, y, prec); fmprb_mul(x, x, y, prec); if (!fmprb_equal(x, v)) { flint_printf("FAIL (aliasing 3)!\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); flint_printf("v = "); fmprb_print(v); flint_printf("\n\n"); abort(); } break; default: fmprb_mul(v, x, y, prec); fmprb_mul(x, y, x, prec); if (!fmprb_equal(x, v)) { flint_printf("FAIL (aliasing 4)!\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); flint_printf("v = "); fmprb_print(v); flint_printf("\n\n"); abort(); } break; } } fmprb_clear(x); fmprb_clear(y); fmprb_clear(z); fmprb_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-mul_naive.c000066400000000000000000000120401264125401100167300ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_naive...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_randtest(c, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_mul_naive(c, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!fmprb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_mul_naive(a, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!fmprb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_mul_naive(b, a, b, 2 + n_randint(state, 200)); fmpq_mul(z, x, y); if (!fmprb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-overlaps.c000066400000000000000000000060201264125401100166050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("overlaps...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b; fmpq_t am, ar, bm, br, t, u; int c1, c2; fmprb_init(a); fmprb_init(b); fmpq_init(am); fmpq_init(ar); fmpq_init(bm); fmpq_init(br); fmpq_init(t); fmpq_init(u); fmprb_randtest(a, state, 1 + n_randint(state, 500), 14); fmprb_randtest(b, state, 1 + n_randint(state, 500), 14); fmpr_get_fmpq(am, fmprb_midref(a)); fmpr_get_fmpq(ar, fmprb_radref(a)); fmpr_get_fmpq(bm, fmprb_midref(b)); fmpr_get_fmpq(br, fmprb_radref(b)); fmpq_sub(t, am, bm); fmpz_abs(fmpq_numref(t), fmpq_numref(t)); fmpq_add(u, ar, br); c1 = fmprb_overlaps(a, b); c2 = (fmpq_cmp(t, u) <= 0); if (c1 != c2) { flint_printf("FAIL:\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("am = "); fmpq_print(am); flint_printf("\n\n"); flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n"); flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n"); flint_printf("br = "); fmpq_print(br); flint_printf("\n\n"); flint_printf("t = "); fmpq_print(t); flint_printf("\n\n"); flint_printf("u = "); fmpq_print(u); flint_printf("\n\n"); flint_printf("c1 = %d, c2 = %d\n\n", c1, c2); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(am); fmpq_clear(ar); fmpq_clear(bm); fmpq_clear(br); fmpq_clear(t); fmpq_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-rsqrt.c000066400000000000000000000043531264125401100161340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("rsqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; slong prec = 2 + n_randint(state, 200); fmprb_init(a); fmprb_init(b); fmprb_init(c); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_rsqrt(b, a, prec); fmprb_inv(c, b, prec); fmprb_mul(c, c, c, prec); if (!fmprb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); abort(); } fmprb_rsqrt(a, a, prec); if (!fmprb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-set_interval_fmpr.c000066400000000000000000000042151264125401100205010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("set_interval_fmpr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t x; fmpr_t a, b; fmprb_init(x); fmpr_init(a); fmpr_init(b); fmpr_randtest_special(a, state, 200, 10); fmpr_randtest_special(b, state, 200, 10); if (fmpr_cmp(a, b) > 0) fmpr_swap(a, b); fmprb_set_interval_fmpr(x, a, b, 2 + n_randint(state, 200)); if (!fmprb_contains_fmpr(x, a) || !fmprb_contains_fmpr(x, b)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("a = "); fmpr_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpr_print(b); flint_printf("\n\n"); abort(); } fmprb_clear(x); fmpr_clear(a); fmpr_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-special.c000066400000000000000000000701251264125401100164010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" #define ASSERT(cond) if (!(cond)) { flint_printf("FAIL: %d\n", __LINE__); abort(); } int main() { fmprb_t zero, pos, neg, pos_inf, neg_inf, pos_inf_err, neg_inf_err, zero_pm_inf, pos_pm_inf, neg_pm_inf, indet_exact, indet_pos_rad, indet_inf_rad; flint_printf("special...."); fflush(stdout); fmprb_init(zero); fmprb_init(pos); fmprb_init(neg); fmprb_init(pos_inf); fmprb_init(neg_inf); fmprb_init(pos_inf_err); fmprb_init(neg_inf_err); fmprb_init(zero_pm_inf); fmprb_init(pos_pm_inf); fmprb_init(neg_pm_inf); fmprb_init(indet_exact); fmprb_init(indet_pos_rad); fmprb_init(indet_inf_rad); fmprb_set_si(pos, 3); fmprb_div_ui(pos, pos, 5, 53); fmprb_neg(neg, pos); fmprb_pos_inf(pos_inf); fmprb_neg_inf(neg_inf); fmprb_pos_inf(pos_inf_err); fmpr_set_ui(fmprb_radref(pos_inf_err), 3); fmprb_neg(neg_inf_err, pos_inf_err); fmprb_zero_pm_inf(zero_pm_inf); fmpr_set_si(fmprb_midref(pos_pm_inf), 3); fmpr_pos_inf(fmprb_radref(pos_pm_inf)); fmpr_set_si(fmprb_midref(neg_pm_inf), -3); fmpr_pos_inf(fmprb_radref(neg_pm_inf)); fmpr_nan(fmprb_midref(indet_exact)); fmpr_zero(fmprb_radref(indet_exact)); fmpr_nan(fmprb_midref(indet_pos_rad)); fmpr_set_si(fmprb_radref(indet_pos_rad), 3); fmpr_nan(fmprb_midref(indet_inf_rad)); fmpr_pos_inf(fmprb_radref(indet_inf_rad)); ASSERT(fmprb_is_zero(zero)); ASSERT(!fmprb_is_zero(pos)); ASSERT(!fmprb_is_zero(neg)); ASSERT(!fmprb_is_zero(pos_inf)); ASSERT(!fmprb_is_zero(neg_inf)); ASSERT(!fmprb_is_zero(pos_inf_err)); ASSERT(!fmprb_is_zero(neg_inf_err)); ASSERT(!fmprb_is_zero(zero_pm_inf)); ASSERT(!fmprb_is_zero(pos_pm_inf)); ASSERT(!fmprb_is_zero(neg_pm_inf)); ASSERT(!fmprb_is_zero(indet_exact)); ASSERT(!fmprb_is_zero(indet_pos_rad)); ASSERT(!fmprb_is_zero(indet_inf_rad)); ASSERT(!fmprb_is_nonzero(zero)); ASSERT(fmprb_is_nonzero(pos)); ASSERT(fmprb_is_nonzero(neg)); ASSERT(fmprb_is_nonzero(pos_inf)); ASSERT(fmprb_is_nonzero(neg_inf)); ASSERT(fmprb_is_nonzero(pos_inf_err)); ASSERT(fmprb_is_nonzero(neg_inf_err)); ASSERT(!fmprb_is_nonzero(zero_pm_inf)); ASSERT(!fmprb_is_nonzero(pos_pm_inf)); ASSERT(!fmprb_is_nonzero(neg_pm_inf)); ASSERT(!fmprb_is_nonzero(indet_exact)); ASSERT(!fmprb_is_nonzero(indet_pos_rad)); ASSERT(!fmprb_is_nonzero(indet_inf_rad)); ASSERT(!fmprb_is_positive(zero)); ASSERT(fmprb_is_positive(pos)); ASSERT(!fmprb_is_positive(neg)); ASSERT(fmprb_is_positive(pos_inf)); ASSERT(!fmprb_is_positive(neg_inf)); ASSERT(fmprb_is_positive(pos_inf_err)); ASSERT(!fmprb_is_positive(neg_inf_err)); ASSERT(!fmprb_is_positive(zero_pm_inf)); ASSERT(!fmprb_is_positive(pos_pm_inf)); ASSERT(!fmprb_is_positive(neg_pm_inf)); ASSERT(!fmprb_is_positive(indet_exact)); ASSERT(!fmprb_is_positive(indet_pos_rad)); ASSERT(!fmprb_is_positive(indet_inf_rad)); ASSERT(!fmprb_is_negative(zero)); ASSERT(!fmprb_is_negative(pos)); ASSERT(fmprb_is_negative(neg)); ASSERT(!fmprb_is_negative(pos_inf)); ASSERT(fmprb_is_negative(neg_inf)); ASSERT(!fmprb_is_negative(pos_inf_err)); ASSERT(fmprb_is_negative(neg_inf_err)); ASSERT(!fmprb_is_negative(zero_pm_inf)); ASSERT(!fmprb_is_negative(pos_pm_inf)); ASSERT(!fmprb_is_negative(neg_pm_inf)); ASSERT(!fmprb_is_negative(indet_exact)); ASSERT(!fmprb_is_negative(indet_pos_rad)); ASSERT(!fmprb_is_negative(indet_inf_rad)); ASSERT(fmprb_is_nonnegative(zero)); ASSERT(fmprb_is_nonnegative(pos)); ASSERT(!fmprb_is_nonnegative(neg)); ASSERT(fmprb_is_nonnegative(pos_inf)); ASSERT(!fmprb_is_nonnegative(neg_inf)); ASSERT(fmprb_is_nonnegative(pos_inf_err)); ASSERT(!fmprb_is_nonnegative(neg_inf_err)); ASSERT(!fmprb_is_nonnegative(zero_pm_inf)); ASSERT(!fmprb_is_nonnegative(pos_pm_inf)); ASSERT(!fmprb_is_nonnegative(neg_pm_inf)); ASSERT(!fmprb_is_nonnegative(indet_exact)); ASSERT(!fmprb_is_nonnegative(indet_pos_rad)); ASSERT(!fmprb_is_nonnegative(indet_inf_rad)); ASSERT(fmprb_is_nonpositive(zero)); ASSERT(!fmprb_is_nonpositive(pos)); ASSERT(fmprb_is_nonpositive(neg)); ASSERT(!fmprb_is_nonpositive(pos_inf)); ASSERT(fmprb_is_nonpositive(neg_inf)); ASSERT(!fmprb_is_nonpositive(pos_inf_err)); ASSERT(fmprb_is_nonpositive(neg_inf_err)); ASSERT(!fmprb_is_nonpositive(zero_pm_inf)); ASSERT(!fmprb_is_nonpositive(pos_pm_inf)); ASSERT(!fmprb_is_nonpositive(neg_pm_inf)); ASSERT(!fmprb_is_nonpositive(indet_exact)); ASSERT(!fmprb_is_nonpositive(indet_pos_rad)); ASSERT(!fmprb_is_nonpositive(indet_inf_rad)); ASSERT(!fmprb_contains_negative(zero)); ASSERT(!fmprb_contains_negative(pos)); ASSERT(fmprb_contains_negative(neg)); ASSERT(!fmprb_contains_negative(pos_inf)); ASSERT(fmprb_contains_negative(neg_inf)); ASSERT(!fmprb_contains_negative(pos_inf_err)); ASSERT(fmprb_contains_negative(neg_inf_err)); ASSERT(fmprb_contains_negative(zero_pm_inf)); ASSERT(fmprb_contains_negative(pos_pm_inf)); ASSERT(fmprb_contains_negative(neg_pm_inf)); ASSERT(fmprb_contains_negative(indet_exact)); ASSERT(fmprb_contains_negative(indet_pos_rad)); ASSERT(fmprb_contains_negative(indet_inf_rad)); ASSERT(fmprb_contains_nonpositive(zero)); ASSERT(!fmprb_contains_nonpositive(pos)); ASSERT(fmprb_contains_nonpositive(neg)); ASSERT(!fmprb_contains_nonpositive(pos_inf)); ASSERT(fmprb_contains_nonpositive(neg_inf)); ASSERT(!fmprb_contains_nonpositive(pos_inf_err)); ASSERT(fmprb_contains_nonpositive(neg_inf_err)); ASSERT(fmprb_contains_nonpositive(zero_pm_inf)); ASSERT(fmprb_contains_nonpositive(pos_pm_inf)); ASSERT(fmprb_contains_nonpositive(neg_pm_inf)); ASSERT(fmprb_contains_nonpositive(indet_exact)); ASSERT(fmprb_contains_nonpositive(indet_pos_rad)); ASSERT(fmprb_contains_nonpositive(indet_inf_rad)); ASSERT(!fmprb_contains_positive(zero)); ASSERT(fmprb_contains_positive(pos)); ASSERT(!fmprb_contains_positive(neg)); ASSERT(fmprb_contains_positive(pos_inf)); ASSERT(!fmprb_contains_positive(neg_inf)); ASSERT(fmprb_contains_positive(pos_inf_err)); ASSERT(!fmprb_contains_positive(neg_inf_err)); ASSERT(fmprb_contains_positive(zero_pm_inf)); ASSERT(fmprb_contains_positive(pos_pm_inf)); ASSERT(fmprb_contains_positive(neg_pm_inf)); ASSERT(fmprb_contains_positive(indet_exact)); ASSERT(fmprb_contains_positive(indet_pos_rad)); ASSERT(fmprb_contains_positive(indet_inf_rad)); ASSERT(fmprb_contains_nonnegative(zero)); ASSERT(fmprb_contains_nonnegative(pos)); ASSERT(!fmprb_contains_nonnegative(neg)); ASSERT(fmprb_contains_nonnegative(pos_inf)); ASSERT(!fmprb_contains_nonnegative(neg_inf)); ASSERT(fmprb_contains_nonnegative(pos_inf_err)); ASSERT(!fmprb_contains_nonnegative(neg_inf_err)); ASSERT(fmprb_contains_nonnegative(zero_pm_inf)); ASSERT(fmprb_contains_nonnegative(pos_pm_inf)); ASSERT(fmprb_contains_nonnegative(neg_pm_inf)); ASSERT(fmprb_contains_nonnegative(indet_exact)); ASSERT(fmprb_contains_nonnegative(indet_pos_rad)); ASSERT(fmprb_contains_nonnegative(indet_inf_rad)); ASSERT(fmprb_is_finite(zero)); ASSERT(fmprb_is_finite(pos)); ASSERT(fmprb_is_finite(neg)); ASSERT(!fmprb_is_finite(pos_inf)); ASSERT(!fmprb_is_finite(neg_inf)); ASSERT(!fmprb_is_finite(pos_inf_err)); ASSERT(!fmprb_is_finite(neg_inf_err)); ASSERT(!fmprb_is_finite(zero_pm_inf)); ASSERT(!fmprb_is_finite(pos_pm_inf)); ASSERT(!fmprb_is_finite(neg_pm_inf)); ASSERT(!fmprb_is_finite(indet_exact)); ASSERT(!fmprb_is_finite(indet_pos_rad)); ASSERT(!fmprb_is_finite(indet_inf_rad)); ASSERT(fmprb_contains(zero, zero)); ASSERT(!fmprb_contains(zero, pos)); ASSERT(!fmprb_contains(zero, neg)); ASSERT(!fmprb_contains(zero, pos_inf)); ASSERT(!fmprb_contains(zero, neg_inf)); ASSERT(!fmprb_contains(zero, pos_inf_err)); ASSERT(!fmprb_contains(zero, neg_inf_err)); ASSERT(!fmprb_contains(zero, zero_pm_inf)); ASSERT(!fmprb_contains(zero, pos_pm_inf)); ASSERT(!fmprb_contains(zero, neg_pm_inf)); ASSERT(!fmprb_contains(zero, indet_exact)); ASSERT(!fmprb_contains(zero, indet_pos_rad)); ASSERT(!fmprb_contains(zero, indet_inf_rad)); ASSERT(!fmprb_contains(pos, zero)); ASSERT(fmprb_contains(pos, pos)); ASSERT(!fmprb_contains(pos, neg)); ASSERT(!fmprb_contains(pos, pos_inf)); ASSERT(!fmprb_contains(pos, neg_inf)); ASSERT(!fmprb_contains(pos, pos_inf_err)); ASSERT(!fmprb_contains(pos, neg_inf_err)); ASSERT(!fmprb_contains(pos, zero_pm_inf)); ASSERT(!fmprb_contains(pos, pos_pm_inf)); ASSERT(!fmprb_contains(pos, neg_pm_inf)); ASSERT(!fmprb_contains(pos, indet_exact)); ASSERT(!fmprb_contains(pos, indet_pos_rad)); ASSERT(!fmprb_contains(pos, indet_inf_rad)); ASSERT(!fmprb_contains(neg, zero)); ASSERT(!fmprb_contains(neg, pos)); ASSERT(fmprb_contains(neg, neg)); ASSERT(!fmprb_contains(neg, pos_inf)); ASSERT(!fmprb_contains(neg, neg_inf)); ASSERT(!fmprb_contains(neg, pos_inf_err)); ASSERT(!fmprb_contains(neg, neg_inf_err)); ASSERT(!fmprb_contains(neg, zero_pm_inf)); ASSERT(!fmprb_contains(neg, pos_pm_inf)); ASSERT(!fmprb_contains(neg, neg_pm_inf)); ASSERT(!fmprb_contains(neg, indet_exact)); ASSERT(!fmprb_contains(neg, indet_pos_rad)); ASSERT(!fmprb_contains(neg, indet_inf_rad)); ASSERT(!fmprb_contains(pos_inf, zero)); ASSERT(!fmprb_contains(pos_inf, pos)); ASSERT(!fmprb_contains(pos_inf, neg)); ASSERT(fmprb_contains(pos_inf, pos_inf)); ASSERT(!fmprb_contains(pos_inf, neg_inf)); ASSERT(fmprb_contains(pos_inf, pos_inf_err)); ASSERT(!fmprb_contains(pos_inf, neg_inf_err)); ASSERT(!fmprb_contains(pos_inf, zero_pm_inf)); ASSERT(!fmprb_contains(pos_inf, pos_pm_inf)); ASSERT(!fmprb_contains(pos_inf, neg_pm_inf)); ASSERT(!fmprb_contains(pos_inf, indet_exact)); ASSERT(!fmprb_contains(pos_inf, indet_pos_rad)); ASSERT(!fmprb_contains(pos_inf, indet_inf_rad)); ASSERT(!fmprb_contains(neg_inf, zero)); ASSERT(!fmprb_contains(neg_inf, pos)); ASSERT(!fmprb_contains(neg_inf, neg)); ASSERT(!fmprb_contains(neg_inf, pos_inf)); ASSERT(fmprb_contains(neg_inf, neg_inf)); ASSERT(!fmprb_contains(neg_inf, pos_inf_err)); ASSERT(fmprb_contains(neg_inf, neg_inf_err)); ASSERT(!fmprb_contains(neg_inf, zero_pm_inf)); ASSERT(!fmprb_contains(neg_inf, pos_pm_inf)); ASSERT(!fmprb_contains(neg_inf, neg_pm_inf)); ASSERT(!fmprb_contains(neg_inf, indet_exact)); ASSERT(!fmprb_contains(neg_inf, indet_pos_rad)); ASSERT(!fmprb_contains(neg_inf, indet_inf_rad)); ASSERT(!fmprb_contains(pos_inf_err, zero)); ASSERT(!fmprb_contains(pos_inf_err, pos)); ASSERT(!fmprb_contains(pos_inf_err, neg)); ASSERT(fmprb_contains(pos_inf_err, pos_inf)); ASSERT(!fmprb_contains(pos_inf_err, neg_inf)); ASSERT(fmprb_contains(pos_inf_err, pos_inf_err)); ASSERT(!fmprb_contains(pos_inf_err, neg_inf_err)); ASSERT(!fmprb_contains(pos_inf_err, zero_pm_inf)); ASSERT(!fmprb_contains(pos_inf_err, pos_pm_inf)); ASSERT(!fmprb_contains(pos_inf_err, neg_pm_inf)); ASSERT(!fmprb_contains(pos_inf_err, indet_exact)); ASSERT(!fmprb_contains(pos_inf_err, indet_pos_rad)); ASSERT(!fmprb_contains(pos_inf_err, indet_inf_rad)); ASSERT(!fmprb_contains(neg_inf_err, zero)); ASSERT(!fmprb_contains(neg_inf_err, pos)); ASSERT(!fmprb_contains(neg_inf_err, neg)); ASSERT(!fmprb_contains(neg_inf_err, pos_inf)); ASSERT(fmprb_contains(neg_inf_err, neg_inf)); ASSERT(!fmprb_contains(neg_inf_err, pos_inf_err)); ASSERT(fmprb_contains(neg_inf_err, neg_inf_err)); ASSERT(!fmprb_contains(neg_inf_err, zero_pm_inf)); ASSERT(!fmprb_contains(neg_inf_err, pos_pm_inf)); ASSERT(!fmprb_contains(neg_inf_err, neg_pm_inf)); ASSERT(!fmprb_contains(neg_inf_err, indet_exact)); ASSERT(!fmprb_contains(neg_inf_err, indet_pos_rad)); ASSERT(!fmprb_contains(neg_inf_err, indet_inf_rad)); ASSERT(fmprb_contains(zero_pm_inf, zero)); ASSERT(fmprb_contains(zero_pm_inf, pos)); ASSERT(fmprb_contains(zero_pm_inf, neg)); ASSERT(fmprb_contains(zero_pm_inf, pos_inf)); ASSERT(fmprb_contains(zero_pm_inf, neg_inf)); ASSERT(fmprb_contains(zero_pm_inf, pos_inf_err)); ASSERT(fmprb_contains(zero_pm_inf, neg_inf_err)); ASSERT(fmprb_contains(zero_pm_inf, zero_pm_inf)); ASSERT(fmprb_contains(zero_pm_inf, pos_pm_inf)); ASSERT(fmprb_contains(zero_pm_inf, neg_pm_inf)); ASSERT(!fmprb_contains(zero_pm_inf, indet_exact)); ASSERT(!fmprb_contains(zero_pm_inf, indet_pos_rad)); ASSERT(!fmprb_contains(zero_pm_inf, indet_inf_rad)); ASSERT(fmprb_contains(pos_pm_inf, zero)); ASSERT(fmprb_contains(pos_pm_inf, pos)); ASSERT(fmprb_contains(pos_pm_inf, neg)); ASSERT(fmprb_contains(pos_pm_inf, pos_inf)); ASSERT(fmprb_contains(pos_pm_inf, neg_inf)); ASSERT(fmprb_contains(pos_pm_inf, pos_inf_err)); ASSERT(fmprb_contains(pos_pm_inf, neg_inf_err)); ASSERT(fmprb_contains(pos_pm_inf, zero_pm_inf)); ASSERT(fmprb_contains(pos_pm_inf, pos_pm_inf)); ASSERT(fmprb_contains(pos_pm_inf, neg_pm_inf)); ASSERT(!fmprb_contains(pos_pm_inf, indet_exact)); ASSERT(!fmprb_contains(pos_pm_inf, indet_pos_rad)); ASSERT(!fmprb_contains(pos_pm_inf, indet_inf_rad)); ASSERT(fmprb_contains(neg_pm_inf, zero)); ASSERT(fmprb_contains(neg_pm_inf, pos)); ASSERT(fmprb_contains(neg_pm_inf, neg)); ASSERT(fmprb_contains(neg_pm_inf, pos_inf)); ASSERT(fmprb_contains(neg_pm_inf, neg_inf)); ASSERT(fmprb_contains(neg_pm_inf, pos_inf_err)); ASSERT(fmprb_contains(neg_pm_inf, neg_inf_err)); ASSERT(fmprb_contains(neg_pm_inf, zero_pm_inf)); ASSERT(fmprb_contains(neg_pm_inf, pos_pm_inf)); ASSERT(fmprb_contains(neg_pm_inf, neg_pm_inf)); ASSERT(!fmprb_contains(neg_pm_inf, indet_exact)); ASSERT(!fmprb_contains(neg_pm_inf, indet_pos_rad)); ASSERT(!fmprb_contains(neg_pm_inf, indet_inf_rad)); ASSERT(fmprb_contains(indet_exact, zero)); ASSERT(fmprb_contains(indet_exact, pos)); ASSERT(fmprb_contains(indet_exact, neg)); ASSERT(fmprb_contains(indet_exact, pos_inf)); ASSERT(fmprb_contains(indet_exact, neg_inf)); ASSERT(fmprb_contains(indet_exact, pos_inf_err)); ASSERT(fmprb_contains(indet_exact, neg_inf_err)); ASSERT(fmprb_contains(indet_exact, zero_pm_inf)); ASSERT(fmprb_contains(indet_exact, pos_pm_inf)); ASSERT(fmprb_contains(indet_exact, neg_pm_inf)); ASSERT(fmprb_contains(indet_exact, indet_exact)); ASSERT(fmprb_contains(indet_exact, indet_pos_rad)); ASSERT(fmprb_contains(indet_exact, indet_inf_rad)); ASSERT(fmprb_contains(indet_pos_rad, zero)); ASSERT(fmprb_contains(indet_pos_rad, pos)); ASSERT(fmprb_contains(indet_pos_rad, neg)); ASSERT(fmprb_contains(indet_pos_rad, pos_inf)); ASSERT(fmprb_contains(indet_pos_rad, neg_inf)); ASSERT(fmprb_contains(indet_pos_rad, pos_inf_err)); ASSERT(fmprb_contains(indet_pos_rad, neg_inf_err)); ASSERT(fmprb_contains(indet_pos_rad, zero_pm_inf)); ASSERT(fmprb_contains(indet_pos_rad, pos_pm_inf)); ASSERT(fmprb_contains(indet_pos_rad, neg_pm_inf)); ASSERT(fmprb_contains(indet_pos_rad, indet_exact)); ASSERT(fmprb_contains(indet_pos_rad, indet_pos_rad)); ASSERT(fmprb_contains(indet_pos_rad, indet_inf_rad)); ASSERT(fmprb_contains(indet_inf_rad, zero)); ASSERT(fmprb_contains(indet_inf_rad, pos)); ASSERT(fmprb_contains(indet_inf_rad, neg)); ASSERT(fmprb_contains(indet_inf_rad, pos_inf)); ASSERT(fmprb_contains(indet_inf_rad, neg_inf)); ASSERT(fmprb_contains(indet_inf_rad, pos_inf_err)); ASSERT(fmprb_contains(indet_inf_rad, neg_inf_err)); ASSERT(fmprb_contains(indet_inf_rad, zero_pm_inf)); ASSERT(fmprb_contains(indet_inf_rad, pos_pm_inf)); ASSERT(fmprb_contains(indet_inf_rad, neg_pm_inf)); ASSERT(fmprb_contains(indet_inf_rad, indet_exact)); ASSERT(fmprb_contains(indet_inf_rad, indet_pos_rad)); ASSERT(fmprb_contains(indet_inf_rad, indet_inf_rad)); ASSERT(fmprb_overlaps(zero, zero)); ASSERT(!fmprb_overlaps(zero, pos)); ASSERT(!fmprb_overlaps(zero, neg)); ASSERT(!fmprb_overlaps(zero, pos_inf)); ASSERT(!fmprb_overlaps(zero, neg_inf)); ASSERT(!fmprb_overlaps(zero, pos_inf_err)); ASSERT(!fmprb_overlaps(zero, neg_inf_err)); ASSERT(fmprb_overlaps(zero, zero_pm_inf)); ASSERT(fmprb_overlaps(zero, pos_pm_inf)); ASSERT(fmprb_overlaps(zero, neg_pm_inf)); ASSERT(fmprb_overlaps(zero, indet_exact)); ASSERT(fmprb_overlaps(zero, indet_pos_rad)); ASSERT(fmprb_overlaps(zero, indet_inf_rad)); ASSERT(!fmprb_overlaps(pos, zero)); ASSERT(fmprb_overlaps(pos, pos)); ASSERT(!fmprb_overlaps(pos, neg)); ASSERT(!fmprb_overlaps(pos, pos_inf)); ASSERT(!fmprb_overlaps(pos, neg_inf)); ASSERT(!fmprb_overlaps(pos, pos_inf_err)); ASSERT(!fmprb_overlaps(pos, neg_inf_err)); ASSERT(fmprb_overlaps(pos, zero_pm_inf)); ASSERT(fmprb_overlaps(pos, pos_pm_inf)); ASSERT(fmprb_overlaps(pos, neg_pm_inf)); ASSERT(fmprb_overlaps(pos, indet_exact)); ASSERT(fmprb_overlaps(pos, indet_pos_rad)); ASSERT(fmprb_overlaps(pos, indet_inf_rad)); ASSERT(!fmprb_overlaps(neg, zero)); ASSERT(!fmprb_overlaps(neg, pos)); ASSERT(fmprb_overlaps(neg, neg)); ASSERT(!fmprb_overlaps(neg, pos_inf)); ASSERT(!fmprb_overlaps(neg, neg_inf)); ASSERT(!fmprb_overlaps(neg, pos_inf_err)); ASSERT(!fmprb_overlaps(neg, neg_inf_err)); ASSERT(fmprb_overlaps(neg, zero_pm_inf)); ASSERT(fmprb_overlaps(neg, pos_pm_inf)); ASSERT(fmprb_overlaps(neg, neg_pm_inf)); ASSERT(fmprb_overlaps(neg, indet_exact)); ASSERT(fmprb_overlaps(neg, indet_pos_rad)); ASSERT(fmprb_overlaps(neg, indet_inf_rad)); ASSERT(!fmprb_overlaps(pos_inf, zero)); ASSERT(!fmprb_overlaps(pos_inf, pos)); ASSERT(!fmprb_overlaps(pos_inf, neg)); ASSERT(fmprb_overlaps(pos_inf, pos_inf)); ASSERT(!fmprb_overlaps(pos_inf, neg_inf)); ASSERT(fmprb_overlaps(pos_inf, pos_inf_err)); ASSERT(!fmprb_overlaps(pos_inf, neg_inf_err)); ASSERT(fmprb_overlaps(pos_inf, zero_pm_inf)); ASSERT(fmprb_overlaps(pos_inf, pos_pm_inf)); ASSERT(fmprb_overlaps(pos_inf, neg_pm_inf)); ASSERT(fmprb_overlaps(pos_inf, indet_exact)); ASSERT(fmprb_overlaps(pos_inf, indet_pos_rad)); ASSERT(fmprb_overlaps(pos_inf, indet_inf_rad)); ASSERT(!fmprb_overlaps(neg_inf, zero)); ASSERT(!fmprb_overlaps(neg_inf, pos)); ASSERT(!fmprb_overlaps(neg_inf, neg)); ASSERT(!fmprb_overlaps(neg_inf, pos_inf)); ASSERT(fmprb_overlaps(neg_inf, neg_inf)); ASSERT(!fmprb_overlaps(neg_inf, pos_inf_err)); ASSERT(fmprb_overlaps(neg_inf, neg_inf_err)); ASSERT(fmprb_overlaps(neg_inf, zero_pm_inf)); ASSERT(fmprb_overlaps(neg_inf, pos_pm_inf)); ASSERT(fmprb_overlaps(neg_inf, neg_pm_inf)); ASSERT(fmprb_overlaps(neg_inf, indet_exact)); ASSERT(fmprb_overlaps(neg_inf, indet_pos_rad)); ASSERT(fmprb_overlaps(neg_inf, indet_inf_rad)); ASSERT(!fmprb_overlaps(pos_inf_err, zero)); ASSERT(!fmprb_overlaps(pos_inf_err, pos)); ASSERT(!fmprb_overlaps(pos_inf_err, neg)); ASSERT(fmprb_overlaps(pos_inf_err, pos_inf)); ASSERT(!fmprb_overlaps(pos_inf_err, neg_inf)); ASSERT(fmprb_overlaps(pos_inf_err, pos_inf_err)); ASSERT(!fmprb_overlaps(pos_inf_err, neg_inf_err)); ASSERT(fmprb_overlaps(pos_inf_err, zero_pm_inf)); ASSERT(fmprb_overlaps(pos_inf_err, pos_pm_inf)); ASSERT(fmprb_overlaps(pos_inf_err, neg_pm_inf)); ASSERT(fmprb_overlaps(pos_inf_err, indet_exact)); ASSERT(fmprb_overlaps(pos_inf_err, indet_pos_rad)); ASSERT(fmprb_overlaps(pos_inf_err, indet_inf_rad)); ASSERT(!fmprb_overlaps(neg_inf_err, zero)); ASSERT(!fmprb_overlaps(neg_inf_err, pos)); ASSERT(!fmprb_overlaps(neg_inf_err, neg)); ASSERT(!fmprb_overlaps(neg_inf_err, pos_inf)); ASSERT(fmprb_overlaps(neg_inf_err, neg_inf)); ASSERT(!fmprb_overlaps(neg_inf_err, pos_inf_err)); ASSERT(fmprb_overlaps(neg_inf_err, neg_inf_err)); ASSERT(fmprb_overlaps(neg_inf_err, zero_pm_inf)); ASSERT(fmprb_overlaps(neg_inf_err, pos_pm_inf)); ASSERT(fmprb_overlaps(neg_inf_err, neg_pm_inf)); ASSERT(fmprb_overlaps(neg_inf_err, indet_exact)); ASSERT(fmprb_overlaps(neg_inf_err, indet_pos_rad)); ASSERT(fmprb_overlaps(neg_inf_err, indet_inf_rad)); ASSERT(fmprb_overlaps(zero_pm_inf, zero)); ASSERT(fmprb_overlaps(zero_pm_inf, pos)); ASSERT(fmprb_overlaps(zero_pm_inf, neg)); ASSERT(fmprb_overlaps(zero_pm_inf, pos_inf)); ASSERT(fmprb_overlaps(zero_pm_inf, neg_inf)); ASSERT(fmprb_overlaps(zero_pm_inf, pos_inf_err)); ASSERT(fmprb_overlaps(zero_pm_inf, neg_inf_err)); ASSERT(fmprb_overlaps(zero_pm_inf, zero_pm_inf)); ASSERT(fmprb_overlaps(zero_pm_inf, pos_pm_inf)); ASSERT(fmprb_overlaps(zero_pm_inf, neg_pm_inf)); ASSERT(fmprb_overlaps(zero_pm_inf, indet_exact)); ASSERT(fmprb_overlaps(zero_pm_inf, indet_pos_rad)); ASSERT(fmprb_overlaps(zero_pm_inf, indet_inf_rad)); ASSERT(fmprb_overlaps(pos_pm_inf, zero)); ASSERT(fmprb_overlaps(pos_pm_inf, pos)); ASSERT(fmprb_overlaps(pos_pm_inf, neg)); ASSERT(fmprb_overlaps(pos_pm_inf, pos_inf)); ASSERT(fmprb_overlaps(pos_pm_inf, neg_inf)); ASSERT(fmprb_overlaps(pos_pm_inf, pos_inf_err)); ASSERT(fmprb_overlaps(pos_pm_inf, neg_inf_err)); ASSERT(fmprb_overlaps(pos_pm_inf, zero_pm_inf)); ASSERT(fmprb_overlaps(pos_pm_inf, pos_pm_inf)); ASSERT(fmprb_overlaps(pos_pm_inf, neg_pm_inf)); ASSERT(fmprb_overlaps(pos_pm_inf, indet_exact)); ASSERT(fmprb_overlaps(pos_pm_inf, indet_pos_rad)); ASSERT(fmprb_overlaps(pos_pm_inf, indet_inf_rad)); ASSERT(fmprb_overlaps(neg_pm_inf, zero)); ASSERT(fmprb_overlaps(neg_pm_inf, pos)); ASSERT(fmprb_overlaps(neg_pm_inf, neg)); ASSERT(fmprb_overlaps(neg_pm_inf, pos_inf)); ASSERT(fmprb_overlaps(neg_pm_inf, neg_inf)); ASSERT(fmprb_overlaps(neg_pm_inf, pos_inf_err)); ASSERT(fmprb_overlaps(neg_pm_inf, neg_inf_err)); ASSERT(fmprb_overlaps(neg_pm_inf, zero_pm_inf)); ASSERT(fmprb_overlaps(neg_pm_inf, pos_pm_inf)); ASSERT(fmprb_overlaps(neg_pm_inf, neg_pm_inf)); ASSERT(fmprb_overlaps(neg_pm_inf, indet_exact)); ASSERT(fmprb_overlaps(neg_pm_inf, indet_pos_rad)); ASSERT(fmprb_overlaps(neg_pm_inf, indet_inf_rad)); ASSERT(fmprb_overlaps(indet_exact, zero)); ASSERT(fmprb_overlaps(indet_exact, pos)); ASSERT(fmprb_overlaps(indet_exact, neg)); ASSERT(fmprb_overlaps(indet_exact, pos_inf)); ASSERT(fmprb_overlaps(indet_exact, neg_inf)); ASSERT(fmprb_overlaps(indet_exact, pos_inf_err)); ASSERT(fmprb_overlaps(indet_exact, neg_inf_err)); ASSERT(fmprb_overlaps(indet_exact, zero_pm_inf)); ASSERT(fmprb_overlaps(indet_exact, pos_pm_inf)); ASSERT(fmprb_overlaps(indet_exact, neg_pm_inf)); ASSERT(fmprb_overlaps(indet_exact, indet_exact)); ASSERT(fmprb_overlaps(indet_exact, indet_pos_rad)); ASSERT(fmprb_overlaps(indet_exact, indet_inf_rad)); ASSERT(fmprb_overlaps(indet_pos_rad, zero)); ASSERT(fmprb_overlaps(indet_pos_rad, pos)); ASSERT(fmprb_overlaps(indet_pos_rad, neg)); ASSERT(fmprb_overlaps(indet_pos_rad, pos_inf)); ASSERT(fmprb_overlaps(indet_pos_rad, neg_inf)); ASSERT(fmprb_overlaps(indet_pos_rad, pos_inf_err)); ASSERT(fmprb_overlaps(indet_pos_rad, neg_inf_err)); ASSERT(fmprb_overlaps(indet_pos_rad, zero_pm_inf)); ASSERT(fmprb_overlaps(indet_pos_rad, pos_pm_inf)); ASSERT(fmprb_overlaps(indet_pos_rad, neg_pm_inf)); ASSERT(fmprb_overlaps(indet_pos_rad, indet_exact)); ASSERT(fmprb_overlaps(indet_pos_rad, indet_pos_rad)); ASSERT(fmprb_overlaps(indet_pos_rad, indet_inf_rad)); ASSERT(fmprb_overlaps(indet_inf_rad, zero)); ASSERT(fmprb_overlaps(indet_inf_rad, pos)); ASSERT(fmprb_overlaps(indet_inf_rad, neg)); ASSERT(fmprb_overlaps(indet_inf_rad, pos_inf)); ASSERT(fmprb_overlaps(indet_inf_rad, neg_inf)); ASSERT(fmprb_overlaps(indet_inf_rad, pos_inf_err)); ASSERT(fmprb_overlaps(indet_inf_rad, neg_inf_err)); ASSERT(fmprb_overlaps(indet_inf_rad, zero_pm_inf)); ASSERT(fmprb_overlaps(indet_inf_rad, pos_pm_inf)); ASSERT(fmprb_overlaps(indet_inf_rad, neg_pm_inf)); ASSERT(fmprb_overlaps(indet_inf_rad, indet_exact)); ASSERT(fmprb_overlaps(indet_inf_rad, indet_pos_rad)); ASSERT(fmprb_overlaps(indet_inf_rad, indet_inf_rad)); { fmpz_t t; fmpz_init(t); ASSERT(fmprb_get_unique_fmpz(t, zero)); ASSERT(!fmprb_get_unique_fmpz(t, pos_inf)); ASSERT(!fmprb_get_unique_fmpz(t, neg_inf)); ASSERT(!fmprb_get_unique_fmpz(t, pos_inf_err)); ASSERT(!fmprb_get_unique_fmpz(t, neg_inf_err)); ASSERT(!fmprb_get_unique_fmpz(t, zero_pm_inf)); ASSERT(!fmprb_get_unique_fmpz(t, pos_pm_inf)); ASSERT(!fmprb_get_unique_fmpz(t, neg_pm_inf)); ASSERT(!fmprb_get_unique_fmpz(t, indet_exact)); ASSERT(!fmprb_get_unique_fmpz(t, indet_pos_rad)); ASSERT(!fmprb_get_unique_fmpz(t, indet_inf_rad)); fmpz_clear(t); } { fmpr_t b; slong wp = 30; fmpr_init(b); fmprb_get_abs_ubound_fmpr(b, zero, wp); ASSERT(fmpr_is_zero(b)); fmprb_get_abs_ubound_fmpr(b, pos, wp); ASSERT(fmpr_sgn(b) > 0); fmprb_get_abs_ubound_fmpr(b, neg, wp); ASSERT(fmpr_sgn(b) > 0); fmprb_get_abs_ubound_fmpr(b, pos_inf, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_ubound_fmpr(b, neg_inf, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_ubound_fmpr(b, pos_inf_err, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_ubound_fmpr(b, neg_inf_err, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_ubound_fmpr(b, zero_pm_inf, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_ubound_fmpr(b, indet_exact, wp); ASSERT(fmpr_is_nan(b)); fmprb_get_abs_ubound_fmpr(b, indet_pos_rad, wp); ASSERT(fmpr_is_nan(b)); fmprb_get_abs_ubound_fmpr(b, indet_inf_rad, wp); ASSERT(fmpr_is_nan(b)); fmprb_get_abs_lbound_fmpr(b, zero, wp); ASSERT(fmpr_is_zero(b)); fmprb_get_abs_lbound_fmpr(b, pos, wp); ASSERT(fmpr_sgn(b) > 0); fmprb_get_abs_lbound_fmpr(b, neg, wp); ASSERT(fmpr_sgn(b) > 0); fmprb_get_abs_lbound_fmpr(b, pos_inf, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_lbound_fmpr(b, neg_inf, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_lbound_fmpr(b, pos_inf_err, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_lbound_fmpr(b, neg_inf_err, wp); ASSERT(fmpr_is_pos_inf(b)); fmprb_get_abs_lbound_fmpr(b, zero_pm_inf, wp); ASSERT(fmpr_is_zero(b)); fmprb_get_abs_lbound_fmpr(b, indet_exact, wp); ASSERT(fmpr_is_nan(b)); fmprb_get_abs_lbound_fmpr(b, indet_pos_rad, wp); ASSERT(fmpr_is_nan(b)); fmprb_get_abs_lbound_fmpr(b, indet_inf_rad, wp); ASSERT(fmpr_is_nan(b)); fmpr_clear(b); } fmprb_clear(zero); fmprb_clear(pos); fmprb_clear(neg); fmprb_clear(pos_inf); fmprb_clear(neg_inf); fmprb_clear(pos_inf_err); fmprb_clear(neg_inf_err); fmprb_clear(zero_pm_inf); fmprb_clear(pos_pm_inf); fmprb_clear(neg_pm_inf); fmprb_clear(indet_exact); fmprb_clear(indet_pos_rad); fmprb_clear(indet_inf_rad); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-sqrt.c000066400000000000000000000043101264125401100157430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; slong prec = 2 + n_randint(state, 200); fmprb_init(a); fmprb_init(b); fmprb_init(c); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_sqrt(b, a, prec); fmprb_mul(c, b, b, prec); if (!fmprb_contains(c, a)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); abort(); } fmprb_sqrt(a, a, prec); if (!fmprb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-sqrtpos.c000066400000000000000000000044741264125401100165000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrtpos...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; slong prec = 2 + n_randint(state, 200); fmprb_init(a); fmprb_init(b); fmprb_init(c); do { fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); } while (fmprb_contains_negative(a)); fmprb_sqrtpos(b, a, prec); fmprb_mul(c, b, b, prec); if (!fmprb_contains(c, a) || fmprb_contains_negative(b)) { flint_printf("FAIL: containment / positivity\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); abort(); } fmprb_sqrtpos(a, a, prec); if (!fmprb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-sub.c000066400000000000000000000120101264125401100155370ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("sub...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_randtest(c, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_sub(c, a, b, 2 + n_randint(state, 200)); fmpq_sub(z, x, y); if (!fmprb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_sub(a, a, b, 2 + n_randint(state, 200)); fmpq_sub(z, x, y); if (!fmprb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_sub(b, a, b, 2 + n_randint(state, 200)); fmpq_sub(z, x, y); if (!fmprb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-submul.c000066400000000000000000000122221264125401100162620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("submul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t a, b, c; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmprb_init(c); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_randtest(c, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(z, state, c, 1 + n_randint(state, 200)); fmprb_submul(c, a, b, 2 + n_randint(state, 200)); fmpq_submul(z, x, y); if (!fmprb_contains_fmpq(c, z)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("c = "); fmprb_print(c); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmprb_clear(c); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and a */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, x); fmprb_submul(a, a, b, 2 + n_randint(state, 200)); fmpq_submul(z, x, y); if (!fmprb_contains_fmpq(a, z)) { flint_printf("FAIL: aliasing (c, a)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } /* aliasing of c and b */ for (iter = 0; iter < 10000; iter++) { fmprb_t a, b; fmpq_t x, y, z; fmprb_init(a); fmprb_init(b); fmpq_init(x); fmpq_init(y); fmpq_init(z); fmprb_randtest(a, state, 1 + n_randint(state, 200), 10); fmprb_randtest(b, state, 1 + n_randint(state, 200), 10); fmprb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200)); fmprb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200)); fmpq_set(z, y); fmprb_submul(b, a, b, 2 + n_randint(state, 200)); fmpq_submul(z, x, y); if (!fmprb_contains_fmpq(b, z)) { flint_printf("FAIL: aliasing (c, b)\n\n"); flint_printf("a = "); fmprb_print(a); flint_printf("\n\n"); flint_printf("x = "); fmpq_print(x); flint_printf("\n\n"); flint_printf("b = "); fmprb_print(b); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpq_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(a); fmprb_clear(b); fmpq_clear(x); fmpq_clear(y); fmpq_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-trim.c000066400000000000000000000052161264125401100157330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("trim...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t x, y; slong acc1, acc2; int accuracy_ok; fmprb_init(x); fmprb_init(y); fmprb_randtest_special(x, state, 1000, 100); fmprb_trim(y, x); if (!fmprb_contains(y, x)) { flint_printf("FAIL (containment):\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); abort(); } acc1 = fmprb_rel_accuracy_bits(x); acc2 = fmprb_rel_accuracy_bits(y); accuracy_ok = (acc1 < 0 && acc2 <= acc1) || (acc2 >= acc1 - 1); if (!accuracy_ok) { flint_printf("FAIL (accuracy):\n\n"); flint_printf("x: %wd, y = %wd\n\n", acc1, acc2); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); abort(); } fmprb_trim(x, x); if (!fmprb_equal(y, x)) { flint_printf("FAIL (aliasing):\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); abort(); } fmprb_clear(x); fmprb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/test/t-union.c000066400000000000000000000053241264125401100161100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" int main() { slong iter; flint_rand_t state; flint_printf("union...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmprb_t x, y, z; slong prec; int alias; fmprb_init(x); fmprb_init(y); fmprb_init(z); fmprb_randtest_special(x, state, 200, 10); fmprb_randtest_special(y, state, 200, 10); fmprb_randtest_special(z, state, 200, 10); prec = 2 + n_randint(state, 200); fmprb_union(z, x, y, prec); if (!fmprb_contains(z, x) || !fmprb_contains(z, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); flint_printf("z = "); fmprb_print(z); flint_printf("\n\n"); abort(); } if (n_randint(state, 2)) { fmprb_union(x, x, y, prec); alias = fmprb_equal(x, z); } else { fmprb_union(y, x, y, prec); alias = fmprb_equal(y, z); } if (!alias) { flint_printf("FAIL (aliasing):\n\n"); flint_printf("x = "); fmprb_print(x); flint_printf("\n\n"); flint_printf("y = "); fmprb_print(y); flint_printf("\n\n"); flint_printf("z = "); fmprb_print(z); flint_printf("\n\n"); abort(); } fmprb_clear(x); fmprb_clear(y); fmprb_clear(z); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmprb/trim.c000066400000000000000000000042121264125401100145060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" #define TRIM_PADDING 16 void fmprb_trim(fmprb_t y, const fmprb_t x) { if (fmpr_is_zero(fmprb_radref(x)) || fmpr_is_special(fmprb_midref(x))) { fmprb_set(y, x); } else if (fmpr_is_special(fmprb_radref(x))) { /* midpoint must be finite, so set to 0 +/- inf */ fmprb_zero_pm_inf(y); } else { slong bits, accuracy; bits = fmprb_bits(x); accuracy = fmprb_rel_accuracy_bits(x); if (accuracy < -TRIM_PADDING) { /* set to 0 +/- rad */ if (fmpr_sgn(fmprb_midref(x)) < 0) fmpr_sub(fmprb_radref(y), fmprb_radref(x), fmprb_midref(x), FMPRB_RAD_PREC, FMPR_RND_UP); else fmpr_add(fmprb_radref(y), fmprb_radref(x), fmprb_midref(x), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_zero(fmprb_midref(y)); } else if (accuracy < bits - TRIM_PADDING) { fmprb_set_round(y, x, FLINT_MAX(0, accuracy) + TRIM_PADDING); } else { fmprb_set(y, x); } } } arb-2.8.1/fmprb/union.c000066400000000000000000000037441264125401100146740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmprb.h" void fmprb_union(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec) { fmpr_t left, right, t; if (fmpr_is_nan(fmprb_midref(x)) || fmpr_is_nan(fmprb_midref(y))) { fmprb_indeterminate(z); return; } if (fmpr_is_pos_inf(fmprb_radref(x)) || fmpr_is_pos_inf(fmprb_radref(y))) { fmprb_zero_pm_inf(z); return; } fmpr_init(left); fmpr_init(right); fmpr_init(t); fmpr_sub(left, fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_FLOOR); fmpr_sub(t, fmprb_midref(y), fmprb_radref(y), prec, FMPR_RND_FLOOR); fmpr_min(left, left, t); fmpr_add(right, fmprb_midref(x), fmprb_radref(x), prec, FMPR_RND_CEIL); fmpr_add(t, fmprb_midref(y), fmprb_radref(y), prec, FMPR_RND_CEIL); fmpr_max(right, right, t); fmprb_set_interval_fmpr(z, left, right, prec); fmpr_clear(left); fmpr_clear(right); fmpr_clear(t); } arb-2.8.1/fmpz_extras.h000066400000000000000000000141761264125401100150060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #ifndef FMPZ_EXTRAS_H #define FMPZ_EXTRAS_H #include #include "flint.h" #include "fmpz.h" #ifdef __cplusplus extern "C" { #endif static __inline__ void fmpz_add_inline(fmpz_t z, const fmpz_t x, const fmpz_t y) { fmpz f, g; f = *x; g = *y; if (!COEFF_IS_MPZ(f) && !COEFF_IS_MPZ(g)) fmpz_set_si(z, f + g); else fmpz_add(z, x, y); } static __inline__ void fmpz_add_si(fmpz_t z, const fmpz_t x, slong y) { if (y >= 0) fmpz_add_ui(z, x, y); else fmpz_sub_ui(z, x, -y); } static __inline__ void fmpz_sub_si(fmpz_t z, const fmpz_t x, slong y) { if (y >= 0) fmpz_sub_ui(z, x, y); else fmpz_add_ui(z, x, -y); } static __inline__ void fmpz_add_si_inline(fmpz_t z, const fmpz_t x, slong y) { fmpz f; f = *x; if (!COEFF_IS_MPZ(f) && (COEFF_MIN <= y && y <= COEFF_MAX)) fmpz_set_si(z, f + y); else fmpz_add_si(z, x, y); } static __inline__ void fmpz_sub_si_inline(fmpz_t z, const fmpz_t x, slong y) { fmpz f; f = *x; if (!COEFF_IS_MPZ(f) && (COEFF_MIN <= y && y <= COEFF_MAX)) fmpz_set_si(z, f - y); else fmpz_sub_si(z, x, y); } static __inline__ void fmpz_add_ui_inline(fmpz_t z, const fmpz_t x, ulong y) { fmpz f = *x; if (!COEFF_IS_MPZ(f) && y <= COEFF_MAX) fmpz_set_si(z, f + y); else fmpz_add_ui(z, x, y); } static __inline__ void fmpz_add2_fmpz_si_inline(fmpz_t z, const fmpz_t x, const fmpz_t y, slong c) { fmpz f, g, h; f = *x; g = *y; if (!COEFF_IS_MPZ(f) && !COEFF_IS_MPZ(g)) { h = f + g; if ((COEFF_MIN <= h && h <= COEFF_MAX) && (COEFF_MIN <= c && c <= COEFF_MAX)) { fmpz_set_si(z, h + c); return; } } fmpz_add(z, x, y); fmpz_add_si(z, z, c); } /* sets z = +/- ({src, n} >> shift) where 0 <= shift < FLINT_BITS and the top limb of src is nonzero */ /* TODO: optimize for result = 1 limb */ static __inline__ void fmpz_set_mpn_rshift(fmpz_t z, mp_srcptr src, mp_size_t n, unsigned int shift, int negative) { __mpz_struct * zptr; zptr = _fmpz_promote(z); if (zptr->_mp_alloc < n) mpz_realloc2(zptr, n * FLINT_BITS); if (shift == 0) { flint_mpn_copyi(zptr->_mp_d, src, n); } else { mpn_rshift(zptr->_mp_d, src, n, shift); while (zptr->_mp_d[n - 1] == 0) /* todo: can only do one iter? */ n--; } zptr->_mp_size = negative ? -n : n; _fmpz_demote_val(z); } /* sets z = +/- {src, n} where n >= 2 and the top limb of src is nonzero */ static __inline__ void fmpz_set_mpn_large(fmpz_t z, mp_srcptr src, mp_size_t n, int negative) { __mpz_struct * zz; zz = _fmpz_promote(z); if (zz->_mp_alloc < n) mpz_realloc2(zz, n * FLINT_BITS); flint_mpn_copyi(zz->_mp_d, src, n); zz->_mp_size = negative ? -n : n; } /* round away from zero */ static __inline__ void fmpz_adiv_q_2exp(fmpz_t z, const fmpz_t x, mp_bitcnt_t exp) { int sign = fmpz_sgn(x); if (sign > 0) fmpz_cdiv_q_2exp(z, x, exp); else fmpz_fdiv_q_2exp(z, x, exp); } /* sets z = x + y*2^shift */ static __inline__ void fmpz_add_mul2exp(fmpz_t z, const fmpz_t x, const fmpz_t y, ulong shift) { fmpz_t t; fmpz_init(t); fmpz_mul_2exp(t, y, shift); fmpz_add(z, x, t); fmpz_clear(t); } static __inline__ void fmpz_sub_mul2exp(fmpz_t z, const fmpz_t x, const fmpz_t y, ulong shift) { fmpz_t t; fmpz_init(t); fmpz_mul_2exp(t, y, shift); fmpz_sub(z, x, t); fmpz_clear(t); } slong _fmpz_sub_small_large(const fmpz_t x, const fmpz_t y); static __inline__ slong _fmpz_sub_small(const fmpz_t x, const fmpz_t y) { if (!COEFF_IS_MPZ(*x) && !COEFF_IS_MPZ(*y)) { return (*x) - (*y); } else { return _fmpz_sub_small_large(x, y); } } static __inline__ mp_size_t _fmpz_size(const fmpz_t f) { fmpz d = *f; if (!COEFF_IS_MPZ(d)) return 1; else return mpz_size(COEFF_TO_PTR(d)); } static __inline__ void fmpz_ui_pow_ui(fmpz_t x, ulong b, ulong e) { if (e <= 1) { fmpz_set_ui(x, e == 0 ? UWORD(1) : b); } else { fmpz_set_ui(x, b); fmpz_pow_ui(x, x, e); } } static __inline__ void fmpz_max(fmpz_t z, const fmpz_t x, const fmpz_t y) { if (fmpz_cmp(x, y) >= 0) fmpz_set(z, x); else fmpz_set(z, y); } static __inline__ void fmpz_min(fmpz_t z, const fmpz_t x, const fmpz_t y) { if (fmpz_cmp(x, y) < 0) fmpz_set(z, x); else fmpz_set(z, y); } #define FMPZ_GET_MPN_READONLY(zsign, zn, zptr, ztmp, zv) \ if (!COEFF_IS_MPZ(zv)) \ { \ (zsign) = (zv) < 0; \ (ztmp) = FLINT_ABS(zv); \ (zptr) = &(ztmp); \ (zn) = 1; \ } \ else \ { \ __mpz_struct * ___zz = COEFF_TO_PTR(zv); \ (zptr) = ___zz->_mp_d; \ (zn) = ___zz->_mp_size; \ (zsign) = (zn) < 0; \ (zn) = FLINT_ABS(zn); \ } void fmpz_lshift_mpn(fmpz_t z, mp_srcptr d, mp_size_t dn, int sgnbit, mp_bitcnt_t shift); #ifdef __cplusplus } #endif #endif arb-2.8.1/fmpz_extras/000077500000000000000000000000001264125401100146245ustar00rootroot00000000000000arb-2.8.1/fmpz_extras/dummy.c000066400000000000000000000022221264125401100161210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" void fmpz_dummy(const fmpz_t x) { fmpz_print(x); } arb-2.8.1/fmpz_extras/lshift_mpn.c000066400000000000000000000035531264125401100171410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" void fmpz_lshift_mpn(fmpz_t z, mp_srcptr d, mp_size_t dn, int sgnbit, mp_bitcnt_t shift) { __mpz_struct * zmpz; mp_ptr zp; mp_size_t zn, shift_limbs; mp_bitcnt_t shift_bits; zmpz = _fmpz_promote(z); shift_limbs = shift / FLINT_BITS; shift_bits = shift % FLINT_BITS; zn = dn + shift_limbs + (shift_bits != 0); if (zmpz->_mp_alloc < zn) mpz_realloc2(zmpz, zn * FLINT_BITS); zp = zmpz->_mp_d; flint_mpn_zero(zp, shift_limbs); if (shift_bits == 0) { flint_mpn_copyi(zp + shift_limbs, d, dn); } else { zp[zn - 1] = mpn_lshift(zp + shift_limbs, d, dn, shift_bits); while (zp[zn - 1] == 0) zn--; } zmpz->_mp_size = sgnbit ? -(slong) zn : zn; _fmpz_demote_val(z); } arb-2.8.1/fmpz_extras/sub_small_large.c000066400000000000000000000026511264125401100201270ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" slong _fmpz_sub_small_large(const fmpz_t x, const fmpz_t y) { fmpz_t t; fmpz_init(t); fmpz_sub(t, x, y); if (!COEFF_IS_MPZ(*t)) { /* no need to free t */ return *t; } else { int sign = fmpz_sgn(t); fmpz_clear(t); return (sign > 0) ? WORD_MAX : -WORD_MAX; } } arb-2.8.1/fmpz_extras/test/000077500000000000000000000000001264125401100156035ustar00rootroot00000000000000arb-2.8.1/fmpz_extras/test/t-add2_fmpz_si_inline.c000066400000000000000000000101671264125401100221140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("add2_fmpz_si_inline...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpz_t a, b, c, d; slong e; fmpz_init(a); fmpz_init(b); fmpz_init(c); fmpz_init(d); fmpz_randtest(a, state, 1 + n_randint(state, 200)); fmpz_randtest(b, state, 1 + n_randint(state, 200)); fmpz_randtest(c, state, 1 + n_randint(state, 200)); fmpz_randtest(d, state, 1 + n_randint(state, 200)); e = n_randtest(state); fmpz_add(c, a, b); fmpz_add_si(c, c, e); fmpz_add2_fmpz_si_inline(d, a, b, e); if (!fmpz_equal(c, d)) { flint_printf("FAIL\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); flint_printf("%wd\n\n", e); abort(); } fmpz_add2_fmpz_si_inline(a, a, b, e); if (!fmpz_equal(c, a)) { flint_printf("FAIL (aliasing 1)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); flint_printf("%wd\n\n", e); abort(); } fmpz_randtest(a, state, 1 + n_randint(state, 200)); fmpz_add(c, a, b); fmpz_add_si(c, c, e); fmpz_add2_fmpz_si_inline(b, a, b, e); if (!fmpz_equal(c, b)) { flint_printf("FAIL (aliasing 2)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); flint_printf("%wd\n\n", e); abort(); } fmpz_add(d, a, a); fmpz_add_si(d, d, e); fmpz_add2_fmpz_si_inline(c, a, a, e); if (!fmpz_equal(c, d)) { flint_printf("FAIL (aliasing 3)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); flint_printf("%wd\n\n", e); abort(); } fmpz_add(d, a, a); fmpz_add_si(d, d, e); fmpz_add2_fmpz_si_inline(a, a, a, e); if (!fmpz_equal(d, a)) { flint_printf("FAIL (aliasing 4)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); flint_printf("%wd\n\n", e); abort(); } fmpz_clear(a); fmpz_clear(b); fmpz_clear(c); fmpz_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpz_extras/test/t-add_inline.c000066400000000000000000000073021264125401100203000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("add_inline...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpz_t a, b, c, d; fmpz_init(a); fmpz_init(b); fmpz_init(c); fmpz_init(d); fmpz_randtest(a, state, 1 + n_randint(state, 200)); fmpz_randtest(b, state, 1 + n_randint(state, 200)); fmpz_randtest(c, state, 1 + n_randint(state, 200)); fmpz_randtest(d, state, 1 + n_randint(state, 200)); fmpz_add(c, a, b); fmpz_add_inline(d, a, b); if (!fmpz_equal(c, d)) { flint_printf("FAIL\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_add_inline(a, a, b); if (!fmpz_equal(c, a)) { flint_printf("FAIL (aliasing 1)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_randtest(a, state, 1 + n_randint(state, 200)); fmpz_add(c, a, b); fmpz_add_inline(b, a, b); if (!fmpz_equal(c, b)) { flint_printf("FAIL (aliasing 2)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_add(d, a, a); fmpz_add_inline(c, a, a); if (!fmpz_equal(c, d)) { flint_printf("FAIL (aliasing 3)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_add(d, a, a); fmpz_add_inline(a, a, a); if (!fmpz_equal(d, a)) { flint_printf("FAIL (aliasing 4)\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_clear(a); fmpz_clear(b); fmpz_clear(c); fmpz_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpz_extras/test/t-add_si_inline.c000066400000000000000000000047661264125401100210060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("add_si_inline...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpz_t a, c, d; slong b; fmpz_init(a); fmpz_init(c); fmpz_init(d); fmpz_randtest(a, state, 1 + n_randint(state, 200)); fmpz_randtest(c, state, 1 + n_randint(state, 200)); fmpz_randtest(d, state, 1 + n_randint(state, 200)); b = n_randtest(state); fmpz_add_si(c, a, b); fmpz_add_si_inline(d, a, b); if (!fmpz_equal(c, d)) { flint_printf("FAIL\n"); fmpz_print(a); flint_printf("\n\n"); flint_printf("%wd", b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_add_si_inline(a, a, b); if (!fmpz_equal(c, a)) { flint_printf("FAIL (aliasing)\n"); fmpz_print(a); flint_printf("\n\n"); flint_printf("%wd", b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_clear(a); fmpz_clear(c); fmpz_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpz_extras/test/t-add_ui_inline.c000066400000000000000000000047661264125401100210100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("add_ui_inline...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpz_t a, c, d; ulong b; fmpz_init(a); fmpz_init(c); fmpz_init(d); fmpz_randtest(a, state, 1 + n_randint(state, 200)); fmpz_randtest(c, state, 1 + n_randint(state, 200)); fmpz_randtest(d, state, 1 + n_randint(state, 200)); b = n_randtest(state); fmpz_add_ui(c, a, b); fmpz_add_ui_inline(d, a, b); if (!fmpz_equal(c, d)) { flint_printf("FAIL\n"); fmpz_print(a); flint_printf("\n\n"); flint_printf("%wu", b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_add_ui_inline(a, a, b); if (!fmpz_equal(c, a)) { flint_printf("FAIL (aliasing)\n"); fmpz_print(a); flint_printf("\n\n"); flint_printf("%wu", b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_clear(a); fmpz_clear(c); fmpz_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpz_extras/test/t-lshift_mpn.c000066400000000000000000000044041264125401100203550ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("lshift_mpn...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpz_t a, b, c; ulong e; mp_limb_t atmp; mp_ptr aptr; mp_size_t an; int asgnbit; fmpz_init(a); fmpz_init(b); fmpz_init(c); fmpz_randtest_not_zero(a, state, 1 + n_randint(state, 2000)); fmpz_randtest(b, state, 1 + n_randint(state, 2000)); fmpz_randtest(c, state, 1 + n_randint(state, 2000)); e = n_randint(state, 1000); FMPZ_GET_MPN_READONLY(asgnbit, an, aptr, atmp, *a) fmpz_lshift_mpn(b, aptr, an, asgnbit, e); fmpz_mul_2exp(c, a, e); if (!fmpz_equal(b, c)) { flint_printf("FAIL\n"); fmpz_print(a); flint_printf("\n\n"); fmpz_print(b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); abort(); } fmpz_clear(a); fmpz_clear(b); fmpz_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/fmpz_extras/test/t-sub_si_inline.c000066400000000000000000000047661264125401100210470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "fmpz_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("sub_si_inline...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpz_t a, c, d; slong b; fmpz_init(a); fmpz_init(c); fmpz_init(d); fmpz_randtest(a, state, 1 + n_randint(state, 200)); fmpz_randtest(c, state, 1 + n_randint(state, 200)); fmpz_randtest(d, state, 1 + n_randint(state, 200)); b = n_randtest(state); fmpz_sub_si(c, a, b); fmpz_sub_si_inline(d, a, b); if (!fmpz_equal(c, d)) { flint_printf("FAIL\n"); fmpz_print(a); flint_printf("\n\n"); flint_printf("%wd", b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_sub_si_inline(a, a, b); if (!fmpz_equal(c, a)) { flint_printf("FAIL (aliasing)\n"); fmpz_print(a); flint_printf("\n\n"); flint_printf("%wd", b); flint_printf("\n\n"); fmpz_print(c); flint_printf("\n\n"); fmpz_print(d); flint_printf("\n\n"); abort(); } fmpz_clear(a); fmpz_clear(c); fmpz_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/gpl-2.0.txt000066400000000000000000000432541264125401100141120ustar00rootroot00000000000000 GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Lesser General Public License instead.) You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things. To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it. For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software. Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations. Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all. The precise terms and conditions for copying, distribution and modification follow. GNU GENERAL PUBLIC LICENSE TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION 0. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you". Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does. 1. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program. You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee. 2. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions: a) You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change. b) You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License. c) If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.) These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it. Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program. In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License. 3. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following: a) Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, b) Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or, c) Accompany it with the information you received as to the offer to distribute corresponding source code. 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If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. 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IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. arb-2.8.1/hypgeom.h000066400000000000000000000042521264125401100141060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #ifndef HYPGEOM_H #define HYPGEOM_H #include "fmprb.h" #include "arb.h" #include "mag.h" #include "fmpz_poly.h" #ifdef __cplusplus extern "C" { #endif typedef struct { fmpz_poly_t A; fmpz_poly_t B; fmpz_poly_t P; fmpz_poly_t Q; /* precomputation data */ int have_precomputed; slong r; slong boundC; slong boundD; slong boundK; mag_t MK; } hypgeom_struct; typedef hypgeom_struct hypgeom_t[1]; void hypgeom_init(hypgeom_t hyp); void hypgeom_clear(hypgeom_t hyp); void hypgeom_precompute(hypgeom_t hyp); slong hypgeom_estimate_terms(const mag_t z, int r, slong prec); slong hypgeom_bound(mag_t error, int r, slong C, slong D, slong K, const mag_t TK, const mag_t z, slong prec); void fmprb_hypgeom_sum(fmprb_t P, fmprb_t Q, const hypgeom_t hyp, slong n, slong prec); void fmprb_hypgeom_infsum(fmprb_t P, fmprb_t Q, hypgeom_t hyp, slong target_prec, slong prec); void arb_hypgeom_sum(arb_t P, arb_t Q, const hypgeom_t hyp, slong n, slong prec); void arb_hypgeom_infsum(arb_t P, arb_t Q, hypgeom_t hyp, slong target_prec, slong prec); #ifdef __cplusplus } #endif #endif arb-2.8.1/hypgeom/000077500000000000000000000000001264125401100137325ustar00rootroot00000000000000arb-2.8.1/hypgeom/bound.c000066400000000000000000000116261264125401100152130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include "double_extras.h" #include "hypgeom.h" slong hypgeom_root_bound(const mag_t z, int r) { if (r == 0) { return 0; } else { fmpr_t t; slong v; fmpr_init(t); mag_get_fmpr(t, z); fmpr_root(t, t, r, MAG_BITS, FMPR_RND_UP); fmpr_add_ui(t, t, 1, MAG_BITS, FMPR_RND_UP); v = fmpr_get_si(t, FMPR_RND_UP); fmpr_clear(t); return v; } } /* Given T(K), compute bound for T(n) z^n. We need to multiply by z^n * 1/rf(K+1,m)^r * (rf(K+1,m)/rf(K+1-A,m)) * (rf(K+1-B,m)/rf(K+1-2B,m)) where m = n - K. This is equal to z^n * (K+A)! (K-2B)! (K-B+m)! ----------------------- * ((K+m)! / K!)^(1-r) (K-B)! (K-A+m)! (K-2B+m)! */ void hypgeom_term_bound(mag_t Tn, const mag_t TK, slong K, slong A, slong B, int r, const mag_t z, slong n) { mag_t t, u, num; slong m; mag_init(t); mag_init(u); mag_init(num); m = n - K; if (m < 0) { flint_printf("hypgeom term bound\n"); abort(); } /* TK * z^n */ mag_pow_ui(t, z, n); mag_mul(num, TK, t); /* numerator: (K+A)! (K-2B)! (K-B+m)! */ mag_fac_ui(t, K+A); mag_mul(num, num, t); mag_fac_ui(t, K-2*B); mag_mul(num, num, t); mag_fac_ui(t, K-B+m); mag_mul(num, num, t); /* denominator: (K-B)! (K-A+m)! (K-2B+m)! */ mag_rfac_ui(t, K-B); mag_mul(num, num, t); mag_rfac_ui(t, K-A+m); mag_mul(num, num, t); mag_rfac_ui(t, K-2*B+m); mag_mul(num, num, t); /* ((K+m)! / K!)^(1-r) */ if (r == 0) { mag_fac_ui(t, K+m); mag_mul(num, num, t); mag_rfac_ui(t, K); mag_mul(num, num, t); } else if (r != 1) { mag_fac_ui(t, K); mag_rfac_ui(u, K+m); mag_mul(t, t, u); mag_pow_ui(t, t, r-1); mag_mul(num, num, t); } mag_set(Tn, num); mag_clear(t); mag_clear(u); mag_clear(num); } slong hypgeom_bound(mag_t error, int r, slong A, slong B, slong K, const mag_t TK, const mag_t z, slong tol_2exp) { mag_t Tn, t, u, one, tol, num, den; slong n, m; mag_init(Tn); mag_init(t); mag_init(u); mag_init(one); mag_init(tol); mag_init(num); mag_init(den); mag_one(one); mag_set_ui_2exp_si(tol, UWORD(1), -tol_2exp); /* approximate number of needed terms */ n = hypgeom_estimate_terms(z, r, tol_2exp); /* required for 1 + O(1/k) part to be decreasing */ n = FLINT_MAX(n, K + 1); /* required for z^k / (k!)^r to be decreasing */ m = hypgeom_root_bound(z, r); n = FLINT_MAX(n, m); /* We now have |R(k)| <= G(k) where G(k) is monotonically decreasing, and can bound the tail using a geometric series as soon as soon as G(k) < 1. */ /* bound T(n-1) */ hypgeom_term_bound(Tn, TK, K, A, B, r, z, n-1); while (1) { /* bound R(n) */ mag_mul_ui(num, z, n); mag_mul_ui(num, num, n - B); mag_set_ui_lower(den, n - A); mag_mul_ui_lower(den, den, n - 2*B); if (r != 0) { mag_set_ui_lower(u, n); mag_pow_ui_lower(u, u, r); mag_mul_lower(den, den, u); } mag_div(t, num, den); /* multiply bound for T(n-1) by bound for R(n) to bound T(n) */ mag_mul(Tn, Tn, t); /* geometric series termination check */ /* u = max(1-t, 0), rounding down [lower bound] */ mag_sub_lower(u, one, t); if (!mag_is_zero(u)) { mag_div(u, Tn, u); if (mag_cmp(u, tol) < 0) { mag_set(error, u); break; } } /* move on to next term */ n++; } mag_clear(Tn); mag_clear(t); mag_clear(u); mag_clear(one); mag_clear(tol); mag_clear(num); mag_clear(den); return n; } arb-2.8.1/hypgeom/estimate_terms_d.c000066400000000000000000000037061264125401100174340ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include "double_extras.h" #include "hypgeom.h" #define LOG2 0.69314718055994530942 #define EXP1 2.7182818284590452354 static __inline__ double d_root(double x, int r) { if (r == 1) return x; if (r == 2) return sqrt(x); return pow(x, 1. / r); } slong hypgeom_estimate_terms(const mag_t z, int r, slong prec) { double y, t; t = mag_get_d(z); if (t == 0) return 1; if (r == 0) { if (t >= 1) { flint_printf("z must be smaller than 1\n"); abort(); } y = (log(1-t) - prec * LOG2) / log(t) + 1; } else { y = (prec * LOG2) / (d_root(t, r) * EXP1 * r); y = (prec * LOG2) / (r * d_lambertw(y)) + 1; } if (y >= WORD_MAX / 2) { flint_printf("error: series will converge too slowly\n"); abort(); } return y; } arb-2.8.1/hypgeom/init.c000066400000000000000000000027241264125401100150460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "hypgeom.h" void hypgeom_init(hypgeom_t hyp) { fmpz_poly_init(hyp->A); fmpz_poly_init(hyp->B); fmpz_poly_init(hyp->P); fmpz_poly_init(hyp->Q); mag_init(hyp->MK); hyp->have_precomputed = 0; } void hypgeom_clear(hypgeom_t hyp) { fmpz_poly_clear(hyp->A); fmpz_poly_clear(hyp->B); fmpz_poly_clear(hyp->P); fmpz_poly_clear(hyp->Q); mag_clear(hyp->MK); } arb-2.8.1/hypgeom/precompute.c000066400000000000000000000077661264125401100163010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include #include "hypgeom.h" /* Compute a pure ratio P2(k)/Q2(k) for the term A(k)/B(k) * [P(1)P(2)...P(k)] / [Q(1)Q(2)...Q(k)] */ void hypgeom_standardize(fmpz_poly_t P2, fmpz_poly_t Q2, const fmpz_poly_t A, const fmpz_poly_t B, const fmpz_poly_t P, const fmpz_poly_t Q) { fmpz_t s; fmpz_poly_t T; fmpz_init(s); fmpz_poly_init(T); fmpz_set_si(s, -WORD(1)); /* P = A * B(k-1) * P */ fmpz_poly_taylor_shift(T, B, s); fmpz_poly_mul(P2, A, T); fmpz_poly_mul(P2, P2, P); /* Q = B * A(k-1) * Q */ fmpz_poly_taylor_shift(T, A, s); fmpz_poly_mul(Q2, B, T); fmpz_poly_mul(Q2, Q2, Q); fmpz_clear(s); fmpz_poly_clear(T); } /* quotient of absolute value, rounded up */ static __inline__ void fmpz_cdiv_abs_q(fmpz_t q, const fmpz_t x, const fmpz_t y) { if (fmpz_sgn(x) == fmpz_sgn(y)) { fmpz_cdiv_q(q, x, y); } else { fmpz_fdiv_q(q, x, y); fmpz_neg(q, q); } } slong hypgeom_root_norm(const fmpz_poly_t P) { slong res, i, p; fmpz_t t, A; fmpz_init(A); fmpz_init(t); p = fmpz_poly_degree(P); fmpz_zero(A); for (i = 1; i <= p; i++) { fmpz_cdiv_abs_q(t, P->coeffs + p - i, P->coeffs + p); fmpz_root(t, t, i); fmpz_add_ui(t, t, 1); if (fmpz_cmp(t, A) > 0) fmpz_swap(t, A); } if (!fmpz_fits_si(A)) abort(); res = fmpz_get_si(A); fmpz_clear(A); fmpz_clear(t); return res; } static __inline__ void fmpz_poly_evaluate_si(fmpz_t y, const fmpz_poly_t poly, slong x) { fmpz_set_si(y, x); fmpz_poly_evaluate_fmpz(y, poly, y); } void _hypgeom_precompute(hypgeom_t hyp, const fmpz_poly_t P, const fmpz_poly_t Q) { slong k; fmpz_t t; fmpz_init(t); hyp->r = fmpz_poly_degree(Q) - fmpz_poly_degree(P); hyp->boundC = hypgeom_root_norm(P); hyp->boundD = hypgeom_root_norm(Q); hyp->boundK = 1 + FLINT_MAX(hyp->boundC, 2 * hyp->boundD); mag_one(hyp->MK); for (k = 1; k <= hyp->boundK; k++) { fmpz_poly_evaluate_si(t, P, k); mag_mul_fmpz(hyp->MK, hyp->MK, t); fmpz_poly_evaluate_si(t, Q, k); mag_div_fmpz(hyp->MK, hyp->MK, t); } fmpz_clear(t); } void hypgeom_precompute(hypgeom_t hyp) { if (fmpz_poly_is_one(hyp->A) && fmpz_poly_is_one(hyp->B)) { _hypgeom_precompute(hyp, hyp->P, hyp->Q); } else { fmpz_poly_t P2, Q2; fmpz_poly_init(P2); fmpz_poly_init(Q2); hypgeom_standardize(P2, Q2, hyp->A, hyp->B, hyp->P, hyp->Q); _hypgeom_precompute(hyp, P2, Q2); { fmpz_t t; fmpz_init(t); fmpz_poly_evaluate_si(t, hyp->A, 0); mag_mul_fmpz(hyp->MK, hyp->MK, t); fmpz_poly_evaluate_si(t, hyp->B, 0); mag_div_fmpz(hyp->MK, hyp->MK, t); fmpz_clear(t); } fmpz_poly_clear(P2); fmpz_poly_clear(Q2); } } arb-2.8.1/hypgeom/sum.c000066400000000000000000000202741264125401100147070ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2012 Fredrik Johansson ******************************************************************************/ #include "hypgeom.h" static __inline__ void fmpz_poly_evaluate_si(fmpz_t y, const fmpz_poly_t poly, slong x) { fmpz_set_si(y, x); fmpz_poly_evaluate_fmpz(y, poly, y); } static void bsplit_recursive_fmpz(fmpz_t P, fmpz_t Q, fmpz_t B, fmpz_t T, const hypgeom_t hyp, slong a, slong b, int cont) { if (b - a == 1) { if (a == 0) { fmpz_one(P); fmpz_one(Q); } else { fmpz_poly_evaluate_si(P, hyp->P, a); fmpz_poly_evaluate_si(Q, hyp->Q, a); } fmpz_poly_evaluate_si(B, hyp->B, a); fmpz_poly_evaluate_si(T, hyp->A, a); fmpz_mul(T, T, P); } else { slong m; fmpz_t P2, Q2, B2, T2; m = (a + b) / 2; fmpz_init(P2); fmpz_init(Q2); fmpz_init(B2); fmpz_init(T2); bsplit_recursive_fmpz(P, Q, B, T, hyp, a, m, 1); bsplit_recursive_fmpz(P2, Q2, B2, T2, hyp, m, b, 1); if (fmpz_is_one(B) && fmpz_is_one(B2)) { fmpz_mul(T, T, Q2); fmpz_addmul(T, P, T2); } else { fmpz_mul(T, T, B2); fmpz_mul(T, T, Q2); fmpz_mul(T2, T2, B); fmpz_addmul(T, P, T2); } fmpz_mul(B, B, B2); fmpz_mul(Q, Q, Q2); if (cont) fmpz_mul(P, P, P2); fmpz_clear(P2); fmpz_clear(Q2); fmpz_clear(B2); fmpz_clear(T2); } } static void bsplit_recursive_fmprb(fmprb_t P, fmprb_t Q, fmprb_t B, fmprb_t T, const hypgeom_t hyp, slong a, slong b, int cont, slong prec) { if (b - a < 4) { fmpz_t PP, QQ, BB, TT; fmpz_init(PP); fmpz_init(QQ); fmpz_init(BB); fmpz_init(TT); bsplit_recursive_fmpz(PP, QQ, BB, TT, hyp, a, b, cont); fmprb_set_fmpz(P, PP); fmprb_set_fmpz(Q, QQ); fmprb_set_fmpz(B, BB); fmprb_set_fmpz(T, TT); fmpz_clear(PP); fmpz_clear(QQ); fmpz_clear(BB); fmpz_clear(TT); } else { slong m; fmprb_t P2, Q2, B2, T2; m = (a + b) / 2; fmprb_init(P2); fmprb_init(Q2); fmprb_init(B2); fmprb_init(T2); bsplit_recursive_fmprb(P, Q, B, T, hyp, a, m, 1, prec); bsplit_recursive_fmprb(P2, Q2, B2, T2, hyp, m, b, 1, prec); if (fmprb_is_one(B) && fmprb_is_one(B2)) { fmprb_mul(T, T, Q2, prec); fmprb_addmul(T, P, T2, prec); } else { fmprb_mul(T, T, B2, prec); fmprb_mul(T, T, Q2, prec); fmprb_mul(T2, T2, B, prec); fmprb_addmul(T, P, T2, prec); } fmprb_mul(B, B, B2, prec); fmprb_mul(Q, Q, Q2, prec); if (cont) fmprb_mul(P, P, P2, prec); fmprb_clear(P2); fmprb_clear(Q2); fmprb_clear(B2); fmprb_clear(T2); } } void fmprb_hypgeom_sum(fmprb_t P, fmprb_t Q, const hypgeom_t hyp, slong n, slong prec) { if (n < 1) { fmprb_zero(P); fmprb_one(Q); } else { fmprb_t B, T; fmprb_init(B); fmprb_init(T); bsplit_recursive_fmprb(P, Q, B, T, hyp, 0, n, 0, prec); if (!fmprb_is_one(B)) fmprb_mul(Q, Q, B, prec); fmprb_swap(P, T); fmprb_clear(B); fmprb_clear(T); } } void fmprb_hypgeom_infsum(fmprb_t P, fmprb_t Q, hypgeom_t hyp, slong target_prec, slong prec) { mag_t err, z; slong n; mag_init(err); mag_init(z); mag_set_fmpz(z, hyp->P->coeffs + hyp->P->length - 1); mag_div_fmpz(z, z, hyp->Q->coeffs + hyp->Q->length - 1); if (!hyp->have_precomputed) { hypgeom_precompute(hyp); hyp->have_precomputed = 1; } n = hypgeom_bound(err, hyp->r, hyp->boundC, hyp->boundD, hyp->boundK, hyp->MK, z, target_prec); fmprb_hypgeom_sum(P, Q, hyp, n, prec); if (fmpr_sgn(fmprb_midref(Q)) < 0) { fmprb_neg(P, P); fmprb_neg(Q, Q); } /* We have p/q = s + err i.e. (p + q*err)/q = s */ { fmpr_t u, v; fmpr_init(u); fmpr_init(v); mag_get_fmpr(v, err); fmpr_add(u, fmprb_midref(Q), fmprb_radref(Q), FMPRB_RAD_PREC, FMPR_RND_UP); fmpr_mul(u, u, v, FMPRB_RAD_PREC, FMPR_RND_UP); fmprb_add_error_fmpr(P, u); fmpr_clear(u); fmpr_clear(v); } mag_clear(z); mag_clear(err); } static void bsplit_recursive_arb(arb_t P, arb_t Q, arb_t B, arb_t T, const hypgeom_t hyp, slong a, slong b, int cont, slong prec) { if (b - a < 4) { fmpz_t PP, QQ, BB, TT; fmpz_init(PP); fmpz_init(QQ); fmpz_init(BB); fmpz_init(TT); bsplit_recursive_fmpz(PP, QQ, BB, TT, hyp, a, b, cont); arb_set_fmpz(P, PP); arb_set_fmpz(Q, QQ); arb_set_fmpz(B, BB); arb_set_fmpz(T, TT); fmpz_clear(PP); fmpz_clear(QQ); fmpz_clear(BB); fmpz_clear(TT); } else { slong m; arb_t P2, Q2, B2, T2; m = (a + b) / 2; arb_init(P2); arb_init(Q2); arb_init(B2); arb_init(T2); bsplit_recursive_arb(P, Q, B, T, hyp, a, m, 1, prec); bsplit_recursive_arb(P2, Q2, B2, T2, hyp, m, b, 1, prec); if (arb_is_one(B) && arb_is_one(B2)) { arb_mul(T, T, Q2, prec); arb_addmul(T, P, T2, prec); } else { arb_mul(T, T, B2, prec); arb_mul(T, T, Q2, prec); arb_mul(T2, T2, B, prec); arb_addmul(T, P, T2, prec); } arb_mul(B, B, B2, prec); arb_mul(Q, Q, Q2, prec); if (cont) arb_mul(P, P, P2, prec); arb_clear(P2); arb_clear(Q2); arb_clear(B2); arb_clear(T2); } } void arb_hypgeom_sum(arb_t P, arb_t Q, const hypgeom_t hyp, slong n, slong prec) { if (n < 1) { arb_zero(P); arb_one(Q); } else { arb_t B, T; arb_init(B); arb_init(T); bsplit_recursive_arb(P, Q, B, T, hyp, 0, n, 0, prec); if (!arb_is_one(B)) arb_mul(Q, Q, B, prec); arb_swap(P, T); arb_clear(B); arb_clear(T); } } void arb_hypgeom_infsum(arb_t P, arb_t Q, hypgeom_t hyp, slong target_prec, slong prec) { mag_t err, z; slong n; mag_init(err); mag_init(z); mag_set_fmpz(z, hyp->P->coeffs + hyp->P->length - 1); mag_div_fmpz(z, z, hyp->Q->coeffs + hyp->Q->length - 1); if (!hyp->have_precomputed) { hypgeom_precompute(hyp); hyp->have_precomputed = 1; } n = hypgeom_bound(err, hyp->r, hyp->boundC, hyp->boundD, hyp->boundK, hyp->MK, z, target_prec); arb_hypgeom_sum(P, Q, hyp, n, prec); if (arf_sgn(arb_midref(Q)) < 0) { arb_neg(P, P); arb_neg(Q, Q); } /* We have p/q = s + err i.e. (p + q*err)/q = s */ { mag_t u; mag_init(u); arb_get_mag(u, Q); mag_mul(u, u, err); mag_add(arb_radref(P), arb_radref(P), u); mag_clear(u); } mag_clear(z); mag_clear(err); } arb-2.8.1/mag.h000066400000000000000000000343231264125401100132040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #ifndef MAG_H #define MAG_H #ifdef MAG_INLINES_C #define MAG_INLINE #else #define MAG_INLINE static __inline__ #endif #include #include "flint.h" #include "fmpz.h" #include "fmpz_extras.h" #ifdef __cplusplus extern "C" { #endif #define LIMB_ONE ((mp_limb_t) 1) #define LIMB_ONES (-(mp_limb_t) 1) #define LIMB_TOP (((mp_limb_t) 1) << (FLINT_BITS - 1)) #define MASK_LIMB(n, c) ((n) & (LIMB_ONES << (c))) #define MAG_MAX_LAGOM_EXP (COEFF_MAX / 4) #define MAG_MIN_LAGOM_EXP (-MAG_MAX_LAGOM_EXP) #define ADD2_FAST_MAX (COEFF_MAX / 4) #define ADD2_FAST_MIN (-ADD2_FAST_MAX) /* TODO: rename these and move them to fmpz_extras */ static __inline__ void _fmpz_set_fast(fmpz_t f, const fmpz_t g) { if (!COEFF_IS_MPZ(*f) && !COEFF_IS_MPZ(*g)) *f = *g; else fmpz_set(f, g); } static __inline__ void _fmpz_add_fast(fmpz_t z, const fmpz_t x, slong c) { fmpz ze, xe; ze = *z; xe = *x; if (!COEFF_IS_MPZ(ze) && (xe > ADD2_FAST_MIN && xe < ADD2_FAST_MAX)) *z = xe + c; else fmpz_add_si(z, x, c); } static __inline__ void _fmpz_add2_fast(fmpz_t z, const fmpz_t x, const fmpz_t y, slong c) { fmpz ze, xe, ye; ze = *z; xe = *x; ye = *y; if (!COEFF_IS_MPZ(ze) && (xe > ADD2_FAST_MIN && xe < ADD2_FAST_MAX) && (ye > ADD2_FAST_MIN && ye < ADD2_FAST_MAX)) { *z = xe + ye + c; } else { fmpz_add(z, x, y); fmpz_add_si(z, z, c); } } static __inline__ void _fmpz_sub2_fast(fmpz_t z, const fmpz_t x, const fmpz_t y, slong c) { fmpz ze, xe, ye; ze = *z; xe = *x; ye = *y; if (!COEFF_IS_MPZ(ze) && (xe > ADD2_FAST_MIN && xe < ADD2_FAST_MAX) && (ye > ADD2_FAST_MIN && ye < ADD2_FAST_MAX)) { *z = xe - ye + c; } else { fmpz_sub(z, x, y); fmpz_add_si(z, z, c); } } #define MAG_EXP_POS_INF (COEFF_MIN+1) /* Finite and with lagom big exponents. */ #define MAG_IS_LAGOM(x) (MAG_EXP(x) >= MAG_MIN_LAGOM_EXP && \ MAG_EXP(x) <= MAG_MAX_LAGOM_EXP) #define MAG_EXPREF(x) (&(x)->exp) #define MAG_EXP(x) ((x)->exp) #define MAG_MAN(x) ((x)->man) #define MAG_BITS 30 #define MAG_ONE_HALF (UWORD(1) << (MAG_BITS - 1)) static __inline__ mp_limb_t __mag_fixmul32(mp_limb_t x, mp_limb_t y) { mp_limb_t u, v; umul_ppmm(u, v, x, y); return (u << (32 - MAG_BITS)) | (v >> MAG_BITS); } #if FLINT_BITS == 64 #define MAG_FIXMUL(x, y) (((x) * (y)) >> MAG_BITS) #else #define MAG_FIXMUL(x, y) __mag_fixmul32((x), (y)) #endif #define MAG_CHECK_BITS(rr) \ if (MAG_MAN(rr) != 0 && FLINT_BIT_COUNT(MAG_MAN(rr)) != MAG_BITS) \ { \ flint_printf("FAIL: wrong number of bits in mantissa!\n"); \ abort(); \ } /* Note: assumes mantissa either has the right number of bits, or one more bit (but in that case must not be all ones, as that would round up to one extra bit again, requiring a second correction). */ #define MAG_ADJUST_ONE_TOO_LARGE(x) \ do { \ mp_limb_t __t = MAG_MAN(x) >> MAG_BITS; \ MAG_MAN(x) = (MAG_MAN(x) >> __t) + __t; \ if (__t) \ fmpz_add_ui(MAG_EXPREF(x), MAG_EXPREF(x), __t); \ } while (0) #define MAG_FAST_ADJUST_ONE_TOO_LARGE(x) \ do { \ mp_limb_t __t = MAG_MAN(x) >> MAG_BITS; \ MAG_MAN(x) = (MAG_MAN(x) >> __t) + __t; \ MAG_EXP(x) += __t; \ } while (0) #define MAG_ADJUST_ONE_TOO_SMALL(x) \ do { \ mp_limb_t __t = !(MAG_MAN(x) >> (MAG_BITS - 1)); \ MAG_MAN(x) = (MAG_MAN(x) << __t); \ if (__t) \ fmpz_sub_ui(MAG_EXPREF(x), MAG_EXPREF(x), __t); \ } while (0) #define MAG_FAST_ADJUST_ONE_TOO_SMALL(x) \ do { \ mp_limb_t __t = !(MAG_MAN(x) >> (MAG_BITS - 1)); \ MAG_MAN(x) = (MAG_MAN(x) << __t); \ MAG_EXP(x) -= __t; \ } while (0) typedef struct { fmpz exp; mp_limb_t man; } mag_struct; typedef mag_struct mag_t[1]; typedef mag_struct * mag_ptr; typedef const mag_struct * mag_srcptr; MAG_INLINE void mag_init(mag_t x) { fmpz_init(MAG_EXPREF(x)); MAG_MAN(x) = 0; } MAG_INLINE void mag_init_set(mag_t x, const mag_t y) { fmpz_init_set(MAG_EXPREF(x), MAG_EXPREF(y)); MAG_MAN(x) = MAG_MAN(y); } MAG_INLINE void mag_clear(mag_t x) { fmpz_clear(MAG_EXPREF(x)); } MAG_INLINE void mag_swap(mag_t x, mag_t y) { mag_struct t = *x; *x = *y; *y = t; } MAG_INLINE void mag_set(mag_t x, const mag_t y) { _fmpz_set_fast(MAG_EXPREF(x), MAG_EXPREF(y)); x->man = y->man; } MAG_INLINE void mag_zero(mag_t x) { fmpz_zero(MAG_EXPREF(x)); MAG_MAN(x) = 0; } MAG_INLINE void mag_one(mag_t x) { fmpz_one(MAG_EXPREF(x)); MAG_MAN(x) = MAG_ONE_HALF; } MAG_INLINE int mag_is_special(const mag_t x) { return MAG_MAN(x) == 0; } MAG_INLINE int mag_is_zero(const mag_t x) { return (MAG_MAN(x) == 0) && (MAG_EXP(x) == 0); } MAG_INLINE void mag_inf(mag_t x) { fmpz_clear(MAG_EXPREF(x)); MAG_EXP(x) = MAG_EXP_POS_INF; MAG_MAN(x) = 0; } MAG_INLINE int mag_is_inf(const mag_t x) { return (MAG_MAN(x) == 0) && (MAG_EXP(x) != 0); } MAG_INLINE int mag_is_finite(const mag_t x) { return !mag_is_inf(x); } MAG_INLINE int mag_equal(const mag_t x, const mag_t y) { return (MAG_MAN(x) == MAG_MAN(y)) && fmpz_equal(MAG_EXPREF(x), MAG_EXPREF(y)); } /* general versions */ void mag_mul(mag_t z, const mag_t x, const mag_t y); void mag_mul_lower(mag_t z, const mag_t x, const mag_t y); void mag_addmul(mag_t z, const mag_t x, const mag_t y); void mag_add_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t e); void mag_add(mag_t z, const mag_t x, const mag_t y); void mag_add_lower(mag_t z, const mag_t x, const mag_t y); void mag_div(mag_t z, const mag_t x, const mag_t y); MAG_INLINE void mag_mul_2exp_si(mag_t z, const mag_t x, slong y) { if (mag_is_special(x)) { mag_set(z, x); } else { if (y >= ADD2_FAST_MIN && y <= ADD2_FAST_MAX) _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(x), y); else fmpz_add_si(MAG_EXPREF(z), MAG_EXPREF(x), y); MAG_MAN(z) = MAG_MAN(x); } } MAG_INLINE void mag_mul_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t y) { if (mag_is_special(x)) { mag_set(z, x); } else { _fmpz_add2_fast(MAG_EXPREF(z), MAG_EXPREF(x), y, 0); MAG_MAN(z) = MAG_MAN(x); } } void mag_sub_lower(mag_t z, const mag_t x, const mag_t y); /* Fast versions (no infs/nans, small exponents). Note that this applies to outputs too! */ MAG_INLINE void mag_fast_init_set(mag_t x, const mag_t y) { MAG_EXP(x) = MAG_EXP(y); MAG_MAN(x) = MAG_MAN(y); } MAG_INLINE void mag_fast_zero(mag_t x) { MAG_EXP(x) = 0; MAG_MAN(x) = 0; } MAG_INLINE int mag_fast_is_zero(const mag_t x) { return MAG_MAN(x) == 0; } MAG_INLINE void mag_fast_mul(mag_t z, const mag_t x, const mag_t y) { if (MAG_MAN(x) == 0 || MAG_MAN(y) == 0) { mag_fast_zero(z); } else { MAG_MAN(z) = MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) + LIMB_ONE; MAG_EXP(z) = MAG_EXP(x) + MAG_EXP(y); MAG_FAST_ADJUST_ONE_TOO_SMALL(z); } } MAG_INLINE void mag_fast_mul_2exp_si(mag_t z, const mag_t x, slong y) { if (MAG_MAN(x) == 0) { mag_fast_zero(z); } else { MAG_MAN(z) = MAG_MAN(x); MAG_EXP(z) = MAG_EXP(x) + y; } } MAG_INLINE void mag_fast_addmul(mag_t z, const mag_t x, const mag_t y) { if (MAG_MAN(z) == 0) { mag_fast_mul(z, x, y); } else if (MAG_MAN(x) == 0 || MAG_MAN(y) == 0) { return; } else { slong shift, e; /* x*y < 2^e */ e = MAG_EXP(x) + MAG_EXP(y); shift = MAG_EXP(z) - e; if (shift >= 0) { if (shift >= MAG_BITS) MAG_MAN(z)++; else MAG_MAN(z) = MAG_MAN(z) + (MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) >> shift) + 1; } else { shift = -shift; MAG_EXP(z) = e; if (shift >= MAG_BITS) MAG_MAN(z) = MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) + 2; else MAG_MAN(z) = MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) + (MAG_MAN(z) >> shift) + 2; MAG_FAST_ADJUST_ONE_TOO_SMALL(z); } MAG_FAST_ADJUST_ONE_TOO_LARGE(z); } } MAG_INLINE void mag_fast_add_2exp_si(mag_t z, const mag_t x, slong e) { /* Must be zero */ if (mag_is_special(x)) { MAG_MAN(z) = MAG_ONE_HALF; MAG_EXP(z) = e + 1; } else { slong shift; shift = MAG_EXP(x) - e; if (shift > 0) { MAG_EXP(z) = MAG_EXP(x); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_MAN(x) + LIMB_ONE; else MAG_MAN(z) = MAG_MAN(x) + (LIMB_ONE << (MAG_BITS - shift)); } else { shift = -shift; MAG_EXP(z) = e + 1; if (shift >= MAG_BITS) MAG_MAN(z) = MAG_ONE_HALF + LIMB_ONE; else MAG_MAN(z) = MAG_ONE_HALF + (MAG_MAN(x) >> (shift + 1)) + LIMB_ONE; } MAG_FAST_ADJUST_ONE_TOO_LARGE(z); } } void mag_set_d_2exp_fmpz(mag_t z, double c, const fmpz_t exp); void mag_set_fmpz_2exp_fmpz(mag_t z, const fmpz_t man, const fmpz_t exp); #include "fmpr.h" void mag_set_fmpr(mag_t x, const fmpr_t y); void mag_get_fmpr(fmpr_t x, const mag_t r); void mag_randtest_special(mag_t x, flint_rand_t state, slong expbits); void mag_randtest(mag_t x, flint_rand_t state, slong expbits); void mag_print(const mag_t x); void mag_printd(const mag_t x, slong d); void mag_get_fmpq(fmpq_t y, const mag_t x); int mag_cmp(const mag_t x, const mag_t y); int mag_cmp_2exp_si(const mag_t x, slong e); MAG_INLINE void mag_min(mag_t z, const mag_t x, const mag_t y) { if (mag_cmp(x, y) <= 0) mag_set(z, x); else mag_set(z, y); } MAG_INLINE void mag_max(mag_t z, const mag_t x, const mag_t y) { if (mag_cmp(x, y) >= 0) mag_set(z, x); else mag_set(z, y); } MAG_INLINE mag_ptr _mag_vec_init(slong n) { slong i; mag_ptr v = (mag_ptr) flint_malloc(sizeof(mag_struct) * n); for (i = 0; i < n; i++) mag_init(v + i); return v; } MAG_INLINE void _mag_vec_clear(mag_ptr v, slong n) { slong i; for (i = 0; i < n; i++) mag_clear(v + i); flint_free(v); } MAG_INLINE void mag_set_d(mag_t z, double x) { fmpz_t e; fmpz_init(e); mag_set_d_2exp_fmpz(z, x, e); fmpz_clear(e); } /* TODO: test/document */ double mag_get_d(const mag_t z); /* TODO: document */ double mag_d_log_upper_bound(double x); double mag_d_log_lower_bound(double x); void mag_log1p(mag_t z, const mag_t x); void mag_log_ui(mag_t t, ulong n); void mag_exp_maglim(mag_t y, const mag_t x, slong maglim); MAG_INLINE void mag_exp(mag_t y, const mag_t x) { mag_exp_maglim(y, x, 128); } void mag_expm1(mag_t y, const mag_t x); void mag_exp_tail(mag_t z, const mag_t x, ulong N); void mag_pow_ui(mag_t z, const mag_t x, ulong e); void mag_pow_ui_lower(mag_t z, const mag_t x, ulong e); void mag_pow_fmpz(mag_t z, const mag_t x, const fmpz_t e); void mag_fac_ui(mag_t z, ulong n); void mag_rfac_ui(mag_t z, ulong n); /* TODO: test */ void mag_bernoulli_div_fac_ui(mag_t z, ulong n); /* TODO: test */ void mag_set_fmpz_2exp_fmpz_lower(mag_t z, const fmpz_t man, const fmpz_t exp); void mag_sqrt(mag_t y, const mag_t x); void mag_rsqrt(mag_t y, const mag_t x); void mag_root(mag_t y, const mag_t x, ulong n); void mag_hypot(mag_t z, const mag_t x, const mag_t y); void mag_binpow_uiui(mag_t b, ulong m, ulong n); void mag_polylog_tail(mag_t u, const mag_t z, slong sigma, ulong d, ulong N); void mag_geom_series(mag_t res, const mag_t x, ulong n); void mag_set_ui(mag_t z, ulong x); void mag_set_ui_lower(mag_t z, ulong x); /* TODO: test functions below */ MAG_INLINE void mag_set_ui_2exp_si(mag_t z, ulong v, slong e) { mag_set_ui(z, v); mag_mul_2exp_si(z, z, e); } MAG_INLINE void mag_set_fmpz(mag_t z, const fmpz_t x) { fmpz_t exp; *exp = 0; mag_set_fmpz_2exp_fmpz(z, x, exp); } MAG_INLINE void mag_set_fmpz_lower(mag_t z, const fmpz_t x) { fmpz_t exp; *exp = 0; mag_set_fmpz_2exp_fmpz_lower(z, x, exp); } MAG_INLINE void mag_mul_ui(mag_t z, const mag_t x, ulong y) { mag_t t; mag_init(t); mag_set_ui(t, y); mag_mul(z, x, t); mag_clear(t); } MAG_INLINE void mag_mul_ui_lower(mag_t z, const mag_t x, ulong y) { mag_t t; mag_init(t); mag_set_ui_lower(t, y); mag_mul_lower(z, x, t); mag_clear(t); } MAG_INLINE void mag_mul_fmpz(mag_t z, const mag_t x, const fmpz_t y) { mag_t t; mag_init(t); mag_set_fmpz(t, y); mag_mul(z, x, t); mag_clear(t); } MAG_INLINE void mag_mul_fmpz_lower(mag_t z, const mag_t x, const fmpz_t y) { mag_t t; mag_init(t); mag_set_fmpz_lower(t, y); mag_mul_lower(z, x, t); mag_clear(t); } MAG_INLINE void mag_div_ui(mag_t z, const mag_t x, ulong y) { mag_t t; mag_init(t); mag_set_ui_lower(t, y); mag_div(z, x, t); mag_clear(t); } MAG_INLINE void mag_div_fmpz(mag_t z, const mag_t x, const fmpz_t y) { mag_t t; mag_init(t); mag_set_fmpz_lower(t, y); mag_div(z, x, t); mag_clear(t); } #ifdef __cplusplus } #endif #endif arb-2.8.1/mag/000077500000000000000000000000001264125401100130265ustar00rootroot00000000000000arb-2.8.1/mag/add.c000066400000000000000000000067451264125401100137360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_add(mag_t z, const mag_t x, const mag_t y) { if (mag_is_zero(x)) { mag_set(z, y); } else if (mag_is_zero(y)) { mag_set(z, x); } else if (mag_is_inf(x) || mag_is_inf(y)) { mag_inf(z); } else { slong shift; shift = _fmpz_sub_small(MAG_EXPREF(x), MAG_EXPREF(y)); if (shift == 0) { _fmpz_set_fast(MAG_EXPREF(z), MAG_EXPREF(x)); MAG_MAN(z) = MAG_MAN(x) + MAG_MAN(y); MAG_ADJUST_ONE_TOO_LARGE(z); /* may need two adjustments */ } else if (shift > 0) { _fmpz_set_fast(MAG_EXPREF(z), MAG_EXPREF(x)); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_MAN(x) + LIMB_ONE; else MAG_MAN(z) = MAG_MAN(x) + (MAG_MAN(y) >> shift) + LIMB_ONE; } else { shift = -shift; _fmpz_set_fast(MAG_EXPREF(z), MAG_EXPREF(y)); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_MAN(y) + LIMB_ONE; else MAG_MAN(z) = MAG_MAN(y) + (MAG_MAN(x) >> shift) + LIMB_ONE; } /* TODO: combine */ MAG_ADJUST_ONE_TOO_LARGE(z); } } void mag_add_lower(mag_t z, const mag_t x, const mag_t y) { if (mag_is_zero(x)) { mag_set(z, y); } else if (mag_is_zero(y)) { mag_set(z, x); } else if (mag_is_inf(x) || mag_is_inf(y)) { mag_inf(z); } else { slong shift; shift = _fmpz_sub_small(MAG_EXPREF(x), MAG_EXPREF(y)); if (shift == 0) { _fmpz_set_fast(MAG_EXPREF(z), MAG_EXPREF(x)); MAG_MAN(z) = MAG_MAN(x) + MAG_MAN(y); } else if (shift > 0) { _fmpz_set_fast(MAG_EXPREF(z), MAG_EXPREF(x)); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_MAN(x); else MAG_MAN(z) = MAG_MAN(x) + (MAG_MAN(y) >> shift); } else { shift = -shift; _fmpz_set_fast(MAG_EXPREF(z), MAG_EXPREF(y)); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_MAN(y); else MAG_MAN(z) = MAG_MAN(y) + (MAG_MAN(x) >> shift); } if (MAG_MAN(z) >> MAG_BITS) { MAG_MAN(z) >>= 1; _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(z), 1); } } } arb-2.8.1/mag/add_2exp_fmpz.c000066400000000000000000000041131264125401100157130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_add_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t e) { if (mag_is_special(x)) { if (mag_is_zero(x)) { MAG_MAN(z) = MAG_ONE_HALF; _fmpz_add_fast(MAG_EXPREF(z), e, 1); } else { mag_inf(z); } } else { slong shift; shift = _fmpz_sub_small(MAG_EXPREF(x), e); if (shift > 0) { _fmpz_set_fast(MAG_EXPREF(z), MAG_EXPREF(x)); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_MAN(x) + LIMB_ONE; else MAG_MAN(z) = MAG_MAN(x) + (LIMB_ONE << (MAG_BITS - shift)); } else { shift = -shift; _fmpz_add_fast(MAG_EXPREF(z), e, 1); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_ONE_HALF + LIMB_ONE; else MAG_MAN(z) = MAG_ONE_HALF + (MAG_MAN(x) >> (shift + 1)) + LIMB_ONE; } MAG_ADJUST_ONE_TOO_LARGE(z); } } arb-2.8.1/mag/addmul.c000066400000000000000000000044571264125401100144520ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_addmul(mag_t z, const mag_t x, const mag_t y) { if (mag_is_zero(z)) { mag_mul(z, x, y); } else if (mag_is_inf(z) || mag_is_inf(x) || mag_is_inf(y)) { mag_inf(z); } else if (mag_is_zero(x) || mag_is_zero(y)) { return; } else { slong shift; fmpz_t e; fmpz_init(e); /* x*y < 2^e */ _fmpz_add2_fast(e, MAG_EXPREF(x), MAG_EXPREF(y), 0); shift = _fmpz_sub_small(MAG_EXPREF(z), e); if (shift >= 0) { if (shift >= MAG_BITS) MAG_MAN(z)++; else MAG_MAN(z) = MAG_MAN(z) + (MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) >> shift) + LIMB_ONE; } else { shift = -shift; fmpz_swap(MAG_EXPREF(z), e); if (shift >= MAG_BITS) MAG_MAN(z) = MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) + (2 * LIMB_ONE); else MAG_MAN(z) = MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) + (MAG_MAN(z) >> shift) + (2 * LIMB_ONE); MAG_ADJUST_ONE_TOO_SMALL(z); } MAG_ADJUST_ONE_TOO_LARGE(z); fmpz_clear(e); } } arb-2.8.1/mag/bernoulli_div_fac_ui.c000066400000000000000000000044731264125401100173450ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" const int mag_bernoulli_div_fac_ui_tab[32] = { 1, 536870912, -3, 715827883, -9, 763549742, -14, 581752185, -20, 930803495, -25, 752164440, -30, 609225645, -36, 987456906, -41, 800365631, -46, 648744507, -52, 1051701970, -57, 852476898, -62, 690991623, -67, 560096688, -73, 907994540, -78, 735992650, }; /* computes upper bound for B_n / n! */ void mag_bernoulli_div_fac_ui(mag_t z, ulong n) { if (n % 2 == 1) { if (n == 1) { mag_one(z); mag_mul_2exp_si(z, z, -1); } else { mag_zero(z); } } else if (n < 32) { _fmpz_demote(MAG_EXPREF(z)); MAG_EXP(z) = mag_bernoulli_div_fac_ui_tab[n]; MAG_MAN(z) = mag_bernoulli_div_fac_ui_tab[n + 1]; } else { /* upper bound for 1/(2pi) */ mag_set_ui_2exp_si(z, 683565276, -32); /* 2 (1/(2pi))^n */ mag_pow_ui(z, z, n); mag_mul_2exp_si(z, z, 1); /* we should multiply by an upper bound for zeta(n), but the error in the upper bound for 1/(2pi) used above is already larger than this factor when n >= 32, so there is no need */ } } arb-2.8.1/mag/binpow_uiui.c000066400000000000000000000033131264125401100155230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" /* bound (1 + 1/m)^n, m > 0, n >= 0 */ void mag_binpow_uiui(mag_t b, ulong m, ulong n) { mag_t t; if (m == 0) { mag_inf(b); return; } mag_init(t); /* bound by exp(n/m) <= 1 + (n/m) + (n/m)^2 */ if (m > n) { mag_set_ui(t, n); /* x = n/m */ mag_div_ui(t, t, m); mag_mul(b, t, t); /* x^2 */ mag_add(b, b, t); /* x */ mag_one(t); mag_add(b, b, t); /* 1 */ } else { mag_one(b); mag_div_ui(b, b, m); mag_one(t); mag_add(t, t, b); mag_pow_ui(b, t, n); } mag_clear(t); } arb-2.8.1/mag/cmp.c000066400000000000000000000030401264125401100137460ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int mag_cmp(const mag_t x, const mag_t y) { int c; if (mag_equal(x, y)) return 0; if (mag_is_special(x) || mag_is_special(y)) { if (mag_is_zero(x)) return -1; if (mag_is_zero(y)) return 1; if (mag_is_inf(x)) return 1; if (mag_is_inf(y)) return -1; } c = fmpz_cmp(MAG_EXPREF(x), MAG_EXPREF(y)); if (c == 0) return (MAG_MAN(x) < MAG_MAN(y)) ? -1 : 1; return (c < 0) ? -1 : 1; } arb-2.8.1/mag/cmp_2exp_si.c000066400000000000000000000034551264125401100154110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int mag_cmp_2exp_si(const mag_t x, slong e) { int ispow2; if (mag_is_special(x)) { if (mag_is_zero(x)) return -1; return 1; } ispow2 = (MAG_MAN(x) == MAG_ONE_HALF); /* Fast path. */ if (!COEFF_IS_MPZ(MAG_EXP(x))) { if (ispow2 && (MAG_EXP(x) - 1 == e)) return 0; else return (MAG_EXP(x) <= e) ? -1 : 1; } if (ispow2) { fmpz_t t; fmpz_init(t); fmpz_one(t); fmpz_add_si(t, t, e); if (fmpz_equal(MAG_EXPREF(x), t)) { fmpz_clear(t); return 0; } fmpz_clear(t); } return (fmpz_cmp_si(MAG_EXPREF(x), e) <= 0) ? -1 : 1; } arb-2.8.1/mag/d_log.c000066400000000000000000000166131264125401100142650ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "double_extras.h" /* This is a bad implementation the logarithm function, Any decent libm should compute log() with < 1 ulp error, but we have no way to know that this is the case (the IEEE 754 and C language standards make virtually no guarantees whatsoever about transcendental functions). So here is a bad implementation which almost certainly has much worse accuracy than the libm log(), but which is simple and for which we can give an explicit error bound. The only precomputed constants are rational numbers and logarithms of rational numbers, which are easy to validate. First write x = 2^n * t with sqrt(2)/2 < t < sqrt(2) (a few ulps outside this range is fine). Then write t = m/32 + u with |u| <= 1/64. We have 23 <= m <= 45. Let v = 32*u/m (note that |v| <= 1/46). Then we have log(x) = log(2^n*t) = n*log(2) + log(t) = n*log(2) + log(m/32 + u) = n*log(2) + log(m/32 + m/32 * 32*u/m) = n*log(2) + log(m/32) + log(1 + 32*u/m) = n*log(2) + (log(m/32) + log(1 + v)) We compute log(x) as t1 + (t2 + t3) where t1 ~= n*log(2) involves two roundings, t2 involves one rounding, and t3 ~= v - [v^2/2 + ...] involves two roundings for the multiplication by 1/m, one rounding for subtraction, plus a much smaller error contribution due to the error in the approximation of the terms in brackets. Now consider the outer sum t1 + (t2 + t3). When n != 0, t1 will always be about twice as large as (t2+t3). When n = 0, t2 will always be exactly zero or about twice as large as t3. So there can be no significant cancellation, and most of the final error comes from the largest nonzero term. By inspection, the final error is clearly bounded by 10 ulp (a 3 ulp or maybe even 2 ulp bound could probably be proved with a careful calculation). Multiplying the output by 1 +/- 1e-14, we get guaranteed upper/lower bounds for the logarithm. This factor is chosen conservatively so that we get correct bounds even on x87 or if the CPU rounding mode has been changed. */ #define LOG_TAB_STEP 32 const double d_log_tab[] = { -0.6931471805599453094172, /* log(16/32) */ -0.6325225587435104668366, /* log(17/32) */ -0.5753641449035618548784, /* log(18/32) */ -0.5212969236332860870771, /* log(19/32) */ -0.4700036292457355536509, /* log(20/32) */ -0.4212134650763035505856, /* log(21/32) */ -0.374693449441410693607, /* log(22/32) */ -0.3302416868705768562794, /* log(23/32) */ -0.2876820724517809274392, /* log(24/32) */ -0.2468600779315257978846, /* log(25/32) */ -0.2076393647782445016154, /* log(26/32) */ -0.1698990367953974729004, /* log(27/32) */ -0.1335313926245226231463, /* log(28/32) */ -0.09844007281325251990289, /* log(29/32) */ -0.06453852113757117167292, /* log(30/32) */ -0.031748698314580301157, /* log(31/32) */ 0.0, /* log(32/32) */ 0.03077165866675368837103, /* log(33/32) */ 0.06062462181643484258061, /* log(34/32) */ 0.08961215868968713261995, /* log(35/32) */ 0.1177830356563834545388, /* log(36/32) */ 0.1451820098444978972819, /* log(37/32) */ 0.1718502569266592223401, /* log(38/32) */ 0.1978257433299198803626, /* log(39/32) */ 0.2231435513142097557663, /* log(40/32) */ 0.2478361639045812567806, /* log(41/32) */ 0.2719337154836417588317, /* log(42/32) */ 0.2954642128938358763867, /* log(43/32) */ 0.3184537311185346158102, /* log(44/32) */ 0.3409265869705932103051, /* log(45/32) */ 0.3629054936893684531378, /* log(46/32) */ 0.3844116989103320397348, /* log(47/32) */ }; const double d_log_inverses[] = { 0.0, 1.0, /* 1/1 */ 0.5, /* 1/2 */ 0.3333333333333333333333, /* 1/3 */ 0.25, /* 1/4 */ 0.2, /* 1/5 */ 0.1666666666666666666667, /* 1/6 */ 0.1428571428571428571429, /* 1/7 */ 0.125, /* 1/8 */ 0.1111111111111111111111, /* 1/9 */ 0.1, /* 1/10 */ 0.09090909090909090909091, /* 1/11 */ 0.08333333333333333333333, /* 1/12 */ 0.07692307692307692307692, /* 1/13 */ 0.07142857142857142857143, /* 1/14 */ 0.06666666666666666666667, /* 1/15 */ 0.0625, /* 1/16 */ 0.05882352941176470588235, /* 1/17 */ 0.05555555555555555555556, /* 1/18 */ 0.05263157894736842105263, /* 1/19 */ 0.05, /* 1/20 */ 0.04761904761904761904762, /* 1/21 */ 0.04545454545454545454545, /* 1/22 */ 0.0434782608695652173913, /* 1/23 */ 0.04166666666666666666667, /* 1/24 */ 0.04, /* 1/25 */ 0.03846153846153846153846, /* 1/26 */ 0.03703703703703703703704, /* 1/27 */ 0.03571428571428571428571, /* 1/28 */ 0.03448275862068965517241, /* 1/29 */ 0.03333333333333333333333, /* 1/30 */ 0.03225806451612903225806, /* 1/31 */ 0.03125, /* 1/32 */ 0.0303030303030303030303, /* 1/33 */ 0.02941176470588235294118, /* 1/34 */ 0.02857142857142857142857, /* 1/35 */ 0.02777777777777777777778, /* 1/36 */ 0.02702702702702702702703, /* 1/37 */ 0.02631578947368421052632, /* 1/38 */ 0.02564102564102564102564, /* 1/39 */ 0.025, /* 1/40 */ 0.02439024390243902439024, /* 1/41 */ 0.02380952380952380952381, /* 1/42 */ 0.02325581395348837209302, /* 1/43 */ 0.02272727272727272727273, /* 1/44 */ 0.02222222222222222222222, /* 1/45 */ 0.02173913043478260869565, /* 1/46 */ 0.02127659574468085106383, /* 1/47 */ }; double mag_d_bad_log(double x) { double t, u, v, t1, t2, t3; int m, n; if (x <= 0.0 || (x-x) != (x-x)) { if (x == 0.0) return -D_INF; else if (x > 0.0) return D_INF; else return D_NAN; } if (x < 1 + 1./LOG_TAB_STEP && x > 1 - 1./LOG_TAB_STEP) { return -d_polyval(d_log_inverses, 12, 1.-x); } t = frexp(x, &n); if (t < 0.7071067811865475244008) { t *= 2.0; n -= 1; } m = floor(t * LOG_TAB_STEP + 0.5); u = t * LOG_TAB_STEP - m; /* v = -u / m; */ v = -u * d_log_inverses[m]; t1 = n * (-d_log_tab[0]); t2 = d_log_tab[m - LOG_TAB_STEP / 2]; t3 = -d_polyval(d_log_inverses, 11, v); return t1 + (t2 + t3); } double mag_d_log_upper_bound(double x) { if (x >= 1.0) return mag_d_bad_log(x) * (1 + 1e-14); else return mag_d_bad_log(x) * (1 - 1e-14); } double mag_d_log_lower_bound(double x) { if (x >= 1.0) return mag_d_bad_log(x) * (1 - 1e-14); else return mag_d_bad_log(x) * (1 + 1e-14); } arb-2.8.1/mag/div.c000066400000000000000000000036511264125401100137610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_div(mag_t z, const mag_t x, const mag_t y) { if (mag_is_special(x) || mag_is_special(y)) { if (mag_is_zero(y) || mag_is_inf(x)) mag_inf(z); else mag_zero(z); } else { mp_limb_t q; slong fix; #if FLINT_BITS == 64 q = (MAG_MAN(x) << MAG_BITS) / MAG_MAN(y) + 1; #else mp_limb_t hi, lo, r; lo = MAG_MAN(x) << MAG_BITS; hi = MAG_MAN(x) >> (FLINT_BITS - MAG_BITS); udiv_qrnnd(q, r, hi, lo, MAG_MAN(y)); q += 1; #endif fix = q >> MAG_BITS; q = (q >> fix) + fix; /* could overflow to next power of two */ if (q >> MAG_BITS) { q >>= 1; fix += 1; } MAG_MAN(z) = q; _fmpz_sub2_fast(MAG_EXPREF(z), MAG_EXPREF(x), MAG_EXPREF(y), fix); } } arb-2.8.1/mag/exp.c000066400000000000000000000074121264125401100137720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "double_extras.h" static const double inverse_factorials[] = { 1.0, 1.0, 0.5, 0.16666666666666666667, 0.041666666666666666667, 0.0083333333333333333333, 0.0013888888888888888889, 0.0001984126984126984127, 0.000024801587301587301587, 2.7557319223985890653e-6, 2.7557319223985890653e-7, 2.5052108385441718775e-8, 2.0876756987868098979e-9, 1.6059043836821614599e-10, 1.1470745597729724714e-11, 7.6471637318198164759e-13 }; static __inline__ double _mag_d_exp_upper_reduced(double u) { if (u < -0.375 || u > 0.375) abort(); return d_polyval(inverse_factorials, 11, u) + 1e-12; } void mag_exp_maglim(mag_t y, const mag_t x, slong maglim) { if (mag_is_special(x)) { if (mag_is_zero(x)) mag_one(y); else mag_inf(y); } else if (COEFF_IS_MPZ(MAG_EXP(x))) { if (fmpz_sgn(MAG_EXPREF(x)) > 0) { mag_inf(y); } else { MAG_MAN(y) = MAG_ONE_HALF + 1; fmpz_one(MAG_EXPREF(y)); } } else { slong e = MAG_EXP(x); if (e <= -MAG_BITS) /* assumes MAG_BITS == 30 */ { MAG_MAN(y) = MAG_ONE_HALF + 1; fmpz_one(MAG_EXPREF(y)); } else if (e <= -(MAG_BITS / 2)) /* assumes MAG_BITS == 30 */ { MAG_MAN(y) = MAG_ONE_HALF + (MAG_MAN(x) >> (1-e)) + 2; fmpz_one(MAG_EXPREF(y)); } else if (e < 24) { double t, u; ulong n; t = ldexp(MAG_MAN(x), e - MAG_BITS); /* does not need to be exact */ n = (ulong)(t * 1.4426950408889634074 + 0.5); /* here u must be rounded up */ u = t - n * (0.69314718055994530942 * (1.0 - 1e-13)) + 1e-13; u = _mag_d_exp_upper_reduced(u); fmpz_set_ui(MAG_EXPREF(y), n); mag_set_d_2exp_fmpz(y, u, MAG_EXPREF(y)); } else if (e > maglim) { mag_inf(y); } else { /* we really want a multiprecision algorithm here for huge n, but for most purposes, it's fine to just get a few leading digits of the *exponent* accurately */ fmpz_t t; fmpz_init(t); fmpz_set_ui(t, MAG_MAN(x)); if (e >= MAG_BITS) fmpz_mul_2exp(t, t, e - MAG_BITS); else fmpz_cdiv_q_2exp(t, t, MAG_BITS - e); /* upper bound for e */ MAG_MAN(y) = 729683223; fmpz_set_ui(MAG_EXPREF(y), 2); mag_pow_fmpz(y, y, t); fmpz_clear(t); } } } arb-2.8.1/mag/exp_tail.c000066400000000000000000000033311264125401100147770ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_exp_tail(mag_t z, const mag_t x, ulong N) { if (N == 0 || mag_is_inf(x)) { mag_exp(z, x); } else if (mag_is_zero(x)) { mag_zero(z); } else { mag_t t; mag_init(t); mag_set_ui_2exp_si(t, N, -1); /* bound by geometric series when N >= 2*x <=> N/2 >= x */ if (mag_cmp(t, x) >= 0) { /* 2 c^N / N! */ mag_pow_ui(t, x, N); mag_rfac_ui(z, N); mag_mul(z, z, t); mag_mul_2exp_si(z, z, 1); } else { mag_exp(z, x); } mag_clear(t); } } arb-2.8.1/mag/expm1.c000066400000000000000000000046511264125401100142320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_expm1(mag_t y, const mag_t x) { if (mag_is_special(x)) { if (mag_is_zero(x)) mag_zero(y); else mag_inf(y); } else if (COEFF_IS_MPZ(MAG_EXP(x))) { if (fmpz_sgn(MAG_EXPREF(x)) > 0) { mag_inf(y); } else { fmpz_set(MAG_EXPREF(y), MAG_EXPREF(x)); MAG_MAN(y) = MAG_MAN(x) + 1; MAG_ADJUST_ONE_TOO_LARGE(y); } } else { slong e = MAG_EXP(x); if (e <= -16) { fmpz_set(MAG_EXPREF(y), MAG_EXPREF(x)); if (e < -MAG_BITS) MAG_MAN(y) = MAG_MAN(x) + 1; else MAG_MAN(y) = MAG_MAN(x) + (MAG_ONE_HALF >> 15); MAG_ADJUST_ONE_TOO_LARGE(y); } else { mag_exp(y, x); /* subtract 1 */ if (e < 6) { slong e2 = MAG_EXP(y); unsigned int c; if (e2 < MAG_BITS) { /* this is correct since exp(x) >= 1 */ MAG_MAN(y) -= (MAG_ONE_HALF >> (e2 - 1)); c = MAG_BITS - FLINT_BIT_COUNT(MAG_MAN(y)); MAG_MAN(y) <<= c; MAG_EXP(y) -= c; } } } } } arb-2.8.1/mag/fac_ui.c000066400000000000000000000313231264125401100144220ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #define MAG_FAC_TABLE_NUM 256 const int mag_fac_tab[MAG_FAC_TABLE_NUM * 2] = { 1, 536870912, 1, 536870912, 2, 536870912, 3, 805306368, 5, 805306368, 7, 1006632960, 10, 754974720, 13, 660602880, 16, 660602880, 19, 743178240, 22, 928972800, 26, 638668800, 29, 958003200, 33, 778377600, 37, 681080400, 41, 638512875, 45, 638512875, 49, 678419930, 53, 763222421, 57, 906326625, 62, 566454141, 66, 743471060, 70, 1022272707, 75, 734758508, 80, 551068881, 84, 861045127, 89, 699599166, 94, 590286796, 98, 1033001893, 103, 936157966, 108, 877648093, 113, 850221590, 118, 850221590, 123, 876791015, 128, 931590453, 133, 1018927058, 139, 573146470, 144, 662700606, 149, 786956970, 154, 959103807, 160, 599439879, 165, 768032345, 170, 1008042453, 176, 677278523, 181, 931257969, 187, 654790760, 192, 941261717, 198, 691239074, 203, 1036858610, 209, 793844874, 215, 620191308, 220, 988429896, 226, 803099291, 232, 665066600, 238, 561149944, 243, 964476466, 249, 843916908, 255, 751613496, 261, 681149731, 267, 627934908, 273, 588688976, 279, 561094181, 285, 543559988, 290, 1070133725, 296, 1070133725, 303, 543427282, 309, 560409385, 315, 586678575, 321, 623345986, 327, 672044891, 333, 735049099, 339, 815445095, 345, 917375731, 351, 1046381693, 358, 604939417, 364, 708913379, 370, 841834637, 376, 1012832298, 383, 617194682, 389, 761849685, 395, 952312106, 402, 602635005, 408, 772126100, 414, 1001351036, 421, 657136617, 427, 872759570, 434, 586385336, 440, 797117566, 447, 548018327, 453, 762087986, 459, 1071686230, 466, 761901929, 473, 547617012, 479, 795755970, 486, 584383290, 492, 867443946, 499, 650582960, 505, 986039798, 512, 754936721, 519, 583896370, 525, 912338078, 532, 719891765, 539, 573663750, 545, 923240098, 552, 750132579, 559, 615343132, 565, 1019162061, 572, 851955786, 579, 718837694, 586, 612135224, 592, 1052107416, 599, 912374400, 606, 798327600, 613, 704773585, 620, 627688974, 627, 563939312, 633, 1022140003, 640, 934299847, 647, 861307671, 654, 800746976, 661, 750700290, 668, 709646368, 675, 676381694, 682, 649960534, 689, 629649268, 696, 614891863, 703, 605284178, 710, 600555395, 717, 600555395, 724, 605247234, 731, 614704222, 738, 629111352, 745, 648771082, 752, 674113702, 759, 705712782, 766, 744306450, 773, 790825603, 780, 846430528, 787, 912557913, 794, 990980859, 802, 541942657, 809, 596983708, 816, 662278801, 823, 739889598, 830, 832375798, 837, 942925709, 845, 537762319, 852, 617586413, 859, 714084290, 866, 831238743, 873, 974107902, 881, 574571458, 888, 682303606, 895, 815566029, 902, 981227879, 910, 594102818, 917, 724062809, 924, 888108289, 932, 548129335, 939, 680879408, 946, 851099260, 953, 1070523287, 961, 677440518, 968, 862678159, 976, 552653196, 983, 712404510, 990, 923899599, 998, 602700129, 1005, 791043920, 1012, 1044425175, 1020, 693563593, 1027, 926557612, 1035, 622530896, 1042, 841389414, 1050, 571881867, 1057, 781869740, 1065, 537535447, 1072, 743310735, 1079, 1033666490, 1087, 722758991, 1094, 1016379831, 1102, 718612303, 1109, 1021776868, 1117, 730410808, 1124, 1049965536, 1132, 758764157, 1140, 551289583, 1147, 805399625, 1155, 591465350, 1162, 873335555, 1170, 648178733, 1177, 967204202, 1185, 725403152, 1193, 546885970, 1200, 828874048, 1208, 631368904, 1215, 966783634, 1223, 743970218, 1231, 575414466, 1238, 894589677, 1246, 698898186, 1254, 548744279, 1261, 865987064, 1269, 686700680, 1277, 547214604, 1284, 876398390, 1292, 705226829, 1300, 570242007, 1307, 926643260, 1315, 756517349, 1323, 620580638, 1330, 1022988396, 1338, 847162265, 1346, 704865479, 1354, 589223486, 1361, 989711324, 1369, 835068930, 1377, 707851397, 1385, 602779706, 1392, 1031318402, 1400, 886289252, 1408, 765116894, 1416, 663499806, 1424, 577970534, 1431, 1011448435, 1439, 888968351, 1447, 784792372, 1455, 695890111, 1463, 619777131, 1471, 554410011, 1478, 996205489, 1486, 898919797, 1494, 814646066, 1502, 741455208, 1510, 677736401, 1518, 622140837, 1526, 573536084, 1533, 1061937906, 1541, 987270397, 1549, 921709472, 1557, 864102630, 1565, 813471617, 1573, 768984888, 1581, 729934874, 1589, 695719177, 1597, 665824993, 1605, 639816204, 1613, 617322666, 1621, 598031333, 1629, 581678914, 1637, 568045814, 1645, 556951169, 1653, 548248807, 1661, 541824017, 1669, 537591016, 1676, 1070982102, }; const int mag_rfac_tab[MAG_FAC_TABLE_NUM * 2] = { 1, 536870912, 1, 536870912, 0, 536870912, -2, 715827883, -4, 715827883, -6, 572662307, -9, 763549742, -12, 872628277, -15, 872628277, -18, 775669579, -21, 620535663, -25, 902597328, -28, 601731552, -32, 740592680, -36, 846391634, -40, 902817743, -44, 902817743, -48, 849710817, -52, 755298504, -56, 636040846, -61, 1017665353, -65, 775364078, -69, 563901148, -74, 784558119, -79, 1046077491, -83, 669489595, -88, 823987193, -93, 976577414, -97, 558044237, -102, 615772951, -107, 656824481, -112, 678012368, -117, 678012368, -122, 657466538, -127, 618792036, -132, 565752719, -138, 1005782611, -143, 869866042, -148, 732518772, -153, 601041044, -159, 961665670, -164, 750568328, -169, 571861583, -175, 851142821, -180, 619012961, -186, 880373989, -191, 612434079, -197, 833952789, -202, 555968526, -208, 726162972, -214, 929488605, -219, 583208536, -225, 717795122, -231, 866771468, -237, 1027284702, -242, 597692918, -248, 683077620, -254, 766964346, -260, 846305485, -266, 918026288, -272, 979228041, -278, 1027386797, -284, 1060528307, -289, 538681045, -295, 538681045, -302, 1060787288, -308, 1028642219, -314, 982583612, -320, 924784576, -326, 857771201, -332, 784247955, -338, 706927734, -344, 628380208, -350, 550908676, -357, 952923115, -363, 813161058, -369, 684767207, -375, 569157159, -382, 934001491, -388, 756659436, -394, 605327549, -401, 956566990, -407, 746588871, -413, 575682985, -420, 877231215, -426, 660503503, -433, 983074981, -439, 723181595, -446, 1051900502, -452, 756422833, -458, 537900681, -465, 756607552, -472, 1052671376, -478, 724419012, -485, 986442909, -491, 664551013, -498, 886068017, -504, 584622197, -511, 763588175, -518, 987265519, -524, 631849933, -531, 800760310, -538, 1004875684, -544, 624388774, -551, 768478492, -558, 936811875, -564, 565622264, -571, 676632242, -578, 801934508, -585, 941721257, -591, 547910550, -598, 631824778, -605, 722085461, -612, 817937513, -619, 918385980, -626, 1022203525, -632, 563974359, -639, 616997589, -646, 669285520, -653, 719903753, -660, 767897336, -667, 812321149, -674, 852271370, -681, 886916547, -688, 915526759, -695, 937499401, -702, 952380344, -709, 959879401, -716, 959879401, -723, 952438476, -730, 937785576, -737, 916309571, -744, 888542614, -751, 855138756, -758, 816848961, -765, 774493830, -772, 728935369, -779, 681049104, -786, 631697720, -793, 581707253, -801, 1063693262, -808, 965622252, -815, 870420058, -822, 779117255, -829, 692548671, -836, 611353310, -844, 1071961968, -851, 933409060, -858, 807272701, -865, 693496012, -872, 591783263, -880, 1003288181, -887, 844874258, -894, 706822909, -901, 587489171, -909, 970304695, -916, 796147442, -923, 649088360, -931, 1051687470, -938, 846641485, -945, 677313188, -952, 538485019, -960, 850939290, -967, 668222264, -975, 1043078656, -982, 809176170, -989, 623943071, -997, 956463629, -1004, 728734194, -1011, 551940691, -1019, 831157747, -1026, 622153167, -1034, 925995411, -1041, 685129553, -1049, 1008006698, -1056, 737284900, -1064, 1072414399, -1071, 775531317, -1078, 557685442, -1086, 797583648, -1093, 567170594, -1101, 802186034, -1108, 564174793, -1116, 789228126, -1123, 549028262, -1131, 759736405, -1139, 1045658708, -1146, 715744998, -1154, 974631486, -1161, 660067885, -1169, 889354624, -1176, 596007287, -1184, 794676383, -1192, 1054078518, -1199, 695474487, -1207, 913033172, -1214, 596266561, -1222, 774843856, -1230, 1001818319, -1237, 644385653, -1245, 824813635, -1253, 1050508908, -1260, 665669011, -1268, 839464369, -1276, 1053445483, -1283, 657761082, -1291, 817411830, -1299, 1010905451, -1306, 622095663, -1314, 761992773, -1322, 928905476, -1329, 563506640, -1337, 680460848, -1345, 817830878, -1353, 978339742, -1360, 582453428, -1368, 690315174, -1376, 814381034, -1384, 956337361, -1391, 558955170, -1399, 650420562, -1407, 753428343, -1415, 868818269, -1423, 997387789, -1430, 569935879, -1438, 648460378, -1446, 734539189, -1454, 828378998, -1462, 930109752, -1470, 1039773347, -1477, 578656472, -1485, 641281631, -1493, 707621110, -1501, 777472121, -1509, 850567790, -1517, 926575975, -1525, 1005099363, -1532, 542838475, -1540, 583893485, -1548, 625425658, -1556, 667120702, -1564, 708642737, -1572, 749638598, -1580, 789742721, -1588, 828582526, -1596, 865784191, -1604, 900978670, -1612, 933807852, -1620, 963930686, -1628, 991029139, -1636, 1014813839, -1644, 1035029254, -1652, 1051458290, -1660, 1063926174, -1668, 1072303546, -1675, 538254329, }; void mag_fac_ui(mag_t z, ulong n) { if (n < MAG_FAC_TABLE_NUM) { _fmpz_demote(MAG_EXPREF(z)); MAG_EXP(z) = mag_fac_tab[n * 2]; MAG_MAN(z) = mag_fac_tab[n * 2 + 1]; } else { double x = n; x = ceil((((x+0.5)*mag_d_log_upper_bound(x) - x) * 1.4426950408889634074 + 2) * 1.0000001); /* x + 1 could round down for huge x, but this doesn't matter as long as the result was perturbed up above */ fmpz_set_d(MAG_EXPREF(z), x + 1); MAG_MAN(z) = MAG_ONE_HALF; } } void mag_rfac_ui(mag_t z, ulong n) { if (n < MAG_FAC_TABLE_NUM) { _fmpz_demote(MAG_EXPREF(z)); MAG_EXP(z) = mag_rfac_tab[n * 2]; MAG_MAN(z) = mag_rfac_tab[n * 2 + 1]; } else { double x = n; x = ceil((((x+0.5)*mag_d_log_lower_bound(x) - x) * 1.4426950408889634074) * -0.9999999); /* x + 1 could round down for huge x, but this doesn't matter as long as the value was perturbed up above */ fmpz_set_d(MAG_EXPREF(z), x + 1); MAG_MAN(z) = MAG_ONE_HALF; } } arb-2.8.1/mag/geom_series.c000066400000000000000000000031761264125401100155020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_geom_series(mag_t res, const mag_t x, ulong n) { if (mag_is_zero(x)) { if (n == 0) mag_one(res); else mag_zero(res); } else if (mag_is_inf(x)) { mag_inf(res); } else { mag_t t; mag_init(t); mag_one(t); mag_sub_lower(t, t, x); if (mag_is_zero(t)) { mag_inf(res); } else { mag_pow_ui(res, x, n); mag_div(res, res, t); } mag_clear(t); } } arb-2.8.1/mag/get_d.c000066400000000000000000000030161264125401100142540ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "double_extras.h" #include "mag.h" double mag_get_d(const mag_t z) { if (mag_is_zero(z)) { return 0.0; } else if (mag_is_inf(z)) { return D_INF; } else if (MAG_EXP(z) < -1000 || MAG_EXP(z) > 1000) { if (fmpz_sgn(MAG_EXPREF(z)) < 0) return ldexp(1.0, -1000); else return D_INF; } else { return ldexp(MAG_MAN(z), MAG_EXP(z) - MAG_BITS); } } arb-2.8.1/mag/get_fmpq.c000066400000000000000000000023461264125401100150010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_get_fmpq(fmpq_t y, const mag_t x) { fmpr_t t; fmpr_init(t); mag_get_fmpr(t, x); fmpr_get_fmpq(y, t); fmpr_clear(t); } arb-2.8.1/mag/get_fmpr.c000066400000000000000000000026241264125401100150010ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_get_fmpr(fmpr_t x, const mag_t r) { if (mag_is_zero(r)) { fmpr_zero(x); } else if (mag_is_inf(r)) { fmpr_pos_inf(x); } else { fmpr_set_ui_2exp_si(x, MAG_MAN(r), -MAG_BITS); _fmpz_add2_fast(fmpr_expref(x), fmpr_expref(x), MAG_EXPREF(r), 0); } } arb-2.8.1/mag/hypot.c000066400000000000000000000026501264125401100143400ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_hypot(mag_t z, const mag_t x, const mag_t y) { if (mag_is_zero(y)) { mag_set(z, x); } else if (mag_is_zero(x)) { mag_set(z, y); } else { mag_t t; mag_init(t); mag_mul(t, x, x); mag_addmul(t, y, y); mag_sqrt(z, t); mag_clear(t); } } arb-2.8.1/mag/inlines.c000066400000000000000000000021501264125401100146310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #define MAG_INLINES_C #include "mag.h" arb-2.8.1/mag/log1p.c000066400000000000000000000053011264125401100142130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "double_extras.h" void mag_log1p(mag_t z, const mag_t x) { if (mag_is_special(x)) { if (mag_is_zero(x)) mag_zero(z); else mag_inf(z); } else { fmpz exp = MAG_EXP(x); if (!COEFF_IS_MPZ(exp)) { /* Quick bound by x */ if (exp < -10) { mag_set(z, x); return; } else if (exp < 1000) { double t; t = ldexp(MAG_MAN(x), exp - MAG_BITS); t = (1.0 + t) * (1 + 1e-14); t = mag_d_log_upper_bound(t); mag_set_d(z, t); return; } } else if (fmpz_sgn(MAG_EXPREF(x)) < 0) { /* Quick bound by x */ mag_set(z, x); return; } /* Now we must have x >= 2^1000 */ /* Use log(2^(exp-1) * (2*v)) = exp*log(2) + log(2*v) */ { double t; fmpz_t b; mag_t u; mag_init(u); fmpz_init(b); /* incrementing the mantissa gives an upper bound for x+1 */ t = ldexp(MAG_MAN(x) + 1, 1 - MAG_BITS); t = mag_d_log_upper_bound(t); mag_set_d(u, t); /* log(2) < 744261118/2^30 */ _fmpz_add_fast(b, MAG_EXPREF(x), -1); fmpz_mul_ui(b, b, 744261118); mag_set_fmpz(z, b); _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(z), -30); mag_add(z, z, u); mag_clear(u); fmpz_clear(b); } } } arb-2.8.1/mag/log_ui.c000066400000000000000000000024611264125401100144530ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_log_ui(mag_t t, ulong n) { if (n <= 1) { if (n == 1) mag_zero(t); else mag_inf(t); } else { mag_set_ui(t, n-1); mag_log1p(t, t); } } arb-2.8.1/mag/mul.c000066400000000000000000000040251264125401100137700ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_mul(mag_t z, const mag_t x, const mag_t y) { if (mag_is_special(x) || mag_is_special(y)) { if (mag_is_inf(x) || mag_is_inf(y)) mag_inf(z); else mag_zero(z); } else { slong fix; MAG_MAN(z) = MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)) + LIMB_ONE; fix = !(MAG_MAN(z) >> (MAG_BITS - 1)); MAG_MAN(z) <<= fix; _fmpz_add2_fast(MAG_EXPREF(z), MAG_EXPREF(x), MAG_EXPREF(y), -fix); } } void mag_mul_lower(mag_t z, const mag_t x, const mag_t y) { if (mag_is_special(x) || mag_is_special(y)) { if (mag_is_zero(x) || mag_is_zero(y)) mag_zero(z); else mag_inf(z); } else { slong fix; MAG_MAN(z) = MAG_FIXMUL(MAG_MAN(x), MAG_MAN(y)); fix = !(MAG_MAN(z) >> (MAG_BITS - 1)); MAG_MAN(z) <<= fix; _fmpz_add2_fast(MAG_EXPREF(z), MAG_EXPREF(x), MAG_EXPREF(y), -fix); } } arb-2.8.1/mag/polylog_tail.c000066400000000000000000000053061264125401100156740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_polylog_tail(mag_t u, const mag_t z, slong sigma, ulong d, ulong N) { mag_t TN, UN, t; if (N < 2) { mag_inf(u); return; } mag_init(TN); mag_init(UN); mag_init(t); if (mag_cmp_2exp_si(z, 0) >= 0) { mag_inf(u); } else { /* Bound T(N) */ mag_pow_ui(TN, z, N); /* multiply by log(N)^d */ if (d > 0) { mag_log_ui(t, N); mag_pow_ui(t, t, d); mag_mul(TN, TN, t); } /* multiply by 1/k^s */ if (sigma > 0) { mag_set_ui_lower(t, N); mag_pow_ui_lower(t, t, sigma); mag_div(TN, TN, t); } else if (sigma < 0) { mag_set_ui(t, N); mag_pow_ui(t, t, -sigma); mag_mul(TN, TN, t); } /* Bound U(N) */ mag_set(UN, z); /* multiply by (1 + 1/N)**S */ if (sigma < 0) { mag_binpow_uiui(t, N, -sigma); mag_mul(UN, UN, t); } /* multiply by (1 + 1/(N log(N)))^d */ if (d > 0) { ulong nl; /* rounds down */ nl = mag_d_log_lower_bound(N) * N * (1 - 1e-13); mag_binpow_uiui(t, nl, d); mag_mul(UN, UN, t); } /* T(N) / (1 - U(N)) */ if (mag_cmp_2exp_si(UN, 0) >= 0) { mag_inf(u); } else { mag_one(t); mag_sub_lower(t, t, UN); mag_div(u, TN, t); } } mag_clear(TN); mag_clear(UN); mag_clear(t); } arb-2.8.1/mag/pow_fmpz.c000066400000000000000000000033071264125401100150360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_pow_fmpz(mag_t z, const mag_t x, const fmpz_t e) { if (fmpz_sgn(e) < 0) { abort(); } else if (!COEFF_IS_MPZ(*e)) { mag_pow_ui(z, x, fmpz_get_ui(e)); } else { mag_t y; mp_srcptr elimbs; slong i, bits; mag_init_set(y, x); bits = fmpz_bits(e); elimbs = COEFF_TO_PTR(*e)->_mp_d; for (i = bits - 2; i >= 0; i--) { mag_mul(y, y, y); if ((elimbs[i / FLINT_BITS] >> (i % FLINT_BITS)) & 1) mag_mul(y, y, x); } mag_swap(z, y); mag_clear(y); } } arb-2.8.1/mag/pow_ui.c000066400000000000000000000044661264125401100145060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_pow_ui(mag_t z, const mag_t x, ulong e) { if (mag_is_inf(x)) { mag_inf(z); } else if (e <= 2) { if (e == 0) mag_one(z); else if (e == 1) mag_set(z, x); else mag_mul(z, x, x); } else { mag_t y; int i, bits; mag_init_set(y, x); bits = FLINT_BIT_COUNT(e); for (i = bits - 2; i >= 0; i--) { mag_mul(y, y, y); if (e & (UWORD(1) << i)) mag_mul(y, y, x); } mag_swap(z, y); mag_clear(y); } } void mag_pow_ui_lower(mag_t z, const mag_t x, ulong e) { if (e <= 2) { if (e == 0) mag_one(z); else if (e == 1) mag_set(z, x); else mag_mul_lower(z, x, x); } else if (mag_is_inf(x)) { mag_inf(z); } else { mag_t y; int i, bits; mag_init_set(y, x); bits = FLINT_BIT_COUNT(e); for (i = bits - 2; i >= 0; i--) { mag_mul_lower(y, y, y); if (e & (UWORD(1) << i)) mag_mul_lower(y, y, x); } mag_swap(z, y); mag_clear(y); } } arb-2.8.1/mag/print.c000066400000000000000000000031641264125401100143320ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "arf.h" void mag_print(const mag_t x) { flint_printf("("); if (mag_is_zero(x)) flint_printf("0"); else if (mag_is_inf(x)) flint_printf("inf"); else { fmpz_t t; fmpz_init(t); fmpz_sub_ui(t, MAG_EXPREF(x), MAG_BITS); flint_printf("%wu * 2^", MAG_MAN(x)); fmpz_print(t); fmpz_clear(t); } flint_printf(")"); } void mag_printd(const mag_t x, slong d) { arf_t t; arf_init(t); arf_set_mag(t, x); arf_printd(t, d); arf_clear(t); } arb-2.8.1/mag/randtest.c000066400000000000000000000037161264125401100150250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_randtest_special(mag_t x, flint_rand_t state, slong expbits) { switch (n_randint(state, 32)) { case 0: mag_zero(x); break; case 1: mag_inf(x); break; case 2: MAG_MAN(x) = (LIMB_ONE << MAG_BITS) - 1; fmpz_randtest(MAG_EXPREF(x), state, expbits); break; case 3: MAG_MAN(x) = LIMB_ONE << (MAG_BITS - 1); fmpz_randtest(MAG_EXPREF(x), state, expbits); break; default: MAG_MAN(x) = (n_randtest(state) >> (FLINT_BITS - MAG_BITS)); MAG_MAN(x) |= (LIMB_ONE << (MAG_BITS - 1)); fmpz_randtest(MAG_EXPREF(x), state, expbits); } } void mag_randtest(mag_t x, flint_rand_t state, slong expbits) { mag_randtest_special(x, state, expbits); if (mag_is_inf(x)) mag_zero(x); } arb-2.8.1/mag/root.c000066400000000000000000000034701264125401100141610ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_root(mag_t y, const mag_t x, ulong n) { if (n == 0) { mag_inf(y); } else if (n == 1 || mag_is_special(x)) { mag_set(y, x); } else if (n == 2) { mag_sqrt(y, x); } else if (n == 4) { mag_sqrt(y, x); mag_sqrt(y, y); } else { fmpz_t e, f; fmpz_init_set_ui(e, MAG_BITS); fmpz_init(f); fmpz_sub(e, e, MAG_EXPREF(x)); fmpz_cdiv_q_ui(e, e, n); fmpz_mul_ui(f, e, n); mag_mul_2exp_fmpz(y, x, f); mag_log1p(y, y); mag_div_ui(y, y, n); mag_exp(y, y); fmpz_neg(e, e); mag_mul_2exp_fmpz(y, y, e); fmpz_clear(e); fmpz_clear(f); } } arb-2.8.1/mag/rsqrt.c000066400000000000000000000040131264125401100143430ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_rsqrt(mag_t y, const mag_t x) { if (mag_is_special(x)) { if (mag_is_zero(x)) mag_inf(y); else mag_zero(y); } else { double t; fmpz e; t = MAG_MAN(x) * ldexp(1.0, -MAG_BITS); e = MAG_EXP(x); if (!COEFF_IS_MPZ(e)) { if (e % 2 != 0) { e = (1 - e) >> 1; t *= 2.0; } else { e = (-e) >> 1; } t = (1.0 / sqrt(t)) * (1 + 1e-13); mag_set_d_2exp_fmpz(y, t, &e); } else { if (fmpz_is_odd(MAG_EXPREF(x))) t *= 2.0; fmpz_fdiv_q_2exp(MAG_EXPREF(y), MAG_EXPREF(x), 1); fmpz_neg(MAG_EXPREF(y), MAG_EXPREF(y)); t = (1.0 / sqrt(t)) * (1 + 1e-13); mag_set_d_2exp_fmpz(y, t, MAG_EXPREF(y)); } } } arb-2.8.1/mag/set_d_2exp_fmpz.c000066400000000000000000000032361264125401100162660ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_set_d_2exp_fmpz(mag_t z, double c, const fmpz_t exp) { if (c == 0.0) { mag_zero(z); } else if (c > 1e300 || c < 0.0) /* not implemented */ { flint_printf("mag_set_d_2exp_fmpz\n"); abort(); } else { int cexp, fix; mp_limb_t man; c = frexp(c, &cexp); man = (mp_limb_t)(c * (double)(LIMB_ONE << MAG_BITS)) + 1; fix = man >> (MAG_BITS); man = (man >> fix) + fix; /* XXX: need +fix? */ MAG_MAN(z) = man; _fmpz_add_fast(MAG_EXPREF(z), exp, cexp + fix); } } arb-2.8.1/mag/set_fmpr.c000066400000000000000000000025561264125401100150210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "arf.h" void mag_set_fmpr(mag_t x, const fmpr_t y) { if (fmpr_is_special(y)) { if (fmpr_is_zero(y)) mag_zero(x); else mag_inf(x); } else { mag_set_fmpz_2exp_fmpz(x, fmpr_manref(y), fmpr_expref(y)); } } arb-2.8.1/mag/set_fmpz_2exp_fmpz.c000066400000000000000000000034121264125401100170130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_set_fmpz_2exp_fmpz(mag_t z, const fmpz_t man, const fmpz_t exp) { if (fmpz_is_zero(man)) { mag_zero(z); } else { mp_limb_t m; slong cexp; m = fmpz_abs_ubound_ui_2exp(&cexp, man, MAG_BITS); MAG_MAN(z) = m; _fmpz_add_fast(MAG_EXPREF(z), exp, cexp + MAG_BITS); } } void mag_set_fmpz_2exp_fmpz_lower(mag_t z, const fmpz_t man, const fmpz_t exp) { if (fmpz_is_zero(man)) { mag_zero(z); } else { mp_limb_t m; slong cexp; m = fmpz_abs_lbound_ui_2exp(&cexp, man, MAG_BITS); MAG_MAN(z) = m; _fmpz_add_fast(MAG_EXPREF(z), exp, cexp + MAG_BITS); } } arb-2.8.1/mag/set_ui.c000066400000000000000000000041611264125401100144640ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_set_ui(mag_t z, ulong x) { _fmpz_demote(MAG_EXPREF(z)); if (x == 0) { MAG_EXP(z) = 0; MAG_MAN(z) = 0; } else { slong bits; mp_limb_t overflow; count_leading_zeros(bits, x); bits = FLINT_BITS - bits; if (bits <= MAG_BITS) { x = x << (MAG_BITS - bits); } else { x = (x >> (bits - MAG_BITS)) + 1; overflow = x >> MAG_BITS; bits += overflow; x >>= overflow; } MAG_EXP(z) = bits; MAG_MAN(z) = x; } } void mag_set_ui_lower(mag_t z, ulong x) { _fmpz_demote(MAG_EXPREF(z)); if (x == 0) { MAG_EXP(z) = 0; MAG_MAN(z) = 0; } else { unsigned int bits; count_leading_zeros(bits, x); bits = FLINT_BITS - bits; if (bits <= MAG_BITS) x <<= (MAG_BITS - bits); else x >>= (bits - MAG_BITS); MAG_EXP(z) = bits; MAG_MAN(z) = x; } } arb-2.8.1/mag/sqrt.c000066400000000000000000000035741264125401100141740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" void mag_sqrt(mag_t y, const mag_t x) { if (mag_is_special(x)) { mag_set(y, x); } else { double t; fmpz e; t = MAG_MAN(x) * ldexp(1.0, -MAG_BITS); e = MAG_EXP(x); if (!COEFF_IS_MPZ(e)) { if (e % 2 != 0) { e = (e - 1) >> 1; t *= 2.0; } else { e >>= 1; } t = sqrt(t) * (1 + 1e-13); mag_set_d_2exp_fmpz(y, t, &e); } else { if (fmpz_is_odd(MAG_EXPREF(x))) t *= 2.0; fmpz_fdiv_q_2exp(MAG_EXPREF(y), MAG_EXPREF(x), 1); t = sqrt(t) * (1 + 1e-13); mag_set_d_2exp_fmpz(y, t, MAG_EXPREF(y)); } } } arb-2.8.1/mag/sub_lower.c000066400000000000000000000056751264125401100152100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "arf.h" void mag_sub_lower(mag_t z, const mag_t x, const mag_t y) { if (mag_is_special(x) || mag_is_special(y)) { if (mag_is_zero(y)) mag_set(z, x); else if (mag_is_zero(x) || mag_is_inf(y)) mag_zero(z); else mag_inf(z); } else { slong shift, fix; shift = _fmpz_sub_small(MAG_EXPREF(x), MAG_EXPREF(y)); /* y > x */ if (shift < 0) { mag_zero(z); } else if (shift == 0) { if (MAG_MAN(y) >= MAG_MAN(x)) { mag_zero(z); } else { MAG_MAN(z) = MAG_MAN(x) - MAG_MAN(y); fix = MAG_BITS - FLINT_BIT_COUNT(MAG_MAN(z)); MAG_MAN(z) <<= fix; _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(x), -fix); } } else { if (shift <= MAG_BITS) { mp_limb_t c = MAG_MAN(x) - (MAG_MAN(y) >> shift) - 1; /* too much cancellation -- compute precisely */ if (c < (UWORD(1) << (MAG_BITS - 4))) { arf_t t, u; arf_init(t); arf_init(u); arf_set_mag(t, x); arf_set_mag(u, y); arf_sub(t, t, u, MAG_BITS, ARF_RND_DOWN); arf_get_mag_lower(z, t); arf_clear(t); arf_clear(u); return; } MAG_MAN(z) = c; } else { MAG_MAN(z) = MAG_MAN(x) - 1; } fix = MAG_BITS - FLINT_BIT_COUNT(MAG_MAN(z)); MAG_MAN(z) <<= fix; _fmpz_add_fast(MAG_EXPREF(z), MAG_EXPREF(x), -fix); } } } arb-2.8.1/mag/test/000077500000000000000000000000001264125401100140055ustar00rootroot00000000000000arb-2.8.1/mag/test/t-add.c000066400000000000000000000053041264125401100151440ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_add(z, x, y, MAG_BITS + 10, FMPR_RND_DOWN); if (fmpr_is_nan(z)) fmpr_pos_inf(z); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_add(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-add_2exp_fmpz.c000066400000000000000000000053251264125401100171410ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("add_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, zb; fmpz_t e; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); fmpz_init(e); mag_init(xb); mag_init(zb); fmpr_randtest(x, state, MAG_BITS, 100); fmpr_abs(x, x); fmpz_randtest(e, state, 100); fmpr_one(y); fmpr_mul_2exp_fmpz(y, y, e); fmpr_add(z, x, y, MAG_BITS + 10, FMPR_RND_DOWN); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_set_fmpr(xb, x); mag_add_2exp_fmpz(zb, xb, e); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); flint_printf("w = "); fmpr_printd(w, 15); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(zb); fmpz_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-add_lower.c000066400000000000000000000052161264125401100163560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("add_lower...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_add(z2, x, y, 100, FMPR_RND_DOWN); fmpr_mul_ui(z, z2, 1023, MAG_BITS, FMPR_RND_DOWN); fmpr_mul_2exp_si(z, z, -10); mag_add_lower(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-addmul.c000066400000000000000000000054301264125401100156620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("addmul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_randtest_special(zb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); mag_get_fmpr(z, zb); fmpr_addmul(z, x, y, MAG_BITS + 10, FMPR_RND_DOWN); if (fmpr_is_nan(z)) fmpr_pos_inf(z); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_addmul(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-binpow_uiui.c000066400000000000000000000043531264125401100167500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("binpow_uiui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpr_t x, y; mag_t b; ulong m, n; fmpr_init(x); fmpr_init(y); mag_init(b); m = n_randtest(state); n = n_randtest(state); fmpr_one(x); fmpr_div_ui(x, x, m, 128, FMPR_RND_UP); fmpr_add_ui(x, x, 1, 128, FMPR_RND_UP); fmpr_pow_sloppy_ui(x, x, n, 128, FMPR_RND_UP); mag_binpow_uiui(b, m, n); mag_get_fmpr(y, b); MAG_CHECK_BITS(b) if (!(fmpr_cmpabs(x, y) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("m = %wu\n\n", m); flint_printf("n = %wu\n\n", n); flint_printf("x = "); fmpr_printd(x, 10); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 10); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); mag_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-cmp.c000066400000000000000000000043051264125401100151730ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("cmp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y; mag_t xb, yb; int c1, c2; fmpr_init(x); fmpr_init(y); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); c1 = fmpr_cmp(x, y); c2 = mag_cmp(xb, yb); if (c1 != c2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("xb = "); mag_print(xb); flint_printf("\n\n"); flint_printf("yb = "); mag_print(yb); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-cmp_2exp_si.c000066400000000000000000000040371264125401100166260ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("cmp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x; mag_t xb; slong y; int c1, c2; fmpr_init(x); mag_init(xb); mag_randtest_special(xb, state, 100); y = z_randtest(state); mag_get_fmpr(x, xb); c1 = fmpr_cmp_2exp_si(x, y); c2 = mag_cmp_2exp_si(xb, y); if (c1 != c2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = %wd", y); flint_printf("\n\n"); flint_printf("xb = "); mag_print(xb); flint_printf("\n\n"); abort(); } fmpr_clear(x); mag_clear(xb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-d_log_lower_bound.c000066400000000000000000000057721264125401100201100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "double_extras.h" #include "mag.h" /* XXX: d_randtest is not good enough */ #define EXP_MINUS_32 2.3283064365386962891e-10 #define EXP_MINUS_64 5.42101086242752217e-20 double d_randtest2(flint_rand_t state) { mp_limb_t m1, m2; double t; if (FLINT_BITS == 64) { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); t = ((double) m1) * EXP_MINUS_64; } else { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); m2 = n_randtest(state); t = ((double) m1) * EXP_MINUS_32 + ((double) m2) * EXP_MINUS_64; } return t; } int main() { slong iter; flint_rand_t state; flint_printf("d_log_lower_bound...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { mpfr_t t; double x, y, z; mpfr_init2(t, 53); x = d_randtest2(state); x = ldexp(x, 100 - n_randint(state, 200)); switch (n_randint(state, 10)) { case 0: x = 1.0 + x; break; case 1: x = 1.0 - x; break; case 2: x = D_INF; break; case 3: x = 0.0; break; case 4: x = D_NAN; break; default: break; } y = mag_d_log_lower_bound(x); mpfr_set_d(t, x, MPFR_RNDD); mpfr_log(t, t, MPFR_RNDD); z = mpfr_get_d(t, MPFR_RNDD); if (y > z || fabs(y-z) > 0.000001 * fabs(z)) { flint_printf("FAIL\n"); flint_printf("x = %.20g\n", x); flint_printf("y = %.20g\n", y); flint_printf("z = %.20g\n", z); abort(); } mpfr_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-d_log_upper_bound.c000066400000000000000000000057721264125401100201130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "double_extras.h" #include "mag.h" /* XXX: d_randtest is not good enough */ #define EXP_MINUS_32 2.3283064365386962891e-10 #define EXP_MINUS_64 5.42101086242752217e-20 double d_randtest2(flint_rand_t state) { mp_limb_t m1, m2; double t; if (FLINT_BITS == 64) { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); t = ((double) m1) * EXP_MINUS_64; } else { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); m2 = n_randtest(state); t = ((double) m1) * EXP_MINUS_32 + ((double) m2) * EXP_MINUS_64; } return t; } int main() { slong iter; flint_rand_t state; flint_printf("d_log_upper_bound...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { mpfr_t t; double x, y, z; mpfr_init2(t, 53); x = d_randtest2(state); x = ldexp(x, 100 - n_randint(state, 200)); switch (n_randint(state, 10)) { case 0: x = 1.0 + x; break; case 1: x = 1.0 - x; break; case 2: x = D_INF; break; case 3: x = 0.0; break; case 4: x = D_NAN; break; default: break; } y = mag_d_log_upper_bound(x); mpfr_set_d(t, x, MPFR_RNDD); mpfr_log(t, t, MPFR_RNDU); z = mpfr_get_d(t, MPFR_RNDD); if (y < z || fabs(y-z) > 0.000001 * fabs(z)) { flint_printf("FAIL\n"); flint_printf("x = %.20g\n", x); flint_printf("y = %.20g\n", y); flint_printf("z = %.20g\n", z); abort(); } mpfr_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-div.c000066400000000000000000000052101264125401100151720ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("div...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest_special(xb, state, 10); mag_randtest_special(yb, state, 10); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_div(z, x, y, MAG_BITS + 10, FMPR_RND_DOWN); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_div(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-exp.c000066400000000000000000000055021264125401100152100ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2; mag_t xb, yb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 0); mag_randtest_special(yb, state, 0); mag_mul_2exp_si(xb, xb, -28 + n_randint(state,56)); mag_exp(yb, xb); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_exp(z, x, MAG_BITS, FMPR_RND_UP); if (fmpr_cmpabs_ui(x, 1000) < 0) { fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); } else { fmpr_mul_2exp_si(z2, z, 2); } MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z2 = "); fmpr_print(z2); flint_printf("\n\n"); abort(); } mag_exp(xb, xb); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-exp_tail.c000066400000000000000000000057021264125401100162230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("exp_tail...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { fmpr_t x, t, y, z; fmpz_t f; mag_t xb, yb; ulong N, k; fmpr_init(x); fmpr_init(t); fmpr_init(y); fmpr_init(z); fmpz_init(f); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 6); mag_randtest_special(yb, state, 6); N = n_randint(state, 100); mag_exp_tail(yb, xb, N); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_pow_sloppy_ui(t, x, N, MAG_BITS, FMPR_RND_DOWN); fmpz_fac_ui(f, N); fmpr_div_fmpz(t, t, f, MAG_BITS, FMPR_RND_DOWN); fmpr_set(z, t); for (k = 1; k < 50; k++) { fmpr_mul(t, t, x, MAG_BITS, FMPR_RND_DOWN); fmpr_div_ui(t, t, N + k, MAG_BITS, FMPR_RND_DOWN); fmpr_add(z, z, t, MAG_BITS, FMPR_RND_DOWN); } MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("N = %wu\n\n", N); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); abort(); } mag_exp_tail(xb, xb, N); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(t); fmpr_clear(y); fmpr_clear(z); fmpz_clear(f); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-expm1.c000066400000000000000000000055401264125401100154500ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("expm1...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2; mag_t xb, yb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 0); mag_randtest_special(yb, state, 0); mag_mul_2exp_si(xb, xb, -100 + n_randint(state,120)); mag_expm1(yb, xb); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_expm1(z, x, MAG_BITS, FMPR_RND_UP); if (fmpr_cmpabs_ui(x, 1000) < 0) { fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); } else { fmpr_mul_2exp_si(z2, z, 2); } MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); flint_printf("z2 = "); fmpr_printd(z2, 15); flint_printf("\n\n"); abort(); } mag_expm1(xb, xb); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-fac_ui.c000066400000000000000000000042111264125401100156360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("fac_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { fmpr_t x, y; fmpz_t f; mag_t xb; ulong n; fmpr_init(x); fmpr_init(y); fmpz_init(f); mag_init(xb); mag_randtest_special(xb, state, 80); n = n_randtest(state) % 2000; mag_fac_ui(xb, n); fmpz_fac_ui(f, n); fmpr_set_fmpz(x, f); mag_get_fmpr(y, xb); MAG_CHECK_BITS(xb) if (!(fmpr_cmpabs(y, x) >= 0)) { flint_printf("FAIL\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpz_clear(f); mag_clear(xb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-fast_add_2exp_si.c000066400000000000000000000052611264125401100176140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("fast_add_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, zb; slong e; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(zb); fmpr_randtest(x, state, MAG_BITS, 15); fmpr_abs(x, x); e = n_randint(state, 10000) - n_randint(state, 10000); fmpr_set_ui_2exp_si(y, 1, e); fmpr_add(z, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_set_fmpr(xb, x); mag_fast_add_2exp_si(zb, xb, e); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); flint_printf("w = "); fmpr_printd(w, 15); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-fast_addmul.c000066400000000000000000000053411264125401100167000ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("fast_addmul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest(xb, state, 15); mag_randtest(yb, state, 15); mag_randtest(zb, state, 15); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); mag_get_fmpr(z, zb); fmpr_addmul(z, x, y, MAG_BITS + 10, FMPR_RND_DOWN); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_fast_addmul(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); flint_printf("w = "); fmpr_printd(w, 15); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-fast_mul.c000066400000000000000000000052301264125401100162240ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("fast_mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest(xb, state, 15); mag_randtest(yb, state, 15); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_mul(z, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_fast_mul(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); flint_printf("w = "); fmpr_printd(w, 15); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-fast_mul_2exp_si.c000066400000000000000000000044031264125401100176560ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("fast_mul_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z; mag_t xb, yb; slong e; fmpr_init(x); fmpr_init(y); fmpr_init(z); mag_init(xb); mag_init(yb); mag_randtest(xb, state, 15); e = n_randint(state, 10000) - n_randint(state, 10000); mag_get_fmpr(x, xb); mag_fast_mul_2exp_si(yb, xb, e); fmpr_mul_2exp_si(y, x, e); mag_get_fmpr(z, yb); MAG_CHECK_BITS(yb) if (!fmpr_equal(z, y)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-geom_series.c000066400000000000000000000053711264125401100167210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2015 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("geom_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { fmpr_t x, t, y, z; mag_t xb, yb; ulong N, k; fmpr_init(x); fmpr_init(t); fmpr_init(y); fmpr_init(z); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 6); mag_randtest_special(yb, state, 6); N = n_randint(state, 100); mag_geom_series(yb, xb, N); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_pow_sloppy_ui(t, x, N, MAG_BITS, FMPR_RND_DOWN); fmpr_set(z, t); for (k = 1; k < 50; k++) { fmpr_mul(t, t, x, MAG_BITS, FMPR_RND_DOWN); fmpr_add(z, z, t, MAG_BITS, FMPR_RND_DOWN); } MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("N = %wu\n\n", N); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); abort(); } mag_geom_series(xb, xb, N); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(t); fmpr_clear(y); fmpr_clear(z); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-log1p.c000066400000000000000000000052001264125401100154310ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("log1p...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2; mag_t xb, yb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 25); mag_randtest_special(yb, state, 25); mag_log1p(yb, xb); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_log1p(z, x, MAG_BITS, FMPR_RND_UP); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z2 = "); fmpr_print(z2); flint_printf("\n\n"); abort(); } mag_log1p(xb, xb); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-mul.c000066400000000000000000000053061264125401100152130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("mul...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_mul(z, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); if (fmpr_is_nan(z)) fmpr_pos_inf(z); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); mag_mul(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-mul_2exp_fmpz.c000066400000000000000000000044371264125401100172110ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z; mag_t xb, yb; fmpz_t e; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpz_init(e); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 100); fmpz_randtest(e, state, 100); mag_get_fmpr(x, xb); mag_mul_2exp_fmpz(yb, xb, e); fmpr_mul_2exp_fmpz(y, x, e); mag_get_fmpr(z, yb); MAG_CHECK_BITS(yb) if (!fmpr_equal(z, y)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); mag_clear(xb); mag_clear(yb); fmpz_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-mul_2exp_si.c000066400000000000000000000043731264125401100166470ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "long_extras.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_2exp_si...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z; mag_t xb, yb; slong e; fmpr_init(x); fmpr_init(y); fmpr_init(z); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 100); e = z_randtest(state); mag_get_fmpr(x, xb); mag_mul_2exp_si(yb, xb, e); fmpr_mul_2exp_si(y, x, e); mag_get_fmpr(z, yb); MAG_CHECK_BITS(yb) if (!fmpr_equal(z, y)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_printd(x, 15); flint_printf("\n\n"); flint_printf("y = "); fmpr_printd(y, 15); flint_printf("\n\n"); flint_printf("z = "); fmpr_printd(z, 15); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-mul_lower.c000066400000000000000000000053221264125401100164210ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("mul_lower...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_mul(z2, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN); if (fmpr_is_nan(z2)) fmpr_zero(z2); fmpr_mul_ui(z, z2, 1023, MAG_BITS, FMPR_RND_DOWN); fmpr_mul_2exp_si(z, z, -10); mag_mul_lower(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-polylog_tail.c000066400000000000000000000067621264125401100171230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" #include "arb.h" int main() { slong iter; flint_rand_t state; flint_printf("polylog_tail...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { mag_t xb, yb; ulong N, k, d; slong s, prec; arb_t z, t, u, r; mag_init(xb); mag_init(yb); arb_init(z); arb_init(t); arb_init(u); arb_init(r); mag_randtest_special(xb, state, 6); mag_randtest_special(yb, state, 6); N = n_randint(state, 100); d = n_randint(state, 100); s = n_randint(state, 100) - 50; prec = 4 * MAG_BITS; mag_polylog_tail(yb, xb, s, d, N); arb_zero(z); arf_set_mag(arb_midref(z), xb); arb_zero(r); for (k = N; k < N + 100; k++) { arb_pow_ui(t, z, k, prec); arb_log_ui(u, k, prec); arb_pow_ui(u, u, d, prec); arb_mul(t, t, u, prec); arb_set_ui(u, k); if (s >= 0) { arb_pow_ui(u, u, s, prec); arb_div(t, t, u, prec); } else { arb_pow_ui(u, u, -s, prec); arb_mul(t, t, u, prec); } arb_add(r, r, t, prec); } MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) arb_zero(z); mag_set(arb_radref(z), yb); if (!arb_is_finite(z)) arb_indeterminate(z); if (!arb_contains(z, r)) { flint_printf("FAIL\n\n"); flint_printf("N = %wu\n\n", N); flint_printf("d = %wu\n\n", d); flint_printf("s = %wd\n\n", s); flint_printf("xb = "); mag_printd(xb, 15); flint_printf("\n\n"); flint_printf("yb = "); mag_printd(yb, 15); flint_printf("\n\n"); flint_printf("z = "); arb_printd(z, 15); flint_printf("\n\n"); flint_printf("r = "); arb_printd(r, 15); flint_printf("\n\n"); abort(); } mag_polylog_tail(xb, xb, s, d, N); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } mag_clear(xb); mag_clear(yb); arb_clear(z); arb_clear(t); arb_clear(u); arb_clear(r); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-pow_fmpz.c000066400000000000000000000055161264125401100162620ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { fmpr_t x, y, w; mag_t xb, yb; fmpz_t e; fmpr_init(x); fmpr_init(y); fmpr_init(w); fmpz_init(e); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 80); mag_randtest_special(yb, state, 80); fmpz_randtest(e, state, 200); fmpz_abs(e, e); mag_get_fmpr(x, xb); fmpr_pow_sloppy_fmpz(y, x, e, 2 * MAG_BITS, FMPR_RND_UP); if (fmpr_is_nan(y)) fmpr_pos_inf(y); mag_pow_fmpz(yb, xb, e); mag_get_fmpr(w, yb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(y, w) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("e = "); fmpz_print(e); flint_printf("\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } mag_pow_fmpz(xb, xb, e); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("e = "); fmpz_print(e); flint_printf("\n\n"); mag_print(xb); flint_printf("\n\n"); mag_print(yb); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(w); fmpz_clear(e); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-pow_ui.c000066400000000000000000000053041264125401100157160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, w; mag_t xb, yb; ulong e; fmpr_init(x); fmpr_init(y); fmpr_init(w); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 80); mag_randtest_special(yb, state, 80); e = n_randtest(state); mag_get_fmpr(x, xb); fmpr_pow_sloppy_ui(y, x, e, 2 * MAG_BITS, FMPR_RND_UP); if (fmpr_is_nan(y)) fmpr_pos_inf(y); mag_pow_ui(yb, xb, e); mag_get_fmpr(w, yb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(y, w) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("e = %wu\n\n", e); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } mag_pow_ui(xb, xb, e); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("e = %wu\n\n", e); mag_print(xb); flint_printf("\n\n"); mag_print(yb); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(w); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-pow_ui_lower.c000066400000000000000000000053301264125401100171250ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("pow_ui_lower...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, w; mag_t xb, yb; ulong e; fmpr_init(x); fmpr_init(y); fmpr_init(w); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 80); mag_randtest_special(yb, state, 80); e = n_randtest(state); mag_get_fmpr(x, xb); fmpr_pow_sloppy_ui(y, x, e, 2 * MAG_BITS, FMPR_RND_DOWN); if (fmpr_is_nan(y)) fmpr_pos_inf(y); mag_pow_ui_lower(yb, xb, e); mag_get_fmpr(w, yb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(w, y) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("e = %wu\n\n", e); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } mag_pow_ui_lower(xb, xb, e); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); flint_printf("e = %wu\n\n", e); mag_print(xb); flint_printf("\n\n"); mag_print(yb); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(w); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-rfac_ui.c000066400000000000000000000042761264125401100160330ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("rfac_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000; iter++) { fmpr_t x, y; fmpz_t f; mag_t xb; ulong n; fmpr_init(x); fmpr_init(y); fmpz_init(f); mag_init(xb); mag_randtest_special(xb, state, 80); n = n_randtest(state) % 2000; mag_rfac_ui(xb, n); fmpz_fac_ui(f, n); fmpr_one(x); fmpr_div_fmpz(x, x, f, 2 * MAG_BITS, FMPR_RND_UP); mag_get_fmpr(y, xb); MAG_CHECK_BITS(xb) if (!(fmpr_cmpabs(y, x) >= 0)) { flint_printf("FAIL\n\n"); flint_printf("n = %wu\n\n", n); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpz_clear(f); mag_clear(xb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-root.c000066400000000000000000000053451264125401100154040ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("root...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2; mag_t xb, yb; ulong n; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 1 + n_randint(state, 200)); mag_randtest_special(yb, state, 1 + n_randint(state, 200)); n = n_randint(state, 30); mag_root(yb, xb, n); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_root(z, x, n, MAG_BITS, FMPR_RND_UP); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z2 = "); fmpr_print(z2); flint_printf("\n\n"); abort(); } mag_root(xb, xb, n); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-rsqrt.c000066400000000000000000000052551264125401100155740ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("rsqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2; mag_t xb, yb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 1 + n_randint(state, 200)); mag_randtest_special(yb, state, 1 + n_randint(state, 200)); mag_rsqrt(yb, xb); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_rsqrt(z, x, MAG_BITS, FMPR_RND_UP); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z2 = "); fmpr_print(z2); flint_printf("\n\n"); abort(); } mag_rsqrt(xb, xb); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-set_d.c000066400000000000000000000056411264125401100155160ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "double_extras.h" #include "mag.h" /* XXX: d_randtest is not good enough */ #define EXP_MINUS_32 2.3283064365386962891e-10 #define EXP_MINUS_64 5.42101086242752217e-20 double d_randtest2(flint_rand_t state) { mp_limb_t m1, m2; double t; if (FLINT_BITS == 64) { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); t = ((double) m1) * EXP_MINUS_64; } else { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); m2 = n_randtest(state); t = ((double) m1) * EXP_MINUS_32 + ((double) m2) * EXP_MINUS_64; } return t; } int main() { slong iter; flint_rand_t state; flint_printf("set_d...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t a, b, c; mag_t m; double x; fmpr_init(a); fmpr_init(b); fmpr_init(c); mag_init(m); x = d_randtest2(state); x = ldexp(x, 100 - n_randint(state, 200)); if (n_randint(state, 100) == 0) x = 0.0; fmpr_set_d(a, x); mag_set_d(m, x); mag_get_fmpr(b, m); fmpr_set(c, a); fmpr_mul_ui(c, c, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(c, c, -10); MAG_CHECK_BITS(m) if (!(fmpr_cmpabs(a, b) <= 0 && fmpr_cmpabs(b, c) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("a = "); fmpr_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpr_print(b); flint_printf("\n\n"); flint_printf("c = "); fmpr_print(c); flint_printf("\n\n"); abort(); } fmpr_clear(a); fmpr_clear(b); fmpr_clear(c); mag_clear(m); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-set_d_2exp_fmpz.c000066400000000000000000000061031264125401100175020ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "double_extras.h" #include "mag.h" /* XXX: d_randtest is not good enough */ #define EXP_MINUS_32 2.3283064365386962891e-10 #define EXP_MINUS_64 5.42101086242752217e-20 double d_randtest2(flint_rand_t state) { mp_limb_t m1, m2; double t; if (FLINT_BITS == 64) { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); t = ((double) m1) * EXP_MINUS_64; } else { m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1)); m2 = n_randtest(state); t = ((double) m1) * EXP_MINUS_32 + ((double) m2) * EXP_MINUS_64; } return t; } int main() { slong iter; flint_rand_t state; flint_printf("set_d_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t a, b, c; fmpz_t e; mag_t m; double x; fmpr_init(a); fmpr_init(b); fmpr_init(c); fmpz_init(e); mag_init(m); x = d_randtest2(state); x = ldexp(x, 100 - n_randint(state, 200)); if (n_randint(state, 100) == 0) x = 0.0; fmpz_randtest(e, state, 10); fmpr_set_d(a, x); fmpr_mul_2exp_fmpz(a, a, e); mag_set_d_2exp_fmpz(m, x, e); mag_get_fmpr(b, m); fmpr_set(c, a); fmpr_mul_ui(c, c, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(c, c, -10); MAG_CHECK_BITS(m) if (!(fmpr_cmpabs(a, b) <= 0 && fmpr_cmpabs(b, c) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("a = "); fmpr_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpr_print(b); flint_printf("\n\n"); flint_printf("c = "); fmpr_print(c); flint_printf("\n\n"); abort(); } fmpr_clear(a); fmpr_clear(b); fmpr_clear(c); fmpz_clear(e); mag_clear(m); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-set_ui.c000066400000000000000000000043751264125401100157130ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("set_ui...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t a, b, c; mag_t m; ulong x; fmpr_init(a); fmpr_init(b); fmpr_init(c); mag_init(m); x = n_randtest(state); fmpr_set_ui(a, x); mag_set_ui(m, x); mag_get_fmpr(b, m); fmpr_set(c, a); fmpr_mul_ui(c, c, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(c, c, -10); MAG_CHECK_BITS(m) if (!(fmpr_cmpabs(a, b) <= 0 && fmpr_cmpabs(b, c) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = %wu\n\n", x); flint_printf("a = "); fmpr_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpr_print(b); flint_printf("\n\n"); flint_printf("c = "); fmpr_print(c); flint_printf("\n\n"); abort(); } fmpr_clear(a); fmpr_clear(b); fmpr_clear(c); mag_clear(m); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-set_ui_lower.c000066400000000000000000000044131264125401100171140ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("set_ui_lower...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t a, b, c; mag_t m; ulong x; fmpr_init(a); fmpr_init(b); fmpr_init(c); mag_init(m); x = n_randtest(state); fmpr_set_ui(a, x); mag_set_ui_lower(m, x); mag_get_fmpr(b, m); fmpr_set(c, a); fmpr_mul_ui(c, c, 1023, MAG_BITS, FMPR_RND_DOWN); fmpr_mul_2exp_si(c, c, -10); MAG_CHECK_BITS(m) if (!(fmpr_cmpabs(c, b) <= 0 && fmpr_cmpabs(b, a) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = %wu\n\n", x); flint_printf("a = "); fmpr_print(a); flint_printf("\n\n"); flint_printf("b = "); fmpr_print(b); flint_printf("\n\n"); flint_printf("c = "); fmpr_print(c); flint_printf("\n\n"); abort(); } fmpr_clear(a); fmpr_clear(b); fmpr_clear(c); mag_clear(m); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-sqrt.c000066400000000000000000000052511264125401100154060ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("sqrt...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2; mag_t xb, yb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 1 + n_randint(state, 200)); mag_randtest_special(yb, state, 1 + n_randint(state, 200)); mag_sqrt(yb, xb); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_sqrt(z, x, MAG_BITS, FMPR_RND_UP); fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP); fmpr_mul_2exp_si(z2, z2, -10); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) if (!(fmpr_cmpabs(z, y) <= 0 && fmpr_cmpabs(y, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("z2 = "); fmpr_print(z2); flint_printf("\n\n"); abort(); } mag_sqrt(xb, xb); if (!mag_equal(xb, yb)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/mag/test/t-sub_lower.c000066400000000000000000000062161264125401100164200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2014 Fredrik Johansson ******************************************************************************/ #include "mag.h" int main() { slong iter; flint_rand_t state; flint_printf("sub_lower...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { fmpr_t x, y, z, z2, w; mag_t xb, yb, zb; fmpr_init(x); fmpr_init(y); fmpr_init(z); fmpr_init(z2); fmpr_init(w); mag_init(xb); mag_init(yb); mag_init(zb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); fmpr_sub(z2, x, y, 100, FMPR_RND_DOWN); if (fmpr_sgn(z2) < 0) fmpr_zero(z2); fmpr_mul_ui(z, z2, 1023, MAG_BITS, FMPR_RND_DOWN); fmpr_mul_2exp_si(z, z, -10); mag_sub_lower(zb, xb, yb); mag_get_fmpr(w, zb); MAG_CHECK_BITS(xb) MAG_CHECK_BITS(yb) MAG_CHECK_BITS(zb) if (!(fmpr_cmpabs(z, w) <= 0 && fmpr_cmpabs(w, z2) <= 0)) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("z = "); fmpr_print(z); flint_printf("\n\n"); flint_printf("w = "); fmpr_print(w); flint_printf("\n\n"); abort(); } if (n_randint(state, 2)) { mag_sub_lower(xb, xb, yb); if (!mag_equal(xb, zb)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } } else { mag_sub_lower(yb, xb, yb); if (!mag_equal(yb, zb)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } } fmpr_clear(x); fmpr_clear(y); fmpr_clear(z); fmpr_clear(z2); fmpr_clear(w); mag_clear(xb); mag_clear(yb); mag_clear(zb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; } arb-2.8.1/partitions.h000066400000000000000000000031201264125401100146230ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #ifndef PARTITIONS_H #define PARTITIONS_H #include #include "flint.h" #include "arith.h" #include "arb.h" #ifdef __cplusplus extern "C" { #endif void partitions_rademacher_bound(arf_t b, const fmpz_t n, ulong N); void partitions_hrr_sum_arb(arb_t x, const fmpz_t n, slong N0, slong N, int use_doubles); void partitions_fmpz_fmpz(fmpz_t p, const fmpz_t n, int use_doubles); void partitions_fmpz_ui(fmpz_t p, ulong n); void partitions_fmpz_ui_using_doubles(fmpz_t p, ulong n); #ifdef __cplusplus } #endif #endif arb-2.8.1/partitions/000077500000000000000000000000001264125401100144565ustar00rootroot00000000000000arb-2.8.1/partitions/fmpz_fmpz.c000066400000000000000000000077001264125401100166360ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013-2014 Fredrik Johansson ******************************************************************************/ #include #include "partitions.h" /* defined in flint*/ #define NUMBER_OF_SMALL_PARTITIONS 128 extern const unsigned int partitions_lookup[NUMBER_OF_SMALL_PARTITIONS]; slong partitions_hrr_needed_terms(double n); typedef struct { arb_ptr x; fmpz * n; ulong N0; ulong N; int use_doubles; } worker_arg_t; static void * worker(void * arg_ptr) { worker_arg_t arg = *((worker_arg_t *) arg_ptr); partitions_hrr_sum_arb(arg.x, arg.n, arg.N0, arg.N, arg.use_doubles); flint_cleanup(); return NULL; } /* TODO: set number of threads in child threads, for future multithreaded evaluation of single terms */ static void hrr_sum_threaded(arb_t x, const fmpz_t n, slong N, int use_doubles) { arb_t y; pthread_t threads[2]; worker_arg_t args[2]; arb_init(y); args[0].x = x; args[0].n = (fmpz *) n; args[0].N0 = 1; args[0].N = 16; args[0].use_doubles = use_doubles; args[1].x = y; args[1].n = (fmpz *) n; args[1].N0 = 17; args[1].N = N; args[1].use_doubles = use_doubles; pthread_create(&threads[0], NULL, worker, &args[0]); pthread_create(&threads[1], NULL, worker, &args[1]); pthread_join(threads[0], NULL); pthread_join(threads[1], NULL); arb_add(x, x, y, ARF_PREC_EXACT); arb_clear(y); } void partitions_fmpz_fmpz(fmpz_t p, const fmpz_t n, int use_doubles) { if (fmpz_cmp_ui(n, NUMBER_OF_SMALL_PARTITIONS) < 0) { if (fmpz_sgn(n) < 0) fmpz_zero(p); else fmpz_set_ui(p, partitions_lookup[fmpz_get_ui(n)]); } else { arb_t x; arf_t bound; slong N; arb_init(x); arf_init(bound); N = partitions_hrr_needed_terms(fmpz_get_d(n)); if (fmpz_cmp_ui(n, 4e8) >= 0 && flint_get_num_threads() > 1) { hrr_sum_threaded(x, n, N, use_doubles); } else { partitions_hrr_sum_arb(x, n, 1, N, use_doubles); } partitions_rademacher_bound(bound, n, N); arb_add_error_arf(x, bound); if (!arb_get_unique_fmpz(p, x)) { flint_printf("not unique!\n"); arb_printd(x, 50); flint_printf("\n"); abort(); } arb_clear(x); arf_clear(bound); } } void partitions_fmpz_ui(fmpz_t p, ulong n) { if (n < NUMBER_OF_SMALL_PARTITIONS) { fmpz_set_ui(p, partitions_lookup[n]); } else { fmpz_t t; fmpz_init(t); fmpz_set_ui(t, n); partitions_fmpz_fmpz(p, t, 0); fmpz_clear(t); } } void partitions_fmpz_ui_using_doubles(fmpz_t p, ulong n) { if (n < NUMBER_OF_SMALL_PARTITIONS) { fmpz_set_ui(p, partitions_lookup[n]); } else { fmpz_t t; fmpz_init(t); fmpz_set_ui(t, n); partitions_fmpz_fmpz(p, t, 1); fmpz_clear(t); } } arb-2.8.1/partitions/hrr_sum_arb.c000066400000000000000000000211101264125401100171200ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "partitions.h" #include "arith.h" #include "arb.h" #include "math.h" #define DOUBLE_CUTOFF 40 #define DOUBLE_ERR 1e-12 #define DOUBLE_PREC 53 #define MIN_PREC 20 #define PI 3.141592653589793238462643 #define INV_LOG2 (1.44269504088896340735992468 + 1e-12) #define HRR_A (1.1143183348516376904 + 1e-12) /* 44*pi^2/(225*sqrt(3)) */ #define HRR_B (0.0592384391754448833 + 1e-12) /* pi*sqrt(2)/75 */ #define HRR_C (2.5650996603237281911 + 1e-12) /* pi*sqrt(2/3) */ #define HRR_D (1.2424533248940001551 + 1e-12) /* log(2) + log(3)/2 */ static double partitions_remainder_bound(double n, double terms) { return HRR_A/sqrt(terms) + HRR_B*sqrt(terms/(n-1)) * sinh(HRR_C * sqrt(n)/terms); } /* Crude upper bound, sufficient to estimate the precision */ static double log_sinh(double x) { if (x > 4) return x; else return log(x) + x*x*(1/6.); } static double partitions_remainder_bound_log2(double n, double N) { double t1, t2; t1 = log(HRR_A) - 0.5*log(N); t2 = log(HRR_B) + 0.5*(log(N) - log(n-1)) + log_sinh(HRR_C * sqrt(n)/N); return (FLINT_MAX(t1, t2) + 1) * INV_LOG2; } slong partitions_hrr_needed_terms(double n) { slong N; for (N = 1; partitions_remainder_bound_log2(n, N) > 10; N++); for ( ; partitions_remainder_bound(n, N) > 0.4; N++); return N; } static double partitions_term_bound(double n, double k) { return ((PI*sqrt(24*n-1) / (6.0*k)) + HRR_D - log(24.0*n-1) + 0.5*log(k)) * INV_LOG2; } /* Bound number of prime factors in k */ static mp_limb_t primorial_tab[] = { 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, #if FLINT64 UWORD(6469693230), UWORD(200560490130), UWORD(7420738134810), UWORD(304250263527210), UWORD(13082761331670030), UWORD(614889782588491410) #endif }; static __inline__ int bound_primes(ulong k) { int i; for (i = 0; i < sizeof(primorial_tab) / sizeof(mp_limb_t); i++) if (k <= primorial_tab[i]) return i; return i; } static __inline__ long log2_ceil(double x) { /* ceil(log2(n)) = bitcount(n-1); this is too large if x is a power of two */ return FLINT_BIT_COUNT((slong) x); } static slong partitions_prec_bound(double n, slong k, slong N) { slong prec; prec = partitions_term_bound(n, k); prec += log2_ceil(8 * N * (26 * (sqrt(n) / k) + 7 * bound_primes(k) + 22)); return prec; } static double cos_pi_pq(mp_limb_signed_t p, mp_limb_signed_t q) { /* Force 0 <= p < q */ p = FLINT_ABS(p); p %= (2 * q); if (p >= q) p = 2 * q - p; if (4 * p <= q) return cos(p * PI / q); else if (4 * p < 3 * q) return sin((q - 2*p) * PI / (2 * q)); else return -cos((q - p) * PI / q); } static double eval_trig_prod_d(trig_prod_t prod) { int i; double s; mp_limb_t v; if (prod->prefactor == 0) return 0.0; s = prod->prefactor; v = n_gcd(FLINT_MAX(prod->sqrt_p, prod->sqrt_q), FLINT_MIN(prod->sqrt_p, prod->sqrt_q)); prod->sqrt_p /= v; prod->sqrt_q /= v; if (prod->sqrt_p != 1) s *= sqrt(prod->sqrt_p); if (prod->sqrt_q != 1) s /= sqrt(prod->sqrt_q); for (i = 0; i < prod->n; i++) s *= cos_pi_pq(prod->cos_p[i], prod->cos_q[i]); return s; } static void eval_trig_prod(arb_t sum, trig_prod_t prod, slong prec) { int i; mp_limb_t v; arb_t t; if (prod->prefactor == 0) { arb_zero(sum); return; } arb_init(t); arb_set_si(sum, prod->prefactor); v = n_gcd(FLINT_MAX(prod->sqrt_p, prod->sqrt_q), FLINT_MIN(prod->sqrt_p, prod->sqrt_q)); prod->sqrt_p /= v; prod->sqrt_q /= v; if (prod->sqrt_p != 1) { arb_sqrt_ui(t, prod->sqrt_p, prec); arb_mul(sum, sum, t, prec); } if (prod->sqrt_q != 1) { arb_rsqrt_ui(t, prod->sqrt_q, prec); arb_mul(sum, sum, t, prec); } for (i = 0; i < prod->n; i++) { fmpq_t pq; *fmpq_numref(pq) = prod->cos_p[i]; *fmpq_denref(pq) = prod->cos_q[i]; arb_cos_pi_fmpq(t, pq, prec); arb_mul(sum, sum, t, prec); } arb_clear(t); } static void sinh_cosh_divk_precomp(arb_t sh, arb_t ch, arb_t ex, slong k, slong prec) { arb_t t; arb_init(t); arb_set_round(t, ex, prec); arb_root_ui(ch, t, k, prec); /* The second term doesn't need full precision, but this doesn't affect performance that much... */ arb_inv(t, ch, prec); arb_sub(sh, ch, t, prec); arb_add(ch, ch, t, prec); arb_mul_2exp_si(ch, ch, -1); arb_mul_2exp_si(sh, sh, -1); arb_clear(t); } void partitions_hrr_sum_arb(arb_t x, const fmpz_t n, slong N0, slong N, int use_doubles) { trig_prod_t prod; arb_t acc, C, t1, t2, t3, t4, exp1; fmpz_t n24; slong k, prec, res_prec, acc_prec, guard_bits; double nd, Cd; if (fmpz_cmp_ui(n, 2) <= 0) { abort(); } nd = fmpz_get_d(n); /* compute initial precision */ guard_bits = 2 * FLINT_BIT_COUNT(N) + 32; prec = partitions_remainder_bound_log2(nd, N0) + guard_bits; prec = FLINT_MAX(prec, DOUBLE_PREC); res_prec = acc_prec = prec; arb_init(acc); arb_init(C); arb_init(t1); arb_init(t2); arb_init(t3); arb_init(t4); arb_init(exp1); fmpz_init(n24); arb_zero(x); /* n24 = 24n - 1 */ fmpz_set(n24, n); fmpz_mul_ui(n24, n24, 24); fmpz_sub_ui(n24, n24, 1); /* C = (pi/6) sqrt(24n-1) */ arb_const_pi(t1, prec); arb_sqrt_fmpz(t2, n24, prec); arb_mul(t1, t1, t2, prec); arb_div_ui(C, t1, 6, prec); /* exp1 = exp(C) */ arb_exp(exp1, C, prec); Cd = PI * sqrt(24*nd-1) / 6; for (k = N0; k <= N; k++) { trig_prod_init(prod); arith_hrr_expsum_factored(prod, k, fmpz_fdiv_ui(n, k)); if (prod->prefactor != 0) { if (prec > MIN_PREC) prec = partitions_prec_bound(nd, k, N); prod->prefactor *= 4; prod->sqrt_p *= 3; prod->sqrt_q *= k; if (prec > DOUBLE_CUTOFF || !use_doubles) { /* Compute A_k(n) * sqrt(3/k) * 4 / (24*n-1) */ eval_trig_prod(t1, prod, prec); arb_div_fmpz(t1, t1, n24, prec); /* Multiply by (cosh(z) - sinh(z)/z) where z = C / k */ arb_set_round(t2, C, prec); arb_div_ui(t2, t2, k, prec); if (k < 35 && prec > 1000) sinh_cosh_divk_precomp(t3, t4, exp1, k, prec); else arb_sinh_cosh(t3, t4, t2, prec); arb_div(t3, t3, t2, prec); arb_sub(t2, t4, t3, prec); arb_mul(t1, t1, t2, prec); } else { double xx, zz, xxerr; xx = eval_trig_prod_d(prod) / (24*nd - 1); zz = Cd / k; xx = xx * (cosh(zz) - sinh(zz) / zz); xxerr = fabs(xx) * DOUBLE_ERR + DOUBLE_ERR; arf_set_d(arb_midref(t1), xx); mag_set_d(arb_radref(t1), xxerr); } /* Add to accumulator */ arb_add(acc, acc, t1, acc_prec); if (acc_prec > 2 * prec + 32) { arb_add(x, x, acc, res_prec); arb_zero(acc); acc_prec = prec + 32; } } } arb_add(x, x, acc, res_prec); fmpz_clear(n24); arb_clear(acc); arb_clear(exp1); arb_clear(C); arb_clear(t1); arb_clear(t2); arb_clear(t3); arb_clear(t4); } arb-2.8.1/partitions/rademacher_bound.c000066400000000000000000000050241264125401100201050ustar00rootroot00000000000000/*============================================================================= This file is part of ARB. ARB is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. ARB is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with ARB; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2013 Fredrik Johansson ******************************************************************************/ #include "partitions.h" static void _arf_sinh(arf_t y, const arf_t x, slong prec) { arb_t t; arb_init(t); arb_set_arf(t, x); arb_sinh(t, t, prec); arb_get_abs_ubound_arf(y, t, prec); arb_clear(t); } /* Equation (1.8) in the paper */ void partitions_rademacher_bound(arf_t b, const fmpz_t n, ulong N) { arf_t A, B, C, t, u; fmpz_t n1; arf_init(A); arf_init(B); arf_init(C); arf_init(t); arf_init(u); fmpz_init(n1); /* bound for 44*pi^2/(225*sqrt(3)) */ arf_set_si_2exp_si(A, 18695160, -24); /* bound for pi*sqrt(2)/75 */ arf_set_si_2exp_si(B, 993857, -24); /* bound for pi*sqrt(2/3) */ arf_set_si_2exp_si(C, 43035232, -24); /* first term: A / sqrt(N) */ arf_sqrt_ui(t, N, MAG_BITS, ARF_RND_DOWN); arf_div(b, A, t, MAG_BITS, ARF_RND_UP); /* B * sqrt(N/(n-1)) */ arf_set_ui(t, N); fmpz_sub_ui(n1, n, 1); arf_div_fmpz(t, t, n1, MAG_BITS, ARF_RND_UP); arf_sqrt(t, t, MAG_BITS, ARF_RND_UP); arf_mul(t, B, t, MAG_BITS, ARF_RND_UP); /* sinh(C*sqrt(n)/N) */ arf_sqrt_fmpz(u, n, MAG_BITS, ARF_RND_UP); arf_div_ui(u, u, N, MAG_BITS, ARF_RND_UP); arf_mul(u, C, u, MAG_BITS, ARF_RND_UP); _arf_sinh(u, u, MAG_BITS); /* second term: B * ... * sinh... */ arf_mul(t, t, u, MAG_BITS, ARF_RND_UP); arf_add(b, b, t, MAG_BITS, ARF_RND_UP); arf_clear(A); arf_clear(B); arf_clear(C); arf_clear(t); arf_clear(u); fmpz_clear(n1); } arb-2.8.1/partitions/test/000077500000000000000000000000001264125401100154355ustar00rootroot00000000000000arb-2.8.1/partitions/test/t-partitions_fmpz_ui.c000066400000000000000000000102731264125401100217720ustar00rootroot00000000000000/*============================================================================= This file is part of FLINT. FLINT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. FLINT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "partitions.h" /* Values mod 10^9 generated with Sage */ static const ulong testdata[][2] = { {100000, 421098519}, {100001, 33940350}, {100002, 579731933}, {100003, 625213730}, {100004, 539454200}, {100005, 69672418}, {100006, 865684292}, {100007, 641916724}, {100008, 36737908}, {100009, 293498270}, {100010, 177812057}, {100011, 756857293}, {100012, 950821113}, {100013, 824882014}, {100014, 533894560}, {100015, 660734788}, {100016, 835912257}, {100017, 302982816}, {100018, 468609888}, {100019, 221646940}, {1000000, 104673818}, {1000001, 980212296}, {1000002, 709795681}, {1000003, 530913758}, {1000004, 955452980}, {1000005, 384388683}, {1000006, 138665072}, {1000007, 144832602}, {1000008, 182646067}, {1000009, 659145045}, {1000010, 17911162}, {1000011, 606326324}, {1000012, 99495156}, {1000013, 314860251}, {1000014, 497563335}, {1000015, 726842109}, {1000016, 301469541}, {1000017, 227491620}, {1000018, 704160927}, {1000019, 995311980}, {10000000, 677288980}, {10000001, 433805210}, {10000002, 365406948}, {10000003, 120899894}, {10000004, 272822040}, {10000005, 71938624}, {10000006, 637670808}, {10000007, 766947591}, {10000008, 980210244}, {10000009, 965734705}, {10000010, 187411691}, {10000011, 485652153}, {10000012, 825498761}, {10000013, 895802660}, {10000014, 152775845}, {10000015, 791493402}, {10000016, 299640598}, {10000017, 383615481}, {10000018, 378922331}, {10000019, 37059200}, {100000000, 836637702}, {100000001, 66421565}, {100000002, 747849093}, {100000003, 465329748}, {100000004, 166747980}, {0, 0}, }; #define NUM 5000 int main(void) { flint_rand_t state; slong i; flint_printf("partitions_fmpz_ui...."); fflush(stdout); flint_randinit(state); { fmpz_t p; fmpz * v; fmpz_init(p); v = _fmpz_vec_init(NUM); arith_number_of_partitions_vec(v, NUM); for (i = 0; i < NUM; i++) { partitions_fmpz_ui(p, i); if (!fmpz_equal(p, v + i)) { flint_printf("FAIL:\n"); flint_printf("p(%wd) does not agree with power series\n", i); flint_printf("Computed p(%wd): ", i); fmpz_print(p); flint_printf("\n"); flint_printf("Expected: "); fmpz_print(v + i); flint_printf("\n"); abort(); } } _fmpz_vec_clear(v, NUM); for (i = 0; testdata[i][0] != 0; i++) { partitions_fmpz_ui(p, testdata[i][0]); if (fmpz_fdiv_ui(p, 1000000000) != testdata[i][1]) { flint_printf("FAIL:\n"); flint_printf("p(%wd) does not agree with known value mod 10^9\n", testdata[i][0]); flint_printf("Computed: %wu\n", fmpz_fdiv_ui(p, 1000000000)); flint_printf("Expected: %wu\n", testdata[i][1]); abort(); } } fmpz_clear(p); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/partitions/test/t-partitions_fmpz_ui_threaded.c000066400000000000000000000104531264125401100236320ustar00rootroot00000000000000/*============================================================================= This file is part of FLINT. FLINT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. FLINT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011-2014 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "partitions.h" /* Values mod 10^9 */ static const ulong testdata[][2] = { {100000, 421098519}, {100001, 33940350}, {100002, 579731933}, {100003, 625213730}, {100004, 539454200}, {100005, 69672418}, {100006, 865684292}, {100007, 641916724}, {100008, 36737908}, {100009, 293498270}, {100010, 177812057}, {100011, 756857293}, {100012, 950821113}, {100013, 824882014}, {100014, 533894560}, {100015, 660734788}, {100016, 835912257}, {100017, 302982816}, {100018, 468609888}, {100019, 221646940}, {1000000, 104673818}, {1000001, 980212296}, {1000002, 709795681}, {1000003, 530913758}, {1000004, 955452980}, {1000005, 384388683}, {1000006, 138665072}, {1000007, 144832602}, {1000008, 182646067}, {1000009, 659145045}, {1000010, 17911162}, {1000011, 606326324}, {1000012, 99495156}, {1000013, 314860251}, {1000014, 497563335}, {1000015, 726842109}, {1000016, 301469541}, {1000017, 227491620}, {1000018, 704160927}, {1000019, 995311980}, {10000000, 677288980}, {10000001, 433805210}, {10000002, 365406948}, {10000003, 120899894}, {10000004, 272822040}, {10000005, 71938624}, {10000006, 637670808}, {10000007, 766947591}, {10000008, 980210244}, {10000009, 965734705}, {10000010, 187411691}, {10000011, 485652153}, {10000012, 825498761}, {10000013, 895802660}, {10000014, 152775845}, {10000015, 791493402}, {10000016, 299640598}, {10000017, 383615481}, {10000018, 378922331}, {10000019, 37059200}, {100000000, 836637702}, {100000001, 66421565}, {100000002, 747849093}, {100000003, 465329748}, {100000004, 166747980}, {500000000, 143535392}, {1000000000, 685688339}, {UWORD(4000000000), 525944299}, {0, 0}, }; #define NUM 5000 int main(void) { flint_rand_t state; slong i; flint_printf("partitions_fmpz_ui_threaded...."); fflush(stdout); flint_randinit(state); flint_set_num_threads(2); { fmpz_t p; fmpz * v; fmpz_init(p); v = _fmpz_vec_init(NUM); arith_number_of_partitions_vec(v, NUM); for (i = 0; i < NUM; i++) { partitions_fmpz_ui(p, i); if (!fmpz_equal(p, v + i)) { flint_printf("FAIL:\n"); flint_printf("p(%wd) does not agree with power series\n", i); flint_printf("Computed p(%wd): ", i); fmpz_print(p); flint_printf("\n"); flint_printf("Expected: "); fmpz_print(v + i); flint_printf("\n"); abort(); } } _fmpz_vec_clear(v, NUM); for (i = 0; testdata[i][0] != 0; i++) { partitions_fmpz_ui(p, testdata[i][0]); if (fmpz_fdiv_ui(p, 1000000000) != testdata[i][1]) { flint_printf("FAIL:\n"); flint_printf("p(%wd) does not agree with known value mod 10^9\n", testdata[i][0]); flint_printf("Computed: %wu\n", fmpz_fdiv_ui(p, 1000000000)); flint_printf("Expected: %wu\n", testdata[i][1]); abort(); } } fmpz_clear(p); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; } arb-2.8.1/partitions/test/t-partitions_fmpz_ui_using_doubles.c000066400000000000000000000103451264125401100247140ustar00rootroot00000000000000/*============================================================================= This file is part of FLINT. FLINT is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. FLINT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with FLINT; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA =============================================================================*/ /****************************************************************************** Copyright (C) 2011 Fredrik Johansson ******************************************************************************/ #include "arith.h" #include "partitions.h" /* Values mod 10^9 generated with Sage */ static const ulong testdata[][2] = { {100000, 421098519}, {100001, 33940350}, {100002, 579731933}, {100003, 625213730}, {100004, 539454200}, {100005, 69672418}, {100006, 865684292}, {100007, 641916724}, {100008, 36737908}, {100009, 293498270}, {100010, 177812057}, {100011, 756857293}, {100012, 950821113}, {100013, 824882014}, {100014, 533894560}, {100015, 660734788}, {100016, 835912257}, {100017, 302982816}, {100018, 468609888}, {100019, 221646940}, {1000000, 104673818}, {1000001, 980212296}, {1000002, 709795681}, {1000003, 530913758}, {1000004, 955452980}, {1000005, 384388683}, {1000006, 138665072}, {1000007, 144832602}, {1000008, 182646067}, {1000009, 659145045}, {1000010, 17911162}, {1000011, 606326324}, {1000012, 99495156}, {1000013, 314860251}, {1000014, 497563335}, {1000015, 726842109}, {1000016, 301469541}, {1000017, 227491620}, {1000018, 704160927}, {1000019, 995311980}, {10000000, 677288980}, {10000001, 433805210}, {10000002, 365406948}, {10000003, 120899894}, {10000004, 272822040}, {10000005, 71938624}, {10000006, 637670808}, {10000007, 766947591}, {10000008, 980210244}, {10000009, 965734705}, {10000010, 187411691}, {10000011, 485652153}, {10000012, 825498761}, {10000013, 895802660}, {10000014, 152775845}, {10000015, 791493402}, {10000016, 299640598}, {10000017, 383615481}, {10000018, 378922331}, {10000019, 37059200}, {100000000, 836637702}, {100000001, 66421565}, {100000002, 747849093}, {100000003, 465329748}, {100000004, 166747980}, {0, 0}, }; #define NUM 5000 int main(void) { flint_rand_t state; slong i; flint_printf("partitions_fmpz_ui_using_doubles...."); fflush(stdout); flint_randinit(state); { fmpz_t p; fmpz * v; fmpz_init(p); v = _fmpz_vec_init(NUM); arith_number_of_partitions_vec(v, NUM); for (i = 0; i < NUM; i++) { partitions_fmpz_ui_using_doubles(p, i); if (!fmpz_equal(p, v + i)) { flint_printf("FAIL:\n"); flint_printf("p(%wd) does not agree with power series\n", i); flint_printf("Computed p(%wd): ", i); fmpz_print(p); flint_printf("\n"); flint_printf("Expected: "); fmpz_print(v + i); flint_printf("\n"); abort(); } } _fmpz_vec_clear(v, NUM); for (i = 0; testdata[i][0] != 0; i++) { partitions_fmpz_ui_using_doubles(p, testdata[i][0]); if (fmpz_fdiv_ui(p, 1000000000) != testdata[i][1]) { flint_printf("FAIL:\n"); flint_printf("p(%wd) does not agree with known value mod 10^9\n", testdata[i][0]); flint_printf("Computed: %wu\n", fmpz_fdiv_ui(p, 1000000000)); flint_printf("Expected: %wu\n", testdata[i][1]); abort(); } } fmpz_clear(p); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return 0; }