Math-BigInt-1.999808/0000705403072340010010000000000013035476253014341 5ustar ospjadomain usersMath-BigInt-1.999808/BUGS0000644403072340010010000000355213013420212015012 0ustar ospjadomain usersFor an updated list of bugs, see https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt The following list is not up to date: Known bugs: * TODO BUGS: + implement test for the upgrading bug in bsub() * NaN handling in comparisons slightly broken. See also [perl #33106]. * General: + BigInt can not the IEEE '-0'. Currently there are no plans to add this. If you need it, please bug the author(s) about it. * BigFloat: + comparing (<=> or == or !=) a BigFloat to a BigInt don't work yet + new is first running the entire number trough _split, then again the parts to construct BigInts. Could be a bit more optimized. + fdiv() using F (fallback) mode does not work properly in all cases of local (aka $x's or $y's) A or P settings. Not definite test case yet, but it might calculate not enough digits to satisfy the rounding needs. * BigInt: + exponent on input is limited to a Perl int (bigger numbers won't fit into your memory, anyway - use BigFloat) + doesn't have a mode akin to 'use integer;', e.g. it always emulates Perl (this is solved partially by use bigint ;) + Handling of undef arguments is somewhat broken (no proper warnings) + eval('use...') and use Math::BigInt qw/:constant/ fail on Perl prior 5.6.0 This is likely an Exporter bug, and causes Math::BigInt to eval require on earlier Perls when loading the core math lib. Thus the loading can fail under older Perls on filesystems that can not cope with the 'Math/BigInt/Calc.pm'-style filenames. ############################################################################### Mixing of classes does not always work like expected. "use bignum;", "use bigint;" and "use bigrat;" should solve this problem for most cases. Please send me test-reports, your experiences with this and your ideas - I love to hear about my work! Tels Math-BigInt-1.999808/CHANGES0000644403072340010010000024137713035464155015355 0ustar ospjadomain users2017-01-11 v1.999808 pjacklam * In Math::BigInt and Math::BigFloat, add methods bdfac() for double factorial. Add tests for this method. * In Math::BigInt and Math::BigFloat, add methods to_hex(), to_oct(), and to_bin() for hexadecimal, octal, and binary string output without prefix. Even for Math::BigFloat there is still only support for integer output. Add tests for these methods. * Add test for as_oct() corresponding to the old tests for as_hex() and as_bin(). * In Math::BigInt::Lib, add method _dfac() for double factorial. Add corresponding tests. * In Math::BigInt::Lib, fix bug in overloaded "int". * In Math::BigInt::Lib, implement much faster versions of _from_hex(), _from_oct(), and _from_bin(). * In Makefile.PL, improve the wording in the message displayed if some of the installed backend libraries are not a subclass of Math::BigInt::Lib (and hence will not provide * Fix minor bugs in some of the author library test files (t/author-lib*.t). * Allow leading and trailing whitespace in the input to from_hex(), from_oct(), and from_bin(). Add tests to verify. This is a regressions (CPAN RT #119805). 2016-12-23 v1.999807 pjacklam * Add a message to Makefile.PL recommending upgrade if old libraries are installed. This message is more or less equivalent to the one appearing in Math-BigInt up until v1.997. * Improve the documentation (POD) in Math::BigInt::Lib. * Speed up _sqrt() and _root() in Math::BigInt::Lib. * Remove checking for exception cases (cases that would return +Inf, -Inf, or NaN) in Math::BigInt::Lib. It has been documented for a long time that such checking should be done by the caller. * Add library methods _to_bin(), _to_oct(), _to_hex(), which are equivalent to the _as_bin(), _as_oct(), and _as_hex() methods respectively, except that the _to_*() methods don't use a prefix in the output. This removes the need for the frequent removal of the various prefixes. Now each _as_*() method calls the equivalent _to_*() method, adds a prefix, and returns the output. The _to_*() methods are faster than the equivalent _as_*() methods were. * Add author test files for the methods _to_bin(), _to_oct(), and _to_hex(). * Add library method _to_bytes(). The method _as_bytes() would have been called _to_bytes() if I had thought of it earlier. The method _as_bytes() is now just an alias to _to_bytes(). The _to_bytes() method also fixes a bug that was present in the _as_bytes() method. (CPAN RT #119346). * Add author test files for the method _to_bytes(). * Add more tests for library methods _inc() and _dec(). When trying to bring the Math::BigInt::BitVect library back to life I realized that the test suite didn't catch certain errors in _inc() and _dec(). * Die if trying to use as_bytes() or from_bytes() with a backend library that doesn't support the corresponding library methods. * Correct minor errors in the output messages in the test files. * Improve/correct various comments in the source code. * More diagnostic output is displayed by the author test files if the AUTHOR_DEBUGGING environment variable is set. 2016-12-13 v1.999806 pjacklam * Add more logic to Makefile.PL regarding INSTALLDIRS (CPAN RT #119199 and #119225). * In the TODO file, remove stuff that has been implemented. 2016-12-11 v1.999805 pjacklam * Fix Makefile.PL so that this module installs over the core version. * Add more tests for _nok() (binomial coefficient "n over k"). These new tests revealed some problems with some of the backend libraries when _nok() was given very large arguments. * Remove t/Math/BigFloat/#Subclass.pm#, which is an Emacs temporary file included by accident. 2016-12-07 v1.999804 pjacklam * Implement as_bytes(), as requested (CPAN RT 119096). Also implement the inverse conversion from_bytes(). This applies to Math::BigInt only. (Alas, these methods will be inherited from Math::BigInt into Math::BigFloat, Math::BigRat etc. where the methods won't work. Fixing this class relationship is an issue of its own.) * Implement _as_bytes() and _from_bytes() in Math::BigInt::Lib. Preferably, the various backend libraries will implement faster versions of their own. Add author test files for testing these methods thorougly. * Fix from_hex(), from_oct(), and from_bin(). - When called as instance methods, the new value should be assigned to the invocand unless the invocand is read-only (a constant). - When called as instance methods, the assigned value was incorrect, if the invocand was inf or NaN. - Add tests to t/from_hex-mbf.t, t/from_oct-mbf.t, and t/from_bin-mbf.t to confirm the fix. - Add new test files t/from_hex-mbi.t, t/from_oct-mbi.t, and t/from_bin-mbi.t for better testing of these methods with Math::BigInt. * Correct typo in Math/BigInt/Lib.pm (otherise -> otherwise) (CPAN RT 118829). * Add POD coverage testing of Math::BigInt::Lib to t/03podcov.t. 2016-12-03 v1.999803 pjacklam * Remove BENCHMARK file. The information was obsolete. * Use ExtUtils::MakeMaker rather than Module::Install in Makefile.PL * Reorder CHANGES file (this file) so the newest entries appear at the top. * Fix error in test information text in various author test files. * Remove author information in LICENSE file. * Inform that the TODO file is not up to date. 2016-11-28 v1.999802 pjacklam * When bzero(), bone(), binf(), and bnan() are used as constructors, don't check whether the class allows the object to be modified. A constructor isn't modifying any existing object. This applies to both Math::BigInt and Math::BigFloat. * Improve bgcd() and blcm(). This applies to both Math::BigInt and Math::BigFloat. 2016-11-23 v1.999801 pjacklam * Fix, hopefully once and for all, the longstanding problem of handling undef as an operand to mathematical methods. The only method that accepts undef as an operand is blog(), where the second operand might be undef, as in $x->blog() or $x->blog($b), where $b is undef. The undef signifies that Euler's number should be used as the base. With this fix, we should be able to get Math::BigInt::Lite working again. * Add least common multiple method _lcm() to Math::BigInt::Lib, and add corresponding test file t/author-lib-arithmetic-binary-_lcm.t and test data file t/author-lib-arithmetic-binary-_lcm.dat. * Remove internal function __lcm() which has become redundant now that _lcm() is in the library. * Make it possible to use bgcd() and blcm() as class methods, since other methods can be used as class methods. This applies to both Math::BigInt and Math::BigFloat. * Fix blcm() with negative input. The LCM should always be non-negative. This applies to both Math::BigInt and Math::BigFloat. * Add tests for bgcd() and blcm() in t/bigintpm.t and t/bigfltpm.t. * Fix tests for blcm() assuming that LCM(0,0) should be a NaN. LCM(0,0) is 0 by convention. * Prefer Class->config('option') over Class->config()->{option}. However, this does not seem to be working for all options. It seems that this won't work properly until we move the global variables into the OO interface. * Explicitly specify the library in all test files that are shared between Math-BigInt and the library distributions (FaatCalc, GMP, Pari, ...) with, e.g., "use Math::BigInt only => 'Calc';". This way, it will fail immediately if the specified library can't be loaded rather than using the fallback library. 2016-11-15 v1.999800 pjacklam * Upgrade bundled Module::Install from version 1.16 to version 1.17. * Add Math::BigInt::Lib (lib/Math/BigInt/Lib.pm), a parent class for Math::BigInt backend libraries. * Use objects in Math::BigInt::Calc, not just array refs. Also use OO-style, i.e., use $class->_add($x, $y) rather than _add($class, $x, $y). * Not all library methods modify the invocand, so call library methods as, e.g, $x = $LIB->method($x, $y) rather than just $LIB->method($x, $y). * Math::BigInt::Calc is now a subclass of Math::BigInt::Lib. * Add Math::BigInt::Lib::Minimal (t/Math/BigInt/Lib/Minimal.pm) for testing inheritance from Math::BigInt::Lib. * Minor simplification in Math::BigInt::Calc->_str(). * Speed up Math::BigInt::Calc->_root(). * Remove test files that were included in the previous release by accident. * Add more tests and use more verbose output in some tests. * Fix typo in lib/Math/BigFloat.pm * Fix documentation error in lib/Math/Calc.pm * Use Config::Tiny and an .ini file to handle the library specific configuration for the author-lib*.t test files. 2016-11-04 v1.999727 pjacklam * Skip test exceeding the range of VAX floating point number in t/bigintpm.inc (CPAN RT 118468). * Fix typo in lib/Math/BigInt.pm (CPAN RT 118550). 2016-07-15 v1.999726 pjacklam * Re-insert Math::BigFloat->DESTROY, which was accidentally removed in v1.999725. 2016-07-13 v1.999725 pjacklam Changes: * Add method is_finite(). * In Math::BigInt and Math::BigFloat, remove warnings about deprecated usage, at least until we have removed this usage from the "bignum" distribution. These warnings were too annoying for some people. Improvements: * Faster bnok() when the library (backend) does not support it. * In the Math::BigFloat method bpi(), use a precomputed list of digits when the accuracy is <= 1000. This speeds up the trigonometric functions considerably, when I will introduce range reduction in a later release. This makes the _atan_inv() method redundant, so remove it. Also, the _alen() library method is now only used in _log_int(), which is good, because it isn't clear from the docs and tests what it was supposed to do. Fixes: * Fix bug in the Math::BigInt::Calc library method _digit(). It would sometimes return undef or an empty string when it should have returned zero. * Fix bug in the Math::BigInt::Calc library method _rsft(). It would sometimes return two output arguments. * Fix bug in the Math::BigInt::Calc library method _lsft(). When the number zero was shifted N places in base 10, the result was not zero, but an invalid object. * Fix bug in the Math::BigInt::Calc library methods _and(), _or(), and _xor(). They always assigned zero to the first input argument (the invocand). * Improve the Math::BigInt::Calc library method _log_int() for the cases when the output is zero or one. Also simplify the code. * Simplify the code for the Math::BigInt::Calc library method _zeros(). * Reformat Math::BigInt::Calc so it is easier to read, for me anyway. * Add file t/author-bnok-mbi.t * Add one test file for every method in the libraries, including t/Math/BigInt/Lib/TestUtil.pm with test utilities. * Clean up whitespace in all files in the distribution. * Better testing in t/author-bpi-mbf.t * The Math::BigInt::Calc library now always uses integers inside the objects, so there is no longer any need for all the "0 + ..." to convert strings to numbers, and the "int()" inside "length(int(...))" to determine the length of an array element. The only case that needs "0 + ..." now is the constructor _new(), whose input is a string. Note, however, that the Math::BigInt::FastCalc library method _new() still creates objects with leading zeros, so until that is fixed, we can't remove all the "0 + ..." etc. until Math::BigInt::FastCalc has been modified. 2016-06-19 v1.999724 pjacklam * In Math/BigInt.pm and Math/BigFloat.pm, correct and improve to the documentation, e.g., reorder the methods so that methods that belogin together are grouped together. * In Math/BigInt.pm and Math/BigFloat.pm, refactor the code so that methods that belong together are grouped together. Also use consistent code formatting. * In Math/BigInt/Calc.pm, reformat the code. 2016-06-09 v1.999723 pjacklam * Add Math::BigInt and Math::BigFloat methods bnstr(), bestr(), and bdstr(), as well as corresponding methods nparts(), eparts(), and dparts(). Also add test files bdstr-mbf.t, bdstr-mbi.t, bestr-mbf.t, bestr-mbi.t, bnstr-mbf.t, bnstr-mbi.t, bsstr-mbf.t, bsstr-mbi.t, dparts-mbf.t, dparts-mbi.t, eparts-mbf.t, eparts-mbi.t, nparts-mbf.t, nparts-mbi.t, sparts-mbf.t, and sparts-mbi.t. * Fix documentation errors. 2016-04-26 v1.999722 pjacklam * Fix bug in bone() and binf() when used as a function. The error caused warnings about using an unitialized variable. This fix applies to both Math::BigInt and Math::BigFloat. 2016-04-26 v1.999721 pjacklam * Prevent Math::BigFloat methods band(), bior(), bxor(), and bnot() from modifying unmodifiable objects. 2016-04-26 v1.999720 pjacklam * Overloaded 'int' should not modify it's argument. * Better documentation of blsft() and brsft(). 2016-04-25 v1.999719 pjacklam * Revert the change to Math::BigFloat's blsft() and brsft() methods, which truncated the input (and output) to integers. However, now convert the base to an object only when the base isn't an object already. Also return NaN if any of the three operands is a NaN. * Change t/bigfltpm.inc to reflect the changes to blsft() and brsft(). Also, when a method should be tested, actually test that method, not the overloaded operator, which doesn't necessarily behave in the exact same manner as the method. This applies to the methods binc(), bdec(), bpow(), badd(), bsub(), bmul(), bdiv() in scalar context, brsft(), blsft(), and bmod(). * The first output argument from objectify() is the class name, so use the variable name $class, not $self. 2016-04-22 v1.999718 pjacklam * Improve documentation on large, unquoted input values to Math::BigInt. * Remove stuff from bitfltpm.inc that was placed into author-numify-mbf.t, but accidentally still present in bitfltpm.inc. Adjusted test counts as needed. * Fix file headers in author-bmod-bdiv-mbi.t and author-btmod-btdiv-mbi.t. * Add bnan(), binf(), and bsub() methods to Math::BigFloat. This is a step along the way to having Math::BigFloat no longer being a subclass of Math::BigInt. * Using bnan, binf(), bzero() and bone() as functions is deprecated. This is a step along the way to a pure object oriented design. * When bnan() and binf() are used as instance methods, they no longer delete the accuracy and precision instance variables. * Add test files from_bin-mbf.t, from_oct-mbf.t, and new-mbf.t. * Remove some code for Perl prior to 5.6. Such old versions are no longer support anyway. * Fix buggy handling of NaN in bcmp(). * Add methods beq(), bne(), blt(), ble(), bgt(), and bge() to Math::BigInt and Math::BigFloat. These methods are called for the overloaded operators. * Add overloading of '==', '!=', '<', '<=', '>', to to Math::BigInt and Math::BigFloat and fix the broken overloading of '>='. These overloaded operators now behave like the equivalent core Perl operators. * Add test file author-relop-mbi-mbf.t for testing bcmp(), beq(), bne(), blt(), ble(), bgt(), and bge(), as well as the overloaded operators '==', '!=', '<', '<=', '>', and '>='. * 'int' now truncates a Math::BigFloat object to an integer without converting it to a Math::BigInt. When an object becomes a Math::BigInt, further computations with that object as invocand causes the arguments to be converted to Math::BigInt objects too, leading to unexpected results. This is confusing people. Unless downgrading is in effect, no Math::BigFloat object should become a Math::BigInt unless a Math::BigInt is explicitly requested. * For Math::BigFloat, modify bitwise operations brsft() and brsft(), and add band(), bior(), bxor(), and bnot(). These now handle floating point numbers the same way as core Perl does, i.e., truncate non-integers to integers before applying the bitwise operator. This change will also make Perl's behaviour more consistent whether 'use bignum' is in effect or not. * Add overloading of '~' (bitwise not). It just calls bnot(), which has been implemented for ages. * Fix error in POD for bone(). * Take parts of the code in t/calling.t and move it into the new files t/calling-class-methods.t and t/calling-instance-methods.t. * Improve test descriptions in t/mbimbf.inc. 2016-04-16 v1.999717 pjacklam * Using new() with an undefined argument no longer gives a warning. Explicit use of this is discouraged, but it is sometimes used by the modules themselves issuing warnings that is confusing to the end user. Just uncomment the code, since we plan to reintroduce this warning later. * Avoid using L<> around e-mail addressess in POD. 2016-04-03 v1.999716 pjacklam * $x->new(...) can no longer be used to assign a value to $x. This was a mistake introduced in v1.999712. As the name "new" implies, it should always return a new object. * Using new() with no argument no longer gives a warning. This use has been discouraged, in favour of bzero(), for many years, but people are still using it, so I am reintroducing the support for this. * Added btdiv() and btmod() for truncated division (T-division) and ditto remainder. Add tests. * Add test files author-bmod-bdiv-mbi.t author-btmod-btdiv-mbi.t with more thorough testing of bdiv(), bmod(), btdiv(), and btmod(). * When new() is used as an instance method, the new object is initialized as a copy of the invocand. * Move test for numfiy() of +Inf, -Inf, NaN, and big integers from bigfltpm.inc and bigintpm.inc into author-numify-mbi.t and author-numify-mbf.t. * Improved wording and fixed typos in earlier changelog entries. 2016-01-05 v1.999715 pjacklam * Fix Math::BigFloat->bexp() based on patch by DANAJ (Dana Jacobsen). * Add Math::BigFloat->bexp() tests to "t/biglog.t" and new file "t/author-bexp-mbf.t". * Fix flawed test in test_bpow. It used ok($x, $y) rather than is($x, $y). * Add better descriptions (test names) to a few tests. * Wrap long line in the CHANGES file. 2016-01-03 v1.999714 pjacklam * Add code to speed up Math::BigFloat->batan(). Thanks to DANAJ (Dana Jacobsen) for the patch. * Re-write Math::BigFloat->batan2() completely, except for the parts related to the rounding. The old version was sometimes correct, sometimes off by pi, and sometimes very inaccurate. Also add more tests. * Make it clearer in Math::BigFloat->bpi() when it is called as a method vs. as a function. * The Math::BigFloat->bpi() method can now be used as an instance method to assign pi to $x, as in $x->bpi(). * Add tests for as_oct(). * Minor simplifications in Math::BigInt->as_oct() and Math::BigInt::Calc::_as_oct(). 2015-12-31 v1.999713 pjacklam * Fix Math::BigInt->new(), which had a faulty handling in the shortcut for non-zero scalar integers with no non-zero exponent, like "12", "12.000", "12e3", and "12.000e4". Added tests for this in t/bigintpm.inc. 2015-12-29 v1.999712 pjacklam * Fix bug in internal function _e_add() and _e_sub() which causes it to return "-0" in some cases. * Let new() be used for assignment. Now $x->new(3) assigns 3 to $x. * Improve code in new() for non-zero scalar integers with no exponent. * Allow both "inf" and "infinity". Allow a leading sign, and ignore letter case. This is to be consistent with core Perl. * Be more consistent about allowed whitespace in input. E.g., "23 " gave 23, but "inf " gave a NaN. * Core Perl allows both "0x" and "0X" as hexadecimal prefix, and both "0b" and "0B" as binary prefix, so we do too. Previously, only 0x and 0b were allowed. * Math::BigFloat now has its own from_bin() method which supports binary floating point numbers, e.g., "0b1.1001p-4". This complements from_hex(). * Math::BigFloat now has its own from_oct() method which supports octal floating point numbers, e.g., "1.3267p-4". This complements from_hex(). * The Math::BigInt and Math::BigFloat methods from_hex(), from_oct(), and from_bin() can now be used as instance methods to assign values to the invocand, e.g, $x->from_oct("10") assigns 8 to $x. * Update documentation. Perl now uses "Inf", not "inf" to represent infinity. * When the new() method is called with an undefined argument, the round parameters are now passed on to bzero(). This applies to both Math::BigInt and Math::BigFloat. * Replace "UNIVERSAL::isa($this, $that)" with "$this->isa($that)", and ditto for "can()", where possible. Not every instance of "UNIVERSAL::Isa()" has been replaced, though, since the change causes some tests to fail. This must be looked into. * Simplify the copy() methods. Always copy accuracy and precision parameters, even when they are undefined. * Reformat more of the code in accordancw with the "perlstyle" manual page. This makes the code a lot easier to read -- for me, anyway. * Use a more generic regex in t/calling.t, since the exact wording of the error message depends not on the Perl version, but on the module that does the version checking. * Avoid infinite loop in the Math::BigFloat->batan() method. Thanks to DANAJ (Dana Jacobsen) for the patch. This was not intended to be added before the next release, but was included in this release by accident. 2015-11-12 v1.999710 pjacklam * New method Math::BigFloat -> from_hex() which supports hexadecimal floating point numbers, e.g., "0x1.999ap-4". * New test file t/from_hex-mbf.t for testing Math::BigFloat -> from_hex(). * Add 'from_hex' and 'from_bin' to list of methods in the Math::BigInt POD. 2015-11-06 v1.999709 pjacklam * Represent and return zero as 0E0, not 0E1. The old POD said "A zero is represented and returned as 0E1, not 0E0 (after Knuth)." I find no references to Knuth ever having said this. The closest reference I can find is that Knuth says 0**0 should be defined to be 1, not 0, but that is something else than 0e0, which is 0*10**0. I have yet to see any other mathematical software that represents and returns zero as 0e1 rather than 0e0. * Required version of Test::More is 0.9301. 2015-11-03 v1.999708 pjacklam * Use bxxx() method names consistently, rather than mixing bxxx() and fxxx() in code and test files. The fxxx() methods for Math::BigFloat objects are still available through autoloading. However, we leave the fround() method in Math::BigInt, as it seems to provide some kind of compatibility with Math::BigFloat. * Correct author information in the README file. * Remove INSTALL file, which by accident wasn't removed in v1.999707. * Use present tense, not past tense, in CHANGES file. * Add '#!perl' to Makefile.PL for correct syntax highlighting in editors supporting this. * Use Math::Complex::Inf() in testfiles also (for generating Perl scalar infinity) since it is more portable. 2015-10-29 v1.999707 pjacklam * Add dependency on Math::Complex 1.39 for Math::Complex::Inf(), which is used for numifying infinity. * Update author information. * Update information in the file README. * Remove the files INSTALL and LICENSE as this information is already covered in the file README. * Enable 'use warnings' in all modules. We require a Perl newer than 5.6.0 anyway. * Replace 'use vars ...' with 'our ...'. We require a Perl newer than 5.6.0 anyway. * Avoid indirect object syntax in documentation. * Moved 'Test::More' from 'build_requires' to 'test_requires' in Makefile.PL. 2015-10-28 v1.999706 pjacklam * Correct release date of v1.999705 in CHANGES. * Add code and tests for numify() on non-finite objects. 2015-10-26 v1.999705 pjacklam * Avoid using "my" in a false conditional. See "Deprecated use of my() in false conditional" in perldiag(1). * Faster algorithm for bpi() when accuracy is >= 1000. 2015-09-25 v1.999704 pjacklam * objectify() in lib/Math/BigInt.pm now uses 'isa' not 'eq' to check object relationship. This is necessary for correct handling of subclasses. * objectify() in lib/Math/BigInt.pm no longer expects as_int(), as_number() and as_float() to return objects, but allows them to return numbers formatted as strings. This is used by some other modules on CPAN. * Better documentation of as_int() and as_number() in lib/Math/BigInt.pm. * Add documentation for as_float() in lib/Math/BigFloat.pm * Add test files t/objectify_mbf.t and t/objectify_mbi.t. 2015-09-21 v1.999703 pjacklam * Fix blog() in Math::BigInt and Math::BigFloat to work correctly regardless of the base. * Correct existing tests in bigintpm.inc and bigfltpm.inc. * Update test plans (number of tests) in t/bare_mbi.t, t/bigintpm.t, and t/sub_mbi.t. * Add test files t/blog-mbf.t and t/blog-mbi.t for better testing of the blog() methods. 2015-09-17 v1.999702 pjacklam * The overloaded log() is a unary operator, so don't pass additional arguments. * Fix blog() so the cases $x->blog() and $x->blog(undef) work correctly. An undefined base means that blog() should use base e (Euler's number). * Both CORE::log() and other mathematical software returns inf for log(inf), so we do the same. * Add tests for log() as well as templates for future tests of the other overloadable functions. * Improve descriptions of a few tests. 2015-09-11 v1.999701 pjacklam * The POD documentation, as well as the comments in the code, said that $x->bdiv($y) in list context should return quotient $q and remainder $r so that $x = $q * $y + $r, and that the remainder (modulo) $r should correspond to Perl's % operator as well as the bmod() method. This has not been the actual behaviour. This is now fixed. In scalar context, only the quotient is returned. * Clearer POD documentation for the bdiv() and bmod() methods. * All non-integer input values to Math::BigInt gave a NaN, except non-zero numbers in the range (-1,1) that were written without an exponent, e.g., "-0.75" and "0.5". Now also these return a NaN. * Input values with a large (absolute value) negative exponent, e.g., 1e-9999999, now return NaN. The former behaviour was to die with the message "Quantifier in {,} bigger than 32766 in regex; marked by ..." * Intermediate computations in blog() increased the number of digits significantly in some cases. Now reduce the number of digits by rounding. However, keep some extra digits for remaining intermediate computations before the final rounding. * When $x is a Math::BigFloat, $x -> bceil() and $x -> bint() for -1 < $x < 0 returned -0. Negative zero is never used by Math::Big(Int|Float), and care has been taken to avoid it, so this bug is surely an oversight. * Explicitly specify the backend (lib => 'Calc') in t/mbimbf.t for easier release management of the backend distributions. * Add "use warnings" to test scripts, since Perl 5.6.2 is required anyway, and "use warnings" was introduced in Perl 5.6.1. * Modified test scripts so the difference between the test files in the Math-BigInt distribution and the backend distributions are as few and as small as possible. This makes for easier release management. 2015-08-12 v1.9997 pjacklam CHANGES * Add recent changes. t/bigintpm.inc * Correct spelling errors. t/upgrade.inc * Correct spelling errors. 2015-08-12 v1.9996 pjacklam CHANGES * Add recent changes. * Use present tense in change descriptions. lib/Math/BigInt.pm * Change incorrect use of ok() to is() in example. 2015-08-11 v1.9995 pjacklam CHANGES * Move changes that were incorrectly reported as being for the release 1.9994 when they were in fact for release 1.9993. * Add changes both for release 1.9994 and 1.9995. lib/Math/BigInt.pm * Break lines to avoid lines with more than 80 characters. * Improve objectify() for better handling of subclasses. 2015-08-10 v1.9994 pjacklam CHANGES * Add recent changes. lib/Math/BigFloat.pm * Fix blog() which sometimes returns incorrect result. * bdiv() in list context now returns the integer quotient and the remainder. t/bigfltpm.inc * Modify tests for blog() in list context. t/biglog.t * Change incorrect use of ok() to is(). t/upgrade.inc * Modify tests for blog() in list context. inc/Module/Install* * Upgrade bundled Module::Install from version 1.08 to version 1.16. 2014-04-03 v1.9993 pjacklam BUGS * Add reference to CPAN RT for the Math-BigInt distro. CHANGES * Add recent changes. examples/hailstone.pl * Remove this file as it doesn't seem to be working. lib/Math/BigFloat.pm * Correct spelling errors. * Reformat code to avoid long lines. * Improve POD formatting. * Add meta-documentation (CPAN ratings, CPAN testers matrix, etc.) * Add the bint() method. lib/Math/BigInt.pm * Correct spelling errors. * Reformat code to avoid long lines. * Improve POD formatting. * Add meta-documentation (CPAN ratings, CPAN testers matrix, etc.) * Add the bint() method. * Remove references to the obsolete Math::Big lib/Math/BigInt/Calc.pm * Correct spelling errors. * Added meta-documentation (CPAN ratings, CPAN testers matrix, etc.) lib/Math/BigInt/CalcEmu.pm * Correct spelling errors. * Improve POD formatting. * Add meta-documentation (CPAN ratings, CPAN testers matrix, etc.) * Remove references to Math::BigInt::BitVect, which is no longer on CPAN. Makefile.PL * Remove code that checks for compatible versions of distributions that depend on Math-BigInt. Such checking should be done in the distributions that depend on Math-BigInt, not in Math-BigInt itself. NEW * This file now only refers to the change log. t/bigfltpm.inc * Add tests for fint(). t/bigintpm.inc * Add tests for int(). t/upgrade.inc * Add tests for int(). t/*.t * Increment test counts as needed for the new tests in the t/*.inc files. inc/Module/Install* * Upgrade bundled Module::Install from version 1.01 to version 1.08. 2012-12-10 v1.9997_11 pjacklam This release introduces no changes in the library code, i.e., the .pm files in the 'lib' directory, but there are a lot of changes in the test files. Since there are so many changes, I let this be a development release. * Add 'use strict;' and 'use warnings;' to all test files. * Reformat code in the test files according to the "perlstyle" manual page. This makes the code a lot easier to read -- for me, anyway. * Decrement required version of Perl from v5.6.2 to v5.6.1. All tests pass when running the test suite with Perl 5.6.1 on Cygwin. * Replace "use vars ..." with "our ..." in test files. * Replace "BEGIN { unshift @INC, 't'; }" with "use lib 't';" in test files. * Use "our $x; $x = ...;" rather than "our $x = ...;" since the latter causes Perl 5.6.1 to complain about variables only used once. * Add comment to all tests. Now the tests no longer says just "ok 123", but rather "ok 123 - $x->blog(2)" etc. This makes it easier to identify failed tests, especially in the smoke testing reports. * Fix various flawed tests, e.g., ok($x, 2) was used testing whether $x was 2. * Use the skip() feature of Test::More for skipping tests. * Use more descriptive variable names in test files. * Remove unused variables in test files. * Move variable declarations to limit their scope in test files. * Remove trailing whitespace in test files. * Wrap (most) lines to fit 80 columns in test files. 2011-09-04 v1.997 pjacklam * Document actual behaviour of from_xxx() methods. [perl #85334] (Peter John Acklam) * Make bmuladd() able to handle third arg properly. [perl #85482] (Peter John Acklam) * Add sign function bsgn() as a complement to babs(). (Peter John Acklam) * Fix objectify()'s handling of "foreign objects". (RT #16221 and #52124) (Peter John Acklam) * Rewrap some verbatim pod in Math::BigInt. (Father Chrysostomos) * Correct links to sections. (Alexandr Ciornii) * Remove incorrect formatting inside verbatim paragraphs. (Alexandr Ciornii) * Upgrade bundled modules in "inc" to latest version. (Peter John Acklam) * Include "^MYMETA\.(yml|json)\z" in MANIFEST.SKIP. Whereas META.* are generated by the distribution author at packaging time, MYMETA.* are generated by the end user at configure time after any dynamic dependencies are known. (Peter John Acklam) 2011-02-26 v1.993 pjacklam * Change default backend library from Math::BigInt::FastCalc to Math::BigInt::Calc, which is included in the Math-BigInt distro. This avoids recursive distribution dependency (RT #65976) (Peter John Acklam). 2011-02-18 v1.992 pjacklam * Math::BigInt::Calc->_nok(): Use symmetry property nok(n,k) = nok(n,n-k) to speed up execution when k is large. Also general code cleanup. (Peter John Acklam). * Math::BigInt::Calc->_gcd(): Speed up by reducing amount of data copying (Peter John Acklam). * Add '01load.t' for basic module loading and diagnostics useful for debugging. Rename '00-signature.t' to '00sig.t', 'pod.t' to '02pod.t', and 'pod_cov.t' to '03podcov.t' (Peter John Acklam). * Math::BigInt:: Make from_hex(), from_oct(), and behave more like hex() and oct() in the Perl core, and make from_bin() consistent with from_hex() and from_oct() (this is related to RT #58954) (Peter John Acklam). * Math::BigInt::Calc->_rem(): Modify first input arg always, not just sometimes (Peter John Acklam). * Math::BigInt::Calc->_modinv(): be more consistent with the _modinv() method in other libraries (Math::BigInt::GMP, etc.) (Peter John Acklam) * Math::BigInt::Calc->_nok(): use symmetry property nok(n,k) = nok(n,n-k). This cuts computation time tremendously when n and k are large (Peter John Acklam). * Math::BigInt::Calc->_gcd(): quickly handle zero cases, avoid code duplication, and always modify the first input argument in-place (Peter John Acklam). * Clean up code and add more code comments (Peter John Acklam). * Fix typos (Peter John Acklam). 2011-02-05 v1.991 pjacklam * Add workaround for library inconsistencies (Math::BigInt::Calc vs. Math::BigInt::GMP). This makes older versions of Math::BigInt::GMP work with latest version of Math::BigInt (Peter John Acklam). * Correct and extend API documentation (Peter John Acklam). 2011-01-29 v1.99_05 pjacklam * Fix typos (reminder -> remainder etc.) (Peter John Acklam) * Fix Math::BigInt::Calc::_num returning NaN, not Inf, when it overflowed (Peter John Acklam) (Closes: RT #25274). * Fix Math::BigFloat->bcmp() so it can handle arbitrarily large exponents (Peter John Acklam) (Closes: RT #62764). * Fix bmodpow() in Math::BigInt 1.99 mis-calculating powers of one (Peter John Acklam) (Closes: RT #63237). * Fix bmodpow() and bmodinv() in Math::BigInt to handle negative input (Peter John Acklam) (Closes: RT #61543) * Clean up whitespace (Nicholas Clark). * Added file t/00-signature.t for testing SIGNATURE (Peter John Acklam). Complete version history of the rewrite project =============================================== If you just want to see which things are new and different from the original Math::* in the Perl core, see HISTORY. ############################################################################## Math::BigInt::Calc: 2007-09-16 v0.52 Tels * fix 64bit ints on Perl v5.8.0 (thanx zefram) 2007-05-30 v0.51 Tels * use CORE::hex() instead of hex() to help bigint/bignum/bigrat * use 9 digit parts on 64bit integer or long double systems 2007-05-05 v0.50 Tels * speed up _mul() by "use integer;" * we do not need to remove zeros after mul() * implement an alternative algorithm for _fac() 2007-04-16 v0.49 Tels * API version 2.0 support: add _1ex(), _alen() * make _fac() about twice as fast 2007-01-27 v0.48 Tels * support for octal numbers 2005-05-17 v0.47 Tels * remove shortcut in div(), it wasn't working properly 2005-03-29 v0.46 Tels * avoid crash in FastCalc by making $BASE and $BASE_LEN use vars qw//; 2005-03-20 v0.45 Tels * fix the div() shortcut for short numbers to actually work 2005-01-01 v0.44 Tels * small cleanups * shortcut for numbers of same length in _div, where X > Y 2004-10-10 v0.42 Tels * fix critical bug in _from_hex() with parts that were to big for one part (introduced in v1.72, thanx Mark Lakata for finding it!) 2004-07-30 v0.41 Tels * from_hex() convert 28 bits (vs 16) at a time, faster (helps from_bin(), too) * potential bug in padding with '0' in _digit() * fixed undef warnings in fceil(0.222222222222...) (thanx kenny!) 2004-04-05 v0.41a Tels (not released) * removed the unused integer-detection code and combined the two BEGIN blocks 2004-03-12 v0.40 Tels * added: api_version(), _ten(), _two(), _is_ten(), _is_two(), _gcd() * streamlined: is_foo() methods * _new() takes scalar, not scalar ref * _str() returns scalar, not scalar ref * _and(): bugfix for [perl #26559]: negative arguments that are shorter than the positive one caused an error due to cutting instead padding * _ior(): forgot to calculate the proper sing of result, making, for instance, 30 | -4 go wrong 2004-01-25 v0.39 Tels (not released) * _zeros(0) is 0, not 1 2003-12-30 v0.38 Tels * guess _log_int() result based on $base if $base < $BASE * _pow() handle cases 0 ** Y, 1 ** Y, X ** 0 and X ** 1 * _new(): shortcut for short numbers, makes MBI->new() about 20% faster * _root() was wrong for numbers like 9 (0b1001) because they start with the pattern /^0b1(0+)/ (missing '$' in regexp) and after fixing this it was dead slow for large numbers. 2003-12-11 v0.37 Tels * implemented _log_int() with a simple and fast "iterative" method * fixed bug in _root(): int() rounds sometimes wrong, so use sprintf() * _as_bin() and _as_hex() are faster (for small values) due to inlining is_zero() * _acmp() is about 26% faster for very small numbers or numbers that differ in length, and slightly faster for bigger numbers. This helps both bacmp() and bcmp() * _fac() did: + not modify $x in place for small arguments + something strange for large arguments + not handle 0..2 optimal (code now simplified) * _as_bin() used %b, which was not known to v5.5.3 - workaround that * implemented _log_int(), which is simple and very fast * implemented the missing pieces for _root() (which is quite fast) 2003-08-31 v0.36 Tels * fixed a bug in div_use_div() that computed remainder wrong if X == X and X was very large * fixed a off-by-one error discovered with mbi_rand.t in _div_use_XXX() (one internal in $x overflowed, thus the wrong computation) 2003-07-06 v0.35 Tels * fixed a bug in _floor() which caused ffloor(0.1234567) to fail. (Thanx to cpan@ali.as for finding it and sending a fix/testcases) * make _as_hex() and _as_bin() handle 0, and make them faster for very short numbers (less than BASE_LEN digits) 2002-09-27 v0.34 Tels * fixed bug in mul_use_div() shortcut that used * $RBASE instead of / $MBASE * $caught & 1 != 0 vs ($caught & 1) != 0 (changed to $caught != 2) * $i %= $MBASE does not work on ARM (v5.003), so make it $i -= $car * $MBASE * removed unused LEN_CONVERT code (smaller memory footprint) 2002-09-09 v0.33 Tels * _fac() keep $n as scalar if possible * test for when to USE_MUL or not was inverted * _mul() is about 6 times faster if $y is small and $x is big 2002-08-21 v0.32 Tels * fixed bug in _rsft() that did not set result to 0 in some cases * _modinv() now works, thanx to the all-positive algorithm * much more tests in bigintc.t (taken over from FastCalc) 2002-08-13 v0.31 Tels * _acmp() no longer calls _len() => tad faster * some cleanup of old code, added some more comments 2002-06-10 v0.30 Tels * undef mul/div in case Calc.pm get's loaded twice * fix in _as_hex() and _as_bin() for older Perls * speedups in _pow() and _modpow() 2002-06-09 v0.29 Tels * filled in _modpow() 2002-05-30 v0.28 Tels * added _modinv(), _modpow() (not yet implemented) 2002-03-17 v0.26 Tels * a fix in _rsft() that left empty array instead of (0) * a fix in _sub(): early out made -1 + 100000000001 == 0 (if length($y) > 8) 2002-03-03 v0.25 Tels * started _square() (not done yet) 2002-02-27 v0.24 Tels * streamlined _mod() shortcuts * _div() has shortcut if $y is very small 2002-02-24 v0.23 Tels * from_bin() repack input and use from_hex(): twice as fast 2002-02-10 v0.22 Tels * _sqrt1() => _sqrt() (oups) * much better guess for _sqrt() resulting in faster sqrt * added _fac() 2002-01-07 v0.20 Tels * better detection of higher-int-only base (but disabled due to failures) * streamlined converting * turned dual-basis off by default (now 7-7 on 32 bit and 9-9 on most 64 it) * _str() uses int() on first part to avoid '0000' instead of '0' 2001-12-23 v0.19 Tels * first working version of using two different bases: one for mul/div, the other for all other ops, including converting via _to_large()/_to_small() 2001-12-20 v0.18 Tels * added _as_hex() and _as_bin() with 16 bit chunks * from_bin() now uses oct() and 16 bits per iteration * removed needless return statements 2001-12-06 v0.17 Tels * added _sqrt() for more speed * _sqrt() shortcut for small (< $BASE) numbers for better performance * shortcut in _mul for small numbers (< $BASE_LEN2) * added _and, _or, and _xor and let them use more than 16 bits * find out how many bits _and, _or and _xor can safely use (cap at 23) * div() might leave empty array, so __strip_zeros fixes these * streamlined _acmp() * cap of 5 for BASE for UTS and UNICOS/Cray * better test to find out what BASE should be (use +0.0 to force floats) 2001-11-19 v0.16 Tels * fixed comments a bit * finished _mod() when $y < $BASE and $BASE % $y != 0 and $BASE % $y != 1 * streamlined _mod() loops a bit * added _pow() for faster bpow() * small fix to make 5.005_03 happy ($x = shift @prod vs $x = shift @prod || 0) 2001-11-11 v0.15 Tels * added _dec() and _inc() for much faster $x++ and $x-- 2001-11-04 v0.14 Tels * added _mod() for faster $x % $y 2001-10-23 v0.13 Tels * better detection of BASELEN by matching against expected pattern 2001-10-03 v0.12 Tels * _div: 99999 => $BASE-1 ($MAX_VAL), that made some div's fail if $BASE != 5 2001-09-07 v0.11 Tels * automatically USE_MUL or USE_DIV 2001-08-24 v0.10 Tels * no longer export anything, ignore import calls 2001-07-20 v0.09 Tels * don't use warnings for older Perls 2001-07-15 v0.08 Tels * fixed bug in mul() shortcut 2001-07-15 v0.07 Tels * applied Philip Newtons spelling and doc patch(s) * accidentally had the old, slow mul() code in. Oups. * fixed also a bug in that new code * also the speedup in mul() occurs with $x having lots of zeros, not $y. * first argument is always classname, so removed checks and shift * shift in base ten by _lsft() and _rsft() 2001-07-09 v0.06 Tels * first release ############################################################################## Math::BigInt::CalcEmu: 2004-03-12 v0.04 Tels * removed unnec. emulation routines (all except _signed_foo) 2004-01-13 v0.03 Tels * $VERSION was overriding the $VERSION from MBI (Thanx Gisle Aas!) 2003-12-30 v0.02 Tels * the code in Calc::_root() uses now sprintf(), but the one in Emu was not 2003-12-26 v0.01 Tels * first version, taken over all the code from BigInt ############################################################################## Math::BigInt::Scalar: 2002-01-07 v0.11 Tels * fixed version * added DESCRIPTION section to stop pod2man complaining * added _dec, _inc 2001-08-24 v0.10 Tels * no longer export anything, ignore import calls 2001-07-20 v0.06 Tels * don't use warnings for older Perls 2001-07-15 v0.05 Tels * first argument is always classname, so removed checks and shift 2001-07-09 v0.04 Tels * first release ############################################################################## Math::BigFloat: 2008-04-20 v1.60 Tels * fix #34459: bsqrt() breaks on floats with enough digits (Thanx Niko Tyni!) * fix #35238: batan2() handles inf/+inf wrong * fix #35162: MBI segfault (as_number(Math::BigRat()) was wrong) 2007-06-30 v1.58 Tels * remove Exporer from @ISA * support config('lib') as shortcut for config()->{lib} * add bpi(), bcos(), bsin(), batan(), batan2() methods * add bmuladd() * streamline the is_xxx() and copy() methods 2007-05-05 v1.57 Tels * add bnok() method (n over k) * add all the missing modify() hooks 2007-04-16 v1.55 Tels * make bexp() much faster (esp. under GMP) by caching the first coefficients and rewriting the inner loop * support "try" and "only" in import() 2007-04-09 v1.54 Tels * fix bug #21747: Re: weirdity in bignum... (powers and high precision): infinite loops for blog() (and consequently bpow()) if you requested an accuracy greater than 67 digits (uses _log() now, and not blog()) Thanx to darconc! * cache the result of _log(2) and _log(10) so that subsequent calculations can re-use the already done work * instead of computing _log(10), compute _log(1.25) and _log(2) and then do: _log(1.25 * 2 * 2 * 2) = _log(1.25) + _log(2) + _log(2) + _log(2) This makes computing _log(10) much faster, so that computing blog(N) is about a factor of 5 faster when N >= 10 or N <= 0.1 * add bexp() 2007-03-04 v1.53 Tels * fix #25144: [PATCH] Math::BigFloat->new considers any reference a BigInt (Thanx mschwern!) * fix bug #13866: NaN (in bignum queue) * fix bug #21586: Incorrect result when comparing with NaN * fix bug #15896: "==" overloading is broken for "NaN" 2007-01-27 v1.52 Tels * fix brsft() and bpow() in list context only return on number (bug #21413) * make as_int() return a BigInt, too (not just as_number()) (bug #21412) * add as_oct() * bpow(): handle negative X and negative Y (instead of returning NaN) 2005-04-10 v1.51 Tels * fix new() to work with Math::BigInt::Pari 2005-03-29 v1.50 Tels * fix rounding doc, add notes about prevision vs. accuracy * set FastCalc as default (we still use whatever MBI uses) 2005-03-20 v1.49 Tels * remove dependecy on Scalar::Util in bdiv() * bdiv() cache result of "!$y->is_one()" for wantarray case to make ($res,$rem) = $x->bdiv($y); about 10% faster 2005-01-01 v1.48 Tels * use new interface to _scale_a() and _scale_p() in BigInt * add bneg() and inline is_zero() in it, making it 1.6 times faster * replace ref($_[0]) w/ undef when it isn't actually needed. This makes some ops (bsstr(), bneg etc) about 2% faster for small numbers * use MBI::_register_callback() to get notified of lib changes * bgcd()/blcm() never worked, so fix them for integers and add tests 2004-10-10 v1.47 Tels * inf/NaN fixes for bpow() * eliminate the need for _zeros() in new() (speed-up for GMP et. al.) * eliminate _is_zero() in new() (small speed up) * added shortcut for simple numbers in new() (speed up) 2004-08-13 v1.46 Tels * blog(10,10) ($x == $y) returned '1.0000...' instead of '1' 2004-07-30 v1.45 Tels * simple inherit bsub() from BigInt, also fixes bsub() failing under $x -= $x - Thanx Peter J. Acklam! * bdiv() failed when passed a variable twice (thanx Peter J. Acklam!) * bfround() and bround() are about 10% faster when going via Math::BigInt's bround() due to constructing a fake BigInt instead of going via ->new() * fixed undef warnings in bpow(0,$y) ($y non-integer) (thanx kenny!) 2004-03-12 v1.44 Tels * bpow() computed -X ** Y wrong for Y that are odd * use $HALF instead of 0.5 to speed up broot() * use Calc instead of BigInt for parts, that makes it roughly 2x faster it also saves memory (419 vs. 767 bytes per (small number) object) * bmod() did needlessly test for NaN arguments twice 2004-01-13 v1.43 Tels * small fixes in AUTOLOAD * delete $x->{_a} vs. $x->{_a} = undef to save memory 2003-12-30 v1.42 Tels * ffac(inf) is inf, not NaN * flog() calculate integer result first, and if it fits, return it this makes it much faster in case the result is a perfect integer * require (instead of use) Exporter * froot() calculates an integer result first, and it if fits, returns it 2003-12-11 v1.41 Tels * flog(): 0.5, 0.25, 0.125, 2, 4 and 8 were not scaled properly back to 1, instead they remained 0.5 and 2, respectively. This was a '<' vs. '>=' respective '<' vs. '<=' issue. No other values are affected (neither getting slower nor faster), but the ones in question (incl. their multiples like 20, 80, 0.0125 etc) are now tremendously faster - about a factor of 30 to 60! :-) * removed some crufty logic from _log_10() and made the special cases of 2, 10 and 0.1 slightly faster. This also helps log($x,2) and log($x,10). * bfac() slightly faster for small arguments * downgrading to bigint failed for .2e2 (produced 200 vs. 20) 2003-09-23 v1.40 Tels * bstr(): removed unnec. BigInt math and inlined is_zero() => great speedup (10% to factor 6.5 depending on input) * replace $self->_one() by $self->bone() 2003-07-06 v1.39 Tels * $x->blog($base) can handle a $base which is a Math::Bigint * replace die() with Carp::croak 2002-11-03 v1.39 Tels * $x->bpow($y,0), $x->blog($base,0) and $x->bdiv($y,0) were still not doing the right thing and no tests caught it *sigh* * blog(): + MUCH faster when $x > 10 or $x < 0.1 (constant time vs. time * 10 when doubling/halving $x) + also much faster if $x has many digits (like 1/3 or 123**123) + for $x < 1 and $x > 0 did not work at all (bacmp vs bcmp) + returns now NaN if $base <= 0 or $base == 1 + does handle other bases than "undef" (aka e) properly now * require Math::BigFloat did not work (opposed to BigInt, where it does) * _pow() suffered the same bug of bacmp vs bcmp (so 0.2 ** 0.2 failed) * removed unused _pow2() routine * _find_round_parameters() returns ($x,$a,$p,$r) and not ($a,$p,$r), so use it correctly, and also test for $x = NaN afterwards (happens when $a and $p were set and thus $x became NaN) * bsqrt() failed since v1.63 for values like 0.2, 0.002, 0.00134 etc * added broot() method (albeit slow for now) * $x->is_one('-') was broken (never returned true for $x == -1) * config() can take arguments and set them, croak on wrong ones * config(trap_nan => 1) to manipulate former $NaNOK variable * config(trap_inf => 1), too * trap_nan/trap_inf really croak on any attempt to create an NaN/inf * spellings of Bigint => BigInt * simplify config() by using SUPER::config() 2002-09-08 v1.38 Tels * fix that bsqrt() would hang for certain inputs. Instead of using Newton's, we now rely on the fact that sqrt(x*y) = sqrt(x) * sqrt(y) by setting y to 100. This removes the while loop entirely and makes it much faster while fixing the bug at the same time. * $x->bsqrt(0) did needless warn about undef values, and round to 4 digits instead of beeing equivalent to $x->bsqrt(undef) * ditto for $x->bpow($y,0), $x->blog($base,0) and $x->bdiv($y,0) * use File::Spec was needless, since it was required later on again 2002-08-20 v1.37 Tels * bcmp()/bacmp() upgrade now if requested 2002-08-13 v1.36 Tels * as_hex() and as_bin() work now at least for inf, NaN and integers * fixed bsstr() (and thus also numify()) for negative numbers - Ouch! * $x->new("0.02"); $x->accuracy($a); $x->bdiv($y,$d) failed to round when $d > $a * numify() returned '+inf' instead of 'inf' * (more) tests for bsstr(), numify(), as_hex(), as_bin 2002-07-07 v1.35 Tels * bfround() used accidentally BigInt math; is now about 5.6 times faster for small numbers * bdiv()/badd() etc skip objectify() if possible and are thus faster * doc for accuracy()/precision() * $x->bmod() was not modifying $x in place when returning NaN/inf/-inf * avoid unec. calls to objectify() for binary op's 2002-06-10 v1.34 Tels * upgrade used badd() instead of bmul() inside bmul() (again! arg!) 2002-06-09 v1.33 Tels * import() fixed for older Perls 2002-05-19 v1.32 Tels * upgrade used badd() instead of bmul() inside bmul() * bpow() now uses slower, but more correct way for fractions (this needs work) 2002-03-03 v1.31 Tels * bpow() can handle second arguments beeing non-integer (f.i. 2 ** 0.2) * $x->bpow(0.5) optimized to $x->bsqrt(); 2002-02-25 v1.30 Tels * bug in bsub() with not rounding when $x->bsub(0) was also in MBF * bcmp() and bacmp() 5 times faster due to numify() (might have now impose a limit on exponent - but I couldn't find a test that breaks it) * streamlined ffloor() and fceil() * fixed bug in $x->bsub(0) and $x->badd(0) (both forgot to round result) * new() downgrade integers if $downgrade is in effect * optimized fpow() (one is_zero() less) * optimized as_number (nearly twice as fast) * $x->badd(0) forgot to round $x * downgrade and upgrade are valid methods for inheritance 2002-02-24 v1.29 Tels * overload for 'log' now inherited by BigInt * _binf(), _bnan(), _bone() and _bzero() instead of longer bone() etc * inf/NaN fixes from v1.51 were missing for BigFloat * bdiv() upgrades if applicable 2002-02-16 v1.28 Tels * fixed use Math::BigFloat ':constant'; * fixed flog() function to calc right result, honour rounding-globals 2002-02-10 v1.27 Tels (forgot to increase version) * ffac() * various: disable Math::BigInt::upgrade to avoid deep recursion 2002-01-06 v1.27 Tels * overload for log() and flog()/blog() * bzero()/bone() handling of A & P was broken * bround()/bfround() handling of zeros forgot to set A & P * fdiv: fixed a bug in round to A with given round_mode (always used global) * fsqrt(): would hang/fail if either $x's or global A or P were set * fsqrt() didn't modify $x sometimes, but returned a new reference * fsqrt(): calc 4 more digits for rounding, not 1 (endless looping otherwise) * fmod() now actually works 2001-12-06 v1.26 Tels * fneg() failed (now hand up to MBI) * frsft() and flsft() were no aliases to brsft() and blsft() * fone() was no alias for bone() * blsft() and brsft() were missing altogether * streamlined: fpow() and fmul() * removed the EXPORT_OK * fqsrt() uses now BigInt::bsqrt() as guess: greatly improved performance * make fsqrt() subclass proof by using $self instead of Math::BigFloat * bzero(), bone(): take additional A and P and store 'em * bnan(), binf(): clear A and P 2001-11-18 v1.25 Tels * streamlining fixes in new() were missing * further streamlining in new() for 12345e1234 cases (fraction part empty) * added $rnd_mode support for compatibility * replaced the 'laber schwad blah blah' pod section by a pointer to MBI 2001-11-11 v1.24 Tels * bacmp() fix for +-inf * streamlined new() * faster finc()/fdec() 2001-10-05 v1.23 Tels * fixed facmp() (was broken the same way as fcmp()) * more rounding fixes from John P. 2001-10-03 v1.22 Tels * Quite a lot of rounding fixes * $x->bnorm() is 4 times faster if $x == 0 * $x->bround($n) is 43 times faster if $n > $x->{_a} (no-op) * added as_number() 2001-09-03 v1.21 Tels * serious bug in bcmp() caused 1.5 to be greater than 2. Yikes! * bcmp() did not only return -1,0,1 and undef but other values, too * new('inf') produced NaN (was expecting '+inf') * exponent(), mantissa() & parts() failed or returned scalars for inf,-inf,NaN * include finf in AUTOLOAD list 2001-08-03 v1.20 Tels * streamlined bcmp * drop leading '+' for inf 2001-08-02 v1.19 Tels * 123/+-inf => 0, test for that and -1,0 / NaN => NaN * +123 / 0 => +inf, -123 / 0 => -inf (was missing in MBF) * fixed +-inf handling in bacmp/bcmp/bsub/badd/bdiv and tests for that * padd bstr() output of numbers with set A or P * remove bfloat() (Math::BigInt->bfloat() did not work, anyway, see bint()) 2001-07-15 v1.17 Tels * applied Philip Newtons spelling and doc patch(s) * added bone() * tests for bnan() and bone() 2001-07-09 v1.16 Tels * is_positive(), is_negative() * various pod fixes (overlong =item, spelling erorrs etc) * removed internal _set() and the tests for it * infinity support for fcmp(), fpow() * nailed the bug in fdiv() that caused fsqrt() to fail. fsqr() works now, too. * more tests 2001-06-15 v1.15 Tels * added bfloor(), bceil() 2001-06-13 1.14 Tels: * accuracy/precision rounding after fdiv() was missing * binary integer input (0b01110 etc) * A/P rounding after fdiv() was missing * '-0x0' would wrongly leave '-0' * as_number() was wrong for negative numbers and had no tests * added is_even(), is_odd(), _set(), the inherited ones were broken * fixed is_zero() for NaN * $x->bpow($y) for negative $y was unfinished * added is_inf(), binf() and some support for +-inf in new(), bsstr() etc * added tests for is_odd(), is_even(), _set() and is_zero(), is_inf(), bsstr() 2001-06-09 1.13 Tels: * adjusted fdiv() so that it now works proper with old testcases * (except a few nits, see testsuite and ACCURACY) * fdiv() in listmode (uses non-working fmod()) * fixed/test A/P after each op * $x->accuracy(), $x->precision() actually round $x to the value A/P * fixed fpow(), added tests for it * hexadecimal integer input (0xdeadbeef) * is_one() for -1 was wrongly true, tests for is_one() 2001-05-11 1.12 Tels * taken over testsuite from John P. * added tests for compare with fraction * fixed fcmp/fround/ffround * added accuracy/precision/fallback/round_mode * bsstr('NaN') returned 'NaNeNaN' 2001-05-09 1.11: bug bcmp() (1e-08 was < 0, aka fractions were broken) 2001-05-07 1.10: Tom's round fixes (minus one nit) new: .xxx, -.xxx, +.xxx etc are valid inputs, while '.', 'x x x' and 'Exxx' are now invalid finally got rid of C&P of overload section and clone() 2001-04-23 1.09: length() in list context return length of mantissa & exponent bug in bstr() for '0.x' style strings added bsqrt() workaround for Perl v5.6.0 overload-bool bug (via MBI) fixed rounding 2001-04-18 1.08: exponent(), mantissa() and parts() now return BigInt's bnorm: 0Ey => 0E1 (was wrongly 0E0) fixed is_zero() added bround() and bfround() (only truncate mode) fixed bug in bstr() for 1.203E-2 style numbers (Thanx Tom!) 2001-04-07 1.07: bug in bstr() for 0.xxx style numbers, as well as for "-xxx" babs(), bneg(), bint() work now empty stubs for bsqrt(), bround() and bmod() exponent(), mantissa(), parts() work now as expected 2001-04-05 1.06: bstr() returns NaN for NaN's renamed _norm to bnorm, added it to AUTOLOAD for compatibility fixed bug Math::BigFloat->new(Math::BigInt->new(3)); bug mul/div when second arg was BigInt bdiv() works now with precision precision() doc about mixing different objects in overloaded math 2001-03-31 1.05: fixed bstr() and bsstr() added AUTOLOAD for fxxx() to work as well as bxxx() enhanced and fixed testsuite for mul/cmp/add/new 2001-03-27 1.04: bmul/bdiv/cmp work now, better _norm() 2001-03-06 1.03: layed more foundations (mul() etc) 2001-02-24 1.02: add()/sub() should work now 2001-02-22 1.01: new() and bstr() work now (sort of) 2001-02-18 1.00: started work ############################################################################## Math::BigInt: 2010-11-15 v1.99 rafl * Stop as_int/as_number from losing precision (Peter John Acklam) (Closes: RT#43694) * Fix Math::BigInt::Calc::_modpow for (0 ** $x) % $y, with $x > 0 (Peter John Acklam) (Closes: RT#62918). * Stop $x -> bmodpow(1, 1) from failing when $x is large (Peter John Acklam) (Closes: RT#62949). 2010-11-08 v1.98 rafl * Fix from_bin() documentation error (Peter John Acklam) (Closes: RT#61845). * Make as_int($inf) return inf, not NaN (Peter John Acklam) (Closes RT#62101). * Fix various typos in documentation and tests (Peter John Acklam) (Closes RT#62643). * Make digit($n) return 0 for "out of range"-digits (Peter John Acklam) (Closes RT#61812). 2010-11-07 v1.97 rafl * Reorder the list return of Math::BigInt::Calc::_base_len() (Nicholas Clark) This change requires an update of Math::BigInt::FastCalc to version 0.24. * Fix segfault when upgrading irrational numbers (Father Chrysostomos) 2010-09-28 v1.96 rafl * Various documentation fixes provided by gregor herrmann 2010-09-14 v1.95 rafl * Re-upload v1.94 as a stable release 2010-09-13 v1.94 rafl DEVELOPMENT RELEASE * Attempt to fix Math::BigInt::Lite failures 2010-09-13 v1.93 rafl * Depend on perl >= 5.6.2 * Remove obsolete core test directory boilerplate * Convert from Test to Test::More 2010-09-10 v1.92 rafl * re-upload v1.91 with a fixed SIGNATURE 2010-09-10 v1.91 rafl * fix various documentation bugs 2010-09-03 v1.90 rafl * fix bnok() for k==0 and k==n-1 2008-04-20 v1.89 Tels * fix #35238: batan2() handles inf/+inf wrong 2007-09-22 v1.88 Tels * fix wide ints on Perl v5.8.0 (Thanx zefram!) * minimum required is Perl v5.6 (tested by zefram) * _find_round_parameters(), _scale_a() and _scale_p(): trunc A/P to integers * fix from_oct(), from_bin() and from_hex() 2007-06-30 v1.87 Tels * fix undef base in blog() * support config('lib') as shortcut for config()->{lib} * _find_round_parameters(): convert $a & $p to normal scalars, or bad things will happen during rounding of BigFloats * add bpi(), bcos(), bsin(), batan(), batan2() methods * add bmuladd() * streamline the is_xxx() and copy() methods 2007-05-05 v1.86 Tels * bump version 2007-05-05 v1.85 Tels * bump version 2007-05-04 v1.84 Tels * add bnok() method (n over k) 2007-04-16 v1.83 Tels * bump version 2007-04-09 v1.82 Tels * use $CALC->_zeros() directly (instead _trailing_zeros()) to speed up exponent() and mantissa() * fix documentation that blsft() and brsft() default to base 2 (not 10) * add bexp() and fix overloading for exp() 2007-03-16 v1.81 Tels * no code change, just a package update 2007-03-04 v1.80 Tels * require Perl v5.6.2 as minimum * fix bug #24969 (Can't use an undefined value as an ARRAY reference) * fix bug #12857: Subclasses and overload * fix bug #13866: NaN (in bignum queue) * fix bug #21586: Incorrect result when comparing with NaN * fix bug #15896: "==" overloading is broken for "NaN" 2007-02-02 v1.79 Tels * fix typos 2007-01-27 v1.78 Tels * implement "try" and "only" as replacements for "lib" * make 'use Math::BigInt lib => "foo"' warn if foo cannot be loaded and a fallback occurs * fix bug #21446 - Docs/code inconsistency for bnorm() method * fix bug #21964 - A patch to include a rounding mode of 'common' * fix bug #21445 - Documentation error for exponent() method * fix bug perl #41050 - NaN returned when raising integer value to negative power * add from_hex(), from_oct(), and from_bin() * add as_oct() 2005-05-17 v1.77 Tels * bump version 2005-04-10 v1.76 Tels * fix rounding doc, add notes about prevision vs. accuracy * trap inf and -inf in new() * load FastCalc as default 2005-03-20 v1.75 Tels * use a trick to remove the dependency on Scalar::Util in bsub() * fix atan2(), it did not preserve the order of arguments (Thanx to Ambros & Zaxo for report and patch!) 2005-01-01 v1.74 Tels * streamline _scale_a() and _scale_p() for more speed in rounding * remove the now unnec. support for MB_NEVER_ROUND and {_f}, this makes all ops that call round() a tad faster (one exists is removed) and shrinks the codesize a bit * streamline bneg(), inline is_zero(): makes it 1.6 times faster * replace ref($_[0]) w/ undef when it isn't actually needed. This makes some ops (bsstr(), bneg etc) about 2% faster for small numbers * restrict low-level math library names to sane chars to avoid exploitation of eval() * fill_can_cache() accidentally did checks for 'or' & 'xor' * inline _fill_can_cache * add _register_callback() to notify subclasses of lower math lib changes * bgcd() is now about 10% faster * is_positive(0) == 0, since 0 is neither positive nor negative * streamline bmod() a bit * fix blog() constructing arguments (broke Math::BigInt::Constant) 2004-10-10 v1.73 Tels * overloading of <<= and >>= makes these ops about 10% faster and fixes the problem that "$a <<= 2" would create a different object for $a to point to * quite a lot of fixes for NaN/inf handling in bpow() (bmul already did it right) - bug report by jeff at thekidders com and Hugo - Thank you! 2004-07-13 v1.72 Tels * no changes 2004-07-08 v1.71 Tels * fixed bsub() failing under $x -= $x; Thanx Peter J. Acklam! * _scan_for_nonzero() reuses length/stringform of $x and is thus faster, this helps rounding if the number after the roundposition is '5' 2004-03-12 v1.70 Tels * bpow() computed -X ** Y wrong for Y that are odd * 0 ** -Y => +inf (was NaN) due to 0 ** -Y => 1/0**Y => 1/0 => +inf * fixed bug in perl -Mbignum -le 'print 2 ** 46 * 3' under Bigint::Lite leading to "Can't use an undefined value as an ARRAY reference at /usr/local/lib/perl5/5.8.2/Math/BigInt/Calc.pm line 462." * fixed upgrading of blog() with base = undef (means: base e) * make the synopsis actually runnable (Thanx Paul McCarthy) * blcm(): handle a list of strings (instead one obj and some strings), too 2004-01-13 v1.69 Tels * bacmp(+-$x,-inf) was wrong (Thanx William T. Morgan!) * digit($x,$y) segfaulted under 5.6.1 if $y was a BigInt * blog() was missing the modify() check (breaking MBI::Constant) * delete $x->{_a} vs. $x->{_a} = undef to save memory 2003-12-26 v1.68 Tels * bfac(inf) is inf, not NaN * added alias names: as_int() (as_number()), is_pos(), is_neg() and doc * factored out all the emulation code and moved it to Math::BigInt::CalcEmu * binary/hexadecimal input was twice as slow as v1.66 due to a typo in v1.67 * streamlined overload for boolean context (20% faster "... if $x;") * round() was missing a croak() in path testing for wrong roundmode * badd(): optimize away setting of sign if it is already right * bdec() is about 10% faster for negative numbers * bpow(): removed some now needless tests for 0 and 1: about 30% faster for small numbers * streamlined exponent() (parts() benefits from this, too) 2003-12-02 v1.67 Tels * overload for cos/sin/exp/atan2 to make cos(Math::BigInt->new(...)) work * implemented blog() with a simple and fast "iterative" method * use _log_int() in $CALC if possible * cache $CALC->can(...) calls in global %CAN hash for speed * reorder is_zero() check for band(), bior() and bxor() to speed up the case for when the underlying lib has _and(), _ior() and _xor() * implement a new way of emulating AND, OR and XOR, this tremendously helps if band() et. al. are called with negative arguments * try to call _signed_or(), _signed_and() and _signed_xor() in lib * is_foobar() methods are slightly faster * bnot() is about 12% faster * bsqrt(): moved is_zero() || is_one() test out of the way => 28% faster for "small" values (Calc and GMP) * small change for overload::constant * bfac(): do 0 or 1 check only if CALC cannot do _fac() (thus faster) * removed a needless _copy in bmod() with negative arguments (slightly faster) 2003-09-01 v1.66 Tels * document accepted inputs better * fix wrong upgrade and undef-parameter handling in broot() * implement broot() if lib doesn't have a _root() routine for $y that are powers of two and for small $x * warn if broot() cannot yet compute proper result * remove needless _one(): 3% speedup for binc() * remove needless _swap(): 1% (Calc) - 6% (GMP) speedup for overloaded math 2003-07-13 v1.65 Tels * document that config() can set certain values * replace die() with Carp::croak() * remove needless is_zero() check in as_bin() and as_hex(), making them faster, especially when under a different lib like GMP. * Fixed the infinite recursion in bignum. See http://xrl.us/k6y * fix handling of 0e999, 0e-999 etc 2002-11-03 v1.64 Tels * removed needless "my $c = ...;" statements in binf() and bnan() * forgot () around "$x->{_f} & MB_NEVER_ROUND" * bsqrt(inf) == inf, not NaN * $x->bdiv($x) did not round the resulting 1 properly * removed the shortcut testcode in bdiv() (Calc handles this now) * added (non-working for now) broot() method * changed length() to CORE::length() in two places (thanx Liz!) * config() can take arguments and set them, croak on wrong ones * config(trap_nan => 1) to manipulate former $NaNOK variable * config(trap_inf => 1), too * trap_nan/trap_inf really croak on any attempt to create an NaN/inf * spellings of Bigint => BigInt * _find_rounding_parameters(): set $a to undef if it is 0 2002-09-08 v1.63 Tels * bsqrt() did not modify $x but returned new object when lib does not have a _sqrt() routine (BareCalc, BitVect and Pari are affected, Calc, FastCalc and GMP were not) 2002-08-21 v1.62 Tels * bcmp()/bacmp() upgrade now if requested * bmodinv() uses an all-positive algorithm, speeding it up by about 5-8% and allowing to implement the same algorithm in Calc for factor 4 speedup 2002-08-13 v1.61 Tels * tests for bsstr()/numify() with negative/special inputs * bround() keeps $scale as scalar for speed and less problems * fix for trailing newlines in input * some doc fixes (especially return values of is_foo() methods) * make testsuite so that it will pass under FastCalc easily 2002-07-07 v1.60 Tels * shortcuts to avoid calls to objectify for add/sub/mul/div/mod/pow/bcmp etc * fix overloaded bcmp() so that the objectify()-avoidance kicks in * avoid calling round() when BigFloat requested 'no rounding please' * bcmp()'s shortcut for comparing x <=> 0, 0 <=> 0, 0 <=> $y was making things slower than just handing the compare to Calc. Even more so for Pari et al. * $x->accuracy() and $x->precision() returned undef, instead of 0 if A/P of $x was 0 and global A/P was undef. * $x->bmod() did not modify $x in place when returning NaN/inf/-inf * some binary ops (band/bxor/bior/bpow) were not properly rounding the result to the requested A/P/R; the same ops also forgot to take $y into account * doc for accuracy()/precision() 2002-06-10 v1.59 Tels * pod fixes for bmodpow()/bmodinv() * fix in as_hex() and as_bin() for older Perls * speedups in bpow(), bmodin() and bmodpow() 2002-06-09 v1.58 Tels * invalid inputs with two dot's (1.2.3 or 1..2 etc) are now really invalid 2002-05-30 v1.57 Tels * fixed objectify() to make "perl -Mbigrat -le 'print 1+2/3'" work * added bmodpow() and bmodinv() as (not-working yet) stubs 2002-03-17 v1.56 Tels * documented config() * simplified import() logic a bit * changed some isa->($upgrade) => !$isa->($self); 2002-03-17 v1.55 Tels * :constant picks up binary/hexadecimal constants * Math::BigInt->digit(123) works now 2002-03-03 v1.54 Tels * really fixed overlong pod =item * downgrade() and upgrade() with undef as argument didn't clear the variable * bmul() upgrades if second argument is non-integer * bdiv() upgrades if $x > $y * bpow() upgrades if second argument is non-integer * objectify disable downgrade (for MBF) * new() twice as fast due to shortcut simple numbers, save _split() & _round() 2002-02-27 v1.53 Tels * precisision typo * fixed overlong pod =item * added downgrade() 2002-02-24 v1.52 Tels * hooks for _bin(), _bnan(), _bone() and _bzero() * =head2 section for accuracy 2002-02-16 v1.51 Tels * fixed bfround(-x) (f.i. 0.004->bfround(-2) resulted in 0.01, not 0.00) * bfround(x) rounded at wrong place (off by one) * calling bfround(x) rounded further and further instead of keeping result * blog() upgrades if requested * added doc stub for every public function 2002-02-10 v1.50 Tels * bfac() and hook for _fac() in libs * documented sub-classing and auto-upgrade * < 4 test in bsqrt() after the CALC call for more performance * added overload for sqrt() * added possibility to upgrade via use Math::BigInt upgrade => 'Foo::Bar' * Math::Big(Int|Float)->accuracy() clears precision, and vice versa * small optimization in bdiv() regarding abs($x) < abs($y) * brsft() for negative numbers in base 2 was completely wrong 2002-01-07 v1.49 Tels * as_hex() and as_bin() use 16 instead of 8 bits per iteration * overload for log() and blog() * tricks to make 'require Math::BigInt' and 'use Math::BigInt();' work again * use $CALC instead of require for newer Perls (test for $] > 5.006 vs 5.6) * bzero()/bone() handling of A & P was broken * bround()/bfround() forgot to set A or P for zeros * embedded _find_round_parameters into round(), streamlined both versions * round() now uses string-add to make it almost twice as fast * bnot() did round twice 2001-12-06 v1.48 Tels * fixed pod in many places * bmod: use round(), not bround() * bsqrt: use _sqrt() from lib, if possible * bsqrt: would hang for certain (most?) inputs * bdiv: slow check for 1 || -1 replaced by much faster version * bdiv: call _div() only when nec. in list context, otherwise scalar * streamlined copy(), _find_round_parameters() * removed the EXPORT_OK except for objectify, _swap and bgcd/blcm * bzero(), bone(): take additional A and P and store 'em * bnan(), binf(): clear A and P 2001-11-18 v1.47 Tels * added $rnd_mode support for compatibility * two 'my $t = ... if ..;' cases to 'my $t; $t = ... if ...;' * added overload for %=, |=, &= and ^= for more speed * _split(): check for 1e2e3 and reject it 2001-11-11 v1.46 Tels * binc(),bdec() use lib (via _inc(),_dec()) => faster (see BENCHMARK) * avoid the unnec. rounding bsub()/binc()/bdec() (badd() already took care) * made bsub() faster by removing the bneg() overhead from it 2001-11-04 v1.45 Tels * tests run now in subclass, too * bmod() can use _mod in lib * lots of tests fixed (assumed wrong base etc) and added * bpow() about 10-15% faster for small numbers (like 2 ** 150, 3 * 200 etc) 2001-10-05 v1.43 Tels * $x->bround($n) is 43 times faster if $n > $x->{_a} (no-op) * Heaploads of rounding fixes (and tests) * Test for 99999-bug in Calc 2001-09-03 v1.42 Tels * bug in overload section causing performance losses in subclasses * call $CALC->import() with list of libs * odd numbers never have trailing zeros, so don't convert them to DEC to look * as_hex() and as_bin() * $x->bmod() did not modify $x, only returned result. Oups. * new('inf') produced NaN (was expecting '+inf') * exponent(), mantissa() & parts() failed or returned scalars for inf,-inf,NaN 2001-08-08 v1.41 Tels * fixed inf test (coredumps) 2001-08-03 v1.40 Tels * bxor(-$x,-$y) was broken (and not tested *sigh*) * streamlined bcmp * drop leading '+' for inf * bxor(), band(), bior() with negative arguments don't get passed to lib (makes it work with BitVect, Pari, GMP etc) 2001-08-02 v1.39 Tels * fixed history (duh!) * assign return values from $CALC back to $x->{value} * fixed +-inf handling in a lot of places and tests for that * band(), bxor() and bior() now work with negative inputs * remove bint() (Math::BigFloat->bint() just DNDWIM and no sense, either) 2001-07-15 v1.38 Tels * test for mul() shortcut 2001-07-15 v1.37 Tels * applied Philip Newtons spelling and doc patch(s) * Benjamin Trott: _split() is faster for numbers that need no splitting * Benjamin Trott: don't take shortcut in badd(), or Pari won't work * allow use Math::BigInt lib => 'Pari,BitVect,Foo,Bar'; * delegate shifting to CALC if possible, otherwise fallback * test for self-pow, to see if lib's fail (since BitVect failed for self-pow) * _one() => bone() * +x / 0 => +inf, -x / 0 => -inf, while 0/0 and +-x % 0 are still NaN * tests for bnan() and bone() * Math::BigInt::Calc now determines biggest $BASE to use. Default should now be 1e7 on most systems, giving 20% to 40% speedups. 2001-07-04 v1.36 Tels * is_positive(), is_negative() * various pod fixes (overlong =item, spelling erorrs etc) * torn out the bones from under the flesh and moved them to Math::BigInt::Calc * added Math::BigInt::Calc, Math::BigInt::Small (and Math::BigInt::BitVect) * fixed tests for bacmp() (could never fail) * removed internal _set() and tests for it * +-inf handling in bcmp(), bpow() 2001-06-15 v1.35 Tels * added bfloor(), bceil() * fixed bior(), bxor(), band() for $x->bxxx(NaN,0), added modify() to them 2001-06-13 v1.34 Tels * binary integer input (0b01110 etc) * fixed: '-0x0' left '-0' * added is_inf(), binf() and some support for +-inf in new(), bsstr() etc * added tests for is_odd(), is_even(), _set() and is_zero(), is_inf(), bsstr() 2001-06-09 v1.33 Tels * bround() no longer uses 10 ** $pad and is thus much faster when rounding up * fixed and added rounding benchmark (did time bmul instead bround) * blsft(),brsft(): can work in different bases, check against invalid inputs, more tests, speedup when in base 10 * _trailing_zeros is 50% faster * A/P after each op, tests for it in accuracy.t * round() instead of bnorm() * $x->accuracy(), $x->precision() actually round $x to the set value * tests for is_one() * hexadecimal integer input (0xcafebabe etc) 2001-05-11 v1.32 Tels * added accuracy/precision/fallback/round_mode 2001-05-08 v1.31 Tels * _ between digits now accepted, ' ' no longer valid inside (but at front/end) * Exxx is NaN, and no longer produces warning * .xxx style numbers are valid input * tests for 1E1, 123E-2, 1E2 etc style input to Bigint.pm * fixed overload (w/ _swap/copy), subclasses can inherit it easily * removed clone() * added bsstr() 2001-04-23 v1.3 Tels * added (compatible to MBF) mantissa(), exponent() & parts() as well as tests * _trailing_zeros() * fixed as_number() to return copy of BigInt * added bround(), bfround() and support for round_mode() as well as $rnd_mode * fixed bug in bdiv() wich left reminder "-0", causing further op's to die() * added is_valid to testsuite to see whether invalid objects are created * added bsqrt() * workaround coredump bug in bool() for v5.6.1 2001-04-07 v1.23 Tels * spelling errors in pod 2001-04-05 v1.22 Tels * documented Peters OS/390 patch/changes (fix was in for quite some time) * fixed bug Math::BigInt->new(Math::BigFloat->new(3)); * objectify() with other objects than BigInt as further args, copy() etc * $x->digit($n) to query fast value of Nth digit * as_number() 2001-03-30 v1.21 Tels * bool() works now under 5_005 * bug in bsub where numbers with at least 6 trailing digits after any op failed 2001-03-24 v1.20 Tels * added: is_nan() * bug in bmod/bdiv, I forgot some cases with negatives. Thanx to Bruce Fields! * documented ':constant' and eval() crash on Perl 5.00x * documented BigInts behaviour of bmod/bdiv and use integer 2001-03-09 v1.16 Tels * Math::BigInt::badd(4,5) and Math::SomeChildOfBI->badd(4,5) work now * '$x = scalar (**|%|+|-|*|\) $object;' failed (was not tested, either) * 'if ($x)' is now O(1) instead of O(N) and at least twice as fast * fixed nasty bug in _digits that caused <=> after add/sub/mul etc to fail if result was between 100001 and 109999, added test for this * added test cases for op's that should preserve args (+,+=,abs(), neg() etc) * added tests for overloaded 'bool' * added test.pl and some examples (prime.pl, bigprimes.pl) * tests after "use Math::BigInt :constant" were screwed due to not using eval * $x->numify() (for $array[$x] = 0; etc) is much faster now * added caveat documentation for $x = -$x; and $x *= string1 operator string2; 2001-02-24 v1.15 Tels * $x / $x is now a lot faster (more O(1) than O(N)) * 10 ** $x is now a lot faster (more O(N/5) instead of O(N)) * overload of **= makes $x **= $y faster * 0 ** 0 was NaN, not 1 * -a % b = +c (was -c) to be compatible with perl * added $x->length() and test for it; fixed _digits() (was off by 1) * objectify() was not exported, added tests for objectify() 2001-02-21 v1.14 Tels * overload +=, -=, *= and /= for about 20-30% more speed if both args have roughly same length * shortcut in add() makes $x += $y; $x -= $y; for large $x and small $y an O(1) case instead of O(N) * fixed (non-critical) bug that caused objectify in numify/bool/stringify to create scratch objects from undef params. 2001-02-18 v1.13 Tels * got rid of duplicated copy() code in new() 2001-02-16 v1.12 Tels * accidentally dropped self-multiply test in bigintpm.t * fixed bug in overloading cmp * after correcting the overload for 'cmp', I got a lot of test failings and finally discovered that the bstr()'s return of '[+-][0-9]+' instead of Perls ways of '[-]?[0-9]+' breaks string comparisons with numbers :( F.i. ok() from Test.pm uses 'eq' and you can not do ok($a,3*3) where $a is a BigInt. IMNSHO clearly wrong. And only changing the way cmp is overloaded would lead to the curios situation that the following: 'print "$a eq $b" if $a eq $b;' would print "+3 eq 3", which looks wrong. Mark B. said go ahead and change bstr(), so I changed it ;) to drop the '+', adapted all the tests, changed the doc, etc. BigInts behave now transparently like build-in scalars in integer/string context ;o) 2001-02-14 v1.11 Tels (first release) * fixed bug in band(), bxor(), etc that used badd($x, fixed_number_here); * since subclasses might not be happy with fixed numbers, make sure we pass BigInts all the time if using something like $someclass->badd(); * fixed bug in band/bxor/bior which destroyed second argument * bxor/band/bior work now correctly for subclasses * ++ and -- are now a tad (ca 5%) faster 2000-11-24 v1.10 Tels * finally made it Math::BigInt (w/o trailing 's') 2000-11-23 v1.09 Tels * fixed bug in bmul (and thus bpow) (self multiply works now) 2000-11-22 v1.08 Tels * fixed all but one test (band bior bxor etc) 2000-11-20 v1.07 Tels * objectify fixed to not make copies and work with subclasses 2000-11-19 v1.06 Tels * 7 tests remain * bgcd accepts lists, added blcm 2000-11-16 v1.05 Tels * 8 tests remain * new copies _all_ fields, not only Math::Bigint ones 2000-11-15 v1.04 Tels * fixed bigintpm to test '++' and '--' properly * done div, fixed mul/bpow (13 tests remain) 2000-11-14 v1.03 Tels * x**0 => 1 (instead of x) * fixed bigintpm to include bpow, binc, bdec, new() test 2000-11-13 v1.02 Tels * fixed sub and mul (sort of) * found out that "$wanted = shift || return bzero()" causes a call to numify, * testing for undefined fixes this problem (but might waste more time for * a new(0), will save time on average. Math-BigInt-1.999808/CREDITS0000644403072340010010000000343513013420212015347 0ustar ospjadomain usersI wish to thank the following people: * Mark A. Biggar and Ilya for the original versions. * Steffen Beyer for the discussions and ideas, and for Bit::Vector. * Bruce Fields for spotting bugs. * Mark Dickinson for spotting bugs. * HH for listening to my boring explanations. * Peter Prymmer for spotting the OS/390 problems with / 1e5 * Tom Phoenix for the discussions about factoring/primes/speed. * John Peacock for pushing me to finish Math::BigInt::Calc. * Benjamin Trott for the _split optimization and finding the bug in badd() * Daniel Pfeiffer for v0.49 * Compaq for their TestDrive accounts and the admins managing them - this makes testing on a large variety of platforms possible. Thanx! * Sisyphus for the discussions and ideas * Jarkko for the inf/NaN help and for beeing generally helpful and witty * Creager, Robert S for pointing me towards the precision/accuracy bug and for general asking questions and providing feedback * Feztaa for the report that let to the discovery of the _rsft() bug in v1.61 He also deserves the mention as the first known user of bignum :) * Tim Rushing for reporting the bsqrt() hang and giving me the chance to improve BigInt/BigFloat. * cpan@ali.as for reporting the floor() bug with 0.1412024 and providing a fix and testcase - thanx! * Stephen Ross for finding the -2 ** Y with odd Y bug Special thanx must go to John Peacock and Tom Roche, both have helped me a lot in developing the latest version, not only by cheerfully kicking my lazy butt from time to time, but also by providing advice, bug-reports, suggestions and nagging questions, as well as bearing with my countless ranting emails. So, thank you very much! Also I want to thank all the ever-busy people on p5p. You guys (and gals) rock! List still not complete ;o) Tels Math-BigInt-1.999808/examples/0000705403072340010010000000000013035475727016164 5ustar ospjadomain usersMath-BigInt-1.999808/examples/1000.txt0000644403072340010010000001615213013420212017266 0ustar ospjadomain users# The First 1,000 Primes # (the 1,000th is 7919) # For more information on primes see http://www.utm.edu/research/primes 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 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(we want to see run-time behaviour) # Also there is len(), since the old BigInt has not got length() and we want # this script to be comparable between old and new version. ############################################################################## # Todo: these do not complete in reasonable time: # $x = $two ** 6972593; $x--; #ok (len($x),'2098960'); # $x = $two ** 3021377; $x--; #ok (len($x),'909526'); # $x = $two ** 756839; $x--; #ok (len($x),'227832'); # $x = 1041870 ** 32768; $x++; #ok (len($x),'197192'); ############################################################################## # but these do: # some twin primes (first in list at 03/2001) $x = ($two ** 80025) * 665551035; $x++; $y = $x-2; ok (len($x),'24099'); $x = ($two ** 66443) * 1693965; $x++; $y = $x-2; ok (len($x),'20008'); $x = ($two ** 64955) * 83475759; $x++; $y = $x-2; ok (len($x),'19562'); # ... $x = ($two ** 38880) * 242206083; $x++; $y = $x-2; ok (len($x),'11713'); ############################################################################## # Sophie Germain primes # todo: does not finish after 30 m on 800 Mhz # $x = Math::BigInt->new(72021)**223630; $x--; ok (len($x),'7119'); ############################################################################## # some quadruplet primes... # 3510160221387831655*(2^3363-2^1121)-6*2^1121-7 $x = '3510160221387831655' * (2 ** 3363 - 2**1121) - 6*(2**1121); my @q = ( $x-7,$x-5,$x-1,$x+1); ok (len($q[0]),'1031'); ok (len($q[1]),'1031'); ok (len($q[2]),'1031'); ok (len($q[3]),'1031'); ############################################################################## # some real weird primes: # (2^3833-1)/(14193959303*340789152474053904109001) $x = Math::BigInt->new('340789152474053904109001'); $x *= '14193959303'; $x = (2**3833-1) / $x; ok (len($x),'1121'); #(2^4751-1)/(268982617*3274778783*629530076753*81630665742097*1507074535068001) $x = Math::BigInt->new('268982617'); $x = $x * '3274778783' * '629530076753' * '81630665742097' * '1507074535068001'; $x = ((2**4751)-1) / $x; ok (len($x),'1372'); # 2^7039-1)/ (1252943*1057032553*8541573097*218216841131937276721 $x = Math::BigInt->new('1252943')*'1057032553'*'8541573097'; $x *= '218216841131937276721'; $x = ((2**7039)-1) / $x; ok (len($x),'2074'); # 5616^1153-1)/5615 $x = Math::BigInt->new(5616) ** 1153; $x--; $x /= 5616; ok (len($x),'4320'); # (7147^2161-1)/7146 $x = Math::BigInt->new(7147) ** 2161; $x--; $x /= 7146; ok (len($x),'8325'); # 16*R(5700)*(150093*10^8000+1)+1 # most ending 7's # gives error in BigInt $x = 16 * R(5700); $x *= (150093*(Math::BigInt->new(10)**8000))+1; $x++; ok (len($x),'13706'); # 2*11^13359+1 $x = 2*(Math::BigInt->new(11)**13359)+1; ok(len($x),'13913'); # 10^14800+5*(10^8880+10^5920)+7*10^7400+1 # palindrome $x = Math::BigInt->new(10) ** 14800; $x += 5*((Math::BigInt->new(10) ** 8800) + (Math::BigInt->new(10)**5920)); $x += 7*(Math::BigInt->new(10) ** 7400); ok(len($x),'14801'); $y = "$x"; $y =~ s/^\+//; my $left = substr("$y",7400); my $right = substr("$y",-7401); ok($left,$right); # EOF ############################################################################## # some helper functions sub R { my $x = shift; # These numbers have a decimal expansion of n '1's, # and are usually called "repunits". return ((Math::BigInt->new(10) ** $x) - 1)/9; } sub len { # old bigint has not got length, so use "" and strip it's sign my $x = shift; $x = "$x"; $x =~ s/^\+//; return length($x); } Math-BigInt-1.999808/examples/prime.pl0000644403072340010010000000361213013420212017613 0ustar ospjadomain users#!/usr/bin/perl -w BEGIN { unshift @INC, '../lib'; } # uncomment to use old, org version $| = 1; use Math::BigInt; # this is a complicated version of the prime number sieve. # It is not optimized (since we want to benchmark as many features as # possible). $amount = Math::BigInt->new( shift || 1000000 ); @primes = (1,1,0); # any not defined number is prime, 0,1 are not, but 2 is my $prime = Math::BigInt->new (3); # start # the loop below is faster in the old version than in the new, since it is # the worst case for new lib: small numbers and lot's of bstr()/new(). # It also slows down the benchmark too much so we use slightly faster int here $r = 0; my $a = $amount->numify(); for ($i = 3; $i < $a; $i++) # int version { $primes[$i] = $r; $r = 1-$r; } # find primes OUTER: while ($prime < $amount) { # find first unmarked, it is the next prime $cur = $prime; while ($primes[$cur]) { $cur += 2; last OUTER if $cur >= $amount; # no more to do } # $cur is now new prime $str = "$cur"; $str =~ s/\+//; # unify output for comapre #print "$str $prime $amount\n"; # now strike out all multiples of $cur $add = $cur*2; $prime = $cur + 2; # next round start two higher $cur += $add; while ($cur < $amount) { $primes[$cur] = 1; $cur += $add; } } $i = 0; foreach (@primes) { push @real_primes, $i if $primes[$i] == 0; $i++; } # uncomment to print em: # foreach (@real_primes) { print "$_\n"; } print "last prime: $real_primes[-1]\n"; # check against text open FILE, '1000.txt' or die "Can't read 1000.txt: $!"; my @test; while () { next if /^#/; next if /^\s*$/; $_ =~ s/\s+/ /g; $_ =~ s/^\s+//; $_ =~ s/\s+$//; push @test, split /\s+/,$_; } close FILE; my $i = 0; foreach (@real_primes) { print "oups: $i: $test[$i] != $real_primes[$i]\n" if $test[$i] != $real_primes[$i]; $i++; last if $i >= 1000; } print "done\n"; Math-BigInt-1.999808/GOALS0000644403072340010010000000246413013420212015120 0ustar ospjadomain usersThis file contains a short description of what the goals of this project are, building guidelines etc. This was born after discussions with John Peacock, who provided helpfull feedback. * KISS - Keep It Simple, Stupid! * Favour correctness over speed * Make your code maintable, so avoid Copy&Paste, unclear constructs, read-only code and special hacks whenever possible * Optimize more for the average case than the worst, while trying to avoid performance hits for the worst case. The average case is more for longer numbers than short, based on the assumption that if you wanted to add 1 and 2 _fast_ together, you wouldn't use BigInt nor Perl, now would you? ;) (Or in other words: Time saved in one case of a large number may be multitudes of what you can waste on a small number) * Make subclassing as easy and painless as possible. This means clean inheritance and overload section, no C&P code etc. * Keep the interface as consistent and easy as possible. Secondary goals: * Make mixing of classes work, like in: $x = Math::BigFloat->new(10); $y = Math::BigInt->new(2); $z = $x / $y; # $z = Math::BigFloat = 5 * Make auto-upgrading/downgrading work See also BUGS. Please send me test-reports, your experiences with this and your ideas - I love to hear about my work! Tels Math-BigInt-1.999808/HISTORY0000644403072340010010000001136612740677021015437 0ustar ospjadomain usersThis file contains all the changes and bugfixes from the original version of BigInt/BigFloat to the rewritten one. For what has changed in the latest version see NEW and for a complete list of changes see the file CHANGES. v1.82: general: + It is subsequent faster than the original in many places + Use more than 16 bit at a time, greater BASELEN for 64 bit systems + overload for things like += + special operations like binc() + many optimizations and shortcuts in normal operations + Can use Math::BigInt lib => 'name'; for Pari, GMP, Bit::Vector or others + regression test suite greatly enhanced to cover more problematic cases + added example scripts (prime.pl, bigprimes.pl, hailstone.pl) + documentation fixed and greatly enhanced + BigInt is sub-classable with very little effort, see M::S or M::BF + subclasses of Math::BigInt know all the same methods, so that you can call $x->some_method() without having to know which type of class $x is + added infinity handling + much better NaN handling caveats: + bstr() and stringify now drop the leading '+' (to make overloaded cmp work as expected when cmp'aring to scalars and other objects (read: bugfix) + due to the dropping of '+' the string sort order has changed. It is now compatible to the way perl sorts it's strings. + spaces are no longer allowed in a number (but may precede or follow it) !! You can always make a subclass and change all these things quite easily !! input: + underscores are now valid between any two digits (in hex/binary input, too) + integers of the form 1E2, 1.23E2, 2.00 etc now valid for BigInt.pm, too + hexadecimal numbers of the form 0xabcdefABCDEF0123456789 + binary numbers of the form 0b01010101101000001000100101 + octal numbers can be input via from_oct() output: + as_hex(), as_bin() and as_oct() for easier conversation between bases bugs and buglets fixed over Mark's original: + 0**0 gave NaN instead of 1 + -1**y gave -1 instead of +1 for even y + fsqrt() gave slightly wrong results (like for fsqrt(9)) + +x/0 is now +inf, -x/0 is -inf (both were NaN), as well as other inf cases + mod/div for negative numbers were incompatible to Perl's way + added P. Prymmer's OS/390 '/1e5 vs *1e-5' patch w/o the performance snag + incorporated all the patches to the core modules by John Peacock + BigFloat::bxxx() works as well as BigFloat::fxxx() + Math::BigInt->new(10) / Math::BigFloat->new(2) returned NaN (ditto for other subclasses of Math::BigInt) + $a = new Math::BigInt; creates now a +0, while "" still gives a NaN This suppresses all warnings on undef arguments. Wether this is better... + import() would always use "Math::BigInt" and clash with Exporter + use Math::BigInt qw(bneg); $a = bneg('1234'); etc did not work at all + $x->xxx() now modifies $x in all cases of modifiers and actually returns the same $x (e.g. not a plain scalar or a different reference). All testing routines leave $x alone. bpow(), bmod(), fround(), ffround() etc were broken in this regard. accuracy and precision: + there is now support for both accuracy (significant digits) and precision (fixed number of digits after decimal point), which by default is off + objects/numbers now can have a local accuracy/precision internal fixes: + uses a blessed hash ref instead scalar ref (easier subclassable) + my instead of local + use strict and -w + s/$[/0/ (after all, $[ = 1; in main does not effect this package) + $# partially removed ($#y is scalar @y -1, $#$y is scalar @$y-1 - ugh!) + added LICENSE section and file new stuff: + MBF: :constant works now + MBI: :constant picks up binary and hexadecimal constants + brsft()/blsft() also can do other bases than 2 + bacmp (acmp), because needed for more efficient add() + bzero(), bnan(), bone(), binf() + binc(), bdec(), bfac() + is_zero(), is_nan(), is_one(), is_odd(), is_even(), is_inf(), is_int() + digit(), length(), copy() + as_number() (alias: as_int()), as_hex(), as_bin() + is_positive(), is_negative() (alias: is_pos() and is_neg()) + mantissa(), exponent(), parts(), sign() + bgcd() accepts now lists, blcm() (also accepts lists) + flog()/blog() for overloading of log() + fexp()/bexp() for overloading of exp() + round(accuracy,precision,mode) round to accuracy/precision using mode + MBF: fpow(), fmod(), fdiv() in list context (Thanx J. Peacock) + fpow() can now handle non-integer arguments, like in fpow(2.1 ** 0.2) + MBI: bsqrt() + bmodpow(), bmodinv() (Thanx John Borwick) + bfloor(), bceil(), broot() + CORE cos()/sin()/exp()/atan2() now work when passed BigInts or BigFloats Please send me test-reports, your experiences with this and your ideas - I love to hear about my work! Tels Math-BigInt-1.999808/lib/0000705403072340010010000000000013035475727015114 5ustar ospjadomain usersMath-BigInt-1.999808/lib/Math/0000705403072340010010000000000013035475727016005 5ustar ospjadomain usersMath-BigInt-1.999808/lib/Math/BigFloat.pm0000644403072340010010000054435113035443641020041 0ustar ospjadomain userspackage Math::BigFloat; # # Mike grinned. 'Two down, infinity to go' - Mike Nostrus in 'Before and After' # # The following hash values are used internally: # sign : "+", "-", "+inf", "-inf", or "NaN" if not a number # _m : mantissa ($CALC object) # _es : sign of _e # _e : exponent ($CALC object) # _a : accuracy # _p : precision use 5.006001; use strict; use warnings; use Carp (); use Math::BigInt (); our $VERSION = '1.999808'; require Exporter; our @ISA = qw/Math::BigInt/; our @EXPORT_OK = qw/bpi/; # $_trap_inf/$_trap_nan are internal and should never be accessed from outside our ($AUTOLOAD, $accuracy, $precision, $div_scale, $round_mode, $rnd_mode, $upgrade, $downgrade, $_trap_nan, $_trap_inf); my $class = "Math::BigFloat"; use overload # overload key: with_assign '+' => sub { $_[0] -> copy() -> badd($_[1]); }, '-' => sub { my $c = $_[0] -> copy(); $_[2] ? $c -> bneg() -> badd($_[1]) : $c -> bsub($_[1]); }, '*' => sub { $_[0] -> copy() -> bmul($_[1]); }, '/' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bdiv($_[0]) : $_[0] -> copy() -> bdiv($_[1]); }, '%' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bmod($_[0]) : $_[0] -> copy() -> bmod($_[1]); }, '**' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bpow($_[0]) : $_[0] -> copy() -> bpow($_[1]); }, '<<' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> blsft($_[0]) : $_[0] -> copy() -> blsft($_[1]); }, '>>' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> brsft($_[0]) : $_[0] -> copy() -> brsft($_[1]); }, # overload key: assign '+=' => sub { $_[0]->badd($_[1]); }, '-=' => sub { $_[0]->bsub($_[1]); }, '*=' => sub { $_[0]->bmul($_[1]); }, '/=' => sub { scalar $_[0]->bdiv($_[1]); }, '%=' => sub { $_[0]->bmod($_[1]); }, '**=' => sub { $_[0]->bpow($_[1]); }, '<<=' => sub { $_[0]->blsft($_[1]); }, '>>=' => sub { $_[0]->brsft($_[1]); }, # 'x=' => sub { }, # '.=' => sub { }, # overload key: num_comparison '<' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> blt($_[0]) : $_[0] -> blt($_[1]); }, '<=' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> ble($_[0]) : $_[0] -> ble($_[1]); }, '>' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bgt($_[0]) : $_[0] -> bgt($_[1]); }, '>=' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bge($_[0]) : $_[0] -> bge($_[1]); }, '==' => sub { $_[0] -> beq($_[1]); }, '!=' => sub { $_[0] -> bne($_[1]); }, # overload key: 3way_comparison '<=>' => sub { my $cmp = $_[0] -> bcmp($_[1]); defined($cmp) && $_[2] ? -$cmp : $cmp; }, 'cmp' => sub { $_[2] ? "$_[1]" cmp $_[0] -> bstr() : $_[0] -> bstr() cmp "$_[1]"; }, # overload key: str_comparison # 'lt' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrlt($_[0]) # : $_[0] -> bstrlt($_[1]); }, # # 'le' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrle($_[0]) # : $_[0] -> bstrle($_[1]); }, # # 'gt' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrgt($_[0]) # : $_[0] -> bstrgt($_[1]); }, # # 'ge' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrge($_[0]) # : $_[0] -> bstrge($_[1]); }, # # 'eq' => sub { $_[0] -> bstreq($_[1]); }, # # 'ne' => sub { $_[0] -> bstrne($_[1]); }, # overload key: binary '&' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> band($_[0]) : $_[0] -> copy() -> band($_[1]); }, '&=' => sub { $_[0] -> band($_[1]); }, '|' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bior($_[0]) : $_[0] -> copy() -> bior($_[1]); }, '|=' => sub { $_[0] -> bior($_[1]); }, '^' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bxor($_[0]) : $_[0] -> copy() -> bxor($_[1]); }, '^=' => sub { $_[0] -> bxor($_[1]); }, # '&.' => sub { }, # '&.=' => sub { }, # '|.' => sub { }, # '|.=' => sub { }, # '^.' => sub { }, # '^.=' => sub { }, # overload key: unary 'neg' => sub { $_[0] -> copy() -> bneg(); }, # '!' => sub { }, '~' => sub { $_[0] -> copy() -> bnot(); }, # '~.' => sub { }, # overload key: mutators '++' => sub { $_[0] -> binc() }, '--' => sub { $_[0] -> bdec() }, # overload key: func 'atan2' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> batan2($_[0]) : $_[0] -> copy() -> batan2($_[1]); }, 'cos' => sub { $_[0] -> copy() -> bcos(); }, 'sin' => sub { $_[0] -> copy() -> bsin(); }, 'exp' => sub { $_[0] -> copy() -> bexp($_[1]); }, 'abs' => sub { $_[0] -> copy() -> babs(); }, 'log' => sub { $_[0] -> copy() -> blog(); }, 'sqrt' => sub { $_[0] -> copy() -> bsqrt(); }, 'int' => sub { $_[0] -> copy() -> bint(); }, # overload key: conversion 'bool' => sub { $_[0] -> is_zero() ? '' : 1; }, '""' => sub { $_[0] -> bstr(); }, '0+' => sub { $_[0] -> numify(); }, '=' => sub { $_[0]->copy(); }, ; ############################################################################## # global constants, flags and assorted stuff # the following are public, but their usage is not recommended. Use the # accessor methods instead. # class constants, use Class->constant_name() to access # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common' $round_mode = 'even'; $accuracy = undef; $precision = undef; $div_scale = 40; $upgrade = undef; $downgrade = undef; # the package we are using for our private parts, defaults to: # Math::BigInt->config('lib') my $MBI = 'Math::BigInt::Calc'; # are NaNs ok? (otherwise it dies when encountering an NaN) set w/ config() $_trap_nan = 0; # the same for infinity $_trap_inf = 0; # constant for easier life my $nan = 'NaN'; my $IMPORT = 0; # was import() called yet? used to make require work # some digits of accuracy for blog(undef, 10); which we use in blog() for speed my $LOG_10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726097'; my $LOG_10_A = length($LOG_10)-1; # ditto for log(2) my $LOG_2 = '0.6931471805599453094172321214581765680755001343602552541206800094933936220'; my $LOG_2_A = length($LOG_2)-1; my $HALF = '0.5'; # made into an object if nec. ############################################################################## # the old code had $rnd_mode, so we need to support it, too sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } sub FETCH { return $round_mode; } sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } BEGIN { # when someone sets $rnd_mode, we catch this and check the value to see # whether it is valid or not. $rnd_mode = 'even'; tie $rnd_mode, 'Math::BigFloat'; # we need both of them in this package: *as_int = \&as_number; } sub DESTROY { # going through AUTOLOAD for every DESTROY is costly, avoid it by empty sub } sub AUTOLOAD { # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx() my $name = $AUTOLOAD; $name =~ s/(.*):://; # split package my $c = $1 || $class; no strict 'refs'; $c->import() if $IMPORT == 0; if (!_method_alias($name)) { if (!defined $name) { # delayed load of Carp and avoid recursion Carp::croak("$c: Can't call a method without name"); } if (!_method_hand_up($name)) { # delayed load of Carp and avoid recursion Carp::croak("Can't call $c\-\>$name, not a valid method"); } # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx() $name =~ s/^f/b/; return &{"Math::BigInt"."::$name"}(@_); } my $bname = $name; $bname =~ s/^f/b/; $c .= "::$name"; *{$c} = \&{$bname}; &{$c}; # uses @_ } ############################################################################## { # valid method aliases for AUTOLOAD my %methods = map { $_ => 1 } qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm fint facmp fcmp fzero fnan finf finc fdec ffac fneg fceil ffloor frsft flsft fone flog froot fexp /; # valid methods that can be handed up (for AUTOLOAD) my %hand_ups = map { $_ => 1 } qw / is_nan is_inf is_negative is_positive is_pos is_neg accuracy precision div_scale round_mode fabs fnot objectify upgrade downgrade bone binf bnan bzero bsub /; sub _method_alias { exists $methods{$_[0]||''}; } sub _method_hand_up { exists $hand_ups{$_[0]||''}; } } sub DEBUG () { 0; } sub isa { my ($self, $class) = @_; return if $class =~ /^Math::BigInt/; # we aren't one of these UNIVERSAL::isa($self, $class); } sub config { # return (later set?) configuration data as hash ref my $class = shift || 'Math::BigFloat'; if (@_ == 1 && ref($_[0]) ne 'HASH') { my $cfg = $class->SUPER::config(); return $cfg->{$_[0]}; } my $cfg = $class->SUPER::config(@_); # now we need only to override the ones that are different from our parent $cfg->{class} = $class; $cfg->{with} = $MBI; $cfg; } ############################################################################### # Constructor methods ############################################################################### sub new { # Create a new Math::BigFloat object from a string or another bigfloat object. # _e: exponent # _m: mantissa # sign => ("+", "-", "+inf", "-inf", or "NaN") my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; my ($wanted, @r) = @_; # avoid numify-calls by not using || on $wanted! unless (defined $wanted) { #Carp::carp("Use of uninitialized value in new"); return $self->bzero(@r); } # Using $wanted->isa("Math::BigFloat") here causes a 'Deep recursion on # subroutine "Math::BigFloat::as_number"' in some tests. Fixme! if (UNIVERSAL::isa($wanted, 'Math::BigFloat')) { my $copy = $wanted -> copy(); if ($selfref) { # if new() called as instance method %$self = %$copy; } else { # if new() called as class method $self = $copy; } return $copy; } $class->import() if $IMPORT == 0; # make require work # If called as a class method, initialize a new object. $self = bless {}, $class unless $selfref; # shortcut for bigints and its subclasses if ((ref($wanted)) && $wanted -> can("as_number")) { $self->{_m} = $wanted->as_number()->{value}; # get us a bigint copy $self->{_e} = $MBI->_zero(); $self->{_es} = '+'; $self->{sign} = $wanted->sign(); return $self->bnorm(); } # else: got a string or something masquerading as number (with overload) # Handle Infs. if ($wanted =~ /^\s*([+-]?)inf(inity)?\s*\z/i) { return $downgrade->new($wanted) if $downgrade; my $sgn = $1 || '+'; $self->{sign} = $sgn . 'inf'; # set a default sign for bstr() return $self->binf($sgn); } # Handle explicit NaNs (not the ones returned due to invalid input). if ($wanted =~ /^\s*([+-]?)nan\s*\z/i) { return $downgrade->new($wanted) if $downgrade; $self = $class -> bnan(); $self->round(@r) unless @r >= 2 && !defined $r[0] && !defined $r[1]; return $self; } # Handle hexadecimal numbers. if ($wanted =~ /^\s*[+-]?0[Xx]/) { $self = $class -> from_hex($wanted); $self->round(@r) unless @r >= 2 && !defined $r[0] && !defined $r[1]; return $self; } # Handle binary numbers. if ($wanted =~ /^\s*[+-]?0[Bb]/) { $self = $class -> from_bin($wanted); $self->round(@r) unless @r >= 2 && !defined $r[0] && !defined $r[1]; return $self; } # Shortcut for simple forms like '12' that have no trailing zeros. if ($wanted =~ /^([+-]?)0*([1-9][0-9]*[1-9])$/) { $self->{_e} = $MBI -> _zero(); $self->{_es} = '+'; $self->{sign} = $1 || '+'; $self->{_m} = $MBI -> _new($2); if (!$downgrade) { $self->round(@r) unless @r >= 2 && !defined $r[0] && !defined $r[1]; return $self; } } my ($mis, $miv, $mfv, $es, $ev) = Math::BigInt::_split($wanted); if (!ref $mis) { if ($_trap_nan) { Carp::croak("$wanted is not a number initialized to $class"); } return $downgrade->bnan() if $downgrade; $self->{_e} = $MBI->_zero(); $self->{_es} = '+'; $self->{_m} = $MBI->_zero(); $self->{sign} = $nan; } else { # make integer from mantissa by adjusting exp, then convert to int $self->{_e} = $MBI->_new($$ev); # exponent $self->{_es} = $$es || '+'; my $mantissa = "$$miv$$mfv"; # create mant. $mantissa =~ s/^0+(\d)/$1/; # strip leading zeros $self->{_m} = $MBI->_new($mantissa); # create mant. # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5 if (CORE::length($$mfv) != 0) { my $len = $MBI->_new(CORE::length($$mfv)); ($self->{_e}, $self->{_es}) = _e_sub($self->{_e}, $len, $self->{_es}, '+'); } # we can only have trailing zeros on the mantissa if $$mfv eq '' else { # Use a regexp to count the trailing zeros in $$miv instead of # _zeros() because that is faster, especially when _m is not stored # in base 10. my $zeros = 0; $zeros = CORE::length($1) if $$miv =~ /[1-9](0*)$/; if ($zeros != 0) { my $z = $MBI->_new($zeros); # turn '120e2' into '12e3' $self->{_m} = $MBI->_rsft($self->{_m}, $z, 10); ($self->{_e}, $self->{_es}) = _e_add($self->{_e}, $z, $self->{_es}, '+'); } } $self->{sign} = $$mis; # for something like 0Ey, set y to 0, and -0 => +0 # Check $$miv for being '0' and $$mfv eq '', because otherwise _m could not # have become 0. That's faster than to call $MBI->_is_zero(). $self->{sign} = '+', $self->{_e} = $MBI->_zero() if $$miv eq '0' and $$mfv eq ''; if (!$downgrade) { $self->round(@r) unless @r >= 2 && !defined $r[0] && !defined $r[1]; return $self; } } # if downgrade, inf, NaN or integers go down if ($downgrade && $self->{_es} eq '+') { if ($MBI->_is_zero($self->{_e})) { return $downgrade->new($$mis . $MBI->_str($self->{_m})); } return $downgrade->new($self->bsstr()); } $self->bnorm(); $self->round(@r) unless @r >= 2 && !defined $r[0] && !defined $r[1]; return $self; } sub from_hex { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # Don't modify constant (read-only) objects. return if $selfref && $self->modify('from_hex'); my $str = shift; # If called as a class method, initialize a new object. $self = $class -> bzero() unless $selfref; if ($str =~ s/ ^ \s* # sign ( [+-]? ) # optional "hex marker" (?: 0? x )? # significand using the hex digits 0..9 and a..f ( [0-9a-fA-F]+ (?: _ [0-9a-fA-F]+ )* (?: \. (?: [0-9a-fA-F]+ (?: _ [0-9a-fA-F]+ )* )? )? | \. [0-9a-fA-F]+ (?: _ [0-9a-fA-F]+ )* ) # exponent (power of 2) using decimal digits (?: [Pp] ( [+-]? ) ( \d+ (?: _ \d+ )* ) )? \s* $ //x) { my $s_sign = $1 || '+'; my $s_value = $2; my $e_sign = $3 || '+'; my $e_value = $4 || '0'; $s_value =~ tr/_//d; $e_value =~ tr/_//d; # The significand must be multiplied by 2 raised to this exponent. my $two_expon = $class -> new($e_value); $two_expon -> bneg() if $e_sign eq '-'; # If there is a dot in the significand, remove it and adjust the # exponent according to the number of digits in the fraction part of # the significand. Since the digits in the significand are in base 16, # but the exponent is only in base 2, multiply the exponent adjustment # value by log(16) / log(2) = 4. my $idx = index($s_value, '.'); if ($idx >= 0) { substr($s_value, $idx, 1) = ''; $two_expon -= $class -> new(CORE::length($s_value)) -> bsub($idx) -> bmul("4"); } $self -> {sign} = $s_sign; $self -> {_m} = $MBI -> _from_hex('0x' . $s_value); if ($two_expon > 0) { my $factor = $class -> new("2") -> bpow($two_expon); $self -> bmul($factor); } elsif ($two_expon < 0) { my $factor = $class -> new("0.5") -> bpow(-$two_expon); $self -> bmul($factor); } return $self; } return $self->bnan(); } sub from_oct { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # Don't modify constant (read-only) objects. return if $selfref && $self->modify('from_oct'); my $str = shift; # If called as a class method, initialize a new object. $self = $class -> bzero() unless $selfref; if ($str =~ s/ ^ \s* # sign ( [+-]? ) # significand using the octal digits 0..7 ( [0-7]+ (?: _ [0-7]+ )* (?: \. (?: [0-7]+ (?: _ [0-7]+ )* )? )? | \. [0-7]+ (?: _ [0-7]+ )* ) # exponent (power of 2) using decimal digits (?: [Pp] ( [+-]? ) ( \d+ (?: _ \d+ )* ) )? \s* $ //x) { my $s_sign = $1 || '+'; my $s_value = $2; my $e_sign = $3 || '+'; my $e_value = $4 || '0'; $s_value =~ tr/_//d; $e_value =~ tr/_//d; # The significand must be multiplied by 2 raised to this exponent. my $two_expon = $class -> new($e_value); $two_expon -> bneg() if $e_sign eq '-'; # If there is a dot in the significand, remove it and adjust the # exponent according to the number of digits in the fraction part of # the significand. Since the digits in the significand are in base 8, # but the exponent is only in base 2, multiply the exponent adjustment # value by log(8) / log(2) = 3. my $idx = index($s_value, '.'); if ($idx >= 0) { substr($s_value, $idx, 1) = ''; $two_expon -= $class -> new(CORE::length($s_value)) -> bsub($idx) -> bmul("3"); } $self -> {sign} = $s_sign; $self -> {_m} = $MBI -> _from_oct($s_value); if ($two_expon > 0) { my $factor = $class -> new("2") -> bpow($two_expon); $self -> bmul($factor); } elsif ($two_expon < 0) { my $factor = $class -> new("0.5") -> bpow(-$two_expon); $self -> bmul($factor); } return $self; } return $self->bnan(); } sub from_bin { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # Don't modify constant (read-only) objects. return if $selfref && $self->modify('from_bin'); my $str = shift; # If called as a class method, initialize a new object. $self = $class -> bzero() unless $selfref; if ($str =~ s/ ^ \s* # sign ( [+-]? ) # optional "bin marker" (?: 0? b )? # significand using the binary digits 0 and 1 ( [01]+ (?: _ [01]+ )* (?: \. (?: [01]+ (?: _ [01]+ )* )? )? | \. [01]+ (?: _ [01]+ )* ) # exponent (power of 2) using decimal digits (?: [Pp] ( [+-]? ) ( \d+ (?: _ \d+ )* ) )? \s* $ //x) { my $s_sign = $1 || '+'; my $s_value = $2; my $e_sign = $3 || '+'; my $e_value = $4 || '0'; $s_value =~ tr/_//d; $e_value =~ tr/_//d; # The significand must be multiplied by 2 raised to this exponent. my $two_expon = $class -> new($e_value); $two_expon -> bneg() if $e_sign eq '-'; # If there is a dot in the significand, remove it and adjust the # exponent according to the number of digits in the fraction part of # the significand. my $idx = index($s_value, '.'); if ($idx >= 0) { substr($s_value, $idx, 1) = ''; $two_expon -= $class -> new(CORE::length($s_value)) -> bsub($idx); } $self -> {sign} = $s_sign; $self -> {_m} = $MBI -> _from_bin('0b' . $s_value); if ($two_expon > 0) { my $factor = $class -> new("2") -> bpow($two_expon); $self -> bmul($factor); } elsif ($two_expon < 0) { my $factor = $class -> new("0.5") -> bpow(-$two_expon); $self -> bmul($factor); } return $self; } return $self->bnan(); } sub bzero { # create/assign '+0' if (@_ == 0) { #Carp::carp("Using bone() as a function is deprecated;", # " use bone() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; $self->import() if $IMPORT == 0; # make require work return if $selfref && $self->modify('bzero'); $self = bless {}, $class unless $selfref; $self -> {sign} = '+'; $self -> {_m} = $MBI -> _zero(); $self -> {_es} = '+'; $self -> {_e} = $MBI -> _zero(); if (@_ > 0) { if (@_ > 3) { # call like: $x->bzero($a, $p, $r, $y); ($self, $self->{_a}, $self->{_p}) = $self->_find_round_parameters(@_); } else { # call like: $x->bzero($a, $p, $r); $self->{_a} = $_[0] if !defined $self->{_a} || (defined $_[0] && $_[0] > $self->{_a}); $self->{_p} = $_[1] if !defined $self->{_p} || (defined $_[1] && $_[1] > $self->{_p}); } } return $self; } sub bone { # Create or assign '+1' (or -1 if given sign '-'). if (@_ == 0 || (defined($_[0]) && ($_[0] eq '+' || $_[0] eq '-'))) { #Carp::carp("Using bone() as a function is deprecated;", # " use bone() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; $self->import() if $IMPORT == 0; # make require work return if $selfref && $self->modify('bone'); my $sign = shift; $sign = defined $sign && $sign =~ /^\s*-/ ? "-" : "+"; $self = bless {}, $class unless $selfref; $self -> {sign} = $sign; $self -> {_m} = $MBI -> _one(); $self -> {_es} = '+'; $self -> {_e} = $MBI -> _zero(); if (@_ > 0) { if (@_ > 3) { # call like: $x->bone($sign, $a, $p, $r, $y, ...); ($self, $self->{_a}, $self->{_p}) = $self->_find_round_parameters(@_); } else { # call like: $x->bone($sign, $a, $p, $r); $self->{_a} = $_[0] if ((!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a})); $self->{_p} = $_[1] if ((!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p})); } } return $self; } sub binf { # create/assign a '+inf' or '-inf' if (@_ == 0 || (defined($_[0]) && !ref($_[0]) && $_[0] =~ /^\s*[+-](inf(inity)?)?\s*$/)) { #Carp::carp("Using binf() as a function is deprecated;", # " use binf() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; { no strict 'refs'; if (${"${class}::_trap_inf"}) { Carp::croak("Tried to create +-inf in $class->binf()"); } } $self->import() if $IMPORT == 0; # make require work return if $selfref && $self->modify('binf'); my $sign = shift; $sign = defined $sign && $sign =~ /^\s*-/ ? "-" : "+"; $self = bless {}, $class unless $selfref; $self -> {sign} = $sign . 'inf'; $self -> {_m} = $MBI -> _zero(); $self -> {_es} = '+'; $self -> {_e} = $MBI -> _zero(); return $self; } sub bnan { # create/assign a 'NaN' if (@_ == 0) { #Carp::carp("Using bnan() as a function is deprecated;", # " use bnan() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; { no strict 'refs'; if (${"${class}::_trap_nan"}) { Carp::croak("Tried to create NaN in $class->bnan()"); } } $self->import() if $IMPORT == 0; # make require work return if $selfref && $self->modify('bnan'); $self = bless {}, $class unless $selfref; $self -> {sign} = $nan; $self -> {_m} = $MBI -> _zero(); $self -> {_es} = '+'; $self -> {_e} = $MBI -> _zero(); return $self; } sub bpi { # Called as Argument list # --------- ------------- # Math::BigFloat->bpi() ("Math::BigFloat") # Math::BigFloat->bpi(10) ("Math::BigFloat", 10) # $x->bpi() ($x) # $x->bpi(10) ($x, 10) # Math::BigFloat::bpi() () # Math::BigFloat::bpi(10) (10) # # In ambiguous cases, we favour the OO-style, so the following case # # $n = Math::BigFloat->new("10"); # $x = Math::BigFloat->bpi($n); # # which gives an argument list with the single element $n, is resolved as # # $n->bpi(); my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; my @r; # rounding paramters # If bpi() is called as a function ... # # This cludge is necessary because we still support bpi() as a function. If # bpi() is called with either no argument or one argument, and that one # argument is either undefined or a scalar that looks like a number, then # we assume bpi() is called as a function. if (@_ == 0 && (defined($self) && !ref($self) && $self =~ /^\s*[+-]?\d/i) || !defined($self)) { $r[0] = $self; $class = __PACKAGE__; $self = $class -> bzero(@r); # initialize } # ... or if bpi() is called as a method ... else { @r = @_; if ($selfref) { # bpi() called as instance method return $self if $self -> modify('bpi'); } else { # bpi() called as class method $self = $class -> bzero(@r); # initialize } } ($self, @r) = $self -> _find_round_parameters(@r); # The accuracy, i.e., the number of digits. Pi has one digit before the # dot, so a precision of 4 digits is equivalent to an accuracy of 5 digits. my $n = defined $r[0] ? $r[0] : defined $r[1] ? 1 - $r[1] : $self -> div_scale(); my $rmode = defined $r[2] ? $r[2] : $self -> round_mode(); my $pi; if ($n <= 1000) { # 75 x 14 = 1050 digits my $all_digits = < new($digits . 'e-' . ($n - 1)); } else { # For large accuracy, the arctan formulas become very inefficient with # Math::BigFloat, so use Brent-Salamin (aka AGM or Gauss-Legendre). # Use a few more digits in the intermediate computations. my $nextra = 8; $HALF = $class -> new($HALF) unless ref($HALF); my ($an, $bn, $tn, $pn) = ($class -> bone, $HALF -> copy() -> bsqrt($n), $HALF -> copy() -> bmul($HALF), $class -> bone); while ($pn < $n) { my $prev_an = $an -> copy(); $an -> badd($bn) -> bmul($HALF, $n); $bn -> bmul($prev_an) -> bsqrt($n); $prev_an -> bsub($an); $tn -> bsub($pn * $prev_an * $prev_an); $pn -> badd($pn); } $an -> badd($bn); $an -> bmul($an, $n) -> bdiv(4 * $tn, $n); $an -> round(@r); $pi = $an; } if (defined $r[0]) { $pi -> accuracy($r[0]); } elsif (defined $r[1]) { $pi -> precision($r[1]); } for my $key (qw/ sign _m _es _e _a _p /) { $self -> {$key} = $pi -> {$key}; } return $self; } sub copy { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # If called as a class method, the object to copy is the next argument. $self = shift() unless $selfref; my $copy = bless {}, $class; $copy->{sign} = $self->{sign}; $copy->{_es} = $self->{_es}; $copy->{_m} = $MBI->_copy($self->{_m}); $copy->{_e} = $MBI->_copy($self->{_e}); $copy->{_a} = $self->{_a} if exists $self->{_a}; $copy->{_p} = $self->{_p} if exists $self->{_p}; return $copy; } sub as_number { # return copy as a bigint representation of this Math::BigFloat number my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); return $x if $x->modify('as_number'); if (!$x->isa('Math::BigFloat')) { # if the object can as_number(), use it return $x->as_number() if $x->can('as_number'); # otherwise, get us a float and then a number $x = $x->can('as_float') ? $x->as_float() : $class->new(0+"$x"); } return Math::BigInt->binf($x->sign()) if $x->is_inf(); return Math::BigInt->bnan() if $x->is_nan(); my $z = $MBI->_copy($x->{_m}); if ($x->{_es} eq '-') { # < 0 $z = $MBI->_rsft($z, $x->{_e}, 10); } elsif (! $MBI->_is_zero($x->{_e})) { # > 0 $z = $MBI->_lsft($z, $x->{_e}, 10); } $z = Math::BigInt->new($x->{sign} . $MBI->_str($z)); $z; } ############################################################################### # Boolean methods ############################################################################### sub is_zero { # return true if arg (BFLOAT or num_str) is zero my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); ($x->{sign} eq '+' && $MBI->_is_zero($x->{_m})) ? 1 : 0; } sub is_one { # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given my ($class, $x, $sign) = ref($_[0]) ? (undef, @_) : objectify(1, @_); $sign = '+' if !defined $sign || $sign ne '-'; ($x->{sign} eq $sign && $MBI->_is_zero($x->{_e}) && $MBI->_is_one($x->{_m})) ? 1 : 0; } sub is_odd { # return true if arg (BFLOAT or num_str) is odd or false if even my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); (($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't ($MBI->_is_zero($x->{_e})) && ($MBI->_is_odd($x->{_m}))) ? 1 : 0; } sub is_even { # return true if arg (BINT or num_str) is even or false if odd my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); (($x->{sign} =~ /^[+-]$/) && # NaN & +-inf aren't ($x->{_es} eq '+') && # 123.45 isn't ($MBI->_is_even($x->{_m}))) ? 1 : 0; # but 1200 is } sub is_int { # return true if arg (BFLOAT or num_str) is an integer my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); (($x->{sign} =~ /^[+-]$/) && # NaN and +-inf aren't ($x->{_es} eq '+')) ? 1 : 0; # 1e-1 => no integer } ############################################################################### # Comparison methods ############################################################################### sub bcmp { # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) # set up parameters my ($class, $x, $y) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y) = objectify(2, @_); } return $upgrade->bcmp($x, $y) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); # Handle all 'nan' cases. return undef if ($x->{sign} eq $nan) || ($y->{sign} eq $nan); # Handle all '+inf' and '-inf' cases. return 0 if ($x->{sign} eq '+inf' && $y->{sign} eq '+inf' || $x->{sign} eq '-inf' && $y->{sign} eq '-inf'); return +1 if $x->{sign} eq '+inf'; # x = +inf and y < +inf return -1 if $x->{sign} eq '-inf'; # x = -inf and y > -inf return -1 if $y->{sign} eq '+inf'; # x < +inf and y = +inf return +1 if $y->{sign} eq '-inf'; # x > -inf and y = -inf # Handle all cases with opposite signs. return +1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # also does 0 <=> -y return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # also does -x <=> 0 # Handle all remaining zero cases. my $xz = $x->is_zero(); my $yz = $y->is_zero(); return 0 if $xz && $yz; # 0 <=> 0 return -1 if $xz && $y->{sign} eq '+'; # 0 <=> +y return +1 if $yz && $x->{sign} eq '+'; # +x <=> 0 # Both arguments are now finite, non-zero numbers with the same sign. my $cmp; # The next step is to compare the exponents, but since each mantissa is an # integer of arbitrary value, the exponents must be normalized by the length # of the mantissas before we can compare them. my $mxl = $MBI->_len($x->{_m}); my $myl = $MBI->_len($y->{_m}); # If the mantissas have the same length, there is no point in normalizing the # exponents by the length of the mantissas, so treat that as a special case. if ($mxl == $myl) { # First handle the two cases where the exponents have different signs. if ($x->{_es} eq '+' && $y->{_es} eq '-') { $cmp = +1; } elsif ($x->{_es} eq '-' && $y->{_es} eq '+') { $cmp = -1; } # Then handle the case where the exponents have the same sign. else { $cmp = $MBI->_acmp($x->{_e}, $y->{_e}); $cmp = -$cmp if $x->{_es} eq '-'; } # Adjust for the sign, which is the same for x and y, and bail out if # we're done. $cmp = -$cmp if $x->{sign} eq '-'; # 124 > 123, but -124 < -123 return $cmp if $cmp; } # We must normalize each exponent by the length of the corresponding # mantissa. Life is a lot easier if we first make both exponents # non-negative. We do this by adding the same positive value to both # exponent. This is safe, because when comparing the exponents, only the # relative difference is important. my $ex; my $ey; if ($x->{_es} eq '+') { # If the exponent of x is >= 0 and the exponent of y is >= 0, there is no # need to do anything special. if ($y->{_es} eq '+') { $ex = $MBI->_copy($x->{_e}); $ey = $MBI->_copy($y->{_e}); } # If the exponent of x is >= 0 and the exponent of y is < 0, add the # absolute value of the exponent of y to both. else { $ex = $MBI->_copy($x->{_e}); $ex = $MBI->_add($ex, $y->{_e}); # ex + |ey| $ey = $MBI->_zero(); # -ex + |ey| = 0 } } else { # If the exponent of x is < 0 and the exponent of y is >= 0, add the # absolute value of the exponent of x to both. if ($y->{_es} eq '+') { $ex = $MBI->_zero(); # -ex + |ex| = 0 $ey = $MBI->_copy($y->{_e}); $ey = $MBI->_add($ey, $x->{_e}); # ey + |ex| } # If the exponent of x is < 0 and the exponent of y is < 0, add the # absolute values of both exponents to both exponents. else { $ex = $MBI->_copy($y->{_e}); # -ex + |ey| + |ex| = |ey| $ey = $MBI->_copy($x->{_e}); # -ey + |ex| + |ey| = |ex| } } # Now we can normalize the exponents by adding lengths of the mantissas. $ex = $MBI->_add($ex, $MBI->_new($mxl)); $ey = $MBI->_add($ey, $MBI->_new($myl)); # We're done if the exponents are different. $cmp = $MBI->_acmp($ex, $ey); $cmp = -$cmp if $x->{sign} eq '-'; # 124 > 123, but -124 < -123 return $cmp if $cmp; # Compare the mantissas, but first normalize them by padding the shorter # mantissa with zeros (shift left) until it has the same length as the longer # mantissa. my $mx = $x->{_m}; my $my = $y->{_m}; if ($mxl > $myl) { $my = $MBI->_lsft($MBI->_copy($my), $MBI->_new($mxl - $myl), 10); } elsif ($mxl < $myl) { $mx = $MBI->_lsft($MBI->_copy($mx), $MBI->_new($myl - $mxl), 10); } $cmp = $MBI->_acmp($mx, $my); $cmp = -$cmp if $x->{sign} eq '-'; # 124 > 123, but -124 < -123 return $cmp; } sub bacmp { # Compares 2 values, ignoring their signs. # Returns one of undef, <0, =0, >0. (suitable for sort) # set up parameters my ($class, $x, $y) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y) = objectify(2, @_); } return $upgrade->bacmp($x, $y) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); # handle +-inf and NaN's if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) { return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); return 0 if ($x->is_inf() && $y->is_inf()); return 1 if ($x->is_inf() && !$y->is_inf()); return -1; } # shortcut my $xz = $x->is_zero(); my $yz = $y->is_zero(); return 0 if $xz && $yz; # 0 <=> 0 return -1 if $xz && !$yz; # 0 <=> +y return 1 if $yz && !$xz; # +x <=> 0 # adjust so that exponents are equal my $lxm = $MBI->_len($x->{_m}); my $lym = $MBI->_len($y->{_m}); my ($xes, $yes) = (1, 1); $xes = -1 if $x->{_es} ne '+'; $yes = -1 if $y->{_es} ne '+'; # the numify somewhat limits our length, but makes it much faster my $lx = $lxm + $xes * $MBI->_num($x->{_e}); my $ly = $lym + $yes * $MBI->_num($y->{_e}); my $l = $lx - $ly; return $l <=> 0 if $l != 0; # lengths (corrected by exponent) are equal # so make mantissa equal-length by padding with zero (shift left) my $diff = $lxm - $lym; my $xm = $x->{_m}; # not yet copy it my $ym = $y->{_m}; if ($diff > 0) { $ym = $MBI->_copy($y->{_m}); $ym = $MBI->_lsft($ym, $MBI->_new($diff), 10); } elsif ($diff < 0) { $xm = $MBI->_copy($x->{_m}); $xm = $MBI->_lsft($xm, $MBI->_new(-$diff), 10); } $MBI->_acmp($xm, $ym); } ############################################################################### # Arithmetic methods ############################################################################### sub bneg { # (BINT or num_str) return BINT # negate number or make a negated number from string my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return $x if $x->modify('bneg'); # for +0 do not negate (to have always normalized +0). Does nothing for 'NaN' $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_m})); $x; } sub bnorm { # adjust m and e so that m is smallest possible my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return $x if $x->{sign} !~ /^[+-]$/; # inf, nan etc my $zeros = $MBI->_zeros($x->{_m}); # correct for trailing zeros if ($zeros != 0) { my $z = $MBI->_new($zeros); $x->{_m} = $MBI->_rsft($x->{_m}, $z, 10); if ($x->{_es} eq '-') { if ($MBI->_acmp($x->{_e}, $z) >= 0) { $x->{_e} = $MBI->_sub($x->{_e}, $z); $x->{_es} = '+' if $MBI->_is_zero($x->{_e}); } else { $x->{_e} = $MBI->_sub($MBI->_copy($z), $x->{_e}); $x->{_es} = '+'; } } else { $x->{_e} = $MBI->_add($x->{_e}, $z); } } else { # $x can only be 0Ey if there are no trailing zeros ('0' has 0 trailing # zeros). So, for something like 0Ey, set y to 1, and -0 => +0 $x->{sign} = '+', $x->{_es} = '+', $x->{_e} = $MBI->_one() if $MBI->_is_zero($x->{_m}); } $x; } sub binc { # increment arg by one my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('binc'); if ($x->{_es} eq '-') { return $x->badd($class->bone(), @r); # digits after dot } if (!$MBI->_is_zero($x->{_e})) # _e == 0 for NaN, inf, -inf { # 1e2 => 100, so after the shift below _m has a '0' as last digit $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e}, 10); # 1e2 => 100 $x->{_e} = $MBI->_zero(); # normalize $x->{_es} = '+'; # we know that the last digit of $x will be '1' or '9', depending on the # sign } # now $x->{_e} == 0 if ($x->{sign} eq '+') { $x->{_m} = $MBI->_inc($x->{_m}); return $x->bnorm()->bround(@r); } elsif ($x->{sign} eq '-') { $x->{_m} = $MBI->_dec($x->{_m}); $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # -1 +1 => -0 => +0 return $x->bnorm()->bround(@r); } # inf, nan handling etc $x->badd($class->bone(), @r); # badd() does round } sub bdec { # decrement arg by one my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bdec'); if ($x->{_es} eq '-') { return $x->badd($class->bone('-'), @r); # digits after dot } if (!$MBI->_is_zero($x->{_e})) { $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e}, 10); # 1e2 => 100 $x->{_e} = $MBI->_zero(); # normalize $x->{_es} = '+'; } # now $x->{_e} == 0 my $zero = $x->is_zero(); # <= 0 if (($x->{sign} eq '-') || $zero) { $x->{_m} = $MBI->_inc($x->{_m}); $x->{sign} = '-' if $zero; # 0 => 1 => -1 $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # -1 +1 => -0 => +0 return $x->bnorm()->round(@r); } # > 0 elsif ($x->{sign} eq '+') { $x->{_m} = $MBI->_dec($x->{_m}); return $x->bnorm()->round(@r); } # inf, nan handling etc $x->badd($class->bone('-'), @r); # does round } sub badd { # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first) # return result as BFLOAT # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('badd'); # inf and NaN handling if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) { # NaN first return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); # inf handling if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) { # +inf++inf or -inf+-inf => same, rest is NaN return $x if $x->{sign} eq $y->{sign}; return $x->bnan(); } # +-inf + something => +inf; something +-inf => +-inf $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; return $x; } return $upgrade->badd($x, $y, @r) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); $r[3] = $y; # no push! # speed: no add for 0+y or x+0 return $x->bround(@r) if $y->is_zero(); # x+0 if ($x->is_zero()) # 0+y { # make copy, clobbering up x (modify in place!) $x->{_e} = $MBI->_copy($y->{_e}); $x->{_es} = $y->{_es}; $x->{_m} = $MBI->_copy($y->{_m}); $x->{sign} = $y->{sign} || $nan; return $x->round(@r); } # take lower of the two e's and adapt m1 to it to match m2 my $e = $y->{_e}; $e = $MBI->_zero() if !defined $e; # if no BFLOAT? $e = $MBI->_copy($e); # make copy (didn't do it yet) my $es; ($e, $es) = _e_sub($e, $x->{_e}, $y->{_es} || '+', $x->{_es}); my $add = $MBI->_copy($y->{_m}); if ($es eq '-') # < 0 { $x->{_m} = $MBI->_lsft($x->{_m}, $e, 10); ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $e, $x->{_es}, $es); } elsif (!$MBI->_is_zero($e)) # > 0 { $add = $MBI->_lsft($add, $e, 10); } # else: both e are the same, so just leave them if ($x->{sign} eq $y->{sign}) { # add $x->{_m} = $MBI->_add($x->{_m}, $add); } else { ($x->{_m}, $x->{sign}) = _e_add($x->{_m}, $add, $x->{sign}, $y->{sign}); } # delete trailing zeros, then round $x->bnorm()->round(@r); } sub bsub { # (BINT or num_str, BINT or num_str) return BINT # subtract second arg from first, modify first # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x -> modify('bsub'); return $upgrade -> new($x) -> bsub($upgrade -> new($y), @r) if defined $upgrade && (!$x -> isa($class) || !$y -> isa($class)); return $x -> round(@r) if $y -> is_zero(); # To correctly handle the lone special case $x -> bsub($x), we note the # sign of $x, then flip the sign from $y, and if the sign of $x did change, # too, then we caught the special case: my $xsign = $x -> {sign}; $y -> {sign} =~ tr/+-/-+/; # does nothing for NaN if ($xsign ne $x -> {sign}) { # special case of $x -> bsub($x) results in 0 return $x -> bzero(@r) if $xsign =~ /^[+-]$/; return $x -> bnan(); # NaN, -inf, +inf } $x -> badd($y, @r); # badd does not leave internal zeros $y -> {sign} =~ tr/+-/-+/; # refix $y (does nothing for NaN) $x; # already rounded by badd() or no rounding } sub bmul { # multiply two numbers # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bmul'); return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); # inf handling if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) { return $x->bnan() if $x->is_zero() || $y->is_zero(); # result will always be +-inf: # +inf * +/+inf => +inf, -inf * -/-inf => +inf # +inf * -/-inf => -inf, -inf * +/+inf => -inf return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); return $x->binf('-'); } return $upgrade->bmul($x, $y, @r) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); # aEb * cEd = (a*c)E(b+d) $x->{_m} = $MBI->_mul($x->{_m}, $y->{_m}); ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es}); $r[3] = $y; # no push! # adjust sign: $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; $x->bnorm->round(@r); } sub bmuladd { # multiply two numbers and add the third to the result # set up parameters my ($class, $x, $y, $z, @r) = objectify(3, @_); return $x if $x->modify('bmuladd'); return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan) || ($z->{sign} eq $nan)); # inf handling if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) { return $x->bnan() if $x->is_zero() || $y->is_zero(); # result will always be +-inf: # +inf * +/+inf => +inf, -inf * -/-inf => +inf # +inf * -/-inf => -inf, -inf * +/+inf => -inf return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); return $x->binf('-'); } return $upgrade->bmul($x, $y, @r) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); # aEb * cEd = (a*c)E(b+d) $x->{_m} = $MBI->_mul($x->{_m}, $y->{_m}); ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es}); $r[3] = $y; # no push! # adjust sign: $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+'; # z=inf handling (z=NaN handled above) $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/; # take lower of the two e's and adapt m1 to it to match m2 my $e = $z->{_e}; $e = $MBI->_zero() if !defined $e; # if no BFLOAT? $e = $MBI->_copy($e); # make copy (didn't do it yet) my $es; ($e, $es) = _e_sub($e, $x->{_e}, $z->{_es} || '+', $x->{_es}); my $add = $MBI->_copy($z->{_m}); if ($es eq '-') # < 0 { $x->{_m} = $MBI->_lsft($x->{_m}, $e, 10); ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $e, $x->{_es}, $es); } elsif (!$MBI->_is_zero($e)) # > 0 { $add = $MBI->_lsft($add, $e, 10); } # else: both e are the same, so just leave them if ($x->{sign} eq $z->{sign}) { # add $x->{_m} = $MBI->_add($x->{_m}, $add); } else { ($x->{_m}, $x->{sign}) = _e_add($x->{_m}, $add, $x->{sign}, $z->{sign}); } # delete trailing zeros, then round $x->bnorm()->round(@r); } sub bdiv { # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return # (BFLOAT, BFLOAT) (quo, rem) or BFLOAT (only quo) # set up parameters my ($class, $x, $y, $a, $p, $r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $a, $p, $r) = objectify(2, @_); } return $x if $x->modify('bdiv'); my $wantarray = wantarray; # call only once # At least one argument is NaN. This is handled the same way as in # Math::BigInt -> bdiv(). if ($x -> is_nan() || $y -> is_nan()) { return $wantarray ? ($x -> bnan(), $class -> bnan()) : $x -> bnan(); } # Divide by zero and modulo zero. This is handled the same way as in # Math::BigInt -> bdiv(). See the comment in the code for Math::BigInt -> # bdiv() for further details. if ($y -> is_zero()) { my ($quo, $rem); if ($wantarray) { $rem = $x -> copy(); } if ($x -> is_zero()) { $quo = $x -> bnan(); } else { $quo = $x -> binf($x -> {sign}); } return $wantarray ? ($quo, $rem) : $quo; } # Numerator (dividend) is +/-inf. This is handled the same way as in # Math::BigInt -> bdiv(). See the comment in the code for Math::BigInt -> # bdiv() for further details. if ($x -> is_inf()) { my ($quo, $rem); $rem = $class -> bnan() if $wantarray; if ($y -> is_inf()) { $quo = $x -> bnan(); } else { my $sign = $x -> bcmp(0) == $y -> bcmp(0) ? '+' : '-'; $quo = $x -> binf($sign); } return $wantarray ? ($quo, $rem) : $quo; } # Denominator (divisor) is +/-inf. This is handled the same way as in # Math::BigInt -> bdiv(), with one exception: In scalar context, # Math::BigFloat does true division (although rounded), not floored division # (F-division), so a finite number divided by +/-inf is always zero. See the # comment in the code for Math::BigInt -> bdiv() for further details. if ($y -> is_inf()) { my ($quo, $rem); if ($wantarray) { if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) { $rem = $x -> copy(); $quo = $x -> bzero(); } else { $rem = $class -> binf($y -> {sign}); $quo = $x -> bone('-'); } return ($quo, $rem); } else { if ($y -> is_inf()) { if ($x -> is_nan() || $x -> is_inf()) { return $x -> bnan(); } else { return $x -> bzero(); } } } } # At this point, both the numerator and denominator are finite numbers, and # the denominator (divisor) is non-zero. # x == 0? return wantarray ? ($x, $class->bzero()) : $x if $x->is_zero(); # upgrade ? return $upgrade->bdiv($upgrade->new($x), $y, $a, $p, $r) if defined $upgrade; # we need to limit the accuracy to protect against overflow my $fallback = 0; my (@params, $scale); ($x, @params) = $x->_find_round_parameters($a, $p, $r, $y); return $x if $x->is_nan(); # error in _find_round_parameters? # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $scale = $params[0]+4; # at least four more for proper round $params[2] = $r; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } my $rem; $rem = $class -> bzero() if wantarray; $y = $class->new($y) unless $y->isa('Math::BigFloat'); my $lx = $MBI -> _len($x->{_m}); my $ly = $MBI -> _len($y->{_m}); $scale = $lx if $lx > $scale; $scale = $ly if $ly > $scale; my $diff = $ly - $lx; $scale += $diff if $diff > 0; # if lx << ly, but not if ly << lx! # check that $y is not 1 nor -1 and cache the result: my $y_not_one = !($MBI->_is_zero($y->{_e}) && $MBI->_is_one($y->{_m})); # flipping the sign of $y will also flip the sign of $x for the special # case of $x->bsub($x); so we can catch it below: my $xsign = $x->{sign}; $y->{sign} =~ tr/+-/-+/; if ($xsign ne $x->{sign}) { # special case of $x /= $x results in 1 $x->bone(); # "fixes" also sign of $y, since $x is $y } else { # correct $y's sign again $y->{sign} =~ tr/+-/-+/; # continue with normal div code: # make copy of $x in case of list context for later remainder calculation if (wantarray && $y_not_one) { $rem = $x->copy(); } $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; # check for / +-1 (+/- 1E0) if ($y_not_one) { # promote BigInts and it's subclasses (except when already a Math::BigFloat) $y = $class->new($y) unless $y->isa('Math::BigFloat'); # calculate the result to $scale digits and then round it # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d) $x->{_m} = $MBI->_lsft($x->{_m}, $MBI->_new($scale), 10); $x->{_m} = $MBI->_div($x->{_m}, $y->{_m}); # a/c # correct exponent of $x ($x->{_e}, $x->{_es}) = _e_sub($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es}); # correct for 10**scale ($x->{_e}, $x->{_es}) = _e_sub($x->{_e}, $MBI->_new($scale), $x->{_es}, '+'); $x->bnorm(); # remove trailing 0's } } # end else $x != $y # shortcut to not run through _find_round_parameters again if (defined $params[0]) { delete $x->{_a}; # clear before round $x->bround($params[0], $params[2]); # then round accordingly } else { delete $x->{_p}; # clear before round $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } if (wantarray) { if ($y_not_one) { $x -> bfloor(); $rem->bmod($y, @params); # copy already done } if ($fallback) { # clear a/p after round, since user did not request it delete $rem->{_a}; delete $rem->{_p}; } return ($x, $rem); } $x; } sub bmod { # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return remainder # set up parameters my ($class, $x, $y, $a, $p, $r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $a, $p, $r) = objectify(2, @_); } return $x if $x->modify('bmod'); # At least one argument is NaN. This is handled the same way as in # Math::BigInt -> bmod(). if ($x -> is_nan() || $y -> is_nan()) { return $x -> bnan(); } # Modulo zero. This is handled the same way as in Math::BigInt -> bmod(). if ($y -> is_zero()) { return $x; } # Numerator (dividend) is +/-inf. This is handled the same way as in # Math::BigInt -> bmod(). if ($x -> is_inf()) { return $x -> bnan(); } # Denominator (divisor) is +/-inf. This is handled the same way as in # Math::BigInt -> bmod(). if ($y -> is_inf()) { if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) { return $x; } else { return $x -> binf($y -> sign()); } } return $x->bzero() if $x->is_zero() || ($x->is_int() && # check that $y == +1 or $y == -1: ($MBI->_is_zero($y->{_e}) && $MBI->_is_one($y->{_m}))); my $cmp = $x->bacmp($y); # equal or $x < $y? if ($cmp == 0) { # $x == $y => result 0 return $x -> bzero($a, $p); } # only $y of the operands negative? my $neg = $x->{sign} ne $y->{sign} ? 1 : 0; $x->{sign} = $y->{sign}; # calc sign first if ($cmp < 0 && $neg == 0) { # $x < $y => result $x return $x -> round($a, $p, $r); } my $ym = $MBI->_copy($y->{_m}); # 2e1 => 20 $ym = $MBI->_lsft($ym, $y->{_e}, 10) if $y->{_es} eq '+' && !$MBI->_is_zero($y->{_e}); # if $y has digits after dot my $shifty = 0; # correct _e of $x by this if ($y->{_es} eq '-') # has digits after dot { # 123 % 2.5 => 1230 % 25 => 5 => 0.5 $shifty = $MBI->_num($y->{_e}); # no more digits after dot $x->{_m} = $MBI->_lsft($x->{_m}, $y->{_e}, 10); # 123 => 1230, $y->{_m} is already 25 } # $ym is now mantissa of $y based on exponent 0 my $shiftx = 0; # correct _e of $x by this if ($x->{_es} eq '-') # has digits after dot { # 123.4 % 20 => 1234 % 200 $shiftx = $MBI->_num($x->{_e}); # no more digits after dot $ym = $MBI->_lsft($ym, $x->{_e}, 10); # 123 => 1230 } # 123e1 % 20 => 1230 % 20 if ($x->{_es} eq '+' && !$MBI->_is_zero($x->{_e})) { $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e}, 10); # es => '+' here } $x->{_e} = $MBI->_new($shiftx); $x->{_es} = '+'; $x->{_es} = '-' if $shiftx != 0 || $shifty != 0; $x->{_e} = $MBI->_add($x->{_e}, $MBI->_new($shifty)) if $shifty != 0; # now mantissas are equalized, exponent of $x is adjusted, so calc result $x->{_m} = $MBI->_mod($x->{_m}, $ym); $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # fix sign for -0 $x->bnorm(); if ($neg != 0 && ! $x -> is_zero()) # one of them negative => correct in place { my $r = $y - $x; $x->{_m} = $r->{_m}; $x->{_e} = $r->{_e}; $x->{_es} = $r->{_es}; $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # fix sign for -0 $x->bnorm(); } $x->round($a, $p, $r, $y); # round and return } sub bmodpow { # takes a very large number to a very large exponent in a given very # large modulus, quickly, thanks to binary exponentiation. Supports # negative exponents. my ($class, $num, $exp, $mod, @r) = objectify(3, @_); return $num if $num->modify('bmodpow'); # check modulus for valid values return $num->bnan() if ($mod->{sign} ne '+' # NaN, -, -inf, +inf || $mod->is_zero()); # check exponent for valid values if ($exp->{sign} =~ /\w/) { # i.e., if it's NaN, +inf, or -inf... return $num->bnan(); } $num->bmodinv ($mod) if ($exp->{sign} eq '-'); # check num for valid values (also NaN if there was no inverse but $exp < 0) return $num->bnan() if $num->{sign} !~ /^[+-]$/; # $mod is positive, sign on $exp is ignored, result also positive # XXX TODO: speed it up when all three numbers are integers $num->bpow($exp)->bmod($mod); } sub bpow { # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT # compute power of two numbers, second arg is used as integer # modifies first argument # set up parameters my ($class, $x, $y, $a, $p, $r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $a, $p, $r) = objectify(2, @_); } return $x if $x->modify('bpow'); return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; return $x if $x->{sign} =~ /^[+-]inf$/; # cache the result of is_zero my $y_is_zero = $y->is_zero(); return $x->bone() if $y_is_zero; return $x if $x->is_one() || $y->is_one(); my $x_is_zero = $x->is_zero(); return $x->_pow($y, $a, $p, $r) if !$x_is_zero && !$y->is_int(); # non-integer power my $y1 = $y->as_number()->{value}; # make MBI part # if ($x == -1) if ($x->{sign} eq '-' && $MBI->_is_one($x->{_m}) && $MBI->_is_zero($x->{_e})) { # if $x == -1 and odd/even y => +1/-1 because +-1 ^ (+-1) => +-1 return $MBI->_is_odd($y1) ? $x : $x->babs(1); } if ($x_is_zero) { return $x if $y->{sign} eq '+'; # 0**y => 0 (if not y <= 0) # 0 ** -y => 1 / (0 ** y) => 1 / 0! (1 / 0 => +inf) return $x->binf(); } my $new_sign = '+'; $new_sign = $MBI->_is_odd($y1) ? '-' : '+' if $x->{sign} ne '+'; # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster) $x->{_m} = $MBI->_pow($x->{_m}, $y1); $x->{_e} = $MBI->_mul ($x->{_e}, $y1); $x->{sign} = $new_sign; $x->bnorm(); if ($y->{sign} eq '-') { # modify $x in place! my $z = $x->copy(); $x->bone(); return scalar $x->bdiv($z, $a, $p, $r); # round in one go (might ignore y's A!) } $x->round($a, $p, $r, $y); } sub blog { my ($class, $x, $base, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(2, @_); # If called as $x -> blog() or $x -> blog(undef), don't objectify the # undefined base, since undef signals that the base is Euler's number. #unless (ref($x) && !defined($base)) { # # objectify is costly, so avoid it # if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { # ($class, $x, $base, $a, $p, $r) = objectify(2, @_); # } #} return $x if $x->modify('blog'); return $x -> bnan() if $x -> is_nan(); # we need to limit the accuracy to protect against overflow my $fallback = 0; my ($scale, @params); ($x, @params) = $x->_find_round_parameters($a, $p, $r); # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $params[1] = undef; # P = undef $scale = $params[0]+4; # at least four more for proper round $params[2] = $r; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } my $done = 0; if (defined $base) { $base = $class -> new($base) unless ref $base; if ($base -> is_nan() || $base -> is_one()) { $x -> bnan(); $done = 1; } elsif ($base -> is_inf() || $base -> is_zero()) { if ($x -> is_inf() || $x -> is_zero()) { $x -> bnan(); } else { $x -> bzero(@params); } $done = 1; } elsif ($base -> is_negative()) { # -inf < base < 0 if ($x -> is_one()) { # x = 1 $x -> bzero(@params); } elsif ($x == $base) { $x -> bone('+', @params); # x = base } else { $x -> bnan(); # otherwise } $done = 1; } elsif ($x == $base) { $x -> bone('+', @params); # 0 < base && 0 < x < inf $done = 1; } } # We now know that the base is either undefined or positive and finite. unless ($done) { if ($x -> is_inf()) { # x = +/-inf my $sign = defined $base && $base < 1 ? '-' : '+'; $x -> binf($sign); $done = 1; } elsif ($x -> is_neg()) { # -inf < x < 0 $x -> bnan(); $done = 1; } elsif ($x -> is_one()) { # x = 1 $x -> bzero(@params); $done = 1; } elsif ($x -> is_zero()) { # x = 0 my $sign = defined $base && $base < 1 ? '+' : '-'; $x -> binf($sign); $done = 1; } } if ($done) { if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } return $x; } # when user set globals, they would interfere with our calculation, so # disable them and later re-enable them no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # we also need to disable any set A or P on $x (_find_round_parameters took # them already into account), since these would interfere, too delete $x->{_a}; delete $x->{_p}; # need to disable $upgrade in BigInt, to avoid deep recursion local $Math::BigInt::upgrade = undef; local $Math::BigFloat::downgrade = undef; # upgrade $x if $x is not a Math::BigFloat (handle BigInt input) # XXX TODO: rebless! if (!$x->isa('Math::BigFloat')) { $x = Math::BigFloat->new($x); $class = ref($x); } $done = 0; # If the base is defined and an integer, try to calculate integer result # first. This is very fast, and in case the real result was found, we can # stop right here. if (defined $base && $base->is_int() && $x->is_int()) { my $i = $MBI->_copy($x->{_m}); $i = $MBI->_lsft($i, $x->{_e}, 10) unless $MBI->_is_zero($x->{_e}); my $int = Math::BigInt->bzero(); $int->{value} = $i; $int->blog($base->as_number()); # if ($exact) if ($base->as_number()->bpow($int) == $x) { # found result, return it $x->{_m} = $int->{value}; $x->{_e} = $MBI->_zero(); $x->{_es} = '+'; $x->bnorm(); $done = 1; } } if ($done == 0) { # base is undef, so base should be e (Euler's number), so first calculate the # log to base e (using reduction by 10 (and probably 2)): $class->_log_10($x, $scale); # and if a different base was requested, convert it if (defined $base) { $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat'); # not ln, but some other base (don't modify $base) $x->bdiv($base->copy()->blog(undef, $scale), $scale); } } # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $x; } sub bexp { # Calculate e ** X (Euler's number to the power of X) my ($class, $x, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bexp'); return $x->binf() if $x->{sign} eq '+inf'; return $x->bzero() if $x->{sign} eq '-inf'; # we need to limit the accuracy to protect against overflow my $fallback = 0; my ($scale, @params); ($x, @params) = $x->_find_round_parameters($a, $p, $r); # also takes care of the "error in _find_round_parameters?" case return $x if $x->{sign} eq 'NaN'; # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $params[1] = undef; # P = undef $scale = $params[0]+4; # at least four more for proper round $params[2] = $r; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it's not enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } return $x->bone(@params) if $x->is_zero(); if (!$x->isa('Math::BigFloat')) { $x = Math::BigFloat->new($x); $class = ref($x); } # when user set globals, they would interfere with our calculation, so # disable them and later re-enable them no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # we also need to disable any set A or P on $x (_find_round_parameters took # them already into account), since these would interfere, too delete $x->{_a}; delete $x->{_p}; # need to disable $upgrade in BigInt, to avoid deep recursion local $Math::BigInt::upgrade = undef; local $Math::BigFloat::downgrade = undef; my $x_org = $x->copy(); # We use the following Taylor series: # x x^2 x^3 x^4 # e = 1 + --- + --- + --- + --- ... # 1! 2! 3! 4! # The difference for each term is X and N, which would result in: # 2 copy, 2 mul, 2 add, 1 inc, 1 div operations per term # But it is faster to compute exp(1) and then raising it to the # given power, esp. if $x is really big and an integer because: # * The numerator is always 1, making the computation faster # * the series converges faster in the case of x == 1 # * We can also easily check when we have reached our limit: when the # term to be added is smaller than "1E$scale", we can stop - f.i. # scale == 5, and we have 1/40320, then we stop since 1/40320 < 1E-5. # * we can compute the *exact* result by simulating bigrat math: # 1 1 gcd(3, 4) = 1 1*24 + 1*6 5 # - + - = ---------- = -- # 6 24 6*24 24 # We do not compute the gcd() here, but simple do: # 1 1 1*24 + 1*6 30 # - + - = --------- = -- # 6 24 6*24 144 # In general: # a c a*d + c*b and note that c is always 1 and d = (b*f) # - + - = --------- # b d b*d # This leads to: which can be reduced by b to: # a 1 a*b*f + b a*f + 1 # - + - = --------- = ------- # b b*f b*b*f b*f # The first terms in the series are: # 1 1 1 1 1 1 1 1 13700 # -- + -- + -- + -- + -- + --- + --- + ---- = ----- # 1 1 2 6 24 120 720 5040 5040 # Note that we cannot simple reduce 13700/5040 to 685/252, but must keep A and B! if ($scale <= 75) { # set $x directly from a cached string form $x->{_m} = $MBI->_new( "27182818284590452353602874713526624977572470936999595749669676277240766303535476"); $x->{sign} = '+'; $x->{_es} = '-'; $x->{_e} = $MBI->_new(79); } else { # compute A and B so that e = A / B. # After some terms we end up with this, so we use it as a starting point: my $A = $MBI->_new("90933395208605785401971970164779391644753259799242"); my $F = $MBI->_new(42); my $step = 42; # Compute how many steps we need to take to get $A and $B sufficiently big my $steps = _len_to_steps($scale - 4); # print STDERR "# Doing $steps steps for ", $scale-4, " digits\n"; while ($step++ <= $steps) { # calculate $a * $f + 1 $A = $MBI->_mul($A, $F); $A = $MBI->_inc($A); # increment f $F = $MBI->_inc($F); } # compute $B as factorial of $steps (this is faster than doing it manually) my $B = $MBI->_fac($MBI->_new($steps)); # print "A ", $MBI->_str($A), "\nB ", $MBI->_str($B), "\n"; # compute A/B with $scale digits in the result (truncate, not round) $A = $MBI->_lsft($A, $MBI->_new($scale), 10); $A = $MBI->_div($A, $B); $x->{_m} = $A; $x->{sign} = '+'; $x->{_es} = '-'; $x->{_e} = $MBI->_new($scale); } # $x contains now an estimate of e, with some surplus digits, so we can round if (!$x_org->is_one()) { # Reduce size of fractional part, followup with integer power of two. my $lshift = 0; while ($lshift < 30 && $x_org->bacmp(2 << $lshift) > 0) { $lshift++; } # Raise $x to the wanted power and round it. if ($lshift == 0) { $x->bpow($x_org, @params); } else { my($mul, $rescale) = (1 << $lshift, $scale+1+$lshift); $x->bpow(scalar $x_org->bdiv($mul, $rescale), $rescale)->bpow($mul, @params); } } else { # else just round the already computed result delete $x->{_a}; delete $x->{_p}; # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $x; # return modified $x } sub bnok { # Calculate n over k (binomial coefficient or "choose" function) as integer. # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bnok'); return $x->bnan() if $x->is_nan() || $y->is_nan(); return $x->binf() if $x->is_inf(); my $u = $x->as_int(); $u->bnok($y->as_int()); $x->{_m} = $u->{value}; $x->{_e} = $MBI->_zero(); $x->{_es} = '+'; $x->{sign} = '+'; $x->bnorm(@r); } sub bsin { # Calculate a sinus of x. my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); # taylor: x^3 x^5 x^7 x^9 # sin = x - --- + --- - --- + --- ... # 3! 5! 7! 9! # we need to limit the accuracy to protect against overflow my $fallback = 0; my ($scale, @params); ($x, @params) = $x->_find_round_parameters(@r); # constant object or error in _find_round_parameters? return $x if $x->modify('bsin') || $x->is_nan(); return $x->bzero(@r) if $x->is_zero(); # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $params[1] = undef; # disable P $scale = $params[0]+4; # at least four more for proper round $params[2] = $r[2]; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } # when user set globals, they would interfere with our calculation, so # disable them and later re-enable them no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # we also need to disable any set A or P on $x (_find_round_parameters took # them already into account), since these would interfere, too delete $x->{_a}; delete $x->{_p}; # need to disable $upgrade in BigInt, to avoid deep recursion local $Math::BigInt::upgrade = undef; my $last = 0; my $over = $x * $x; # X ^ 2 my $x2 = $over->copy(); # X ^ 2; difference between terms $over->bmul($x); # X ^ 3 as starting value my $sign = 1; # start with -= my $below = $class->new(6); my $factorial = $class->new(4); delete $x->{_a}; delete $x->{_p}; my $limit = $class->new("1E-". ($scale-1)); #my $steps = 0; while (3 < 5) { # we calculate the next term, and add it to the last # when the next term is below our limit, it won't affect the outcome # anymore, so we stop: my $next = $over->copy()->bdiv($below, $scale); last if $next->bacmp($limit) <= 0; if ($sign == 0) { $x->badd($next); } else { $x->bsub($next); } $sign = 1-$sign; # alternate # calculate things for the next term $over->bmul($x2); # $x*$x $below->bmul($factorial); $factorial->binc(); # n*(n+1) $below->bmul($factorial); $factorial->binc(); # n*(n+1) } # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $x; } sub bcos { # Calculate a cosinus of x. my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); # Taylor: x^2 x^4 x^6 x^8 # cos = 1 - --- + --- - --- + --- ... # 2! 4! 6! 8! # we need to limit the accuracy to protect against overflow my $fallback = 0; my ($scale, @params); ($x, @params) = $x->_find_round_parameters(@r); # constant object or error in _find_round_parameters? return $x if $x->modify('bcos') || $x->is_nan(); return $x->bone(@r) if $x->is_zero(); # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $params[1] = undef; # disable P $scale = $params[0]+4; # at least four more for proper round $params[2] = $r[2]; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } # when user set globals, they would interfere with our calculation, so # disable them and later re-enable them no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # we also need to disable any set A or P on $x (_find_round_parameters took # them already into account), since these would interfere, too delete $x->{_a}; delete $x->{_p}; # need to disable $upgrade in BigInt, to avoid deep recursion local $Math::BigInt::upgrade = undef; my $last = 0; my $over = $x * $x; # X ^ 2 my $x2 = $over->copy(); # X ^ 2; difference between terms my $sign = 1; # start with -= my $below = $class->new(2); my $factorial = $class->new(3); $x->bone(); delete $x->{_a}; delete $x->{_p}; my $limit = $class->new("1E-". ($scale-1)); #my $steps = 0; while (3 < 5) { # we calculate the next term, and add it to the last # when the next term is below our limit, it won't affect the outcome # anymore, so we stop: my $next = $over->copy()->bdiv($below, $scale); last if $next->bacmp($limit) <= 0; if ($sign == 0) { $x->badd($next); } else { $x->bsub($next); } $sign = 1-$sign; # alternate # calculate things for the next term $over->bmul($x2); # $x*$x $below->bmul($factorial); $factorial->binc(); # n*(n+1) $below->bmul($factorial); $factorial->binc(); # n*(n+1) } # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $x; } sub batan { # Calculate a arcus tangens of x. my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; my (@r) = @_; # taylor: x^3 x^5 x^7 x^9 # atan = x - --- + --- - --- + --- ... # 3 5 7 9 # We need to limit the accuracy to protect against overflow. my $fallback = 0; my ($scale, @params); ($self, @params) = $self->_find_round_parameters(@r); # Constant object or error in _find_round_parameters? return $self if $self->modify('batan') || $self->is_nan(); if ($self->{sign} =~ /^[+-]inf\z/) { # +inf result is PI/2 # -inf result is -PI/2 # calculate PI/2 my $pi = $class->bpi(@r); # modify $self in place $self->{_m} = $pi->{_m}; $self->{_e} = $pi->{_e}; $self->{_es} = $pi->{_es}; # -y => -PI/2, +y => PI/2 $self->{sign} = substr($self->{sign}, 0, 1); # "+inf" => "+" $self -> {_m} = $MBI->_div($self->{_m}, $MBI->_new(2)); return $self; } return $self->bzero(@r) if $self->is_zero(); # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $params[1] = undef; # disable P $scale = $params[0]+4; # at least four more for proper round $params[2] = $r[2]; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } # 1 or -1 => PI/4 # inlined is_one() && is_one('-') if ($MBI->_is_one($self->{_m}) && $MBI->_is_zero($self->{_e})) { my $pi = $class->bpi($scale - 3); # modify $self in place $self->{_m} = $pi->{_m}; $self->{_e} = $pi->{_e}; $self->{_es} = $pi->{_es}; # leave the sign of $self alone (+1 => +PI/4, -1 => -PI/4) $self->{_m} = $MBI->_div($self->{_m}, $MBI->_new(4)); return $self; } # This series is only valid if -1 < x < 1, so for other x we need to # calculate PI/2 - atan(1/x): my $one = $MBI->_new(1); my $pi = undef; if ($self->bacmp($self->copy()->bone) >= 0) { # calculate PI/2 $pi = $class->bpi($scale - 3); $pi->{_m} = $MBI->_div($pi->{_m}, $MBI->_new(2)); # calculate 1/$self: my $self_copy = $self->copy(); # modify $self in place $self->bone(); $self->bdiv($self_copy, $scale); } my $fmul = 1; foreach my $k (0 .. int($scale / 20)) { $fmul *= 2; $self->bdiv($self->copy()->bmul($self)->binc->bsqrt($scale + 4)->binc, $scale + 4); } # When user set globals, they would interfere with our calculation, so # disable them and later re-enable them. no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # We also need to disable any set A or P on $self (_find_round_parameters # took them already into account), since these would interfere, too delete $self->{_a}; delete $self->{_p}; # Need to disable $upgrade in BigInt, to avoid deep recursion. local $Math::BigInt::upgrade = undef; my $last = 0; my $over = $self * $self; # X ^ 2 my $self2 = $over->copy(); # X ^ 2; difference between terms $over->bmul($self); # X ^ 3 as starting value my $sign = 1; # start with -= my $below = $class->new(3); my $two = $class->new(2); delete $self->{_a}; delete $self->{_p}; my $limit = $class->new("1E-". ($scale-1)); #my $steps = 0; while (1) { # We calculate the next term, and add it to the last. When the next # term is below our limit, it won't affect the outcome anymore, so we # stop: my $next = $over->copy()->bdiv($below, $scale); last if $next->bacmp($limit) <= 0; if ($sign == 0) { $self->badd($next); } else { $self->bsub($next); } $sign = 1-$sign; # alternatex # calculate things for the next term $over->bmul($self2); # $self*$self $below->badd($two); # n += 2 } $self->bmul($fmul); if (defined $pi) { my $self_copy = $self->copy(); # modify $self in place $self->{_m} = $pi->{_m}; $self->{_e} = $pi->{_e}; $self->{_es} = $pi->{_es}; # PI/2 - $self $self->bsub($self_copy); } # Shortcut to not run through _find_round_parameters again. if (defined $params[0]) { $self->bround($params[0], $params[2]); # then round accordingly } else { $self->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # Clear a/p after round, since user did not request it. delete $self->{_a}; delete $self->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $self; } sub batan2 { # $y -> batan2($x) returns the arcus tangens of $y / $x. # Set up parameters. my ($class, $y, $x, @r) = (ref($_[0]), @_); # Objectify is costly, so avoid it if we can. if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $y, $x, @r) = objectify(2, @_); } # Quick exit if $y is read-only. return $y if $y -> modify('batan2'); # Handle all NaN cases. return $y -> bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; # We need to limit the accuracy to protect against overflow. my $fallback = 0; my ($scale, @params); ($y, @params) = $y -> _find_round_parameters(@r); # Error in _find_round_parameters? return $y if $y->is_nan(); # No rounding at all, so must use fallback. if (scalar @params == 0) { # Simulate old behaviour $params[0] = $class -> div_scale(); # and round to it as accuracy $params[1] = undef; # disable P $scale = $params[0] + 4; # at least four more for proper round $params[2] = $r[2]; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # The 4 below is empirical, and there might be cases where it is not # enough ... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } if ($x -> is_inf("+")) { # x = inf if ($y -> is_inf("+")) { # y = inf $y -> bpi($scale) -> bmul("0.25"); # pi/4 } elsif ($y -> is_inf("-")) { # y = -inf $y -> bpi($scale) -> bmul("-0.25"); # -pi/4 } else { # -inf < y < inf return $y -> bzero(@r); # 0 } } elsif ($x -> is_inf("-")) { # x = -inf if ($y -> is_inf("+")) { # y = inf $y -> bpi($scale) -> bmul("0.75"); # 3/4 pi } elsif ($y -> is_inf("-")) { # y = -inf $y -> bpi($scale) -> bmul("-0.75"); # -3/4 pi } elsif ($y >= 0) { # y >= 0 $y -> bpi($scale); # pi } else { # y < 0 $y -> bpi($scale) -> bneg(); # -pi } } elsif ($x > 0) { # 0 < x < inf if ($y -> is_inf("+")) { # y = inf $y -> bpi($scale) -> bmul("0.5"); # pi/2 } elsif ($y -> is_inf("-")) { # y = -inf $y -> bpi($scale) -> bmul("-0.5"); # -pi/2 } else { # -inf < y < inf $y -> bdiv($x, $scale) -> batan($scale); # atan(y/x) } } elsif ($x < 0) { # -inf < x < 0 my $pi = $class -> bpi($scale); if ($y >= 0) { # y >= 0 $y -> bdiv($x, $scale) -> batan() # atan(y/x) + pi -> badd($pi); } else { # y < 0 $y -> bdiv($x, $scale) -> batan() # atan(y/x) - pi -> bsub($pi); } } else { # x = 0 if ($y > 0) { # y > 0 $y -> bpi($scale) -> bmul("0.5"); # pi/2 } elsif ($y < 0) { # y < 0 $y -> bpi($scale) -> bmul("-0.5"); # -pi/2 } else { # y = 0 return $y -> bzero(@r); # 0 } } $y -> round(@r); if ($fallback) { delete $y->{_a}; delete $y->{_p}; } return $y; } ############################################################################## sub bsqrt { # calculate square root my ($class, $x, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bsqrt'); return $x->bnan() if $x->{sign} !~ /^[+]/; # NaN, -inf or < 0 return $x if $x->{sign} eq '+inf'; # sqrt(inf) == inf return $x->round($a, $p, $r) if $x->is_zero() || $x->is_one(); # we need to limit the accuracy to protect against overflow my $fallback = 0; my (@params, $scale); ($x, @params) = $x->_find_round_parameters($a, $p, $r); return $x if $x->is_nan(); # error in _find_round_parameters? # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $scale = $params[0]+4; # at least four more for proper round $params[2] = $r; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } # when user set globals, they would interfere with our calculation, so # disable them and later re-enable them no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # we also need to disable any set A or P on $x (_find_round_parameters took # them already into account), since these would interfere, too delete $x->{_a}; delete $x->{_p}; # need to disable $upgrade in BigInt, to avoid deep recursion local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI my $i = $MBI->_copy($x->{_m}); $i = $MBI->_lsft($i, $x->{_e}, 10) unless $MBI->_is_zero($x->{_e}); my $xas = Math::BigInt->bzero(); $xas->{value} = $i; my $gs = $xas->copy()->bsqrt(); # some guess if (($x->{_es} ne '-') # guess can't be accurate if there are # digits after the dot && ($xas->bacmp($gs * $gs) == 0)) # guess hit the nail on the head? { # exact result, copy result over to keep $x $x->{_m} = $gs->{value}; $x->{_e} = $MBI->_zero(); $x->{_es} = '+'; $x->bnorm(); # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # re-enable A and P, upgrade is taken care of by "local" ${"$class\::accuracy"} = $ab; ${"$class\::precision"} = $pb; return $x; } # sqrt(2) = 1.4 because sqrt(2*100) = 1.4*10; so we can increase the accuracy # of the result by multiplying the input by 100 and then divide the integer # result of sqrt(input) by 10. Rounding afterwards returns the real result. # The following steps will transform 123.456 (in $x) into 123456 (in $y1) my $y1 = $MBI->_copy($x->{_m}); my $length = $MBI->_len($y1); # Now calculate how many digits the result of sqrt(y1) would have my $digits = int($length / 2); # But we need at least $scale digits, so calculate how many are missing my $shift = $scale - $digits; # This happens if the input had enough digits # (we take care of integer guesses above) $shift = 0 if $shift < 0; # Multiply in steps of 100, by shifting left two times the "missing" digits my $s2 = $shift * 2; # We now make sure that $y1 has the same odd or even number of digits than # $x had. So when _e of $x is odd, we must shift $y1 by one digit left, # because we always must multiply by steps of 100 (sqrt(100) is 10) and not # steps of 10. The length of $x does not count, since an even or odd number # of digits before the dot is not changed by adding an even number of digits # after the dot (the result is still odd or even digits long). $s2++ if $MBI->_is_odd($x->{_e}); $y1 = $MBI->_lsft($y1, $MBI->_new($s2), 10); # now take the square root and truncate to integer $y1 = $MBI->_sqrt($y1); # By "shifting" $y1 right (by creating a negative _e) we calculate the final # result, which is than later rounded to the desired scale. # calculate how many zeros $x had after the '.' (or before it, depending # on sign of $dat, the result should have half as many: my $dat = $MBI->_num($x->{_e}); $dat = -$dat if $x->{_es} eq '-'; $dat += $length; if ($dat > 0) { # no zeros after the dot (e.g. 1.23, 0.49 etc) # preserve half as many digits before the dot than the input had # (but round this "up") $dat = int(($dat+1)/2); } else { $dat = int(($dat)/2); } $dat -= $MBI->_len($y1); if ($dat < 0) { $dat = abs($dat); $x->{_e} = $MBI->_new($dat); $x->{_es} = '-'; } else { $x->{_e} = $MBI->_new($dat); $x->{_es} = '+'; } $x->{_m} = $y1; $x->bnorm(); # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $x; } sub broot { # calculate $y'th root of $x # set up parameters my ($class, $x, $y, $a, $p, $r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $a, $p, $r) = objectify(2, @_); } return $x if $x->modify('broot'); # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || $y->{sign} !~ /^\+$/; return $x if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); # we need to limit the accuracy to protect against overflow my $fallback = 0; my (@params, $scale); ($x, @params) = $x->_find_round_parameters($a, $p, $r); return $x if $x->is_nan(); # error in _find_round_parameters? # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $scale = $params[0]+4; # at least four more for proper round $params[2] = $r; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } # when user set globals, they would interfere with our calculation, so # disable them and later re-enable them no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # we also need to disable any set A or P on $x (_find_round_parameters took # them already into account), since these would interfere, too delete $x->{_a}; delete $x->{_p}; # need to disable $upgrade in BigInt, to avoid deep recursion local $Math::BigInt::upgrade = undef; # should be really parent class vs MBI # remember sign and make $x positive, since -4 ** (1/2) => -2 my $sign = 0; $sign = 1 if $x->{sign} eq '-'; $x->{sign} = '+'; my $is_two = 0; if ($y->isa('Math::BigFloat')) { $is_two = ($y->{sign} eq '+' && $MBI->_is_two($y->{_m}) && $MBI->_is_zero($y->{_e})); } else { $is_two = ($y == 2); } # normal square root if $y == 2: if ($is_two) { $x->bsqrt($scale+4); } elsif ($y->is_one('-')) { # $x ** -1 => 1/$x my $u = $class->bone()->bdiv($x, $scale); # copy private parts over $x->{_m} = $u->{_m}; $x->{_e} = $u->{_e}; $x->{_es} = $u->{_es}; } else { # calculate the broot() as integer result first, and if it fits, return # it rightaway (but only if $x and $y are integer): my $done = 0; # not yet if ($y->is_int() && $x->is_int()) { my $i = $MBI->_copy($x->{_m}); $i = $MBI->_lsft($i, $x->{_e}, 10) unless $MBI->_is_zero($x->{_e}); my $int = Math::BigInt->bzero(); $int->{value} = $i; $int->broot($y->as_number()); # if ($exact) if ($int->copy()->bpow($y) == $x) { # found result, return it $x->{_m} = $int->{value}; $x->{_e} = $MBI->_zero(); $x->{_es} = '+'; $x->bnorm(); $done = 1; } } if ($done == 0) { my $u = $class->bone()->bdiv($y, $scale+4); delete $u->{_a}; delete $u->{_p}; # otherwise it conflicts $x->bpow($u, $scale+4); # el cheapo } } $x->bneg() if $sign == 1; # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $x; } sub bfac { # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT # compute factorial number, modifies first argument # set up parameters my ($class, $x, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it ($class, $x, @r) = objectify(1, @_) if !ref($x); # inf => inf return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; return $x->bnan() if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN ($x->{_es} ne '+')); # digits after dot? # use BigInt's bfac() for faster calc if (! $MBI->_is_zero($x->{_e})) { $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e}, 10); # change 12e1 to 120e0 $x->{_e} = $MBI->_zero(); # normalize $x->{_es} = '+'; } $x->{_m} = $MBI->_fac($x->{_m}); # calculate factorial $x->bnorm()->round(@r); # norm again and round result } sub bdfac { # compute double factorial # set up parameters my ($class, $x, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it ($class, $x, @r) = objectify(1, @_) if !ref($x); # inf => inf return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; return $x->bnan() if (($x->{sign} ne '+') || # inf, NaN, <0 etc => NaN ($x->{_es} ne '+')); # digits after dot? # use BigInt's bdfac() for faster calc if (! $MBI->_is_zero($x->{_e})) { $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e}, 10); # change 12e1 to 120e0 $x->{_e} = $MBI->_zero(); # normalize $x->{_es} = '+'; } $x->{_m} = $MBI->_dfac($x->{_m}); # calculate factorial $x->bnorm()->round(@r); # norm again and round result } sub blsft { # shift left by $y (multiply by $b ** $y) # set up parameters my ($class, $x, $y, $b, $a, $p, $r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $b, $a, $p, $r) = objectify(2, @_); } return $x if $x -> modify('blsft'); return $x if $x -> {sign} !~ /^[+-]$/; # nan, +inf, -inf $b = 2 if !defined $b; $b = $class -> new($b) unless ref($b) && $b -> isa($class); return $x -> bnan() if $x -> is_nan() || $y -> is_nan() || $b -> is_nan(); # shift by a negative amount? return $x -> brsft($y -> copy() -> babs(), $b) if $y -> {sign} =~ /^-/; $x -> bmul($b -> bpow($y), $a, $p, $r, $y); } sub brsft { # shift right by $y (divide $b ** $y) # set up parameters my ($class, $x, $y, $b, $a, $p, $r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $b, $a, $p, $r) = objectify(2, @_); } return $x if $x -> modify('brsft'); return $x if $x -> {sign} !~ /^[+-]$/; # nan, +inf, -inf $b = 2 if !defined $b; $b = $class -> new($b) unless ref($b) && $b -> isa($class); return $x -> bnan() if $x -> is_nan() || $y -> is_nan() || $b -> is_nan(); # shift by a negative amount? return $x -> blsft($y -> copy() -> babs(), $b) if $y -> {sign} =~ /^-/; # the following call to bdiv() will return either quotient (scalar context) # or quotient and remainder (list context). $x -> bdiv($b -> bpow($y), $a, $p, $r, $y); } ############################################################################### # Bitwise methods ############################################################################### sub band { my $x = shift; my $xref = ref($x); my $class = $xref || $x; Carp::croak 'band() is an instance method, not a class method' unless $xref; Carp::croak 'Not enough arguments for band()' if @_ < 1; return if $x -> modify('band'); my $y = shift; $y = $class -> new($y) unless ref($y); my @r = @_; my $xtmp = Math::BigInt -> new($x -> bint()); # to Math::BigInt $xtmp -> band($y); $xtmp = $class -> new($xtmp); # back to Math::BigFloat $x -> {sign} = $xtmp -> {sign}; $x -> {_m} = $xtmp -> {_m}; $x -> {_es} = $xtmp -> {_es}; $x -> {_e} = $xtmp -> {_e}; return $x -> round(@r); } sub bior { my $x = shift; my $xref = ref($x); my $class = $xref || $x; Carp::croak 'bior() is an instance method, not a class method' unless $xref; Carp::croak 'Not enough arguments for bior()' if @_ < 1; return if $x -> modify('bior'); my $y = shift; $y = $class -> new($y) unless ref($y); my @r = @_; my $xtmp = Math::BigInt -> new($x -> bint()); # to Math::BigInt $xtmp -> bior($y); $xtmp = $class -> new($xtmp); # back to Math::BigFloat $x -> {sign} = $xtmp -> {sign}; $x -> {_m} = $xtmp -> {_m}; $x -> {_es} = $xtmp -> {_es}; $x -> {_e} = $xtmp -> {_e}; return $x -> round(@r); } sub bxor { my $x = shift; my $xref = ref($x); my $class = $xref || $x; Carp::croak 'bxor() is an instance method, not a class method' unless $xref; Carp::croak 'Not enough arguments for bxor()' if @_ < 1; return if $x -> modify('bxor'); my $y = shift; $y = $class -> new($y) unless ref($y); my @r = @_; my $xtmp = Math::BigInt -> new($x -> bint()); # to Math::BigInt $xtmp -> bxor($y); $xtmp = $class -> new($xtmp); # back to Math::BigFloat $x -> {sign} = $xtmp -> {sign}; $x -> {_m} = $xtmp -> {_m}; $x -> {_es} = $xtmp -> {_es}; $x -> {_e} = $xtmp -> {_e}; return $x -> round(@r); } sub bnot { my $x = shift; my $xref = ref($x); my $class = $xref || $x; Carp::croak 'bnot() is an instance method, not a class method' unless $xref; return if $x -> modify('bnot'); my @r = @_; my $xtmp = Math::BigInt -> new($x -> bint()); # to Math::BigInt $xtmp -> bnot(); $xtmp = $class -> new($xtmp); # back to Math::BigFloat $x -> {sign} = $xtmp -> {sign}; $x -> {_m} = $xtmp -> {_m}; $x -> {_es} = $xtmp -> {_es}; $x -> {_e} = $xtmp -> {_e}; return $x -> round(@r); } ############################################################################### # Rounding methods ############################################################################### sub bround { # accuracy: preserve $N digits, and overwrite the rest with 0's my $x = shift; my $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); if (($_[0] || 0) < 0) { Carp::croak('bround() needs positive accuracy'); } my ($scale, $mode) = $x->_scale_a(@_); return $x if !defined $scale || $x->modify('bround'); # no-op # scale is now either $x->{_a}, $accuracy, or the user parameter # test whether $x already has lower accuracy, do nothing in this case # but do round if the accuracy is the same, since a math operation might # want to round a number with A=5 to 5 digits afterwards again return $x if defined $x->{_a} && $x->{_a} < $scale; # scale < 0 makes no sense # scale == 0 => keep all digits # never round a +-inf, NaN return $x if ($scale <= 0) || $x->{sign} !~ /^[+-]$/; # 1: never round a 0 # 2: if we should keep more digits than the mantissa has, do nothing if ($x->is_zero() || $MBI->_len($x->{_m}) <= $scale) { $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; return $x; } # pass sign to bround for '+inf' and '-inf' rounding modes my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt'; $m->bround($scale, $mode); # round mantissa $x->{_m} = $m->{value}; # get our mantissa back $x->{_a} = $scale; # remember rounding delete $x->{_p}; # and clear P $x->bnorm(); # del trailing zeros gen. by bround() } sub bfround { # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' # $n == 0 means round to integer # expects and returns normalized numbers! my $x = shift; my $class = ref($x) || $x; $x = $class->new(shift) if !ref($x); my ($scale, $mode) = $x->_scale_p(@_); return $x if !defined $scale || $x->modify('bfround'); # no-op # never round a 0, +-inf, NaN if ($x->is_zero()) { $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2 return $x; } return $x if $x->{sign} !~ /^[+-]$/; # don't round if x already has lower precision return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p}); $x->{_p} = $scale; # remember round in any case delete $x->{_a}; # and clear A if ($scale < 0) { # round right from the '.' return $x if $x->{_es} eq '+'; # e >= 0 => nothing to round $scale = -$scale; # positive for simplicity my $len = $MBI->_len($x->{_m}); # length of mantissa # the following poses a restriction on _e, but if _e is bigger than a # scalar, you got other problems (memory etc) anyway my $dad = -(0+ ($x->{_es}.$MBI->_num($x->{_e}))); # digits after dot my $zad = 0; # zeros after dot $zad = $dad - $len if (-$dad < -$len); # for 0.00..00xxx style # print "scale $scale dad $dad zad $zad len $len\n"; # number bsstr len zad dad # 0.123 123e-3 3 0 3 # 0.0123 123e-4 3 1 4 # 0.001 1e-3 1 2 3 # 1.23 123e-2 3 0 2 # 1.2345 12345e-4 5 0 4 # do not round after/right of the $dad return $x if $scale > $dad; # 0.123, scale >= 3 => exit # round to zero if rounding inside the $zad, but not for last zero like: # 0.0065, scale -2, round last '0' with following '65' (scale == zad case) return $x->bzero() if $scale < $zad; if ($scale == $zad) # for 0.006, scale -3 and trunc { $scale = -$len; } else { # adjust round-point to be inside mantissa if ($zad != 0) { $scale = $scale-$zad; } else { my $dbd = $len - $dad; $dbd = 0 if $dbd < 0; # digits before dot $scale = $dbd+$scale; } } } else { # round left from the '.' # 123 => 100 means length(123) = 3 - $scale (2) => 1 my $dbt = $MBI->_len($x->{_m}); # digits before dot my $dbd = $dbt + ($x->{_es} . $MBI->_num($x->{_e})); # should be the same, so treat it as this $scale = 1 if $scale == 0; # shortcut if already integer return $x if $scale == 1 && $dbt <= $dbd; # maximum digits before dot ++$dbd; if ($scale > $dbd) { # not enough digits before dot, so round to zero return $x->bzero; } elsif ($scale == $dbd) { # maximum $scale = -$dbt; } else { $scale = $dbd - $scale; } } # pass sign to bround for rounding modes '+inf' and '-inf' my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt'; $m->bround($scale, $mode); $x->{_m} = $m->{value}; # get our mantissa back $x->bnorm(); } sub bfloor { # round towards minus infinity my ($class, $x, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bfloor'); return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf # if $x has digits after dot if ($x->{_es} eq '-') { $x->{_m} = $MBI->_rsft($x->{_m}, $x->{_e}, 10); # cut off digits after dot $x->{_e} = $MBI->_zero(); # trunc/norm $x->{_es} = '+'; # abs e $x->{_m} = $MBI->_inc($x->{_m}) if $x->{sign} eq '-'; # increment if negative } $x->round($a, $p, $r); } sub bceil { # round towards plus infinity my ($class, $x, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bceil'); return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf # if $x has digits after dot if ($x->{_es} eq '-') { $x->{_m} = $MBI->_rsft($x->{_m}, $x->{_e}, 10); # cut off digits after dot $x->{_e} = $MBI->_zero(); # trunc/norm $x->{_es} = '+'; # abs e if ($x->{sign} eq '+') { $x->{_m} = $MBI->_inc($x->{_m}); # increment if positive } else { $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # avoid -0 } } $x->round($a, $p, $r); } sub bint { # round towards zero my ($class, $x, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bint'); return $x if $x->{sign} !~ /^[+-]$/; # nan, +inf, -inf # if $x has digits after the decimal point if ($x->{_es} eq '-') { $x->{_m} = $MBI->_rsft($x->{_m}, $x->{_e}, 10); # cut off digits after dot $x->{_e} = $MBI->_zero(); # truncate/normalize $x->{_es} = '+'; # abs e $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # avoid -0 } $x->round($a, $p, $r); } ############################################################################### # Other mathematical methods ############################################################################### sub bgcd { # (BINT or num_str, BINT or num_str) return BINT # does not modify arguments, but returns new object unshift @_, __PACKAGE__ unless ref($_[0]) || $_[0] =~ /^[a-z]\w*(?:::[a-z]\w*)*$/i; my ($class, @args) = objectify(0, @_); my $x = shift @args; $x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x); return $class->bnan() unless $x -> is_int(); while (@args) { my $y = shift @args; $y = $class->new($y) unless ref($y) && $y -> isa($class); return $class->bnan() unless $y -> is_int(); # greatest common divisor while (! $y->is_zero()) { ($x, $y) = ($y->copy(), $x->copy()->bmod($y)); } last if $x -> is_one(); } return $x -> babs(); } sub blcm { # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT # does not modify arguments, but returns new object # Least Common Multiple unshift @_, __PACKAGE__ unless ref($_[0]) || $_[0] =~ /^[a-z]\w*(?:::[a-z]\w*)*$/i; my ($class, @args) = objectify(0, @_); my $x = shift @args; $x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x); return $class->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN? while (@args) { my $y = shift @args; $y = $class -> new($y) unless ref($y) && $y -> isa($class); return $x->bnan() unless $y -> is_int(); my $gcd = $x -> bgcd($y); $x -> bdiv($gcd) -> bmul($y); } return $x -> babs(); } ############################################################################### # Object property methods ############################################################################### sub length { my $x = shift; my $class = ref($x) || $x; $x = $class->new(shift) unless ref($x); return 1 if $MBI->_is_zero($x->{_m}); my $len = $MBI->_len($x->{_m}); $len += $MBI->_num($x->{_e}) if $x->{_es} eq '+'; if (wantarray()) { my $t = 0; $t = $MBI->_num($x->{_e}) if $x->{_es} eq '-'; return ($len, $t); } $len; } sub mantissa { # return a copy of the mantissa my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); if ($x->{sign} !~ /^[+-]$/) { my $s = $x->{sign}; $s =~ s/^[+]//; return Math::BigInt->new($s, undef, undef); # -inf, +inf => +inf } my $m = Math::BigInt->new($MBI->_str($x->{_m}), undef, undef); $m->bneg() if $x->{sign} eq '-'; $m; } sub exponent { # return a copy of the exponent my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); if ($x->{sign} !~ /^[+-]$/) { my $s = $x->{sign}; $s =~ s/^[+-]//; return Math::BigInt->new($s, undef, undef); # -inf, +inf => +inf } Math::BigInt->new($x->{_es} . $MBI->_str($x->{_e}), undef, undef); } sub parts { # return a copy of both the exponent and the mantissa my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); if ($x->{sign} !~ /^[+-]$/) { my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//; return ($class->new($s), $class->new($se)); # +inf => inf and -inf, +inf => inf } my $m = Math::BigInt->bzero(); $m->{value} = $MBI->_copy($x->{_m}); $m->bneg() if $x->{sign} eq '-'; ($m, Math::BigInt->new($x->{_es} . $MBI->_num($x->{_e}))); } sub sparts { my $self = shift; my $class = ref $self; Carp::croak("sparts() is an instance method, not a class method") unless $class; # Not-a-number. if ($self -> is_nan()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> bnan(); # exponent return ($mant, $expo); # list context } # Infinity. if ($self -> is_inf()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> binf('+'); # exponent return ($mant, $expo); # list context } # Finite number. my $mant = $class -> bzero(); $mant -> {sign} = $self -> {sign}; $mant -> {_m} = $MBI->_copy($self -> {_m}); return $mant unless wantarray; my $expo = $class -> bzero(); $expo -> {sign} = $self -> {_es}; $expo -> {_m} = $MBI->_copy($self -> {_e}); return ($mant, $expo); } sub nparts { my $self = shift; my $class = ref $self; Carp::croak("nparts() is an instance method, not a class method") unless $class; # Not-a-number. if ($self -> is_nan()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> bnan(); # exponent return ($mant, $expo); # list context } # Infinity. if ($self -> is_inf()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> binf('+'); # exponent return ($mant, $expo); # list context } # Finite number. my ($mant, $expo) = $self -> sparts(); if ($mant -> bcmp(0)) { my ($ndigtot, $ndigfrac) = $mant -> length(); my $expo10adj = $ndigtot - $ndigfrac - 1; if ($expo10adj != 0) { my $factor = "1e" . -$expo10adj; $mant -> bmul($factor); return $mant unless wantarray; $expo -> badd($expo10adj); return ($mant, $expo); } } return $mant unless wantarray; return ($mant, $expo); } sub eparts { my $self = shift; my $class = ref $self; Carp::croak("eparts() is an instance method, not a class method") unless $class; # Not-a-number and Infinity. return $self -> sparts() if $self -> is_nan() || $self -> is_inf(); # Finite number. my ($mant, $expo) = $self -> nparts(); my $c = $expo -> copy() -> bmod(3); $mant -> blsft($c, 10); return $mant unless wantarray; $expo -> bsub($c); return ($mant, $expo); } sub dparts { my $self = shift; my $class = ref $self; Carp::croak("dparts() is an instance method, not a class method") unless $class; # Not-a-number and Infinity. if ($self -> is_nan() || $self -> is_inf()) { my $int = $self -> copy(); return $int unless wantarray; my $frc = $class -> bzero(); return ($int, $frc); } my $int = $self -> copy(); my $frc = $class -> bzero(); # If the input has a fraction part. if ($int->{_es} eq '-') { $int->{_m} = $MBI -> _rsft($int->{_m}, $int->{_e}, 10); $int->{_e} = $MBI -> _zero(); $int->{_es} = '+'; $int->{sign} = '+' if $MBI->_is_zero($int->{_m}); # avoid -0 return $int unless wantarray; $frc = $self -> copy() -> bsub($int); return ($int, $frc); } return $int unless wantarray; return ($int, $frc); } ############################################################################### # String conversion methods ############################################################################### sub bstr { # (ref to BFLOAT or num_str) return num_str # Convert number from internal format to (non-scientific) string format. # internal format is always normalized (no leading zeros, "-0" => "+0") my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); if ($x->{sign} !~ /^[+-]$/) { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.'; # $x is zero? my $not_zero = !($x->{sign} eq '+' && $MBI->_is_zero($x->{_m})); if ($not_zero) { $es = $MBI->_str($x->{_m}); $len = CORE::length($es); my $e = $MBI->_num($x->{_e}); $e = -$e if $x->{_es} eq '-'; if ($e < 0) { $dot = ''; # if _e is bigger than a scalar, the following will blow your memory if ($e <= -$len) { my $r = abs($e) - $len; $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r); } else { substr($es, $e, 0) = '.'; $cad = $MBI->_num($x->{_e}); $cad = -$cad if $x->{_es} eq '-'; } } elsif ($e > 0) { # expand with zeros $es .= '0' x $e; $len += $e; $cad = 0; } } # if not zero $es = '-'.$es if $x->{sign} eq '-'; # if set accuracy or precision, pad with zeros on the right side if ((defined $x->{_a}) && ($not_zero)) { # 123400 => 6, 0.1234 => 4, 0.001234 => 4 my $zeros = $x->{_a} - $cad; # cad == 0 => 12340 $zeros = $x->{_a} - $len if $cad != $len; $es .= $dot.'0' x $zeros if $zeros > 0; } elsif ((($x->{_p} || 0) < 0)) { # 123400 => 6, 0.1234 => 4, 0.001234 => 6 my $zeros = -$x->{_p} + $cad; $es .= $dot.'0' x $zeros if $zeros > 0; } $es; } # Decimal notation, e.g., "12345.6789". sub bdstr { my $x = shift; if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my $mant = $MBI->_str($x->{_m}); my $expo = $x -> exponent(); my $str = $mant; if ($expo >= 0) { $str .= "0" x $expo; } else { my $mantlen = CORE::length($mant); my $c = $mantlen + $expo; $str = "0" x (1 - $c) . $str if $c <= 0; substr($str, $expo, 0) = '.'; } return $x->{sign} eq '-' ? "-$str" : $str; } # Scientific notation with significand/mantissa as an integer, e.g., "12345.6789" # is written as "123456789e-4". sub bsstr { my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my $str = $MBI->_str($x->{_m}) . 'e' . $x->{_es}. $MBI->_str($x->{_e}); return $x->{sign} eq '-' ? "-$str" : $str; } # Normalized notation, e.g., "12345.6789" is written as "1.23456789e+4". sub bnstr { my $x = shift; if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my ($mant, $expo) = $x -> nparts(); my $esgn = $expo < 0 ? '-' : '+'; my $eabs = $expo -> babs() -> bfround(0) -> bstr(); #$eabs = '0' . $eabs if length($eabs) < 2; return $mant . 'e' . $esgn . $eabs; } # Engineering notation, e.g., "12345.6789" is written as "12.3456789e+3". sub bestr { my $x = shift; if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my ($mant, $expo) = $x -> eparts(); my $esgn = $expo < 0 ? '-' : '+'; my $eabs = $expo -> babs() -> bfround(0) -> bstr(); #$eabs = '0' . $eabs if length($eabs) < 2; return $mant . 'e' . $esgn . $eabs; } sub to_hex { # return number as hexadecimal string (only for integers defined) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc return '0x0' if $x->is_zero(); return $nan if $x->{_es} ne '+'; # how to do 1e-1 in hex? my $z = $MBI->_copy($x->{_m}); if (! $MBI->_is_zero($x->{_e})) { # > 0 $z = $MBI->_lsft($z, $x->{_e}, 10); } $z = Math::BigInt->new($x->{sign} . $MBI->_num($z)); $z->to_hex(); } sub to_oct { # return number as octal digit string (only for integers defined) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc return '0' if $x->is_zero(); return $nan if $x->{_es} ne '+'; # how to do 1e-1 in octal? my $z = $MBI->_copy($x->{_m}); if (! $MBI->_is_zero($x->{_e})) { # > 0 $z = $MBI->_lsft($z, $x->{_e}, 10); } $z = Math::BigInt->new($x->{sign} . $MBI->_num($z)); $z->to_oct(); } sub to_bin { # return number as binary digit string (only for integers defined) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc return '0b0' if $x->is_zero(); return $nan if $x->{_es} ne '+'; # how to do 1e-1 in binary? my $z = $MBI->_copy($x->{_m}); if (! $MBI->_is_zero($x->{_e})) { # > 0 $z = $MBI->_lsft($z, $x->{_e}, 10); } $z = Math::BigInt->new($x->{sign} . $MBI->_num($z)); $z->to_bin(); } sub as_hex { # return number as hexadecimal string (only for integers defined) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc return '0x0' if $x->is_zero(); return $nan if $x->{_es} ne '+'; # how to do 1e-1 in hex? my $z = $MBI->_copy($x->{_m}); if (! $MBI->_is_zero($x->{_e})) { # > 0 $z = $MBI->_lsft($z, $x->{_e}, 10); } $z = Math::BigInt->new($x->{sign} . $MBI->_num($z)); $z->as_hex(); } sub as_oct { # return number as octal digit string (only for integers defined) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc return '0' if $x->is_zero(); return $nan if $x->{_es} ne '+'; # how to do 1e-1 in octal? my $z = $MBI->_copy($x->{_m}); if (! $MBI->_is_zero($x->{_e})) { # > 0 $z = $MBI->_lsft($z, $x->{_e}, 10); } $z = Math::BigInt->new($x->{sign} . $MBI->_num($z)); $z->as_oct(); } sub as_bin { # return number as binary digit string (only for integers defined) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc return '0b0' if $x->is_zero(); return $nan if $x->{_es} ne '+'; # how to do 1e-1 in binary? my $z = $MBI->_copy($x->{_m}); if (! $MBI->_is_zero($x->{_e})) { # > 0 $z = $MBI->_lsft($z, $x->{_e}, 10); } $z = Math::BigInt->new($x->{sign} . $MBI->_num($z)); $z->as_bin(); } sub numify { # Make a Perl scalar number from a Math::BigFloat object. my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); if ($x -> is_nan()) { require Math::Complex; my $inf = Math::Complex::Inf(); return $inf - $inf; } if ($x -> is_inf()) { require Math::Complex; my $inf = Math::Complex::Inf(); return $x -> is_negative() ? -$inf : $inf; } # Create a string and let Perl's atoi()/atof() handle the rest. return 0 + $x -> bsstr(); } ############################################################################### # Private methods and functions. ############################################################################### sub import { my $class = shift; my $l = scalar @_; my $lib = ''; my @a; my $lib_kind = 'try'; $IMPORT=1; for (my $i = 0; $i < $l ; $i++) { if ($_[$i] eq ':constant') { # This causes overlord er load to step in. 'binary' and 'integer' # are handled by BigInt. overload::constant float => sub { $class->new(shift); }; } elsif ($_[$i] eq 'upgrade') { # this causes upgrading $upgrade = $_[$i+1]; # or undef to disable $i++; } elsif ($_[$i] eq 'downgrade') { # this causes downgrading $downgrade = $_[$i+1]; # or undef to disable $i++; } elsif ($_[$i] =~ /^(lib|try|only)\z/) { # alternative library $lib = $_[$i+1] || ''; # default Calc $lib_kind = $1; # lib, try or only $i++; } elsif ($_[$i] eq 'with') { # alternative class for our private parts() # XXX: no longer supported # $MBI = $_[$i+1] || 'Math::BigInt'; $i++; } else { push @a, $_[$i]; } } $lib =~ tr/a-zA-Z0-9,://cd; # restrict to sane characters # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work my $mbilib = eval { Math::BigInt->config('lib') }; if ((defined $mbilib) && ($MBI eq 'Math::BigInt::Calc')) { # MBI already loaded Math::BigInt->import($lib_kind, "$lib, $mbilib", 'objectify'); } else { # MBI not loaded, or with ne "Math::BigInt::Calc" $lib .= ",$mbilib" if defined $mbilib; $lib =~ s/^,//; # don't leave empty # replacement library can handle lib statement, but also could ignore it # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is # used in the same script, or eval inside import(). So we require MBI: require Math::BigInt; Math::BigInt->import($lib_kind => $lib, 'objectify'); } if ($@) { Carp::croak("Couldn't load $lib: $! $@"); } # find out which one was actually loaded $MBI = Math::BigInt->config('lib'); # register us with MBI to get notified of future lib changes Math::BigInt::_register_callback($class, sub { $MBI = $_[0]; }); $class->export_to_level(1, $class, @a); # export wanted functions } sub _len_to_steps { # Given D (digits in decimal), compute N so that N! (N factorial) is # at least D digits long. D should be at least 50. my $d = shift; # two constants for the Ramanujan estimate of ln(N!) my $lg2 = log(2 * 3.14159265) / 2; my $lg10 = log(10); # D = 50 => N => 42, so L = 40 and R = 50 my $l = 40; my $r = $d; # Otherwise this does not work under -Mbignum and we do not yet have "no bignum;" :( $l = $l->numify if ref($l); $r = $r->numify if ref($r); $lg2 = $lg2->numify if ref($lg2); $lg10 = $lg10->numify if ref($lg10); # binary search for the right value (could this be written as the reverse of lg(n!)?) while ($r - $l > 1) { my $n = int(($r - $l) / 2) + $l; my $ramanujan = int(($n * log($n) - $n + log($n * (1 + 4*$n*(1+2*$n))) / 6 + $lg2) / $lg10); $ramanujan > $d ? $r = $n : $l = $n; } $l; } sub _log { # internal log function to calculate ln() based on Taylor series. # Modifies $x in place. my ($class, $x, $scale) = @_; # in case of $x == 1, result is 0 return $x->bzero() if $x->is_one(); # XXX TODO: rewrite this in a similar manner to bexp() # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log # u = x-1, v = x+1 # _ _ # Taylor: | u 1 u^3 1 u^5 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 0 # |_ v 3 v^3 5 v^5 _| # This takes much more steps to calculate the result and is thus not used # u = x-1 # _ _ # Taylor: | u 1 u^2 1 u^3 | # ln (x) = 2 | --- + - * --- + - * --- + ... | x > 1/2 # |_ x 2 x^2 3 x^3 _| my ($limit, $v, $u, $below, $factor, $two, $next, $over, $f); $v = $x->copy(); $v->binc(); # v = x+1 $x->bdec(); $u = $x->copy(); # u = x-1; x = x-1 $x->bdiv($v, $scale); # first term: u/v $below = $v->copy(); $over = $u->copy(); $u *= $u; $v *= $v; # u^2, v^2 $below->bmul($v); # u^3, v^3 $over->bmul($u); $factor = $class->new(3); $f = $class->new(2); my $steps = 0; $limit = $class->new("1E-". ($scale-1)); while (3 < 5) { # we calculate the next term, and add it to the last # when the next term is below our limit, it won't affect the outcome # anymore, so we stop # calculating the next term simple from over/below will result in quite # a time hog if the input has many digits, since over and below will # accumulate more and more digits, and the result will also have many # digits, but in the end it is rounded to $scale digits anyway. So if we # round $over and $below first, we save a lot of time for the division # (not with log(1.2345), but try log (123**123) to see what I mean. This # can introduce a rounding error if the division result would be f.i. # 0.1234500000001 and we round it to 5 digits it would become 0.12346, but # if we truncated $over and $below we might get 0.12345. Does this matter # for the end result? So we give $over and $below 4 more digits to be # on the safe side (unscientific error handling as usual... :+D $next = $over->copy()->bround($scale+4) ->bdiv($below->copy()->bmul($factor)->bround($scale+4), $scale); ## old version: ## $next = $over->copy()->bdiv($below->copy()->bmul($factor), $scale); last if $next->bacmp($limit) <= 0; delete $next->{_a}; delete $next->{_p}; $x->badd($next); # calculate things for the next term $over *= $u; $below *= $v; $factor->badd($f); if (DEBUG) { $steps++; print "step $steps = $x\n" if $steps % 10 == 0; } } print "took $steps steps\n" if DEBUG; $x->bmul($f); # $x *= 2 } sub _log_10 { # Internal log function based on reducing input to the range of 0.1 .. 9.99 # and then "correcting" the result to the proper one. Modifies $x in place. my ($class, $x, $scale) = @_; # Taking blog() from numbers greater than 10 takes a *very long* time, so we # break the computation down into parts based on the observation that: # blog(X*Y) = blog(X) + blog(Y) # We set Y here to multiples of 10 so that $x becomes below 1 - the smaller # $x is the faster it gets. Since 2*$x takes about 10 times as # long, we make it faster by about a factor of 100 by dividing $x by 10. # The same observation is valid for numbers smaller than 0.1, e.g. computing # log(1) is fastest, and the further away we get from 1, the longer it takes. # So we also 'break' this down by multiplying $x with 10 and subtract the # log(10) afterwards to get the correct result. # To get $x even closer to 1, we also divide by 2 and then use log(2) to # correct for this. For instance if $x is 2.4, we use the formula: # blog(2.4 * 2) == blog (1.2) + blog(2) # and thus calculate only blog(1.2) and blog(2), which is faster in total # than calculating blog(2.4). # In addition, the values for blog(2) and blog(10) are cached. # Calculate nr of digits before dot: my $dbd = $MBI->_num($x->{_e}); $dbd = -$dbd if $x->{_es} eq '-'; $dbd += $MBI->_len($x->{_m}); # more than one digit (e.g. at least 10), but *not* exactly 10 to avoid # infinite recursion my $calc = 1; # do some calculation? # disable the shortcut for 10, since we need log(10) and this would recurse # infinitely deep if ($x->{_es} eq '+' && $MBI->_is_one($x->{_e}) && $MBI->_is_one($x->{_m})) { $dbd = 0; # disable shortcut # we can use the cached value in these cases if ($scale <= $LOG_10_A) { $x->bzero(); $x->badd($LOG_10); # modify $x in place $calc = 0; # no need to calc, but round } # if we can't use the shortcut, we continue normally } else { # disable the shortcut for 2, since we maybe have it cached if (($MBI->_is_zero($x->{_e}) && $MBI->_is_two($x->{_m}))) { $dbd = 0; # disable shortcut # we can use the cached value in these cases if ($scale <= $LOG_2_A) { $x->bzero(); $x->badd($LOG_2); # modify $x in place $calc = 0; # no need to calc, but round } # if we can't use the shortcut, we continue normally } } # if $x = 0.1, we know the result must be 0-log(10) if ($calc != 0 && $x->{_es} eq '-' && $MBI->_is_one($x->{_e}) && $MBI->_is_one($x->{_m})) { $dbd = 0; # disable shortcut # we can use the cached value in these cases if ($scale <= $LOG_10_A) { $x->bzero(); $x->bsub($LOG_10); $calc = 0; # no need to calc, but round } } return if $calc == 0; # already have the result # default: these correction factors are undef and thus not used my $l_10; # value of ln(10) to A of $scale my $l_2; # value of ln(2) to A of $scale my $two = $class->new(2); # $x == 2 => 1, $x == 13 => 2, $x == 0.1 => 0, $x == 0.01 => -1 # so don't do this shortcut for 1 or 0 if (($dbd > 1) || ($dbd < 0)) { # convert our cached value to an object if not already (avoid doing this # at import() time, since not everybody needs this) $LOG_10 = $class->new($LOG_10, undef, undef) unless ref $LOG_10; #print "x = $x, dbd = $dbd, calc = $calc\n"; # got more than one digit before the dot, or more than one zero after the # dot, so do: # log(123) == log(1.23) + log(10) * 2 # log(0.0123) == log(1.23) - log(10) * 2 if ($scale <= $LOG_10_A) { # use cached value $l_10 = $LOG_10->copy(); # copy for mul } else { # else: slower, compute and cache result # also disable downgrade for this code path local $Math::BigFloat::downgrade = undef; # shorten the time to calculate log(10) based on the following: # log(1.25 * 8) = log(1.25) + log(8) # = log(1.25) + log(2) + log(2) + log(2) # first get $l_2 (and possible compute and cache log(2)) $LOG_2 = $class->new($LOG_2, undef, undef) unless ref $LOG_2; if ($scale <= $LOG_2_A) { # use cached value $l_2 = $LOG_2->copy(); # copy() for the mul below } else { # else: slower, compute and cache result $l_2 = $two->copy(); $class->_log($l_2, $scale); # scale+4, actually $LOG_2 = $l_2->copy(); # cache the result for later # the copy() is for mul below $LOG_2_A = $scale; } # now calculate log(1.25): $l_10 = $class->new('1.25'); $class->_log($l_10, $scale); # scale+4, actually # log(1.25) + log(2) + log(2) + log(2): $l_10->badd($l_2); $l_10->badd($l_2); $l_10->badd($l_2); $LOG_10 = $l_10->copy(); # cache the result for later # the copy() is for mul below $LOG_10_A = $scale; } $dbd-- if ($dbd > 1); # 20 => dbd=2, so make it dbd=1 $l_10->bmul($class->new($dbd)); # log(10) * (digits_before_dot-1) my $dbd_sign = '+'; if ($dbd < 0) { $dbd = -$dbd; $dbd_sign = '-'; } ($x->{_e}, $x->{_es}) = _e_sub($x->{_e}, $MBI->_new($dbd), $x->{_es}, $dbd_sign); # 123 => 1.23 } # Now: 0.1 <= $x < 10 (and possible correction in l_10) ### Since $x in the range 0.5 .. 1.5 is MUCH faster, we do a repeated div ### or mul by 2 (maximum times 3, since x < 10 and x > 0.1) $HALF = $class->new($HALF) unless ref($HALF); my $twos = 0; # default: none (0 times) while ($x->bacmp($HALF) <= 0) { # X <= 0.5 $twos--; $x->bmul($two); } while ($x->bacmp($two) >= 0) { # X >= 2 $twos++; $x->bdiv($two, $scale+4); # keep all digits } $x->bround($scale+4); # $twos > 0 => did mul 2, < 0 => did div 2 (but we never did both) # So calculate correction factor based on ln(2): if ($twos != 0) { $LOG_2 = $class->new($LOG_2, undef, undef) unless ref $LOG_2; if ($scale <= $LOG_2_A) { # use cached value $l_2 = $LOG_2->copy(); # copy() for the mul below } else { # else: slower, compute and cache result # also disable downgrade for this code path local $Math::BigFloat::downgrade = undef; $l_2 = $two->copy(); $class->_log($l_2, $scale); # scale+4, actually $LOG_2 = $l_2->copy(); # cache the result for later # the copy() is for mul below $LOG_2_A = $scale; } $l_2->bmul($twos); # * -2 => subtract, * 2 => add } else { undef $l_2; } $class->_log($x, $scale); # need to do the "normal" way $x->badd($l_10) if defined $l_10; # correct it by ln(10) $x->badd($l_2) if defined $l_2; # and maybe by ln(2) # all done, $x contains now the result $x; } sub _e_add { # Internal helper sub to take two positive integers and their signs and # then add them. Input ($CALC, $CALC, ('+'|'-'), ('+'|'-')), output # ($CALC, ('+'|'-')). my ($x, $y, $xs, $ys) = @_; # if the signs are equal we can add them (-5 + -3 => -(5 + 3) => -8) if ($xs eq $ys) { $x = $MBI->_add($x, $y); # +a + +b or -a + -b } else { my $a = $MBI->_acmp($x, $y); if ($a == 0) { # This does NOT modify $x in-place. TODO: Fix this? $x = $MBI->_zero(); # result is 0 $xs = '+'; return ($x, $xs); } if ($a > 0) { $x = $MBI->_sub($x, $y); # abs sub } else { # a < 0 $x = $MBI->_sub ($y, $x, 1); # abs sub $xs = $ys; } } $xs = '+' if $xs eq '-' && $MBI->_is_zero($x); # no "-0" return ($x, $xs); } sub _e_sub { # Internal helper sub to take two positive integers and their signs and # then subtract them. Input ($CALC, $CALC, ('+'|'-'), ('+'|'-')), # output ($CALC, ('+'|'-')) my ($x, $y, $xs, $ys) = @_; # flip sign $ys = $ys eq '+' ? '-' : '+'; # swap sign of second operand ... _e_add($x, $y, $xs, $ys); # ... and let _e_add() do the job } sub _pow { # Calculate a power where $y is a non-integer, like 2 ** 0.3 my ($x, $y, @r) = @_; my $class = ref($x); # if $y == 0.5, it is sqrt($x) $HALF = $class->new($HALF) unless ref($HALF); return $x->bsqrt(@r, $y) if $y->bcmp($HALF) == 0; # Using: # a ** x == e ** (x * ln a) # u = y * ln x # _ _ # Taylor: | u u^2 u^3 | # x ** y = 1 + | --- + --- + ----- + ... | # |_ 1 1*2 1*2*3 _| # we need to limit the accuracy to protect against overflow my $fallback = 0; my ($scale, @params); ($x, @params) = $x->_find_round_parameters(@r); return $x if $x->is_nan(); # error in _find_round_parameters? # no rounding at all, so must use fallback if (scalar @params == 0) { # simulate old behaviour $params[0] = $class->div_scale(); # and round to it as accuracy $params[1] = undef; # disable P $scale = $params[0]+4; # at least four more for proper round $params[2] = $r[2]; # round mode by caller or undef $fallback = 1; # to clear a/p afterwards } else { # the 4 below is empirical, and there might be cases where it is not # enough... $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined } # when user set globals, they would interfere with our calculation, so # disable them and later re-enable them no strict 'refs'; my $abr = "$class\::accuracy"; my $ab = $$abr; $$abr = undef; my $pbr = "$class\::precision"; my $pb = $$pbr; $$pbr = undef; # we also need to disable any set A or P on $x (_find_round_parameters took # them already into account), since these would interfere, too delete $x->{_a}; delete $x->{_p}; # need to disable $upgrade in BigInt, to avoid deep recursion local $Math::BigInt::upgrade = undef; my ($limit, $v, $u, $below, $factor, $next, $over); $u = $x->copy()->blog(undef, $scale)->bmul($y); my $do_invert = ($u->{sign} eq '-'); $u->bneg() if $do_invert; $v = $class->bone(); # 1 $factor = $class->new(2); # 2 $x->bone(); # first term: 1 $below = $v->copy(); $over = $u->copy(); $limit = $class->new("1E-". ($scale-1)); #my $steps = 0; while (3 < 5) { # we calculate the next term, and add it to the last # when the next term is below our limit, it won't affect the outcome # anymore, so we stop: $next = $over->copy()->bdiv($below, $scale); last if $next->bacmp($limit) <= 0; $x->badd($next); # calculate things for the next term $over *= $u; $below *= $factor; $factor->binc(); last if $x->{sign} !~ /^[-+]$/; #$steps++; } if ($do_invert) { my $x_copy = $x->copy(); $x->bone->bdiv($x_copy, $scale); } # shortcut to not run through _find_round_parameters again if (defined $params[0]) { $x->bround($params[0], $params[2]); # then round accordingly } else { $x->bfround($params[1], $params[2]); # then round accordingly } if ($fallback) { # clear a/p after round, since user did not request it delete $x->{_a}; delete $x->{_p}; } # restore globals $$abr = $ab; $$pbr = $pb; $x; } 1; __END__ =pod =head1 NAME Math::BigFloat - Arbitrary size floating point math package =head1 SYNOPSIS use Math::BigFloat; # Configuration methods (may be used as class methods and instance methods) Math::BigFloat->accuracy(); # get class accuracy Math::BigFloat->accuracy($n); # set class accuracy Math::BigFloat->precision(); # get class precision Math::BigFloat->precision($n); # set class precision Math::BigFloat->round_mode(); # get class rounding mode Math::BigFloat->round_mode($m); # set global round mode, must be one of # 'even', 'odd', '+inf', '-inf', 'zero', # 'trunc', or 'common' Math::BigFloat->config(); # return hash with configuration # Constructor methods (when the class methods below are used as instance # methods, the value is assigned the invocand) $x = Math::BigFloat->new($str); # defaults to 0 $x = Math::BigFloat->new('0x123'); # from hexadecimal $x = Math::BigFloat->new('0b101'); # from binary $x = Math::BigFloat->from_hex('0xc.afep+3'); # from hex $x = Math::BigFloat->from_hex('cafe'); # ditto $x = Math::BigFloat->from_oct('1.3267p-4'); # from octal $x = Math::BigFloat->from_oct('0377'); # ditto $x = Math::BigFloat->from_bin('0b1.1001p-4'); # from binary $x = Math::BigFloat->from_bin('0101'); # ditto $x = Math::BigFloat->bzero(); # create a +0 $x = Math::BigFloat->bone(); # create a +1 $x = Math::BigFloat->bone('-'); # create a -1 $x = Math::BigFloat->binf(); # create a +inf $x = Math::BigFloat->binf('-'); # create a -inf $x = Math::BigFloat->bnan(); # create a Not-A-Number $x = Math::BigFloat->bpi(); # returns pi $y = $x->copy(); # make a copy (unlike $y = $x) $y = $x->as_int(); # return as BigInt # Boolean methods (these don't modify the invocand) $x->is_zero(); # if $x is 0 $x->is_one(); # if $x is +1 $x->is_one("+"); # ditto $x->is_one("-"); # if $x is -1 $x->is_inf(); # if $x is +inf or -inf $x->is_inf("+"); # if $x is +inf $x->is_inf("-"); # if $x is -inf $x->is_nan(); # if $x is NaN $x->is_positive(); # if $x > 0 $x->is_pos(); # ditto $x->is_negative(); # if $x < 0 $x->is_neg(); # ditto $x->is_odd(); # if $x is odd $x->is_even(); # if $x is even $x->is_int(); # if $x is an integer # Comparison methods $x->bcmp($y); # compare numbers (undef, < 0, == 0, > 0) $x->bacmp($y); # compare absolutely (undef, < 0, == 0, > 0) $x->beq($y); # true if and only if $x == $y $x->bne($y); # true if and only if $x != $y $x->blt($y); # true if and only if $x < $y $x->ble($y); # true if and only if $x <= $y $x->bgt($y); # true if and only if $x > $y $x->bge($y); # true if and only if $x >= $y # Arithmetic methods $x->bneg(); # negation $x->babs(); # absolute value $x->bsgn(); # sign function (-1, 0, 1, or NaN) $x->bnorm(); # normalize (no-op) $x->binc(); # increment $x by 1 $x->bdec(); # decrement $x by 1 $x->badd($y); # addition (add $y to $x) $x->bsub($y); # subtraction (subtract $y from $x) $x->bmul($y); # multiplication (multiply $x by $y) $x->bmuladd($y,$z); # $x = $x * $y + $z $x->bdiv($y); # division (floored), set $x to quotient # return (quo,rem) or quo if scalar $x->btdiv($y); # division (truncated), set $x to quotient # return (quo,rem) or quo if scalar $x->bmod($y); # modulus (x % y) $x->btmod($y); # modulus (truncated) $x->bmodinv($mod); # modular multiplicative inverse $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod) $x->bpow($y); # power of arguments (x ** y) $x->blog(); # logarithm of $x to base e (Euler's number) $x->blog($base); # logarithm of $x to base $base (e.g., base 2) $x->bexp(); # calculate e ** $x where e is Euler's number $x->bnok($y); # x over y (binomial coefficient n over k) $x->bsin(); # sine $x->bcos(); # cosine $x->batan(); # inverse tangent $x->batan2($y); # two-argument inverse tangent $x->bsqrt(); # calculate square-root $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) $x->bfac(); # factorial of $x (1*2*3*4*..$x) $x->blsft($n); # left shift $n places in base 2 $x->blsft($n,$b); # left shift $n places in base $b # returns (quo,rem) or quo (scalar context) $x->brsft($n); # right shift $n places in base 2 $x->brsft($n,$b); # right shift $n places in base $b # returns (quo,rem) or quo (scalar context) # Bitwise methods $x->band($y); # bitwise and $x->bior($y); # bitwise inclusive or $x->bxor($y); # bitwise exclusive or $x->bnot(); # bitwise not (two's complement) # Rounding methods $x->round($A,$P,$mode); # round to accuracy or precision using # rounding mode $mode $x->bround($n); # accuracy: preserve $n digits $x->bfround($n); # $n > 0: round to $nth digit left of dec. point # $n < 0: round to $nth digit right of dec. point $x->bfloor(); # round towards minus infinity $x->bceil(); # round towards plus infinity $x->bint(); # round towards zero # Other mathematical methods $x->bgcd($y); # greatest common divisor $x->blcm($y); # least common multiple # Object property methods (do not modify the invocand) $x->sign(); # the sign, either +, - or NaN $x->digit($n); # the nth digit, counting from the right $x->digit(-$n); # the nth digit, counting from the left $x->length(); # return number of digits in number ($xl,$f) = $x->length(); # length of number and length of fraction # part, latter is always 0 digits long # for Math::BigInt objects $x->mantissa(); # return (signed) mantissa as BigInt $x->exponent(); # return exponent as BigInt $x->parts(); # return (mantissa,exponent) as BigInt $x->sparts(); # mantissa and exponent (as integers) $x->nparts(); # mantissa and exponent (normalised) $x->eparts(); # mantissa and exponent (engineering notation) $x->dparts(); # integer and fraction part # Conversion methods (do not modify the invocand) $x->bstr(); # decimal notation, possibly zero padded $x->bsstr(); # string in scientific notation with integers $x->bnstr(); # string in normalized notation $x->bestr(); # string in engineering notation $x->bdstr(); # string in decimal notation $x->as_hex(); # as signed hexadecimal string with prefixed 0x $x->as_bin(); # as signed binary string with prefixed 0b $x->as_oct(); # as signed octal string with prefixed 0 # Other conversion methods $x->numify(); # return as scalar (might overflow or underflow) =head1 DESCRIPTION Math::BigFloat provides support for arbitrary precision floating point. Overloading is also provided for Perl operators. All operators (including basic math operations) are overloaded if you declare your big floating point numbers as $x = Math::BigFloat -> new('12_3.456_789_123_456_789E-2'); Operations with overloaded operators preserve the arguments, which is exactly what you expect. =head2 Input Input values to these routines may be any scalar number or string that looks like a number and represents a floating point number. =over =item * Leading and trailing whitespace is ignored. =item * Leading and trailing zeros are ignored. =item * If the string has a "0x" prefix, it is interpreted as a hexadecimal number. =item * If the string has a "0b" prefix, it is interpreted as a binary number. =item * For hexadecimal and binary numbers, the exponent must be separated from the significand (mantissa) by the letter "p" or "P", not "e" or "E" as with decimal numbers. =item * One underline is allowed between any two digits, including hexadecimal and binary digits. =item * If the string can not be interpreted, NaN is returned. =back Octal numbers are typically prefixed by "0", but since leading zeros are stripped, these methods can not automatically recognize octal numbers, so use the constructor from_oct() to interpret octal strings. Some examples of valid string input Input string Resulting value 123 123 1.23e2 123 12300e-2 123 0xcafe 51966 0b1101 13 67_538_754 67538754 -4_5_6.7_8_9e+0_1_0 -4567890000000 0x1.921fb5p+1 3.14159262180328369140625e+0 0b1.1001p-4 9.765625e-2 =head2 Output Output values are usually Math::BigFloat objects. Boolean operators C, C, C, etc. return true or false. Comparison operators C and C) return -1, 0, 1, or undef. =head1 METHODS Math::BigFloat supports all methods that Math::BigInt supports, except it calculates non-integer results when possible. Please see L for a full description of each method. Below are just the most important differences: =head2 Configuration methods =over =item accuracy() $x->accuracy(5); # local for $x CLASS->accuracy(5); # global for all members of CLASS # Note: This also applies to new()! $A = $x->accuracy(); # read out accuracy that affects $x $A = CLASS->accuracy(); # read out global accuracy Set or get the global or local accuracy, aka how many significant digits the results have. If you set a global accuracy, then this also applies to new()! Warning! The accuracy I, e.g. once you created a number under the influence of C<< CLASS->accuracy($A) >>, all results from math operations with that number will also be rounded. In most cases, you should probably round the results explicitly using one of L, L or L or by passing the desired accuracy to the math operation as additional parameter: my $x = Math::BigInt->new(30000); my $y = Math::BigInt->new(7); print scalar $x->copy()->bdiv($y, 2); # print 4300 print scalar $x->copy()->bdiv($y)->bround(2); # print 4300 =item precision() $x->precision(-2); # local for $x, round at the second # digit right of the dot $x->precision(2); # ditto, round at the second digit # left of the dot CLASS->precision(5); # Global for all members of CLASS # This also applies to new()! CLASS->precision(-5); # ditto $P = CLASS->precision(); # read out global precision $P = $x->precision(); # read out precision that affects $x Note: You probably want to use L instead. With L you set the number of digits each result should have, with L you set the place where to round! =back =head2 Constructor methods =over =item from_hex() $x -> from_hex("0x1.921fb54442d18p+1"); $x = Math::BigFloat -> from_hex("0x1.921fb54442d18p+1"); Interpret input as a hexadecimal string.A prefix ("0x", "x", ignoring case) is optional. A single underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal digits. If called as an instance method, the value is assigned to the invocand. =item from_oct() $x -> from_oct("1.3267p-4"); $x = Math::BigFloat -> from_oct("1.3267p-4"); Interpret input as an octal string. A single underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal digits. If called as an instance method, the value is assigned to the invocand. =item from_bin() $x -> from_bin("0b1.1001p-4"); $x = Math::BigFloat -> from_bin("0b1.1001p-4"); Interpret input as a hexadecimal string. A prefix ("0b" or "b", ignoring case) is optional. A single underscore character ("_") may be placed between any two digits. If the input is invalid, a NaN is returned. The exponent is in base 2 using decimal digits. If called as an instance method, the value is assigned to the invocand. =item bpi() print Math::BigFloat->bpi(100), "\n"; Calculate PI to N digits (including the 3 before the dot). The result is rounded according to the current rounding mode, which defaults to "even". This method was added in v1.87 of Math::BigInt (June 2007). =back =head2 Arithmetic methods =over =item bmuladd() $x->bmuladd($y,$z); Multiply $x by $y, and then add $z to the result. This method was added in v1.87 of Math::BigInt (June 2007). =item bdiv() $q = $x->bdiv($y); ($q, $r) = $x->bdiv($y); In scalar context, divides $x by $y and returns the result to the given or default accuracy/precision. In list context, does floored division (F-division), returning an integer $q and a remainder $r so that $x = $q * $y + $r. The remainer (modulo) is equal to what is returned by C<$x->bmod($y)>. =item bmod() $x->bmod($y); Returns $x modulo $y. When $x is finite, and $y is finite and non-zero, the result is identical to the remainder after floored division (F-division). If, in addition, both $x and $y are integers, the result is identical to the result from Perl's % operator. =item bexp() $x->bexp($accuracy); # calculate e ** X Calculates the expression C where C is Euler's number. This method was added in v1.82 of Math::BigInt (April 2007). =item bnok() $x->bnok($y); # x over y (binomial coefficient n over k) Calculates the binomial coefficient n over k, also called the "choose" function. The result is equivalent to: ( n ) n! | - | = ------- ( k ) k!(n-k)! This method was added in v1.84 of Math::BigInt (April 2007). =item bsin() my $x = Math::BigFloat->new(1); print $x->bsin(100), "\n"; Calculate the sinus of $x, modifying $x in place. This method was added in v1.87 of Math::BigInt (June 2007). =item bcos() my $x = Math::BigFloat->new(1); print $x->bcos(100), "\n"; Calculate the cosinus of $x, modifying $x in place. This method was added in v1.87 of Math::BigInt (June 2007). =item batan() my $x = Math::BigFloat->new(1); print $x->batan(100), "\n"; Calculate the arcus tanges of $x, modifying $x in place. See also L. This method was added in v1.87 of Math::BigInt (June 2007). =item batan2() my $y = Math::BigFloat->new(2); my $x = Math::BigFloat->new(3); print $y->batan2($x), "\n"; Calculate the arcus tanges of C<$y> divided by C<$x>, modifying $y in place. See also L. This method was added in v1.87 of Math::BigInt (June 2007). =item as_float() This method is called when Math::BigFloat encounters an object it doesn't know how to handle. For instance, assume $x is a Math::BigFloat, or subclass thereof, and $y is defined, but not a Math::BigFloat, or subclass thereof. If you do $x -> badd($y); $y needs to be converted into an object that $x can deal with. This is done by first checking if $y is something that $x might be upgraded to. If that is the case, no further attempts are made. The next is to see if $y supports the method C. The method C is expected to return either an object that has the same class as $x, a subclass thereof, or a string that Cnew()> can parse to create an object. In Math::BigFloat, C has the same effect as C. =back =head2 ACCURACY AND PRECISION See also: L. Math::BigFloat supports both precision (rounding to a certain place before or after the dot) and accuracy (rounding to a certain number of digits). For a full documentation, examples and tips on these topics please see the large section about rounding in L. Since things like C or C<1 / 3> must presented with a limited accuracy lest a operation consumes all resources, each operation produces no more than the requested number of digits. If there is no global precision or accuracy set, B the operation in question was not called with a requested precision or accuracy, B the input $x has no accuracy or precision set, then a fallback parameter will be used. For historical reasons, it is called C and can be accessed via: $d = Math::BigFloat->div_scale(); # query Math::BigFloat->div_scale($n); # set to $n digits The default value for C is 40. In case the result of one operation has more digits than specified, it is rounded. The rounding mode taken is either the default mode, or the one supplied to the operation after the I: $x = Math::BigFloat->new(2); Math::BigFloat->accuracy(5); # 5 digits max $y = $x->copy()->bdiv(3); # gives 0.66667 $y = $x->copy()->bdiv(3,6); # gives 0.666667 $y = $x->copy()->bdiv(3,6,undef,'odd'); # gives 0.666667 Math::BigFloat->round_mode('zero'); $y = $x->copy()->bdiv(3,6); # will also give 0.666667 Note that C<< Math::BigFloat->accuracy() >> and C<< Math::BigFloat->precision() >> set the global variables, and thus B newly created number will be subject to the global rounding B. This means that in the examples above, the C<3> as argument to C will also get an accuracy of B<5>. It is less confusing to either calculate the result fully, and afterwards round it explicitly, or use the additional parameters to the math functions like so: use Math::BigFloat; $x = Math::BigFloat->new(2); $y = $x->copy()->bdiv(3); print $y->bround(5),"\n"; # gives 0.66667 or use Math::BigFloat; $x = Math::BigFloat->new(2); $y = $x->copy()->bdiv(3,5); # gives 0.66667 print "$y\n"; =head2 Rounding =over =item bfround ( +$scale ) Rounds to the $scale'th place left from the '.', counting from the dot. The first digit is numbered 1. =item bfround ( -$scale ) Rounds to the $scale'th place right from the '.', counting from the dot. =item bfround ( 0 ) Rounds to an integer. =item bround ( +$scale ) Preserves accuracy to $scale digits from the left (aka significant digits) and pads the rest with zeros. If the number is between 1 and -1, the significant digits count from the first non-zero after the '.' =item bround ( -$scale ) and bround ( 0 ) These are effectively no-ops. =back All rounding functions take as a second parameter a rounding mode from one of the following: 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'. The default rounding mode is 'even'. By using C<< Math::BigFloat->round_mode($round_mode); >> you can get and set the default mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is no longer supported. The second parameter to the round functions then overrides the default temporarily. The C function returns a BigInt from a Math::BigFloat. It uses 'trunc' as rounding mode to make it equivalent to: $x = 2.5; $y = int($x) + 2; You can override this by passing the desired rounding mode as parameter to C: $x = Math::BigFloat->new(2.5); $y = $x->as_number('odd'); # $y = 3 =head1 Autocreating constants After C all the floating point constants in the given scope are converted to C. This conversion happens at compile time. In particular perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"' prints the value of C<2E-100>. Note that without conversion of constants the expression 2E-100 will be calculated as normal floating point number. Please note that ':constant' does not affect integer constants, nor binary nor hexadecimal constants. Use L or L to get this to work. =head2 Math library Math with the numbers is done (by default) by a module called Math::BigInt::Calc. This is equivalent to saying: use Math::BigFloat lib => 'Calc'; You can change this by using: use Math::BigFloat lib => 'GMP'; B: General purpose packages should not be explicit about the library to use; let the script author decide which is best. Note: The keyword 'lib' will warn when the requested library could not be loaded. To suppress the warning use 'try' instead: use Math::BigFloat try => 'GMP'; If your script works with huge numbers and Calc is too slow for them, you can also for the loading of one of these libraries and if none of them can be used, the code will die: use Math::BigFloat only => 'GMP,Pari'; The following would first try to find Math::BigInt::Foo, then Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: use Math::BigFloat lib => 'Foo,Math::BigInt::Bar'; See the respective low-level library documentation for further details. Please note that Math::BigFloat does B use the denoted library itself, but it merely passes the lib argument to Math::BigInt. So, instead of the need to do: use Math::BigInt lib => 'GMP'; use Math::BigFloat; you can roll it all into one line: use Math::BigFloat lib => 'GMP'; It is also possible to just require Math::BigFloat: require Math::BigFloat; This will load the necessary things (like BigInt) when they are needed, and automatically. See L for more details than you ever wanted to know about using a different low-level library. =head2 Using Math::BigInt::Lite For backwards compatibility reasons it is still possible to request a different storage class for use with Math::BigFloat: use Math::BigFloat with => 'Math::BigInt::Lite'; However, this request is ignored, as the current code now uses the low-level math library for directly storing the number parts. =head1 EXPORTS C exports nothing by default, but can export the C method: use Math::BigFloat qw/bpi/; print bpi(10), "\n"; =head1 CAVEATS Do not try to be clever to insert some operations in between switching libraries: require Math::BigFloat; my $matter = Math::BigFloat->bone() + 4; # load BigInt and Calc Math::BigFloat->import( lib => 'Pari' ); # load Pari, too my $anti_matter = Math::BigFloat->bone()+4; # now use Pari This will create objects with numbers stored in two different backend libraries, and B will happen when you use these together: my $flash_and_bang = $matter + $anti_matter; # Don't do this! =over =item stringify, bstr() Both stringify and bstr() now drop the leading '+'. The old code would return '+1.23', the new returns '1.23'. See the documentation in L for reasoning and details. =item brsft() The following will probably not print what you expect: my $c = Math::BigFloat->new('3.14159'); print $c->brsft(3,10),"\n"; # prints 0.00314153.1415 It prints both quotient and remainder, since print calls C in list context. Also, C<< $c->brsft() >> will modify $c, so be careful. You probably want to use print scalar $c->copy()->brsft(3,10),"\n"; # or if you really want to modify $c print scalar $c->brsft(3,10),"\n"; instead. =item Modifying and = Beware of: $x = Math::BigFloat->new(5); $y = $x; It will not do what you think, e.g. making a copy of $x. Instead it just makes a second reference to the B object and stores it in $y. Thus anything that modifies $x will modify $y (except overloaded math operators), and vice versa. See L for details and how to avoid that. =item precision() vs. accuracy() A common pitfall is to use L when you want to round a result to a certain number of digits: use Math::BigFloat; Math::BigFloat->precision(4); # does not do what you # think it does my $x = Math::BigFloat->new(12345); # rounds $x to "12000"! print "$x\n"; # print "12000" my $y = Math::BigFloat->new(3); # rounds $y to "0"! print "$y\n"; # print "0" $z = $x / $y; # 12000 / 0 => NaN! print "$z\n"; print $z->precision(),"\n"; # 4 Replacing L with L is probably not what you want, either: use Math::BigFloat; Math::BigFloat->accuracy(4); # enables global rounding: my $x = Math::BigFloat->new(123456); # rounded immediately # to "12350" print "$x\n"; # print "123500" my $y = Math::BigFloat->new(3); # rounded to "3 print "$y\n"; # print "3" print $z = $x->copy()->bdiv($y),"\n"; # 41170 print $z->accuracy(),"\n"; # 4 What you want to use instead is: use Math::BigFloat; my $x = Math::BigFloat->new(123456); # no rounding print "$x\n"; # print "123456" my $y = Math::BigFloat->new(3); # no rounding print "$y\n"; # print "3" print $z = $x->copy()->bdiv($y,4),"\n"; # 41150 print $z->accuracy(),"\n"; # undef In addition to computing what you expected, the last example also does B "taint" the result with an accuracy or precision setting, which would influence any further operation. =back =head1 BUGS Please report any bugs or feature requests to C, or through the web interface at L (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes. =head1 SUPPORT You can find documentation for this module with the perldoc command. perldoc Math::BigFloat You can also look for information at: =over 4 =item * RT: CPAN's request tracker L =item * AnnoCPAN: Annotated CPAN documentation L =item * CPAN Ratings L =item * Search CPAN L =item * CPAN Testers Matrix L =item * The Bignum mailing list =over 4 =item * Post to mailing list C =item * View mailing list L =item * Subscribe/Unsubscribe L =back =back =head1 LICENSE This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. =head1 SEE ALSO L and L as well as the backends L, L, and L. The pragmas L, L and L also might be of interest because they solve the autoupgrading/downgrading issue, at least partly. =head1 AUTHORS =over 4 =item * Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001. =item * Completely rewritten by Tels L in 2001-2008. =item * Florian Ragwitz Eflora@cpan.orgE, 2010. =item * Peter John Acklam Epjacklam@online.noE, 2011-. =back =cut Math-BigInt-1.999808/lib/Math/BigInt/0000705403072340010010000000000013035475727017161 5ustar ospjadomain usersMath-BigInt-1.999808/lib/Math/BigInt/Calc.pm0000644403072340010010000022607213030153342020354 0ustar ospjadomain userspackage Math::BigInt::Calc; use 5.006001; use strict; use warnings; use Carp; use Math::BigInt::Lib; our $VERSION = '1.999808'; our @ISA = ('Math::BigInt::Lib'); # Package to store unsigned big integers in decimal and do math with them # Internally the numbers are stored in an array with at least 1 element, no # leading zero parts (except the first) and in base 1eX where X is determined # automatically at loading time to be the maximum possible value # todo: # - fully remove funky $# stuff in div() (maybe - that code scares me...) # USE_MUL: due to problems on certain os (os390, posix-bc) "* 1e-5" is used # instead of "/ 1e5" at some places, (marked with USE_MUL). Other platforms # BS2000, some Crays need USE_DIV instead. # The BEGIN block is used to determine which of the two variants gives the # correct result. # Beware of things like: # $i = $i * $y + $car; $car = int($i / $BASE); $i = $i % $BASE; # This works on x86, but fails on ARM (SA1100, iPAQ) due to who knows what # reasons. So, use this instead (slower, but correct): # $i = $i * $y + $car; $car = int($i / $BASE); $i -= $BASE * $car; ############################################################################## # global constants, flags and accessory # announce that we are compatible with MBI v1.83 and up sub api_version () { 2; } # constants for easier life my ($BASE, $BASE_LEN, $RBASE, $MAX_VAL); my ($AND_BITS, $XOR_BITS, $OR_BITS); my ($AND_MASK, $XOR_MASK, $OR_MASK); sub _base_len { # Set/get the BASE_LEN and assorted other, related values. # Used only by the testsuite, the set variant is used only by the BEGIN # block below: my ($class, $b, $int) = @_; if (defined $b) { # avoid redefinitions undef &_mul; undef &_div; if ($] >= 5.008 && $int && $b > 7) { $BASE_LEN = $b; *_mul = \&_mul_use_div_64; *_div = \&_div_use_div_64; $BASE = int("1e" . $BASE_LEN); $MAX_VAL = $BASE-1; return $BASE_LEN unless wantarray; return ($BASE_LEN, $BASE, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN, $MAX_VAL); } # find whether we can use mul or div in mul()/div() $BASE_LEN = $b + 1; my $caught = 0; while (--$BASE_LEN > 5) { $BASE = int("1e" . $BASE_LEN); $RBASE = abs('1e-' . $BASE_LEN); # see USE_MUL $caught = 0; $caught += 1 if (int($BASE * $RBASE) != 1); # should be 1 $caught += 2 if (int($BASE / $BASE) != 1); # should be 1 last if $caught != 3; } $BASE = int("1e" . $BASE_LEN); $RBASE = abs('1e-' . $BASE_LEN); # see USE_MUL $MAX_VAL = $BASE-1; # ($caught & 1) != 0 => cannot use MUL # ($caught & 2) != 0 => cannot use DIV if ($caught == 2) # 2 { # must USE_MUL since we cannot use DIV *_mul = \&_mul_use_mul; *_div = \&_div_use_mul; } else # 0 or 1 { # can USE_DIV instead *_mul = \&_mul_use_div; *_div = \&_div_use_div; } } return $BASE_LEN unless wantarray; return ($BASE_LEN, $BASE, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN, $MAX_VAL); } sub _new { # Given a string representing an integer, returns a reference to an array # of integers, where each integer represents a chunk of the original input # integer. my ($class, $str) = @_; #unless ($str =~ /^([1-9]\d*|0)\z/) { # require Carp; # Carp::croak("Invalid input string '$str'"); #} my $input_len = length($str) - 1; # Shortcut for small numbers. return bless [ $str ], $class if $input_len < $BASE_LEN; my $format = "a" . (($input_len % $BASE_LEN) + 1); $format .= $] < 5.008 ? "a$BASE_LEN" x int($input_len / $BASE_LEN) : "(a$BASE_LEN)*"; my $self = [ reverse(map { 0 + $_ } unpack($format, $str)) ]; return bless $self, $class; } BEGIN { # from Daniel Pfeiffer: determine largest group of digits that is precisely # multipliable with itself plus carry # Test now changed to expect the proper pattern, not a result off by 1 or 2 my ($e, $num) = 3; # lowest value we will use is 3+1-1 = 3 do { $num = '9' x ++$e; $num *= $num + 1; } while $num =~ /9{$e}0{$e}/; # must be a certain pattern $e--; # last test failed, so retract one step # the limits below brush the problems with the test above under the rug: # the test should be able to find the proper $e automatically $e = 5 if $^O =~ /^uts/; # UTS get's some special treatment $e = 5 if $^O =~ /^unicos/; # unicos is also problematic (6 seems to work # there, but we play safe) my $int = 0; if ($e > 7) { use integer; my $e1 = 7; $num = 7; do { $num = ('9' x ++$e1) + 0; $num *= $num + 1; } while ("$num" =~ /9{$e1}0{$e1}/); # must be a certain pattern $e1--; # last test failed, so retract one step if ($e1 > 7) { $int = 1; $e = $e1; } } __PACKAGE__ -> _base_len($e, $int); # set and store use integer; # find out how many bits _and, _or and _xor can take (old default = 16) # I don't think anybody has yet 128 bit scalars, so let's play safe. local $^W = 0; # don't warn about 'nonportable number' $AND_BITS = 15; $XOR_BITS = 15; $OR_BITS = 15; # find max bits, we will not go higher than numberofbits that fit into $BASE # to make _and etc simpler (and faster for smaller, slower for large numbers) my $max = 16; while (2 ** $max < $BASE) { $max++; } { no integer; $max = 16 if $] < 5.006; # older Perls might not take >16 too well } my ($x, $y, $z); do { $AND_BITS++; $x = CORE::oct('0b' . '1' x $AND_BITS); $y = $x & $x; $z = (2 ** $AND_BITS) - 1; } while ($AND_BITS < $max && $x == $z && $y == $x); $AND_BITS --; # retreat one step do { $XOR_BITS++; $x = CORE::oct('0b' . '1' x $XOR_BITS); $y = $x ^ 0; $z = (2 ** $XOR_BITS) - 1; } while ($XOR_BITS < $max && $x == $z && $y == $x); $XOR_BITS --; # retreat one step do { $OR_BITS++; $x = CORE::oct('0b' . '1' x $OR_BITS); $y = $x | $x; $z = (2 ** $OR_BITS) - 1; } while ($OR_BITS < $max && $x == $z && $y == $x); $OR_BITS--; # retreat one step $AND_MASK = __PACKAGE__->_new(( 2 ** $AND_BITS )); $XOR_MASK = __PACKAGE__->_new(( 2 ** $XOR_BITS )); $OR_MASK = __PACKAGE__->_new(( 2 ** $OR_BITS )); # We can compute the approximate length no faster than the real length: *_alen = \&_len; } ############################################################################### sub _zero { # create a zero my $class = shift; return bless [ 0 ], $class; } sub _one { # create a one my $class = shift; return bless [ 1 ], $class; } sub _two { # create a two my $class = shift; return bless [ 2 ], $class; } sub _ten { # create a 10 my $class = shift; bless [ 10 ], $class; } sub _1ex { # create a 1Ex my $class = shift; my $rem = $_[0] % $BASE_LEN; # remainder my $parts = $_[0] / $BASE_LEN; # parts # 000000, 000000, 100 bless [ (0) x $parts, '1' . ('0' x $rem) ], $class; } sub _copy { # make a true copy my $class = shift; return bless [ @{ $_[0] } ], $class; } # catch and throw away sub import { } ############################################################################## # convert back to string and number sub _str { # Convert number from internal base 1eN format to string format. Internal # format is always normalized, i.e., no leading zeros. my $ary = $_[1]; my $idx = $#$ary; # index of last element if ($idx < 0) { # should not happen require Carp; Carp::croak("$_[1] has no elements"); } # Handle first one differently, since it should not have any leading zeros. my $ret = int($ary->[$idx]); if ($idx > 0) { # Interestingly, the pre-padd method uses more time. # The old grep variant takes longer (14 vs. 10 sec). my $z = '0' x ($BASE_LEN - 1); while (--$idx >= 0) { $ret .= substr($z . $ary->[$idx], -$BASE_LEN); } } $ret; } sub _num { # Make a Perl scalar number (int/float) from a BigInt object. my $x = $_[1]; return $x->[0] if @$x == 1; # below $BASE # Start with the most significant element and work towards the least # significant element. Avoid multiplying "inf" (which happens if the number # overflows) with "0" (if there are zero elements in $x) since this gives # "nan" which propagates to the output. my $num = 0; for (my $i = $#$x ; $i >= 0 ; --$i) { $num *= $BASE; $num += $x -> [$i]; } return $num; } ############################################################################## # actual math code sub _add { # (ref to int_num_array, ref to int_num_array) # # Routine to add two base 1eX numbers stolen from Knuth Vol 2 Algorithm A # pg 231. There are separate routines to add and sub as per Knuth pg 233. # This routine modifies array x, but not y. my ($c, $x, $y) = @_; # $x + 0 => $x return $x if @$y == 1 && $y->[0] == 0; # 0 + $y => $y->copy if (@$x == 1 && $x->[0] == 0) { @$x = @$y; return $x; } # For each in Y, add Y to X and carry. If after that, something is left in # X, foreach in X add carry to X and then return X, carry. Trades one # "$j++" for having to shift arrays. my $i; my $car = 0; my $j = 0; for $i (@$y) { $x->[$j] -= $BASE if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0; $j++; } while ($car != 0) { $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++; } $x; } sub _inc { # (ref to int_num_array, ref to int_num_array) # Add 1 to $x, modify $x in place my ($c, $x) = @_; for my $i (@$x) { return $x if ($i += 1) < $BASE; # early out $i = 0; # overflow, next } push @$x, 1 if $x->[-1] == 0; # last overflowed, so extend $x; } sub _dec { # (ref to int_num_array, ref to int_num_array) # Sub 1 from $x, modify $x in place my ($c, $x) = @_; my $MAX = $BASE - 1; # since MAX_VAL based on BASE for my $i (@$x) { last if ($i -= 1) >= 0; # early out $i = $MAX; # underflow, next } pop @$x if $x->[-1] == 0 && @$x > 1; # last underflowed (but leave 0) $x; } sub _sub { # (ref to int_num_array, ref to int_num_array, swap) # # Subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y # subtract Y from X by modifying x in place my ($c, $sx, $sy, $s) = @_; my $car = 0; my $i; my $j = 0; if (!$s) { for $i (@$sx) { last unless defined $sy->[$j] || $car; $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++; } # might leave leading zeros, so fix that return __strip_zeros($sx); } for $i (@$sx) { # We can't do an early out if $x < $y, since we need to copy the high # chunks from $y. Found by Bob Mathews. #last unless defined $sy->[$j] || $car; $sy->[$j] += $BASE if $car = ($sy->[$j] = $i - ($sy->[$j] || 0) - $car) < 0; $j++; } # might leave leading zeros, so fix that __strip_zeros($sy); } sub _mul_use_mul { # (ref to int_num_array, ref to int_num_array) # multiply two numbers in internal representation # modifies first arg, second need not be different from first my ($c, $xv, $yv) = @_; if (@$yv == 1) { # shortcut for two very short numbers (improved by Nathan Zook) # works also if xv and yv are the same reference, and handles also $x == 0 if (@$xv == 1) { if (($xv->[0] *= $yv->[0]) >= $BASE) { $xv->[0] = $xv->[0] - ($xv->[1] = int($xv->[0] * $RBASE)) * $BASE; } ; return $xv; } # $x * 0 => 0 if ($yv->[0] == 0) { @$xv = (0); return $xv; } # multiply a large number a by a single element one, so speed up my $y = $yv->[0]; my $car = 0; foreach my $i (@$xv) { $i = $i * $y + $car; $car = int($i * $RBASE); $i -= $car * $BASE; } push @$xv, $car if $car != 0; return $xv; } # shortcut for result $x == 0 => result = 0 return $xv if @$xv == 1 && $xv->[0] == 0; # since multiplying $x with $x fails, make copy in this case $yv = [ @$xv ] if $xv == $yv; # same references? my @prod = (); my ($prod, $car, $cty, $xi, $yi); for $xi (@$xv) { $car = 0; $cty = 0; # slow variant # for $yi (@$yv) # { # $prod = $xi * $yi + ($prod[$cty] || 0) + $car; # $prod[$cty++] = # $prod - ($car = int($prod * RBASE)) * $BASE; # see USE_MUL # } # $prod[$cty] += $car if $car; # need really to check for 0? # $xi = shift @prod; # faster variant # looping through this if $xi == 0 is silly - so optimize it away! $xi = (shift @prod || 0), next if $xi == 0; for $yi (@$yv) { $prod = $xi * $yi + ($prod[$cty] || 0) + $car; ## this is actually a tad slower ## $prod = $prod[$cty]; $prod += ($car + $xi * $yi); # no ||0 here $prod[$cty++] = $prod - ($car = int($prod * $RBASE)) * $BASE; # see USE_MUL } $prod[$cty] += $car if $car; # need really to check for 0? $xi = shift @prod || 0; # || 0 makes v5.005_3 happy } push @$xv, @prod; # can't have leading zeros # __strip_zeros($xv); $xv; } sub _mul_use_div_64 { # (ref to int_num_array, ref to int_num_array) # multiply two numbers in internal representation # modifies first arg, second need not be different from first # works for 64 bit integer with "use integer" my ($c, $xv, $yv) = @_; use integer; if (@$yv == 1) { # shortcut for two small numbers, also handles $x == 0 if (@$xv == 1) { # shortcut for two very short numbers (improved by Nathan Zook) # works also if xv and yv are the same reference, and handles also $x == 0 if (($xv->[0] *= $yv->[0]) >= $BASE) { $xv->[0] = $xv->[0] - ($xv->[1] = $xv->[0] / $BASE) * $BASE; } return $xv; } # $x * 0 => 0 if ($yv->[0] == 0) { @$xv = (0); return $xv; } # multiply a large number a by a single element one, so speed up my $y = $yv->[0]; my $car = 0; foreach my $i (@$xv) { #$i = $i * $y + $car; $car = $i / $BASE; $i -= $car * $BASE; $i = $i * $y + $car; $i -= ($car = $i / $BASE) * $BASE; } push @$xv, $car if $car != 0; return $xv; } # shortcut for result $x == 0 => result = 0 return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) ); # since multiplying $x with $x fails, make copy in this case $yv = $c->_copy($xv) if $xv == $yv; # same references? my @prod = (); my ($prod, $car, $cty, $xi, $yi); for $xi (@$xv) { $car = 0; $cty = 0; # looping through this if $xi == 0 is silly - so optimize it away! $xi = (shift @prod || 0), next if $xi == 0; for $yi (@$yv) { $prod = $xi * $yi + ($prod[$cty] || 0) + $car; $prod[$cty++] = $prod - ($car = $prod / $BASE) * $BASE; } $prod[$cty] += $car if $car; # need really to check for 0? $xi = shift @prod || 0; # || 0 makes v5.005_3 happy } push @$xv, @prod; $xv; } sub _mul_use_div { # (ref to int_num_array, ref to int_num_array) # multiply two numbers in internal representation # modifies first arg, second need not be different from first my ($c, $xv, $yv) = @_; if (@$yv == 1) { # shortcut for two small numbers, also handles $x == 0 if (@$xv == 1) { # shortcut for two very short numbers (improved by Nathan Zook) # works also if xv and yv are the same reference, and handles also $x == 0 if (($xv->[0] *= $yv->[0]) >= $BASE) { $xv->[0] = $xv->[0] - ($xv->[1] = int($xv->[0] / $BASE)) * $BASE; } ; return $xv; } # $x * 0 => 0 if ($yv->[0] == 0) { @$xv = (0); return $xv; } # multiply a large number a by a single element one, so speed up my $y = $yv->[0]; my $car = 0; foreach my $i (@$xv) { $i = $i * $y + $car; $car = int($i / $BASE); $i -= $car * $BASE; # This (together with use integer;) does not work on 32-bit Perls #$i = $i * $y + $car; $i -= ($car = $i / $BASE) * $BASE; } push @$xv, $car if $car != 0; return $xv; } # shortcut for result $x == 0 => result = 0 return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) ); # since multiplying $x with $x fails, make copy in this case $yv = $c->_copy($xv) if $xv == $yv; # same references? my @prod = (); my ($prod, $car, $cty, $xi, $yi); for $xi (@$xv) { $car = 0; $cty = 0; # looping through this if $xi == 0 is silly - so optimize it away! $xi = (shift @prod || 0), next if $xi == 0; for $yi (@$yv) { $prod = $xi * $yi + ($prod[$cty] || 0) + $car; $prod[$cty++] = $prod - ($car = int($prod / $BASE)) * $BASE; } $prod[$cty] += $car if $car; # need really to check for 0? $xi = shift @prod || 0; # || 0 makes v5.005_3 happy } push @$xv, @prod; # can't have leading zeros # __strip_zeros($xv); $xv; } sub _div_use_mul { # ref to array, ref to array, modify first array and return remainder if # in list context # see comments in _div_use_div() for more explanations my ($c, $x, $yorg) = @_; # the general div algorithm here is about O(N*N) and thus quite slow, so # we first check for some special cases and use shortcuts to handle them. # This works, because we store the numbers in a chunked format where each # element contains 5..7 digits (depending on system). # if both numbers have only one element: if (@$x == 1 && @$yorg == 1) { # shortcut, $yorg and $x are two small numbers if (wantarray) { my $rem = [ $x->[0] % $yorg->[0] ]; bless $rem, $c; $x->[0] = int($x->[0] / $yorg->[0]); return ($x, $rem); } else { $x->[0] = int($x->[0] / $yorg->[0]); return $x; } } # if x has more than one, but y has only one element: if (@$yorg == 1) { my $rem; $rem = $c->_mod($c->_copy($x), $yorg) if wantarray; # shortcut, $y is < $BASE my $j = @$x; my $r = 0; my $y = $yorg->[0]; my $b; while ($j-- > 0) { $b = $r * $BASE + $x->[$j]; $x->[$j] = int($b/$y); $r = $b % $y; } pop @$x if @$x > 1 && $x->[-1] == 0; # splice up a leading zero return ($x, $rem) if wantarray; return $x; } # now x and y have more than one element # check whether y has more elements than x, if yet, the result will be 0 if (@$yorg > @$x) { my $rem; $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; # only x, which is [0] now } # check whether the numbers have the same number of elements, in that case # the result will fit into one element and can be computed efficiently if (@$yorg == @$x) { # if $yorg has more digits than $x (it's leading element is longer than # the one from $x), the result will also be 0: if (length(int($yorg->[-1])) > length(int($x->[-1]))) { my $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; } # now calculate $x / $yorg if (length(int($yorg->[-1])) == length(int($x->[-1]))) { # same length, so make full compare my $a = 0; my $j = @$x - 1; # manual way (abort if unequal, good for early ne) while ($j >= 0) { last if ($a = $x->[$j] - $yorg->[$j]); $j--; } # $a contains the result of the compare between X and Y # a < 0: x < y, a == 0: x == y, a > 0: x > y if ($a <= 0) { # a = 0 => x == y => rem 0 # a < 0 => x < y => rem = x my $rem = $a == 0 ? $c->_zero() : $c->_copy($x); @$x = 0; # if $a < 0 $x->[0] = 1 if $a == 0; # $x == $y return ($x, $rem) if wantarray; return $x; } # $x >= $y, so proceed normally } } # all other cases: my $y = $c->_copy($yorg); # always make copy to preserve my ($car, $bar, $prd, $dd, $xi, $yi, @q, $v2, $v1, @d, $tmp, $q, $u2, $u1, $u0); $car = $bar = $prd = 0; if (($dd = int($BASE / ($y->[-1] + 1))) != 1) { for $xi (@$x) { $xi = $xi * $dd + $car; $xi -= ($car = int($xi * $RBASE)) * $BASE; # see USE_MUL } push(@$x, $car); $car = 0; for $yi (@$y) { $yi = $yi * $dd + $car; $yi -= ($car = int($yi * $RBASE)) * $BASE; # see USE_MUL } } else { push(@$x, 0); } @q = (); ($v2, $v1) = @$y[-2, -1]; $v2 = 0 unless $v2; while ($#$x > $#$y) { ($u2, $u1, $u0) = @$x[-3 .. -1]; $u2 = 0 unless $u2; #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" # if $v1 == 0; $q = (($u0 == $v1) ? $MAX_VAL : int(($u0 * $BASE + $u1) / $v1)); --$q while ($v2 * $q > ($u0 * $BASE + $u1 - $q * $v1) * $BASE + $u2); if ($q) { ($car, $bar) = (0, 0); for ($yi = 0, $xi = $#$x - $#$y-1; $yi <= $#$y; ++$yi, ++$xi) { $prd = $q * $y->[$yi] + $car; $prd -= ($car = int($prd * $RBASE)) * $BASE; # see USE_MUL $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); } if ($x->[-1] < $car + $bar) { $car = 0; --$q; for ($yi = 0, $xi = $#$x - $#$y-1; $yi <= $#$y; ++$yi, ++$xi) { $x->[$xi] -= $BASE if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE)); } } } pop(@$x); unshift(@q, $q); } if (wantarray) { my $d = bless [], $c; if ($dd != 1) { $car = 0; for $xi (reverse @$x) { $prd = $car * $BASE + $xi; $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL unshift(@$d, $tmp); } } else { @$d = @$x; } @$x = @q; __strip_zeros($x); __strip_zeros($d); return ($x, $d); } @$x = @q; __strip_zeros($x); $x; } sub _div_use_div_64 { # ref to array, ref to array, modify first array and return remainder if # in list context # This version works on 64 bit integers my ($c, $x, $yorg) = @_; use integer; # the general div algorithm here is about O(N*N) and thus quite slow, so # we first check for some special cases and use shortcuts to handle them. # This works, because we store the numbers in a chunked format where each # element contains 5..7 digits (depending on system). # if both numbers have only one element: if (@$x == 1 && @$yorg == 1) { # shortcut, $yorg and $x are two small numbers if (wantarray) { my $rem = [ $x->[0] % $yorg->[0] ]; bless $rem, $c; $x->[0] = int($x->[0] / $yorg->[0]); return ($x, $rem); } else { $x->[0] = int($x->[0] / $yorg->[0]); return $x; } } # if x has more than one, but y has only one element: if (@$yorg == 1) { my $rem; $rem = $c->_mod($c->_copy($x), $yorg) if wantarray; # shortcut, $y is < $BASE my $j = @$x; my $r = 0; my $y = $yorg->[0]; my $b; while ($j-- > 0) { $b = $r * $BASE + $x->[$j]; $x->[$j] = int($b/$y); $r = $b % $y; } pop @$x if @$x > 1 && $x->[-1] == 0; # splice up a leading zero return ($x, $rem) if wantarray; return $x; } # now x and y have more than one element # check whether y has more elements than x, if yet, the result will be 0 if (@$yorg > @$x) { my $rem; $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; # only x, which is [0] now } # check whether the numbers have the same number of elements, in that case # the result will fit into one element and can be computed efficiently if (@$yorg == @$x) { my $rem; # if $yorg has more digits than $x (it's leading element is longer than # the one from $x), the result will also be 0: if (length(int($yorg->[-1])) > length(int($x->[-1]))) { $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; } # now calculate $x / $yorg if (length(int($yorg->[-1])) == length(int($x->[-1]))) { # same length, so make full compare my $a = 0; my $j = @$x - 1; # manual way (abort if unequal, good for early ne) while ($j >= 0) { last if ($a = $x->[$j] - $yorg->[$j]); $j--; } # $a contains the result of the compare between X and Y # a < 0: x < y, a == 0: x == y, a > 0: x > y if ($a <= 0) { $rem = $c->_zero(); # a = 0 => x == y => rem 0 $rem = $c->_copy($x) if $a != 0; # a < 0 => x < y => rem = x @$x = 0; # if $a < 0 $x->[0] = 1 if $a == 0; # $x == $y return ($x, $rem) if wantarray; # including remainder? return $x; } # $x >= $y, so proceed normally } } # all other cases: my $y = $c->_copy($yorg); # always make copy to preserve my ($car, $bar, $prd, $dd, $xi, $yi, @q, $v2, $v1, @d, $tmp, $q, $u2, $u1, $u0); $car = $bar = $prd = 0; if (($dd = int($BASE / ($y->[-1] + 1))) != 1) { for $xi (@$x) { $xi = $xi * $dd + $car; $xi -= ($car = int($xi / $BASE)) * $BASE; } push(@$x, $car); $car = 0; for $yi (@$y) { $yi = $yi * $dd + $car; $yi -= ($car = int($yi / $BASE)) * $BASE; } } else { push(@$x, 0); } # @q will accumulate the final result, $q contains the current computed # part of the final result @q = (); ($v2, $v1) = @$y[-2, -1]; $v2 = 0 unless $v2; while ($#$x > $#$y) { ($u2, $u1, $u0) = @$x[-3..-1]; $u2 = 0 unless $u2; #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" # if $v1 == 0; $q = (($u0 == $v1) ? $MAX_VAL : int(($u0 * $BASE + $u1) / $v1)); --$q while ($v2 * $q > ($u0 * $BASE +$ u1- $q*$v1) * $BASE + $u2); if ($q) { ($car, $bar) = (0, 0); for ($yi = 0, $xi = $#$x - $#$y - 1; $yi <= $#$y; ++$yi, ++$xi) { $prd = $q * $y->[$yi] + $car; $prd -= ($car = int($prd / $BASE)) * $BASE; $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); } if ($x->[-1] < $car + $bar) { $car = 0; --$q; for ($yi = 0, $xi = $#$x - $#$y - 1; $yi <= $#$y; ++$yi, ++$xi) { $x->[$xi] -= $BASE if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE)); } } } pop(@$x); unshift(@q, $q); } if (wantarray) { my $d = bless [], $c; if ($dd != 1) { $car = 0; for $xi (reverse @$x) { $prd = $car * $BASE + $xi; $car = $prd - ($tmp = int($prd / $dd)) * $dd; unshift(@$d, $tmp); } } else { @$d = @$x; } @$x = @q; __strip_zeros($x); __strip_zeros($d); return ($x, $d); } @$x = @q; __strip_zeros($x); $x; } sub _div_use_div { # ref to array, ref to array, modify first array and return remainder if # in list context my ($c, $x, $yorg) = @_; # the general div algorithm here is about O(N*N) and thus quite slow, so # we first check for some special cases and use shortcuts to handle them. # This works, because we store the numbers in a chunked format where each # element contains 5..7 digits (depending on system). # if both numbers have only one element: if (@$x == 1 && @$yorg == 1) { # shortcut, $yorg and $x are two small numbers if (wantarray) { my $rem = [ $x->[0] % $yorg->[0] ]; bless $rem, $c; $x->[0] = int($x->[0] / $yorg->[0]); return ($x, $rem); } else { $x->[0] = int($x->[0] / $yorg->[0]); return $x; } } # if x has more than one, but y has only one element: if (@$yorg == 1) { my $rem; $rem = $c->_mod($c->_copy($x), $yorg) if wantarray; # shortcut, $y is < $BASE my $j = @$x; my $r = 0; my $y = $yorg->[0]; my $b; while ($j-- > 0) { $b = $r * $BASE + $x->[$j]; $x->[$j] = int($b/$y); $r = $b % $y; } pop @$x if @$x > 1 && $x->[-1] == 0; # splice up a leading zero return ($x, $rem) if wantarray; return $x; } # now x and y have more than one element # check whether y has more elements than x, if yet, the result will be 0 if (@$yorg > @$x) { my $rem; $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; # only x, which is [0] now } # check whether the numbers have the same number of elements, in that case # the result will fit into one element and can be computed efficiently if (@$yorg == @$x) { my $rem; # if $yorg has more digits than $x (it's leading element is longer than # the one from $x), the result will also be 0: if (length(int($yorg->[-1])) > length(int($x->[-1]))) { $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; } # now calculate $x / $yorg if (length(int($yorg->[-1])) == length(int($x->[-1]))) { # same length, so make full compare my $a = 0; my $j = @$x - 1; # manual way (abort if unequal, good for early ne) while ($j >= 0) { last if ($a = $x->[$j] - $yorg->[$j]); $j--; } # $a contains the result of the compare between X and Y # a < 0: x < y, a == 0: x == y, a > 0: x > y if ($a <= 0) { $rem = $c->_zero(); # a = 0 => x == y => rem 0 $rem = $c->_copy($x) if $a != 0; # a < 0 => x < y => rem = x @$x = 0; $x->[0] = 0; # if $a < 0 $x->[0] = 1 if $a == 0; # $x == $y return ($x, $rem) if wantarray; # including remainder? return $x; } # $x >= $y, so proceed normally } } # all other cases: my $y = $c->_copy($yorg); # always make copy to preserve my ($car, $bar, $prd, $dd, $xi, $yi, @q, $v2, $v1, @d, $tmp, $q, $u2, $u1, $u0); $car = $bar = $prd = 0; if (($dd = int($BASE / ($y->[-1] + 1))) != 1) { for $xi (@$x) { $xi = $xi * $dd + $car; $xi -= ($car = int($xi / $BASE)) * $BASE; } push(@$x, $car); $car = 0; for $yi (@$y) { $yi = $yi * $dd + $car; $yi -= ($car = int($yi / $BASE)) * $BASE; } } else { push(@$x, 0); } # @q will accumulate the final result, $q contains the current computed # part of the final result @q = (); ($v2, $v1) = @$y[-2, -1]; $v2 = 0 unless $v2; while ($#$x > $#$y) { ($u2, $u1, $u0) = @$x[-3..-1]; $u2 = 0 unless $u2; #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" # if $v1 == 0; $q = (($u0 == $v1) ? $MAX_VAL : int(($u0 * $BASE + $u1) / $v1)); --$q while ($v2 * $q > ($u0 * $BASE + $u1 - $q * $v1) * $BASE + $u2); if ($q) { ($car, $bar) = (0, 0); for ($yi = 0, $xi = $#$x - $#$y - 1; $yi <= $#$y; ++$yi, ++$xi) { $prd = $q * $y->[$yi] + $car; $prd -= ($car = int($prd / $BASE)) * $BASE; $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); } if ($x->[-1] < $car + $bar) { $car = 0; --$q; for ($yi = 0, $xi = $#$x - $#$y - 1; $yi <= $#$y; ++$yi, ++$xi) { $x->[$xi] -= $BASE if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE)); } } } pop(@$x); unshift(@q, $q); } if (wantarray) { my $d = bless [], $c; if ($dd != 1) { $car = 0; for $xi (reverse @$x) { $prd = $car * $BASE + $xi; $car = $prd - ($tmp = int($prd / $dd)) * $dd; unshift(@$d, $tmp); } } else { @$d = @$x; } @$x = @q; __strip_zeros($x); __strip_zeros($d); return ($x, $d); } @$x = @q; __strip_zeros($x); $x; } ############################################################################## # testing sub _acmp { # Internal absolute post-normalized compare (ignore signs) # ref to array, ref to array, return <0, 0, >0 # Arrays must have at least one entry; this is not checked for. my ($c, $cx, $cy) = @_; # shortcut for short numbers return (($cx->[0] <=> $cy->[0]) <=> 0) if @$cx == 1 && @$cy == 1; # fast comp based on number of array elements (aka pseudo-length) my $lxy = (@$cx - @$cy) # or length of first element if same number of elements (aka difference 0) || # need int() here because sometimes the last element is '00018' vs '18' (length(int($cx->[-1])) - length(int($cy->[-1]))); return -1 if $lxy < 0; # already differs, ret return 1 if $lxy > 0; # ditto # manual way (abort if unequal, good for early ne) my $a; my $j = @$cx; while (--$j >= 0) { last if $a = $cx->[$j] - $cy->[$j]; } $a <=> 0; } sub _len { # compute number of digits in base 10 # int() because add/sub sometimes leaves strings (like '00005') instead of # '5' in this place, thus causing length() to report wrong length my $cx = $_[1]; (@$cx - 1) * $BASE_LEN + length(int($cx->[-1])); } sub _digit { # Return the nth digit. Zero is rightmost, so _digit(123, 0) gives 3. # Negative values count from the left, so _digit(123, -1) gives 1. my ($c, $x, $n) = @_; my $len = _len('', $x); $n += $len if $n < 0; # -1 last, -2 second-to-last # Math::BigInt::Calc returns 0 if N is out of range, but this is not done # by the other backend libraries. return "0" if $n < 0 || $n >= $len; # return 0 for digits out of range my $elem = int($n / $BASE_LEN); # index of array element my $digit = $n % $BASE_LEN; # index of digit within the element substr("0" x $BASE_LEN . "$x->[$elem]", -1 - $digit, 1); } sub _zeros { # Return number of trailing zeros in decimal. # Check each array element for having 0 at end as long as elem == 0 # Upon finding a elem != 0, stop. my $x = $_[1]; return 0 if @$x == 1 && $x->[0] == 0; my $zeros = 0; foreach my $elem (@$x) { if ($elem != 0) { $elem =~ /[^0](0*)\z/; $zeros += length($1); # count trailing zeros last; # early out } $zeros += $BASE_LEN; } $zeros; } ############################################################################## # _is_* routines sub _is_zero { # return true if arg is zero @{$_[1]} == 1 && $_[1]->[0] == 0 ? 1 : 0; } sub _is_even { # return true if arg is even $_[1]->[0] & 1 ? 0 : 1; } sub _is_odd { # return true if arg is odd $_[1]->[0] & 1 ? 1 : 0; } sub _is_one { # return true if arg is one @{$_[1]} == 1 && $_[1]->[0] == 1 ? 1 : 0; } sub _is_two { # return true if arg is two @{$_[1]} == 1 && $_[1]->[0] == 2 ? 1 : 0; } sub _is_ten { # return true if arg is ten @{$_[1]} == 1 && $_[1]->[0] == 10 ? 1 : 0; } sub __strip_zeros { # Internal normalization function that strips leading zeros from the array. # Args: ref to array my $x = shift; push @$x, 0 if @$x == 0; # div might return empty results, so fix it return $x if @$x == 1; # early out #print "strip: cnt $cnt i $i\n"; # '0', '3', '4', '0', '0', # 0 1 2 3 4 # cnt = 5, i = 4 # i = 4 # i = 3 # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos) # >= 1: skip first part (this can be zero) my $i = $#$x; while ($i > 0) { last if $x->[$i] != 0; $i--; } $i++; splice(@$x, $i) if $i < @$x; $x; } ############################################################################### # check routine to test internal state for corruptions sub _check { # used by the test suite my ($class, $x) = @_; my $msg = $class -> SUPER::_check($x); return $msg if $msg; my $n; eval { $n = @$x }; return "Not an array reference" unless $@ eq ''; return "Reference to an empty array" unless $n > 0; # The following fails with Math::BigInt::FastCalc because a # Math::BigInt::FastCalc "object" is an unblessed array ref. # #return 0 unless ref($x) eq $class; for (my $i = 0 ; $i <= $#$x ; ++ $i) { my $e = $x -> [$i]; return "Element at index $i is undefined" unless defined $e; return "Element at index $i is a '" . ref($e) . "', which is not a scalar" unless ref($e) eq ""; # It would be better to use the regex /^([1-9]\d*|0)\z/, but that fails # in Math::BigInt::FastCalc, because it sometimes creates array # elements like "000000". return "Element at index $i is '$e', which does not look like an" . " normal integer" unless $e =~ /^\d+\z/; return "Element at index $i is '$e', which is not smaller than" . " the base '$BASE'" if $e >= $BASE; return "Element at index $i (last element) is zero" if $#$x > 0 && $i == $#$x && $e == 0; } return 0; } ############################################################################### sub _mod { # if possible, use mod shortcut my ($c, $x, $yo) = @_; # slow way since $y too big if (@$yo > 1) { my ($xo, $rem) = $c->_div($x, $yo); @$x = @$rem; return $x; } my $y = $yo->[0]; # if both are single element arrays if (@$x == 1) { $x->[0] %= $y; return $x; } # if @$x has more than one element, but @$y is a single element my $b = $BASE % $y; if ($b == 0) { # when BASE % Y == 0 then (B * BASE) % Y == 0 # (B * BASE) % $y + A % Y => A % Y # so need to consider only last element: O(1) $x->[0] %= $y; } elsif ($b == 1) { # else need to go through all elements in @$x: O(N), but loop is a bit # simplified my $r = 0; foreach (@$x) { $r = ($r + $_) % $y; # not much faster, but heh... #$r += $_ % $y; $r %= $y; } $r = 0 if $r == $y; $x->[0] = $r; } else { # else need to go through all elements in @$x: O(N) my $r = 0; my $bm = 1; foreach (@$x) { $r = ($_ * $bm + $r) % $y; $bm = ($bm * $b) % $y; #$r += ($_ % $y) * $bm; #$bm *= $b; #$bm %= $y; #$r %= $y; } $r = 0 if $r == $y; $x->[0] = $r; } @$x = $x->[0]; # keep one element of @$x return $x; } ############################################################################## # shifts sub _rsft { my ($c, $x, $y, $n) = @_; if ($n != 10) { $n = $c->_new($n); return scalar $c->_div($x, $c->_pow($n, $y)); } # shortcut (faster) for shifting by 10) # multiples of $BASE_LEN my $dst = 0; # destination my $src = $c->_num($y); # as normal int my $xlen = (@$x - 1) * $BASE_LEN + length(int($x->[-1])); if ($src >= $xlen or ($src == $xlen and !defined $x->[1])) { # 12345 67890 shifted right by more than 10 digits => 0 splice(@$x, 1); # leave only one element $x->[0] = 0; # set to zero return $x; } my $rem = $src % $BASE_LEN; # remainder to shift $src = int($src / $BASE_LEN); # source if ($rem == 0) { splice(@$x, 0, $src); # even faster, 38.4 => 39.3 } else { my $len = @$x - $src; # elems to go my $vd; my $z = '0' x $BASE_LEN; $x->[ @$x ] = 0; # avoid || 0 test inside loop while ($dst < $len) { $vd = $z . $x->[$src]; $vd = substr($vd, -$BASE_LEN, $BASE_LEN - $rem); $src++; $vd = substr($z . $x->[$src], -$rem, $rem) . $vd; $vd = substr($vd, -$BASE_LEN, $BASE_LEN) if length($vd) > $BASE_LEN; $x->[$dst] = int($vd); $dst++; } splice(@$x, $dst) if $dst > 0; # kill left-over array elems pop @$x if $x->[-1] == 0 && @$x > 1; # kill last element if 0 } # else rem == 0 $x; } sub _lsft { my ($c, $x, $n, $b) = @_; return $x if $c->_is_zero($x); # Handle the special case when the base is a power of 10. Don't check # whether log($b)/log(10) is an integer, because log(1000)/log(10) is not # exactly 3. my $log10 = sprintf "%.0f", log($b) / log(10); if ($b == 10 ** $log10) { $b = 10; $n = $c->_mul($n, $c->_new($log10)); # shortcut (faster) for shifting by 10) since we are in base 10eX # multiples of $BASE_LEN: my $src = @$x; # source my $len = $c->_num($n); # shift-len as normal int my $rem = $len % $BASE_LEN; # remainder to shift my $dst = $src + int($len / $BASE_LEN); # destination my $vd; # further speedup $x->[$src] = 0; # avoid first ||0 for speed my $z = '0' x $BASE_LEN; while ($src >= 0) { $vd = $x->[$src]; $vd = $z . $vd; $vd = substr($vd, -$BASE_LEN + $rem, $BASE_LEN - $rem); $vd .= $src > 0 ? substr($z . $x->[$src - 1], -$BASE_LEN, $rem) : '0' x $rem; $vd = substr($vd, -$BASE_LEN, $BASE_LEN) if length($vd) > $BASE_LEN; $x->[$dst] = int($vd); $dst--; $src--; } # set lowest parts to 0 while ($dst >= 0) { $x->[$dst--] = 0; } # fix spurious last zero element splice @$x, -1 if $x->[-1] == 0; return $x; } else { $b = $c->_new($b); #print $c->_str($b); return $c->_mul($x, $c->_pow($b, $n)); } } sub _pow { # power of $x to $y # ref to array, ref to array, return ref to array my ($c, $cx, $cy) = @_; if (@$cy == 1 && $cy->[0] == 0) { splice(@$cx, 1); $cx->[0] = 1; # y == 0 => x => 1 return $cx; } if ((@$cx == 1 && $cx->[0] == 1) || # x == 1 (@$cy == 1 && $cy->[0] == 1)) # or y == 1 { return $cx; } if (@$cx == 1 && $cx->[0] == 0) { splice (@$cx, 1); $cx->[0] = 0; # 0 ** y => 0 (if not y <= 0) return $cx; } my $pow2 = $c->_one(); my $y_bin = $c->_as_bin($cy); $y_bin =~ s/^0b//; my $len = length($y_bin); while (--$len > 0) { $c->_mul($pow2, $cx) if substr($y_bin, $len, 1) eq '1'; # is odd? $c->_mul($cx, $cx); } $c->_mul($cx, $pow2); $cx; } sub _nok { # Return binomial coefficient (n over k). # Given refs to arrays, return ref to array. # First input argument is modified. my ($c, $n, $k) = @_; # If k > n/2, or, equivalently, 2*k > n, compute nok(n, k) as # nok(n, n-k), to minimize the number if iterations in the loop. { my $twok = $c->_mul($c->_two(), $c->_copy($k)); # 2 * k if ($c->_acmp($twok, $n) > 0) { # if 2*k > n $k = $c->_sub($c->_copy($n), $k); # k = n - k } } # Example: # # / 7 \ 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 6 7 # | | = --------- = --------------- = --------- = 5 * - * - # \ 3 / (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 2 3 if ($c->_is_zero($k)) { @$n = 1; } else { # Make a copy of the original n, since we'll be modifying n in-place. my $n_orig = $c->_copy($n); # n = 5, f = 6, d = 2 (cf. example above) $c->_sub($n, $k); $c->_inc($n); my $f = $c->_copy($n); $c->_inc($f); my $d = $c->_two(); # while f <= n (the original n, that is) ... while ($c->_acmp($f, $n_orig) <= 0) { # n = (n * f / d) == 5 * 6 / 2 (cf. example above) $c->_mul($n, $f); $c->_div($n, $d); # f = 7, d = 3 (cf. example above) $c->_inc($f); $c->_inc($d); } } return $n; } my @factorials = ( 1, 1, 2, 2*3, 2*3*4, 2*3*4*5, 2*3*4*5*6, 2*3*4*5*6*7, ); sub _fac { # factorial of $x # ref to array, return ref to array my ($c, $cx) = @_; if ((@$cx == 1) && ($cx->[0] <= 7)) { $cx->[0] = $factorials[$cx->[0]]; # 0 => 1, 1 => 1, 2 => 2 etc. return $cx; } if ((@$cx == 1) && # we do this only if $x >= 12 and $x <= 7000 ($cx->[0] >= 12 && $cx->[0] < 7000)) { # Calculate (k-j) * (k-j+1) ... k .. (k+j-1) * (k + j) # See http://blogten.blogspot.com/2007/01/calculating-n.html # The above series can be expressed as factors: # k * k - (j - i) * 2 # We cache k*k, and calculate (j * j) as the sum of the first j odd integers # This will not work when N exceeds the storage of a Perl scalar, however, # in this case the algorithm would be way too slow to terminate, anyway. # As soon as the last element of $cx is 0, we split it up and remember # how many zeors we got so far. The reason is that n! will accumulate # zeros at the end rather fast. my $zero_elements = 0; # If n is even, set n = n -1 my $k = $c->_num($cx); my $even = 1; if (($k & 1) == 0) { $even = $k; $k --; } # set k to the center point $k = ($k + 1) / 2; # print "k $k even: $even\n"; # now calculate k * k my $k2 = $k * $k; my $odd = 1; my $sum = 1; my $i = $k - 1; # keep reference to x my $new_x = $c->_new($k * $even); @$cx = @$new_x; if ($cx->[0] == 0) { $zero_elements ++; shift @$cx; } # print STDERR "x = ", $c->_str($cx), "\n"; my $BASE2 = int(sqrt($BASE))-1; my $j = 1; while ($j <= $i) { my $m = ($k2 - $sum); $odd += 2; $sum += $odd; $j++; while ($j <= $i && ($m < $BASE2) && (($k2 - $sum) < $BASE2)) { $m *= ($k2 - $sum); $odd += 2; $sum += $odd; $j++; # print STDERR "\n k2 $k2 m $m sum $sum odd $odd\n"; sleep(1); } if ($m < $BASE) { $c->_mul($cx, [$m]); } else { $c->_mul($cx, $c->_new($m)); } if ($cx->[0] == 0) { $zero_elements ++; shift @$cx; } # print STDERR "Calculate $k2 - $sum = $m (x = ", $c->_str($cx), ")\n"; } # multiply in the zeros again unshift @$cx, (0) x $zero_elements; return $cx; } # go forward until $base is exceeded limit is either $x steps (steps == 100 # means a result always too high) or $base. my $steps = 100; $steps = $cx->[0] if @$cx == 1; my $r = 2; my $cf = 3; my $step = 2; my $last = $r; while ($r * $cf < $BASE && $step < $steps) { $last = $r; $r *= $cf++; $step++; } if ((@$cx == 1) && $step == $cx->[0]) { # completely done, so keep reference to $x and return $cx->[0] = $r; return $cx; } # now we must do the left over steps my $n; # steps still to do if (@$cx == 1) { $n = $cx->[0]; } else { $n = $c->_copy($cx); } # Set $cx to the last result below $BASE (but keep ref to $x) $cx->[0] = $last; splice (@$cx, 1); # As soon as the last element of $cx is 0, we split it up and remember # how many zeors we got so far. The reason is that n! will accumulate # zeros at the end rather fast. my $zero_elements = 0; # do left-over steps fit into a scalar? if (ref $n eq 'ARRAY') { # No, so use slower inc() & cmp() # ($n is at least $BASE here) my $base_2 = int(sqrt($BASE)) - 1; #print STDERR "base_2: $base_2\n"; while ($step < $base_2) { if ($cx->[0] == 0) { $zero_elements ++; shift @$cx; } my $b = $step * ($step + 1); $step += 2; $c->_mul($cx, [$b]); } $step = [$step]; while ($c->_acmp($step, $n) <= 0) { if ($cx->[0] == 0) { $zero_elements ++; shift @$cx; } $c->_mul($cx, $step); $c->_inc($step); } } else { # Yes, so we can speed it up slightly # print "# left over steps $n\n"; my $base_4 = int(sqrt(sqrt($BASE))) - 2; #print STDERR "base_4: $base_4\n"; my $n4 = $n - 4; while ($step < $n4 && $step < $base_4) { if ($cx->[0] == 0) { $zero_elements ++; shift @$cx; } my $b = $step * ($step + 1); $step += 2; $b *= $step * ($step + 1); $step += 2; $c->_mul($cx, [$b]); } my $base_2 = int(sqrt($BASE)) - 1; my $n2 = $n - 2; #print STDERR "base_2: $base_2\n"; while ($step < $n2 && $step < $base_2) { if ($cx->[0] == 0) { $zero_elements ++; shift @$cx; } my $b = $step * ($step + 1); $step += 2; $c->_mul($cx, [$b]); } # do what's left over while ($step <= $n) { $c->_mul($cx, [$step]); $step++; if ($cx->[0] == 0) { $zero_elements ++; shift @$cx; } } } # multiply in the zeros again unshift @$cx, (0) x $zero_elements; $cx; # return result } sub _log_int { # calculate integer log of $x to base $base # ref to array, ref to array - return ref to array my ($c, $x, $base) = @_; # X == 0 => NaN return if @$x == 1 && $x->[0] == 0; # BASE 0 or 1 => NaN return if @$base == 1 && $base->[0] < 2; # X == 1 => 0 (is exact) if (@$x == 1 && $x->[0] == 1) { @$x = 0; return $x, 1; } my $cmp = $c->_acmp($x, $base); # X == BASE => 1 (is exact) if ($cmp == 0) { @$x = 1; return $x, 1; } # 1 < X < BASE => 0 (is truncated) if ($cmp < 0) { @$x = 0; return $x, 0; } my $x_org = $c->_copy($x); # preserve x # Compute a guess for the result based on: # $guess = int ( length_in_base_10(X) / ( log(base) / log(10) ) ) my $len = $c->_len($x_org); my $log = log($base->[-1]) / log(10); # for each additional element in $base, we add $BASE_LEN to the result, # based on the observation that log($BASE, 10) is BASE_LEN and # log(x*y) == log(x) + log(y): $log += (@$base - 1) * $BASE_LEN; # calculate now a guess based on the values obtained above: my $res = int($len / $log); @$x = $res; my $trial = $c->_pow($c->_copy($base), $x); my $acmp = $c->_acmp($trial, $x_org); # Did we get the exact result? return $x, 1 if $acmp == 0; # Too small? while ($acmp < 0) { $c->_mul($trial, $base); $c->_inc($x); $acmp = $c->_acmp($trial, $x_org); } # Too big? while ($acmp > 0) { $c->_div($trial, $base); $c->_dec($x); $acmp = $c->_acmp($trial, $x_org); } return $x, 1 if $acmp == 0; # result is exact return $x, 0; # result is too small } # for debugging: use constant DEBUG => 0; my $steps = 0; sub steps { $steps }; sub _sqrt { # square-root of $x in place # Compute a guess of the result (by rule of thumb), then improve it via # Newton's method. my ($c, $x) = @_; if (@$x == 1) { # fits into one Perl scalar, so result can be computed directly $x->[0] = int(sqrt($x->[0])); return $x; } my $y = $c->_copy($x); # hopefully _len/2 is < $BASE, the -1 is to always undershot the guess # since our guess will "grow" my $l = int(($c->_len($x)-1) / 2); my $lastelem = $x->[-1]; # for guess my $elems = @$x - 1; # not enough digits, but could have more? if ((length($lastelem) <= 3) && ($elems > 1)) { # right-align with zero pad my $len = length($lastelem) & 1; print "$lastelem => " if DEBUG; $lastelem .= substr($x->[-2] . '0' x $BASE_LEN, 0, $BASE_LEN); # former odd => make odd again, or former even to even again $lastelem = $lastelem / 10 if (length($lastelem) & 1) != $len; print "$lastelem\n" if DEBUG; } # construct $x (instead of $c->_lsft($x, $l, 10) my $r = $l % $BASE_LEN; # 10000 00000 00000 00000 ($BASE_LEN=5) $l = int($l / $BASE_LEN); print "l = $l " if DEBUG; splice @$x, $l; # keep ref($x), but modify it # we make the first part of the guess not '1000...0' but int(sqrt($lastelem)) # that gives us: # 14400 00000 => sqrt(14400) => guess first digits to be 120 # 144000 000000 => sqrt(144000) => guess 379 print "$lastelem (elems $elems) => " if DEBUG; $lastelem = $lastelem / 10 if ($elems & 1 == 1); # odd or even? my $g = sqrt($lastelem); $g =~ s/\.//; # 2.345 => 2345 $r -= 1 if $elems & 1 == 0; # 70 => 7 # padd with zeros if result is too short $x->[$l--] = int(substr($g . '0' x $r, 0, $r+1)); print "now ", $x->[-1] if DEBUG; print " would have been ", int('1' . '0' x $r), "\n" if DEBUG; # If @$x > 1, we could compute the second elem of the guess, too, to create # an even better guess. Not implemented yet. Does it improve performance? $x->[$l--] = 0 while ($l >= 0); # all other digits of guess are zero print "start x= ", $c->_str($x), "\n" if DEBUG; my $two = $c->_two(); my $last = $c->_zero(); my $lastlast = $c->_zero(); $steps = 0 if DEBUG; while ($c->_acmp($last, $x) != 0 && $c->_acmp($lastlast, $x) != 0) { $steps++ if DEBUG; $lastlast = $c->_copy($last); $last = $c->_copy($x); $c->_add($x, $c->_div($c->_copy($y), $x)); $c->_div($x, $two ); print " x= ", $c->_str($x), "\n" if DEBUG; } print "\nsteps in sqrt: $steps, " if DEBUG; $c->_dec($x) if $c->_acmp($y, $c->_mul($c->_copy($x), $x)) < 0; # overshot? print " final ", $x->[-1], "\n" if DEBUG; $x; } sub _root { # Take n'th root of $x in place. my ($c, $x, $n) = @_; # Small numbers. if (@$x == 1 && @$n == 1) { # Result can be computed directly. Adjust initial result for numerical # errors, e.g., int(1000**(1/3)) is 2, not 3. my $y = int($x->[0] ** (1 / $n->[0])); my $yp1 = $y + 1; $y = $yp1 if $yp1 ** $n->[0] == $x->[0]; $x->[0] = $y; return $x; } # If x <= n, the result is always (truncated to) 1. if ((@$x > 1 || $x -> [0] > 0) && # if x is non-zero ... $c -> _acmp($x, $n) <= 0) # ... and x <= n { my $one = $x -> _one(); @$x = @$one; return $x; } # If $n is a power of two, take sqrt($x) repeatedly, e.g., root($x, 4) = # sqrt(sqrt($x)), root($x, 8) = sqrt(sqrt(sqrt($x))). my $b = $c -> _as_bin($n); if ($b =~ /0b1(0+)$/) { my $count = length($1); # 0b100 => len('00') => 2 my $cnt = $count; # counter for loop unshift @$x, 0; # add one element, together with one # more below in the loop this makes 2 while ($cnt-- > 0) { # 'Inflate' $x by adding one element, basically computing # $x * $BASE * $BASE. This gives us more $BASE_LEN digits for # result since len(sqrt($X)) approx == len($x) / 2. unshift @$x, 0; # Calculate sqrt($x), $x is now one element to big, again. In the # next round we make that two, again. $c -> _sqrt($x); } # $x is now one element too big, so truncate result by removing it. shift @$x; return $x; } my $DEBUG = 0; # Now the general case. This works by finding an initial guess. If this # guess is incorrect, a relatively small delta is chosen. This delta is # used to find a lower and upper limit for the correct value. The delta is # doubled in each iteration. When a lower and upper limit is found, # bisection is applied to narrow down the region until we have the correct # value. # Split x into mantissa and exponent in base 10, so that # # x = xm * 10^xe, where 0 < xm < 1 and xe is an integer my $x_str = $c -> _str($x); my $xm = "." . $x_str; my $xe = length($x_str); # From this we compute the base 10 logarithm of x # # log_10(x) = log_10(xm) + log_10(xe^10) # = log(xm)/log(10) + xe # # and then the base 10 logarithm of y, where y = x^(1/n) # # log_10(y) = log_10(x)/n my $log10x = log($xm) / log(10) + $xe; my $log10y = $log10x / $c -> _num($n); # And from this we compute ym and ye, the mantissa and exponent (in # base 10) of y, where 1 < ym <= 10 and ye is an integer. my $ye = int $log10y; my $ym = 10 ** ($log10y - $ye); # Finally, we scale the mantissa and exponent to incraese the integer # part of ym, before building the string representing our guess of y. if ($DEBUG) { print "\n"; print "xm = $xm\n"; print "xe = $xe\n"; print "log10x = $log10x\n"; print "log10y = $log10y\n"; print "ym = $ym\n"; print "ye = $ye\n"; print "\n"; } my $d = $ye < 15 ? $ye : 15; $ym *= 10 ** $d; $ye -= $d; my $y_str = sprintf('%.0f', $ym) . "0" x $ye; my $y = $c -> _new($y_str); if ($DEBUG) { print "ym = $ym\n"; print "ye = $ye\n"; print "\n"; print "y_str = $y_str (initial guess)\n"; print "\n"; } # See if our guess y is correct. my $trial = $c -> _pow($c -> _copy($y), $n); my $acmp = $c -> _acmp($trial, $x); if ($acmp == 0) { @$x = @$y; return $x; } # Find a lower and upper limit for the correct value of y. Start off with a # delta value that is approximately the size of the accuracy of the guess. my $lower; my $upper; my $delta = $c -> _new("1" . ("0" x $ye)); my $two = $c -> _two(); if ($acmp < 0) { $lower = $y; while ($acmp < 0) { $upper = $c -> _add($c -> _copy($lower), $delta); if ($DEBUG) { print "lower = $lower\n"; print "upper = $upper\n"; print "delta = $delta\n"; print "\n"; } $acmp = $c -> _acmp($c -> _pow($c -> _copy($upper), $n), $x); if ($acmp == 0) { @$x = @$upper; return $x; } $delta = $c -> _mul($delta, $two); } } elsif ($acmp > 0) { $upper = $y; my $zero = $c -> _zero(); while ($acmp > 0) { if ($c -> _acmp($upper, $delta) <= 0) { $lower = $c -> _zero(); last; } $lower = $c -> _sub($c -> _copy($upper), $delta); if ($DEBUG) { print "lower = $lower\n"; print "upper = $upper\n"; print "delta = $delta\n"; print "\n"; } $acmp = $c -> _acmp($c -> _pow($c -> _copy($lower), $n), $x); if ($acmp == 0) { @$x = @$lower; return $x; } $delta = $c -> _mul($delta, $two); } } # Use bisection to narrow down the interval. my $one = $c -> _one(); { $delta = $c -> _sub($c -> _copy($upper), $lower); if ($c -> _acmp($delta, $one) <= 0) { @$x = @$lower; return $x; } if ($DEBUG) { print "lower = $lower\n"; print "upper = $upper\n"; print "delta = $delta\n"; print "\n"; } $delta = $c -> _div($delta, $two); my $middle = $c -> _add($c -> _copy($lower), $delta); $acmp = $c -> _acmp($c -> _pow($c -> _copy($middle), $n), $x); if ($acmp < 0) { $lower = $middle; } elsif ($acmp > 0) { $upper = $middle; } else { @$x = @$middle; return $x; } redo; } $x; } ############################################################################## # binary stuff sub _and { my ($c, $x, $y) = @_; # the shortcut makes equal, large numbers _really_ fast, and makes only a # very small performance drop for small numbers (e.g. something with less # than 32 bit) Since we optimize for large numbers, this is enabled. return $x if $c->_acmp($x, $y) == 0; # shortcut my $m = $c->_one(); my ($xr, $yr); my $mask = $AND_MASK; my $x1 = $c->_copy($x); my $y1 = $c->_copy($y); my $z = $c->_zero(); use integer; until ($c->_is_zero($x1) || $c->_is_zero($y1)) { ($x1, $xr) = $c->_div($x1, $mask); ($y1, $yr) = $c->_div($y1, $mask); $c->_add($z, $c->_mul([ 0 + $xr->[0] & 0 + $yr->[0] ], $m)); $c->_mul($m, $mask); } @$x = @$z; return $x; } sub _xor { my ($c, $x, $y) = @_; return $c->_zero() if $c->_acmp($x, $y) == 0; # shortcut (see -and) my $m = $c->_one(); my ($xr, $yr); my $mask = $XOR_MASK; my $x1 = $c->_copy($x); my $y1 = $c->_copy($y); # make copy my $z = $c->_zero(); use integer; until ($c->_is_zero($x1) || $c->_is_zero($y1)) { ($x1, $xr) = $c->_div($x1, $mask); ($y1, $yr) = $c->_div($y1, $mask); # make ints() from $xr, $yr (see _and()) #$b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } #$b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } #$c->_add($x, $c->_mul($c->_new($xrr ^ $yrr)), $m) ); $c->_add($z, $c->_mul([ 0 + $xr->[0] ^ 0 + $yr->[0] ], $m)); $c->_mul($m, $mask); } # the loop stops when the shorter of the two numbers is exhausted # the remainder of the longer one will survive bit-by-bit, so we simple # multiply-add it in $c->_add($z, $c->_mul($x1, $m) ) if !$c->_is_zero($x1); $c->_add($z, $c->_mul($y1, $m) ) if !$c->_is_zero($y1); @$x = @$z; return $x; } sub _or { my ($c, $x, $y) = @_; return $x if $c->_acmp($x, $y) == 0; # shortcut (see _and) my $m = $c->_one(); my ($xr, $yr); my $mask = $OR_MASK; my $x1 = $c->_copy($x); my $y1 = $c->_copy($y); # make copy my $z = $c->_zero(); use integer; until ($c->_is_zero($x1) || $c->_is_zero($y1)) { ($x1, $xr) = $c->_div($x1, $mask); ($y1, $yr) = $c->_div($y1, $mask); # make ints() from $xr, $yr (see _and()) # $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; } # $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; } # $c->_add($x, $c->_mul(_new( $c, ($xrr | $yrr) ), $m) ); $c->_add($z, $c->_mul([ 0 + $xr->[0] | 0 + $yr->[0] ], $m)); $c->_mul($m, $mask); } # the loop stops when the shorter of the two numbers is exhausted # the remainder of the longer one will survive bit-by-bit, so we simple # multiply-add it in $c->_add($z, $c->_mul($x1, $m) ) if !$c->_is_zero($x1); $c->_add($z, $c->_mul($y1, $m) ) if !$c->_is_zero($y1); @$x = @$z; return $x; } sub _as_hex { # convert a decimal number to hex (ref to array, return ref to string) my ($c, $x) = @_; # fits into one element (handle also 0x0 case) return sprintf("0x%x", $x->[0]) if @$x == 1; my $x1 = $c->_copy($x); my $es = ''; my ($xr, $h, $x10000); if ($] >= 5.006) { $x10000 = [ 0x10000 ]; $h = 'h4'; } else { $x10000 = [ 0x1000 ]; $h = 'h3'; } while (@$x1 != 1 || $x1->[0] != 0) # _is_zero() { ($x1, $xr) = $c->_div($x1, $x10000); $es .= unpack($h, pack('V', $xr->[0])); } $es = reverse $es; $es =~ s/^[0]+//; # strip leading zeros '0x' . $es; # return result prepended with 0x } sub _as_bin { # convert a decimal number to bin (ref to array, return ref to string) my ($c, $x) = @_; # fits into one element (and Perl recent enough), handle also 0b0 case # handle zero case for older Perls if ($] <= 5.005 && @$x == 1 && $x->[0] == 0) { my $t = '0b0'; return $t; } if (@$x == 1 && $] >= 5.006) { my $t = sprintf("0b%b", $x->[0]); return $t; } my $x1 = $c->_copy($x); my $es = ''; my ($xr, $b, $x10000); if ($] >= 5.006) { $x10000 = [ 0x10000 ]; $b = 'b16'; } else { $x10000 = [ 0x1000 ]; $b = 'b12'; } while (!(@$x1 == 1 && $x1->[0] == 0)) # _is_zero() { ($x1, $xr) = $c->_div($x1, $x10000); $es .= unpack($b, pack('v', $xr->[0])); } $es = reverse $es; $es =~ s/^[0]+//; # strip leading zeros '0b' . $es; # return result prepended with 0b } sub _as_oct { # convert a decimal number to octal (ref to array, return ref to string) my ($c, $x) = @_; # fits into one element (handle also 0 case) return sprintf("0%o", $x->[0]) if @$x == 1; my $x1 = $c->_copy($x); my $es = ''; my $xr; my $x1000 = [ 0100000 ]; while (@$x1 != 1 || $x1->[0] != 0) # _is_zero() { ($x1, $xr) = $c->_div($x1, $x1000); $es .= reverse sprintf("%05o", $xr->[0]); } $es = reverse $es; $es =~ s/^0+//; # strip leading zeros '0' . $es; # return result prepended with 0 } sub _from_oct { # convert a octal number to decimal (string, return ref to array) my ($c, $os) = @_; # for older Perls, play safe my $m = [ 0100000 ]; my $d = 5; # 5 digits at a time my $mul = $c->_one(); my $x = $c->_zero(); my $len = int((length($os) - 1) / $d); # $d digit parts, w/o the '0' my $val; my $i = -$d; while ($len >= 0) { $val = substr($os, $i, $d); # get oct digits $val = CORE::oct($val); $i -= $d; $len --; my $adder = [ $val ]; $c->_add($x, $c->_mul($adder, $mul)) if $val != 0; $c->_mul($mul, $m) if $len >= 0; # skip last mul } $x; } sub _from_hex { # convert a hex number to decimal (string, return ref to array) my ($c, $hs) = @_; my $m = $c->_new(0x10000000); # 28 bit at a time (<32 bit!) my $d = 7; # 7 digits at a time my $mul = $c->_one(); my $x = $c->_zero(); my $len = int((length($hs) - 2) / $d); # $d digit parts, w/o the '0x' my $val; my $i = -$d; while ($len >= 0) { $val = substr($hs, $i, $d); # get hex digits $val =~ s/^0x// if $len == 0; # for last part only because $val = CORE::hex($val); # hex does not like wrong chars $i -= $d; $len --; my $adder = [ $val ]; # if the resulting number was to big to fit into one element, create a # two-element version (bug found by Mark Lakata - Thanx!) if (CORE::length($val) > $BASE_LEN) { $adder = $c->_new($val); } $c->_add($x, $c->_mul($adder, $mul)) if $val != 0; $c->_mul($mul, $m) if $len >= 0; # skip last mul } $x; } sub _from_bin { # convert a hex number to decimal (string, return ref to array) my ($c, $bs) = @_; # instead of converting X (8) bit at a time, it is faster to "convert" the # number to hex, and then call _from_hex. my $hs = $bs; $hs =~ s/^[+-]?0b//; # remove sign and 0b my $l = length($hs); # bits $hs = '0' x (8 - ($l % 8)) . $hs if ($l % 8) != 0; # padd left side w/ 0 my $h = '0x' . unpack('H*', pack ('B*', $hs)); # repack as hex $c->_from_hex($h); } ############################################################################## # special modulus functions sub _modinv { # modular multiplicative inverse my ($c, $x, $y) = @_; # modulo zero if ($c->_is_zero($y)) { return undef, undef; } # modulo one if ($c->_is_one($y)) { return $c->_zero(), '+'; } my $u = $c->_zero(); my $v = $c->_one(); my $a = $c->_copy($y); my $b = $c->_copy($x); # Euclid's Algorithm for bgcd(), only that we calc bgcd() ($a) and the result # ($u) at the same time. See comments in BigInt for why this works. my $q; my $sign = 1; { ($a, $q, $b) = ($b, $c->_div($a, $b)); # step 1 last if $c->_is_zero($b); my $t = $c->_add( # step 2: $c->_mul($c->_copy($v), $q), # t = v * q $u); # + u $u = $v; # u = v $v = $t; # v = t $sign = -$sign; redo; } # if the gcd is not 1, then return NaN return (undef, undef) unless $c->_is_one($a); ($v, $sign == 1 ? '+' : '-'); } sub _modpow { # modulus of power ($x ** $y) % $z my ($c, $num, $exp, $mod) = @_; # a^b (mod 1) = 0 for all a and b if ($c->_is_one($mod)) { @$num = 0; return $num; } # 0^a (mod m) = 0 if m != 0, a != 0 # 0^0 (mod m) = 1 if m != 0 if ($c->_is_zero($num)) { if ($c->_is_zero($exp)) { @$num = 1; } else { @$num = 0; } return $num; } # $num = $c->_mod($num, $mod); # this does not make it faster my $acc = $c->_copy($num); my $t = $c->_one(); my $expbin = $c->_as_bin($exp); $expbin =~ s/^0b//; my $len = length($expbin); while (--$len >= 0) { if (substr($expbin, $len, 1) eq '1') { # is_odd $t = $c->_mul($t, $acc); $t = $c->_mod($t, $mod); } $acc = $c->_mul($acc, $acc); $acc = $c->_mod($acc, $mod); } @$num = @$t; $num; } sub _gcd { # Greatest common divisor. my ($c, $x, $y) = @_; # gcd(0, 0) = 0 # gcd(0, a) = a, if a != 0 if (@$x == 1 && $x->[0] == 0) { if (@$y == 1 && $y->[0] == 0) { @$x = 0; } else { @$x = @$y; } return $x; } # Until $y is zero ... until (@$y == 1 && $y->[0] == 0) { # Compute remainder. $c->_mod($x, $y); # Swap $x and $y. my $tmp = $c->_copy($x); @$x = @$y; $y = $tmp; # no deref here; that would modify input $y } return $x; } 1; =pod =head1 NAME Math::BigInt::Calc - Pure Perl module to support Math::BigInt =head1 SYNOPSIS # to use it with Math::BigInt use Math::BigInt lib => 'Calc'; # to use it with Math::BigFloat use Math::BigFloat lib => 'Calc'; # to use it with Math::BigRat use Math::BigRat lib => 'Calc'; =head1 DESCRIPTION Math::BigInt::Calc inherits from Math::BigInt::Lib. In this library, the numbers are represented in base B = 10**N, where N is the largest possible value that does not cause overflow in the intermediate computations. The base B elements are stored in an array, with the least significant element stored in array element zero. There are no leading zero elements, except a single zero element when the number is zero. For instance, if B = 10000, the number 1234567890 is represented internally as [7890, 3456, 12]. =head1 SEE ALSO L for a description of the API. Alternative libraries L, L, and L. Some of the modules that use these libraries L, L, and L. =cut Math-BigInt-1.999808/lib/Math/BigInt/CalcEmu.pm0000644403072340010010000002336713033512273021032 0ustar ospjadomain userspackage Math::BigInt::CalcEmu; use 5.006001; use strict; use warnings; our $VERSION = '1.999808'; package Math::BigInt; # See SYNOPSIS below. my $CALC_EMU; BEGIN { $CALC_EMU = Math::BigInt->config('lib'); # register us with MBI to get notified of future lib changes Math::BigInt::_register_callback( __PACKAGE__, sub { $CALC_EMU = $_[0]; } ); } sub __emu_band { my ($self,$x,$y,$sx,$sy,@r) = @_; return $x->bzero(@r) if $y->is_zero() || $x->is_zero(); my $sign = 0; # sign of result $sign = 1 if $sx == -1 && $sy == -1; my ($bx,$by); if ($sx == -1) # if x is negative { # two's complement: inc and flip all "bits" in $bx $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc $bx =~ s/-?0x//; $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } else { $bx = $x->as_hex(); # get binary representation $bx =~ s/-?0x//; $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } if ($sy == -1) # if y is negative { # two's complement: inc and flip all "bits" in $by $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc $by =~ s/-?0x//; $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } else { $by = $y->as_hex(); # get binary representation $by =~ s/-?0x//; $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } # now we have bit-strings from X and Y, reverse them for padding $bx = reverse $bx; $by = reverse $by; # padd the shorter string my $xx = "\x00"; $xx = "\x0f" if $sx == -1; my $yy = "\x00"; $yy = "\x0f" if $sy == -1; my $diff = CORE::length($bx) - CORE::length($by); if ($diff > 0) { # if $yy eq "\x00", we can cut $bx, otherwise we need to padd $by $by .= $yy x $diff; } elsif ($diff < 0) { # if $xx eq "\x00", we can cut $by, otherwise we need to padd $bx $bx .= $xx x abs($diff); } # and the strings together my $r = $bx & $by; # and reverse the result again $bx = reverse $r; # One of $x or $y was negative, so need to flip bits in the result. # In both cases (one or two of them negative, or both positive) we need # to get the characters back. if ($sign == 1) { $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/; } else { $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/; } # leading zeros will be stripped by _from_hex() $bx = '0x' . $bx; $x->{value} = $CALC_EMU->_from_hex( $bx ); # calculate sign of result $x->{sign} = '+'; $x->{sign} = '-' if $sign == 1 && !$x->is_zero(); $x->bdec() if $sign == 1; $x->round(@r); } sub __emu_bior { my ($self,$x,$y,$sx,$sy,@r) = @_; return $x->round(@r) if $y->is_zero(); my $sign = 0; # sign of result $sign = 1 if ($sx == -1) || ($sy == -1); my ($bx,$by); if ($sx == -1) # if x is negative { # two's complement: inc and flip all "bits" in $bx $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc $bx =~ s/-?0x//; $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } else { $bx = $x->as_hex(); # get binary representation $bx =~ s/-?0x//; $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } if ($sy == -1) # if y is negative { # two's complement: inc and flip all "bits" in $by $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc $by =~ s/-?0x//; $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } else { $by = $y->as_hex(); # get binary representation $by =~ s/-?0x//; $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } # now we have bit-strings from X and Y, reverse them for padding $bx = reverse $bx; $by = reverse $by; # padd the shorter string my $xx = "\x00"; $xx = "\x0f" if $sx == -1; my $yy = "\x00"; $yy = "\x0f" if $sy == -1; my $diff = CORE::length($bx) - CORE::length($by); if ($diff > 0) { $by .= $yy x $diff; } elsif ($diff < 0) { $bx .= $xx x abs($diff); } # or the strings together my $r = $bx | $by; # and reverse the result again $bx = reverse $r; # one of $x or $y was negative, so need to flip bits in the result # in both cases (one or two of them negative, or both positive) we need # to get the characters back. if ($sign == 1) { $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/; } else { $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/; } # leading zeros will be stripped by _from_hex() $bx = '0x' . $bx; $x->{value} = $CALC_EMU->_from_hex( $bx ); # calculate sign of result $x->{sign} = '+'; $x->{sign} = '-' if $sign == 1 && !$x->is_zero(); # if one of X or Y was negative, we need to decrement result $x->bdec() if $sign == 1; $x->round(@r); } sub __emu_bxor { my ($self,$x,$y,$sx,$sy,@r) = @_; return $x->round(@r) if $y->is_zero(); my $sign = 0; # sign of result $sign = 1 if $x->{sign} ne $y->{sign}; my ($bx,$by); if ($sx == -1) # if x is negative { # two's complement: inc and flip all "bits" in $bx $bx = $x->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc $bx =~ s/-?0x//; $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } else { $bx = $x->as_hex(); # get binary representation $bx =~ s/-?0x//; $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } if ($sy == -1) # if y is negative { # two's complement: inc and flip all "bits" in $by $by = $y->copy()->binc()->as_hex(); # -1 => 0, -2 => 1, -3 => 2 etc $by =~ s/-?0x//; $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } else { $by = $y->as_hex(); # get binary representation $by =~ s/-?0x//; $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/; } # now we have bit-strings from X and Y, reverse them for padding $bx = reverse $bx; $by = reverse $by; # padd the shorter string my $xx = "\x00"; $xx = "\x0f" if $sx == -1; my $yy = "\x00"; $yy = "\x0f" if $sy == -1; my $diff = CORE::length($bx) - CORE::length($by); if ($diff > 0) { $by .= $yy x $diff; } elsif ($diff < 0) { $bx .= $xx x abs($diff); } # xor the strings together my $r = $bx ^ $by; # and reverse the result again $bx = reverse $r; # one of $x or $y was negative, so need to flip bits in the result # in both cases (one or two of them negative, or both positive) we need # to get the characters back. if ($sign == 1) { $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/; } else { $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/; } # leading zeros will be stripped by _from_hex() $bx = '0x' . $bx; $x->{value} = $CALC_EMU->_from_hex( $bx ); # calculate sign of result $x->{sign} = '+'; $x->{sign} = '-' if $sx != $sy && !$x->is_zero(); $x->bdec() if $sign == 1; $x->round(@r); } ############################################################################## ############################################################################## 1; __END__ =pod =head1 NAME Math::BigInt::CalcEmu - Emulate low-level math with BigInt code =head1 SYNOPSIS use Math::BigInt::CalcEmu; =head1 DESCRIPTION Contains routines that emulate low-level math functions in BigInt, e.g. optional routines the low-level math package does not provide on its own. Will be loaded on demand and called automatically by BigInt. Stuff here is really low-priority to optimize, since it is far better to implement the operation in the low-level math library directly, possible even using a call to the native lib. =head1 METHODS =over =item __emu_bxor =item __emu_band =item __emu_bior =back =head1 BUGS Please report any bugs or feature requests to C, or through the web interface at L (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes. =head1 SUPPORT You can find documentation for this module with the perldoc command. perldoc Math::BigInt::CalcEmu You can also look for information at: =over 4 =item * RT: CPAN's request tracker L =item * AnnoCPAN: Annotated CPAN documentation L =item * CPAN Ratings L =item * Search CPAN L =item * CPAN Testers Matrix L =item * The Bignum mailing list =over 4 =item * Post to mailing list C =item * View mailing list L =item * Subscribe/Unsubscribe L =back =back =head1 LICENSE This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. =head1 AUTHORS (c) Tels http://bloodgate.com 2003, 2004 - based on BigInt code by Tels from 2001-2003. =head1 SEE ALSO L, L, L and L. =cut Math-BigInt-1.999808/lib/Math/BigInt/Lib.pm0000644403072340010010000015136413033512270020223 0ustar ospjadomain userspackage Math::BigInt::Lib; use 5.006001; use strict; use warnings; our $VERSION = '1.999808'; use Carp; use overload # overload key: with_assign '+' => sub { my $class = ref $_[0]; my $x = $class -> _copy($_[0]); my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); return $class -> _add($x, $y); }, '-' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _sub($x, $y); }, '*' => sub { my $class = ref $_[0]; my $x = $class -> _copy($_[0]); my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); return $class -> _mul($x, $y); }, '/' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _div($x, $y); }, '%' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _mod($x, $y); }, '**' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _pow($x, $y); }, '<<' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $class -> _num($_[0]); $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $_[0]; $y = ref($_[1]) ? $class -> _num($_[1]) : $_[1]; } return $class -> _blsft($x, $y); }, '>>' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _brsft($x, $y); }, # overload key: num_comparison '<' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _acmp($x, $y) < 0; }, '<=' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _acmp($x, $y) <= 0; }, '>' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _acmp($x, $y) > 0; }, '>=' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _acmp($x, $y) >= 0; }, '==' => sub { my $class = ref $_[0]; my $x = $class -> _copy($_[0]); my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); return $class -> _acmp($x, $y) == 0; }, '!=' => sub { my $class = ref $_[0]; my $x = $class -> _copy($_[0]); my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); return $class -> _acmp($x, $y) != 0; }, # overload key: 3way_comparison '<=>' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _acmp($x, $y); }, # overload key: binary '&' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _and($x, $y); }, '|' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _or($x, $y); }, '^' => sub { my $class = ref $_[0]; my ($x, $y); if ($_[2]) { # if swapped $y = $_[0]; $x = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } else { $x = $class -> _copy($_[0]); $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]); } return $class -> _xor($x, $y); }, # overload key: func 'abs' => sub { $_[0] }, 'sqrt' => sub { my $class = ref $_[0]; return $class -> _sqrt($class -> _copy($_[0])); }, 'int' => sub { $_[0] }, # overload key: conversion 'bool' => sub { ref($_[0]) -> _is_zero($_[0]) ? '' : 1; }, '""' => sub { ref($_[0]) -> _str($_[0]); }, '0+' => sub { ref($_[0]) -> _num($_[0]); }, '=' => sub { ref($_[0]) -> _copy($_[0]); }, ; # Do we need api_version() at all, now that we have a virtual parent class that # will provide any missing methods? Fixme! sub api_version () { croak "@{[(caller 0)[3]]} method not implemented"; } sub _new { croak "@{[(caller 0)[3]]} method not implemented"; } sub _zero { my $class = shift; return $class -> _new("0"); } sub _one { my $class = shift; return $class -> _new("1"); } sub _two { my $class = shift; return $class -> _new("2"); } sub _ten { my $class = shift; return $class -> _new("10"); } sub _1ex { my ($class, $exp) = @_; $exp = $class -> _num($exp) if ref($exp); return $class -> _new("1" . ("0" x $exp)); } sub _copy { my ($class, $x) = @_; return $class -> _new($class -> _str($x)); } # catch and throw away sub import { } ############################################################################## # convert back to string and number sub _str { # Convert number from internal base 1eN format to string format. Internal # format is always normalized, i.e., no leading zeros. croak "@{[(caller 0)[3]]} method not implemented"; } sub _num { my ($class, $x) = @_; 0 + $class -> _str($x); } ############################################################################## # actual math code sub _add { croak "@{[(caller 0)[3]]} method not implemented"; } sub _sub { croak "@{[(caller 0)[3]]} method not implemented"; } sub _mul { my ($class, $x, $y) = @_; my $sum = $class -> _zero(); my $i = $class -> _zero(); while ($class -> _acmp($i, $y) < 0) { $sum = $class -> _add($sum, $x); $i = $class -> _inc($i); } return $sum; } sub _div { my ($class, $x, $y) = @_; croak "@{[(caller 0)[3]]} requires non-zero divisor" if $class -> _is_zero($y); my $r = $class -> _copy($x); my $q = $class -> _zero(); while ($class -> _acmp($r, $y) >= 0) { $q = $class -> _inc($q); $r = $class -> _sub($r, $y); } return $q, $r if wantarray; return $q; } sub _inc { my ($class, $x) = @_; $class -> _add($x, $class -> _one()); } sub _dec { my ($class, $x) = @_; $class -> _sub($x, $class -> _one()); } ############################################################################## # testing sub _acmp { # Compare two (absolute) values. Return -1, 0, or 1. my ($class, $x, $y) = @_; my $xstr = $class -> _str($x); my $ystr = $class -> _str($y); length($xstr) <=> length($ystr) || $xstr cmp $ystr; } sub _len { my ($class, $x) = @_; CORE::length($class -> _str($x)); } sub _alen { my ($class, $x) = @_; $class -> _len($x); } sub _digit { my ($class, $x, $n) = @_; substr($class ->_str($x), -($n+1), 1); } sub _zeros { my ($class, $x) = @_; my $str = $class -> _str($x); $str =~ /[^0](0*)\z/ ? CORE::length($1) : 0; } ############################################################################## # _is_* routines sub _is_zero { # return true if arg is zero my ($class, $x) = @_; $class -> _str($x) == 0; } sub _is_even { # return true if arg is even my ($class, $x) = @_; substr($class -> _str($x), -1, 1) % 2 == 0; } sub _is_odd { # return true if arg is odd my ($class, $x) = @_; substr($class -> _str($x), -1, 1) % 2 != 0; } sub _is_one { # return true if arg is one my ($class, $x) = @_; $class -> _str($x) == 1; } sub _is_two { # return true if arg is two my ($class, $x) = @_; $class -> _str($x) == 2; } sub _is_ten { # return true if arg is ten my ($class, $x) = @_; $class -> _str($x) == 10; } ############################################################################### # check routine to test internal state for corruptions sub _check { # used by the test suite my ($class, $x) = @_; return "Input is undefined" unless defined $x; return "$x is not a reference" unless ref($x); return 0; } ############################################################################### sub _mod { # modulus my ($class, $x, $y) = @_; croak "@{[(caller 0)[3]]} requires non-zero second operand" if $class -> _is_zero($y); if ($class -> can('_div')) { $x = $class -> _copy($x); my ($q, $r) = $class -> _div($x, $y); return $r; } else { my $r = $class -> _copy($x); while ($class -> _acmp($r, $y) >= 0) { $r = $class -> _sub($r, $y); } return $r; } } ############################################################################## # shifts sub _rsft { my ($class, $x, $n, $b) = @_; $b = $class -> _new($b) unless ref $b; return scalar $class -> _div($x, $class -> _pow($class -> _copy($b), $n)); } sub _lsft { my ($class, $x, $n, $b) = @_; $b = $class -> _new($b) unless ref $b; return $class -> _mul($x, $class -> _pow($class -> _copy($b), $n)); } sub _pow { # power of $x to $y my ($class, $x, $y) = @_; if ($class -> _is_zero($y)) { return $class -> _one(); # y == 0 => x => 1 } if (($class -> _is_one($x)) || # x == 1 ($class -> _is_one($y))) # or y == 1 { return $x; } if ($class -> _is_zero($x)) { return $class -> _zero(); # 0 ** y => 0 (if not y <= 0) } my $pow2 = $class -> _one(); my $y_bin = $class -> _as_bin($y); $y_bin =~ s/^0b//; my $len = length($y_bin); while (--$len > 0) { $pow2 = $class -> _mul($pow2, $x) if substr($y_bin, $len, 1) eq '1'; $x = $class -> _mul($x, $x); } $x = $class -> _mul($x, $pow2); return $x; } sub _nok { # Return binomial coefficient (n over k). my ($class, $n, $k) = @_; # If k > n/2, or, equivalently, 2*k > n, compute nok(n, k) as # nok(n, n-k), to minimize the number if iterations in the loop. { my $twok = $class -> _mul($class -> _two(), $class -> _copy($k)); if ($class -> _acmp($twok, $n) > 0) { $k = $class -> _sub($class -> _copy($n), $k); } } # Example: # # / 7 \ 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 # | | = --------- = --------------- = --------- = ((5 * 6) / 2 * 7) / 3 # \ 3 / (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 # # Equivalently, _nok(11, 5) is computed as # # (((((((7 * 8) / 2) * 9) / 3) * 10) / 4) * 11) / 5 if ($class -> _is_zero($k)) { return $class -> _one(); } # Make a copy of the original n, in case the subclass modifies n in-place. my $n_orig = $class -> _copy($n); # n = 5, f = 6, d = 2 (cf. example above) $n = $class -> _sub($n, $k); $n = $class -> _inc($n); my $f = $class -> _copy($n); $f = $class -> _inc($f); my $d = $class -> _two(); # while f <= n (the original n, that is) ... while ($class -> _acmp($f, $n_orig) <= 0) { $n = $class -> _mul($n, $f); $n = $class -> _div($n, $d); $f = $class -> _inc($f); $d = $class -> _inc($d); } return $n; } sub _fac { # factorial my ($class, $x) = @_; my $two = $class -> _two(); if ($class -> _acmp($x, $two) < 0) { return $class -> _one(); } my $i = $class -> _copy($x); while ($class -> _acmp($i, $two) > 0) { $i = $class -> _dec($i); $x = $class -> _mul($x, $i); } return $x; } sub _dfac { # double factorial my ($class, $x) = @_; my $two = $class -> _two(); if ($class -> _acmp($x, $two) < 0) { return $class -> _one(); } my $i = $class -> _copy($x); while ($class -> _acmp($i, $two) > 0) { $i = $class -> _sub($i, $two); $x = $class -> _mul($x, $i); } return $x; } sub _log_int { # calculate integer log of $x to base $base # calculate integer log of $x to base $base # ref to array, ref to array - return ref to array my ($class, $x, $base) = @_; # X == 0 => NaN return if $class -> _is_zero($x); $base = $class -> _new(2) unless defined($base); $base = $class -> _new($base) unless ref($base); # BASE 0 or 1 => NaN return if $class -> _is_zero($base) || $class -> _is_one($base); # X == 1 => 0 (is exact) if ($class -> _is_one($x)) { return $class -> _zero(), 1; } my $cmp = $class -> _acmp($x, $base); # X == BASE => 1 (is exact) if ($cmp == 0) { return $class -> _one(), 1; } # 1 < X < BASE => 0 (is truncated) if ($cmp < 0) { return $class -> _zero(), 0; } my $y; # log(x) / log(b) = log(xm * 10^xe) / log(bm * 10^be) # = (log(xm) + xe*(log(10))) / (log(bm) + be*log(10)) { my $x_str = $class -> _str($x); my $b_str = $class -> _str($base); my $xm = "." . $x_str; my $bm = "." . $b_str; my $xe = length($x_str); my $be = length($b_str); my $log10 = log(10); my $guess = int((log($xm) + $xe * $log10) / (log($bm) + $be * $log10)); $y = $class -> _new($guess); } my $trial = $class -> _pow($class -> _copy($base), $y); my $acmp = $class -> _acmp($trial, $x); # Did we get the exact result? return $y, 1 if $acmp == 0; # Too small? while ($acmp < 0) { $trial = $class -> _mul($trial, $base); $y = $class -> _inc($y); $acmp = $class -> _acmp($trial, $x); } # Too big? while ($acmp > 0) { $trial = $class -> _div($trial, $base); $y = $class -> _dec($y); $acmp = $class -> _acmp($trial, $x); } return $y, 1 if $acmp == 0; # result is exact return $y, 0; # result is too small } sub _sqrt { # square-root of $y in place my ($class, $y) = @_; return $y if $class -> _is_zero($y); my $y_str = $class -> _str($y); my $y_len = length($y_str); # Compute the guess $x. my $xm; my $xe; if ($y_len % 2 == 0) { $xm = sqrt("." . $y_str); $xe = $y_len / 2; $xm = sprintf "%.0f", int($xm * 1e15); $xe -= 15; } else { $xm = sqrt(".0" . $y_str); $xe = ($y_len + 1) / 2; $xm = sprintf "%.0f", int($xm * 1e16); $xe -= 16; } my $x; if ($xe < 0) { $x = substr $xm, 0, length($xm) + $xe; } else { $x = $xm . ("0" x $xe); } $x = $class -> _new($x); # Newton's method for computing square root of y # # x(i+1) = x(i) - f(x(i)) / f'(x(i)) # = x(i) - (x(i)^2 - y) / (2 * x(i)) # use if x(i)^2 > y # = y(i) + (y - x(i)^2) / (2 * x(i)) # use if x(i)^2 < y # Determine if x, our guess, is too small, correct, or too large. my $xsq = $class -> _mul($class -> _copy($x), $x); # x(i)^2 my $acmp = $class -> _acmp($xsq, $y); # x(i)^2 <=> y # Only assign a value to this variable if we will be using it. my $two; $two = $class -> _two() if $acmp != 0; # If x is too small, do one iteration of Newton's method. Since the # function f(x) = x^2 - y is concave and monotonically increasing, the next # guess for x will either be correct or too large. if ($acmp < 0) { # x(i+1) = x(i) + (y - x(i)^2) / (2 * x(i)) my $numer = $class -> _sub($class -> _copy($y), $xsq); # y - x(i)^2 my $denom = $class -> _mul($class -> _copy($two), $x); # 2 * x(i) my $delta = $class -> _div($numer, $denom); unless ($class -> _is_zero($delta)) { $x = $class -> _add($x, $delta); $xsq = $class -> _mul($class -> _copy($x), $x); # x(i)^2 $acmp = $class -> _acmp($xsq, $y); # x(i)^2 <=> y } } # If our guess for x is too large, apply Newton's method repeatedly until # we either have got the correct value, or the delta is zero. while ($acmp > 0) { # x(i+1) = x(i) - (x(i)^2 - y) / (2 * x(i)) my $numer = $class -> _sub($xsq, $y); # x(i)^2 - y my $denom = $class -> _mul($class -> _copy($two), $x); # 2 * x(i) my $delta = $class -> _div($numer, $denom); last if $class -> _is_zero($delta); $x = $class -> _sub($x, $delta); $xsq = $class -> _mul($class -> _copy($x), $x); # x(i)^2 $acmp = $class -> _acmp($xsq, $y); # x(i)^2 <=> y } # When the delta is zero, our value for x might still be too large. We # require that the outout is either exact or too small (i.e., rounded down # to the nearest integer), so do a final check. while ($acmp > 0) { $x = $class -> _dec($x); $xsq = $class -> _mul($class -> _copy($x), $x); # x(i)^2 $acmp = $class -> _acmp($xsq, $y); # x(i)^2 <=> y } return $x; } sub _root { my ($class, $y, $n) = @_; return $y if $class -> _is_zero($y) || $class -> _is_one($y) || $class -> _is_one($n); # If y <= n, the result is always (truncated to) 1. return $class -> _one() if $class -> _acmp($y, $n) <= 0; # Compute the initial guess x of y^(1/n). When n is large, Newton's method # converges slowly if the "guess" (initial value) is poor, so we need a # good guess. It the guess is too small, the next guess will be too large, # and from then on all guesses are too large. my $DEBUG = 0; # Split y into mantissa and exponent in base 10, so that # # y = xm * 10^xe, where 0 < xm < 1 and xe is an integer my $y_str = $class -> _str($y); my $ym = "." . $y_str; my $ye = length($y_str); # From this compute the approximate base 10 logarithm of y # # log_10(y) = log_10(ym) + log_10(ye^10) # = log(ym)/log(10) + ye my $log10y = log($ym) / log(10) + $ye; # And from this compute the approximate base 10 logarithm of x, where # x = y^(1/n) # # log_10(x) = log_10(y)/n my $log10x = $log10y / $class -> _num($n); # From this compute xm and xe, the mantissa and exponent (in base 10) of x, # where 1 < xm <= 10 and xe is an integer. my $xe = int $log10x; my $xm = 10 ** ($log10x - $xe); # Scale the mantissa and exponent to increase the integer part of ym, which # gives us better accuracy. if ($DEBUG) { print "\n"; print "y_str = $y_str\n"; print "ym = $ym\n"; print "ye = $ye\n"; print "log10y = $log10y\n"; print "log10x = $log10x\n"; print "xm = $xm\n"; print "xe = $xe\n"; } my $d = $xe < 15 ? $xe : 15; $xm *= 10 ** $d; $xe -= $d; if ($DEBUG) { print "\n"; print "xm = $xm\n"; print "xe = $xe\n"; } # If the mantissa is not an integer, round up to nearest integer, and then # convert the number to a string. It is important to always round up due to # how Newton's method behaves in this case. If the initial guess is too # small, the next guess will be too large, after which every succeeding # guess converges the correct value from above. Now, if the initial guess # is too small and n is large, the next guess will be much too large and # require a large number of iterations to get close to the solution. # Because of this, we are likely to find the solution faster if we make # sure the initial guess is not too small. my $xm_int = int($xm); my $x_str = sprintf '%.0f', $xm > $xm_int ? $xm_int + 1 : $xm_int; $x_str .= "0" x $xe; my $x = $class -> _new($x_str); if ($DEBUG) { print "xm = $xm\n"; print "xe = $xe\n"; print "\n"; print "x_str = $x_str (initial guess)\n"; print "\n"; } # Use Newton's method for computing n'th root of y. # # x(i+1) = x(i) - f(x(i)) / f'(x(i)) # = x(i) - (x(i)^n - y) / (n * x(i)^(n-1)) # use if x(i)^n > y # = x(i) + (y - x(i)^n) / (n * x(i)^(n-1)) # use if x(i)^n < y # Determine if x, our guess, is too small, correct, or too large. Rather # than computing x(i)^n and x(i)^(n-1) directly, compute x(i)^(n-1) and # then the same value multiplied by x. my $nm1 = $class -> _dec($class -> _copy($n)); # n-1 my $xpownm1 = $class -> _pow($class -> _copy($x), $nm1); # x(i)^(n-1) my $xpown = $class -> _mul($class -> _copy($xpownm1), $x); # x(i)^n my $acmp = $class -> _acmp($xpown, $y); # x(i)^n <=> y if ($DEBUG) { print "\n"; print "x = ", $class -> _str($x), "\n"; print "x^n = ", $class -> _str($xpown), "\n"; print "y = ", $class -> _str($y), "\n"; print "acmp = $acmp\n"; } # If x is too small, do one iteration of Newton's method. Since the # function f(x) = x^n - y is concave and monotonically increasing, the next # guess for x will either be correct or too large. if ($acmp < 0) { # x(i+1) = x(i) + (y - x(i)^n) / (n * x(i)^(n-1)) my $numer = $class -> _sub($class -> _copy($y), $xpown); # y - x(i)^n my $denom = $class -> _mul($class -> _copy($n), $xpownm1); # n * x(i)^(n-1) my $delta = $class -> _div($numer, $denom); if ($DEBUG) { print "\n"; print "numer = ", $class -> _str($numer), "\n"; print "denom = ", $class -> _str($denom), "\n"; print "delta = ", $class -> _str($delta), "\n"; } unless ($class -> _is_zero($delta)) { $x = $class -> _add($x, $delta); $xpownm1 = $class -> _pow($class -> _copy($x), $nm1); # x(i)^(n-1) $xpown = $class -> _mul($class -> _copy($xpownm1), $x); # x(i)^n $acmp = $class -> _acmp($xpown, $y); # x(i)^n <=> y if ($DEBUG) { print "\n"; print "x = ", $class -> _str($x), "\n"; print "x^n = ", $class -> _str($xpown), "\n"; print "y = ", $class -> _str($y), "\n"; print "acmp = $acmp\n"; } } } # If our guess for x is too large, apply Newton's method repeatedly until # we either have got the correct value, or the delta is zero. while ($acmp > 0) { # x(i+1) = x(i) - (x(i)^n - y) / (n * x(i)^(n-1)) my $numer = $class -> _sub($class -> _copy($xpown), $y); # x(i)^n - y my $denom = $class -> _mul($class -> _copy($n), $xpownm1); # n * x(i)^(n-1) if ($DEBUG) { print "numer = ", $class -> _str($numer), "\n"; print "denom = ", $class -> _str($denom), "\n"; } my $delta = $class -> _div($numer, $denom); if ($DEBUG) { print "delta = ", $class -> _str($delta), "\n"; } last if $class -> _is_zero($delta); $x = $class -> _sub($x, $delta); $xpownm1 = $class -> _pow($class -> _copy($x), $nm1); # x(i)^(n-1) $xpown = $class -> _mul($class -> _copy($xpownm1), $x); # x(i)^n $acmp = $class -> _acmp($xpown, $y); # x(i)^n <=> y if ($DEBUG) { print "\n"; print "x = ", $class -> _str($x), "\n"; print "x^n = ", $class -> _str($xpown), "\n"; print "y = ", $class -> _str($y), "\n"; print "acmp = $acmp\n"; } } # When the delta is zero, our value for x might still be too large. We # require that the outout is either exact or too small (i.e., rounded down # to the nearest integer), so do a final check. while ($acmp > 0) { $x = $class -> _dec($x); $xpown = $class -> _pow($class -> _copy($x), $n); # x(i)^n $acmp = $class -> _acmp($xpown, $y); # x(i)^n <=> y } return $x; } ############################################################################## # binary stuff sub _and { my ($class, $x, $y) = @_; return $x if $class -> _acmp($x, $y) == 0; my $m = $class -> _one(); my $mask = $class -> _new("32768"); my ($xr, $yr); # remainders after division my $xc = $class -> _copy($x); my $yc = $class -> _copy($y); my $z = $class -> _zero(); until ($class -> _is_zero($xc) || $class -> _is_zero($yc)) { ($xc, $xr) = $class -> _div($xc, $mask); ($yc, $yr) = $class -> _div($yc, $mask); my $bits = $class -> _new($class -> _num($xr) & $class -> _num($yr)); $z = $class -> _add($z, $class -> _mul($bits, $m)); $m = $class -> _mul($m, $mask); } return $z; } sub _xor { my ($class, $x, $y) = @_; return $class -> _zero() if $class -> _acmp($x, $y) == 0; my $m = $class -> _one(); my $mask = $class -> _new("32768"); my ($xr, $yr); # remainders after division my $xc = $class -> _copy($x); my $yc = $class -> _copy($y); my $z = $class -> _zero(); until ($class -> _is_zero($xc) || $class -> _is_zero($yc)) { ($xc, $xr) = $class -> _div($xc, $mask); ($yc, $yr) = $class -> _div($yc, $mask); my $bits = $class -> _new($class -> _num($xr) ^ $class -> _num($yr)); $z = $class -> _add($z, $class -> _mul($bits, $m)); $m = $class -> _mul($m, $mask); } # The loop above stops when the smallest of the two numbers is exhausted. # The remainder of the longer one will survive bit-by-bit, so we simple # multiply-add it in. $z = $class -> _add($z, $class -> _mul($xc, $m)) unless $class -> _is_zero($xc); $z = $class -> _add($z, $class -> _mul($yc, $m)) unless $class -> _is_zero($yc); return $z; } sub _or { my ($class, $x, $y) = @_; return $x if $class -> _acmp($x, $y) == 0; # shortcut (see _and) my $m = $class -> _one(); my $mask = $class -> _new("32768"); my ($xr, $yr); # remainders after division my $xc = $class -> _copy($x); my $yc = $class -> _copy($y); my $z = $class -> _zero(); until ($class -> _is_zero($xc) || $class -> _is_zero($yc)) { ($xc, $xr) = $class -> _div($xc, $mask); ($yc, $yr) = $class -> _div($yc, $mask); my $bits = $class -> _new($class -> _num($xr) | $class -> _num($yr)); $z = $class -> _add($z, $class -> _mul($bits, $m)); $m = $class -> _mul($m, $mask); } # The loop above stops when the smallest of the two numbers is exhausted. # The remainder of the longer one will survive bit-by-bit, so we simple # multiply-add it in. $z = $class -> _add($z, $class -> _mul($xc, $m)) unless $class -> _is_zero($xc); $z = $class -> _add($z, $class -> _mul($yc, $m)) unless $class -> _is_zero($yc); return $z; } sub _to_bin { # convert the number to a string of binary digits without prefix my ($class, $x) = @_; my $str = ''; my $tmp = $class -> _copy($x); my $chunk = $class -> _new("16777216"); # 2^24 = 24 binary digits my $rem; until ($class -> _acmp($tmp, $chunk) < 0) { ($tmp, $rem) = $class -> _div($tmp, $chunk); $str = sprintf("%024b", $class -> _num($rem)) . $str; } unless ($class -> _is_zero($tmp)) { $str = sprintf("%b", $class -> _num($tmp)) . $str; } return length($str) ? $str : '0'; } sub _to_oct { # convert the number to a string of octal digits without prefix my ($class, $x) = @_; my $str = ''; my $tmp = $class -> _copy($x); my $chunk = $class -> _new("16777216"); # 2^24 = 8 octal digits my $rem; until ($class -> _acmp($tmp, $chunk) < 0) { ($tmp, $rem) = $class -> _div($tmp, $chunk); $str = sprintf("%08o", $class -> _num($rem)) . $str; } unless ($class -> _is_zero($tmp)) { $str = sprintf("%o", $class -> _num($tmp)) . $str; } return length($str) ? $str : '0'; } sub _to_hex { # convert the number to a string of hexadecimal digits without prefix my ($class, $x) = @_; my $str = ''; my $tmp = $class -> _copy($x); my $chunk = $class -> _new("16777216"); # 2^24 = 6 hexadecimal digits my $rem; until ($class -> _acmp($tmp, $chunk) < 0) { ($tmp, $rem) = $class -> _div($tmp, $chunk); $str = sprintf("%06x", $class -> _num($rem)) . $str; } unless ($class -> _is_zero($tmp)) { $str = sprintf("%x", $class -> _num($tmp)) . $str; } return length($str) ? $str : '0'; } sub _as_bin { # convert the number to a string of binary digits with prefix my ($class, $x) = @_; return '0b' . $class -> _to_bin($x); } sub _as_oct { # convert the number to a string of octal digits with prefix my ($class, $x) = @_; return '0' . $class -> _to_oct($x); # yes, 0 becomes "00" } sub _as_hex { # convert the number to a string of hexadecimal digits with prefix my ($class, $x) = @_; return '0x' . $class -> _to_hex($x); } sub _to_bytes { # convert the number to a string of bytes my ($class, $x) = @_; my $str = ''; my $tmp = $class -> _copy($x); my $chunk = $class -> _new("65536"); my $rem; until ($class -> _is_zero($tmp)) { ($tmp, $rem) = $class -> _div($tmp, $chunk); $str = pack('n', $class -> _num($rem)) . $str; } $str =~ s/^\0+//; return length($str) ? $str : "\x00"; } *_as_bytes = \&_to_bytes; sub _from_hex { # Convert a string of hexadecimal digits to a number. my ($class, $hex) = @_; $hex =~ s/^0[xX]//; # Find the largest number of hexadecimal digits that we can safely use with # 32 bit integers. There are 4 bits pr hexadecimal digit, and we use only # 31 bits to play safe. This gives us int(31 / 4) = 7. my $len = length $hex; my $rem = 1 + ($len - 1) % 7; # Do the first chunk. my $ret = $class -> _new(int hex substr $hex, 0, $rem); return $ret if $rem == $len; # Do the remaining chunks, if any. my $shift = $class -> _new(1 << (4 * 7)); for (my $offset = $rem ; $offset < $len ; $offset += 7) { my $part = int hex substr $hex, $offset, 7; $ret = $class -> _mul($ret, $shift); $ret = $class -> _add($ret, $class -> _new($part)); } return $ret; } sub _from_oct { # Convert a string of octal digits to a number. my ($class, $oct) = @_; # Find the largest number of octal digits that we can safely use with 32 # bit integers. There are 3 bits pr octal digit, and we use only 31 bits to # play safe. This gives us int(31 / 3) = 10. my $len = length $oct; my $rem = 1 + ($len - 1) % 10; # Do the first chunk. my $ret = $class -> _new(int oct substr $oct, 0, $rem); return $ret if $rem == $len; # Do the remaining chunks, if any. my $shift = $class -> _new(1 << (3 * 10)); for (my $offset = $rem ; $offset < $len ; $offset += 10) { my $part = int oct substr $oct, $offset, 10; $ret = $class -> _mul($ret, $shift); $ret = $class -> _add($ret, $class -> _new($part)); } return $ret; } sub _from_bin { # Convert a string of binary digits to a number. my ($class, $bin) = @_; $bin =~ s/^0[bB]//; # The largest number of binary digits that we can safely use with 32 bit # integers is 31. We use only 31 bits to play safe. my $len = length $bin; my $rem = 1 + ($len - 1) % 31; # Do the first chunk. my $ret = $class -> _new(int oct '0b' . substr $bin, 0, $rem); return $ret if $rem == $len; # Do the remaining chunks, if any. my $shift = $class -> _new(1 << 31); for (my $offset = $rem ; $offset < $len ; $offset += 31) { my $part = int oct '0b' . substr $bin, $offset, 31; $ret = $class -> _mul($ret, $shift); $ret = $class -> _add($ret, $class -> _new($part)); } return $ret; } sub _from_bytes { # convert string of bytes to a number my ($class, $str) = @_; my $x = $class -> _zero(); my $base = $class -> _new("256"); my $n = length($str); for (my $i = 0 ; $i < $n ; ++$i) { $x = $class -> _mul($x, $base); my $byteval = $class -> _new(unpack 'C', substr($str, $i, 1)); $x = $class -> _add($x, $byteval); } return $x; } ############################################################################## # special modulus functions sub _modinv { # modular multiplicative inverse my ($class, $x, $y) = @_; # modulo zero if ($class -> _is_zero($y)) { return (undef, undef); } # modulo one if ($class -> _is_one($y)) { return ($class -> _zero(), '+'); } my $u = $class -> _zero(); my $v = $class -> _one(); my $a = $class -> _copy($y); my $b = $class -> _copy($x); # Euclid's Algorithm for bgcd(). my $q; my $sign = 1; { ($a, $q, $b) = ($b, $class -> _div($a, $b)); last if $class -> _is_zero($b); my $vq = $class -> _mul($class -> _copy($v), $q); my $t = $class -> _add($vq, $u); $u = $v; $v = $t; $sign = -$sign; redo; } # if the gcd is not 1, there exists no modular multiplicative inverse return (undef, undef) unless $class -> _is_one($a); ($v, $sign == 1 ? '+' : '-'); } sub _modpow { # modulus of power ($x ** $y) % $z my ($class, $num, $exp, $mod) = @_; # a^b (mod 1) = 0 for all a and b if ($class -> _is_one($mod)) { return $class -> _zero(); } # 0^a (mod m) = 0 if m != 0, a != 0 # 0^0 (mod m) = 1 if m != 0 if ($class -> _is_zero($num)) { return $class -> _is_zero($exp) ? $class -> _one() : $class -> _zero(); } # $num = $class -> _mod($num, $mod); # this does not make it faster my $acc = $class -> _copy($num); my $t = $class -> _one(); my $expbin = $class -> _as_bin($exp); $expbin =~ s/^0b//; my $len = length($expbin); while (--$len >= 0) { if (substr($expbin, $len, 1) eq '1') { $t = $class -> _mul($t, $acc); $t = $class -> _mod($t, $mod); } $acc = $class -> _mul($acc, $acc); $acc = $class -> _mod($acc, $mod); } return $t; } sub _gcd { # Greatest common divisor. my ($class, $x, $y) = @_; # gcd(0, 0) = 0 # gcd(0, a) = a, if a != 0 if ($class -> _acmp($x, $y) == 0) { return $class -> _copy($x); } if ($class -> _is_zero($x)) { if ($class -> _is_zero($y)) { return $class -> _zero(); } else { return $class -> _copy($y); } } else { if ($class -> _is_zero($y)) { return $class -> _copy($x); } else { # Until $y is zero ... $x = $class -> _copy($x); until ($class -> _is_zero($y)) { # Compute remainder. $x = $class -> _mod($x, $y); # Swap $x and $y. my $tmp = $x; $x = $class -> _copy($y); $y = $tmp; } return $x; } } } sub _lcm { # Least common multiple. my ($class, $x, $y) = @_; # lcm(0, x) = 0 for all x return $class -> _zero() if ($class -> _is_zero($x) || $class -> _is_zero($y)); my $gcd = $class -> _gcd($class -> _copy($x), $y); $x = $class -> _div($x, $gcd); $x = $class -> _mul($x, $y); return $x; } ############################################################################## ############################################################################## 1; __END__ =pod =head1 NAME Math::BigInt::Lib - virtual parent class for Math::BigInt libraries =head1 SYNOPSIS # In the backend library for Math::BigInt et al. package Math::BigInt::MyBackend; use Math::BigInt::lib; our @ISA = qw< Math::BigInt::lib >; sub _new { ... } sub _str { ... } sub _add { ... } str _sub { ... } ... # In your main program. use Math::BigInt lib => 'MyBackend'; =head1 DESCRIPTION This module provides support for big integer calculations. It is not intended to be used directly, but rather as a parent class for backend libraries used by Math::BigInt, Math::BigFloat, Math::BigRat, and related modules. Other backend libraries include Math::BigInt::Calc, Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari. In order to allow for multiple big integer libraries, Math::BigInt was rewritten to use a plug-in library for core math routines. Any module which conforms to the API can be used by Math::BigInt by using this in your program: use Math::BigInt lib => 'libname'; 'libname' is either the long name, like 'Math::BigInt::Pari', or only the short version, like 'Pari'. =head2 General Notes A library only needs to deal with unsigned big integers. Testing of input parameter validity is done by the caller, so there is no need to worry about underflow (e.g., in C<_sub()> and C<_dec()>) or about division by zero (e.g., in C<_div()> and C<_mod()>)) or similar cases. Some libraries use methods that don't modify their argument, and some libraries don't even use objects, but rather unblessed references. Because of this, liberary methods are always called as class methods, not instance methods: $x = Class -> method($x, $y); # like this $x = $x -> method($y); # not like this ... $x -> method($y); # ... or like this And with boolean methods $bool = Class -> method($x, $y); # like this $bool = $x -> method($y); # not like this Return values are always objects, strings, Perl scalars, or true/false for comparison routines. =head3 API version =over 4 =item CLASS-Eapi_version() Return API version as a Perl scalar, 1 for Math::BigInt v1.70, 2 for Math::BigInt v1.83. This method is no longer used. Methods that are not implemented by a subclass will be inherited from this class. =back =head3 Constructors The following methods are mandatory: _new(), _str(), _add(), and _sub(). However, computations will be very slow without _mul() and _div(). =over 4 =item CLASS-E_new(STR) Convert a string representing an unsigned decimal number to an object representing the same number. The input is normalized, i.e., it matches C<^(0|[1-9]\d*)$>. =item CLASS-E_zero() Return an object representing the number zero. =item CLASS-E_one() Return an object representing the number one. =item CLASS-E_two() Return an object representing the number two. =item CLASS-E_ten() Return an object representing the number ten. =item CLASS-E_from_bin(STR) Return an object given a string representing a binary number. The input has a '0b' prefix and matches the regular expression C<^0[bB](0|1[01]*)$>. =item CLASS-E_from_oct(STR) Return an object given a string representing an octal number. The input has a '0' prefix and matches the regular expression C<^0[1-7]*$>. =item CLASS-E_from_hex(STR) Return an object given a string representing a hexadecimal number. The input has a '0x' prefix and matches the regular expression C<^0x(0|[1-9a-fA-F][\da-fA-F]*)$>. =item CLASS-E_from_bytes(STR) Returns an object given a byte string representing the number. The byte string is in big endian byte order, so the two-byte input string "\x01\x00" should give an output value representing the number 256. =back =head3 Mathematical functions =over 4 =item CLASS-E_add(OBJ1, OBJ2) Returns the result of adding OBJ2 to OBJ1. =item CLASS-E_mul(OBJ1, OBJ2) Returns the result of multiplying OBJ2 and OBJ1. =item CLASS-E_div(OBJ1, OBJ2) In scalar context, returns the quotient after dividing OBJ1 by OBJ2 and truncating the result to an integer. In list context, return the quotient and the remainder. =item CLASS-E_sub(OBJ1, OBJ2, FLAG) =item CLASS-E_sub(OBJ1, OBJ2) Returns the result of subtracting OBJ2 by OBJ1. If C is false or omitted, OBJ1 might be modified. If C is true, OBJ2 might be modified. =item CLASS-E_dec(OBJ) Returns the result after decrementing OBJ by one. =item CLASS-E_inc(OBJ) Returns the result after incrementing OBJ by one. =item CLASS-E_mod(OBJ1, OBJ2) Returns OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1 by OBJ2. =item CLASS-E_sqrt(OBJ) Returns the square root of OBJ, truncated to an integer. =item CLASS-E_root(OBJ, N) Returns the Nth root of OBJ, truncated to an integer. =item CLASS-E_fac(OBJ) Returns the factorial of OBJ, i.e., the product of all positive integers up to and including OBJ. =item CLASS-E_dfac(OBJ) Returns the double factorial of OBJ. If OBJ is an even integer, returns the product of all positive, even integers up to and including OBJ, i.e., 2*4*6*...*OBJ. If OBJ is an odd integer, returns the product of all positive, odd integers, i.e., 1*3*5*...*OBJ. =item CLASS-E_pow(OBJ1, OBJ2) Returns OBJ1 raised to the power of OBJ2. By convention, 0**0 = 1. =item CLASS-E_modinv(OBJ1, OBJ2) Returns the modular multiplicative inverse, i.e., return OBJ3 so that (OBJ3 * OBJ1) % OBJ2 = 1 % OBJ2 The result is returned as two arguments. If the modular multiplicative inverse does not exist, both arguments are undefined. Otherwise, the arguments are a number (object) and its sign ("+" or "-"). The output value, with its sign, must either be a positive value in the range 1,2,...,OBJ2-1 or the same value subtracted OBJ2. For instance, if the input arguments are objects representing the numbers 7 and 5, the method must either return an object representing the number 3 and a "+" sign, since (3*7) % 5 = 1 % 5, or an object representing the number 2 and a "-" sign, since (-2*7) % 5 = 1 % 5. =item CLASS-E_modpow(OBJ1, OBJ2, OBJ3) Returns the modular exponentiation, i.e., (OBJ1 ** OBJ2) % OBJ3. =item CLASS-E_rsft(OBJ, N, B) Returns the result after shifting OBJ N digits to thee right in base B. This is equivalent to performing integer division by B**N and discarding the remainder, except that it might be much faster. For instance, if the object $obj represents the hexadecimal number 0xabcde, then C<_rsft($obj, 2, 16)> returns an object representing the number 0xabc. The "remainer", 0xde, is discarded and not returned. =item CLASS-E_lsft(OBJ, N, B) Returns the result after shifting OBJ N digits to the left in base B. This is equivalent to multiplying by B**N, except that it might be much faster. =item CLASS-E_log_int(OBJ, B) Returns the logarithm of OBJ to base BASE truncted to an integer. This method has two output arguments, the OBJECT and a STATUS. The STATUS is Perl scalar; it is 1 if OBJ is the exact result, 0 if the result was truncted to give OBJ, and undef if it is unknown whether OBJ is the exact result. =item CLASS-E_gcd(OBJ1, OBJ2) Returns the greatest common divisor of OBJ1 and OBJ2. =item CLASS-E_lcm(OBJ1, OBJ2) Return the least common multiple of OBJ1 and OBJ2. =back =head3 Bitwise operators =over 4 =item CLASS-E_and(OBJ1, OBJ2) Returns bitwise and. =item CLASS-E_or(OBJ1, OBJ2) Return bitwise or. =item CLASS-E_xor(OBJ1, OBJ2) Return bitwise exclusive or. =back =head3 Boolean operators =over 4 =item CLASS-E_is_zero(OBJ) Returns a true value if OBJ is zero, and false value otherwise. =item CLASS-E_is_one(OBJ) Returns a true value if OBJ is one, and false value otherwise. =item CLASS-E_is_two(OBJ) Returns a true value if OBJ is two, and false value otherwise. =item CLASS-E_is_ten(OBJ) Returns a true value if OBJ is ten, and false value otherwise. =item CLASS-E_is_even(OBJ) Return a true value if OBJ is an even integer, and a false value otherwise. =item CLASS-E_is_odd(OBJ) Return a true value if OBJ is an even integer, and a false value otherwise. =item CLASS-E_acmp(OBJ1, OBJ2) Compare OBJ1 and OBJ2 and return -1, 0, or 1, if OBJ1 is numerically less than, equal to, or larger than OBJ2, respectively. =back =head3 String conversion =over 4 =item CLASS-E_str(OBJ) Returns a string representing OBJ in decimal notation. The returned string should have no leading zeros, i.e., it should match C<^(0|[1-9]\d*)$>. =item CLASS-E_to_bin(OBJ) Returns the binary string representation of OBJ. =item CLASS-E_to_oct(OBJ) Returns the octal string representation of the number. =item CLASS-E_to_hex(OBJ) Returns the hexadecimal string representation of the number. =item CLASS-E_to_bytes(OBJ) Returns a byte string representation of OBJ. The byte string is in big endian byte order, so if OBJ represents the number 256, the output should be the two-byte string "\x01\x00". =item CLASS-E_as_bin(OBJ) Like C<_to_bin()> but with a '0b' prefix. =item CLASS-E_as_oct(OBJ) Like C<_to_oct()> but with a '0' prefix. =item CLASS-E_as_hex(OBJ) Like C<_to_hex()> but with a '0x' prefix. =item CLASS-E_as_bytes(OBJ) This is an alias to C<_to_bytes()>. =back =head3 Numeric conversion =over 4 =item CLASS-E_num(OBJ) Returns a Perl scalar number representing the number OBJ as close as possible. Since Perl scalars have limited precision, the returned value might not be exactly the same as OBJ. =back =head3 Miscellaneous =over 4 =item CLASS-E_copy(OBJ) Returns a true copy OBJ. =item CLASS-E_len(OBJ) Returns the number of the decimal digits in OBJ. The output is a Perl scalar. =item CLASS-E_zeros(OBJ) Returns the number of trailing decimal zeros. The output is a Perl scalar. The number zero has no trailing decimal zeros. =item CLASS-E_digit(OBJ, N) Returns the Nth digit in OBJ as a Perl scalar. N is a Perl scalar, where zero refers to the rightmost (least significant) digit, and negative values count from the left (most significant digit). If $obj represents the number 123, then CLASS->_digit($obj, 0) # returns 3 CLASS->_digit($obj, 1) # returns 2 CLASS->_digit($obj, 2) # returns 1 CLASS->_digit($obj, -1) # returns 1 =item CLASS-E_check(OBJ) Returns true if the object is invalid and false otherwise. Preferably, the true value is a string describing the problem with the object. This is a check routine to test the internal state of the object for corruption. =item CLASS-E_set(OBJ) xxx =back =head2 API version 2 The following methods are required for an API version of 2 or greater. =head3 Constructors =over 4 =item CLASS-E_1ex(N) Return an object representing the number 10**N where N E= 0 is a Perl scalar. =back =head3 Mathematical functions =over 4 =item CLASS-E_nok(OBJ1, OBJ2) Return the binomial coefficient OBJ1 over OBJ1. =back =head3 Miscellaneous =over 4 =item CLASS-E_alen(OBJ) Return the approximate number of decimal digits of the object. The output is a Perl scalar. =back =head2 API optional methods The following methods are optional, and can be defined if the underlying lib has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence slow) fallback routines to emulate these: =head3 Signed bitwise operators. =over 4 =item CLASS-E_signed_or(OBJ1, OBJ2, SIGN1, SIGN2) Return the signed bitwise or. =item CLASS-E_signed_and(OBJ1, OBJ2, SIGN1, SIGN2) Return the signed bitwise and. =item CLASS-E_signed_xor(OBJ1, OBJ2, SIGN1, SIGN2) Return the signed bitwise exclusive or. =back =head1 WRAP YOUR OWN If you want to port your own favourite C library for big numbers to the Math::BigInt interface, you can take any of the already existing modules as a rough guideline. You should really wrap up the latest Math::BigInt and Math::BigFloat testsuites with your module, and replace in them any of the following: use Math::BigInt; by this: use Math::BigInt lib => 'yourlib'; This way you ensure that your library really works 100% within Math::BigInt. =head1 BUGS Please report any bugs or feature requests to C, or through the web interface at L (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes. =head1 SUPPORT You can find documentation for this module with the perldoc command. perldoc Math::BigInt::Calc You can also look for information at: =over 4 =item * RT: CPAN's request tracker L =item * AnnoCPAN: Annotated CPAN documentation L =item * CPAN Ratings L =item * Search CPAN L =item * CPAN Testers Matrix L =item * The Bignum mailing list =over 4 =item * Post to mailing list C =item * View mailing list L =item * Subscribe/Unsubscribe L =back =back =head1 LICENSE This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. =head1 AUTHOR Peter John Acklam, Epjacklam@online.noE Code and documentation based on the Math::BigInt::Calc module by Tels Enospam-abuse@bloodgate.comE =head1 SEE ALSO L, L, L, L and L. =cut Math-BigInt-1.999808/lib/Math/BigInt.pm0000644403072340010010000062017513035443532017524 0ustar ospjadomain userspackage Math::BigInt; # # "Mike had an infinite amount to do and a negative amount of time in which # to do it." - Before and After # # The following hash values are used: # value: unsigned int with actual value (as a Math::BigInt::Calc or similar) # sign : +, -, NaN, +inf, -inf # _a : accuracy # _p : precision # Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since # underlying lib might change the reference! use 5.006001; use strict; use warnings; use Carp (); our $VERSION = '1.999808'; our @ISA = qw(Exporter); our @EXPORT_OK = qw(objectify bgcd blcm); my $class = "Math::BigInt"; # Inside overload, the first arg is always an object. If the original code had # it reversed (like $x = 2 * $y), then the third parameter is true. # In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes # no difference, but in some cases it does. # For overloaded ops with only one argument we simple use $_[0]->copy() to # preserve the argument. # Thus inheritance of overload operators becomes possible and transparent for # our subclasses without the need to repeat the entire overload section there. use overload # overload key: with_assign '+' => sub { $_[0] -> copy() -> badd($_[1]); }, '-' => sub { my $c = $_[0] -> copy; $_[2] ? $c -> bneg() -> badd($_[1]) : $c -> bsub($_[1]); }, '*' => sub { $_[0] -> copy() -> bmul($_[1]); }, '/' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bdiv($_[0]) : $_[0] -> copy -> bdiv($_[1]); }, '%' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bmod($_[0]) : $_[0] -> copy -> bmod($_[1]); }, '**' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bpow($_[0]) : $_[0] -> copy -> bpow($_[1]); }, '<<' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> blsft($_[0]) : $_[0] -> copy -> blsft($_[1]); }, '>>' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> brsft($_[0]) : $_[0] -> copy -> brsft($_[1]); }, # overload key: assign '+=' => sub { $_[0]->badd($_[1]); }, '-=' => sub { $_[0]->bsub($_[1]); }, '*=' => sub { $_[0]->bmul($_[1]); }, '/=' => sub { scalar $_[0]->bdiv($_[1]); }, '%=' => sub { $_[0]->bmod($_[1]); }, '**=' => sub { $_[0]->bpow($_[1]); }, '<<=' => sub { $_[0]->blsft($_[1]); }, '>>=' => sub { $_[0]->brsft($_[1]); }, # 'x=' => sub { }, # '.=' => sub { }, # overload key: num_comparison '<' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> blt($_[0]) : $_[0] -> blt($_[1]); }, '<=' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> ble($_[0]) : $_[0] -> ble($_[1]); }, '>' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bgt($_[0]) : $_[0] -> bgt($_[1]); }, '>=' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bge($_[0]) : $_[0] -> bge($_[1]); }, '==' => sub { $_[0] -> beq($_[1]); }, '!=' => sub { $_[0] -> bne($_[1]); }, # overload key: 3way_comparison '<=>' => sub { my $cmp = $_[0] -> bcmp($_[1]); defined($cmp) && $_[2] ? -$cmp : $cmp; }, 'cmp' => sub { $_[2] ? "$_[1]" cmp $_[0] -> bstr() : $_[0] -> bstr() cmp "$_[1]"; }, # overload key: str_comparison # 'lt' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrlt($_[0]) # : $_[0] -> bstrlt($_[1]); }, # # 'le' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrle($_[0]) # : $_[0] -> bstrle($_[1]); }, # # 'gt' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrgt($_[0]) # : $_[0] -> bstrgt($_[1]); }, # # 'ge' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bstrge($_[0]) # : $_[0] -> bstrge($_[1]); }, # # 'eq' => sub { $_[0] -> bstreq($_[1]); }, # # 'ne' => sub { $_[0] -> bstrne($_[1]); }, # overload key: binary '&' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> band($_[0]) : $_[0] -> copy -> band($_[1]); }, '&=' => sub { $_[0] -> band($_[1]); }, '|' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bior($_[0]) : $_[0] -> copy -> bior($_[1]); }, '|=' => sub { $_[0] -> bior($_[1]); }, '^' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> bxor($_[0]) : $_[0] -> copy -> bxor($_[1]); }, '^=' => sub { $_[0] -> bxor($_[1]); }, # '&.' => sub { }, # '&.=' => sub { }, # '|.' => sub { }, # '|.=' => sub { }, # '^.' => sub { }, # '^.=' => sub { }, # overload key: unary 'neg' => sub { $_[0] -> copy() -> bneg(); }, # '!' => sub { }, '~' => sub { $_[0] -> copy() -> bnot(); }, # '~.' => sub { }, # overload key: mutators '++' => sub { $_[0] -> binc() }, '--' => sub { $_[0] -> bdec() }, # overload key: func 'atan2' => sub { $_[2] ? ref($_[0]) -> new($_[1]) -> batan2($_[0]) : $_[0] -> copy() -> batan2($_[1]); }, 'cos' => sub { $_[0] -> copy -> bcos(); }, 'sin' => sub { $_[0] -> copy -> bsin(); }, 'exp' => sub { $_[0] -> copy() -> bexp($_[1]); }, 'abs' => sub { $_[0] -> copy() -> babs(); }, 'log' => sub { $_[0] -> copy() -> blog(); }, 'sqrt' => sub { $_[0] -> copy() -> bsqrt(); }, 'int' => sub { $_[0] -> copy() -> bint(); }, # overload key: conversion 'bool' => sub { $_[0] -> is_zero() ? '' : 1; }, '""' => sub { $_[0] -> bstr(); }, '0+' => sub { $_[0] -> numify(); }, '=' => sub { $_[0]->copy(); }, ; ############################################################################## # global constants, flags and accessory # These vars are public, but their direct usage is not recommended, use the # accessor methods instead our $round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common' our $accuracy = undef; our $precision = undef; our $div_scale = 40; our $upgrade = undef; # default is no upgrade our $downgrade = undef; # default is no downgrade # These are internally, and not to be used from the outside at all our $_trap_nan = 0; # are NaNs ok? set w/ config() our $_trap_inf = 0; # are infs ok? set w/ config() my $nan = 'NaN'; # constants for easier life my $CALC = 'Math::BigInt::Calc'; # module to do the low level math # default is Calc.pm my $IMPORT = 0; # was import() called yet? # used to make require work my %WARN; # warn only once for low-level libs my %CAN; # cache for $CALC->can(...) my %CALLBACKS; # callbacks to notify on lib loads my $EMU_LIB = 'Math/BigInt/CalcEmu.pm'; # emulate low-level math ############################################################################## # the old code had $rnd_mode, so we need to support it, too our $rnd_mode = 'even'; sub TIESCALAR { my ($class) = @_; bless \$round_mode, $class; } sub FETCH { return $round_mode; } sub STORE { $rnd_mode = $_[0]->round_mode($_[1]); } BEGIN { # tie to enable $rnd_mode to work transparently tie $rnd_mode, 'Math::BigInt'; # set up some handy alias names *as_int = \&as_number; *is_pos = \&is_positive; *is_neg = \&is_negative; } ############################################################################### # Configuration methods ############################################################################### sub round_mode { no strict 'refs'; # make Class->round_mode() work my $self = shift; my $class = ref($self) || $self || __PACKAGE__; if (defined $_[0]) { my $m = shift; if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/) { Carp::croak("Unknown round mode '$m'"); } return ${"${class}::round_mode"} = $m; } ${"${class}::round_mode"}; } sub upgrade { no strict 'refs'; # make Class->upgrade() work my $self = shift; my $class = ref($self) || $self || __PACKAGE__; # need to set new value? if (@_ > 0) { return ${"${class}::upgrade"} = $_[0]; } ${"${class}::upgrade"}; } sub downgrade { no strict 'refs'; # make Class->downgrade() work my $self = shift; my $class = ref($self) || $self || __PACKAGE__; # need to set new value? if (@_ > 0) { return ${"${class}::downgrade"} = $_[0]; } ${"${class}::downgrade"}; } sub div_scale { no strict 'refs'; # make Class->div_scale() work my $self = shift; my $class = ref($self) || $self || __PACKAGE__; if (defined $_[0]) { if ($_[0] < 0) { Carp::croak('div_scale must be greater than zero'); } ${"${class}::div_scale"} = $_[0]; } ${"${class}::div_scale"}; } sub accuracy { # $x->accuracy($a); ref($x) $a # $x->accuracy(); ref($x) # Class->accuracy(); class # Class->accuracy($a); class $a my $x = shift; my $class = ref($x) || $x || __PACKAGE__; no strict 'refs'; # need to set new value? if (@_ > 0) { my $a = shift; # convert objects to scalars to avoid deep recursion. If object doesn't # have numify(), then hopefully it will have overloading for int() and # boolean test without wandering into a deep recursion path... $a = $a->numify() if ref($a) && $a->can('numify'); if (defined $a) { # also croak on non-numerical if (!$a || $a <= 0) { Carp::croak('Argument to accuracy must be greater than zero'); } if (int($a) != $a) { Carp::croak('Argument to accuracy must be an integer'); } } if (ref($x)) { # $object->accuracy() or fallback to global $x->bround($a) if $a; # not for undef, 0 $x->{_a} = $a; # set/overwrite, even if not rounded delete $x->{_p}; # clear P $a = ${"${class}::accuracy"} unless defined $a; # proper return value } else { ${"${class}::accuracy"} = $a; # set global A ${"${class}::precision"} = undef; # clear global P } return $a; # shortcut } my $a; # $object->accuracy() or fallback to global $a = $x->{_a} if ref($x); # but don't return global undef, when $x's accuracy is 0! $a = ${"${class}::accuracy"} if !defined $a; $a; } sub precision { # $x->precision($p); ref($x) $p # $x->precision(); ref($x) # Class->precision(); class # Class->precision($p); class $p my $x = shift; my $class = ref($x) || $x || __PACKAGE__; no strict 'refs'; if (@_ > 0) { my $p = shift; # convert objects to scalars to avoid deep recursion. If object doesn't # have numify(), then hopefully it will have overloading for int() and # boolean test without wandering into a deep recursion path... $p = $p->numify() if ref($p) && $p->can('numify'); if ((defined $p) && (int($p) != $p)) { Carp::croak('Argument to precision must be an integer'); } if (ref($x)) { # $object->precision() or fallback to global $x->bfround($p) if $p; # not for undef, 0 $x->{_p} = $p; # set/overwrite, even if not rounded delete $x->{_a}; # clear A $p = ${"${class}::precision"} unless defined $p; # proper return value } else { ${"${class}::precision"} = $p; # set global P ${"${class}::accuracy"} = undef; # clear global A } return $p; # shortcut } my $p; # $object->precision() or fallback to global $p = $x->{_p} if ref($x); # but don't return global undef, when $x's precision is 0! $p = ${"${class}::precision"} if !defined $p; $p; } sub config { # return (or set) configuration data as hash ref my $class = shift || __PACKAGE__; no strict 'refs'; if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH'))) { # try to set given options as arguments from hash my $args = $_[0]; if (ref($args) ne 'HASH') { $args = { @_ }; } # these values can be "set" my $set_args = {}; foreach my $key (qw/ accuracy precision round_mode div_scale upgrade downgrade trap_inf trap_nan /) { $set_args->{$key} = $args->{$key} if exists $args->{$key}; delete $args->{$key}; } if (keys %$args > 0) { Carp::croak("Illegal key(s) '", join("', '", keys %$args), "' passed to $class\->config()"); } foreach my $key (keys %$set_args) { if ($key =~ /^trap_(inf|nan)\z/) { ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0); next; } # use a call instead of just setting the $variable to check argument $class->$key($set_args->{$key}); } } # now return actual configuration my $cfg = { lib => $CALC, lib_version => ${"${CALC}::VERSION"}, class => $class, trap_nan => ${"${class}::_trap_nan"}, trap_inf => ${"${class}::_trap_inf"}, version => ${"${class}::VERSION"}, }; foreach my $key (qw/ accuracy precision round_mode div_scale upgrade downgrade /) { $cfg->{$key} = ${"${class}::$key"}; } if (@_ == 1 && (ref($_[0]) ne 'HASH')) { # calls of the style config('lib') return just this value return $cfg->{$_[0]}; } $cfg; } sub _scale_a { # select accuracy parameter based on precedence, # used by bround() and bfround(), may return undef for scale (means no op) my ($x, $scale, $mode) = @_; $scale = $x->{_a} unless defined $scale; no strict 'refs'; my $class = ref($x); $scale = ${ $class . '::accuracy' } unless defined $scale; $mode = ${ $class . '::round_mode' } unless defined $mode; if (defined $scale) { $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale); $scale = int($scale); } ($scale, $mode); } sub _scale_p { # select precision parameter based on precedence, # used by bround() and bfround(), may return undef for scale (means no op) my ($x, $scale, $mode) = @_; $scale = $x->{_p} unless defined $scale; no strict 'refs'; my $class = ref($x); $scale = ${ $class . '::precision' } unless defined $scale; $mode = ${ $class . '::round_mode' } unless defined $mode; if (defined $scale) { $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale); $scale = int($scale); } ($scale, $mode); } ############################################################################### # Constructor methods ############################################################################### sub new { # Create a new Math::BigInt object from a string or another Math::BigInt # object. See hash keys documented at top. # The argument could be an object, so avoid ||, && etc. on it. This would # cause costly overloaded code to be called. The only allowed ops are ref() # and defined. my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # The POD says: # # "Currently, Math::BigInt->new() defaults to 0, while Math::BigInt->new('') # results in 'NaN'. This might change in the future, so use always the # following explicit forms to get a zero or NaN: # $zero = Math::BigInt->bzero(); # $nan = Math::BigInt->bnan(); # # But although this use has been discouraged for more than 10 years, people # apparently still use it, so we still support it. return $self->bzero() unless @_; my ($wanted, $a, $p, $r) = @_; # Always return a new object, so it called as an instance method, copy the # invocand, and if called as a class method, initialize a new object. $self = $selfref ? $self -> copy() : bless {}, $class; unless (defined $wanted) { #Carp::carp("Use of uninitialized value in new()"); return $self->bzero($a, $p, $r); } if (ref($wanted) && $wanted->isa($class)) { # MBI or subclass # Using "$copy = $wanted -> copy()" here fails some tests. Fixme! my $copy = $class -> copy($wanted); if ($selfref) { %$self = %$copy; } else { $self = $copy; } return $self; } $class->import() if $IMPORT == 0; # make require work # Shortcut for non-zero scalar integers with no non-zero exponent. if (!ref($wanted) && $wanted =~ / ^ ([+-]?) # optional sign ([1-9][0-9]*) # non-zero significand (\.0*)? # ... with optional zero fraction ([Ee][+-]?0+)? # optional zero exponent \z /x) { my $sgn = $1; my $abs = $2; $self->{sign} = $sgn || '+'; $self->{value} = $CALC->_new($abs); no strict 'refs'; if (defined($a) || defined($p) || defined(${"${class}::precision"}) || defined(${"${class}::accuracy"})) { $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p; } return $self; } # Handle Infs. if ($wanted =~ /^\s*([+-]?)inf(inity)?\s*\z/i) { my $sgn = $1 || '+'; $self->{sign} = $sgn . 'inf'; # set a default sign for bstr() return $class->binf($sgn); } # Handle explicit NaNs (not the ones returned due to invalid input). if ($wanted =~ /^\s*([+-]?)nan\s*\z/i) { $self = $class -> bnan(); $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p; return $self; } # Handle hexadecimal numbers. if ($wanted =~ /^\s*[+-]?0[Xx]/) { $self = $class -> from_hex($wanted); $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p; return $self; } # Handle binary numbers. if ($wanted =~ /^\s*[+-]?0[Bb]/) { $self = $class -> from_bin($wanted); $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p; return $self; } # Split string into mantissa, exponent, integer, fraction, value, and sign. my ($mis, $miv, $mfv, $es, $ev) = _split($wanted); if (!ref $mis) { if ($_trap_nan) { Carp::croak("$wanted is not a number in $class"); } $self->{value} = $CALC->_zero(); $self->{sign} = $nan; return $self; } if (!ref $miv) { # _from_hex or _from_bin $self->{value} = $mis->{value}; $self->{sign} = $mis->{sign}; return $self; # throw away $mis } # Make integer from mantissa by adjusting exponent, then convert to a # Math::BigInt. $self->{sign} = $$mis; # store sign $self->{value} = $CALC->_zero(); # for all the NaN cases my $e = int("$$es$$ev"); # exponent (avoid recursion) if ($e > 0) { my $diff = $e - CORE::length($$mfv); if ($diff < 0) { # Not integer if ($_trap_nan) { Carp::croak("$wanted not an integer in $class"); } #print "NOI 1\n"; return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade; $self->{sign} = $nan; } else { # diff >= 0 # adjust fraction and add it to value #print "diff > 0 $$miv\n"; $$miv = $$miv . ($$mfv . '0' x $diff); } } else { if ($$mfv ne '') { # e <= 0 # fraction and negative/zero E => NOI if ($_trap_nan) { Carp::croak("$wanted not an integer in $class"); } #print "NOI 2 \$\$mfv '$$mfv'\n"; return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade; $self->{sign} = $nan; } elsif ($e < 0) { # xE-y, and empty mfv # Split the mantissa at the decimal point. E.g., if # $$miv = 12345 and $e = -2, then $frac = 45 and $$miv = 123. my $frac = substr($$miv, $e); # $frac is fraction part substr($$miv, $e) = ""; # $$miv is now integer part if ($frac =~ /[^0]/) { if ($_trap_nan) { Carp::croak("$wanted not an integer in $class"); } #print "NOI 3\n"; return $upgrade->new($wanted, $a, $p, $r) if defined $upgrade; $self->{sign} = $nan; } } } unless ($self->{sign} eq $nan) { $self->{sign} = '+' if $$miv eq '0'; # normalize -0 => +0 $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/; } # If any of the globals are set, use them to round, and store them inside # $self. Do not round for new($x, undef, undef) since that is used by MBF # to signal no rounding. $self->round($a, $p, $r) unless @_ >= 3 && !defined $a && !defined $p; $self; } # Create a Math::BigInt from a hexadecimal string. sub from_hex { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # Don't modify constant (read-only) objects. return if $selfref && $self->modify('from_hex'); my $str = shift; # If called as a class method, initialize a new object. $self = $class -> bzero() unless $selfref; if ($str =~ s/ ^ \s* ( [+-]? ) (0?x)? ( [0-9a-fA-F]* ( _ [0-9a-fA-F]+ )* ) \s* $ //x) { # Get a "clean" version of the string, i.e., non-emtpy and with no # underscores or invalid characters. my $sign = $1; my $chrs = $3; $chrs =~ tr/_//d; $chrs = '0' unless CORE::length $chrs; # The library method requires a prefix. $self->{value} = $CALC->_from_hex('0x' . $chrs); # Place the sign. $self->{sign} = $sign eq '-' && ! $CALC->_is_zero($self->{value}) ? '-' : '+'; return $self; } # CORE::hex() parses as much as it can, and ignores any trailing garbage. # For backwards compatibility, we return NaN. return $self->bnan(); } # Create a Math::BigInt from an octal string. sub from_oct { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # Don't modify constant (read-only) objects. return if $selfref && $self->modify('from_oct'); my $str = shift; # If called as a class method, initialize a new object. $self = $class -> bzero() unless $selfref; if ($str =~ s/ ^ \s* ( [+-]? ) ( [0-7]* ( _ [0-7]+ )* ) \s* $ //x) { # Get a "clean" version of the string, i.e., non-emtpy and with no # underscores or invalid characters. my $sign = $1; my $chrs = $2; $chrs =~ tr/_//d; $chrs = '0' unless CORE::length $chrs; # The library method requires a prefix. $self->{value} = $CALC->_from_oct('0' . $chrs); # Place the sign. $self->{sign} = $sign eq '-' && ! $CALC->_is_zero($self->{value}) ? '-' : '+'; return $self; } # CORE::oct() parses as much as it can, and ignores any trailing garbage. # For backwards compatibility, we return NaN. return $self->bnan(); } # Create a Math::BigInt from a binary string. sub from_bin { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # Don't modify constant (read-only) objects. return if $selfref && $self->modify('from_bin'); my $str = shift; # If called as a class method, initialize a new object. $self = $class -> bzero() unless $selfref; if ($str =~ s/ ^ \s* ( [+-]? ) (0?b)? ( [01]* ( _ [01]+ )* ) \s* $ //x) { # Get a "clean" version of the string, i.e., non-emtpy and with no # underscores or invalid characters. my $sign = $1; my $chrs = $3; $chrs =~ tr/_//d; $chrs = '0' unless CORE::length $chrs; # The library method requires a prefix. $self->{value} = $CALC->_from_bin('0b' . $chrs); # Place the sign. $self->{sign} = $sign eq '-' && ! $CALC->_is_zero($self->{value}) ? '-' : '+'; return $self; } # For consistency with from_hex() and from_oct(), we return NaN when the # input is invalid. return $self->bnan(); } # Create a Math::BigInt from a byte string. sub from_bytes { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # Don't modify constant (read-only) objects. return if $selfref && $self->modify('from_bytes'); Carp::croak("from_bytes() requires a newer version of the $CALC library.") unless $CALC->can('_from_bytes'); my $str = shift; # If called as a class method, initialize a new object. $self = $class -> bzero() unless $selfref; $self -> {sign} = '+'; $self -> {value} = $CALC -> _from_bytes($str); return $self; } sub bzero { # create/assign '+0' if (@_ == 0) { #Carp::carp("Using bzero() as a function is deprecated;", # " use bzero() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; $self->import() if $IMPORT == 0; # make require work # Don't modify constant (read-only) objects. return if $selfref && $self->modify('bzero'); $self = bless {}, $class unless $selfref; $self->{sign} = '+'; $self->{value} = $CALC->_zero(); if (@_ > 0) { if (@_ > 3) { # call like: $x->bzero($a, $p, $r, $y, ...); ($self, $self->{_a}, $self->{_p}) = $self->_find_round_parameters(@_); } else { # call like: $x->bzero($a, $p, $r); $self->{_a} = $_[0] if !defined $self->{_a} || (defined $_[0] && $_[0] > $self->{_a}); $self->{_p} = $_[1] if !defined $self->{_p} || (defined $_[1] && $_[1] > $self->{_p}); } } return $self; } sub bone { # Create or assign '+1' (or -1 if given sign '-'). if (@_ == 0 || (defined($_[0]) && ($_[0] eq '+' || $_[0] eq '-'))) { #Carp::carp("Using bone() as a function is deprecated;", # " use bone() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; $self->import() if $IMPORT == 0; # make require work # Don't modify constant (read-only) objects. return if $selfref && $self->modify('bone'); my $sign = shift; $sign = defined $sign && $sign =~ /^\s*-/ ? "-" : "+"; $self = bless {}, $class unless $selfref; $self->{sign} = $sign; $self->{value} = $CALC->_one(); if (@_ > 0) { if (@_ > 3) { # call like: $x->bone($sign, $a, $p, $r, $y, ...); ($self, $self->{_a}, $self->{_p}) = $self->_find_round_parameters(@_); } else { # call like: $x->bone($sign, $a, $p, $r); $self->{_a} = $_[0] if !defined $self->{_a} || (defined $_[0] && $_[0] > $self->{_a}); $self->{_p} = $_[1] if !defined $self->{_p} || (defined $_[1] && $_[1] > $self->{_p}); } } return $self; } sub binf { # create/assign a '+inf' or '-inf' if (@_ == 0 || (defined($_[0]) && !ref($_[0]) && $_[0] =~ /^\s*[+-](inf(inity)?)?\s*$/)) { #Carp::carp("Using binf() as a function is deprecated;", # " use binf() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; { no strict 'refs'; if (${"${class}::_trap_inf"}) { Carp::croak("Tried to create +-inf in $class->binf()"); } } $self->import() if $IMPORT == 0; # make require work # Don't modify constant (read-only) objects. return if $selfref && $self->modify('binf'); my $sign = shift; $sign = defined $sign && $sign =~ /^\s*-/ ? "-" : "+"; $self = bless {}, $class unless $selfref; $self -> {sign} = $sign . 'inf'; $self -> {value} = $CALC -> _zero(); return $self; } sub bnan { # create/assign a 'NaN' if (@_ == 0) { #Carp::carp("Using bnan() as a function is deprecated;", # " use bnan() as a method instead"); unshift @_, __PACKAGE__; } my $self = shift; my $selfref = ref($self); my $class = $selfref || $self; { no strict 'refs'; if (${"${class}::_trap_nan"}) { Carp::croak("Tried to create NaN in $class->bnan()"); } } $self->import() if $IMPORT == 0; # make require work # Don't modify constant (read-only) objects. return if $selfref && $self->modify('bnan'); $self = bless {}, $class unless $selfref; $self -> {sign} = $nan; $self -> {value} = $CALC -> _zero(); return $self; } sub bpi { # Calculate PI to N digits. Unless upgrading is in effect, returns the # result truncated to an integer, that is, always returns '3'. my ($self, $n) = @_; if (@_ == 1) { # called like Math::BigInt::bpi(10); $n = $self; $self = $class; } $self = ref($self) if ref($self); return $upgrade->new($n) if defined $upgrade; # hard-wired to "3" $self->new(3); } sub copy { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; # If called as a class method, the object to copy is the next argument. $self = shift() unless $selfref; my $copy = bless {}, $class; $copy->{sign} = $self->{sign}; $copy->{value} = $CALC->_copy($self->{value}); $copy->{_a} = $self->{_a} if exists $self->{_a}; $copy->{_p} = $self->{_p} if exists $self->{_p}; return $copy; } sub as_number { # An object might be asked to return itself as bigint on certain overloaded # operations. This does exactly this, so that sub classes can simple inherit # it or override with their own integer conversion routine. $_[0]->copy(); } ############################################################################### # Boolean methods ############################################################################### sub is_zero { # return true if arg (BINT or num_str) is zero (array '+', '0') my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return 0 if $x->{sign} !~ /^\+$/; # -, NaN & +-inf aren't $CALC->_is_zero($x->{value}); } sub is_one { # return true if arg (BINT or num_str) is +1, or -1 if sign is given my ($class, $x, $sign) = ref($_[0]) ? (undef, @_) : objectify(1, @_); $sign = '+' if !defined $sign || $sign ne '-'; return 0 if $x->{sign} ne $sign; # -1 != +1, NaN, +-inf aren't either $CALC->_is_one($x->{value}); } sub is_finite { my $x = shift; return $x->{sign} eq '+' || $x->{sign} eq '-'; } sub is_inf { # return true if arg (BINT or num_str) is +-inf my ($class, $x, $sign) = ref($_[0]) ? (undef, @_) : objectify(1, @_); if (defined $sign) { $sign = '[+-]inf' if $sign eq ''; # +- doesn't matter, only that's inf $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/; # extract '+' or '-' return $x->{sign} =~ /^$sign$/ ? 1 : 0; } $x->{sign} =~ /^[+-]inf$/ ? 1 : 0; # only +-inf is infinity } sub is_nan { # return true if arg (BINT or num_str) is NaN my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); $x->{sign} eq $nan ? 1 : 0; } sub is_positive { # return true when arg (BINT or num_str) is positive (> 0) my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return 1 if $x->{sign} eq '+inf'; # +inf is positive # 0+ is neither positive nor negative ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0; } sub is_negative { # return true when arg (BINT or num_str) is negative (< 0) my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); $x->{sign} =~ /^-/ ? 1 : 0; # -inf is negative, but NaN is not } sub is_odd { # return true when arg (BINT or num_str) is odd, false for even my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't $CALC->_is_odd($x->{value}); } sub is_even { # return true when arg (BINT or num_str) is even, false for odd my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return 0 if $x->{sign} !~ /^[+-]$/; # NaN & +-inf aren't $CALC->_is_even($x->{value}); } sub is_int { # return true when arg (BINT or num_str) is an integer # always true for Math::BigInt, but different for Math::BigFloat objects my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); $x->{sign} =~ /^[+-]$/ ? 1 : 0; # inf/-inf/NaN aren't } ############################################################################### # Comparison methods ############################################################################### sub bcmp { # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) # (BINT or num_str, BINT or num_str) return cond_code # set up parameters my ($class, $x, $y) = ref($_[0]) && ref($_[0]) eq ref($_[1]) ? (ref($_[0]), @_) : objectify(2, @_); return $upgrade->bcmp($x, $y) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) { # handle +-inf and NaN return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/; return +1 if $x->{sign} eq '+inf'; return -1 if $x->{sign} eq '-inf'; return -1 if $y->{sign} eq '+inf'; return +1; } # check sign for speed first return 1 if $x->{sign} eq '+' && $y->{sign} eq '-'; # does also 0 <=> -y return -1 if $x->{sign} eq '-' && $y->{sign} eq '+'; # does also -x <=> 0 # have same sign, so compare absolute values. Don't make tests for zero # here because it's actually slower than testing in Calc (especially w/ Pari # et al) # post-normalized compare for internal use (honors signs) if ($x->{sign} eq '+') { # $x and $y both > 0 return $CALC->_acmp($x->{value}, $y->{value}); } # $x && $y both < 0 $CALC->_acmp($y->{value}, $x->{value}); # swapped acmp (lib returns 0, 1, -1) } sub bacmp { # Compares 2 values, ignoring their signs. # Returns one of undef, <0, =0, >0. (suitable for sort) # (BINT, BINT) return cond_code # set up parameters my ($class, $x, $y) = ref($_[0]) && ref($_[0]) eq ref($_[1]) ? (ref($_[0]), @_) : objectify(2, @_); return $upgrade->bacmp($x, $y) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/)) { # handle +-inf and NaN return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/; return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/; return -1; } $CALC->_acmp($x->{value}, $y->{value}); # lib does only 0, 1, -1 } sub beq { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; Carp::croak 'beq() is an instance method, not a class method' unless $selfref; Carp::croak 'Wrong number of arguments for beq()' unless @_ == 1; my $cmp = $self -> bcmp(shift); return defined($cmp) && ! $cmp; } sub bne { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; Carp::croak 'bne() is an instance method, not a class method' unless $selfref; Carp::croak 'Wrong number of arguments for bne()' unless @_ == 1; my $cmp = $self -> bcmp(shift); return defined($cmp) && ! $cmp ? '' : 1; } sub blt { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; Carp::croak 'blt() is an instance method, not a class method' unless $selfref; Carp::croak 'Wrong number of arguments for blt()' unless @_ == 1; my $cmp = $self -> bcmp(shift); return defined($cmp) && $cmp < 0; } sub ble { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; Carp::croak 'ble() is an instance method, not a class method' unless $selfref; Carp::croak 'Wrong number of arguments for ble()' unless @_ == 1; my $cmp = $self -> bcmp(shift); return defined($cmp) && $cmp <= 0; } sub bgt { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; Carp::croak 'bgt() is an instance method, not a class method' unless $selfref; Carp::croak 'Wrong number of arguments for bgt()' unless @_ == 1; my $cmp = $self -> bcmp(shift); return defined($cmp) && $cmp > 0; } sub bge { my $self = shift; my $selfref = ref $self; my $class = $selfref || $self; Carp::croak 'bge() is an instance method, not a class method' unless $selfref; Carp::croak 'Wrong number of arguments for bge()' unless @_ == 1; my $cmp = $self -> bcmp(shift); return defined($cmp) && $cmp >= 0; } ############################################################################### # Arithmetic methods ############################################################################### sub bneg { # (BINT or num_str) return BINT # negate number or make a negated number from string my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return $x if $x->modify('bneg'); # for +0 do not negate (to have always normalized +0). Does nothing for 'NaN' $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value})); $x; } sub babs { # (BINT or num_str) return BINT # make number absolute, or return absolute BINT from string my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); return $x if $x->modify('babs'); # post-normalized abs for internal use (does nothing for NaN) $x->{sign} =~ s/^-/+/; $x; } sub bsgn { # Signum function. my $self = shift; return $self if $self->modify('bsgn'); return $self -> bone("+") if $self -> is_pos(); return $self -> bone("-") if $self -> is_neg(); return $self; # zero or NaN } sub bnorm { # (numstr or BINT) return BINT # Normalize number -- no-op here my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); $x; } sub binc { # increment arg by one my ($class, $x, $a, $p, $r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('binc'); if ($x->{sign} eq '+') { $x->{value} = $CALC->_inc($x->{value}); return $x->round($a, $p, $r); } elsif ($x->{sign} eq '-') { $x->{value} = $CALC->_dec($x->{value}); $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0 return $x->round($a, $p, $r); } # inf, nan handling etc $x->badd($class->bone(), $a, $p, $r); # badd does round } sub bdec { # decrement arg by one my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bdec'); if ($x->{sign} eq '-') { # x already < 0 $x->{value} = $CALC->_inc($x->{value}); } else { return $x->badd($class->bone('-'), @r) unless $x->{sign} eq '+'; # inf or NaN # >= 0 if ($CALC->_is_zero($x->{value})) { # == 0 $x->{value} = $CALC->_one(); $x->{sign} = '-'; # 0 => -1 } else { # > 0 $x->{value} = $CALC->_dec($x->{value}); } } $x->round(@r); } #sub bstrcmp { # my $self = shift; # my $selfref = ref $self; # my $class = $selfref || $self; # # Carp::croak 'bstrcmp() is an instance method, not a class method' # unless $selfref; # Carp::croak 'Wrong number of arguments for bstrcmp()' unless @_ == 1; # # return $self -> bstr() CORE::cmp shift; #} # #sub bstreq { # my $self = shift; # my $selfref = ref $self; # my $class = $selfref || $self; # # Carp::croak 'bstreq() is an instance method, not a class method' # unless $selfref; # Carp::croak 'Wrong number of arguments for bstreq()' unless @_ == 1; # # my $cmp = $self -> bstrcmp(shift); # return defined($cmp) && ! $cmp; #} # #sub bstrne { # my $self = shift; # my $selfref = ref $self; # my $class = $selfref || $self; # # Carp::croak 'bstrne() is an instance method, not a class method' # unless $selfref; # Carp::croak 'Wrong number of arguments for bstrne()' unless @_ == 1; # # my $cmp = $self -> bstrcmp(shift); # return defined($cmp) && ! $cmp ? '' : 1; #} # #sub bstrlt { # my $self = shift; # my $selfref = ref $self; # my $class = $selfref || $self; # # Carp::croak 'bstrlt() is an instance method, not a class method' # unless $selfref; # Carp::croak 'Wrong number of arguments for bstrlt()' unless @_ == 1; # # my $cmp = $self -> bstrcmp(shift); # return defined($cmp) && $cmp < 0; #} # #sub bstrle { # my $self = shift; # my $selfref = ref $self; # my $class = $selfref || $self; # # Carp::croak 'bstrle() is an instance method, not a class method' # unless $selfref; # Carp::croak 'Wrong number of arguments for bstrle()' unless @_ == 1; # # my $cmp = $self -> bstrcmp(shift); # return defined($cmp) && $cmp <= 0; #} # #sub bstrgt { # my $self = shift; # my $selfref = ref $self; # my $class = $selfref || $self; # # Carp::croak 'bstrgt() is an instance method, not a class method' # unless $selfref; # Carp::croak 'Wrong number of arguments for bstrgt()' unless @_ == 1; # # my $cmp = $self -> bstrcmp(shift); # return defined($cmp) && $cmp > 0; #} # #sub bstrge { # my $self = shift; # my $selfref = ref $self; # my $class = $selfref || $self; # # Carp::croak 'bstrge() is an instance method, not a class method' # unless $selfref; # Carp::croak 'Wrong number of arguments for bstrge()' unless @_ == 1; # # my $cmp = $self -> bstrcmp(shift); # return defined($cmp) && $cmp >= 0; #} sub badd { # add second arg (BINT or string) to first (BINT) (modifies first) # return result as BINT # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('badd'); return $upgrade->badd($upgrade->new($x), $upgrade->new($y), @r) if defined $upgrade && ((!$x->isa($class)) || (!$y->isa($class))); $r[3] = $y; # no push! # inf and NaN handling if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/) { # NaN first return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); # inf handling if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) { # +inf++inf or -inf+-inf => same, rest is NaN return $x if $x->{sign} eq $y->{sign}; return $x->bnan(); } # +-inf + something => +inf # something +-inf => +-inf $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/; return $x; } my ($sx, $sy) = ($x->{sign}, $y->{sign}); # get signs if ($sx eq $sy) { $x->{value} = $CALC->_add($x->{value}, $y->{value}); # same sign, abs add } else { my $a = $CALC->_acmp ($y->{value}, $x->{value}); # absolute compare if ($a > 0) { $x->{value} = $CALC->_sub($y->{value}, $x->{value}, 1); # abs sub w/ swap $x->{sign} = $sy; } elsif ($a == 0) { # speedup, if equal, set result to 0 $x->{value} = $CALC->_zero(); $x->{sign} = '+'; } else # a < 0 { $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub } } $x->round(@r); } sub bsub { # (BINT or num_str, BINT or num_str) return BINT # subtract second arg from first, modify first # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x -> modify('bsub'); return $upgrade -> new($x) -> bsub($upgrade -> new($y), @r) if defined $upgrade && (!$x -> isa($class) || !$y -> isa($class)); return $x -> round(@r) if $y -> is_zero(); # To correctly handle the lone special case $x -> bsub($x), we note the # sign of $x, then flip the sign from $y, and if the sign of $x did change, # too, then we caught the special case: my $xsign = $x -> {sign}; $y -> {sign} =~ tr/+-/-+/; # does nothing for NaN if ($xsign ne $x -> {sign}) { # special case of $x -> bsub($x) results in 0 return $x -> bzero(@r) if $xsign =~ /^[+-]$/; return $x -> bnan(); # NaN, -inf, +inf } $x -> badd($y, @r); # badd does not leave internal zeros $y -> {sign} =~ tr/+-/-+/; # refix $y (does nothing for NaN) $x; # already rounded by badd() or no rounding } sub bmul { # multiply the first number by the second number # (BINT or num_str, BINT or num_str) return BINT # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bmul'); return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan)); # inf handling if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) { return $x->bnan() if $x->is_zero() || $y->is_zero(); # result will always be +-inf: # +inf * +/+inf => +inf, -inf * -/-inf => +inf # +inf * -/-inf => -inf, -inf * +/+inf => -inf return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); return $x->binf('-'); } return $upgrade->bmul($x, $upgrade->new($y), @r) if defined $upgrade && !$y->isa($class); $r[3] = $y; # no push here $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + $x->{value} = $CALC->_mul($x->{value}, $y->{value}); # do actual math $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 $x->round(@r); } sub bmuladd { # multiply two numbers and then add the third to the result # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT # set up parameters my ($class, $x, $y, $z, @r) = objectify(3, @_); return $x if $x->modify('bmuladd'); return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan) || ($z->{sign} eq $nan)); # inf handling of x and y if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) { return $x->bnan() if $x->is_zero() || $y->is_zero(); # result will always be +-inf: # +inf * +/+inf => +inf, -inf * -/-inf => +inf # +inf * -/-inf => -inf, -inf * +/+inf => -inf return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); return $x->binf('-'); } # inf handling x*y and z if (($z->{sign} =~ /^[+-]inf$/)) { # something +-inf => +-inf $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/; } return $upgrade->bmuladd($x, $upgrade->new($y), $upgrade->new($z), @r) if defined $upgrade && (!$y->isa($class) || !$z->isa($class) || !$x->isa($class)); # TODO: what if $y and $z have A or P set? $r[3] = $z; # no push here $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => + $x->{value} = $CALC->_mul($x->{value}, $y->{value}); # do actual math $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # no -0 my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); # get signs if ($sx eq $sz) { $x->{value} = $CALC->_add($x->{value}, $z->{value}); # same sign, abs add } else { my $a = $CALC->_acmp ($z->{value}, $x->{value}); # absolute compare if ($a > 0) { $x->{value} = $CALC->_sub($z->{value}, $x->{value}, 1); # abs sub w/ swap $x->{sign} = $sz; } elsif ($a == 0) { # speedup, if equal, set result to 0 $x->{value} = $CALC->_zero(); $x->{sign} = '+'; } else # a < 0 { $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub } } $x->round(@r); } sub bdiv { # This does floored division, where the quotient is floored, i.e., rounded # towards negative infinity. As a consequence, the remainder has the same # sign as the divisor. # Set up parameters. my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify() is costly, so avoid it if we can. if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x -> modify('bdiv'); my $wantarray = wantarray; # call only once # At least one argument is NaN. Return NaN for both quotient and the # modulo/remainder. if ($x -> is_nan() || $y -> is_nan()) { return $wantarray ? ($x -> bnan(), $class -> bnan()) : $x -> bnan(); } # Divide by zero and modulo zero. # # Division: Use the common convention that x / 0 is inf with the same sign # as x, except when x = 0, where we return NaN. This is also what earlier # versions did. # # Modulo: In modular arithmetic, the congruence relation z = x (mod y) # means that there is some integer k such that z - x = k y. If y = 0, we # get z - x = 0 or z = x. This is also what earlier versions did, except # that 0 % 0 returned NaN. # # inf / 0 = inf inf % 0 = inf # 5 / 0 = inf 5 % 0 = 5 # 0 / 0 = NaN 0 % 0 = 0 # -5 / 0 = -inf -5 % 0 = -5 # -inf / 0 = -inf -inf % 0 = -inf if ($y -> is_zero()) { my $rem; if ($wantarray) { $rem = $x -> copy(); } if ($x -> is_zero()) { $x -> bnan(); } else { $x -> binf($x -> {sign}); } return $wantarray ? ($x, $rem) : $x; } # Numerator (dividend) is +/-inf, and denominator is finite and non-zero. # The divide by zero cases are covered above. In all of the cases listed # below we return the same as core Perl. # # inf / -inf = NaN inf % -inf = NaN # inf / -5 = -inf inf % -5 = NaN # inf / 5 = inf inf % 5 = NaN # inf / inf = NaN inf % inf = NaN # # -inf / -inf = NaN -inf % -inf = NaN # -inf / -5 = inf -inf % -5 = NaN # -inf / 5 = -inf -inf % 5 = NaN # -inf / inf = NaN -inf % inf = NaN if ($x -> is_inf()) { my $rem; $rem = $class -> bnan() if $wantarray; if ($y -> is_inf()) { $x -> bnan(); } else { my $sign = $x -> bcmp(0) == $y -> bcmp(0) ? '+' : '-'; $x -> binf($sign); } return $wantarray ? ($x, $rem) : $x; } # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf # are covered above. In the modulo cases (in the right column) we return # the same as core Perl, which does floored division, so for consistency we # also do floored division in the division cases (in the left column). # # -5 / inf = -1 -5 % inf = inf # 0 / inf = 0 0 % inf = 0 # 5 / inf = 0 5 % inf = 5 # # -5 / -inf = 0 -5 % -inf = -5 # 0 / -inf = 0 0 % -inf = 0 # 5 / -inf = -1 5 % -inf = -inf if ($y -> is_inf()) { my $rem; if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) { $rem = $x -> copy() if $wantarray; $x -> bzero(); } else { $rem = $class -> binf($y -> {sign}) if $wantarray; $x -> bone('-'); } return $wantarray ? ($x, $rem) : $x; } # At this point, both the numerator and denominator are finite numbers, and # the denominator (divisor) is non-zero. return $upgrade -> bdiv($upgrade -> new($x), $upgrade -> new($y), @r) if defined $upgrade; $r[3] = $y; # no push! # Inialize remainder. my $rem = $class -> bzero(); # Are both operands the same object, i.e., like $x -> bdiv($x)? If so, # flipping the sign of $y also flips the sign of $x. my $xsign = $x -> {sign}; my $ysign = $y -> {sign}; $y -> {sign} =~ tr/+-/-+/; # Flip the sign of $y, and see ... my $same = $xsign ne $x -> {sign}; # ... if that changed the sign of $x. $y -> {sign} = $ysign; # Re-insert the original sign. if ($same) { $x -> bone(); } else { ($x -> {value}, $rem -> {value}) = $CALC -> _div($x -> {value}, $y -> {value}); if ($CALC -> _is_zero($rem -> {value})) { if ($xsign eq $ysign || $CALC -> _is_zero($x -> {value})) { $x -> {sign} = '+'; } else { $x -> {sign} = '-'; } } else { if ($xsign eq $ysign) { $x -> {sign} = '+'; } else { if ($xsign eq '+') { $x -> badd(1); } else { $x -> bsub(1); } $x -> {sign} = '-'; } } } $x -> round(@r); if ($wantarray) { unless ($CALC -> _is_zero($rem -> {value})) { if ($xsign ne $ysign) { $rem = $y -> copy() -> babs() -> bsub($rem); } $rem -> {sign} = $ysign; } $rem -> {_a} = $x -> {_a}; $rem -> {_p} = $x -> {_p}; $rem -> round(@r); return ($x, $rem); } return $x; } sub btdiv { # This does truncated division, where the quotient is truncted, i.e., # rounded towards zero. # # ($q, $r) = $x -> btdiv($y) returns $q and $r so that $q is int($x / $y) # and $q * $y + $r = $x. # Set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if we can. if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x -> modify('btdiv'); my $wantarray = wantarray; # call only once # At least one argument is NaN. Return NaN for both quotient and the # modulo/remainder. if ($x -> is_nan() || $y -> is_nan()) { return $wantarray ? ($x -> bnan(), $class -> bnan()) : $x -> bnan(); } # Divide by zero and modulo zero. # # Division: Use the common convention that x / 0 is inf with the same sign # as x, except when x = 0, where we return NaN. This is also what earlier # versions did. # # Modulo: In modular arithmetic, the congruence relation z = x (mod y) # means that there is some integer k such that z - x = k y. If y = 0, we # get z - x = 0 or z = x. This is also what earlier versions did, except # that 0 % 0 returned NaN. # # inf / 0 = inf inf % 0 = inf # 5 / 0 = inf 5 % 0 = 5 # 0 / 0 = NaN 0 % 0 = 0 # -5 / 0 = -inf -5 % 0 = -5 # -inf / 0 = -inf -inf % 0 = -inf if ($y -> is_zero()) { my $rem; if ($wantarray) { $rem = $x -> copy(); } if ($x -> is_zero()) { $x -> bnan(); } else { $x -> binf($x -> {sign}); } return $wantarray ? ($x, $rem) : $x; } # Numerator (dividend) is +/-inf, and denominator is finite and non-zero. # The divide by zero cases are covered above. In all of the cases listed # below we return the same as core Perl. # # inf / -inf = NaN inf % -inf = NaN # inf / -5 = -inf inf % -5 = NaN # inf / 5 = inf inf % 5 = NaN # inf / inf = NaN inf % inf = NaN # # -inf / -inf = NaN -inf % -inf = NaN # -inf / -5 = inf -inf % -5 = NaN # -inf / 5 = -inf -inf % 5 = NaN # -inf / inf = NaN -inf % inf = NaN if ($x -> is_inf()) { my $rem; $rem = $class -> bnan() if $wantarray; if ($y -> is_inf()) { $x -> bnan(); } else { my $sign = $x -> bcmp(0) == $y -> bcmp(0) ? '+' : '-'; $x -> binf($sign); } return $wantarray ? ($x, $rem) : $x; } # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf # are covered above. In the modulo cases (in the right column) we return # the same as core Perl, which does floored division, so for consistency we # also do floored division in the division cases (in the left column). # # -5 / inf = 0 -5 % inf = -5 # 0 / inf = 0 0 % inf = 0 # 5 / inf = 0 5 % inf = 5 # # -5 / -inf = 0 -5 % -inf = -5 # 0 / -inf = 0 0 % -inf = 0 # 5 / -inf = 0 5 % -inf = 5 if ($y -> is_inf()) { my $rem; $rem = $x -> copy() if $wantarray; $x -> bzero(); return $wantarray ? ($x, $rem) : $x; } return $upgrade -> btdiv($upgrade -> new($x), $upgrade -> new($y), @r) if defined $upgrade; $r[3] = $y; # no push! # Inialize remainder. my $rem = $class -> bzero(); # Are both operands the same object, i.e., like $x -> bdiv($x)? If so, # flipping the sign of $y also flips the sign of $x. my $xsign = $x -> {sign}; my $ysign = $y -> {sign}; $y -> {sign} =~ tr/+-/-+/; # Flip the sign of $y, and see ... my $same = $xsign ne $x -> {sign}; # ... if that changed the sign of $x. $y -> {sign} = $ysign; # Re-insert the original sign. if ($same) { $x -> bone(); } else { ($x -> {value}, $rem -> {value}) = $CALC -> _div($x -> {value}, $y -> {value}); $x -> {sign} = $xsign eq $ysign ? '+' : '-'; $x -> {sign} = '+' if $CALC -> _is_zero($x -> {value}); $x -> round(@r); } if (wantarray) { $rem -> {sign} = $xsign; $rem -> {sign} = '+' if $CALC -> _is_zero($rem -> {value}); $rem -> {_a} = $x -> {_a}; $rem -> {_p} = $x -> {_p}; $rem -> round(@r); return ($x, $rem); } return $x; } sub bmod { # This is the remainder after floored division. # Set up parameters. my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x -> modify('bmod'); $r[3] = $y; # no push! # At least one argument is NaN. if ($x -> is_nan() || $y -> is_nan()) { return $x -> bnan(); } # Modulo zero. See documentation for bdiv(). if ($y -> is_zero()) { return $x; } # Numerator (dividend) is +/-inf. if ($x -> is_inf()) { return $x -> bnan(); } # Denominator (divisor) is +/-inf. if ($y -> is_inf()) { if ($x -> is_zero() || $x -> bcmp(0) == $y -> bcmp(0)) { return $x; } else { return $x -> binf($y -> sign()); } } # Calc new sign and in case $y == +/- 1, return $x. $x -> {value} = $CALC -> _mod($x -> {value}, $y -> {value}); if ($CALC -> _is_zero($x -> {value})) { $x -> {sign} = '+'; # do not leave -0 } else { $x -> {value} = $CALC -> _sub($y -> {value}, $x -> {value}, 1) # $y-$x if ($x -> {sign} ne $y -> {sign}); $x -> {sign} = $y -> {sign}; } $x -> round(@r); } sub btmod { # Remainder after truncated division. # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x -> modify('btmod'); # At least one argument is NaN. if ($x -> is_nan() || $y -> is_nan()) { return $x -> bnan(); } # Modulo zero. See documentation for btdiv(). if ($y -> is_zero()) { return $x; } # Numerator (dividend) is +/-inf. if ($x -> is_inf()) { return $x -> bnan(); } # Denominator (divisor) is +/-inf. if ($y -> is_inf()) { return $x; } return $upgrade -> btmod($upgrade -> new($x), $upgrade -> new($y), @r) if defined $upgrade; $r[3] = $y; # no push! my $xsign = $x -> {sign}; my $ysign = $y -> {sign}; $x -> {value} = $CALC -> _mod($x -> {value}, $y -> {value}); $x -> {sign} = $xsign; $x -> {sign} = '+' if $CALC -> _is_zero($x -> {value}); $x -> round(@r); return $x; } sub bmodinv { # Return modular multiplicative inverse: # # z is the modular inverse of x (mod y) if and only if # # x*z ≡ 1 (mod y) # # If the modulus y is larger than one, x and z are relative primes (i.e., # their greatest common divisor is one). # # If no modular multiplicative inverse exists, NaN is returned. # set up parameters my ($class, $x, $y, @r) = (undef, @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bmodinv'); # Return NaN if one or both arguments is +inf, -inf, or nan. return $x->bnan() if ($y->{sign} !~ /^[+-]$/ || $x->{sign} !~ /^[+-]$/); # Return NaN if $y is zero; 1 % 0 makes no sense. return $x->bnan() if $y->is_zero(); # Return 0 in the trivial case. $x % 1 or $x % -1 is zero for all finite # integers $x. return $x->bzero() if ($y->is_one() || $y->is_one('-')); # Return NaN if $x = 0, or $x modulo $y is zero. The only valid case when # $x = 0 is when $y = 1 or $y = -1, but that was covered above. # # Note that computing $x modulo $y here affects the value we'll feed to # $CALC->_modinv() below when $x and $y have opposite signs. E.g., if $x = # 5 and $y = 7, those two values are fed to _modinv(), but if $x = -5 and # $y = 7, the values fed to _modinv() are $x = 2 (= -5 % 7) and $y = 7. # The value if $x is affected only when $x and $y have opposite signs. $x->bmod($y); return $x->bnan() if $x->is_zero(); # Compute the modular multiplicative inverse of the absolute values. We'll # correct for the signs of $x and $y later. Return NaN if no GCD is found. ($x->{value}, $x->{sign}) = $CALC->_modinv($x->{value}, $y->{value}); return $x->bnan() if !defined $x->{value}; # Library inconsistency workaround: _modinv() in Math::BigInt::GMP versions # <= 1.32 return undef rather than a "+" for the sign. $x->{sign} = '+' unless defined $x->{sign}; # When one or both arguments are negative, we have the following # relations. If x and y are positive: # # modinv(-x, -y) = -modinv(x, y) # modinv(-x, y) = y - modinv(x, y) = -modinv(x, y) (mod y) # modinv( x, -y) = modinv(x, y) - y = modinv(x, y) (mod -y) # We must swap the sign of the result if the original $x is negative. # However, we must compensate for ignoring the signs when computing the # inverse modulo. The net effect is that we must swap the sign of the # result if $y is negative. $x -> bneg() if $y->{sign} eq '-'; # Compute $x modulo $y again after correcting the sign. $x -> bmod($y) if $x->{sign} ne $y->{sign}; return $x; } sub bmodpow { # Modular exponentiation. Raises a very large number to a very large exponent # in a given very large modulus quickly, thanks to binary exponentiation. # Supports negative exponents. my ($class, $num, $exp, $mod, @r) = objectify(3, @_); return $num if $num->modify('bmodpow'); # When the exponent 'e' is negative, use the following relation, which is # based on finding the multiplicative inverse 'd' of 'b' modulo 'm': # # b^(-e) (mod m) = d^e (mod m) where b*d = 1 (mod m) $num->bmodinv($mod) if ($exp->{sign} eq '-'); # Check for valid input. All operands must be finite, and the modulus must be # non-zero. return $num->bnan() if ($num->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf $exp->{sign} =~ /NaN|inf/ || # NaN, -inf, +inf $mod->{sign} =~ /NaN|inf/); # NaN, -inf, +inf # Modulo zero. See documentation for Math::BigInt's bmod() method. if ($mod -> is_zero()) { if ($num -> is_zero()) { return $class -> bnan(); } else { return $num -> copy(); } } # Compute 'a (mod m)', ignoring the signs on 'a' and 'm'. If the resulting # value is zero, the output is also zero, regardless of the signs on 'a' and # 'm'. my $value = $CALC->_modpow($num->{value}, $exp->{value}, $mod->{value}); my $sign = '+'; # If the resulting value is non-zero, we have four special cases, depending # on the signs on 'a' and 'm'. unless ($CALC->_is_zero($value)) { # There is a negative sign on 'a' (= $num**$exp) only if the number we # are exponentiating ($num) is negative and the exponent ($exp) is odd. if ($num->{sign} eq '-' && $exp->is_odd()) { # When both the number 'a' and the modulus 'm' have a negative sign, # use this relation: # # -a (mod -m) = -(a (mod m)) if ($mod->{sign} eq '-') { $sign = '-'; } # When only the number 'a' has a negative sign, use this relation: # # -a (mod m) = m - (a (mod m)) else { # Use copy of $mod since _sub() modifies the first argument. my $mod = $CALC->_copy($mod->{value}); $value = $CALC->_sub($mod, $value); $sign = '+'; } } else { # When only the modulus 'm' has a negative sign, use this relation: # # a (mod -m) = (a (mod m)) - m # = -(m - (a (mod m))) if ($mod->{sign} eq '-') { # Use copy of $mod since _sub() modifies the first argument. my $mod = $CALC->_copy($mod->{value}); $value = $CALC->_sub($mod, $value); $sign = '-'; } # When neither the number 'a' nor the modulus 'm' have a negative # sign, directly return the already computed value. # # (a (mod m)) } } $num->{value} = $value; $num->{sign} = $sign; return $num; } sub bpow { # (BINT or num_str, BINT or num_str) return BINT # compute power of two numbers -- stolen from Knuth Vol 2 pg 233 # modifies first argument # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bpow'); return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan; # inf handling if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/)) { if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/)) { # +-inf ** +-inf return $x->bnan(); } # +-inf ** Y if ($x->{sign} =~ /^[+-]inf/) { # +inf ** 0 => NaN return $x->bnan() if $y->is_zero(); # -inf ** -1 => 1/inf => 0 return $x->bzero() if $y->is_one('-') && $x->is_negative(); # +inf ** Y => inf return $x if $x->{sign} eq '+inf'; # -inf ** Y => -inf if Y is odd return $x if $y->is_odd(); return $x->babs(); } # X ** +-inf # 1 ** +inf => 1 return $x if $x->is_one(); # 0 ** inf => 0 return $x if $x->is_zero() && $y->{sign} =~ /^[+]/; # 0 ** -inf => inf return $x->binf() if $x->is_zero(); # -1 ** -inf => NaN return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/; # -X ** -inf => 0 return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/; # -1 ** inf => NaN return $x->bnan() if $x->{sign} eq '-'; # X ** inf => inf return $x->binf() if $y->{sign} =~ /^[+]/; # X ** -inf => 0 return $x->bzero(); } return $upgrade->bpow($upgrade->new($x), $y, @r) if defined $upgrade && (!$y->isa($class) || $y->{sign} eq '-'); $r[3] = $y; # no push! # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu my $new_sign = '+'; $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+'); # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf return $x->binf() if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value}); # 1 ** -y => 1 / (1 ** |y|) # so do test for negative $y after above's clause return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value}); $x->{value} = $CALC->_pow($x->{value}, $y->{value}); $x->{sign} = $new_sign; $x->{sign} = '+' if $CALC->_is_zero($y->{value}); $x->round(@r); } sub blog { # Return the logarithm of the operand. If a second operand is defined, that # value is used as the base, otherwise the base is assumed to be Euler's # constant. # Don't objectify the base, since an undefined base, as in $x->blog() or # $x->blog(undef) signals that the base is Euler's number. # set up parameters my ($class, $x, $base, @r) = (undef, @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $base, @r) = objectify(2, @_); } return $x if $x->modify('blog'); # Handle all exception cases and all trivial cases. I have used Wolfram # Alpha (http://www.wolframalpha.com) as the reference for these cases. return $x -> bnan() if $x -> is_nan(); if (defined $base) { $base = $class -> new($base) unless ref $base; if ($base -> is_nan() || $base -> is_one()) { return $x -> bnan(); } elsif ($base -> is_inf() || $base -> is_zero()) { return $x -> bnan() if $x -> is_inf() || $x -> is_zero(); return $x -> bzero(); } elsif ($base -> is_negative()) { # -inf < base < 0 return $x -> bzero() if $x -> is_one(); # x = 1 return $x -> bone() if $x == $base; # x = base return $x -> bnan(); # otherwise } return $x -> bone() if $x == $base; # 0 < base && 0 < x < inf } # We now know that the base is either undefined or >= 2 and finite. return $x -> binf('+') if $x -> is_inf(); # x = +/-inf return $x -> bnan() if $x -> is_neg(); # -inf < x < 0 return $x -> bzero() if $x -> is_one(); # x = 1 return $x -> binf('-') if $x -> is_zero(); # x = 0 # At this point we are done handling all exception cases and trivial cases. return $upgrade -> blog($upgrade -> new($x), $base, @r) if defined $upgrade; # fix for bug #24969: # the default base is e (Euler's number) which is not an integer if (!defined $base) { require Math::BigFloat; my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int(); # modify $x in place $x->{value} = $u->{value}; $x->{sign} = $u->{sign}; return $x; } my ($rc, $exact) = $CALC->_log_int($x->{value}, $base->{value}); return $x->bnan() unless defined $rc; # not possible to take log? $x->{value} = $rc; $x->round(@r); } sub bexp { # Calculate e ** $x (Euler's number to the power of X), truncated to # an integer value. my ($class, $x, @r) = ref($_[0]) ? (ref($_[0]), @_) : objectify(1, @_); return $x if $x->modify('bexp'); # inf, -inf, NaN, <0 => NaN return $x->bnan() if $x->{sign} eq 'NaN'; return $x->bone() if $x->is_zero(); return $x if $x->{sign} eq '+inf'; return $x->bzero() if $x->{sign} eq '-inf'; my $u; { # run through Math::BigFloat unless told otherwise require Math::BigFloat unless defined $upgrade; local $upgrade = 'Math::BigFloat' unless defined $upgrade; # calculate result, truncate it to integer $u = $upgrade->bexp($upgrade->new($x), @r); } if (defined $upgrade) { $x = $u; } else { $u = $u->as_int(); # modify $x in place $x->{value} = $u->{value}; $x->round(@r); } } sub bnok { # Calculate n over k (binomial coefficient or "choose" function) as integer. # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bnok'); return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN'; return $x->binf() if $x->{sign} eq '+inf'; # k > n or k < 0 => 0 my $cmp = $x->bacmp($y); return $x->bzero() if $cmp < 0 || substr($y->{sign}, 0, 1) eq "-"; if ($CALC->can('_nok')) { $x->{value} = $CALC->_nok($x->{value}, $y->{value}); } else { # ( 7 ) 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 6 7 # ( - ) = --------- = --------------- = --------- = 5 * - * - # ( 3 ) (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 2 3 my $n = $x -> {value}; my $k = $y -> {value}; # If k > n/2, or, equivalently, 2*k > n, compute nok(n, k) as # nok(n, n-k) to minimize the number if iterations in the loop. { my $twok = $CALC->_mul($CALC->_two(), $CALC->_copy($k)); if ($CALC->_acmp($twok, $n) > 0) { $k = $CALC->_sub($CALC->_copy($n), $k); } } if ($CALC->_is_zero($k)) { $n = $CALC->_one(); } else { # Make a copy of the original n, since we'll be modifying n # in-place. my $n_orig = $CALC->_copy($n); $CALC->_sub($n, $k); $CALC->_inc($n); my $f = $CALC->_copy($n); $CALC->_inc($f); my $d = $CALC->_two(); # while f <= n (the original n, that is) ... while ($CALC->_acmp($f, $n_orig) <= 0) { $CALC->_mul($n, $f); $CALC->_div($n, $d); $CALC->_inc($f); $CALC->_inc($d); } } $x -> {value} = $n; } $x->round(@r); } sub bsin { # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the # result truncated to an integer. my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); return $x if $x->modify('bsin'); return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN return $upgrade->new($x)->bsin(@r) if defined $upgrade; require Math::BigFloat; # calculate the result and truncate it to integer my $t = Math::BigFloat->new($x)->bsin(@r)->as_int(); $x->bone() if $t->is_one(); $x->bzero() if $t->is_zero(); $x->round(@r); } sub bcos { # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the # result truncated to an integer. my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); return $x if $x->modify('bcos'); return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN return $upgrade->new($x)->bcos(@r) if defined $upgrade; require Math::BigFloat; # calculate the result and truncate it to integer my $t = Math::BigFloat->new($x)->bcos(@r)->as_int(); $x->bone() if $t->is_one(); $x->bzero() if $t->is_zero(); $x->round(@r); } sub batan { # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the # result truncated to an integer. my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); return $x if $x->modify('batan'); return $x->bnan() if $x->{sign} !~ /^[+-]\z/; # -inf +inf or NaN => NaN return $upgrade->new($x)->batan(@r) if defined $upgrade; # calculate the result and truncate it to integer my $t = Math::BigFloat->new($x)->batan(@r); $x->{value} = $CALC->_new($x->as_int()->bstr()); $x->round(@r); } sub batan2 { # calculate arcus tangens of ($y/$x) # set up parameters my ($class, $y, $x, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $y, $x, @r) = objectify(2, @_); } return $y if $y->modify('batan2'); return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan); # Y X # != 0 -inf result is +- pi if ($x->is_inf() || $y->is_inf()) { # upgrade to Math::BigFloat etc. return $upgrade->new($y)->batan2($upgrade->new($x), @r) if defined $upgrade; if ($y->is_inf()) { if ($x->{sign} eq '-inf') { # calculate 3 pi/4 => 2.3.. => 2 $y->bone(substr($y->{sign}, 0, 1)); $y->bmul($class->new(2)); } elsif ($x->{sign} eq '+inf') { # calculate pi/4 => 0.7 => 0 $y->bzero(); } else { # calculate pi/2 => 1.5 => 1 $y->bone(substr($y->{sign}, 0, 1)); } } else { if ($x->{sign} eq '+inf') { # calculate pi/4 => 0.7 => 0 $y->bzero(); } else { # PI => 3.1415.. => 3 $y->bone(substr($y->{sign}, 0, 1)); $y->bmul($class->new(3)); } } return $y; } return $upgrade->new($y)->batan2($upgrade->new($x), @r) if defined $upgrade; require Math::BigFloat; my $r = Math::BigFloat->new($y) ->batan2(Math::BigFloat->new($x), @r) ->as_int(); $x->{value} = $r->{value}; $x->{sign} = $r->{sign}; $x; } sub bsqrt { # calculate square root of $x my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); return $x if $x->modify('bsqrt'); return $x->bnan() if $x->{sign} !~ /^\+/; # -x or -inf or NaN => NaN return $x if $x->{sign} eq '+inf'; # sqrt(+inf) == inf return $upgrade->bsqrt($x, @r) if defined $upgrade; $x->{value} = $CALC->_sqrt($x->{value}); $x->round(@r); } sub broot { # calculate $y'th root of $x # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); $y = $class->new(2) unless defined $y; # objectify is costly, so avoid it if ((!ref($x)) || (ref($x) ne ref($y))) { ($class, $x, $y, @r) = objectify(2, $class || $class, @_); } return $x if $x->modify('broot'); # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0 return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() || $y->{sign} !~ /^\+$/; return $x->round(@r) if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one(); return $upgrade->new($x)->broot($upgrade->new($y), @r) if defined $upgrade; $x->{value} = $CALC->_root($x->{value}, $y->{value}); $x->round(@r); } sub bfac { # (BINT or num_str, BINT or num_str) return BINT # compute factorial number from $x, modify $x in place my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); return $x if $x->modify('bfac') || $x->{sign} eq '+inf'; # inf => inf return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN $x->{value} = $CALC->_fac($x->{value}); $x->round(@r); } sub bdfac { # compute factorial number from $x, modify $x in place my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); return $x if $x->modify('bdfac') || $x->{sign} eq '+inf'; # inf => inf return $x->bnan() if $x->{sign} ne '+'; # NaN, <0 etc => NaN $x->{value} = $CALC->_dfac($x->{value}); $x->round(@r); } sub blsft { # (BINT or num_str, BINT or num_str) return BINT # compute x << y, base n, y >= 0 # set up parameters my ($class, $x, $y, $b, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $b, @r) = objectify(2, @_); } return $x if $x -> modify('blsft'); return $x -> bnan() if ($x -> {sign} !~ /^[+-]$/ || $y -> {sign} !~ /^[+-]$/); return $x -> round(@r) if $y -> is_zero(); $b = 2 if !defined $b; return $x -> bnan() if $b <= 0 || $y -> {sign} eq '-'; $x -> {value} = $CALC -> _lsft($x -> {value}, $y -> {value}, $b); $x -> round(@r); } sub brsft { # (BINT or num_str, BINT or num_str) return BINT # compute x >> y, base n, y >= 0 # set up parameters my ($class, $x, $y, $b, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, $b, @r) = objectify(2, @_); } return $x if $x -> modify('brsft'); return $x -> bnan() if ($x -> {sign} !~ /^[+-]$/ || $y -> {sign} !~ /^[+-]$/); return $x -> round(@r) if $y -> is_zero(); return $x -> bzero(@r) if $x -> is_zero(); # 0 => 0 $b = 2 if !defined $b; return $x -> bnan() if $b <= 0 || $y -> {sign} eq '-'; # this only works for negative numbers when shifting in base 2 if (($x -> {sign} eq '-') && ($b == 2)) { return $x -> round(@r) if $x -> is_one('-'); # -1 => -1 if (!$y -> is_one()) { # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et # al but perhaps there is a better emulation for two's complement # shift... # if $y != 1, we must simulate it by doing: # convert to bin, flip all bits, shift, and be done $x -> binc(); # -3 => -2 my $bin = $x -> as_bin(); $bin =~ s/^-0b//; # strip '-0b' prefix $bin =~ tr/10/01/; # flip bits # now shift if ($y >= CORE::length($bin)) { $bin = '0'; # shifting to far right creates -1 # 0, because later increment makes # that 1, attached '-' makes it '-1' # because -1 >> x == -1 ! } else { $bin =~ s/.{$y}$//; # cut off at the right side $bin = '1' . $bin; # extend left side by one dummy '1' $bin =~ tr/10/01/; # flip bits back } my $res = $class -> new('0b' . $bin); # add prefix and convert back $res -> binc(); # remember to increment $x -> {value} = $res -> {value}; # take over value return $x -> round(@r); # we are done now, magic, isn't? } # x < 0, n == 2, y == 1 $x -> bdec(); # n == 2, but $y == 1: this fixes it } $x -> {value} = $CALC -> _rsft($x -> {value}, $y -> {value}, $b); $x -> round(@r); } ############################################################################### # Bitwise methods ############################################################################### sub band { #(BINT or num_str, BINT or num_str) return BINT # compute x & y # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('band'); $r[3] = $y; # no push! return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); my $sx = $x->{sign} eq '+' ? 1 : -1; my $sy = $y->{sign} eq '+' ? 1 : -1; if ($sx == 1 && $sy == 1) { $x->{value} = $CALC->_and($x->{value}, $y->{value}); return $x->round(@r); } if ($CAN{signed_and}) { $x->{value} = $CALC->_signed_and($x->{value}, $y->{value}, $sx, $sy); return $x->round(@r); } require $EMU_LIB; __emu_band($class, $x, $y, $sx, $sy, @r); } sub bior { #(BINT or num_str, BINT or num_str) return BINT # compute x | y # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bior'); $r[3] = $y; # no push! return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); my $sx = $x->{sign} eq '+' ? 1 : -1; my $sy = $y->{sign} eq '+' ? 1 : -1; # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior() # don't use lib for negative values if ($sx == 1 && $sy == 1) { $x->{value} = $CALC->_or($x->{value}, $y->{value}); return $x->round(@r); } # if lib can do negative values, let it handle this if ($CAN{signed_or}) { $x->{value} = $CALC->_signed_or($x->{value}, $y->{value}, $sx, $sy); return $x->round(@r); } require $EMU_LIB; __emu_bior($class, $x, $y, $sx, $sy, @r); } sub bxor { #(BINT or num_str, BINT or num_str) return BINT # compute x ^ y # set up parameters my ($class, $x, $y, @r) = (ref($_[0]), @_); # objectify is costly, so avoid it if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1]))) { ($class, $x, $y, @r) = objectify(2, @_); } return $x if $x->modify('bxor'); $r[3] = $y; # no push! return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/); my $sx = $x->{sign} eq '+' ? 1 : -1; my $sy = $y->{sign} eq '+' ? 1 : -1; # don't use lib for negative values if ($sx == 1 && $sy == 1) { $x->{value} = $CALC->_xor($x->{value}, $y->{value}); return $x->round(@r); } # if lib can do negative values, let it handle this if ($CAN{signed_xor}) { $x->{value} = $CALC->_signed_xor($x->{value}, $y->{value}, $sx, $sy); return $x->round(@r); } require $EMU_LIB; __emu_bxor($class, $x, $y, $sx, $sy, @r); } sub bnot { # (num_str or BINT) return BINT # represent ~x as twos-complement number # we don't need $class, so undef instead of ref($_[0]) make it slightly faster my ($class, $x, $a, $p, $r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); return $x if $x->modify('bnot'); $x->binc()->bneg(); # binc already does round } ############################################################################### # Rounding methods ############################################################################### sub round { # Round $self according to given parameters, or given second argument's # parameters or global defaults # for speed reasons, _find_round_parameters is embedded here: my ($self, $a, $p, $r, @args) = @_; # $a accuracy, if given by caller # $p precision, if given by caller # $r round_mode, if given by caller # @args all 'other' arguments (0 for unary, 1 for binary ops) my $class = ref($self); # find out class of argument(s) no strict 'refs'; # now pick $a or $p, but only if we have got "arguments" if (!defined $a) { foreach ($self, @args) { # take the defined one, or if both defined, the one that is smaller $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); } } if (!defined $p) { # even if $a is defined, take $p, to signal error for both defined foreach ($self, @args) { # take the defined one, or if both defined, the one that is bigger # -2 > -3, and 3 > 2 $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); } } # if still none defined, use globals (#2) $a = ${"$class\::accuracy"} unless defined $a; $p = ${"$class\::precision"} unless defined $p; # A == 0 is useless, so undef it to signal no rounding $a = undef if defined $a && $a == 0; # no rounding today? return $self unless defined $a || defined $p; # early out # set A and set P is an fatal error return $self->bnan() if defined $a && defined $p; $r = ${"$class\::round_mode"} unless defined $r; if ($r !~ /^(even|odd|[+-]inf|zero|trunc|common)$/) { Carp::croak("Unknown round mode '$r'"); } # now round, by calling either bround or bfround: if (defined $a) { $self->bround(int($a), $r) if !defined $self->{_a} || $self->{_a} >= $a; } else { # both can't be undefined due to early out $self->bfround(int($p), $r) if !defined $self->{_p} || $self->{_p} <= $p; } # bround() or bfround() already called bnorm() if nec. $self; } sub bround { # accuracy: +$n preserve $n digits from left, # -$n preserve $n digits from right (f.i. for 0.1234 style in MBF) # no-op for $n == 0 # and overwrite the rest with 0's, return normalized number # do not return $x->bnorm(), but $x my $x = shift; $x = $class->new($x) unless ref $x; my ($scale, $mode) = $x->_scale_a(@_); return $x if !defined $scale || $x->modify('bround'); # no-op if ($x->is_zero() || $scale == 0) { $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 return $x; } return $x if $x->{sign} !~ /^[+-]$/; # inf, NaN # we have fewer digits than we want to scale to my $len = $x->length(); # convert $scale to a scalar in case it is an object (put's a limit on the # number length, but this would already limited by memory constraints), makes # it faster $scale = $scale->numify() if ref ($scale); # scale < 0, but > -len (not >=!) if (($scale < 0 && $scale < -$len-1) || ($scale >= $len)) { $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2 return $x; } # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6 my ($pad, $digit_round, $digit_after); $pad = $len - $scale; $pad = abs($scale-1) if $scale < 0; # do not use digit(), it is very costly for binary => decimal # getting the entire string is also costly, but we need to do it only once my $xs = $CALC->_str($x->{value}); my $pl = -$pad-1; # pad: 123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4 # pad+1: 123: 0 => 0, at 1 => -1, at 2 => -2, at 3 => -3 $digit_round = '0'; $digit_round = substr($xs, $pl, 1) if $pad <= $len; $pl++; $pl ++ if $pad >= $len; $digit_after = '0'; $digit_after = substr($xs, $pl, 1) if $pad > 0; # in case of 01234 we round down, for 6789 up, and only in case 5 we look # closer at the remaining digits of the original $x, remember decision my $round_up = 1; # default round up $round_up -- if ($mode eq 'trunc') || # trunc by round down ($digit_after =~ /[01234]/) || # round down anyway, # 6789 => round up ($digit_after eq '5') && # not 5000...0000 ($x->_scan_for_nonzero($pad, $xs, $len) == 0) && ( ($mode eq 'even') && ($digit_round =~ /[24680]/) || ($mode eq 'odd') && ($digit_round =~ /[13579]/) || ($mode eq '+inf') && ($x->{sign} eq '-') || ($mode eq '-inf') && ($x->{sign} eq '+') || ($mode eq 'zero') # round down if zero, sign adjusted below ); my $put_back = 0; # not yet modified if (($pad > 0) && ($pad <= $len)) { substr($xs, -$pad, $pad) = '0' x $pad; # replace with '00...' $put_back = 1; # need to put back } elsif ($pad > $len) { $x->bzero(); # round to '0' } if ($round_up) { # what gave test above? $put_back = 1; # need to put back $pad = $len, $xs = '0' x $pad if $scale < 0; # tlr: whack 0.51=>1.0 # we modify directly the string variant instead of creating a number and # adding it, since that is faster (we already have the string) my $c = 0; $pad ++; # for $pad == $len case while ($pad <= $len) { $c = substr($xs, -$pad, 1) + 1; $c = '0' if $c eq '10'; substr($xs, -$pad, 1) = $c; $pad++; last if $c != 0; # no overflow => early out } $xs = '1'.$xs if $c == 0; } $x->{value} = $CALC->_new($xs) if $put_back == 1; # put back, if needed $x->{_a} = $scale if $scale >= 0; if ($scale < 0) { $x->{_a} = $len+$scale; $x->{_a} = 0 if $scale < -$len; } $x; } sub bfround { # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.' # $n == 0 || $n == 1 => round to integer my $x = shift; my $class = ref($x) || $x; $x = $class->new($x) unless ref $x; my ($scale, $mode) = $x->_scale_p(@_); return $x if !defined $scale || $x->modify('bfround'); # no-op # no-op for Math::BigInt objects if $n <= 0 $x->bround($x->length()-$scale, $mode) if $scale > 0; delete $x->{_a}; # delete to save memory $x->{_p} = $scale; # store new _p $x; } sub fround { # Exists to make life easier for switch between MBF and MBI (should we # autoload fxxx() like MBF does for bxxx()?) my $x = shift; $x = $class->new($x) unless ref $x; $x->bround(@_); } sub bfloor { # round towards minus infinity; no-op since it's already integer my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); $x->round(@r); } sub bceil { # round towards plus infinity; no-op since it's already int my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); $x->round(@r); } sub bint { # round towards zero; no-op since it's already integer my ($class, $x, @r) = ref($_[0]) ? (undef, @_) : objectify(1, @_); $x->round(@r); } ############################################################################### # Other mathematical methods ############################################################################### sub bgcd { # (BINT or num_str, BINT or num_str) return BINT # does not modify arguments, but returns new object # GCD -- Euclid's algorithm, variant C (Knuth Vol 3, pg 341 ff) my ($class, @args) = objectify(0, @_); my $x = shift @args; $x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x); return $class->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN? while (@args) { my $y = shift @args; $y = $class->new($y) unless ref($y) && $y -> isa($class); return $class->bnan() if $y->{sign} !~ /^[+-]$/; # y NaN? $x->{value} = $CALC->_gcd($x->{value}, $y->{value}); last if $CALC->_is_one($x->{value}); } return $x -> babs(); } sub blcm { # (BINT or num_str, BINT or num_str) return BINT # does not modify arguments, but returns new object # Least Common Multiple my ($class, @args) = objectify(0, @_); my $x = shift @args; $x = ref($x) && $x -> isa($class) ? $x -> copy() : $class -> new($x); return $class->bnan() if $x->{sign} !~ /^[+-]$/; # x NaN? while (@args) { my $y = shift @args; $y = $class -> new($y) unless ref($y) && $y -> isa($class); return $x->bnan() if $y->{sign} !~ /^[+-]$/; # y not integer $x -> {value} = $CALC->_lcm($x -> {value}, $y -> {value}); } return $x -> babs(); } ############################################################################### # Object property methods ############################################################################### sub sign { # return the sign of the number: +/-/-inf/+inf/NaN my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); $x->{sign}; } sub digit { # return the nth decimal digit, negative values count backward, 0 is right my ($class, $x, $n) = ref($_[0]) ? (undef, @_) : objectify(1, @_); $n = $n->numify() if ref($n); $CALC->_digit($x->{value}, $n || 0); } sub length { my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); my $e = $CALC->_len($x->{value}); wantarray ? ($e, 0) : $e; } sub exponent { # return a copy of the exponent (here always 0, NaN or 1 for $m == 0) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); if ($x->{sign} !~ /^[+-]$/) { my $s = $x->{sign}; $s =~ s/^[+-]//; # NaN, -inf, +inf => NaN or inf return $class->new($s); } return $class->bzero() if $x->is_zero(); # 12300 => 2 trailing zeros => exponent is 2 $class->new($CALC->_zeros($x->{value})); } sub mantissa { # return the mantissa (compatible to Math::BigFloat, e.g. reduced) my ($class, $x) = ref($_[0]) ? (ref($_[0]), $_[0]) : objectify(1, @_); if ($x->{sign} !~ /^[+-]$/) { # for NaN, +inf, -inf: keep the sign return $class->new($x->{sign}); } my $m = $x->copy(); delete $m->{_p}; delete $m->{_a}; # that's a bit inefficient: my $zeros = $CALC->_zeros($m->{value}); $m->brsft($zeros, 10) if $zeros != 0; $m; } sub parts { # return a copy of both the exponent and the mantissa my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); ($x->mantissa(), $x->exponent()); } sub sparts { my $self = shift; my $class = ref $self; Carp::croak("sparts() is an instance method, not a class method") unless $class; # Not-a-number. if ($self -> is_nan()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> bnan(); # exponent return ($mant, $expo); # list context } # Infinity. if ($self -> is_inf()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> binf('+'); # exponent return ($mant, $expo); # list context } # Finite number. my $mant = $self -> copy(); my $nzeros = $CALC -> _zeros($mant -> {value}); $mant -> brsft($nzeros, 10) if $nzeros != 0; return $mant unless wantarray; my $expo = $class -> new($nzeros); return ($mant, $expo); } sub nparts { my $self = shift; my $class = ref $self; Carp::croak("nparts() is an instance method, not a class method") unless $class; # Not-a-number. if ($self -> is_nan()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> bnan(); # exponent return ($mant, $expo); # list context } # Infinity. if ($self -> is_inf()) { my $mant = $self -> copy(); # mantissa return $mant unless wantarray; # scalar context my $expo = $class -> binf('+'); # exponent return ($mant, $expo); # list context } # Finite number. my ($mant, $expo) = $self -> sparts(); if ($mant -> bcmp(0)) { my ($ndigtot, $ndigfrac) = $mant -> length(); my $expo10adj = $ndigtot - $ndigfrac - 1; if ($expo10adj != 0) { return $upgrade -> new($self) -> nparts() if $upgrade; $mant -> bnan(); return $mant unless wantarray; $expo -> badd($expo10adj); return ($mant, $expo); } } return $mant unless wantarray; return ($mant, $expo); } sub eparts { my $self = shift; my $class = ref $self; Carp::croak("eparts() is an instance method, not a class method") unless $class; # Not-a-number and Infinity. return $self -> sparts() if $self -> is_nan() || $self -> is_inf(); # Finite number. my ($mant, $expo) = $self -> sparts(); if ($mant -> bcmp(0)) { my $ndigmant = $mant -> length(); $expo -> badd($ndigmant); # $c is the number of digits that will be in the integer part of the # final mantissa. my $c = $expo -> copy() -> bdec() -> bmod(3) -> binc(); $expo -> bsub($c); if ($ndigmant > $c) { return $upgrade -> new($self) -> eparts() if $upgrade; $mant -> bnan(); return $mant unless wantarray; return ($mant, $expo); } $mant -> blsft($c - $ndigmant, 10); } return $mant unless wantarray; return ($mant, $expo); } sub dparts { my $self = shift; my $class = ref $self; Carp::croak("dparts() is an instance method, not a class method") unless $class; my $int = $self -> copy(); return $int unless wantarray; my $frc = $class -> bzero(); return ($int, $frc); } ############################################################################### # String conversion methods ############################################################################### sub bstr { my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my $str = $CALC->_str($x->{value}); return $x->{sign} eq '-' ? "-$str" : $str; } # Scientific notation with significand/mantissa as an integer, e.g., "12345" is # written as "1.2345e+4". sub bsstr { my ($class, $x) = ref($_[0]) ? (undef, $_[0]) : objectify(1, @_); if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my ($m, $e) = $x -> parts(); my $str = $CALC->_str($m->{value}) . 'e+' . $CALC->_str($e->{value}); return $x->{sign} eq '-' ? "-$str" : $str; } # Normalized notation, e.g., "12345" is written as "12345e+0". sub bnstr { my $x = shift; if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } return $x -> bstr() if $x -> is_nan() || $x -> is_inf(); my ($mant, $expo) = $x -> parts(); # The "fraction posision" is the position (offset) for the decimal point # relative to the end of the digit string. my $fracpos = $mant -> length() - 1; if ($fracpos == 0) { my $str = $CALC->_str($mant->{value}) . "e+" . $CALC->_str($expo->{value}); return $x->{sign} eq '-' ? "-$str" : $str; } $expo += $fracpos; my $mantstr = $CALC->_str($mant -> {value}); substr($mantstr, -$fracpos, 0) = '.'; my $str = $mantstr . 'e+' . $CALC->_str($expo -> {value}); return $x->{sign} eq '-' ? "-$str" : $str; } # Engineering notation, e.g., "12345" is written as "12.345e+3". sub bestr { my $x = shift; if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my ($mant, $expo) = $x -> parts(); my $sign = $mant -> sign(); $mant -> babs(); my $mantstr = $CALC->_str($mant -> {value}); my $mantlen = CORE::length($mantstr); my $dotidx = 1; $expo += $mantlen - 1; my $c = $expo -> copy() -> bmod(3); $expo -= $c; $dotidx += $c; if ($mantlen < $dotidx) { $mantstr .= "0" x ($dotidx - $mantlen); } elsif ($mantlen > $dotidx) { substr($mantstr, $dotidx, 0) = "."; } my $str = $mantstr . 'e+' . $CALC->_str($expo -> {value}); return $sign eq "-" ? "-$str" : $str; } # Decimal notation, e.g., "12345". sub bdstr { my $x = shift; if ($x->{sign} ne '+' && $x->{sign} ne '-') { return $x->{sign} unless $x->{sign} eq '+inf'; # -inf, NaN return 'inf'; # +inf } my $str = $CALC->_str($x->{value}); return $x->{sign} eq '-' ? "-$str" : $str; } sub to_hex { # return as hex string, with prefixed 0x my $x = shift; $x = $class->new($x) if !ref($x); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc my $hex = $CALC->_to_hex($x->{value}); return $x->{sign} eq '-' ? "-$hex" : $hex; } sub to_oct { # return as octal string, with prefixed 0 my $x = shift; $x = $class->new($x) if !ref($x); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc my $oct = $CALC->_to_oct($x->{value}); return $x->{sign} eq '-' ? "-$oct" : $oct; } sub to_bin { # return as binary string, with prefixed 0b my $x = shift; $x = $class->new($x) if !ref($x); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc my $bin = $CALC->_to_bin($x->{value}); return $x->{sign} eq '-' ? "-$bin" : $bin; } sub to_bytes { # return a byte string my $x = shift; $x = $class->new($x) if !ref($x); Carp::croak("to_bytes() requires a finite, non-negative integer") if $x -> is_neg() || ! $x -> is_int(); Carp::croak("to_bytes() requires a newer version of the $CALC library.") unless $CALC->can('_to_bytes'); return $CALC->_to_bytes($x->{value}); } sub as_hex { # return as hex string, with prefixed 0x my $x = shift; $x = $class->new($x) if !ref($x); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc my $hex = $CALC->_as_hex($x->{value}); return $x->{sign} eq '-' ? "-$hex" : $hex; } sub as_oct { # return as octal string, with prefixed 0 my $x = shift; $x = $class->new($x) if !ref($x); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc my $oct = $CALC->_as_oct($x->{value}); return $x->{sign} eq '-' ? "-$oct" : $oct; } sub as_bin { # return as binary string, with prefixed 0b my $x = shift; $x = $class->new($x) if !ref($x); return $x->bstr() if $x->{sign} !~ /^[+-]$/; # inf, nan etc my $bin = $CALC->_as_bin($x->{value}); return $x->{sign} eq '-' ? "-$bin" : $bin; } *as_bytes = \&to_bytes; ############################################################################### # Other conversion methods ############################################################################### sub numify { # Make a Perl scalar number from a Math::BigInt object. my $x = shift; $x = $class->new($x) unless ref $x; if ($x -> is_nan()) { require Math::Complex; my $inf = Math::Complex::Inf(); return $inf - $inf; } if ($x -> is_inf()) { require Math::Complex; my $inf = Math::Complex::Inf(); return $x -> is_negative() ? -$inf : $inf; } my $num = 0 + $CALC->_num($x->{value}); return $x->{sign} eq '-' ? -$num : $num; } ############################################################################### # Private methods and functions. ############################################################################### sub objectify { # Convert strings and "foreign objects" to the objects we want. # The first argument, $count, is the number of following arguments that # objectify() looks at and converts to objects. The first is a classname. # If the given count is 0, all arguments will be used. # After the count is read, objectify obtains the name of the class to which # the following arguments are converted. If the second argument is a # reference, use the reference type as the class name. Otherwise, if it is # a string that looks like a class name, use that. Otherwise, use $class. # Caller: Gives us: # # $x->badd(1); => ref x, scalar y # Class->badd(1, 2); => classname x (scalar), scalar x, scalar y # Class->badd(Class->(1), 2); => classname x (scalar), ref x, scalar y # Math::BigInt::badd(1, 2); => scalar x, scalar y # A shortcut for the common case $x->unary_op(): return (ref($_[1]), $_[1]) if @_ == 2 && ($_[0] || 0) == 1 && ref($_[1]); # Check the context. unless (wantarray) { Carp::croak("${class}::objectify() needs list context"); } # Get the number of arguments to objectify. my $count = shift; $count ||= @_; # Initialize the output array. my @a = @_; # If the first argument is a reference, use that reference type as our # class name. Otherwise, if the first argument looks like a class name, # then use that as our class name. Otherwise, use the default class name. { if (ref($a[0])) { # reference? unshift @a, ref($a[0]); last; } if ($a[0] =~ /^[A-Z].*::/) { # string with class name? last; } unshift @a, $class; # default class name } no strict 'refs'; # What we upgrade to, if anything. my $up = ${"$a[0]::upgrade"}; # Disable downgrading, because Math::BigFloat -> foo('1.0', '2.0') needs # floats. my $down; if (defined ${"$a[0]::downgrade"}) { $down = ${"$a[0]::downgrade"}; ${"$a[0]::downgrade"} = undef; } for my $i (1 .. $count) { # Don't do anything with undefs. This special treatment is necessary # because blog() might have a second operand which is undef, to signify # that the default Euler base should be used. next unless defined $a[$i]; my $ref = ref $a[$i]; # Perl scalars are fed to the appropriate constructor. unless ($ref) { $a[$i] = $a[0] -> new($a[$i]); next; } # If it is an object of the right class, all is fine. next if $ref -> isa($a[0]); # Upgrading is OK, so skip further tests if the argument is upgraded. if (defined $up && $ref -> isa($up)) { next; } # See if we can call one of the as_xxx() methods. We don't know whether # the as_xxx() method returns an object or a scalar, so re-check # afterwards. my $recheck = 0; if ($a[0] -> isa('Math::BigInt')) { if ($a[$i] -> can('as_int')) { $a[$i] = $a[$i] -> as_int(); $recheck = 1; } elsif ($a[$i] -> can('as_number')) { $a[$i] = $a[$i] -> as_number(); $recheck = 1; } } elsif ($a[0] -> isa('Math::BigFloat')) { if ($a[$i] -> can('as_float')) { $a[$i] = $a[$i] -> as_float(); $recheck = $1; } } # If we called one of the as_xxx() methods, recheck. if ($recheck) { $ref = ref($a[$i]); # Perl scalars are fed to the appropriate constructor. unless ($ref) { $a[$i] = $a[0] -> new($a[$i]); next; } # If it is an object of the right class, all is fine. next if $ref -> isa($a[0]); } # Last resort. $a[$i] = $a[0] -> new($a[$i]); } # Reset the downgrading. ${"$a[0]::downgrade"} = $down; return @a; } sub import { my $class = shift; $IMPORT++; # remember we did import() my @a; my $l = scalar @_; my $warn_or_die = 0; # 0 - no warn, 1 - warn, 2 - die for (my $i = 0; $i < $l ; $i++) { if ($_[$i] eq ':constant') { # this causes overlord er load to step in overload::constant integer => sub { $class->new(shift) }, binary => sub { $class->new(shift) }; } elsif ($_[$i] eq 'upgrade') { # this causes upgrading $upgrade = $_[$i+1]; # or undef to disable $i++; } elsif ($_[$i] =~ /^(lib|try|only)\z/) { # this causes a different low lib to take care... $CALC = $_[$i+1] || ''; # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback) $warn_or_die = 1 if $_[$i] eq 'lib'; $warn_or_die = 2 if $_[$i] eq 'only'; $i++; } else { push @a, $_[$i]; } } # any non :constant stuff is handled by our parent, Exporter if (@a > 0) { require Exporter; $class->SUPER::import(@a); # need it for subclasses $class->export_to_level(1, $class, @a); # need it for MBF } # try to load core math lib my @c = split /\s*,\s*/, $CALC; foreach (@c) { $_ =~ tr/a-zA-Z0-9://cd; # limit to sane characters } push @c, \'Calc' # if all fail, try these if $warn_or_die < 2; # but not for "only" $CALC = ''; # signal error foreach my $l (@c) { # fallback libraries are "marked" as \'string', extract string if nec. my $lib = $l; $lib = $$l if ref($l); next if ($lib || '') eq ''; $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i; $lib =~ s/\.pm$//; if ($] < 5.006) { # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is # used in the same script, or eval("") inside import(). my @parts = split /::/, $lib; # Math::BigInt => Math BigInt my $file = pop @parts; $file .= '.pm'; # BigInt => BigInt.pm require File::Spec; $file = File::Spec->catfile (@parts, $file); eval { require "$file"; $lib->import(@c); } } else { eval "use $lib qw/@c/;"; } if ($@ eq '') { my $ok = 1; # loaded it ok, see if the api_version() is high enough if ($lib->can('api_version') && $lib->api_version() >= 1.0) { $ok = 0; # api_version matches, check if it really provides anything we need for my $method (qw/ one two ten str num add mul div sub dec inc acmp len digit is_one is_zero is_even is_odd is_two is_ten zeros new copy check from_hex from_oct from_bin as_hex as_bin as_oct rsft lsft xor and or mod sqrt root fac pow modinv modpow log_int gcd /) { if (!$lib->can("_$method")) { if (($WARN{$lib} || 0) < 2) { Carp::carp("$lib is missing method '_$method'"); $WARN{$lib} = 1; # still warn about the lib } $ok++; last; } } } if ($ok == 0) { $CALC = $lib; if ($warn_or_die > 0 && ref($l)) { my $msg = "Math::BigInt: couldn't load specified" . " math lib(s), fallback to $lib"; Carp::carp($msg) if $warn_or_die == 1; Carp::croak($msg) if $warn_or_die == 2; } last; # found a usable one, break } else { if (($WARN{$lib} || 0) < 2) { my $ver = eval "\$$lib\::VERSION" || 'unknown'; Carp::carp("Cannot load outdated $lib v$ver, please upgrade"); $WARN{$lib} = 2; # never warn again } } } } if ($CALC eq '') { if ($warn_or_die == 2) { Carp::croak("Couldn't load specified math lib(s)" . " and fallback disallowed"); } else { Carp::croak("Couldn't load any math lib(s), not even fallback to Calc.pm"); } } # notify callbacks foreach my $class (keys %CALLBACKS) { &{$CALLBACKS{$class}}($CALC); } # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib # functions %CAN = (); for my $method (qw/ signed_and signed_or signed_xor /) { $CAN{$method} = $CALC->can("_$method") ? 1 : 0; } # import done } sub _register_callback { my ($class, $callback) = @_; if (ref($callback) ne 'CODE') { Carp::croak("$callback is not a coderef"); } $CALLBACKS{$class} = $callback; } sub _split_dec_string { my $str = shift; if ($str =~ s/ ^ # leading whitespace ( \s* ) # optional sign ( [+-]? ) # significand ( \d+ (?: _ \d+ )* (?: \. (?: \d+ (?: _ \d+ )* )? )? | \. \d+ (?: _ \d+ )* ) # optional exponent (?: [Ee] ( [+-]? ) ( \d+ (?: _ \d+ )* ) )? # trailing stuff ( \D .*? )? \z //x) { my $leading = $1; my $significand_sgn = $2 || '+'; my $significand_abs = $3; my $exponent_sgn = $4 || '+'; my $exponent_abs = $5 || '0'; my $trailing = $6; # Remove underscores and leading zeros. $significand_abs =~ tr/_//d; $exponent_abs =~ tr/_//d; $significand_abs =~ s/^0+(.)/$1/; $exponent_abs =~ s/^0+(.)/$1/; # If the significand contains a dot, remove it and adjust the exponent # accordingly. E.g., "1234.56789e+3" -> "123456789e-2" my $idx = index $significand_abs, '.'; if ($idx > -1) { $significand_abs =~ s/0+\z//; substr($significand_abs, $idx, 1) = ''; my $exponent = $exponent_sgn . $exponent_abs; $exponent .= $idx - CORE::length($significand_abs); $exponent_abs = abs $exponent; $exponent_sgn = $exponent < 0 ? '-' : '+'; } return($leading, $significand_sgn, $significand_abs, $exponent_sgn, $exponent_abs, $trailing); } return undef; } sub _split { # input: num_str; output: undef for invalid or # (\$mantissa_sign, \$mantissa_value, \$mantissa_fraction, # \$exp_sign, \$exp_value) # Internal, take apart a string and return the pieces. # Strip leading/trailing whitespace, leading zeros, underscore and reject # invalid input. my $x = shift; # strip white space at front, also extraneous leading zeros $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g; # will not strip ' .2' $x =~ s/^\s+//; # but this will $x =~ s/\s+$//g; # strip white space at end # shortcut, if nothing to split, return early if ($x =~ /^[+-]?[0-9]+\z/) { $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+'; return (\$sign, \$x, \'', \'', \0); } # invalid starting char? return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/; return Math::BigInt->from_hex($x) if $x =~ /^[+-]?0x/; # hex string return Math::BigInt->from_bin($x) if $x =~ /^[+-]?0b/; # binary string # strip underscores between digits $x =~ s/([0-9])_([0-9])/$1$2/g; $x =~ s/([0-9])_([0-9])/$1$2/g; # do twice for 1_2_3 # some possible inputs: # 2.1234 # 0.12 # 1 # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 # .2 # 1_2_3.4_5_6 # 1.4E1_2_3 # 1e3 # +.2 # 0e999 my ($m, $e, $last) = split /[Ee]/, $x; return if defined $last; # last defined => 1e2E3 or others $e = '0' if !defined $e || $e eq ""; # sign, value for exponent, mantint, mantfrac my ($es, $ev, $mis, $miv, $mfv); # valid exponent? if ($e =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros { $es = $1; $ev = $2; # valid mantissa? return if $m eq '.' || $m eq ''; my ($mi, $mf, $lastf) = split /\./, $m; return if defined $lastf; # lastf defined => 1.2.3 or others $mi = '0' if !defined $mi; $mi .= '0' if $mi =~ /^[\-\+]?$/; $mf = '0' if !defined $mf || $mf eq ''; if ($mi =~ /^([+-]?)0*([0-9]+)$/) # strip leading zeros { $mis = $1 || '+'; $miv = $2; return unless ($mf =~ /^([0-9]*?)0*$/); # strip trailing zeros $mfv = $1; # handle the 0e999 case here $ev = 0 if $miv eq '0' && $mfv eq ''; return (\$mis, \$miv, \$mfv, \$es, \$ev); } } return; # NaN, not a number } sub _trailing_zeros { # return the amount of trailing zeros in $x (as scalar) my $x = shift; $x = $class->new($x) unless ref $x; return 0 if $x->{sign} !~ /^[+-]$/; # NaN, inf, -inf etc $CALC->_zeros($x->{value}); # must handle odd values, 0 etc } sub _scan_for_nonzero { # internal, used by bround() to scan for non-zeros after a '5' my ($x, $pad, $xs, $len) = @_; return 0 if $len == 1; # "5" is trailed by invisible zeros my $follow = $pad - 1; return 0 if $follow > $len || $follow < 1; # use the string form to check whether only '0's follow or not substr ($xs, -$follow) =~ /[^0]/ ? 1 : 0; } sub _find_round_parameters { # After any operation or when calling round(), the result is rounded by # regarding the A & P from arguments, local parameters, or globals. # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!! # This procedure finds the round parameters, but it is for speed reasons # duplicated in round. Otherwise, it is tested by the testsuite and used # by bdiv(). # returns ($self) or ($self, $a, $p, $r) - sets $self to NaN of both A and P # were requested/defined (locally or globally or both) my ($self, $a, $p, $r, @args) = @_; # $a accuracy, if given by caller # $p precision, if given by caller # $r round_mode, if given by caller # @args all 'other' arguments (0 for unary, 1 for binary ops) my $class = ref($self); # find out class of argument(s) no strict 'refs'; # convert to normal scalar for speed and correctness in inner parts $a = $a->can('numify') ? $a->numify() : "$a" if defined $a && ref($a); $p = $p->can('numify') ? $p->numify() : "$p" if defined $p && ref($p); # now pick $a or $p, but only if we have got "arguments" if (!defined $a) { foreach ($self, @args) { # take the defined one, or if both defined, the one that is smaller $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a); } } if (!defined $p) { # even if $a is defined, take $p, to signal error for both defined foreach ($self, @args) { # take the defined one, or if both defined, the one that is bigger # -2 > -3, and 3 > 2 $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p); } } # if still none defined, use globals (#2) $a = ${"$class\::accuracy"} unless defined $a; $p = ${"$class\::precision"} unless defined $p; # A == 0 is useless, so undef it to signal no rounding $a = undef if defined $a && $a == 0; # no rounding today? return ($self) unless defined $a || defined $p; # early out # set A and set P is an fatal error return ($self->bnan()) if defined $a && defined $p; # error $r = ${"$class\::round_mode"} unless defined $r; if ($r !~ /^(even|odd|[+-]inf|zero|trunc|common)$/) { Carp::croak("Unknown round mode '$r'"); } $a = int($a) if defined $a; $p = int($p) if defined $p; ($self, $a, $p, $r); } ############################################################################### # this method returns 0 if the object can be modified, or 1 if not. # We use a fast constant sub() here, to avoid costly calls. Subclasses # may override it with special code (f.i. Math::BigInt::Constant does so) sub modify () { 0; } 1; __END__ =pod =head1 NAME Math::BigInt - Arbitrary size integer/float math package =head1 SYNOPSIS use Math::BigInt; # or make it faster with huge numbers: install (optional) # Math::BigInt::GMP and always use (it falls back to # pure Perl if the GMP library is not installed): # (See also the L section!) # warns if Math::BigInt::GMP cannot be found use Math::BigInt lib => 'GMP'; # to suppress the warning use this: # use Math::BigInt try => 'GMP'; # dies if GMP cannot be loaded: # use Math::BigInt only => 'GMP'; my $str = '1234567890'; my @values = (64, 74, 18); my $n = 1; my $sign = '-'; # Configuration methods (may be used as class methods and instance methods) Math::BigInt->accuracy(); # get class accuracy Math::BigInt->accuracy($n); # set class accuracy Math::BigInt->precision(); # get class precision Math::BigInt->precision($n); # set class precision Math::BigInt->round_mode(); # get class rounding mode Math::BigInt->round_mode($m); # set global round mode, must be one of # 'even', 'odd', '+inf', '-inf', 'zero', # 'trunc', or 'common' Math::BigInt->config(); # return hash with configuration # Constructor methods (when the class methods below are used as instance # methods, the value is assigned the invocand) $x = Math::BigInt->new($str); # defaults to 0 $x = Math::BigInt->new('0x123'); # from hexadecimal $x = Math::BigInt->new('0b101'); # from binary $x = Math::BigInt->from_hex('cafe'); # from hexadecimal $x = Math::BigInt->from_oct('377'); # from octal $x = Math::BigInt->from_bin('1101'); # from binary $x = Math::BigInt->bzero(); # create a +0 $x = Math::BigInt->bone(); # create a +1 $x = Math::BigInt->bone('-'); # create a -1 $x = Math::BigInt->binf(); # create a +inf $x = Math::BigInt->binf('-'); # create a -inf $x = Math::BigInt->bnan(); # create a Not-A-Number $x = Math::BigInt->bpi(); # returns pi $y = $x->copy(); # make a copy (unlike $y = $x) $y = $x->as_int(); # return as a Math::BigInt # Boolean methods (these don't modify the invocand) $x->is_zero(); # if $x is 0 $x->is_one(); # if $x is +1 $x->is_one("+"); # ditto $x->is_one("-"); # if $x is -1 $x->is_inf(); # if $x is +inf or -inf $x->is_inf("+"); # if $x is +inf $x->is_inf("-"); # if $x is -inf $x->is_nan(); # if $x is NaN $x->is_positive(); # if $x > 0 $x->is_pos(); # ditto $x->is_negative(); # if $x < 0 $x->is_neg(); # ditto $x->is_odd(); # if $x is odd $x->is_even(); # if $x is even $x->is_int(); # if $x is an integer # Comparison methods $x->bcmp($y); # compare numbers (undef, < 0, == 0, > 0) $x->bacmp($y); # compare absolutely (undef, < 0, == 0, > 0) $x->beq($y); # true if and only if $x == $y $x->bne($y); # true if and only if $x != $y $x->blt($y); # true if and only if $x < $y $x->ble($y); # true if and only if $x <= $y $x->bgt($y); # true if and only if $x > $y $x->bge($y); # true if and only if $x >= $y # Arithmetic methods $x->bneg(); # negation $x->babs(); # absolute value $x->bsgn(); # sign function (-1, 0, 1, or NaN) $x->bnorm(); # normalize (no-op) $x->binc(); # increment $x by 1 $x->bdec(); # decrement $x by 1 $x->badd($y); # addition (add $y to $x) $x->bsub($y); # subtraction (subtract $y from $x) $x->bmul($y); # multiplication (multiply $x by $y) $x->bmuladd($y,$z); # $x = $x * $y + $z $x->bdiv($y); # division (floored), set $x to quotient # return (quo,rem) or quo if scalar $x->btdiv($y); # division (truncated), set $x to quotient # return (quo,rem) or quo if scalar $x->bmod($y); # modulus (x % y) $x->btmod($y); # modulus (truncated) $x->bmodinv($mod); # modular multiplicative inverse $x->bmodpow($y,$mod); # modular exponentiation (($x ** $y) % $mod) $x->bpow($y); # power of arguments (x ** y) $x->blog(); # logarithm of $x to base e (Euler's number) $x->blog($base); # logarithm of $x to base $base (e.g., base 2) $x->bexp(); # calculate e ** $x where e is Euler's number $x->bnok($y); # x over y (binomial coefficient n over k) $x->bsin(); # sine $x->bcos(); # cosine $x->batan(); # inverse tangent $x->batan2($y); # two-argument inverse tangent $x->bsqrt(); # calculate square-root $x->broot($y); # $y'th root of $x (e.g. $y == 3 => cubic root) $x->bfac(); # factorial of $x (1*2*3*4*..$x) $x->blsft($n); # left shift $n places in base 2 $x->blsft($n,$b); # left shift $n places in base $b # returns (quo,rem) or quo (scalar context) $x->brsft($n); # right shift $n places in base 2 $x->brsft($n,$b); # right shift $n places in base $b # returns (quo,rem) or quo (scalar context) # Bitwise methods $x->band($y); # bitwise and $x->bior($y); # bitwise inclusive or $x->bxor($y); # bitwise exclusive or $x->bnot(); # bitwise not (two's complement) # Rounding methods $x->round($A,$P,$mode); # round to accuracy or precision using # rounding mode $mode $x->bround($n); # accuracy: preserve $n digits $x->bfround($n); # $n > 0: round to $nth digit left of dec. point # $n < 0: round to $nth digit right of dec. point $x->bfloor(); # round towards minus infinity $x->bceil(); # round towards plus infinity $x->bint(); # round towards zero # Other mathematical methods $x->bgcd($y); # greatest common divisor $x->blcm($y); # least common multiple # Object property methods (do not modify the invocand) $x->sign(); # the sign, either +, - or NaN $x->digit($n); # the nth digit, counting from the right $x->digit(-$n); # the nth digit, counting from the left $x->length(); # return number of digits in number ($xl,$f) = $x->length(); # length of number and length of fraction # part, latter is always 0 digits long # for Math::BigInt objects $x->mantissa(); # return (signed) mantissa as a Math::BigInt $x->exponent(); # return exponent as a Math::BigInt $x->parts(); # return (mantissa,exponent) as a Math::BigInt $x->sparts(); # mantissa and exponent (as integers) $x->nparts(); # mantissa and exponent (normalised) $x->eparts(); # mantissa and exponent (engineering notation) $x->dparts(); # integer and fraction part # Conversion methods (do not modify the invocand) $x->bstr(); # decimal notation, possibly zero padded $x->bsstr(); # string in scientific notation with integers $x->bnstr(); # string in normalized notation $x->bestr(); # string in engineering notation $x->bdstr(); # string in decimal notation $x->to_hex(); # as signed hexadecimal string $x->to_bin(); # as signed binary string $x->to_oct(); # as signed octal string $x->to_bytes(); # as byte string $x->as_hex(); # as signed hexadecimal string with prefixed 0x $x->as_bin(); # as signed binary string with prefixed 0b $x->as_oct(); # as signed octal string with prefixed 0 # Other conversion methods $x->numify(); # return as scalar (might overflow or underflow) =head1 DESCRIPTION Math::BigInt provides support for arbitrary precision integers. Overloading is also provided for Perl operators. =head2 Input Input values to these routines may be any scalar number or string that looks like a number and represents an integer. =over =item * Leading and trailing whitespace is ignored. =item * Leading and trailing zeros are ignored. =item * If the string has a "0x" prefix, it is interpreted as a hexadecimal number. =item * If the string has a "0b" prefix, it is interpreted as a binary number. =item * One underline is allowed between any two digits. =item * If the string can not be interpreted, NaN is returned. =back Octal numbers are typically prefixed by "0", but since leading zeros are stripped, these methods can not automatically recognize octal numbers, so use the constructor from_oct() to interpret octal strings. Some examples of valid string input Input string Resulting value 123 123 1.23e2 123 12300e-2 123 0xcafe 51966 0b1101 13 67_538_754 67538754 -4_5_6.7_8_9e+0_1_0 -4567890000000 Input given as scalar numbers might lose precision. Quote your input to ensure that no digits are lost: $x = Math::BigInt->new( 56789012345678901234 ); # bad $x = Math::BigInt->new('56789012345678901234'); # good Currently, Math::BigInt->new() defaults to 0, while Math::BigInt->new('') results in 'NaN'. This might change in the future, so use always the following explicit forms to get a zero or NaN: $zero = Math::BigInt->bzero(); $nan = Math::BigInt->bnan(); =head2 Output Output values are usually Math::BigInt objects. Boolean operators C, C, C, etc. return true or false. Comparison operators C and C) return -1, 0, 1, or undef. =head1 METHODS =head2 Configuration methods Each of the methods below (except config(), accuracy() and precision()) accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R> are C, C and C. Please see the section about L for more information. Setting a class variable effects all object instance that are created afterwards. =over =item accuracy() Math::BigInt->accuracy(5); # set class accuracy $x->accuracy(5); # set instance accuracy $A = Math::BigInt->accuracy(); # get class accuracy $A = $x->accuracy(); # get instance accuracy Set or get the accuracy, i.e., the number of significant digits. The accuracy must be an integer. If the accuracy is set to C, no rounding is done. Alternatively, one can round the results explicitly using one of L, L or L or by passing the desired accuracy to the method as an additional parameter: my $x = Math::BigInt->new(30000); my $y = Math::BigInt->new(7); print scalar $x->copy()->bdiv($y, 2); # prints 4300 print scalar $x->copy()->bdiv($y)->bround(2); # prints 4300 Please see the section about L for further details. $y = Math::BigInt->new(1234567); # $y is not rounded Math::BigInt->accuracy(4); # set class accuracy to 4 $x = Math::BigInt->new(1234567); # $x is rounded automatically print "$x $y"; # prints "1235000 1234567" print $x->accuracy(); # prints "4" print $y->accuracy(); # also prints "4", since # class accuracy is 4 Math::BigInt->accuracy(5); # set class accuracy to 5 print $x->accuracy(); # prints "4", since instance # accuracy is 4 print $y->accuracy(); # prints "5", since no instance # accuracy, and class accuracy is 5 Note: Each class has it's own globals separated from Math::BigInt, but it is possible to subclass Math::BigInt and make the globals of the subclass aliases to the ones from Math::BigInt. =item precision() Math::BigInt->precision(-2); # set class precision $x->precision(-2); # set instance precision $P = Math::BigInt->precision(); # get class precision $P = $x->precision(); # get instance precision Set or get the precision, i.e., the place to round relative to the decimal point. The precision must be a integer. Setting the precision to $P means that each number is rounded up or down, depending on the rounding mode, to the nearest multiple of 10**$P. If the precision is set to C, no rounding is done. You might want to use L instead. With L you set the number of digits each result should have, with L you set the place where to round. Please see the section about L for further details. $y = Math::BigInt->new(1234567); # $y is not rounded Math::BigInt->precision(4); # set class precision to 4 $x = Math::BigInt->new(1234567); # $x is rounded automatically print $x; # prints "1230000" Note: Each class has its own globals separated from Math::BigInt, but it is possible to subclass Math::BigInt and make the globals of the subclass aliases to the ones from Math::BigInt. =item div_scale() Set/get the fallback accuracy. This is the accuracy used when neither accuracy nor precision is set explicitly. It is used when a computation might otherwise attempt to return an infinite number of digits. =item round_mode() Set/get the rounding mode. =item upgrade() Set/get the class for upgrading. When a computation might result in a non-integer, the operands are upgraded to this class. This is used for instance by L. The default is C, thus the following operation creates a Math::BigInt, not a Math::BigFloat: my $i = Math::BigInt->new(123); my $f = Math::BigFloat->new('123.1'); print $i + $f, "\n"; # prints 246 =item downgrade() Set/get the class for downgrading. The default is C. Downgrading is not done by Math::BigInt. =item modify() $x->modify('bpowd'); This method returns 0 if the object can be modified with the given operation, or 1 if not. This is used for instance by L. =item config() use Data::Dumper; print Dumper ( Math::BigInt->config() ); print Math::BigInt->config()->{lib},"\n"; print Math::BigInt->config('lib')},"\n"; Returns a hash containing the configuration, e.g. the version number, lib loaded etc. The following hash keys are currently filled in with the appropriate information. key Description Example ============================================================ lib Name of the low-level math library Math::BigInt::Calc lib_version Version of low-level math library (see 'lib') 0.30 class The class name of config() you just called Math::BigInt upgrade To which class math operations might be upgraded Math::BigFloat downgrade To which class math operations might be downgraded undef precision Global precision undef accuracy Global accuracy undef round_mode Global round mode even version version number of the class you used 1.61 div_scale Fallback accuracy for div 40 trap_nan If true, traps creation of NaN via croak() 1 trap_inf If true, traps creation of +inf/-inf via croak() 1 The following values can be set by passing C a reference to a hash: accuracy precision round_mode div_scale upgrade downgrade trap_inf trap_nan Example: $new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } ); =back =head2 Constructor methods =over =item new() $x = Math::BigInt->new($str,$A,$P,$R); Creates a new Math::BigInt object from a scalar or another Math::BigInt object. The input is accepted as decimal, hexadecimal (with leading '0x') or binary (with leading '0b'). See L for more info on accepted input formats. =item from_hex() $x = Math::BigInt->from_hex("0xcafe"); # input is hexadecimal Interpret input as a hexadecimal string. A "0x" or "x" prefix is optional. A single underscore character may be placed right after the prefix, if present, or between any two digits. If the input is invalid, a NaN is returned. =item from_oct() $x = Math::BigInt->from_oct("0775"); # input is octal Interpret the input as an octal string and return the corresponding value. A "0" (zero) prefix is optional. A single underscore character may be placed right after the prefix, if present, or between any two digits. If the input is invalid, a NaN is returned. =item from_bin() $x = Math::BigInt->from_bin("0b10011"); # input is binary Interpret the input as a binary string. A "0b" or "b" prefix is optional. A single underscore character may be placed right after the prefix, if present, or between any two digits. If the input is invalid, a NaN is returned. =item from_bytes() $x = Math::BigInt->from_bytes("\xf3\x6b"); # $x = 62315 Interpret the input as a byte string, assuming big endian byte order. The output is always a non-negative, finite integer. In some special cases, from_bytes() matches the conversion done by unpack(): $b = "\x4e"; # one char byte string $x = Math::BigInt->from_bytes($b); # = 78 $y = unpack "C", $b; # ditto, but scalar $b = "\xf3\x6b"; # two char byte string $x = Math::BigInt->from_bytes($b); # = 62315 $y = unpack "S>", $b; # ditto, but scalar $b = "\x2d\xe0\x49\xad"; # four char byte string $x = Math::BigInt->from_bytes($b); # = 769673645 $y = unpack "L>", $b; # ditto, but scalar $b = "\x2d\xe0\x49\xad\x2d\xe0\x49\xad"; # eight char byte string $x = Math::BigInt->from_bytes($b); # = 3305723134637787565 $y = unpack "Q>", $b; # ditto, but scalar =item bzero() $x = Math::BigInt->bzero(); $x->bzero(); Returns a new Math::BigInt object representing zero. If used as an instance method, assigns the value to the invocand. =item bone() $x = Math::BigInt->bone(); # +1 $x = Math::BigInt->bone("+"); # +1 $x = Math::BigInt->bone("-"); # -1 $x->bone(); # +1 $x->bone("+"); # +1 $x->bone('-'); # -1 Creates a new Math::BigInt object representing one. The optional argument is either '-' or '+', indicating whether you want plus one or minus one. If used as an instance method, assigns the value to the invocand. =item binf() $x = Math::BigInt->binf($sign); Creates a new Math::BigInt object representing infinity. The optional argument is either '-' or '+', indicating whether you want infinity or minus infinity. If used as an instance method, assigns the value to the invocand. $x->binf(); $x->binf('-'); =item bnan() $x = Math::BigInt->bnan(); Creates a new Math::BigInt object representing NaN (Not A Number). If used as an instance method, assigns the value to the invocand. $x->bnan(); =item bpi() $x = Math::BigInt->bpi(100); # 3 $x->bpi(100); # 3 Creates a new Math::BigInt object representing PI. If used as an instance method, assigns the value to the invocand. With Math::BigInt this always returns 3. If upgrading is in effect, returns PI, rounded to N digits with the current rounding mode: use Math::BigFloat; use Math::BigInt upgrade => "Math::BigFloat"; print Math::BigInt->bpi(3), "\n"; # 3.14 print Math::BigInt->bpi(100), "\n"; # 3.1415.... =item copy() $x->copy(); # make a true copy of $x (unlike $y = $x) =item as_int() =item as_number() These methods are called when Math::BigInt encounters an object it doesn't know how to handle. For instance, assume $x is a Math::BigInt, or subclass thereof, and $y is defined, but not a Math::BigInt, or subclass thereof. If you do $x -> badd($y); $y needs to be converted into an object that $x can deal with. This is done by first checking if $y is something that $x might be upgraded to. If that is the case, no further attempts are made. The next is to see if $y supports the method C. If it does, C is called, but if it doesn't, the next thing is to see if $y supports the method C. If it does, C is called. The method C (and C) is expected to return either an object that has the same class as $x, a subclass thereof, or a string that Cnew()> can parse to create an object. C is an alias to C. C was introduced in v1.22, while C was introduced in v1.68. In Math::BigInt, C has the same effect as C. =back =head2 Boolean methods None of these methods modify the invocand object. =over =item is_zero() $x->is_zero(); # true if $x is 0 Returns true if the invocand is zero and false otherwise. =item is_one( [ SIGN ]) $x->is_one(); # true if $x is +1 $x->is_one("+"); # ditto $x->is_one("-"); # true if $x is -1 Returns true if the invocand is one and false otherwise. =item is_finite() $x->is_finite(); # true if $x is not +inf, -inf or NaN Returns true if the invocand is a finite number, i.e., it is neither +inf, -inf, nor NaN. =item is_inf( [ SIGN ] ) $x->is_inf(); # true if $x is +inf $x->is_inf("+"); # ditto $x->is_inf("-"); # true if $x is -inf Returns true if the invocand is infinite and false otherwise. =item is_nan() $x->is_nan(); # true if $x is NaN =item is_positive() =item is_pos() $x->is_positive(); # true if > 0 $x->is_pos(); # ditto Returns true if the invocand is positive and false otherwise. A C is neither positive nor negative. =item is_negative() =item is_neg() $x->is_negative(); # true if < 0 $x->is_neg(); # ditto Returns true if the invocand is negative and false otherwise. A C is neither positive nor negative. =item is_odd() $x->is_odd(); # true if odd, false for even Returns true if the invocand is odd and false otherwise. C, C<+inf>, and C<-inf> are neither odd nor even. =item is_even() $x->is_even(); # true if $x is even Returns true if the invocand is even and false otherwise. C, C<+inf>, C<-inf> are not integers and are neither odd nor even. =item is_int() $x->is_int(); # true if $x is an integer Returns true if the invocand is an integer and false otherwise. C, C<+inf>, C<-inf> are not integers. =back =head2 Comparison methods None of these methods modify the invocand object. Note that a C is neither less than, greater than, or equal to anything else, even a C. =over =item bcmp() $x->bcmp($y); Returns -1, 0, 1 depending on whether $x is less than, equal to, or grater than $y. Returns undef if any operand is a NaN. =item bacmp() $x->bacmp($y); Returns -1, 0, 1 depending on whether the absolute value of $x is less than, equal to, or grater than the absolute value of $y. Returns undef if any operand is a NaN. =item beq() $x -> beq($y); Returns true if and only if $x is equal to $y, and false otherwise. =item bne() $x -> bne($y); Returns true if and only if $x is not equal to $y, and false otherwise. =item blt() $x -> blt($y); Returns true if and only if $x is equal to $y, and false otherwise. =item ble() $x -> ble($y); Returns true if and only if $x is less than or equal to $y, and false otherwise. =item bgt() $x -> bgt($y); Returns true if and only if $x is greater than $y, and false otherwise. =item bge() $x -> bge($y); Returns true if and only if $x is greater than or equal to $y, and false otherwise. =back =head2 Arithmetic methods These methods modify the invocand object and returns it. =over =item bneg() $x->bneg(); Negate the number, e.g. change the sign between '+' and '-', or between '+inf' and '-inf', respectively. Does nothing for NaN or zero. =item babs() $x->babs(); Set the number to its absolute value, e.g. change the sign from '-' to '+' and from '-inf' to '+inf', respectively. Does nothing for NaN or positive numbers. =item bsgn() $x->bsgn(); Signum function. Set the number to -1, 0, or 1, depending on whether the number is negative, zero, or positive, respectively. Does not modify NaNs. =item bnorm() $x->bnorm(); # normalize (no-op) Normalize the number. This is a no-op and is provided only for backwards compatibility. =item binc() $x->binc(); # increment x by 1 =item bdec() $x->bdec(); # decrement x by 1 =item badd() $x->badd($y); # addition (add $y to $x) =item bsub() $x->bsub($y); # subtraction (subtract $y from $x) =item bmul() $x->bmul($y); # multiplication (multiply $x by $y) =item bmuladd() $x->bmuladd($y,$z); Multiply $x by $y, and then add $z to the result, This method was added in v1.87 of Math::BigInt (June 2007). =item bdiv() $x->bdiv($y); # divide, set $x to quotient Divides $x by $y by doing floored division (F-division), where the quotient is the floored (rounded towards negative infinity) quotient of the two operands. In list context, returns the quotient and the remainder. The remainder is either zero or has the same sign as the second operand. In scalar context, only the quotient is returned. The quotient is always the greatest integer less than or equal to the real-valued quotient of the two operands, and the remainder (when it is non-zero) always has the same sign as the second operand; so, for example, 1 / 4 => ( 0, 1) 1 / -4 => (-1, -3) -3 / 4 => (-1, 1) -3 / -4 => ( 0, -3) -11 / 2 => (-5, 1) 11 / -2 => (-5, -1) The behavior of the overloaded operator % agrees with the behavior of Perl's built-in % operator (as documented in the perlop manpage), and the equation $x == ($x / $y) * $y + ($x % $y) holds true for any finite $x and finite, non-zero $y. Perl's "use integer" might change the behaviour of % and / for scalars. This is because under 'use integer' Perl does what the underlying C library thinks is right, and this varies. However, "use integer" does not change the way things are done with Math::BigInt objects. =item btdiv() $x->btdiv($y); # divide, set $x to quotient Divides $x by $y by doing truncated division (T-division), where quotient is the truncated (rouneded towards zero) quotient of the two operands. In list context, returns the quotient and the remainder. The remainder is either zero or has the same sign as the first operand. In scalar context, only the quotient is returned. =item bmod() $x->bmod($y); # modulus (x % y) Returns $x modulo $y, i.e., the remainder after floored division (F-division). This method is like Perl's % operator. See L. =item btmod() $x->btmod($y); # modulus Returns the remainer after truncated division (T-division). See L. =item bmodinv() $x->bmodinv($mod); # modular multiplicative inverse Returns the multiplicative inverse of C<$x> modulo C<$mod>. If $y = $x -> copy() -> bmodinv($mod) then C<$y> is the number closest to zero, and with the same sign as C<$mod>, satisfying ($x * $y) % $mod = 1 % $mod If C<$x> and C<$y> are non-zero, they must be relative primes, i.e., C. 'C' is returned when no modular multiplicative inverse exists. =item bmodpow() $num->bmodpow($exp,$mod); # modular exponentiation # ($num**$exp % $mod) Returns the value of C<$num> taken to the power C<$exp> in the modulus C<$mod> using binary exponentiation. C is far superior to writing $num ** $exp % $mod because it is much faster - it reduces internal variables into the modulus whenever possible, so it operates on smaller numbers. C also supports negative exponents. bmodpow($num, -1, $mod) is exactly equivalent to bmodinv($num, $mod) =item bpow() $x->bpow($y); # power of arguments (x ** y) C (and the rounding functions) now modifies the first argument and returns it, unlike the old code which left it alone and only returned the result. This is to be consistent with C etc. The first three modifies $x, the last one won't: print bpow($x,$i),"\n"; # modify $x print $x->bpow($i),"\n"; # ditto print $x **= $i,"\n"; # the same print $x ** $i,"\n"; # leave $x alone The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though. =item blog() $x->blog($base, $accuracy); # logarithm of x to the base $base If C<$base> is not defined, Euler's number (e) is used: print $x->blog(undef, 100); # log(x) to 100 digits =item bexp() $x->bexp($accuracy); # calculate e ** X Calculates the expression C where C is Euler's number. This method was added in v1.82 of Math::BigInt (April 2007). See also L. =item bnok() $x->bnok($y); # x over y (binomial coefficient n over k) Calculates the binomial coefficient n over k, also called the "choose" function. The result is equivalent to: ( n ) n! | - | = ------- ( k ) k!(n-k)! This method was added in v1.84 of Math::BigInt (April 2007). =item bsin() my $x = Math::BigInt->new(1); print $x->bsin(100), "\n"; Calculate the sine of $x, modifying $x in place. In Math::BigInt, unless upgrading is in effect, the result is truncated to an integer. This method was added in v1.87 of Math::BigInt (June 2007). =item bcos() my $x = Math::BigInt->new(1); print $x->bcos(100), "\n"; Calculate the cosine of $x, modifying $x in place. In Math::BigInt, unless upgrading is in effect, the result is truncated to an integer. This method was added in v1.87 of Math::BigInt (June 2007). =item batan() my $x = Math::BigFloat->new(0.5); print $x->batan(100), "\n"; Calculate the arcus tangens of $x, modifying $x in place. In Math::BigInt, unless upgrading is in effect, the result is truncated to an integer. This method was added in v1.87 of Math::BigInt (June 2007). =item batan2() my $x = Math::BigInt->new(1); my $y = Math::BigInt->new(1); print $y->batan2($x), "\n"; Calculate the arcus tangens of C<$y> divided by C<$x>, modifying $y in place. In Math::BigInt, unless upgrading is in effect, the result is truncated to an integer. This method was added in v1.87 of Math::BigInt (June 2007). =item bsqrt() $x->bsqrt(); # calculate square-root C returns the square root truncated to an integer. If you want a better approximation of the square root, then use: $x = Math::BigFloat->new(12); Math::BigFloat->precision(0); Math::BigFloat->round_mode('even'); print $x->copy->bsqrt(),"\n"; # 4 Math::BigFloat->precision(2); print $x->bsqrt(),"\n"; # 3.46 print $x->bsqrt(3),"\n"; # 3.464 =item broot() $x->broot($N); Calculates the N'th root of C<$x>. =item bfac() $x->bfac(); # factorial of $x (1*2*3*4*..*$x) Returns the factorial of C<$x>, i.e., the product of all positive integers up to and including C<$x>. =item bdfac() $x->bdfac(); # double factorial of $x (1*2*3*4*..*$x) Returns the double factorial of C<$x>. If C<$x> is an even integer, returns the product of all positive, even integers up to and including C<$x>, i.e., 2*4*6*...*$x. If C<$x> is an odd integer, returns the product of all positive, odd integers, i.e., 1*3*5*...*$x. =item brsft() $x->brsft($n); # right shift $n places in base 2 $x->brsft($n, $b); # right shift $n places in base $b The latter is equivalent to $x -> bdiv($b -> copy() -> bpow($n)) =item blsft() $x->blsft($n); # left shift $n places in base 2 $x->blsft($n, $b); # left shift $n places in base $b The latter is equivalent to $x -> bmul($b -> copy() -> bpow($n)) =back =head2 Bitwise methods =over =item band() $x->band($y); # bitwise and =item bior() $x->bior($y); # bitwise inclusive or =item bxor() $x->bxor($y); # bitwise exclusive or =item bnot() $x->bnot(); # bitwise not (two's complement) Two's complement (bitwise not). This is equivalent to, but faster than, $x->binc()->bneg(); =back =head2 Rounding methods =over =item round() $x->round($A,$P,$round_mode); Round $x to accuracy C<$A> or precision C<$P> using the round mode C<$round_mode>. =item bround() $x->bround($N); # accuracy: preserve $N digits Rounds $x to an accuracy of $N digits. =item bfround() $x->bfround($N); Rounds to a multiple of 10**$N. Examples: Input N Result 123456.123456 3 123500 123456.123456 2 123450 123456.123456 -2 123456.12 123456.123456 -3 123456.123 =item bfloor() $x->bfloor(); Round $x towards minus infinity, i.e., set $x to the largest integer less than or equal to $x. =item bceil() $x->bceil(); Round $x towards plus infinity, i.e., set $x to the smallest integer greater than or equal to $x). =item bint() $x->bint(); Round $x towards zero. =back =head2 Other mathematical methods =over =item bgcd() $x -> bgcd($y); # GCD of $x and $y $x -> bgcd($y, $z, ...); # GCD of $x, $y, $z, ... Returns the greatest common divisor (GCD). =item blcm() $x -> blcm($y); # LCM of $x and $y $x -> blcm($y, $z, ...); # LCM of $x, $y, $z, ... Returns the least common multiple (LCM). =back =head2 Object property methods =over =item sign() $x->sign(); Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN. If you want $x to have a certain sign, use one of the following methods: $x->babs(); # '+' $x->babs()->bneg(); # '-' $x->bnan(); # 'NaN' $x->binf(); # '+inf' $x->binf('-'); # '-inf' =item digit() $x->digit($n); # return the nth digit, counting from right If C<$n> is negative, returns the digit counting from left. =item length() $x->length(); ($xl, $fl) = $x->length(); Returns the number of digits in the decimal representation of the number. In list context, returns the length of the integer and fraction part. For Math::BigInt objects, the length of the fraction part is always 0. The following probably doesn't do what you expect: $c = Math::BigInt->new(123); print $c->length(),"\n"; # prints 30 It prints both the number of digits in the number and in the fraction part since print calls C in list context. Use something like: print scalar $c->length(),"\n"; # prints 3 =item mantissa() $x->mantissa(); Return the signed mantissa of $x as a Math::BigInt. =item exponent() $x->exponent(); Return the exponent of $x as a Math::BigInt. =item parts() $x->parts(); Returns the significand (mantissa) and the exponent as integers. In Math::BigFloat, both are returned as Math::BigInt objects. =item sparts() Returns the significand (mantissa) and the exponent as integers. In scalar context, only the significand is returned. The significand is the integer with the smallest absolute value. The output of C corresponds to the output from C. In Math::BigInt, this method is identical to C. =item nparts() Returns the significand (mantissa) and exponent corresponding to normalized notation. In scalar context, only the significand is returned. For finite non-zero numbers, the significand's absolute value is greater than or equal to 1 and less than 10. The output of C corresponds to the output from C. In Math::BigInt, if the significand can not be represented as an integer, upgrading is performed or NaN is returned. =item eparts() Returns the significand (mantissa) and exponent corresponding to engineering notation. In scalar context, only the significand is returned. For finite non-zero numbers, the significand's absolute value is greater than or equal to 1 and less than 1000, and the exponent is a multiple of 3. The output of C corresponds to the output from C. In Math::BigInt, if the significand can not be represented as an integer, upgrading is performed or NaN is returned. =item dparts() Returns the integer part and the fraction part. If the fraction part can not be represented as an integer, upgrading is performed or NaN is returned. The output of C corresponds to the output from C. =back =head2 String conversion methods =over =item bstr() Returns a string representing the number using decimal notation. In Math::BigFloat, the output is zero padded according to the current accuracy or precision, if any of those are defined. =item bsstr() Returns a string representing the number using scientific notation where both the significand (mantissa) and the exponent are integers. The output corresponds to the output from C. 123 is returned as "123e+0" 1230 is returned as "123e+1" 12300 is returned as "123e+2" 12000 is returned as "12e+3" 10000 is returned as "1e+4" =item bnstr() Returns a string representing the number using normalized notation, the most common variant of scientific notation. For finite non-zero numbers, the absolute value of the significand is less than or equal to 1 and less than 10. The output corresponds to the output from C. 123 is returned as "1.23e+2" 1230 is returned as "1.23e+3" 12300 is returned as "1.23e+4" 12000 is returned as "1.2e+4" 10000 is returned as "1e+4" =item bestr() Returns a string representing the number using engineering notation. For finite non-zero numbers, the absolute value of the significand is less than or equal to 1 and less than 1000, and the exponent is a multiple of 3. The output corresponds to the output from C. 123 is returned as "123e+0" 1230 is returned as "1.23e+3" 12300 is returned as "12.3e+3" 12000 is returned as "12e+3" 10000 is returned as "10e+3" =item bdstr() Returns a string representing the number using decimal notation. The output corresponds to the output from C. 123 is returned as "123" 1230 is returned as "1230" 12300 is returned as "12300" 12000 is returned as "12000" 10000 is returned as "10000" =item to_hex() $x->to_hex(); Returns a hexadecimal string representation of the number. =item to_bin() $x->to_bin(); Returns a binary string representation of the number. =item to_oct() $x->to_oct(); Returns an octal string representation of the number. =item to_bytes() $x = Math::BigInt->new("1667327589"); $s = $x->to_bytes(); # $s = "cafe" Returns a byte string representation of the number using big endian byte order. The invocand must be a non-negative, finite integer. =item as_hex() $x->as_hex(); As, C, but with a "0x" prefix. =item as_bin() $x->as_bin(); As, C, but with a "0b" prefix. =item as_oct() $x->as_oct(); As, C, but with a "0" prefix. =item as_bytes() This is just an alias for C. =back =head2 Other conversion methods =over =item numify() print $x->numify(); Returns a Perl scalar from $x. It is used automatically whenever a scalar is needed, for instance in array index operations. =back =head1 ACCURACY and PRECISION Math::BigInt and Math::BigFloat have full support for accuracy and precision based rounding, both automatically after every operation, as well as manually. This section describes the accuracy/precision handling in Math::BigInt and Math::BigFloat as it used to be and as it is now, complete with an explanation of all terms and abbreviations. Not yet implemented things (but with correct description) are marked with '!', things that need to be answered are marked with '?'. In the next paragraph follows a short description of terms used here (because these may differ from terms used by others people or documentation). During the rest of this document, the shortcuts A (for accuracy), P (for precision), F (fallback) and R (rounding mode) are be used. =head2 Precision P Precision is a fixed number of digits before (positive) or after (negative) the decimal point. For example, 123.45 has a precision of -2. 0 means an integer like 123 (or 120). A precision of 2 means at least two digits to the left of the decimal point are zero, so 123 with P = 1 becomes 120. Note that numbers with zeros before the decimal point may have different precisions, because 1200 can have P = 0, 1 or 2 (depending on what the initial value was). It could also have p < 0, when the digits after the decimal point are zero. The string output (of floating point numbers) is padded with zeros: Initial value P A Result String ------------------------------------------------------------ 1234.01 -3 1000 1000 1234 -2 1200 1200 1234.5 -1 1230 1230 1234.001 1 1234 1234.0 1234.01 0 1234 1234 1234.01 2 1234.01 1234.01 1234.01 5 1234.01 1234.01000 For Math::BigInt objects, no padding occurs. =head2 Accuracy A Number of significant digits. Leading zeros are not counted. A number may have an accuracy greater than the non-zero digits when there are zeros in it or trailing zeros. For example, 123.456 has A of 6, 10203 has 5, 123.0506 has 7, 123.45000 has 8 and 0.000123 has 3. The string output (of floating point numbers) is padded with zeros: Initial value P A Result String ------------------------------------------------------------ 1234.01 3 1230 1230 1234.01 6 1234.01 1234.01 1234.1 8 1234.1 1234.1000 For Math::BigInt objects, no padding occurs. =head2 Fallback F When both A and P are undefined, this is used as a fallback accuracy when dividing numbers. =head2 Rounding mode R When rounding a number, different 'styles' or 'kinds' of rounding are possible. (Note that random rounding, as in Math::Round, is not implemented.) =over =item 'trunc' truncation invariably removes all digits following the rounding place, replacing them with zeros. Thus, 987.65 rounded to tens (P = 1) becomes 980, and rounded to the fourth sigdig becomes 987.6 (A = 4). 123.456 rounded to the second place after the decimal point (P = -2) becomes 123.46. All other implemented styles of rounding attempt to round to the "nearest digit." If the digit D immediately to the right of the rounding place (skipping the decimal point) is greater than 5, the number is incremented at the rounding place (possibly causing a cascade of incrementation): e.g. when rounding to units, 0.9 rounds to 1, and -19.9 rounds to -20. If D < 5, the number is similarly truncated at the rounding place: e.g. when rounding to units, 0.4 rounds to 0, and -19.4 rounds to -19. However the results of other styles of rounding differ if the digit immediately to the right of the rounding place (skipping the decimal point) is 5 and if there are no digits, or no digits other than 0, after that 5. In such cases: =item 'even' rounds the digit at the rounding place to 0, 2, 4, 6, or 8 if it is not already. E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. =item 'odd' rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if it is not already. E.g., when rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6. =item '+inf' round to plus infinity, i.e. always round up. E.g., when rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5, and 0.4501 also becomes 0.5. =item '-inf' round to minus infinity, i.e. always round down. E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5. =item 'zero' round to zero, i.e. positive numbers down, negative ones up. E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.5, but 0.4501 becomes 0.5. =item 'common' round up if the digit immediately to the right of the rounding place is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and 0.149 becomes 0.1. =back The handling of A & P in MBI/MBF (the old core code shipped with Perl versions <= 5.7.2) is like this: =over =item Precision * bfround($p) is able to round to $p number of digits after the decimal point * otherwise P is unused =item Accuracy (significant digits) * bround($a) rounds to $a significant digits * only bdiv() and bsqrt() take A as (optional) parameter + other operations simply create the same number (bneg etc), or more (bmul) of digits + rounding/truncating is only done when explicitly calling one of bround or bfround, and never for Math::BigInt (not implemented) * bsqrt() simply hands its accuracy argument over to bdiv. * the documentation and the comment in the code indicate two different ways on how bdiv() determines the maximum number of digits it should calculate, and the actual code does yet another thing POD: max($Math::BigFloat::div_scale,length(dividend)+length(divisor)) Comment: result has at most max(scale, length(dividend), length(divisor)) digits Actual code: scale = max(scale, length(dividend)-1,length(divisor)-1); scale += length(divisor) - length(dividend); So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10 So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3). Actually, the 'difference' added to the scale is cal- culated from the number of "significant digits" in dividend and divisor, which is derived by looking at the length of the man- tissa. Which is wrong, since it includes the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange assumption that 124 has 3 significant digits, while 120/7 will get you '17', not '17.1' since 120 is thought to have 2 signif- icant digits. The rounding after the division then uses the remainder and $y to determine whether it must round up or down. ? I have no idea which is the right way. That's why I used a slightly more ? simple scheme and tweaked the few failing testcases to match it. =back This is how it works now: =over =item Setting/Accessing * You can set the A global via Math::BigInt->accuracy() or Math::BigFloat->accuracy() or whatever class you are using. * You can also set P globally by using Math::SomeClass->precision() likewise. * Globals are classwide, and not inherited by subclasses. * to undefine A, use Math::SomeCLass->accuracy(undef); * to undefine P, use Math::SomeClass->precision(undef); * Setting Math::SomeClass->accuracy() clears automatically Math::SomeClass->precision(), and vice versa. * To be valid, A must be > 0, P can have any value. * If P is negative, this means round to the P'th place to the right of the decimal point; positive values mean to the left of the decimal point. P of 0 means round to integer. * to find out the current global A, use Math::SomeClass->accuracy() * to find out the current global P, use Math::SomeClass->precision() * use $x->accuracy() respective $x->precision() for the local setting of $x. * Please note that $x->accuracy() respective $x->precision() return eventually defined global A or P, when $x's A or P is not set. =item Creating numbers * When you create a number, you can give the desired A or P via: $x = Math::BigInt->new($number,$A,$P); * Only one of A or P can be defined, otherwise the result is NaN * If no A or P is give ($x = Math::BigInt->new($number) form), then the globals (if set) will be used. Thus changing the global defaults later on will not change the A or P of previously created numbers (i.e., A and P of $x will be what was in effect when $x was created) * If given undef for A and P, NO rounding will occur, and the globals will NOT be used. This is used by subclasses to create numbers without suffering rounding in the parent. Thus a subclass is able to have its own globals enforced upon creation of a number by using $x = Math::BigInt->new($number,undef,undef): use Math::BigInt::SomeSubclass; use Math::BigInt; Math::BigInt->accuracy(2); Math::BigInt::SomeSubClass->accuracy(3); $x = Math::BigInt::SomeSubClass->new(1234); $x is now 1230, and not 1200. A subclass might choose to implement this otherwise, e.g. falling back to the parent's A and P. =item Usage * If A or P are enabled/defined, they are used to round the result of each operation according to the rules below * Negative P is ignored in Math::BigInt, since Math::BigInt objects never have digits after the decimal point * Math::BigFloat uses Math::BigInt internally, but setting A or P inside Math::BigInt as globals does not tamper with the parts of a Math::BigFloat. A flag is used to mark all Math::BigFloat numbers as 'never round'. =item Precedence * It only makes sense that a number has only one of A or P at a time. If you set either A or P on one object, or globally, the other one will be automatically cleared. * If two objects are involved in an operation, and one of them has A in effect, and the other P, this results in an error (NaN). * A takes precedence over P (Hint: A comes before P). If neither of them is defined, nothing is used, i.e. the result will have as many digits as it can (with an exception for bdiv/bsqrt) and will not be rounded. * There is another setting for bdiv() (and thus for bsqrt()). If neither of A or P is defined, bdiv() will use a fallback (F) of $div_scale digits. If either the dividend's or the divisor's mantissa has more digits than the value of F, the higher value will be used instead of F. This is to limit the digits (A) of the result (just consider what would happen with unlimited A and P in the case of 1/3 :-) * bdiv will calculate (at least) 4 more digits than required (determined by A, P or F), and, if F is not used, round the result (this will still fail in the case of a result like 0.12345000000001 with A or P of 5, but this can not be helped - or can it?) * Thus you can have the math done by on Math::Big* class in two modi: + never round (this is the default): This is done by setting A and P to undef. No math operation will round the result, with bdiv() and bsqrt() as exceptions to guard against overflows. You must explicitly call bround(), bfround() or round() (the latter with parameters). Note: Once you have rounded a number, the settings will 'stick' on it and 'infect' all other numbers engaged in math operations with it, since local settings have the highest precedence. So, to get SaferRound[tm], use a copy() before rounding like this: $x = Math::BigFloat->new(12.34); $y = Math::BigFloat->new(98.76); $z = $x * $y; # 1218.6984 print $x->copy()->bround(3); # 12.3 (but A is now 3!) $z = $x * $y; # still 1218.6984, without # copy would have been 1210! + round after each op: After each single operation (except for testing like is_zero()), the method round() is called and the result is rounded appropriately. By setting proper values for A and P, you can have all-the-same-A or all-the-same-P modes. For example, Math::Currency might set A to undef, and P to -2, globally. ?Maybe an extra option that forbids local A & P settings would be in order, ?so that intermediate rounding does not 'poison' further math? =item Overriding globals * you will be able to give A, P and R as an argument to all the calculation routines; the second parameter is A, the third one is P, and the fourth is R (shift right by one for binary operations like badd). P is used only if the first parameter (A) is undefined. These three parameters override the globals in the order detailed as follows, i.e. the first defined value wins: (local: per object, global: global default, parameter: argument to sub) + parameter A + parameter P + local A (if defined on both of the operands: smaller one is taken) + local P (if defined on both of the operands: bigger one is taken) + global A + global P + global F * bsqrt() will hand its arguments to bdiv(), as it used to, only now for two arguments (A and P) instead of one =item Local settings * You can set A or P locally by using $x->accuracy() or $x->precision() and thus force different A and P for different objects/numbers. * Setting A or P this way immediately rounds $x to the new value. * $x->accuracy() clears $x->precision(), and vice versa. =item Rounding * the rounding routines will use the respective global or local settings. bround() is for accuracy rounding, while bfround() is for precision * the two rounding functions take as the second parameter one of the following rounding modes (R): 'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common' * you can set/get the global R by using Math::SomeClass->round_mode() or by setting $Math::SomeClass::round_mode * after each operation, $result->round() is called, and the result may eventually be rounded (that is, if A or P were set either locally, globally or as parameter to the operation) * to manually round a number, call $x->round($A,$P,$round_mode); this will round the number by using the appropriate rounding function and then normalize it. * rounding modifies the local settings of the number: $x = Math::BigFloat->new(123.456); $x->accuracy(5); $x->bround(4); Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy() will be 4 from now on. =item Default values * R: 'even' * F: 40 * A: undef * P: undef =item Remarks * The defaults are set up so that the new code gives the same results as the old code (except in a few cases on bdiv): + Both A and P are undefined and thus will not be used for rounding after each operation. + round() is thus a no-op, unless given extra parameters A and P =back =head1 Infinity and Not a Number While Math::BigInt has extensive handling of inf and NaN, certain quirks remain. =over =item oct()/hex() These perl routines currently (as of Perl v.5.8.6) cannot handle passed inf. te@linux:~> perl -wle 'print 2 ** 3333' Inf te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333' 1 te@linux:~> perl -wle 'print oct(2 ** 3333)' 0 te@linux:~> perl -wle 'print hex(2 ** 3333)' Illegal hexadecimal digit 'I' ignored at -e line 1. 0 The same problems occur if you pass them Math::BigInt->binf() objects. Since overloading these routines is not possible, this cannot be fixed from Math::BigInt. =back =head1 INTERNALS You should neither care about nor depend on the internal representation; it might change without notice. Use B method calls like C<< $x->sign(); >> instead relying on the internal representation. =head2 MATH LIBRARY Math with the numbers is done (by default) by a module called C. This is equivalent to saying: use Math::BigInt try => 'Calc'; You can change this backend library by using: use Math::BigInt try => 'GMP'; B: General purpose packages should not be explicit about the library to use; let the script author decide which is best. If your script works with huge numbers and Calc is too slow for them, you can also for the loading of one of these libraries and if none of them can be used, the code dies: use Math::BigInt only => 'GMP,Pari'; The following would first try to find Math::BigInt::Foo, then Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc: use Math::BigInt try => 'Foo,Math::BigInt::Bar'; The library that is loaded last is used. Note that this can be overwritten at any time by loading a different library, and numbers constructed with different libraries cannot be used in math operations together. =head3 What library to use? B: General purpose packages should not be explicit about the library to use; let the script author decide which is best. L and L are in cases involving big numbers much faster than Calc, however it is slower when dealing with very small numbers (less than about 20 digits) and when converting very large numbers to decimal (for instance for printing, rounding, calculating their length in decimal etc). So please select carefully what library you want to use. Different low-level libraries use different formats to store the numbers. However, you should B depend on the number having a specific format internally. See the respective math library module documentation for further details. =head2 SIGN The sign is either '+', '-', 'NaN', '+inf' or '-inf'. A sign of 'NaN' is used to represent the result when input arguments are not numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively minus infinity. You get '+inf' when dividing a positive number by 0, and '-inf' when dividing any negative number by 0. =head1 EXAMPLES use Math::BigInt; sub bigint { Math::BigInt->new(shift); } $x = Math::BigInt->bstr("1234") # string "1234" $x = "$x"; # same as bstr() $x = Math::BigInt->bneg("1234"); # Math::BigInt "-1234" $x = Math::BigInt->babs("-12345"); # Math::BigInt "12345" $x = Math::BigInt->bnorm("-0.00"); # Math::BigInt "0" $x = bigint(1) + bigint(2); # Math::BigInt "3" $x = bigint(1) + "2"; # ditto (auto-Math::BigIntify of "2") $x = bigint(1); # Math::BigInt "1" $x = $x + 5 / 2; # Math::BigInt "3" $x = $x ** 3; # Math::BigInt "27" $x *= 2; # Math::BigInt "54" $x = Math::BigInt->new(0); # Math::BigInt "0" $x--; # Math::BigInt "-1" $x = Math::BigInt->badd(4,5) # Math::BigInt "9" print $x->bsstr(); # 9e+0 Examples for rounding: use Math::BigFloat; use Test::More; $x = Math::BigFloat->new(123.4567); $y = Math::BigFloat->new(123.456789); Math::BigFloat->accuracy(4); # no more A than 4 is ($x->copy()->bround(),123.4); # even rounding print $x->copy()->bround(),"\n"; # 123.4 Math::BigFloat->round_mode('odd'); # round to odd print $x->copy()->bround(),"\n"; # 123.5 Math::BigFloat->accuracy(5); # no more A than 5 Math::BigFloat->round_mode('odd'); # round to odd print $x->copy()->bround(),"\n"; # 123.46 $y = $x->copy()->bround(4),"\n"; # A = 4: 123.4 print "$y, ",$y->accuracy(),"\n"; # 123.4, 4 Math::BigFloat->accuracy(undef); # A not important now Math::BigFloat->precision(2); # P important print $x->copy()->bnorm(),"\n"; # 123.46 print $x->copy()->bround(),"\n"; # 123.46 Examples for converting: my $x = Math::BigInt->new('0b1'.'01' x 123); print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n"; =head1 Autocreating constants After C all the B decimal, hexadecimal and binary constants in the given scope are converted to C. This conversion happens at compile time. In particular, perl -MMath::BigInt=:constant -e 'print 2**100,"\n"' prints the integer value of C<2**100>. Note that without conversion of constants the expression 2**100 is calculated using Perl scalars. Please note that strings and floating point constants are not affected, so that use Math::BigInt qw/:constant/; $x = 1234567890123456789012345678901234567890 + 123456789123456789; $y = '1234567890123456789012345678901234567890' + '123456789123456789'; does not give you what you expect. You need an explicit Math::BigInt->new() around one of the operands. You should also quote large constants to protect loss of precision: use Math::BigInt; $x = Math::BigInt->new('1234567889123456789123456789123456789'); Without the quotes Perl would convert the large number to a floating point constant at compile time and then hand the result to Math::BigInt, which results in an truncated result or a NaN. This also applies to integers that look like floating point constants: use Math::BigInt ':constant'; print ref(123e2),"\n"; print ref(123.2e2),"\n"; prints nothing but newlines. Use either L or L to get this to work. =head1 PERFORMANCE Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x must be made in the second case. For long numbers, the copy can eat up to 20% of the work (in the case of addition/subtraction, less for multiplication/division). If $y is very small compared to $x, the form $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes more time then the actual addition. With a technique called copy-on-write, the cost of copying with overload could be minimized or even completely avoided. A test implementation of COW did show performance gains for overloaded math, but introduced a performance loss due to a constant overhead for all other operations. So Math::BigInt does currently not COW. The rewritten version of this module (vs. v0.01) is slower on certain operations, like C, C and C. The reason are that it does now more work and handles much more cases. The time spent in these operations is usually gained in the other math operations so that code on the average should get (much) faster. If they don't, please contact the author. Some operations may be slower for small numbers, but are significantly faster for big numbers. Other operations are now constant (O(1), like C, C etc), instead of O(N) and thus nearly always take much less time. These optimizations were done on purpose. If you find the Calc module to slow, try to install any of the replacement modules and see if they help you. =head2 Alternative math libraries You can use an alternative library to drive Math::BigInt. See the section L for more information. For more benchmark results see L. =head1 SUBCLASSING =head2 Subclassing Math::BigInt The basic design of Math::BigInt allows simple subclasses with very little work, as long as a few simple rules are followed: =over =item * The public API must remain consistent, i.e. if a sub-class is overloading addition, the sub-class must use the same name, in this case badd(). The reason for this is that Math::BigInt is optimized to call the object methods directly. =item * The private object hash keys like C<< $x->{sign} >> may not be changed, but additional keys can be added, like C<< $x->{_custom} >>. =item * Accessor functions are available for all existing object hash keys and should be used instead of directly accessing the internal hash keys. The reason for this is that Math::BigInt itself has a pluggable interface which permits it to support different storage methods. =back More complex sub-classes may have to replicate more of the logic internal of Math::BigInt if they need to change more basic behaviors. A subclass that needs to merely change the output only needs to overload C. All other object methods and overloaded functions can be directly inherited from the parent class. At the very minimum, any subclass needs to provide its own C and can store additional hash keys in the object. There are also some package globals that must be defined, e.g.: # Globals $accuracy = undef; $precision = -2; # round to 2 decimal places $round_mode = 'even'; $div_scale = 40; Additionally, you might want to provide the following two globals to allow auto-upgrading and auto-downgrading to work correctly: $upgrade = undef; $downgrade = undef; This allows Math::BigInt to correctly retrieve package globals from the subclass, like C<$SubClass::precision>. See t/Math/BigInt/Subclass.pm or t/Math/BigFloat/SubClass.pm completely functional subclass examples. Don't forget to use overload; in your subclass to automatically inherit the overloading from the parent. If you like, you can change part of the overloading, look at Math::String for an example. =head1 UPGRADING When used like this: use Math::BigInt upgrade => 'Foo::Bar'; certain operations 'upgrade' their calculation and thus the result to the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat: use Math::BigInt upgrade => 'Math::BigFloat'; As a shortcut, you can use the module L: use bignum; Also good for one-liners: perl -Mbignum -le 'print 2 ** 255' This makes it possible to mix arguments of different classes (as in 2.5 + 2) as well es preserve accuracy (as in sqrt(3)). Beware: This feature is not fully implemented yet. =head2 Auto-upgrade The following methods upgrade themselves unconditionally; that is if upgrade is in effect, they always hands up their work: div bsqrt blog bexp bpi bsin bcos batan batan2 All other methods upgrade themselves only when one (or all) of their arguments are of the class mentioned in $upgrade. =head1 EXPORTS C exports nothing by default, but can export the following methods: bgcd blcm =head1 CAVEATS Some things might not work as you expect them. Below is documented what is known to be troublesome: =over =item Comparing numbers as strings Both C and C as well as stringify via overload drop the leading '+'. This is to be consistent with Perl and to make C (especially with overloading) to work as you expect. It also solves problems with C and L, which stringify arguments before comparing them. Mark Biggar said, when asked about to drop the '+' altogether, or make only C work: I agree (with the first alternative), don't add the '+' on positive numbers. It's not as important anymore with the new internal form for numbers. It made doing things like abs and neg easier, but those have to be done differently now anyway. So, the following examples now works as expected: use Test::More tests => 1; use Math::BigInt; my $x = Math::BigInt -> new(3*3); my $y = Math::BigInt -> new(3*3); is($x,3*3, 'multiplication'); print "$x eq 9" if $x eq $y; print "$x eq 9" if $x eq '9'; print "$x eq 9" if $x eq 3*3; Additionally, the following still works: print "$x == 9" if $x == $y; print "$x == 9" if $x == 9; print "$x == 9" if $x == 3*3; There is now a C method to get the string in scientific notation aka C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr() for comparison, but Perl represents some numbers as 100 and others as 1e+308. If in doubt, convert both arguments to Math::BigInt before comparing them as strings: use Test::More tests => 3; use Math::BigInt; $x = Math::BigInt->new('1e56'); $y = 1e56; is($x,$y); # fails is($x->bsstr(),$y); # okay $y = Math::BigInt->new($y); is($x,$y); # okay Alternatively, simply use C<< <=> >> for comparisons, this always gets it right. There is not yet a way to get a number automatically represented as a string that matches exactly the way Perl represents it. See also the section about L for problems in comparing NaNs. =item int() C returns (at least for Perl v5.7.1 and up) another Math::BigInt, not a Perl scalar: $x = Math::BigInt->new(123); $y = int($x); # 123 as a Math::BigInt $x = Math::BigFloat->new(123.45); $y = int($x); # 123 as a Math::BigFloat If you want a real Perl scalar, use C: $y = $x->numify(); # 123 as a scalar This is seldom necessary, though, because this is done automatically, like when you access an array: $z = $array[$x]; # does work automatically =item Modifying and = Beware of: $x = Math::BigFloat->new(5); $y = $x; This makes a second reference to the B object and stores it in $y. Thus anything that modifies $x (except overloaded operators) also modifies $y, and vice versa. Or in other words, C<=> is only safe if you modify your Math::BigInt objects only via overloaded math. As soon as you use a method call it breaks: $x->bmul(2); print "$x, $y\n"; # prints '10, 10' If you want a true copy of $x, use: $y = $x->copy(); You can also chain the calls like this, this first makes a copy and then multiply it by 2: $y = $x->copy()->bmul(2); See also the documentation for overload.pm regarding C<=>. =item Overloading -$x The following: $x = -$x; is slower than $x->bneg(); since overload calls C instead of C. The first variant needs to preserve $x since it does not know that it later gets overwritten. This makes a copy of $x and takes O(N), but $x->bneg() is O(1). =item Mixing different object types With overloaded operators, it is the first (dominating) operand that determines which method is called. Here are some examples showing what actually gets called in various cases. use Math::BigInt; use Math::BigFloat; $mbf = Math::BigFloat->new(5); $mbi2 = Math::BigInt->new(5); $mbi = Math::BigInt->new(2); # what actually gets called: $float = $mbf + $mbi; # $mbf->badd($mbi) $float = $mbf / $mbi; # $mbf->bdiv($mbi) $integer = $mbi + $mbf; # $mbi->badd($mbf) $integer = $mbi2 / $mbi; # $mbi2->bdiv($mbi) $integer = $mbi2 / $mbf; # $mbi2->bdiv($mbf) For instance, Math::BigInt->bdiv() always returns a Math::BigInt, regardless of whether the second operant is a Math::BigFloat. To get a Math::BigFloat you either need to call the operation manually, make sure each operand already is a Math::BigFloat, or cast to that type via Math::BigFloat->new(): $float = Math::BigFloat->new($mbi2) / $mbi; # = 2.5 Beware of casting the entire expression, as this would cast the result, at which point it is too late: $float = Math::BigFloat->new($mbi2 / $mbi); # = 2 Beware also of the order of more complicated expressions like: $integer = ($mbi2 + $mbi) / $mbf; # int / float => int $integer = $mbi2 / Math::BigFloat->new($mbi); # ditto If in doubt, break the expression into simpler terms, or cast all operands to the desired resulting type. Scalar values are a bit different, since: $float = 2 + $mbf; $float = $mbf + 2; both result in the proper type due to the way the overloaded math works. This section also applies to other overloaded math packages, like Math::String. One solution to you problem might be autoupgrading|upgrading. See the pragmas L, L and L for an easy way to do this. =back =head1 BUGS Please report any bugs or feature requests to C, or through the web interface at L (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes. =head1 SUPPORT You can find documentation for this module with the perldoc command. perldoc Math::BigInt You can also look for information at: =over 4 =item * RT: CPAN's request tracker L =item * AnnoCPAN: Annotated CPAN documentation L =item * CPAN Ratings L =item * Search CPAN L =item * CPAN Testers Matrix L =item * The Bignum mailing list =over 4 =item * Post to mailing list C =item * View mailing list L =item * Subscribe/Unsubscribe L =back =back =head1 LICENSE This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. =head1 SEE ALSO L and L as well as the backends L, L, and L. The pragmas L, L and L also might be of interest because they solve the autoupgrading/downgrading issue, at least partly. =head1 AUTHORS =over 4 =item * Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001. =item * Completely rewritten by Tels L, 2001-2008. =item * Florian Ragwitz Eflora@cpan.orgE, 2010. =item * Peter John Acklam Epjacklam@online.noE, 2011-. =back Many people contributed in one or more ways to the final beast, see the file CREDITS for an (incomplete) list. If you miss your name, please drop me a mail. Thank you! =cut Math-BigInt-1.999808/LICENSE0000644403072340010010000000015513017613220015337 0ustar ospjadomain usersThis program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. Math-BigInt-1.999808/Makefile.PL0000644403072340010010000000506413033132075016312 0ustar ospjadomain users#!perl use strict; use warnings; use ExtUtils::MakeMaker; # This is a list of known backend libraries and the version number when these # libraries became subclasses of Math::BigInt::Lib. New library methods are # added to Math::BigInt::Lib first. Later, optimized versions are implemented # for the specific libraries. In the meantime, these new methods won't be # available to libraries that aren't a subclass of Math::BigInt::Lib. my $recommend_versions = { 'Math::BigInt::Calc' => '1.999800', 'Math::BigInt::FastCalc' => '0.5000', 'Math::BigInt::GMP' => '1.6000', 'Math::BigInt::Pari' => '1.3000', 'Math::BigInt::BitVect' => '1.13', #'Math::BigInt::GMPz' => '0.001', }; my $recommend_update = []; while (my ($module, $recommend_version) = each %$recommend_versions) { next unless eval "require $module"; my $version = $module -> VERSION(); next if $version >= $recommend_version; push @$recommend_update, [ $module, $recommend_version, $version ]; } if (@$recommend_update) { print <<"EOF"; ########################################################################## # # Some of the new methods will not work unless the following installed # modules are updated. It is therefore recommended that the modules listed # below are upgraded after installing this distribution. # # Module Recommended Installed # ------ ----------- --------- EOF for my $entry (@$recommend_update) { printf "# %-30s %-14s %s\n", @$entry; } print <<"EOF"; # ########################################################################## Sleeping for a few seconds ... EOF sleep 5; } my %WriteMakefileArgs = ( 'NAME' => 'Math::BigInt', 'VERSION_FROM' => 'lib/Math/BigInt.pm', 'AUTHOR' => 'Peter John Acklam ', 'MIN_PERL_VERSION' => 5.006001, 'PREREQ_PM' => { #'ExtUtils::MakeMaker' => 6.58, 'Test::More' => 0.94, 'Math::Complex' => 1.39, }, 'LICENSE' => 'perl_5', 'LIBS' => [''], # e.g., '-lm' 'DEFINE' => '', # e.g., '-DHAVE_SOMETHING' 'INC' => '', # e.g., '-I/usr/include/other' 'SIGN' => 1, ); # Install over the core version? (Cf. CPAN RT #119199 and #119225.) $WriteMakefileArgs{INSTALLDIRS} = 'perl' if $] < 5.012; WriteMakefile(%WriteMakefileArgs); Math-BigInt-1.999808/MANIFEST0000644403072340010010000001262313035475732015504 0ustar ospjadomain usersBUGS CHANGES CREDITS examples/1000.txt examples/bigprimes.pl examples/prime.pl GOALS HISTORY lib/Math/BigFloat.pm lib/Math/BigInt.pm lib/Math/BigInt/Calc.pm lib/Math/BigInt/CalcEmu.pm lib/Math/BigInt/Lib.pm LICENSE Makefile.PL MANIFEST This list of files MANIFEST.SKIP NEW README t/00sig.t t/01load.t t/02pod.t t/03podcov.t t/_e_math.t t/alias.inc t/author-batan-mbf.t t/author-batan2-mbf.t t/author-bexp-mbf.t t/author-blog-mbf.t t/author-blog-mbi.t t/author-bmod-bdiv-mbi.t t/author-bnok-mbi.t t/author-bpi-mbf.t t/author-btmod-btdiv-mbi.t t/author-lib-arithmetic-binary-_add.dat t/author-lib-arithmetic-binary-_add.t t/author-lib-arithmetic-binary-_div.dat t/author-lib-arithmetic-binary-_div.t t/author-lib-arithmetic-binary-_gcd.dat t/author-lib-arithmetic-binary-_gcd.t 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Math-BigInt-1.999808/META.json0000604403072340010010000000174513035475731015772 0ustar ospjadomain users{ "abstract" : "unknown", "author" : [ "Peter John Acklam " ], "dynamic_config" : 1, "generated_by" : "ExtUtils::MakeMaker version 7.24, CPAN::Meta::Converter version 2.150010", "license" : [ "perl_5" ], "meta-spec" : { "url" : "http://search.cpan.org/perldoc?CPAN::Meta::Spec", "version" : "2" }, "name" : "Math-BigInt", "no_index" : { "directory" : [ "t", "inc" ] }, "prereqs" : { "build" : { "requires" : { "ExtUtils::MakeMaker" : "0" } }, "configure" : { "requires" : { "ExtUtils::MakeMaker" : "0" } }, "runtime" : { "requires" : { "Math::Complex" : "1.39", "Test::More" : "0.94", "perl" : "5.006001" } } }, "release_status" : "stable", "version" : "1.999808", "x_serialization_backend" : "JSON::PP version 2.27400" } Math-BigInt-1.999808/META.yml0000604403072340010010000000111413035475730015607 0ustar ospjadomain users--- abstract: unknown author: - 'Peter John Acklam ' build_requires: ExtUtils::MakeMaker: '0' configure_requires: ExtUtils::MakeMaker: '0' dynamic_config: 1 generated_by: 'ExtUtils::MakeMaker version 7.24, CPAN::Meta::Converter version 2.150010' license: perl meta-spec: url: http://module-build.sourceforge.net/META-spec-v1.4.html version: '1.4' name: Math-BigInt no_index: directory: - t - inc requires: Math::Complex: '1.39' Test::More: '0.94' perl: '5.006001' version: '1.999808' x_serialization_backend: 'CPAN::Meta::YAML version 0.018' Math-BigInt-1.999808/NEW0000644403072340010010000000010012740677022014710 0ustar ospjadomain usersFor the list of recent changes see the end of the CHANGES file. Math-BigInt-1.999808/README0000644403072340010010000000214612740677022015230 0ustar ospjadomain usersMath-BigInt Math::BigInt and Math::BigFloat are modules for arbitrary precision arithmetic. INSTALLATION To install this module, unpack the distribution file, and run the following commands: perl Makefile.PL make make test make install SUPPORT AND DOCUMENTATION After installing, you can find documentation for these modules with the perldoc command. perldoc Math::BigInt perldoc Math::BigFloat You can also look for information at: RT, CPAN's request tracker http://rt.cpan.org/NoAuth/Bugs.html?Dist=Math-BigInt AnnoCPAN, Annotated CPAN documentation http://annocpan.org/dist/Math-BigInt CPAN Ratings http://cpanratings.perl.org/d/Math-BigInt Search CPAN http://search.cpan.org/dist/Math-BigInt COPYRIGHT AND LICENCE Copyright 1996-2001 Mark Biggar, Ilya Zakharevich. Copyright 2001-2008 Tels, L. Copyright 2010 Florian Ragwitz L. Copyright 2011- Peter John Acklam L. 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"so you can verify the integrity of this distribution."; } elsif (!-e 'SIGNATURE') { plan skip_all => "SIGNATURE not found"; } elsif (!-s 'SIGNATURE') { plan skip_all => "SIGNATURE file empty"; } elsif (!eval { require Socket; Socket::inet_aton('pool.sks-keyservers.net') }) { plan skip_all => "Cannot connect to the keyserver to check module ". "signature"; } else { plan tests => 1; } my $ret = Module::Signature::verify(); SKIP: { skip "Module::Signature cannot verify", 1 if $ret eq Module::Signature::CANNOT_VERIFY(); cmp_ok $ret, '==', Module::Signature::SIGNATURE_OK(), "Valid signature"; } Math-BigInt-1.999808/t/01load.t0000644403072340010010000000112413017554107016047 0ustar ospjadomain users#!perl use strict; # restrict unsafe constructs use warnings; # enable optional warnings use Test::More tests => 2; BEGIN { use_ok('Math::BigInt'); use_ok('Math::BigFloat'); }; my @mods = ('Math::BigInt', 'Math::BigFloat', 'Math::BigInt::Lib', 'Math::BigInt::Calc', ); diag(""); diag("Testing with Perl $], $^X"); diag(""); diag(sprintf("%12s %s\n", 'Version', 'Module')); diag(sprintf("%12s %s\n", '-------', '------')); for my $mod (@mods) { diag(sprintf("%12s %s\n", $mod -> VERSION(), $mod)); } diag(""); Math-BigInt-1.999808/t/02pod.t0000644403072340010010000000046512740677022015726 0ustar ospjadomain users#!perl use strict; # restrict unsafe constructs use warnings; # enable optional warnings use Test::More; # Ensure a recent version of Test::Pod my $min_tp = 1.22; eval "use Test::Pod $min_tp"; plan skip_all => "Test::Pod $min_tp required for testing POD" if $@; all_pod_files_ok(); Math-BigInt-1.999808/t/03podcov.t0000644403072340010010000000237313021606261016425 0ustar ospjadomain users#!perl use strict; # restrict unsafe constructs use warnings; # enable optional warnings use Test::More; # Ensure a recent version of Test::Pod::Coverage my $min_tpc = 1.08; eval "use Test::Pod::Coverage $min_tpc"; plan skip_all => "Test::Pod::Coverage $min_tpc required for testing POD coverage" if $@; # Test::Pod::Coverage doesn't require a minimum Pod::Coverage version, # but older versions don't recognize some common documentation styles my $min_pc = 0.18; eval "use Pod::Coverage $min_pc"; plan skip_all => "Pod::Coverage $min_pc required for testing POD coverage" if $@; plan tests => 3; my $trustme; # Math::BigInt $trustme = { trustme => [ 'fround', 'objectify' ], }; pod_coverage_ok('Math::BigInt', $trustme, "Math::BigInt is covered"); # Math::BigFloat $trustme = { trustme => [ 'DEBUG', 'isa' ], coverage_class => 'Pod::Coverage::CountParents', }; pod_coverage_ok('Math::BigFloat', $trustme, "Math::BigFloat is covered"); # Math::BigInt::Lib $trustme = { private => [ qr/^(un)?import$/ ], }; pod_coverage_ok('Math::BigInt::Lib', $trustme, "Math::BigInt::Lib is covered"); Math-BigInt-1.999808/t/alias.inc0000644403072340010010000000103412740677023016373 0ustar ospjadomain users#!perl use strict; use warnings; our $CLASS; # alias subroutine testing, included by sub_ali.t, mbi_ali.t, and mbf_ali.t our $x = $CLASS->new(123); is($x->is_pos(), 1, "$CLASS -> new(123) -> is_pos()"); is($x->is_neg(), 0, "$CLASS -> new(123) -> is_neg()"); is($x->as_int(), 123, "$CLASS -> new(123) -> as_int()"); is(ref($x->as_int()), 'Math::BigInt', "ref($CLASS -> new(123) -> as_int())"); $x->bneg(); is($x->is_pos(), 0, "$CLASS -> new(123) -> bneg() -> is_pos()"); is($x->is_neg(), 1, "$CLASS -> new(123) -> bneg() -> is_neg()"); Math-BigInt-1.999808/t/author-batan-mbf.t0000644403072340010010000000416012740677023020126 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 42; use Math::Complex (); use Math::BigFloat; my $inf = Math::Complex::Inf(); # most portable way to get infinity my $nan = $inf - $inf; my $class = 'Math::BigFloat'; # atan X sub atan { atan2($_[0], 1) } # isnan X #sub isnan { !defined($_[0] <=> 0) } sub isnan { !($_[0] <= 0 || $_[0] > 0) } # linspace MIN, MAX, N # # Returns N linearly spaced elements from MIN to MAX. sub linspace { my ($xmin, $xmax, $n) = @_; if ($n == 0) { return (); } elsif ($n == 1) { return ($xmin); } else { my $c = ($xmax - $xmin) / ($n - 1); return map { $xmin + $c * $_ } 0 .. ($n - 1); } } # logspace MIN, MAX, N # # Returns N logarithmically spaced elements from MIN to MAX. sub logspace { my ($xmin, $xmax, $n) = @_; if ($n == 0) { return (); } elsif ($n == 1) { return ($xmin); } else { my @lin = linspace(log($xmin), log($xmax), $n); my @log = map { exp } @lin; $log[ 0 ] = $xmin; $log[ $#log ] = $xmax; return @log; } } my @x; @x = logspace(0.01, 12, 20); @x = map { sprintf "%.3g", $_ } @x; @x = (reverse(map( { -$_ } @x)), 0, @x, $nan); my $accu = 16; my $tol = 1e-14; my $max_relerr = 0; for (my $i = 0; $i <= $#x ; ++$i) { my $x = $x[$i]; my $pl = atan($x); my $bf = $class -> new("$x") -> batan($accu); my $desc = qq|$class->new("$x")->batan($accu) vs. CORE::atan2("$x", 1)|; if (isnan($x)) { is($bf, "NaN", $desc); } elsif ($x == 0) { cmp_ok($bf, '==', $pl, $desc); } else { my $relerr = abs(($bf - $pl) / $pl); # relative error #printf("# %23.15e %23.15e %23.15e %23.15e\n", $x, $pl, $bf, $relerr); cmp_ok($relerr, '<', $tol, "relative error of $desc"); $max_relerr = $relerr if $relerr > $max_relerr; } } diag("Maximum relative error = ", $max_relerr -> numify(), "\n"); Math-BigInt-1.999808/t/author-batan2-mbf.t0000644403072340010010000000665012740677023020216 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 3528; use Math::Complex (); use Math::BigFloat; my $inf = Math::Complex::Inf(); my $nan = $inf - $inf; my $class = 'Math::BigFloat'; # isnan X #sub isnan { !($_[0] <= 0 || $_[0] > 0) } sub isnan { !defined($_[0] <=> 0) } # linspace MIN, MAX, N # # Returns N linearly spaced elements from MIN to MAX. sub linspace { my ($xmin, $xmax, $n) = @_; if ($n == 0) { return (); } elsif ($n == 1) { return ($xmin); } else { my $c = ($xmax - $xmin) / ($n - 1); return map { $xmin + $c * $_ } 0 .. ($n - 1); } } # logspace MIN, MAX, N # # Returns N logarithmically spaced elements from MIN to MAX. sub logspace { my ($xmin, $xmax, $n) = @_; if ($n == 0) { return (); } elsif ($n == 1) { return ($xmin); } else { my @lin = linspace(log($xmin), log($xmax), $n); my @log = map { exp } @lin; $log[ 0 ] = $xmin; $log[ $#log ] = $xmax; return @log; } } my @x; @x = logspace(0.01, 12, 20); @x = map { sprintf "%.3g", $_ } @x; @x = (reverse(map( { -$_ } @x)), 0, @x, $nan); my $accu = 16; my $tol = 1e-14; my $max_relerr = 0; for my $ply (@x) { for my $plx (@x) { my $plz = CORE::atan2($ply, $plx); # $y -> batan2($x) where $x is a scalar { my $y = $class -> new($ply); $y -> batan2($plx, $accu); my $desc = qq|\$y = $class->new("$ply");| . qq| \$y->batan2("$plx", $accu)| . qq| vs. CORE::atan2($ply, $plx)|; if (isnan($plz)) { is($y, "NaN", $desc); } elsif ($plz == 0) { cmp_ok($y, '==', $plz, $desc); } else { my $relerr = abs(($y - $plz) / $plz); if (!cmp_ok($relerr, '<', $tol, "relative error of $desc")) { diag(sprintf(" CORE::atan2(...): %.15g\n" . " Math::BigFloat->batan2(...): %.15g\n", $plz, $y)); } $max_relerr = $relerr if $relerr > $max_relerr; } } # $y -> batan2($x) where $x is an object { my $x = $class -> new($plx); my $y = $class -> new($ply); $y -> batan2($plx, $accu); my $desc = qq|\$y = $class->new("$ply");| . qq| \$x = $class->new("$plx");| . qq| \$y->batan2(\$x, $accu)| . qq| vs. CORE::atan2($ply, $plx)|; if (isnan($plz)) { is($y, "NaN", $desc); } elsif ($plz == 0) { cmp_ok($y, '==', $plz, $desc); } else { my $relerr = abs(($y - $plz) / $plz); if (!cmp_ok($relerr, '<', $tol, "relative error of $desc")) { diag(sprintf(" CORE::atan2(...): %.15g\n" . " Math::BigFloat->batan2(...): %.15g\n", $plz, $y)); } $max_relerr = $relerr if $relerr > $max_relerr; } } } } diag("Maximum relative error = ", $max_relerr -> numify(), "\n"); Math-BigInt-1.999808/t/author-bexp-mbf.t0000644403072340010010000007414412740677023020010 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 961; use Math::BigFloat; my $class = 'Math::BigFloat'; my $accu = 16; my $tol = 1e-14; my $max_relerr = 0; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x, $wanted) = split /:/; my $test = qq|$class->new("$x", 20)->bexp()->bsstr()|; my $got = eval $test; die $@ if $@; # this should never be true is($got, $wanted, $test); } __DATA__ -120.00:76676480737219996324e-72 -119.75:9845455012875848912e-71 -119.50:12641814475388325097e-71 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102.50:32747970845838552539e+25 102.75:42049226911005857362e+25 103.00:53992276105801688698e+25 103.25:69327454824671601441e+25 103.50:89018214069149526772e+25 103.75:11430164941293829253e+26 104.00:14676622301554423285e+26 104.25:18845156066322017808e+26 104.50:24197659370604648107e+26 104.75:31070409656208665623e+26 105.00:39895195705472158508e+26 105.25:51226445289557882906e+26 105.50:65776057758356352562e+26 105.75:84458129971250466654e+26 106.00:10844638552900230813e+27 106.25:13924791536715664689e+27 106.50:17879786255221267423e+27 106.75:22958099996648240809e+27 107.00:29478783914555093774e+27 107.25:37851507799334495336e+27 107.50:48602298074299772045e+27 107.75:62406586036834580316e+27 108.00:80131642640005911411e+27 108.25:10289106583070678347e+28 108.50:13211474367671911753e+28 108.75:16963868880009342429e+28 109.00:21782038807290206356e+28 109.25:27968691455839362744e+28 109.50:35912510700795012746e+28 109.75:46112576516891291178e+28 110.00:5920972027664670299e+29 110.25:76026785750185898786e+28 110.50:97620325252312095227e+28 110.75:1253469788092928904e+30 111.00:16094870669615180549e+29 111.25:20666223018087941005e+29 111.50:26535955622162162862e+29 111.75:34072841474954187489e+29 112.00:43750394472613410735e+29 112.25:56176618492950496549e+29 112.50:72132205968519045371e+29 112.75:92619585825333660519e+29 113.00:1189259022828200882e+31 113.25:15270388123366368993e+30 113.50:19607566473089040657e+30 113.75:251766137108407451e+32 114.00:32327411910848593114e+30 114.25:4150921854926362193e+31 114.50:53298891644100750211e+30 114.75:68437131552311248574e+30 115.00:87875016358370231131e+30 115.25:11283375449599843527e+31 115.50:14488140863316671496e+31 115.75:18603141109050883756e+31 116.00:23886906014249914255e+31 116.25:30671394448328164271e+31 116.50:39382850036908651969e+31 116.75:5056858042899246693e+32 117.00:64931342556644621362e+31 117.25:83373494182390091402e+31 117.50:10705368560825642761e+32 117.75:13745965327109993311e+32 118.00:17650168856917655833e+32 118.25:22663265421112690832e+32 118.50:29100208825849105824e+32 118.75:37365407763311190463e+32 119.00:4797813327299302186e+33 119.25:61605142567754859039e+32 119.50:7910256885566915324e+33 119.75:10156970893597134655e+33 120.00:13041808783936322797e+33 Math-BigInt-1.999808/t/author-blog-mbf.t0000644403072340010010000001450213016105562017754 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 139; use Scalar::Util qw< refaddr >; my $class; BEGIN { $class = 'Math::BigFloat'; } BEGIN { use_ok($class) } while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines # $in0 - the x value # $in1 - the base # $out0 - the wanted output value # $type - the type of the wanted number (real, non-real, ...) # $expr - mathematical expression of the wanted number my ($in0, $in1, $out0, $type, $expr) = split /:/; # Some of the test data use rational numbers. # - with Math::BigInt, we skip them # - with Math::BigFloat, we convert them to floats # - with Math::BigRat, we use them as they are $in0 = eval $in0 if $in0 =~ m|/|; $in1 = eval $in1 if $in1 =~ m|/|; $out0 = eval $out0 if $out0 =~ m|/|; my ($x, $y); # input values as objects my ($yo); # copy of input value my ($got); # test output my $test = qq|\$x = $class -> new("$in0"); | . qq|\$y = $class -> new("$in1"); | . qq|\$yo = \$y -> copy(); | . qq|\$got = \$x -> blog(\$y);|; my $desc = "logarithm of $in0 to base $in1"; print("#\n", "# Now about to execute the following test.\n", "#\n", "# $test\n", "#\n"); if ($in0 ne 'NaN' && $in1 ne 'NaN') { print("# Enter log($in1, $in0) into Wolfram Alpha", " (http://www.wolframalpha.com/), and it says that the result", " is ", length($type) ? $type : "real", length($expr) ? ": $expr" : "", ".", "\n", "#\n"); } eval $test; die $@ if $@; # this should never happen subtest $desc, sub { plan tests => 5, # Check output. is(ref($got), $class, "output arg is a $class"); is($got, $out0, 'output arg has the right value'); is(refaddr($got), refaddr($x), 'output arg is the invocand'); # The second argument (if the invocand is the first) shall *not* be # modified. is(ref($y), $class, "second input arg is still a $class"); is_deeply($y, $yo, 'second input arg is unmodified'); }; } __END__ # base = -inf -inf:-inf:NaN:undefined: -4:-inf:0:: -2:-inf:0:: -1:-inf:0:: -1/2:-inf:0:: 0:-inf:NaN:undefined: 1/2:-inf:0:: 1:-inf:0:: 2:-inf:0:: 4:-inf:0:: inf:-inf:NaN:undefined: NaN:-inf:NaN:undefined: # base = -4 -4:-4:1:: -2:-4:NaN:non-real and finite:(log(2)+i pi)/(log(4)+i pi) 0:-4:NaN:non-real (directed) infinity:(-sqrt(pi^2+log^2(4))/(log(4)+i pi))infinity 1/2:-4:NaN:non-real and finite:-(log(2))/(log(4)+i pi) 1:-4:0:: 2:-4:NaN:non-real and finite:(log(2))/(log(4)+i pi) 4:-4:NaN:non-real and finite:(log(4))/(log(4)+i pi) NaN:-4:NaN:undefined: # base = -2 -inf:-2:NaN:non-real (directed) infinity:sqrt(pi^2+log^2(2))/(log(2)+i pi)infinity -4:-2:NaN:non-real and finite:(log(4)+i pi)/(log(2)+i pi) -2:-2:1:: -1:-2:NaN:non-real and finite:(i pi)/(log(2)+i pi) -1/2:-2:NaN:non-real and finite:(-log(2)+i pi)/(log(2)+i pi) 0:-2:NaN:complex infinity: 1/2:-2:NaN:non-real and finite:-(log(2))/(log(2)+i pi) 1:-2:0:: 2:-2:NaN:non-real and finite:(log(2))/(log(2)+i pi) 4:-2:NaN:non-real and finite:(log(4))/(log(2)+i pi) inf:-2:NaN:non-real (directed) infinity: NaN:-2:NaN:undefined: # base = -1 -inf:-1:NaN:non-real (directed) infinity: -4:-1:NaN:non-real and finite:-(i (log(4)+i pi))/pi -2:-1:NaN:non-real and finite:-(i (log(2)+i pi))/pi -1:-1:1:: -1/2:-1:NaN:non-real and finite:-(i (-log(2)+i pi))/pi 0:-1:NaN:complex infinity: 1:-1:0:: 1/2:-1:NaN:non-real and finite:(i log(2))/pi 2:-1:NaN:non-real and finite:-(i log(2))/pi 4:-1:NaN:non-real and finite:-(i log(4))/pi inf:-1:NaN:non-real (directed) infinity: NaN:-1:NaN:undefined: # base = -1/2 -inf:-1/2:NaN:non-real (directed) infinity: -4:-1/2:NaN:non-real and finite:(log(4)+i pi)/(-log(2)+i pi) -2:-1/2:NaN:non-real and finite:(log(2)+i pi)/(-log(2)+i pi) -1:-1/2:NaN:non-real and finite:(i pi)/(-log(2)+i pi) -1/2:-1/2:1:: 0:-1/2:NaN:complex infinity: 1:-1/2:0:: 1/2:-1/2:NaN:non-real and finite:-(log(2))/(-log(2)+i pi) 2:-1/2:NaN:non-real and finite:(log(2))/(-log(2)+i pi) 4:-1/2:NaN:non-real and finite:(log(4))/(-log(2)+i pi) inf:-1/2:NaN:non-real (directed) infinity: NaN:-1/2:NaN:undefined: # base = 0 -inf:0:NaN:undefined: -4:0:0:: -2:0:0:: -1:0:0:: -1/2:0:0:: 0:0:NaN:undefined: 1/2:0:0:: 1:0:0:: 2:0:0:: 4:0:0:: inf:0:NaN:undefined: NaN:0:NaN:undefined: # base = 1/2 -inf:1/2:-inf:: -2:-1/2:NaN:non-real and finite:(log(2)+i pi)/(-log(2)+i pi) -1:1/2:NaN:non-real and finite:-(i pi)/(log(2)) -1/2:1/2:NaN:non-real and finite:-(-log(2)+i pi)/(log(2)) 0:1/2:inf:: 1/2:1/2:1:: 1:1/2:0:: 2:1/2:-1:: inf:1/2:-inf:: NaN:1/2:NaN:undefined: # base = 1 -inf:1:NaN:complex infinity: -4:1:NaN:complex infinity: -2:1:NaN:complex infinity: -1:1:NaN:complex infinity: -1/2:1:NaN:complex infinity: 0:1:NaN:complex infinity: 1/2:1:NaN:complex infinity: 1:1:NaN:undefined: 2:1:NaN:complex infinity: 4:1:NaN:complex infinity: inf:1:NaN:complex infinity: NaN:1:NaN:undefined: # base = 2 -inf:2:inf:: -4:2:NaN:non-real and finite:(log(4)+i pi)/(log(2)) -2:2:NaN:non-real and finite:(log(2)+i pi)/(log(2)) -1:2:NaN:non-real and finite:(i pi)/(log(2)) -1/2:2:NaN:non-real and finite:(-log(2)+i pi)/(log(2)) 0:2:-inf:: 1/2:2:-1:: 1:2:0:: 2:2:1:: 4:2:2:: 4:4:1:: inf:2:inf:: NaN:2:NaN:undefined: # base = 4 -inf:4:inf:: -4:4:NaN:non-real and finite:(log(4)+i pi)/(log(4)) -2:4:NaN:non-real and finite:(log(2)+i pi)/(log(4)) -1/2:4:NaN:non-real and finite:(-log(2)+i pi)/(log(4)) 0:4:-inf:: 1:4:0:: 1/2:4:-1/2:: 2:4:1/2:: 4:4:1:: inf:4:inf:: NaN:4:NaN:undefined: # base = inf -inf:inf:NaN:undefined: -4:inf:0:: -2:inf:0:: -1:inf:0:: -1/2:inf:0:: 0:inf:NaN:undefined: 1:inf:0:: 1/2:inf:0:: 2:inf:0:: 4:inf:0:: inf:inf:NaN:undefined: NaN:inf:NaN:undefined: # base is NaN -inf:NaN:NaN:undefined: -4:NaN:NaN:undefined: -2:NaN:NaN:undefined: -1:NaN:NaN:undefined: -1/2:NaN:NaN:undefined: 0:NaN:NaN:undefined: 1:NaN:NaN:undefined: 1/2:NaN:NaN:undefined: 2:NaN:NaN:undefined: 4:NaN:NaN:undefined: inf:NaN:NaN:undefined: NaN:NaN:NaN:undefined: Math-BigInt-1.999808/t/author-blog-mbi.t0000644403072340010010000001443613016105542017763 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 97; use Scalar::Util qw< refaddr >; my $class; BEGIN { $class = 'Math::BigInt'; } BEGIN { use_ok($class) } while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines # $in0 - the x value # $in1 - the base # $out0 - the wanted output value # $type - the type of the wanted number (real, non-real, ...) # $expr - mathematical expression of the wanted number my ($in0, $in1, $out0, $type, $expr) = split /:/; # Some of the test data use rational numbers. # - with Math::BigInt, we skip them # - with Math::BigFloat, we convert them to floats # - with Math::BigRat, we use them as they are next if ($in0 =~ m|/| || $in1 =~ m|/| || $out0 =~ m|/|); my ($x, $y); # input values as objects my ($yo); # copy of input value my ($got); # test output my $test = qq|\$x = $class -> new("$in0"); | . qq|\$y = $class -> new("$in1"); | . qq|\$yo = \$y -> copy(); | . qq|\$got = \$x -> blog(\$y);|; my $desc = "logarithm of $in0 to base $in1"; print("#\n", "# Now about to execute the following test.\n", "#\n", "# $test\n", "#\n"); if ($in0 ne 'NaN' && $in1 ne 'NaN') { print("# Enter log($in1, $in0) into Wolfram Alpha", " (http://www.wolframalpha.com/), and it says that the result", " is ", length($type) ? $type : "real", length($expr) ? ": $expr" : "", ".", "\n", "#\n"); } eval $test; die $@ if $@; # this should never happen subtest $desc, sub { plan tests => 5, # Check output. is(ref($got), $class, "output arg is a $class"); is($got, $out0, 'output arg has the right value'); is(refaddr($got), refaddr($x), 'output arg is the invocand'); # The second argument (if the invocand is the first) shall *not* be # modified. is(ref($y), $class, "second input arg is still a $class"); is_deeply($y, $yo, 'second input arg is unmodified'); }; } __END__ # base = -inf -inf:-inf:NaN:undefined: -4:-inf:0:: -2:-inf:0:: -1:-inf:0:: -1/2:-inf:0:: 0:-inf:NaN:undefined: 1/2:-inf:0:: 1:-inf:0:: 2:-inf:0:: 4:-inf:0:: inf:-inf:NaN:undefined: NaN:-inf:NaN:undefined: # base = -4 -4:-4:1:: -2:-4:NaN:non-real and finite:(log(2)+i pi)/(log(4)+i pi) 0:-4:NaN:non-real (directed) infinity:(-sqrt(pi^2+log^2(4))/(log(4)+i pi))infinity 1/2:-4:NaN:non-real and finite:-(log(2))/(log(4)+i pi) 1:-4:0:: 2:-4:NaN:non-real and finite:(log(2))/(log(4)+i pi) 4:-4:NaN:non-real and finite:(log(4))/(log(4)+i pi) NaN:-4:NaN:undefined: # base = -2 -inf:-2:NaN:non-real (directed) infinity:sqrt(pi^2+log^2(2))/(log(2)+i pi)infinity -4:-2:NaN:non-real and finite:(log(4)+i pi)/(log(2)+i pi) -2:-2:1:: -1:-2:NaN:non-real and finite:(i pi)/(log(2)+i pi) -1/2:-2:NaN:non-real and finite:(-log(2)+i pi)/(log(2)+i pi) 0:-2:NaN:complex infinity: 1/2:-2:NaN:non-real and finite:-(log(2))/(log(2)+i pi) 1:-2:0:: 2:-2:NaN:non-real and finite:(log(2))/(log(2)+i pi) 4:-2:NaN:non-real and finite:(log(4))/(log(2)+i pi) inf:-2:NaN:non-real (directed) infinity: NaN:-2:NaN:undefined: # base = -1 -inf:-1:NaN:non-real (directed) infinity: -4:-1:NaN:non-real and finite:-(i (log(4)+i pi))/pi -2:-1:NaN:non-real and finite:-(i (log(2)+i pi))/pi -1:-1:1:: -1/2:-1:NaN:non-real and finite:-(i (-log(2)+i pi))/pi 0:-1:NaN:complex infinity: 1:-1:0:: 1/2:-1:NaN:non-real and finite:(i log(2))/pi 2:-1:NaN:non-real and finite:-(i log(2))/pi 4:-1:NaN:non-real and finite:-(i log(4))/pi inf:-1:NaN:non-real (directed) infinity: NaN:-1:NaN:undefined: # base = -1/2 -inf:-1/2:NaN:non-real (directed) infinity: -4:-1/2:NaN:non-real and finite:(log(4)+i pi)/(-log(2)+i pi) -2:-1/2:NaN:non-real and finite:(log(2)+i pi)/(-log(2)+i pi) -1:-1/2:NaN:non-real and finite:(i pi)/(-log(2)+i pi) -1/2:-1/2:1:: 0:-1/2:NaN:complex infinity: 1:-1/2:0:: 1/2:-1/2:NaN:non-real and finite:-(log(2))/(-log(2)+i pi) 2:-1/2:NaN:non-real and finite:(log(2))/(-log(2)+i pi) 4:-1/2:NaN:non-real and finite:(log(4))/(-log(2)+i pi) inf:-1/2:NaN:non-real (directed) infinity: NaN:-1/2:NaN:undefined: # base = 0 -inf:0:NaN:undefined: -4:0:0:: -2:0:0:: -1:0:0:: -1/2:0:0:: 0:0:NaN:undefined: 1/2:0:0:: 1:0:0:: 2:0:0:: 4:0:0:: inf:0:NaN:undefined: NaN:0:NaN:undefined: # base = 1/2 -inf:1/2:-inf:: -2:-1/2:NaN:non-real and finite:(log(2)+i pi)/(-log(2)+i pi) -1:1/2:NaN:non-real and finite:-(i pi)/(log(2)) -1/2:1/2:NaN:non-real and finite:-(-log(2)+i pi)/(log(2)) 0:1/2:inf:: 1/2:1/2:1:: 1:1/2:0:: 2:1/2:-1:: inf:1/2:-inf:: NaN:1/2:NaN:undefined: # base = 1 -inf:1:NaN:complex infinity: -4:1:NaN:complex infinity: -2:1:NaN:complex infinity: -1:1:NaN:complex infinity: -1/2:1:NaN:complex infinity: 0:1:NaN:complex infinity: 1/2:1:NaN:complex infinity: 1:1:NaN:undefined: 2:1:NaN:complex infinity: 4:1:NaN:complex infinity: inf:1:NaN:complex infinity: NaN:1:NaN:undefined: # base = 2 -inf:2:inf:: -4:2:NaN:non-real and finite:(log(4)+i pi)/(log(2)) -2:2:NaN:non-real and finite:(log(2)+i pi)/(log(2)) -1:2:NaN:non-real and finite:(i pi)/(log(2)) -1/2:2:NaN:non-real and finite:(-log(2)+i pi)/(log(2)) 0:2:-inf:: 1/2:2:-1:: 1:2:0:: 2:2:1:: 4:2:2:: 4:4:1:: inf:2:inf:: NaN:2:NaN:undefined: # base = 4 -inf:4:inf:: -4:4:NaN:non-real and finite:(log(4)+i pi)/(log(4)) -2:4:NaN:non-real and finite:(log(2)+i pi)/(log(4)) -1/2:4:NaN:non-real and finite:(-log(2)+i pi)/(log(4)) 0:4:-inf:: 1:4:0:: 1/2:4:-1/2:: 2:4:1/2:: 4:4:1:: inf:4:inf:: NaN:4:NaN:undefined: # base = inf -inf:inf:NaN:undefined: -4:inf:0:: -2:inf:0:: -1:inf:0:: -1/2:inf:0:: 0:inf:NaN:undefined: 1:inf:0:: 1/2:inf:0:: 2:inf:0:: 4:inf:0:: inf:inf:NaN:undefined: NaN:inf:NaN:undefined: # base is NaN -inf:NaN:NaN:undefined: -4:NaN:NaN:undefined: -2:NaN:NaN:undefined: -1:NaN:NaN:undefined: -1/2:NaN:NaN:undefined: 0:NaN:NaN:undefined: 1:NaN:NaN:undefined: 1/2:NaN:NaN:undefined: 2:NaN:NaN:undefined: 4:NaN:NaN:undefined: inf:NaN:NaN:undefined: NaN:NaN:NaN:undefined: Math-BigInt-1.999808/t/author-bmod-bdiv-mbi.t0000644403072340010010000003035012734616176020714 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 41301; use Math::BigInt; use Math::Complex; use Scalar::Util; my $inf = Math::Complex::Inf(); my $nan = $inf - $inf; # Return 1 if the input argument is +inf or -inf, and "" otherwise. sub isinf { my $x = shift; return $x == $inf || $x == -$inf; } # Return 1 if the input argument is a nan (Not-a-Number), and "" otherwise. sub isnan { my $x = shift; return !($x <= 0 || $x > 0); } # Convert a Perl scalar to a Math::BigInt object. This function is used for # consistent comparisons. For instance, a Not-a-Number might be stringified to # 'nan', but Math::BigInt uses 'NaN'. sub pl2mbi { my $x = shift; return Math::BigInt -> binf('+') if $x == $inf; return Math::BigInt -> binf('-') if $x == -$inf; return Math::BigInt -> bnan() if isnan($x); return Math::BigInt -> new($x); } # Does a floored division (F-division). sub fdiv { die "Usage: fdiv X Y\n" if @_ != 2; no integer; my $x = shift; # numerator my $y = shift; # denominator # Convert Perl strings representing nan, +inf, and -inf into Perl numbers. if ($x =~ /^\s*nan\s*$/i) { $x = $nan; } elsif ($x =~ /^\s*([+-]?)inf(inity)?\s*$/i) { $x = $1 eq '-' ? -$inf : $inf; } if ($y =~ /^\s*nan\s*$/i) { $y = $nan; } elsif ($y =~ /^\s*([+-]?)inf(inity)?\s*$/i) { $y = $1 eq '-' ? -$inf : $inf; } # If any input is nan, the output is nan. if (isnan($x) || isnan($y)) { return wantarray ? ($nan, $nan) : $nan; } # Divide by zero and modulo zero. if ($y == 0) { # Core Perl gives an "Illegal division by zero" error whenever the # denominator is zero. Math::BigInt, however, has a different # convention. my $q = $x < 0 ? -$inf : $x > 0 ? $inf : $nan; my $r = $x; return wantarray ? ($q, $r) : $q; } # Numerator is +/-infinity, and denominator is non-zero. if (isinf($x)) { my $q = $x / $y; my $r = $nan; return wantarray ? ($q, $r) : $q; if (isinf($y)) { return wantarray ? ($nan, $nan) : $nan; } else { if (($x <=> 0) == ($y <=> 0)) { return wantarray ? ($inf, $nan) : $inf; } else { return wantarray ? (-$inf, $nan) : -$inf; } } } # Denominator is +/- infinity, and the numerator is finite. # # Core Perl: 5 % Inf = 5 # -5 % -Inf = -5 # -5 % Inf = Inf # 5 % -Inf = -Inf if (isinf($y)) { if ($x == 0 || ($x <=> 0) == ($y <=> 0)) { return wantarray ? (0, $x) : 0; } else { return wantarray ? (-1, ($y <=> 0) * $inf) : -1; } } # First do a truncated division. my $q = int($x / $y); my $r = $x - $y * $q; if ($y > 0 && $r < 0 || $y < 0 && $r > 0) { $q -= 1; $r += $y; } return wantarray ? ($q, $r) : $q; } # Tests where the invocand and the argument are two different objects. #for my $num (-20 .. 20) { # for my $den (-20 .. -1, 1 .. 20) { for my $num (-$inf, -20 .. 20, $inf, $nan) { for my $den (-$inf, -20 .. 20, $inf, $nan) { # Compute expected output values. my ($quo, $rem) = fdiv($num, $den); ####################################################################### # bdiv() in list context. ####################################################################### { note(qq|\n(\$quo, \$rem) = | . qq|Math::BigInt -> new("$num") -> bdiv("$den")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); my $mbi_den = Math::BigInt -> new("$den"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); my $mbi_den_addr = Scalar::Util::refaddr($mbi_den); # Compute actual output values. my ($mbi_quo, $mbi_rem) = $mbi_num -> bdiv($mbi_den); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_den), 'Math::BigInt', "class of denominator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $den = $quo"); is($mbi_rem, pl2mbi($rem), "$num % $den = $rem"); is($mbi_den, pl2mbi($den), "value of denominator has not changed"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); ok($mbi_rem_addr != $mbi_num_addr && $mbi_rem_addr != $mbi_den_addr && $mbi_rem_addr != $mbi_quo_addr, "the remainder object is neither the numerator," . " denominator, nor quotient object"); } ####################################################################### # bdiv() in scalar context. ####################################################################### { note(qq|\n\$quo = | . qq|Math::BigInt -> new("$num") -> bdiv("$den")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); my $mbi_den = Math::BigInt -> new("$den"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); my $mbi_den_addr = Scalar::Util::refaddr($mbi_den); # Compute actual output values. my $mbi_quo = $mbi_num -> bdiv($mbi_den); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_den), 'Math::BigInt', "class of denominator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $den = $quo"); is($mbi_den, pl2mbi($den), "value of numerator has not changed"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); } ####################################################################### # bmod() (scalar context only). ####################################################################### { note(qq|\n\$quo = | . qq|Math::BigInt -> new("$num") -> bmod("$den")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); my $mbi_den = Math::BigInt -> new("$den"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); my $mbi_den_addr = Scalar::Util::refaddr($mbi_den); # Compute actual output values. my $mbi_rem = $mbi_num -> bmod($mbi_den); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_den), 'Math::BigInt', "class of denominator is still Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_rem, pl2mbi($rem), "$num % $den = $rem"); is($mbi_den, pl2mbi($den), "value of denominator has not changed"); # Check addresses. my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_rem_addr, $mbi_num_addr, "the remainder object is the numerator object"); } } } # Tests where the invocand and the argument is the same object. #for my $num (-$inf, -20 .. 20, $inf, $nan) { for my $num (-$inf, -20 .. -1, 1 .. 20, $inf, $nan) { # Compute expected output values. my ($quo, $rem) = fdiv($num, $num); ####################################################################### # bdiv() in list context. ####################################################################### { note(qq|\n\$x = Math::BigInt -> new("$num"); | . qq|(\$quo, \$rem) = \$x -> bdiv("\$x")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); # Compute actual output values. my ($mbi_quo, $mbi_rem) = $mbi_num -> bdiv($mbi_num); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $num = $quo"); is($mbi_rem, pl2mbi($rem), "$num % $num = $rem"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); ok($mbi_rem_addr != $mbi_num_addr && $mbi_rem_addr != $mbi_quo_addr, "the remainder object is neither the numerator," . " denominator, nor quotient object"); } ####################################################################### # bdiv() in scalar context. ####################################################################### { note(qq|\n\$x = Math::BigInt -> new("$num"); | . qq|\$quo = \$x -> bdiv(\$x)\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); # Compute actual output values. my $mbi_quo = $mbi_num -> bdiv($mbi_num); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $num = $quo"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); } ####################################################################### # bmod() (scalar context only). ####################################################################### { note(qq|\n\$x = Math::BigInt -> new("$num") | . qq|\$quo = \$x -> bmod(\$x)\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); # Compute actual output values. my $mbi_rem = $mbi_num -> bmod($mbi_num); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_rem, pl2mbi($rem), "$num % $num = $rem"); # Check addresses. my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_rem_addr, $mbi_num_addr, "the remainder object is the numerator object"); } } Math-BigInt-1.999808/t/author-bnok-mbi.t0000644403072340010010000265177412737522457020030 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 60912; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($n_str, $k_str, $expected_str) = split /:/; my ($n, $k, $c); { my $test = qq|\$n = Math::BigInt -> new("$n_str"); | . qq|\$k = Math::BigInt -> new("$k_str"); | . qq|\$c = \$n -> bnok(\$k);|; #note "\n$test\n\n"; eval $test; is($@, "", '$@ is an empty string'); isa_ok($c, "Math::BigInt"); is($c -> bdstr, $expected_str, $test); } } __DATA__ NaN:0:NaN 0:NaN:NaN inf:1:inf # binomial(0, k) for 0 <= k <= 0 0:0:1 # binomial(1, k) for 0 <= k <= 1 1:0:1 1:1:1 # binomial(2, k) for 0 <= k <= 2 2:0:1 2:1:2 2:2:1 # binomial(3, k) for 0 <= k <= 3 3:0:1 3:1:3 3:2:3 3:3:1 # binomial(4, k) for 0 <= k <= 4 4:0:1 4:1:4 4:2:6 4:3:4 4:4:1 # binomial(5, k) for 0 <= k <= 5 5:0:1 5:1:5 5:2:10 5:3:10 5:4:5 5:5:1 # binomial(6, k) for 0 <= k <= 6 6:0:1 6:1:6 6:2:15 6:3:20 6:4:15 6:5:6 6:6:1 # binomial(7, k) for 0 <= k <= 7 7:0:1 7:1:7 7:2:21 7:3:35 7:4:35 7:5:21 7:6:7 7:7:1 # binomial(8, k) for 0 <= k <= 8 8:0:1 8:1:8 8:2:28 8:3:56 8:4:70 8:5:56 8:6:28 8:7:8 8:8:1 # binomial(9, k) for 0 <= k <= 9 9:0:1 9:1:9 9:2:36 9:3:84 9:4:126 9:5:126 9:6:84 9:7:36 9:8:9 9:9:1 # binomial(10, k) for 0 <= k <= 10 10:0:1 10:1:10 10:2:45 10:3:120 10:4:210 10:5:252 10:6:210 10:7:120 10:8:45 10:9:10 10:10:1 # binomial(11, k) for 0 <= k <= 11 11:0:1 11:1:11 11:2:55 11:3:165 11:4:330 11:5:462 11:6:462 11:7:330 11:8:165 11:9:55 11:10:11 11:11:1 # binomial(12, k) for 0 <= k <= 12 12:0:1 12:1:12 12:2:66 12:3:220 12:4:495 12:5:792 12:6:924 12:7:792 12:8:495 12:9:220 12:10:66 12:11:12 12:12:1 # binomial(13, k) for 0 <= k <= 13 13:0:1 13:1:13 13:2:78 13:3:286 13:4:715 13:5:1287 13:6:1716 13:7:1716 13:8:1287 13:9:715 13:10:286 13:11:78 13:12:13 13:13:1 # binomial(14, k) for 0 <= k <= 14 14:0:1 14:1:14 14:2:91 14:3:364 14:4:1001 14:5:2002 14:6:3003 14:7:3432 14:8:3003 14:9:2002 14:10:1001 14:11:364 14:12:91 14:13:14 14:14:1 # binomial(15, k) for 0 <= k <= 15 15:0:1 15:1:15 15:2:105 15:3:455 15:4:1365 15:5:3003 15:6:5005 15:7:6435 15:8:6435 15:9:5005 15:10:3003 15:11:1365 15:12:455 15:13:105 15:14:15 15:15:1 # binomial(16, k) for 0 <= k <= 16 16:0:1 16:1:16 16:2:120 16:3:560 16:4:1820 16:5:4368 16:6:8008 16:7:11440 16:8:12870 16:9:11440 16:10:8008 16:11:4368 16:12:1820 16:13:560 16:14:120 16:15:16 16:16:1 # binomial(17, k) for 0 <= k <= 17 17:0:1 17:1:17 17:2:136 17:3:680 17:4:2380 17:5:6188 17:6:12376 17:7:19448 17:8:24310 17:9:24310 17:10:19448 17:11:12376 17:12:6188 17:13:2380 17:14:680 17:15:136 17:16:17 17:17:1 # binomial(18, k) for 0 <= k <= 18 18:0:1 18:1:18 18:2:153 18:3:816 18:4:3060 18:5:8568 18:6:18564 18:7:31824 18:8:43758 18:9:48620 18:10:43758 18:11:31824 18:12:18564 18:13:8568 18:14:3060 18:15:816 18:16:153 18:17:18 18:18:1 # binomial(19, k) for 0 <= k <= 19 19:0:1 19:1:19 19:2:171 19:3:969 19:4:3876 19:5:11628 19:6:27132 19:7:50388 19:8:75582 19:9:92378 19:10:92378 19:11:75582 19:12:50388 19:13:27132 19:14:11628 19:15:3876 19:16:969 19:17:171 19:18:19 19:19:1 # binomial(20, k) for 0 <= k <= 20 20:0:1 20:1:20 20:2:190 20:3:1140 20:4:4845 20:5:15504 20:6:38760 20:7:77520 20:8:125970 20:9:167960 20:10:184756 20:11:167960 20:12:125970 20:13:77520 20:14:38760 20:15:15504 20:16:4845 20:17:1140 20:18:190 20:19:20 20:20:1 # binomial(21, k) for 0 <= k <= 21 21:0:1 21:1:21 21:2:210 21:3:1330 21:4:5985 21:5:20349 21:6:54264 21:7:116280 21:8:203490 21:9:293930 21:10:352716 21:11:352716 21:12:293930 21:13:203490 21:14:116280 21:15:54264 21:16:20349 21:17:5985 21:18:1330 21:19:210 21:20:21 21:21:1 # binomial(22, k) for 0 <= k <= 22 22:0:1 22:1:22 22:2:231 22:3:1540 22:4:7315 22:5:26334 22:6:74613 22:7:170544 22:8:319770 22:9:497420 22:10:646646 22:11:705432 22:12:646646 22:13:497420 22:14:319770 22:15:170544 22:16:74613 22:17:26334 22:18:7315 22:19:1540 22:20:231 22:21:22 22:22:1 # binomial(23, k) for 0 <= k <= 23 23:0:1 23:1:23 23:2:253 23:3:1771 23:4:8855 23:5:33649 23:6:100947 23:7:245157 23:8:490314 23:9:817190 23:10:1144066 23:11:1352078 23:12:1352078 23:13:1144066 23:14:817190 23:15:490314 23:16:245157 23:17:100947 23:18:33649 23:19:8855 23:20:1771 23:21:253 23:22:23 23:23:1 # binomial(24, k) for 0 <= k <= 24 24:0:1 24:1:24 24:2:276 24:3:2024 24:4:10626 24:5:42504 24:6:134596 24:7:346104 24:8:735471 24:9:1307504 24:10:1961256 24:11:2496144 24:12:2704156 24:13:2496144 24:14:1961256 24:15:1307504 24:16:735471 24:17:346104 24:18:134596 24:19:42504 24:20:10626 24:21:2024 24:22:276 24:23:24 24:24:1 # binomial(25, k) for 0 <= k <= 25 25:0:1 25:1:25 25:2:300 25:3:2300 25:4:12650 25:5:53130 25:6:177100 25:7:480700 25:8:1081575 25:9:2042975 25:10:3268760 25:11:4457400 25:12:5200300 25:13:5200300 25:14:4457400 25:15:3268760 25:16:2042975 25:17:1081575 25:18:480700 25:19:177100 25:20:53130 25:21:12650 25:22:2300 25:23:300 25:24:25 25:25:1 # binomial(26, k) for 0 <= k <= 26 26:0:1 26:1:26 26:2:325 26:3:2600 26:4:14950 26:5:65780 26:6:230230 26:7:657800 26:8:1562275 26:9:3124550 26:10:5311735 26:11:7726160 26:12:9657700 26:13:10400600 26:14:9657700 26:15:7726160 26:16:5311735 26:17:3124550 26:18:1562275 26:19:657800 26:20:230230 26:21:65780 26:22:14950 26:23:2600 26:24:325 26:25:26 26:26:1 # binomial(27, k) for 0 <= k <= 27 27:0:1 27:1:27 27:2:351 27:3:2925 27:4:17550 27:5:80730 27:6:296010 27:7:888030 27:8:2220075 27:9:4686825 27:10:8436285 27:11:13037895 27:12:17383860 27:13:20058300 27:14:20058300 27:15:17383860 27:16:13037895 27:17:8436285 27:18:4686825 27:19:2220075 27:20:888030 27:21:296010 27:22:80730 27:23:17550 27:24:2925 27:25:351 27:26:27 27:27:1 # binomial(28, k) for 0 <= k <= 28 28:0:1 28:1:28 28:2:378 28:3:3276 28:4:20475 28:5:98280 28:6:376740 28:7:1184040 28:8:3108105 28:9:6906900 28:10:13123110 28:11:21474180 28:12:30421755 28:13:37442160 28:14:40116600 28:15:37442160 28:16:30421755 28:17:21474180 28:18:13123110 28:19:6906900 28:20:3108105 28:21:1184040 28:22:376740 28:23:98280 28:24:20475 28:25:3276 28:26:378 28:27:28 28:28:1 # binomial(29, k) for 0 <= k <= 29 29:0:1 29:1:29 29:2:406 29:3:3654 29:4:23751 29:5:118755 29:6:475020 29:7:1560780 29:8:4292145 29:9:10015005 29:10:20030010 29:11:34597290 29:12:51895935 29:13:67863915 29:14:77558760 29:15:77558760 29:16:67863915 29:17:51895935 29:18:34597290 29:19:20030010 29:20:10015005 29:21:4292145 29:22:1560780 29:23:475020 29:24:118755 29:25:23751 29:26:3654 29:27:406 29:28:29 29:29:1 # binomial(30, k) for 0 <= k <= 30 30:0:1 30:1:30 30:2:435 30:3:4060 30:4:27405 30:5:142506 30:6:593775 30:7:2035800 30:8:5852925 30:9:14307150 30:10:30045015 30:11:54627300 30:12:86493225 30:13:119759850 30:14:145422675 30:15:155117520 30:16:145422675 30:17:119759850 30:18:86493225 30:19:54627300 30:20:30045015 30:21:14307150 30:22:5852925 30:23:2035800 30:24:593775 30:25:142506 30:26:27405 30:27:4060 30:28:435 30:29:30 30:30:1 # binomial(31, k) for 0 <= k <= 31 31:0:1 31:1:31 31:2:465 31:3:4495 31:4:31465 31:5:169911 31:6:736281 31:7:2629575 31:8:7888725 31:9:20160075 31:10:44352165 31:11:84672315 31:12:141120525 31:13:206253075 31:14:265182525 31:15:300540195 31:16:300540195 31:17:265182525 31:18:206253075 31:19:141120525 31:20:84672315 31:21:44352165 31:22:20160075 31:23:7888725 31:24:2629575 31:25:736281 31:26:169911 31:27:31465 31:28:4495 31:29:465 31:30:31 31:31:1 # binomial(32, k) for 0 <= k <= 32 32:0:1 32:1:32 32:2:496 32:3:4960 32:4:35960 32:5:201376 32:6:906192 32:7:3365856 32:8:10518300 32:9:28048800 32:10:64512240 32:11:129024480 32:12:225792840 32:13:347373600 32:14:471435600 32:15:565722720 32:16:601080390 32:17:565722720 32:18:471435600 32:19:347373600 32:20:225792840 32:21:129024480 32:22:64512240 32:23:28048800 32:24:10518300 32:25:3365856 32:26:906192 32:27:201376 32:28:35960 32:29:4960 32:30:496 32:31:32 32:32:1 # binomial(33, k) for 0 <= k <= 33 33:0:1 33:1:33 33:2:528 33:3:5456 33:4:40920 33:5:237336 33:6:1107568 33:7:4272048 33:8:13884156 33:9:38567100 33:10:92561040 33:11:193536720 33:12:354817320 33:13:573166440 33:14:818809200 33:15:1037158320 33:16:1166803110 33:17:1166803110 33:18:1037158320 33:19:818809200 33:20:573166440 33:21:354817320 33:22:193536720 33:23:92561040 33:24:38567100 33:25:13884156 33:26:4272048 33:27:1107568 33:28:237336 33:29:40920 33:30:5456 33:31:528 33:32:33 33:33:1 # binomial(34, k) for 0 <= k <= 34 34:0:1 34:1:34 34:2:561 34:3:5984 34:4:46376 34:5:278256 34:6:1344904 34:7:5379616 34:8:18156204 34:9:52451256 34:10:131128140 34:11:286097760 34:12:548354040 34:13:927983760 34:14:1391975640 34:15:1855967520 34:16:2203961430 34:17:2333606220 34:18:2203961430 34:19:1855967520 34:20:1391975640 34:21:927983760 34:22:548354040 34:23:286097760 34:24:131128140 34:25:52451256 34:26:18156204 34:27:5379616 34:28:1344904 34:29:278256 34:30:46376 34:31:5984 34:32:561 34:33:34 34:34:1 # binomial(35, k) for 0 <= k <= 35 35:0:1 35:1:35 35:2:595 35:3:6545 35:4:52360 35:5:324632 35:6:1623160 35:7:6724520 35:8:23535820 35:9:70607460 35:10:183579396 35:11:417225900 35:12:834451800 35:13:1476337800 35:14:2319959400 35:15:3247943160 35:16:4059928950 35:17:4537567650 35:18:4537567650 35:19:4059928950 35:20:3247943160 35:21:2319959400 35:22:1476337800 35:23:834451800 35:24:417225900 35:25:183579396 35:26:70607460 35:27:23535820 35:28:6724520 35:29:1623160 35:30:324632 35:31:52360 35:32:6545 35:33:595 35:34:35 35:35:1 # binomial(36, k) for 0 <= k <= 36 36:0:1 36:1:36 36:2:630 36:3:7140 36:4:58905 36:5:376992 36:6:1947792 36:7:8347680 36:8:30260340 36:9:94143280 36:10:254186856 36:11:600805296 36:12:1251677700 36:13:2310789600 36:14:3796297200 36:15:5567902560 36:16:7307872110 36:17:8597496600 36:18:9075135300 36:19:8597496600 36:20:7307872110 36:21:5567902560 36:22:3796297200 36:23:2310789600 36:24:1251677700 36:25:600805296 36:26:254186856 36:27:94143280 36:28:30260340 36:29:8347680 36:30:1947792 36:31:376992 36:32:58905 36:33:7140 36:34:630 36:35:36 36:36:1 # binomial(37, k) for 0 <= k <= 37 37:0:1 37:1:37 37:2:666 37:3:7770 37:4:66045 37:5:435897 37:6:2324784 37:7:10295472 37:8:38608020 37:9:124403620 37:10:348330136 37:11:854992152 37:12:1852482996 37:13:3562467300 37:14:6107086800 37:15:9364199760 37:16:12875774670 37:17:15905368710 37:18:17672631900 37:19:17672631900 37:20:15905368710 37:21:12875774670 37:22:9364199760 37:23:6107086800 37:24:3562467300 37:25:1852482996 37:26:854992152 37:27:348330136 37:28:124403620 37:29:38608020 37:30:10295472 37:31:2324784 37:32:435897 37:33:66045 37:34:7770 37:35:666 37:36:37 37:37:1 # binomial(38, k) for 0 <= k <= 38 38:0:1 38:1:38 38:2:703 38:3:8436 38:4:73815 38:5:501942 38:6:2760681 38:7:12620256 38:8:48903492 38:9:163011640 38:10:472733756 38:11:1203322288 38:12:2707475148 38:13:5414950296 38:14:9669554100 38:15:15471286560 38:16:22239974430 38:17:28781143380 38:18:33578000610 38:19:35345263800 38:20:33578000610 38:21:28781143380 38:22:22239974430 38:23:15471286560 38:24:9669554100 38:25:5414950296 38:26:2707475148 38:27:1203322288 38:28:472733756 38:29:163011640 38:30:48903492 38:31:12620256 38:32:2760681 38:33:501942 38:34:73815 38:35:8436 38:36:703 38:37:38 38:38:1 # binomial(39, k) for 0 <= k <= 39 39:0:1 39:1:39 39:2:741 39:3:9139 39:4:82251 39:5:575757 39:6:3262623 39:7:15380937 39:8:61523748 39:9:211915132 39:10:635745396 39:11:1676056044 39:12:3910797436 39:13:8122425444 39:14:15084504396 39:15:25140840660 39:16:37711260990 39:17:51021117810 39:18:62359143990 39:19:68923264410 39:20:68923264410 39:21:62359143990 39:22:51021117810 39:23:37711260990 39:24:25140840660 39:25:15084504396 39:26:8122425444 39:27:3910797436 39:28:1676056044 39:29:635745396 39:30:211915132 39:31:61523748 39:32:15380937 39:33:3262623 39:34:575757 39:35:82251 39:36:9139 39:37:741 39:38:39 39:39:1 # binomial(40, k) for 0 <= k <= 40 40:0:1 40:1:40 40:2:780 40:3:9880 40:4:91390 40:5:658008 40:6:3838380 40:7:18643560 40:8:76904685 40:9:273438880 40:10:847660528 40:11:2311801440 40:12:5586853480 40:13:12033222880 40:14:23206929840 40:15:40225345056 40:16:62852101650 40:17:88732378800 40:18:113380261800 40:19:131282408400 40:20:137846528820 40:21:131282408400 40:22:113380261800 40:23:88732378800 40:24:62852101650 40:25:40225345056 40:26:23206929840 40:27:12033222880 40:28:5586853480 40:29:2311801440 40:30:847660528 40:31:273438880 40:32:76904685 40:33:18643560 40:34:3838380 40:35:658008 40:36:91390 40:37:9880 40:38:780 40:39:40 40:40:1 # binomial(41, k) for 0 <= k <= 41 41:0:1 41:1:41 41:2:820 41:3:10660 41:4:101270 41:5:749398 41:6:4496388 41:7:22481940 41:8:95548245 41:9:350343565 41:10:1121099408 41:11:3159461968 41:12:7898654920 41:13:17620076360 41:14:35240152720 41:15:63432274896 41:16:103077446706 41:17:151584480450 41:18:202112640600 41:19:244662670200 41:20:269128937220 41:21:269128937220 41:22:244662670200 41:23:202112640600 41:24:151584480450 41:25:103077446706 41:26:63432274896 41:27:35240152720 41:28:17620076360 41:29:7898654920 41:30:3159461968 41:31:1121099408 41:32:350343565 41:33:95548245 41:34:22481940 41:35:4496388 41:36:749398 41:37:101270 41:38:10660 41:39:820 41:40:41 41:41:1 # binomial(42, k) for 0 <= k <= 42 42:0:1 42:1:42 42:2:861 42:3:11480 42:4:111930 42:5:850668 42:6:5245786 42:7:26978328 42:8:118030185 42:9:445891810 42:10:1471442973 42:11:4280561376 42:12:11058116888 42:13:25518731280 42:14:52860229080 42:15:98672427616 42:16:166509721602 42:17:254661927156 42:18:353697121050 42:19:446775310800 42:20:513791607420 42:21:538257874440 42:22:513791607420 42:23:446775310800 42:24:353697121050 42:25:254661927156 42:26:166509721602 42:27:98672427616 42:28:52860229080 42:29:25518731280 42:30:11058116888 42:31:4280561376 42:32:1471442973 42:33:445891810 42:34:118030185 42:35:26978328 42:36:5245786 42:37:850668 42:38:111930 42:39:11480 42:40:861 42:41:42 42:42:1 # binomial(43, k) for 0 <= k <= 43 43:0:1 43:1:43 43:2:903 43:3:12341 43:4:123410 43:5:962598 43:6:6096454 43:7:32224114 43:8:145008513 43:9:563921995 43:10:1917334783 43:11:5752004349 43:12:15338678264 43:13:36576848168 43:14:78378960360 43:15:151532656696 43:16:265182149218 43:17:421171648758 43:18:608359048206 43:19:800472431850 43:20:960566918220 43:21:1052049481860 43:22:1052049481860 43:23:960566918220 43:24:800472431850 43:25:608359048206 43:26:421171648758 43:27:265182149218 43:28:151532656696 43:29:78378960360 43:30:36576848168 43:31:15338678264 43:32:5752004349 43:33:1917334783 43:34:563921995 43:35:145008513 43:36:32224114 43:37:6096454 43:38:962598 43:39:123410 43:40:12341 43:41:903 43:42:43 43:43:1 # binomial(44, k) for 0 <= k <= 44 44:0:1 44:1:44 44:2:946 44:3:13244 44:4:135751 44:5:1086008 44:6:7059052 44:7:38320568 44:8:177232627 44:9:708930508 44:10:2481256778 44:11:7669339132 44:12:21090682613 44:13:51915526432 44:14:114955808528 44:15:229911617056 44:16:416714805914 44:17:686353797976 44:18:1029530696964 44:19:1408831480056 44:20:1761039350070 44:21:2012616400080 44:22:2104098963720 44:23:2012616400080 44:24:1761039350070 44:25:1408831480056 44:26:1029530696964 44:27:686353797976 44:28:416714805914 44:29:229911617056 44:30:114955808528 44:31:51915526432 44:32:21090682613 44:33:7669339132 44:34:2481256778 44:35:708930508 44:36:177232627 44:37:38320568 44:38:7059052 44:39:1086008 44:40:135751 44:41:13244 44:42:946 44:43:44 44:44:1 # binomial(45, k) for 0 <= k <= 45 45:0:1 45:1:45 45:2:990 45:3:14190 45:4:148995 45:5:1221759 45:6:8145060 45:7:45379620 45:8:215553195 45:9:886163135 45:10:3190187286 45:11:10150595910 45:12:28760021745 45:13:73006209045 45:14:166871334960 45:15:344867425584 45:16:646626422970 45:17:1103068603890 45:18:1715884494940 45:19:2438362177020 45:20:3169870830126 45:21:3773655750150 45:22:4116715363800 45:23:4116715363800 45:24:3773655750150 45:25:3169870830126 45:26:2438362177020 45:27:1715884494940 45:28:1103068603890 45:29:646626422970 45:30:344867425584 45:31:166871334960 45:32:73006209045 45:33:28760021745 45:34:10150595910 45:35:3190187286 45:36:886163135 45:37:215553195 45:38:45379620 45:39:8145060 45:40:1221759 45:41:148995 45:42:14190 45:43:990 45:44:45 45:45:1 # binomial(46, k) for 0 <= k <= 46 46:0:1 46:1:46 46:2:1035 46:3:15180 46:4:163185 46:5:1370754 46:6:9366819 46:7:53524680 46:8:260932815 46:9:1101716330 46:10:4076350421 46:11:13340783196 46:12:38910617655 46:13:101766230790 46:14:239877544005 46:15:511738760544 46:16:991493848554 46:17:1749695026860 46:18:2818953098830 46:19:4154246671960 46:20:5608233007146 46:21:6943526580276 46:22:7890371113950 46:23:8233430727600 46:24:7890371113950 46:25:6943526580276 46:26:5608233007146 46:27:4154246671960 46:28:2818953098830 46:29:1749695026860 46:30:991493848554 46:31:511738760544 46:32:239877544005 46:33:101766230790 46:34:38910617655 46:35:13340783196 46:36:4076350421 46:37:1101716330 46:38:260932815 46:39:53524680 46:40:9366819 46:41:1370754 46:42:163185 46:43:15180 46:44:1035 46:45:46 46:46:1 # binomial(47, k) for 0 <= k <= 47 47:0:1 47:1:47 47:2:1081 47:3:16215 47:4:178365 47:5:1533939 47:6:10737573 47:7:62891499 47:8:314457495 47:9:1362649145 47:10:5178066751 47:11:17417133617 47:12:52251400851 47:13:140676848445 47:14:341643774795 47:15:751616304549 47:16:1503232609098 47:17:2741188875414 47:18:4568648125690 47:19:6973199770790 47:20:9762479679106 47:21:12551759587422 47:22:14833897694226 47:23:16123801841550 47:24:16123801841550 47:25:14833897694226 47:26:12551759587422 47:27:9762479679106 47:28:6973199770790 47:29:4568648125690 47:30:2741188875414 47:31:1503232609098 47:32:751616304549 47:33:341643774795 47:34:140676848445 47:35:52251400851 47:36:17417133617 47:37:5178066751 47:38:1362649145 47:39:314457495 47:40:62891499 47:41:10737573 47:42:1533939 47:43:178365 47:44:16215 47:45:1081 47:46:47 47:47:1 # binomial(48, k) for 0 <= k <= 48 48:0:1 48:1:48 48:2:1128 48:3:17296 48:4:194580 48:5:1712304 48:6:12271512 48:7:73629072 48:8:377348994 48:9:1677106640 48:10:6540715896 48:11:22595200368 48:12:69668534468 48:13:192928249296 48:14:482320623240 48:15:1093260079344 48:16:2254848913647 48:17:4244421484512 48:18:7309837001104 48:19:11541847896480 48:20:16735679449896 48:21:22314239266528 48:22:27385657281648 48:23:30957699535776 48:24:32247603683100 48:25:30957699535776 48:26:27385657281648 48:27:22314239266528 48:28:16735679449896 48:29:11541847896480 48:30:7309837001104 48:31:4244421484512 48:32:2254848913647 48:33:1093260079344 48:34:482320623240 48:35:192928249296 48:36:69668534468 48:37:22595200368 48:38:6540715896 48:39:1677106640 48:40:377348994 48:41:73629072 48:42:12271512 48:43:1712304 48:44:194580 48:45:17296 48:46:1128 48:47:48 48:48:1 # binomial(49, k) for 0 <= k <= 49 49:0:1 49:1:49 49:2:1176 49:3:18424 49:4:211876 49:5:1906884 49:6:13983816 49:7:85900584 49:8:450978066 49:9:2054455634 49:10:8217822536 49:11:29135916264 49:12:92263734836 49:13:262596783764 49:14:675248872536 49:15:1575580702584 49:16:3348108992991 49:17:6499270398159 49:18:11554258485616 49:19:18851684897584 49:20:28277527346376 49:21:39049918716424 49:22:49699896548176 49:23:58343356817424 49:24:63205303218876 49:25:63205303218876 49:26:58343356817424 49:27:49699896548176 49:28:39049918716424 49:29:28277527346376 49:30:18851684897584 49:31:11554258485616 49:32:6499270398159 49:33:3348108992991 49:34:1575580702584 49:35:675248872536 49:36:262596783764 49:37:92263734836 49:38:29135916264 49:39:8217822536 49:40:2054455634 49:41:450978066 49:42:85900584 49:43:13983816 49:44:1906884 49:45:211876 49:46:18424 49:47:1176 49:48:49 49:49:1 # binomial(50, k) for 0 <= k <= 50 50:0:1 50:1:50 50:2:1225 50:3:19600 50:4:230300 50:5:2118760 50:6:15890700 50:7:99884400 50:8:536878650 50:9:2505433700 50:10:10272278170 50:11:37353738800 50:12:121399651100 50:13:354860518600 50:14:937845656300 50:15:2250829575120 50:16:4923689695575 50:17:9847379391150 50:18:18053528883775 50:19:30405943383200 50:20:47129212243960 50:21:67327446062800 50:22:88749815264600 50:23:108043253365600 50:24:121548660036300 50:25:126410606437752 50:26:121548660036300 50:27:108043253365600 50:28:88749815264600 50:29:67327446062800 50:30:47129212243960 50:31:30405943383200 50:32:18053528883775 50:33:9847379391150 50:34:4923689695575 50:35:2250829575120 50:36:937845656300 50:37:354860518600 50:38:121399651100 50:39:37353738800 50:40:10272278170 50:41:2505433700 50:42:536878650 50:43:99884400 50:44:15890700 50:45:2118760 50:46:230300 50:47:19600 50:48:1225 50:49:50 50:50:1 # binomial(51, k) for 0 <= k <= 51 51:0:1 51:1:51 51:2:1275 51:3:20825 51:4:249900 51:5:2349060 51:6:18009460 51:7:115775100 51:8:636763050 51:9:3042312350 51:10:12777711870 51:11:47626016970 51:12:158753389900 51:13:476260169700 51:14:1292706174900 51:15:3188675231420 51:16:7174519270695 51:17:14771069086725 51:18:27900908274925 51:19:48459472266975 51:20:77535155627160 51:21:114456658306760 51:22:156077261327400 51:23:196793068630200 51:24:229591913401900 51:25:247959266474052 51:26:247959266474052 51:27:229591913401900 51:28:196793068630200 51:29:156077261327400 51:30:114456658306760 51:31:77535155627160 51:32:48459472266975 51:33:27900908274925 51:34:14771069086725 51:35:7174519270695 51:36:3188675231420 51:37:1292706174900 51:38:476260169700 51:39:158753389900 51:40:47626016970 51:41:12777711870 51:42:3042312350 51:43:636763050 51:44:115775100 51:45:18009460 51:46:2349060 51:47:249900 51:48:20825 51:49:1275 51:50:51 51:51:1 # binomial(52, k) for 0 <= k <= 52 52:0:1 52:1:52 52:2:1326 52:3:22100 52:4:270725 52:5:2598960 52:6:20358520 52:7:133784560 52:8:752538150 52:9:3679075400 52:10:15820024220 52:11:60403728840 52:12:206379406870 52:13:635013559600 52:14:1768966344600 52:15:4481381406320 52:16:10363194502115 52:17:21945588357420 52:18:42671977361650 52:19:76360380541900 52:20:125994627894135 52:21:191991813933920 52:22:270533919634160 52:23:352870329957600 52:24:426384982032100 52:25:477551179875952 52:26:495918532948104 52:27:477551179875952 52:28:426384982032100 52:29:352870329957600 52:30:270533919634160 52:31:191991813933920 52:32:125994627894135 52:33:76360380541900 52:34:42671977361650 52:35:21945588357420 52:36:10363194502115 52:37:4481381406320 52:38:1768966344600 52:39:635013559600 52:40:206379406870 52:41:60403728840 52:42:15820024220 52:43:3679075400 52:44:752538150 52:45:133784560 52:46:20358520 52:47:2598960 52:48:270725 52:49:22100 52:50:1326 52:51:52 52:52:1 # binomial(53, k) for 0 <= k <= 53 53:0:1 53:1:53 53:2:1378 53:3:23426 53:4:292825 53:5:2869685 53:6:22957480 53:7:154143080 53:8:886322710 53:9:4431613550 53:10:19499099620 53:11:76223753060 53:12:266783135710 53:13:841392966470 53:14:2403979904200 53:15:6250347750920 53:16:14844575908435 53:17:32308782859535 53:18:64617565719070 53:19:119032357903550 53:20:202355008436035 53:21:317986441828055 53:22:462525733568080 53:23:623404249591760 53:24:779255311989700 53:25:903936161908052 53:26:973469712824056 53:27:973469712824056 53:28:903936161908052 53:29:779255311989700 53:30:623404249591760 53:31:462525733568080 53:32:317986441828055 53:33:202355008436035 53:34:119032357903550 53:35:64617565719070 53:36:32308782859535 53:37:14844575908435 53:38:6250347750920 53:39:2403979904200 53:40:841392966470 53:41:266783135710 53:42:76223753060 53:43:19499099620 53:44:4431613550 53:45:886322710 53:46:154143080 53:47:22957480 53:48:2869685 53:49:292825 53:50:23426 53:51:1378 53:52:53 53:53:1 # binomial(54, k) for 0 <= k <= 54 54:0:1 54:1:54 54:2:1431 54:3:24804 54:4:316251 54:5:3162510 54:6:25827165 54:7:177100560 54:8:1040465790 54:9:5317936260 54:10:23930713170 54:11:95722852680 54:12:343006888770 54:13:1108176102180 54:14:3245372870670 54:15:8654327655120 54:16:21094923659355 54:17:47153358767970 54:18:96926348578605 54:19:183649923622620 54:20:321387366339585 54:21:520341450264090 54:22:780512175396135 54:23:1085929983159840 54:24:1402659561581460 54:25:1683191473897752 54:26:1877405874732108 54:27:1946939425648112 54:28:1877405874732108 54:29:1683191473897752 54:30:1402659561581460 54:31:1085929983159840 54:32:780512175396135 54:33:520341450264090 54:34:321387366339585 54:35:183649923622620 54:36:96926348578605 54:37:47153358767970 54:38:21094923659355 54:39:8654327655120 54:40:3245372870670 54:41:1108176102180 54:42:343006888770 54:43:95722852680 54:44:23930713170 54:45:5317936260 54:46:1040465790 54:47:177100560 54:48:25827165 54:49:3162510 54:50:316251 54:51:24804 54:52:1431 54:53:54 54:54:1 # binomial(55, k) for 0 <= k <= 55 55:0:1 55:1:55 55:2:1485 55:3:26235 55:4:341055 55:5:3478761 55:6:28989675 55:7:202927725 55:8:1217566350 55:9:6358402050 55:10:29248649430 55:11:119653565850 55:12:438729741450 55:13:1451182990950 55:14:4353548972850 55:15:11899700525790 55:16:29749251314475 55:17:68248282427325 55:18:144079707346575 55:19:280576272201225 55:20:505037289962205 55:21:841728816603675 55:22:1300853625660225 55:23:1866442158555975 55:24:2488589544741300 55:25:3085851035479212 55:26:3560597348629860 55:27:3824345300380220 55:28:3824345300380220 55:29:3560597348629860 55:30:3085851035479212 55:31:2488589544741300 55:32:1866442158555975 55:33:1300853625660225 55:34:841728816603675 55:35:505037289962205 55:36:280576272201225 55:37:144079707346575 55:38:68248282427325 55:39:29749251314475 55:40:11899700525790 55:41:4353548972850 55:42:1451182990950 55:43:438729741450 55:44:119653565850 55:45:29248649430 55:46:6358402050 55:47:1217566350 55:48:202927725 55:49:28989675 55:50:3478761 55:51:341055 55:52:26235 55:53:1485 55:54:55 55:55:1 # binomial(56, k) for 0 <= k <= 56 56:0:1 56:1:56 56:2:1540 56:3:27720 56:4:367290 56:5:3819816 56:6:32468436 56:7:231917400 56:8:1420494075 56:9:7575968400 56:10:35607051480 56:11:148902215280 56:12:558383307300 56:13:1889912732400 56:14:5804731963800 56:15:16253249498640 56:16:41648951840265 56:17:97997533741800 56:18:212327989773900 56:19:424655979547800 56:20:785613562163430 56:21:1346766106565880 56:22:2142582442263900 56:23:3167295784216200 56:24:4355031703297275 56:25:5574440580220512 56:26:6646448384109072 56:27:7384942649010080 56:28:7648690600760440 56:29:7384942649010080 56:30:6646448384109072 56:31:5574440580220512 56:32:4355031703297275 56:33:3167295784216200 56:34:2142582442263900 56:35:1346766106565880 56:36:785613562163430 56:37:424655979547800 56:38:212327989773900 56:39:97997533741800 56:40:41648951840265 56:41:16253249498640 56:42:5804731963800 56:43:1889912732400 56:44:558383307300 56:45:148902215280 56:46:35607051480 56:47:7575968400 56:48:1420494075 56:49:231917400 56:50:32468436 56:51:3819816 56:52:367290 56:53:27720 56:54:1540 56:55:56 56:56:1 # binomial(57, k) for 0 <= k <= 57 57:0:1 57:1:57 57:2:1596 57:3:29260 57:4:395010 57:5:4187106 57:6:36288252 57:7:264385836 57:8:1652411475 57:9:8996462475 57:10:43183019880 57:11:184509266760 57:12:707285522580 57:13:2448296039700 57:14:7694644696200 57:15:22057981462440 57:16:57902201338905 57:17:139646485582065 57:18:310325523515700 57:19:636983969321700 57:20:1210269541711230 57:21:2132379668729310 57:22:3489348548829780 57:23:5309878226480100 57:24:7522327487513475 57:25:9929472283517787 57:26:12220888964329584 57:27:14031391033119152 57:28:15033633249770520 57:29:15033633249770520 57:30:14031391033119152 57:31:12220888964329584 57:32:9929472283517787 57:33:7522327487513475 57:34:5309878226480100 57:35:3489348548829780 57:36:2132379668729310 57:37:1210269541711230 57:38:636983969321700 57:39:310325523515700 57:40:139646485582065 57:41:57902201338905 57:42:22057981462440 57:43:7694644696200 57:44:2448296039700 57:45:707285522580 57:46:184509266760 57:47:43183019880 57:48:8996462475 57:49:1652411475 57:50:264385836 57:51:36288252 57:52:4187106 57:53:395010 57:54:29260 57:55:1596 57:56:57 57:57:1 # binomial(58, k) for 0 <= k <= 58 58:0:1 58:1:58 58:2:1653 58:3:30856 58:4:424270 58:5:4582116 58:6:40475358 58:7:300674088 58:8:1916797311 58:9:10648873950 58:10:52179482355 58:11:227692286640 58:12:891794789340 58:13:3155581562280 58:14:10142940735900 58:15:29752626158640 58:16:79960182801345 58:17:197548686920970 58:18:449972009097765 58:19:947309492837400 58:20:1847253511032930 58:21:3342649210440540 58:22:5621728217559090 58:23:8799226775309880 58:24:12832205713993575 58:25:17451799771031262 58:26:22150361247847371 58:27:26252279997448736 58:28:29065024282889672 58:29:30067266499541040 58:30:29065024282889672 58:31:26252279997448736 58:32:22150361247847371 58:33:17451799771031262 58:34:12832205713993575 58:35:8799226775309880 58:36:5621728217559090 58:37:3342649210440540 58:38:1847253511032930 58:39:947309492837400 58:40:449972009097765 58:41:197548686920970 58:42:79960182801345 58:43:29752626158640 58:44:10142940735900 58:45:3155581562280 58:46:891794789340 58:47:227692286640 58:48:52179482355 58:49:10648873950 58:50:1916797311 58:51:300674088 58:52:40475358 58:53:4582116 58:54:424270 58:55:30856 58:56:1653 58:57:58 58:58:1 # binomial(59, k) for 0 <= k <= 59 59:0:1 59:1:59 59:2:1711 59:3:32509 59:4:455126 59:5:5006386 59:6:45057474 59:7:341149446 59:8:2217471399 59:9:12565671261 59:10:62828356305 59:11:279871768995 59:12:1119487075980 59:13:4047376351620 59:14:13298522298180 59:15:39895566894540 59:16:109712808959985 59:17:277508869722315 59:18:647520696018735 59:19:1397281501935165 59:20:2794563003870330 59:21:5189902721473470 59:22:8964377427999630 59:23:14420954992868970 59:24:21631432489303455 59:25:30284005485024837 59:26:39602161018878633 59:27:48402641245296107 59:28:55317304280338408 59:29:59132290782430712 59:30:59132290782430712 59:31:55317304280338408 59:32:48402641245296107 59:33:39602161018878633 59:34:30284005485024837 59:35:21631432489303455 59:36:14420954992868970 59:37:8964377427999630 59:38:5189902721473470 59:39:2794563003870330 59:40:1397281501935165 59:41:647520696018735 59:42:277508869722315 59:43:109712808959985 59:44:39895566894540 59:45:13298522298180 59:46:4047376351620 59:47:1119487075980 59:48:279871768995 59:49:62828356305 59:50:12565671261 59:51:2217471399 59:52:341149446 59:53:45057474 59:54:5006386 59:55:455126 59:56:32509 59:57:1711 59:58:59 59:59:1 # binomial(60, k) for 0 <= k <= 60 60:0:1 60:1:60 60:2:1770 60:3:34220 60:4:487635 60:5:5461512 60:6:50063860 60:7:386206920 60:8:2558620845 60:9:14783142660 60:10:75394027566 60:11:342700125300 60:12:1399358844975 60:13:5166863427600 60:14:17345898649800 60:15:53194089192720 60:16:149608375854525 60:17:387221678682300 60:18:925029565741050 60:19:2044802197953900 60:20:4191844505805495 60:21:7984465725343800 60:22:14154280149473100 60:23:23385332420868600 60:24:36052387482172425 60:25:51915437974328292 60:26:69886166503903470 60:27:88004802264174740 60:28:103719945525634515 60:29:114449595062769120 60:30:118264581564861424 60:31:114449595062769120 60:32:103719945525634515 60:33:88004802264174740 60:34:69886166503903470 60:35:51915437974328292 60:36:36052387482172425 60:37:23385332420868600 60:38:14154280149473100 60:39:7984465725343800 60:40:4191844505805495 60:41:2044802197953900 60:42:925029565741050 60:43:387221678682300 60:44:149608375854525 60:45:53194089192720 60:46:17345898649800 60:47:5166863427600 60:48:1399358844975 60:49:342700125300 60:50:75394027566 60:51:14783142660 60:52:2558620845 60:53:386206920 60:54:50063860 60:55:5461512 60:56:487635 60:57:34220 60:58:1770 60:59:60 60:60:1 # binomial(61, k) for 0 <= k <= 61 61:0:1 61:1:61 61:2:1830 61:3:35990 61:4:521855 61:5:5949147 61:6:55525372 61:7:436270780 61:8:2944827765 61:9:17341763505 61:10:90177170226 61:11:418094152866 61:12:1742058970275 61:13:6566222272575 61:14:22512762077400 61:15:70539987842520 61:16:202802465047245 61:17:536830054536825 61:18:1312251244423350 61:19:2969831763694950 61:20:6236646703759395 61:21:12176310231149295 61:22:22138745874816900 61:23:37539612570341700 61:24:59437719903041025 61:25:87967825456500717 61:26:121801604478231762 61:27:157890968768078210 61:28:191724747789809255 61:29:218169540588403635 61:30:232714176627630544 61:31:232714176627630544 61:32:218169540588403635 61:33:191724747789809255 61:34:157890968768078210 61:35:121801604478231762 61:36:87967825456500717 61:37:59437719903041025 61:38:37539612570341700 61:39:22138745874816900 61:40:12176310231149295 61:41:6236646703759395 61:42:2969831763694950 61:43:1312251244423350 61:44:536830054536825 61:45:202802465047245 61:46:70539987842520 61:47:22512762077400 61:48:6566222272575 61:49:1742058970275 61:50:418094152866 61:51:90177170226 61:52:17341763505 61:53:2944827765 61:54:436270780 61:55:55525372 61:56:5949147 61:57:521855 61:58:35990 61:59:1830 61:60:61 61:61:1 # binomial(62, k) for 0 <= k <= 62 62:0:1 62:1:62 62:2:1891 62:3:37820 62:4:557845 62:5:6471002 62:6:61474519 62:7:491796152 62:8:3381098545 62:9:20286591270 62:10:107518933731 62:11:508271323092 62:12:2160153123141 62:13:8308281242850 62:14:29078984349975 62:15:93052749919920 62:16:273342452889765 62:17:739632519584070 62:18:1849081298960175 62:19:4282083008118300 62:20:9206478467454345 62:21:18412956934908690 62:22:34315056105966195 62:23:59678358445158600 62:24:96977332473382725 62:25:147405545359541742 62:26:209769429934732479 62:27:279692573246309972 62:28:349615716557887465 62:29:409894288378212890 62:30:450883717216034179 62:31:465428353255261088 62:32:450883717216034179 62:33:409894288378212890 62:34:349615716557887465 62:35:279692573246309972 62:36:209769429934732479 62:37:147405545359541742 62:38:96977332473382725 62:39:59678358445158600 62:40:34315056105966195 62:41:18412956934908690 62:42:9206478467454345 62:43:4282083008118300 62:44:1849081298960175 62:45:739632519584070 62:46:273342452889765 62:47:93052749919920 62:48:29078984349975 62:49:8308281242850 62:50:2160153123141 62:51:508271323092 62:52:107518933731 62:53:20286591270 62:54:3381098545 62:55:491796152 62:56:61474519 62:57:6471002 62:58:557845 62:59:37820 62:60:1891 62:61:62 62:62:1 # binomial(63, k) for 0 <= k <= 63 63:0:1 63:1:63 63:2:1953 63:3:39711 63:4:595665 63:5:7028847 63:6:67945521 63:7:553270671 63:8:3872894697 63:9:23667689815 63:10:127805525001 63:11:615790256823 63:12:2668424446233 63:13:10468434365991 63:14:37387265592825 63:15:122131734269895 63:16:366395202809685 63:17:1012974972473835 63:18:2588713818544245 63:19:6131164307078475 63:20:13488561475572645 63:21:27619435402363035 63:22:52728013040874885 63:23:93993414551124795 63:24:156655690918541325 63:25:244382877832924467 63:26:357174975294274221 63:27:489462003181042451 63:28:629308289804197437 63:29:759510004936100355 63:30:860778005594247069 63:31:916312070471295267 63:32:916312070471295267 63:33:860778005594247069 63:34:759510004936100355 63:35:629308289804197437 63:36:489462003181042451 63:37:357174975294274221 63:38:244382877832924467 63:39:156655690918541325 63:40:93993414551124795 63:41:52728013040874885 63:42:27619435402363035 63:43:13488561475572645 63:44:6131164307078475 63:45:2588713818544245 63:46:1012974972473835 63:47:366395202809685 63:48:122131734269895 63:49:37387265592825 63:50:10468434365991 63:51:2668424446233 63:52:615790256823 63:53:127805525001 63:54:23667689815 63:55:3872894697 63:56:553270671 63:57:67945521 63:58:7028847 63:59:595665 63:60:39711 63:61:1953 63:62:63 63:63:1 # binomial(64, k) for 0 <= k <= 64 64:0:1 64:1:64 64:2:2016 64:3:41664 64:4:635376 64:5:7624512 64:6:74974368 64:7:621216192 64:8:4426165368 64:9:27540584512 64:10:151473214816 64:11:743595781824 64:12:3284214703056 64:13:13136858812224 64:14:47855699958816 64:15:159518999862720 64:16:488526937079580 64:17:1379370175283520 64:18:3601688791018080 64:19:8719878125622720 64:20:19619725782651120 64:21:41107996877935680 64:22:80347448443237920 64:23:146721427591999680 64:24:250649105469666120 64:25:401038568751465792 64:26:601557853127198688 64:27:846636978475316672 64:28:1118770292985239888 64:29:1388818294740297792 64:30:1620288010530347424 64:31:1777090076065542336 64:32:1832624140942590534 64:33:1777090076065542336 64:34:1620288010530347424 64:35:1388818294740297792 64:36:1118770292985239888 64:37:846636978475316672 64:38:601557853127198688 64:39:401038568751465792 64:40:250649105469666120 64:41:146721427591999680 64:42:80347448443237920 64:43:41107996877935680 64:44:19619725782651120 64:45:8719878125622720 64:46:3601688791018080 64:47:1379370175283520 64:48:488526937079580 64:49:159518999862720 64:50:47855699958816 64:51:13136858812224 64:52:3284214703056 64:53:743595781824 64:54:151473214816 64:55:27540584512 64:56:4426165368 64:57:621216192 64:58:74974368 64:59:7624512 64:60:635376 64:61:41664 64:62:2016 64:63:64 64:64:1 # binomial(65, k) for 0 <= k <= 65 65:0:1 65:1:65 65:2:2080 65:3:43680 65:4:677040 65:5:8259888 65:6:82598880 65:7:696190560 65:8:5047381560 65:9:31966749880 65:10:179013799328 65:11:895068996640 65:12:4027810484880 65:13:16421073515280 65:14:60992558771040 65:15:207374699821536 65:16:648045936942300 65:17:1867897112363100 65:18:4981058966301600 65:19:12321566916640800 65:20:28339603908273840 65:21:60727722660586800 65:22:121455445321173600 65:23:227068876035237600 65:24:397370533061665800 65:25:651687674221131912 65:26:1002596421878664480 65:27:1448194831602515360 65:28:1965407271460556560 65:29:2507588587725537680 65:30:3009106305270645216 65:31:3397378086595889760 65:32:3609714217008132870 65:33:3609714217008132870 65:34:3397378086595889760 65:35:3009106305270645216 65:36:2507588587725537680 65:37:1965407271460556560 65:38:1448194831602515360 65:39:1002596421878664480 65:40:651687674221131912 65:41:397370533061665800 65:42:227068876035237600 65:43:121455445321173600 65:44:60727722660586800 65:45:28339603908273840 65:46:12321566916640800 65:47:4981058966301600 65:48:1867897112363100 65:49:648045936942300 65:50:207374699821536 65:51:60992558771040 65:52:16421073515280 65:53:4027810484880 65:54:895068996640 65:55:179013799328 65:56:31966749880 65:57:5047381560 65:58:696190560 65:59:82598880 65:60:8259888 65:61:677040 65:62:43680 65:63:2080 65:64:65 65:65:1 # binomial(66, k) for 0 <= k <= 66 66:0:1 66:1:66 66:2:2145 66:3:45760 66:4:720720 66:5:8936928 66:6:90858768 66:7:778789440 66:8:5743572120 66:9:37014131440 66:10:210980549208 66:11:1074082795968 66:12:4922879481520 66:13:20448884000160 66:14:77413632286320 66:15:268367258592576 66:16:855420636763836 66:17:2515943049305400 66:18:6848956078664700 66:19:17302625882942400 66:20:40661170824914640 66:21:89067326568860640 66:22:182183167981760400 66:23:348524321356411200 66:24:624439409096903400 66:25:1049058207282797712 66:26:1654284096099796392 66:27:2450791253481179840 66:28:3413602103063071920 66:29:4472995859186094240 66:30:5516694892996182896 66:31:6406484391866534976 66:32:7007092303604022630 66:33:7219428434016265740 66:34:7007092303604022630 66:35:6406484391866534976 66:36:5516694892996182896 66:37:4472995859186094240 66:38:3413602103063071920 66:39:2450791253481179840 66:40:1654284096099796392 66:41:1049058207282797712 66:42:624439409096903400 66:43:348524321356411200 66:44:182183167981760400 66:45:89067326568860640 66:46:40661170824914640 66:47:17302625882942400 66:48:6848956078664700 66:49:2515943049305400 66:50:855420636763836 66:51:268367258592576 66:52:77413632286320 66:53:20448884000160 66:54:4922879481520 66:55:1074082795968 66:56:210980549208 66:57:37014131440 66:58:5743572120 66:59:778789440 66:60:90858768 66:61:8936928 66:62:720720 66:63:45760 66:64:2145 66:65:66 66:66:1 # binomial(67, k) for 0 <= k <= 67 67:0:1 67:1:67 67:2:2211 67:3:47905 67:4:766480 67:5:9657648 67:6:99795696 67:7:869648208 67:8:6522361560 67:9:42757703560 67:10:247994680648 67:11:1285063345176 67:12:5996962277488 67:13:25371763481680 67:14:97862516286480 67:15:345780890878896 67:16:1123787895356412 67:17:3371363686069236 67:18:9364899127970100 67:19:24151581961607100 67:20:57963796707857040 67:21:129728497393775280 67:22:271250494550621040 67:23:530707489338171600 67:24:972963730453314600 67:25:1673497616379701112 67:26:2703342303382594104 67:27:4105075349580976232 67:28:5864393356544251760 67:29:7886597962249166160 67:30:9989690752182277136 67:31:11923179284862717872 67:32:13413576695470557606 67:33:14226520737620288370 67:34:14226520737620288370 67:35:13413576695470557606 67:36:11923179284862717872 67:37:9989690752182277136 67:38:7886597962249166160 67:39:5864393356544251760 67:40:4105075349580976232 67:41:2703342303382594104 67:42:1673497616379701112 67:43:972963730453314600 67:44:530707489338171600 67:45:271250494550621040 67:46:129728497393775280 67:47:57963796707857040 67:48:24151581961607100 67:49:9364899127970100 67:50:3371363686069236 67:51:1123787895356412 67:52:345780890878896 67:53:97862516286480 67:54:25371763481680 67:55:5996962277488 67:56:1285063345176 67:57:247994680648 67:58:42757703560 67:59:6522361560 67:60:869648208 67:61:99795696 67:62:9657648 67:63:766480 67:64:47905 67:65:2211 67:66:67 67:67:1 # binomial(68, k) for 0 <= k <= 68 68:0:1 68:1:68 68:2:2278 68:3:50116 68:4:814385 68:5:10424128 68:6:109453344 68:7:969443904 68:8:7392009768 68:9:49280065120 68:10:290752384208 68:11:1533058025824 68:12:7282025622664 68:13:31368725759168 68:14:123234279768160 68:15:443643407165376 68:16:1469568786235308 68:17:4495151581425648 68:18:12736262814039336 68:19:33516481089577200 68:20:82115378669464140 68:21:187692294101632320 68:22:400978991944396320 68:23:801957983888792640 68:24:1503671219791486200 68:25:2646461346833015712 68:26:4376839919762295216 68:27:6808417652963570336 68:28:9969468706125227992 68:29:13750991318793417920 68:30:17876288714431443296 68:31:21912870037044995008 68:32:25336755980333275478 68:33:27640097433090845976 68:34:28453041475240576740 68:35:27640097433090845976 68:36:25336755980333275478 68:37:21912870037044995008 68:38:17876288714431443296 68:39:13750991318793417920 68:40:9969468706125227992 68:41:6808417652963570336 68:42:4376839919762295216 68:43:2646461346833015712 68:44:1503671219791486200 68:45:801957983888792640 68:46:400978991944396320 68:47:187692294101632320 68:48:82115378669464140 68:49:33516481089577200 68:50:12736262814039336 68:51:4495151581425648 68:52:1469568786235308 68:53:443643407165376 68:54:123234279768160 68:55:31368725759168 68:56:7282025622664 68:57:1533058025824 68:58:290752384208 68:59:49280065120 68:60:7392009768 68:61:969443904 68:62:109453344 68:63:10424128 68:64:814385 68:65:50116 68:66:2278 68:67:68 68:68:1 # binomial(69, k) for 0 <= k <= 69 69:0:1 69:1:69 69:2:2346 69:3:52394 69:4:864501 69:5:11238513 69:6:119877472 69:7:1078897248 69:8:8361453672 69:9:56672074888 69:10:340032449328 69:11:1823810410032 69:12:8815083648488 69:13:38650751381832 69:14:154603005527328 69:15:566877686933536 69:16:1913212193400684 69:17:5964720367660956 69:18:17231414395464984 69:19:46252743903616536 69:20:115631859759041340 69:21:269807672771096460 69:22:588671286046028640 69:23:1202936975833188960 69:24:2305629203680278840 69:25:4150132566624501912 69:26:7023301266595310928 69:27:11185257572725865552 69:28:16777886359088798328 69:29:23720460024918645912 69:30:31627280033224861216 69:31:39789158751476438304 69:32:47249626017378270486 69:33:52976853413424121454 69:34:56093138908331422716 69:35:56093138908331422716 69:36:52976853413424121454 69:37:47249626017378270486 69:38:39789158751476438304 69:39:31627280033224861216 69:40:23720460024918645912 69:41:16777886359088798328 69:42:11185257572725865552 69:43:7023301266595310928 69:44:4150132566624501912 69:45:2305629203680278840 69:46:1202936975833188960 69:47:588671286046028640 69:48:269807672771096460 69:49:115631859759041340 69:50:46252743903616536 69:51:17231414395464984 69:52:5964720367660956 69:53:1913212193400684 69:54:566877686933536 69:55:154603005527328 69:56:38650751381832 69:57:8815083648488 69:58:1823810410032 69:59:340032449328 69:60:56672074888 69:61:8361453672 69:62:1078897248 69:63:119877472 69:64:11238513 69:65:864501 69:66:52394 69:67:2346 69:68:69 69:69:1 # binomial(70, k) for 0 <= k <= 70 70:0:1 70:1:70 70:2:2415 70:3:54740 70:4:916895 70:5:12103014 70:6:131115985 70:7:1198774720 70:8:9440350920 70:9:65033528560 70:10:396704524216 70:11:2163842859360 70:12:10638894058520 70:13:47465835030320 70:14:193253756909160 70:15:721480692460864 70:16:2480089880334220 70:17:7877932561061640 70:18:23196134763125940 70:19:63484158299081520 70:20:161884603662657876 70:21:385439532530137800 70:22:858478958817125100 70:23:1791608261879217600 70:24:3508566179513467800 70:25:6455761770304780752 70:26:11173433833219812840 70:27:18208558839321176480 70:28:27963143931814663880 70:29:40498346384007444240 70:30:55347740058143507128 70:31:71416438784701299520 70:32:87038784768854708790 70:33:100226479430802391940 70:34:109069992321755544170 70:35:112186277816662845432 70:36:109069992321755544170 70:37:100226479430802391940 70:38:87038784768854708790 70:39:71416438784701299520 70:40:55347740058143507128 70:41:40498346384007444240 70:42:27963143931814663880 70:43:18208558839321176480 70:44:11173433833219812840 70:45:6455761770304780752 70:46:3508566179513467800 70:47:1791608261879217600 70:48:858478958817125100 70:49:385439532530137800 70:50:161884603662657876 70:51:63484158299081520 70:52:23196134763125940 70:53:7877932561061640 70:54:2480089880334220 70:55:721480692460864 70:56:193253756909160 70:57:47465835030320 70:58:10638894058520 70:59:2163842859360 70:60:396704524216 70:61:65033528560 70:62:9440350920 70:63:1198774720 70:64:131115985 70:65:12103014 70:66:916895 70:67:54740 70:68:2415 70:69:70 70:70:1 # binomial(71, k) for 0 <= k <= 71 71:0:1 71:1:71 71:2:2485 71:3:57155 71:4:971635 71:5:13019909 71:6:143218999 71:7:1329890705 71:8:10639125640 71:9:74473879480 71:10:461738052776 71:11:2560547383576 71:12:12802736917880 71:13:58104729088840 71:14:240719591939480 71:15:914734449370024 71:16:3201570572795084 71:17:10358022441395860 71:18:31074067324187580 71:19:86680293062207460 71:20:225368761961739396 71:21:547324136192795676 71:22:1243918491347262900 71:23:2650087220696342700 71:24:5300174441392685400 71:25:9964327949818248552 71:26:17629195603524593592 71:27:29381992672540989320 71:28:46171702771135840360 71:29:68461490315822108120 71:30:95846086442150951368 71:31:126764178842844806648 71:32:158455223553556008310 71:33:187265264199657100730 71:34:209296471752557936110 71:35:221256270138418389602 71:36:221256270138418389602 71:37:209296471752557936110 71:38:187265264199657100730 71:39:158455223553556008310 71:40:126764178842844806648 71:41:95846086442150951368 71:42:68461490315822108120 71:43:46171702771135840360 71:44:29381992672540989320 71:45:17629195603524593592 71:46:9964327949818248552 71:47:5300174441392685400 71:48:2650087220696342700 71:49:1243918491347262900 71:50:547324136192795676 71:51:225368761961739396 71:52:86680293062207460 71:53:31074067324187580 71:54:10358022441395860 71:55:3201570572795084 71:56:914734449370024 71:57:240719591939480 71:58:58104729088840 71:59:12802736917880 71:60:2560547383576 71:61:461738052776 71:62:74473879480 71:63:10639125640 71:64:1329890705 71:65:143218999 71:66:13019909 71:67:971635 71:68:57155 71:69:2485 71:70:71 71:71:1 # binomial(72, k) for 0 <= k <= 72 72:0:1 72:1:72 72:2:2556 72:3:59640 72:4:1028790 72:5:13991544 72:6:156238908 72:7:1473109704 72:8:11969016345 72:9:85113005120 72:10:536211932256 72:11:3022285436352 72:12:15363284301456 72:13:70907466006720 72:14:298824321028320 72:15:1155454041309504 72:16:4116305022165108 72:17:13559593014190944 72:18:41432089765583440 72:19:117754360386395040 72:20:312049055023946856 72:21:772692898154535072 72:22:1791242627540058576 72:23:3894005712043605600 72:24:7950261662089028100 72:25:15264502391210933952 72:26:27593523553342842144 72:27:47011188276065582912 72:28:75553695443676829680 72:29:114633193086957948480 72:30:164307576757973059488 72:31:222610265284995758016 72:32:285219402396400814958 72:33:345720487753213109040 72:34:396561735952215036840 72:35:430552741890976325712 72:36:442512540276836779204 72:37:430552741890976325712 72:38:396561735952215036840 72:39:345720487753213109040 72:40:285219402396400814958 72:41:222610265284995758016 72:42:164307576757973059488 72:43:114633193086957948480 72:44:75553695443676829680 72:45:47011188276065582912 72:46:27593523553342842144 72:47:15264502391210933952 72:48:7950261662089028100 72:49:3894005712043605600 72:50:1791242627540058576 72:51:772692898154535072 72:52:312049055023946856 72:53:117754360386395040 72:54:41432089765583440 72:55:13559593014190944 72:56:4116305022165108 72:57:1155454041309504 72:58:298824321028320 72:59:70907466006720 72:60:15363284301456 72:61:3022285436352 72:62:536211932256 72:63:85113005120 72:64:11969016345 72:65:1473109704 72:66:156238908 72:67:13991544 72:68:1028790 72:69:59640 72:70:2556 72:71:72 72:72:1 # binomial(73, k) for 0 <= k <= 73 73:0:1 73:1:73 73:2:2628 73:3:62196 73:4:1088430 73:5:15020334 73:6:170230452 73:7:1629348612 73:8:13442126049 73:9:97082021465 73:10:621324937376 73:11:3558497368608 73:12:18385569737808 73:13:86270750308176 73:14:369731787035040 73:15:1454278362337824 73:16:5271759063474612 73:17:17675898036356052 73:18:54991682779774384 73:19:159186450151978480 73:20:429803415410341896 73:21:1084741953178481928 73:22:2563935525694593648 73:23:5685248339583664176 73:24:11844267374132633700 73:25:23214764053299962052 73:26:42858025944553776096 73:27:74604711829408425056 73:28:122564883719742412592 73:29:190186888530634778160 73:30:278940769844931007968 73:31:386917842042968817504 73:32:507829667681396572974 73:33:630939890149613923998 73:34:742282223705428145880 73:35:827114477843191362552 73:36:873065282167813104916 73:37:873065282167813104916 73:38:827114477843191362552 73:39:742282223705428145880 73:40:630939890149613923998 73:41:507829667681396572974 73:42:386917842042968817504 73:43:278940769844931007968 73:44:190186888530634778160 73:45:122564883719742412592 73:46:74604711829408425056 73:47:42858025944553776096 73:48:23214764053299962052 73:49:11844267374132633700 73:50:5685248339583664176 73:51:2563935525694593648 73:52:1084741953178481928 73:53:429803415410341896 73:54:159186450151978480 73:55:54991682779774384 73:56:17675898036356052 73:57:5271759063474612 73:58:1454278362337824 73:59:369731787035040 73:60:86270750308176 73:61:18385569737808 73:62:3558497368608 73:63:621324937376 73:64:97082021465 73:65:13442126049 73:66:1629348612 73:67:170230452 73:68:15020334 73:69:1088430 73:70:62196 73:71:2628 73:72:73 73:73:1 # binomial(74, k) for 0 <= k <= 74 74:0:1 74:1:74 74:2:2701 74:3:64824 74:4:1150626 74:5:16108764 74:6:185250786 74:7:1799579064 74:8:15071474661 74:9:110524147514 74:10:718406958841 74:11:4179822305984 74:12:21944067106416 74:13:104656320045984 74:14:456002537343216 74:15:1824010149372864 74:16:6726037425812436 74:17:22947657099830664 74:18:72667580816130436 74:19:214178132931752864 74:20:588989865562320376 74:21:1514545368588823824 74:22:3648677478873075576 74:23:8249183865278257824 74:24:17529515713716297876 74:25:35059031427432595752 74:26:66072789997853738148 74:27:117462737773962201152 74:28:197169595549150837648 74:29:312751772250377190752 74:30:469127658375565786128 74:31:665858611887899825472 74:32:894747509724365390478 74:33:1138769557831010496972 74:34:1373222113855042069878 74:35:1569396701548619508432 74:36:1700179760011004467468 74:37:1746130564335626209832 74:38:1700179760011004467468 74:39:1569396701548619508432 74:40:1373222113855042069878 74:41:1138769557831010496972 74:42:894747509724365390478 74:43:665858611887899825472 74:44:469127658375565786128 74:45:312751772250377190752 74:46:197169595549150837648 74:47:117462737773962201152 74:48:66072789997853738148 74:49:35059031427432595752 74:50:17529515713716297876 74:51:8249183865278257824 74:52:3648677478873075576 74:53:1514545368588823824 74:54:588989865562320376 74:55:214178132931752864 74:56:72667580816130436 74:57:22947657099830664 74:58:6726037425812436 74:59:1824010149372864 74:60:456002537343216 74:61:104656320045984 74:62:21944067106416 74:63:4179822305984 74:64:718406958841 74:65:110524147514 74:66:15071474661 74:67:1799579064 74:68:185250786 74:69:16108764 74:70:1150626 74:71:64824 74:72:2701 74:73:74 74:74:1 # binomial(75, k) for 0 <= k <= 75 75:0:1 75:1:75 75:2:2775 75:3:67525 75:4:1215450 75:5:17259390 75:6:201359550 75:7:1984829850 75:8:16871053725 75:9:125595622175 75:10:828931106355 75:11:4898229264825 75:12:26123889412400 75:13:126600387152400 75:14:560658857389200 75:15:2280012686716080 75:16:8550047575185300 75:17:29673694525643100 75:18:95615237915961100 75:19:286845713747883300 75:20:803167998494073240 75:21:2103535234151144200 75:22:5163222847461899400 75:23:11897861344151333400 75:24:25778699578994555700 75:25:52588547141148893628 75:26:101131821425286333900 75:27:183535527771815939300 75:28:314632333323113038800 75:29:509921367799528028400 75:30:781879430625942976880 75:31:1134986270263465611600 75:32:1560606121612265215950 75:33:2033517067555375887450 75:34:2511991671686052566850 75:35:2942618815403661578310 75:36:3269576461559623975900 75:37:3446310324346630677300 75:38:3446310324346630677300 75:39:3269576461559623975900 75:40:2942618815403661578310 75:41:2511991671686052566850 75:42:2033517067555375887450 75:43:1560606121612265215950 75:44:1134986270263465611600 75:45:781879430625942976880 75:46:509921367799528028400 75:47:314632333323113038800 75:48:183535527771815939300 75:49:101131821425286333900 75:50:52588547141148893628 75:51:25778699578994555700 75:52:11897861344151333400 75:53:5163222847461899400 75:54:2103535234151144200 75:55:803167998494073240 75:56:286845713747883300 75:57:95615237915961100 75:58:29673694525643100 75:59:8550047575185300 75:60:2280012686716080 75:61:560658857389200 75:62:126600387152400 75:63:26123889412400 75:64:4898229264825 75:65:828931106355 75:66:125595622175 75:67:16871053725 75:68:1984829850 75:69:201359550 75:70:17259390 75:71:1215450 75:72:67525 75:73:2775 75:74:75 75:75:1 # binomial(76, k) for 0 <= k <= 76 76:0:1 76:1:76 76:2:2850 76:3:70300 76:4:1282975 76:5:18474840 76:6:218618940 76:7:2186189400 76:8:18855883575 76:9:142466675900 76:10:954526728530 76:11:5727160371180 76:12:31022118677225 76:13:152724276564800 76:14:687259244541600 76:15:2840671544105280 76:16:10830060261901380 76:17:38223742100828400 76:18:125288932441604200 76:19:382460951663844400 76:20:1090013712241956540 76:21:2906703232645217440 76:22:7266758081613043600 76:23:17061084191613232800 76:24:37676560923145889100 76:25:78367246720143449328 76:26:153720368566435227528 76:27:284667349197102273200 76:28:498167861094928978100 76:29:824553701122641067200 76:30:1291800798425471005280 76:31:1916865700889408588480 76:32:2695592391875730827550 76:33:3594123189167641103400 76:34:4545508739241428454300 76:35:5454610487089714145160 76:36:6212195276963285554210 76:37:6715886785906254653200 76:38:6892620648693261354600 76:39:6715886785906254653200 76:40:6212195276963285554210 76:41:5454610487089714145160 76:42:4545508739241428454300 76:43:3594123189167641103400 76:44:2695592391875730827550 76:45:1916865700889408588480 76:46:1291800798425471005280 76:47:824553701122641067200 76:48:498167861094928978100 76:49:284667349197102273200 76:50:153720368566435227528 76:51:78367246720143449328 76:52:37676560923145889100 76:53:17061084191613232800 76:54:7266758081613043600 76:55:2906703232645217440 76:56:1090013712241956540 76:57:382460951663844400 76:58:125288932441604200 76:59:38223742100828400 76:60:10830060261901380 76:61:2840671544105280 76:62:687259244541600 76:63:152724276564800 76:64:31022118677225 76:65:5727160371180 76:66:954526728530 76:67:142466675900 76:68:18855883575 76:69:2186189400 76:70:218618940 76:71:18474840 76:72:1282975 76:73:70300 76:74:2850 76:75:76 76:76:1 # binomial(77, k) for 0 <= k <= 77 77:0:1 77:1:77 77:2:2926 77:3:73150 77:4:1353275 77:5:19757815 77:6:237093780 77:7:2404808340 77:8:21042072975 77:9:161322559475 77:10:1096993404430 77:11:6681687099710 77:12:36749279048405 77:13:183746395242025 77:14:839983521106400 77:15:3527930788646880 77:16:13670731806006660 77:17:49053802362729780 77:18:163512674542432600 77:19:507749884105448600 77:20:1472474663905800940 77:21:3996716944887173980 77:22:10173461314258261040 77:23:24327842273226276400 77:24:54737645114759121900 77:25:116043807643289338428 77:26:232087615286578676856 77:27:438387717763537500728 77:28:782835210292031251300 77:29:1322721562217570045300 77:30:2116354499548112072480 77:31:3208666499314879593760 77:32:4612458092765139416030 77:33:6289715581043371930950 77:34:8139631928409069557700 77:35:10000119226331142599460 77:36:11666805764052999699370 77:37:12928082062869540207410 77:38:13608507434599516007800 77:39:13608507434599516007800 77:40:12928082062869540207410 77:41:11666805764052999699370 77:42:10000119226331142599460 77:43:8139631928409069557700 77:44:6289715581043371930950 77:45:4612458092765139416030 77:46:3208666499314879593760 77:47:2116354499548112072480 77:48:1322721562217570045300 77:49:782835210292031251300 77:50:438387717763537500728 77:51:232087615286578676856 77:52:116043807643289338428 77:53:54737645114759121900 77:54:24327842273226276400 77:55:10173461314258261040 77:56:3996716944887173980 77:57:1472474663905800940 77:58:507749884105448600 77:59:163512674542432600 77:60:49053802362729780 77:61:13670731806006660 77:62:3527930788646880 77:63:839983521106400 77:64:183746395242025 77:65:36749279048405 77:66:6681687099710 77:67:1096993404430 77:68:161322559475 77:69:21042072975 77:70:2404808340 77:71:237093780 77:72:19757815 77:73:1353275 77:74:73150 77:75:2926 77:76:77 77:77:1 # binomial(78, k) for 0 <= k <= 78 78:0:1 78:1:78 78:2:3003 78:3:76076 78:4:1426425 78:5:21111090 78:6:256851595 78:7:2641902120 78:8:23446881315 78:9:182364632450 78:10:1258315963905 78:11:7778680504140 78:12:43430966148115 78:13:220495674290430 78:14:1023729916348425 78:15:4367914309753280 78:16:17198662594653540 78:17:62724534168736440 78:18:212566476905162380 78:19:671262558647881200 78:20:1980224548011249540 78:21:5469191608792974920 78:22:14170178259145435020 78:23:34501303587484537440 78:24:79065487387985398300 78:25:170781452758048460328 78:26:348131422929868015284 78:27:670475333050116177584 78:28:1221222928055568752028 78:29:2105556772509601296600 78:30:3439076061765682117780 78:31:5325020998862991666240 78:32:7821124592080019009790 78:33:10902173673808511346980 78:34:14429347509452441488650 78:35:18139751154740212157160 78:36:21666924990384142298830 78:37:24594887826922539906780 78:38:26536589497469056215210 78:39:27217014869199032015600 78:40:26536589497469056215210 78:41:24594887826922539906780 78:42:21666924990384142298830 78:43:18139751154740212157160 78:44:14429347509452441488650 78:45:10902173673808511346980 78:46:7821124592080019009790 78:47:5325020998862991666240 78:48:3439076061765682117780 78:49:2105556772509601296600 78:50:1221222928055568752028 78:51:670475333050116177584 78:52:348131422929868015284 78:53:170781452758048460328 78:54:79065487387985398300 78:55:34501303587484537440 78:56:14170178259145435020 78:57:5469191608792974920 78:58:1980224548011249540 78:59:671262558647881200 78:60:212566476905162380 78:61:62724534168736440 78:62:17198662594653540 78:63:4367914309753280 78:64:1023729916348425 78:65:220495674290430 78:66:43430966148115 78:67:7778680504140 78:68:1258315963905 78:69:182364632450 78:70:23446881315 78:71:2641902120 78:72:256851595 78:73:21111090 78:74:1426425 78:75:76076 78:76:3003 78:77:78 78:78:1 # binomial(79, k) for 0 <= k <= 79 79:0:1 79:1:79 79:2:3081 79:3:79079 79:4:1502501 79:5:22537515 79:6:277962685 79:7:2898753715 79:8:26088783435 79:9:205811513765 79:10:1440680596355 79:11:9036996468045 79:12:51209646652255 79:13:263926640438545 79:14:1244225590638855 79:15:5391644226101705 79:16:21566576904406820 79:17:79923196763389980 79:18:275291011073898820 79:19:883829035553043580 79:20:2651487106659130740 79:21:7449416156804224460 79:22:19639369867938409940 79:23:48671481846629972460 79:24:113566790975469935740 79:25:249846940146033858628 79:26:518912875687916475612 79:27:1018606755979984192868 79:28:1891698261105684929612 79:29:3326779700565170048628 79:30:5544632834275283414380 79:31:8764097060628673784020 79:32:13146145590943010676030 79:33:18723298265888530356770 79:34:25331521183260952835630 79:35:32569098664192653645810 79:36:39806676145124354455990 79:37:46261812817306682205610 79:38:51131477324391596121990 79:39:53753604366668088230810 79:40:53753604366668088230810 79:41:51131477324391596121990 79:42:46261812817306682205610 79:43:39806676145124354455990 79:44:32569098664192653645810 79:45:25331521183260952835630 79:46:18723298265888530356770 79:47:13146145590943010676030 79:48:8764097060628673784020 79:49:5544632834275283414380 79:50:3326779700565170048628 79:51:1891698261105684929612 79:52:1018606755979984192868 79:53:518912875687916475612 79:54:249846940146033858628 79:55:113566790975469935740 79:56:48671481846629972460 79:57:19639369867938409940 79:58:7449416156804224460 79:59:2651487106659130740 79:60:883829035553043580 79:61:275291011073898820 79:62:79923196763389980 79:63:21566576904406820 79:64:5391644226101705 79:65:1244225590638855 79:66:263926640438545 79:67:51209646652255 79:68:9036996468045 79:69:1440680596355 79:70:205811513765 79:71:26088783435 79:72:2898753715 79:73:277962685 79:74:22537515 79:75:1502501 79:76:79079 79:77:3081 79:78:79 79:79:1 # binomial(80, k) for 0 <= k <= 80 80:0:1 80:1:80 80:2:3160 80:3:82160 80:4:1581580 80:5:24040016 80:6:300500200 80:7:3176716400 80:8:28987537150 80:9:231900297200 80:10:1646492110120 80:11:10477677064400 80:12:60246643120300 80:13:315136287090800 80:14:1508152231077400 80:15:6635869816740560 80:16:26958221130508525 80:17:101489773667796800 80:18:355214207837288800 80:19:1159120046626942400 80:20:3535316142212174320 80:21:10100903263463355200 80:22:27088786024742634400 80:23:68310851714568382400 80:24:162238272822099908200 80:25:363413731121503794368 80:26:768759815833950334240 80:27:1537519631667900668480 80:28:2910305017085669122480 80:29:5218477961670854978240 80:30:8871412534840453463008 80:31:14308729894903957198400 80:32:21910242651571684460050 80:33:31869443856831541032800 80:34:44054819449149483192400 80:35:57900619847453606481440 80:36:72375774809317008101800 80:37:86068488962431036661600 80:38:97393290141698278327600 80:39:104885081691059684352800 80:40:107507208733336176461620 80:41:104885081691059684352800 80:42:97393290141698278327600 80:43:86068488962431036661600 80:44:72375774809317008101800 80:45:57900619847453606481440 80:46:44054819449149483192400 80:47:31869443856831541032800 80:48:21910242651571684460050 80:49:14308729894903957198400 80:50:8871412534840453463008 80:51:5218477961670854978240 80:52:2910305017085669122480 80:53:1537519631667900668480 80:54:768759815833950334240 80:55:363413731121503794368 80:56:162238272822099908200 80:57:68310851714568382400 80:58:27088786024742634400 80:59:10100903263463355200 80:60:3535316142212174320 80:61:1159120046626942400 80:62:355214207837288800 80:63:101489773667796800 80:64:26958221130508525 80:65:6635869816740560 80:66:1508152231077400 80:67:315136287090800 80:68:60246643120300 80:69:10477677064400 80:70:1646492110120 80:71:231900297200 80:72:28987537150 80:73:3176716400 80:74:300500200 80:75:24040016 80:76:1581580 80:77:82160 80:78:3160 80:79:80 80:80:1 # binomial(81, k) for 0 <= k <= 81 81:0:1 81:1:81 81:2:3240 81:3:85320 81:4:1663740 81:5:25621596 81:6:324540216 81:7:3477216600 81:8:32164253550 81:9:260887834350 81:10:1878392407320 81:11:12124169174520 81:12:70724320184700 81:13:375382930211100 81:14:1823288518168200 81:15:8144022047817960 81:16:33594090947249085 81:17:128447994798305325 81:18:456703981505085600 81:19:1514334254464231200 81:20:4694436188839116720 81:21:13636219405675529520 81:22:37189689288205989600 81:23:95399637739311016800 81:24:230549124536668290600 81:25:525652003943603702568 81:26:1132173546955454128608 81:27:2306279447501851002720 81:28:4447824648753569790960 81:29:8128782978756524100720 81:30:14089890496511308441248 81:31:23180142429744410661408 81:32:36218972546475641658450 81:33:53779686508403225492850 81:34:75924263305981024225200 81:35:101955439296603089673840 81:36:130276394656770614583240 81:37:158444263771748044763400 81:38:183461779104129314989200 81:39:202278371832757962680400 81:40:212392290424395860814420 81:41:212392290424395860814420 81:42:202278371832757962680400 81:43:183461779104129314989200 81:44:158444263771748044763400 81:45:130276394656770614583240 81:46:101955439296603089673840 81:47:75924263305981024225200 81:48:53779686508403225492850 81:49:36218972546475641658450 81:50:23180142429744410661408 81:51:14089890496511308441248 81:52:8128782978756524100720 81:53:4447824648753569790960 81:54:2306279447501851002720 81:55:1132173546955454128608 81:56:525652003943603702568 81:57:230549124536668290600 81:58:95399637739311016800 81:59:37189689288205989600 81:60:13636219405675529520 81:61:4694436188839116720 81:62:1514334254464231200 81:63:456703981505085600 81:64:128447994798305325 81:65:33594090947249085 81:66:8144022047817960 81:67:1823288518168200 81:68:375382930211100 81:69:70724320184700 81:70:12124169174520 81:71:1878392407320 81:72:260887834350 81:73:32164253550 81:74:3477216600 81:75:324540216 81:76:25621596 81:77:1663740 81:78:85320 81:79:3240 81:80:81 81:81:1 # binomial(82, k) for 0 <= k <= 82 82:0:1 82:1:82 82:2:3321 82:3:88560 82:4:1749060 82:5:27285336 82:6:350161812 82:7:3801756816 82:8:35641470150 82:9:293052087900 82:10:2139280241670 82:11:14002561581840 82:12:82848489359220 82:13:446107250395800 82:14:2198671448379300 82:15:9967310565986160 82:16:41738112995067045 82:17:162042085745554410 82:18:585151976303390925 82:19:1971038235969316800 82:20:6208770443303347920 82:21:18330655594514646240 82:22:50825908693881519120 82:23:132589327027517006400 82:24:325948762275979307400 82:25:756201128480271993168 82:26:1657825550899057831176 82:27:3438452994457305131328 82:28:6754104096255420793680 82:29:12576607627510093891680 82:30:22218673475267832541968 82:31:37270032926255719102656 82:32:59399114976220052319858 82:33:89998659054878867151300 82:34:129703949814384249718050 82:35:177879702602584113899040 82:36:232231833953373704257080 82:37:288720658428518659346640 82:38:341906042875877359752600 82:39:385740150936887277669600 82:40:414670662257153823494820 82:41:424784580848791721628840 82:42:414670662257153823494820 82:43:385740150936887277669600 82:44:341906042875877359752600 82:45:288720658428518659346640 82:46:232231833953373704257080 82:47:177879702602584113899040 82:48:129703949814384249718050 82:49:89998659054878867151300 82:50:59399114976220052319858 82:51:37270032926255719102656 82:52:22218673475267832541968 82:53:12576607627510093891680 82:54:6754104096255420793680 82:55:3438452994457305131328 82:56:1657825550899057831176 82:57:756201128480271993168 82:58:325948762275979307400 82:59:132589327027517006400 82:60:50825908693881519120 82:61:18330655594514646240 82:62:6208770443303347920 82:63:1971038235969316800 82:64:585151976303390925 82:65:162042085745554410 82:66:41738112995067045 82:67:9967310565986160 82:68:2198671448379300 82:69:446107250395800 82:70:82848489359220 82:71:14002561581840 82:72:2139280241670 82:73:293052087900 82:74:35641470150 82:75:3801756816 82:76:350161812 82:77:27285336 82:78:1749060 82:79:88560 82:80:3321 82:81:82 82:82:1 # binomial(83, k) for 0 <= k <= 83 83:0:1 83:1:83 83:2:3403 83:3:91881 83:4:1837620 83:5:29034396 83:6:377447148 83:7:4151918628 83:8:39443226966 83:9:328693558050 83:10:2432332329570 83:11:16141841823510 83:12:96851050941060 83:13:528955739755020 83:14:2644778698775100 83:15:12165982014365460 83:16:51705423561053205 83:17:203780198740621455 83:18:747194062048945335 83:19:2556190212272707725 83:20:8179808679272664720 83:21:24539426037817994160 83:22:69156564288396165360 83:23:183415235721398525520 83:24:458538089303496313800 83:25:1082149890756251300568 83:26:2414026679379329824344 83:27:5096278545356362962504 83:28:10192557090712725925008 83:29:19330711723765514685360 83:30:34795281102777926433648 83:31:59488706401523551644624 83:32:96669147902475771422514 83:33:149397774031098919471158 83:34:219702608869263116869350 83:35:307583652416968363617090 83:36:410111536555957818156120 83:37:520952492381892363603720 83:38:630626701304396019099240 83:39:727646193812764637422200 83:40:800410813194041101164420 83:41:839455243105945545123660 83:42:839455243105945545123660 83:43:800410813194041101164420 83:44:727646193812764637422200 83:45:630626701304396019099240 83:46:520952492381892363603720 83:47:410111536555957818156120 83:48:307583652416968363617090 83:49:219702608869263116869350 83:50:149397774031098919471158 83:51:96669147902475771422514 83:52:59488706401523551644624 83:53:34795281102777926433648 83:54:19330711723765514685360 83:55:10192557090712725925008 83:56:5096278545356362962504 83:57:2414026679379329824344 83:58:1082149890756251300568 83:59:458538089303496313800 83:60:183415235721398525520 83:61:69156564288396165360 83:62:24539426037817994160 83:63:8179808679272664720 83:64:2556190212272707725 83:65:747194062048945335 83:66:203780198740621455 83:67:51705423561053205 83:68:12165982014365460 83:69:2644778698775100 83:70:528955739755020 83:71:96851050941060 83:72:16141841823510 83:73:2432332329570 83:74:328693558050 83:75:39443226966 83:76:4151918628 83:77:377447148 83:78:29034396 83:79:1837620 83:80:91881 83:81:3403 83:82:83 83:83:1 # binomial(84, k) for 0 <= k <= 84 84:0:1 84:1:84 84:2:3486 84:3:95284 84:4:1929501 84:5:30872016 84:6:406481544 84:7:4529365776 84:8:43595145594 84:9:368136785016 84:10:2761025887620 84:11:18574174153080 84:12:112992892764570 84:13:625806790696080 84:14:3173734438530120 84:15:14810760713140560 84:16:63871405575418665 84:17:255485622301674660 84:18:950974260789566790 84:19:3303384274321653060 84:20:10735998891545372445 84:21:32719234717090658880 84:22:93695990326214159520 84:23:252571800009794690880 84:24:641953325024894839320 84:25:1540687980059747614368 84:26:3496176570135581124912 84:27:7510305224735692786848 84:28:15288835636069088887512 84:29:29523268814478240610368 84:30:54125992826543441119008 84:31:94283987504301478078272 84:32:156157854303999323067138 84:33:246066921933574690893672 84:34:369100382900362036340508 84:35:527286261286231480486440 84:36:717695188972926181773210 84:37:931064028937850181759840 84:38:1151579193686288382702960 84:39:1358272895117160656521440 84:40:1528057007006805738586620 84:41:1639866056299986646288080 84:42:1678910486211891090247320 84:43:1639866056299986646288080 84:44:1528057007006805738586620 84:45:1358272895117160656521440 84:46:1151579193686288382702960 84:47:931064028937850181759840 84:48:717695188972926181773210 84:49:527286261286231480486440 84:50:369100382900362036340508 84:51:246066921933574690893672 84:52:156157854303999323067138 84:53:94283987504301478078272 84:54:54125992826543441119008 84:55:29523268814478240610368 84:56:15288835636069088887512 84:57:7510305224735692786848 84:58:3496176570135581124912 84:59:1540687980059747614368 84:60:641953325024894839320 84:61:252571800009794690880 84:62:93695990326214159520 84:63:32719234717090658880 84:64:10735998891545372445 84:65:3303384274321653060 84:66:950974260789566790 84:67:255485622301674660 84:68:63871405575418665 84:69:14810760713140560 84:70:3173734438530120 84:71:625806790696080 84:72:112992892764570 84:73:18574174153080 84:74:2761025887620 84:75:368136785016 84:76:43595145594 84:77:4529365776 84:78:406481544 84:79:30872016 84:80:1929501 84:81:95284 84:82:3486 84:83:84 84:84:1 # binomial(85, k) for 0 <= k <= 85 85:0:1 85:1:85 85:2:3570 85:3:98770 85:4:2024785 85:5:32801517 85:6:437353560 85:7:4935847320 85:8:48124511370 85:9:411731930610 85:10:3129162672636 85:11:21335200040700 85:12:131567066917650 85:13:738799683460650 85:14:3799541229226200 85:15:17984495151670680 85:16:78682166288559225 85:17:319357027877093325 85:18:1206459883091241450 85:19:4254358535111219850 85:20:14039383165867025505 85:21:43455233608636031325 85:22:126415225043304818400 85:23:346267790336008850400 85:24:894525125034689530200 85:25:2182641305084642453688 85:26:5036864550195328739280 85:27:11006481794871273911760 85:28:22799140860804781674360 85:29:44812104450547329497880 85:30:83649261641021681729376 85:31:148409980330844919197280 85:32:250441841808300801145410 85:33:402224776237574013960810 85:34:615167304833936727234180 85:35:896386644186593516826948 85:36:1244981450259157662259650 85:37:1648759217910776363533050 85:38:2082643222624138564462800 85:39:2509852088803449039224400 85:40:2886329902123966395108060 85:41:3167923063306792384874700 85:42:3318776542511877736535400 85:43:3318776542511877736535400 85:44:3167923063306792384874700 85:45:2886329902123966395108060 85:46:2509852088803449039224400 85:47:2082643222624138564462800 85:48:1648759217910776363533050 85:49:1244981450259157662259650 85:50:896386644186593516826948 85:51:615167304833936727234180 85:52:402224776237574013960810 85:53:250441841808300801145410 85:54:148409980330844919197280 85:55:83649261641021681729376 85:56:44812104450547329497880 85:57:22799140860804781674360 85:58:11006481794871273911760 85:59:5036864550195328739280 85:60:2182641305084642453688 85:61:894525125034689530200 85:62:346267790336008850400 85:63:126415225043304818400 85:64:43455233608636031325 85:65:14039383165867025505 85:66:4254358535111219850 85:67:1206459883091241450 85:68:319357027877093325 85:69:78682166288559225 85:70:17984495151670680 85:71:3799541229226200 85:72:738799683460650 85:73:131567066917650 85:74:21335200040700 85:75:3129162672636 85:76:411731930610 85:77:48124511370 85:78:4935847320 85:79:437353560 85:80:32801517 85:81:2024785 85:82:98770 85:83:3570 85:84:85 85:85:1 # binomial(86, k) for 0 <= k <= 86 86:0:1 86:1:86 86:2:3655 86:3:102340 86:4:2123555 86:5:34826302 86:6:470155077 86:7:5373200880 86:8:53060358690 86:9:459856441980 86:10:3540894603246 86:11:24464362713336 86:12:152902266958350 86:13:870366750378300 86:14:4538340912686850 86:15:21784036380896880 86:16:96666661440229905 86:17:398039194165652550 86:18:1525816910968334775 86:19:5460818418202461300 86:20:18293741700978245355 86:21:57494616774503056830 86:22:169870458651940849725 86:23:472683015379313668800 86:24:1240792915370698380600 86:25:3077166430119331983888 86:26:7219505855279971192968 86:27:16043346345066602651040 86:28:33805622655676055586120 86:29:67611245311352111172240 86:30:128461366091569011227256 86:31:232059241971866600926656 86:32:398851822139145720342690 86:33:652666618045874815106220 86:34:1017392081071510741194990 86:35:1511553949020530244061128 86:36:2141368094445751179086598 86:37:2893740668169934025792700 86:38:3731402440534914927995850 86:39:4592495311427587603687200 86:40:5396181990927415434332460 86:41:6054252965430758779982760 86:42:6486699605818670121410100 86:43:6637553085023755473070800 86:44:6486699605818670121410100 86:45:6054252965430758779982760 86:46:5396181990927415434332460 86:47:4592495311427587603687200 86:48:3731402440534914927995850 86:49:2893740668169934025792700 86:50:2141368094445751179086598 86:51:1511553949020530244061128 86:52:1017392081071510741194990 86:53:652666618045874815106220 86:54:398851822139145720342690 86:55:232059241971866600926656 86:56:128461366091569011227256 86:57:67611245311352111172240 86:58:33805622655676055586120 86:59:16043346345066602651040 86:60:7219505855279971192968 86:61:3077166430119331983888 86:62:1240792915370698380600 86:63:472683015379313668800 86:64:169870458651940849725 86:65:57494616774503056830 86:66:18293741700978245355 86:67:5460818418202461300 86:68:1525816910968334775 86:69:398039194165652550 86:70:96666661440229905 86:71:21784036380896880 86:72:4538340912686850 86:73:870366750378300 86:74:152902266958350 86:75:24464362713336 86:76:3540894603246 86:77:459856441980 86:78:53060358690 86:79:5373200880 86:80:470155077 86:81:34826302 86:82:2123555 86:83:102340 86:84:3655 86:85:86 86:86:1 # binomial(87, k) for 0 <= k <= 87 87:0:1 87:1:87 87:2:3741 87:3:105995 87:4:2225895 87:5:36949857 87:6:504981379 87:7:5843355957 87:8:58433559570 87:9:512916800670 87:10:4000751045226 87:11:28005257316582 87:12:177366629671686 87:13:1023269017336650 87:14:5408707663065150 87:15:26322377293583730 87:16:118450697821126785 87:17:494705855605882455 87:18:1923856105133987325 87:19:6986635329170796075 87:20:23754560119180706655 87:21:75788358475481302185 87:22:227365075426443906555 87:23:642553474031254518525 87:24:1713475930750012049400 87:25:4317959345490030364488 87:26:10296672285399303176856 87:27:23262852200346573844008 87:28:49848969000742658237160 87:29:101416867967028166758360 87:30:196072611402921122399496 87:31:360520608063435612153912 87:32:630911064111012321269346 87:33:1051518440185020535448910 87:34:1670058699117385556301210 87:35:2528946030092040985256118 87:36:3652922043466281423147726 87:37:5035108762615685204879298 87:38:6625143108704848953788550 87:39:8323897751962502531683050 87:40:9988677302355003038019660 87:41:11450434956358174214315220 87:42:12540952571249428901392860 87:43:13124252690842425594480900 87:44:13124252690842425594480900 87:45:12540952571249428901392860 87:46:11450434956358174214315220 87:47:9988677302355003038019660 87:48:8323897751962502531683050 87:49:6625143108704848953788550 87:50:5035108762615685204879298 87:51:3652922043466281423147726 87:52:2528946030092040985256118 87:53:1670058699117385556301210 87:54:1051518440185020535448910 87:55:630911064111012321269346 87:56:360520608063435612153912 87:57:196072611402921122399496 87:58:101416867967028166758360 87:59:49848969000742658237160 87:60:23262852200346573844008 87:61:10296672285399303176856 87:62:4317959345490030364488 87:63:1713475930750012049400 87:64:642553474031254518525 87:65:227365075426443906555 87:66:75788358475481302185 87:67:23754560119180706655 87:68:6986635329170796075 87:69:1923856105133987325 87:70:494705855605882455 87:71:118450697821126785 87:72:26322377293583730 87:73:5408707663065150 87:74:1023269017336650 87:75:177366629671686 87:76:28005257316582 87:77:4000751045226 87:78:512916800670 87:79:58433559570 87:80:5843355957 87:81:504981379 87:82:36949857 87:83:2225895 87:84:105995 87:85:3741 87:86:87 87:87:1 # binomial(88, k) for 0 <= k <= 88 88:0:1 88:1:88 88:2:3828 88:3:109736 88:4:2331890 88:5:39175752 88:6:541931236 88:7:6348337336 88:8:64276915527 88:9:571350360240 88:10:4513667845896 88:11:32006008361808 88:12:205371886988268 88:13:1200635647008336 88:14:6431976680401800 88:15:31731084956648880 88:16:144773075114710515 88:17:613156553427009240 88:18:2418561960739869780 88:19:8910491434304783400 88:20:30741195448351502730 88:21:99542918594662008840 88:22:303153433901925208740 88:23:869918549457698425080 88:24:2356029404781266567925 88:25:6031435276240042413888 88:26:14614631630889333541344 88:27:33559524485745877020864 88:28:73111821201089232081168 88:29:151265836967770824995520 88:30:297489479369949289157856 88:31:556593219466356734553408 88:32:991431672174447933423258 88:33:1682429504296032856718256 88:34:2721577139302406091750120 88:35:4199004729209426541557328 88:36:6181868073558322408403844 88:37:8688030806081966628027024 88:38:11660251871320534158667848 88:39:14949040860667351485471600 88:40:18312575054317505569702710 88:41:21439112258713177252334880 88:42:23991387527607603115708080 88:43:25665205262091854495873760 88:44:26248505381684851188961800 88:45:25665205262091854495873760 88:46:23991387527607603115708080 88:47:21439112258713177252334880 88:48:18312575054317505569702710 88:49:14949040860667351485471600 88:50:11660251871320534158667848 88:51:8688030806081966628027024 88:52:6181868073558322408403844 88:53:4199004729209426541557328 88:54:2721577139302406091750120 88:55:1682429504296032856718256 88:56:991431672174447933423258 88:57:556593219466356734553408 88:58:297489479369949289157856 88:59:151265836967770824995520 88:60:73111821201089232081168 88:61:33559524485745877020864 88:62:14614631630889333541344 88:63:6031435276240042413888 88:64:2356029404781266567925 88:65:869918549457698425080 88:66:303153433901925208740 88:67:99542918594662008840 88:68:30741195448351502730 88:69:8910491434304783400 88:70:2418561960739869780 88:71:613156553427009240 88:72:144773075114710515 88:73:31731084956648880 88:74:6431976680401800 88:75:1200635647008336 88:76:205371886988268 88:77:32006008361808 88:78:4513667845896 88:79:571350360240 88:80:64276915527 88:81:6348337336 88:82:541931236 88:83:39175752 88:84:2331890 88:85:109736 88:86:3828 88:87:88 88:88:1 # binomial(89, k) for 0 <= k <= 89 89:0:1 89:1:89 89:2:3916 89:3:113564 89:4:2441626 89:5:41507642 89:6:581106988 89:7:6890268572 89:8:70625252863 89:9:635627275767 89:10:5085018206136 89:11:36519676207704 89:12:237377895350076 89:13:1406007533996604 89:14:7632612327410136 89:15:38163061637050680 89:16:176504160071359395 89:17:757929628541719755 89:18:3031718514166879020 89:19:11329053395044653180 89:20:39651686882656286130 89:21:130284114043013511570 89:22:402696352496587217580 89:23:1173071983359623633820 89:24:3225947954238964993005 89:25:8387464681021308981813 89:26:20646066907129375955232 89:27:48174156116635210562208 89:28:106671345686835109102032 89:29:224377658168860057076688 89:30:448755316337720114153376 89:31:854082698836306023711264 89:32:1548024891640804667976666 89:33:2673861176470480790141514 89:34:4404006643598438948468376 89:35:6920581868511832633307448 89:36:10380872802767748949961172 89:37:14869898879640289036430868 89:38:20348282677402500786694872 89:39:26609292731987885644139448 89:40:33261615914984857055174310 89:41:39751687313030682822037590 89:42:45430499786320780368042960 89:43:49656592789699457611581840 89:44:51913710643776705684835560 89:45:51913710643776705684835560 89:46:49656592789699457611581840 89:47:45430499786320780368042960 89:48:39751687313030682822037590 89:49:33261615914984857055174310 89:50:26609292731987885644139448 89:51:20348282677402500786694872 89:52:14869898879640289036430868 89:53:10380872802767748949961172 89:54:6920581868511832633307448 89:55:4404006643598438948468376 89:56:2673861176470480790141514 89:57:1548024891640804667976666 89:58:854082698836306023711264 89:59:448755316337720114153376 89:60:224377658168860057076688 89:61:106671345686835109102032 89:62:48174156116635210562208 89:63:20646066907129375955232 89:64:8387464681021308981813 89:65:3225947954238964993005 89:66:1173071983359623633820 89:67:402696352496587217580 89:68:130284114043013511570 89:69:39651686882656286130 89:70:11329053395044653180 89:71:3031718514166879020 89:72:757929628541719755 89:73:176504160071359395 89:74:38163061637050680 89:75:7632612327410136 89:76:1406007533996604 89:77:237377895350076 89:78:36519676207704 89:79:5085018206136 89:80:635627275767 89:81:70625252863 89:82:6890268572 89:83:581106988 89:84:41507642 89:85:2441626 89:86:113564 89:87:3916 89:88:89 89:89:1 # binomial(90, k) for 0 <= k <= 90 90:0:1 90:1:90 90:2:4005 90:3:117480 90:4:2555190 90:5:43949268 90:6:622614630 90:7:7471375560 90:8:77515521435 90:9:706252528630 90:10:5720645481903 90:11:41604694413840 90:12:273897571557780 90:13:1643385429346680 90:14:9038619861406740 90:15:45795673964460816 90:16:214667221708410075 90:17:934433788613079150 90:18:3789648142708598775 90:19:14360771909211532200 90:20:50980740277700939310 90:21:169935800925669797700 90:22:532980466539600729150 90:23:1575768335856210851400 90:24:4399019937598588626825 90:25:11613412635260273974818 90:26:29033531588150684937045 90:27:68820223023764586517440 90:28:154845501803470319664240 90:29:331049003855695166178720 90:30:673132974506580171230064 90:31:1302838015174026137864640 90:32:2402107590477110691687930 90:33:4221886068111285458118180 90:34:7077867820068919738609890 90:35:11324588512110271581775824 90:36:17301454671279581583268620 90:37:25250771682408037986392040 90:38:35218181557042789823125740 90:39:46957575409390386430834320 90:40:59870908646972742699313758 90:41:73013303228015539877211900 90:42:85182187099351463190080550 90:43:95087092576020237979624800 90:44:101570303433476163296417400 90:45:103827421287553411369671120 90:46:101570303433476163296417400 90:47:95087092576020237979624800 90:48:85182187099351463190080550 90:49:73013303228015539877211900 90:50:59870908646972742699313758 90:51:46957575409390386430834320 90:52:35218181557042789823125740 90:53:25250771682408037986392040 90:54:17301454671279581583268620 90:55:11324588512110271581775824 90:56:7077867820068919738609890 90:57:4221886068111285458118180 90:58:2402107590477110691687930 90:59:1302838015174026137864640 90:60:673132974506580171230064 90:61:331049003855695166178720 90:62:154845501803470319664240 90:63:68820223023764586517440 90:64:29033531588150684937045 90:65:11613412635260273974818 90:66:4399019937598588626825 90:67:1575768335856210851400 90:68:532980466539600729150 90:69:169935800925669797700 90:70:50980740277700939310 90:71:14360771909211532200 90:72:3789648142708598775 90:73:934433788613079150 90:74:214667221708410075 90:75:45795673964460816 90:76:9038619861406740 90:77:1643385429346680 90:78:273897571557780 90:79:41604694413840 90:80:5720645481903 90:81:706252528630 90:82:77515521435 90:83:7471375560 90:84:622614630 90:85:43949268 90:86:2555190 90:87:117480 90:88:4005 90:89:90 90:90:1 # binomial(91, k) for 0 <= k <= 91 91:0:1 91:1:91 91:2:4095 91:3:121485 91:4:2672670 91:5:46504458 91:6:666563898 91:7:8093990190 91:8:84986896995 91:9:783768050065 91:10:6426898010533 91:11:47325339895743 91:12:315502265971620 91:13:1917283000904460 91:14:10682005290753420 91:15:54834293825867556 91:16:260462895672870891 91:17:1149101010321489225 91:18:4724081931321677925 91:19:18150420051920130975 91:20:65341512186912471510 91:21:220916541203370737010 91:22:702916267465270526850 91:23:2108748802395811580550 91:24:5974788273454799478225 91:25:16012432572858862601643 91:26:40646944223410958911863 91:27:97853754611915271454485 91:28:223665724827234906181680 91:29:485894505659165485842960 91:30:1004181978362275337408784 91:31:1975970989680606309094704 91:32:3704945605651136829552570 91:33:6623993658588396149806110 91:34:11299753888180205196728070 91:35:18402456332179191320385714 91:36:28626043183389853165044444 91:37:42552226353687619569660660 91:38:60468953239450827809517780 91:39:82175756966433176253960060 91:40:106828484056363129130148078 91:41:132884211874988282576525658 91:42:158195490327367003067292450 91:43:180269279675371701169705350 91:44:196657396009496401276042200 91:45:205397724721029574666088520 91:46:205397724721029574666088520 91:47:196657396009496401276042200 91:48:180269279675371701169705350 91:49:158195490327367003067292450 91:50:132884211874988282576525658 91:51:106828484056363129130148078 91:52:82175756966433176253960060 91:53:60468953239450827809517780 91:54:42552226353687619569660660 91:55:28626043183389853165044444 91:56:18402456332179191320385714 91:57:11299753888180205196728070 91:58:6623993658588396149806110 91:59:3704945605651136829552570 91:60:1975970989680606309094704 91:61:1004181978362275337408784 91:62:485894505659165485842960 91:63:223665724827234906181680 91:64:97853754611915271454485 91:65:40646944223410958911863 91:66:16012432572858862601643 91:67:5974788273454799478225 91:68:2108748802395811580550 91:69:702916267465270526850 91:70:220916541203370737010 91:71:65341512186912471510 91:72:18150420051920130975 91:73:4724081931321677925 91:74:1149101010321489225 91:75:260462895672870891 91:76:54834293825867556 91:77:10682005290753420 91:78:1917283000904460 91:79:315502265971620 91:80:47325339895743 91:81:6426898010533 91:82:783768050065 91:83:84986896995 91:84:8093990190 91:85:666563898 91:86:46504458 91:87:2672670 91:88:121485 91:89:4095 91:90:91 91:91:1 # binomial(92, k) for 0 <= k <= 92 92:0:1 92:1:92 92:2:4186 92:3:125580 92:4:2794155 92:5:49177128 92:6:713068356 92:7:8760554088 92:8:93080887185 92:9:868754947060 92:10:7210666060598 92:11:53752237906276 92:12:362827605867363 92:13:2232785266876080 92:14:12599288291657880 92:15:65516299116620976 92:16:315297189498738447 92:17:1409563905994360116 92:18:5873182941643167150 92:19:22874501983241808900 92:20:83491932238832602485 92:21:286258053390283208520 92:22:923832808668641263860 92:23:2811665069861082107400 92:24:8083537075850611058775 92:25:21987220846313662079868 92:26:56659376796269821513506 92:27:138500698835326230366348 92:28:321519479439150177636165 92:29:709560230486400392024640 92:30:1490076484021440823251744 92:31:2980152968042881646503488 92:32:5680916595331743138647274 92:33:10328939264239532979358680 92:34:17923747546768601346534180 92:35:29702210220359396517113784 92:36:47028499515569044485430158 92:37:71178269537077472734705104 92:38:103021179593138447379178440 92:39:142644710205884004063477840 92:40:189004241022796305384108138 92:41:239712695931351411706673736 92:42:291079702202355285643818108 92:43:338464770002738704236997800 92:44:376926675684868102445747550 92:45:402055120730525975942130720 92:46:410795449442059149332177040 92:47:402055120730525975942130720 92:48:376926675684868102445747550 92:49:338464770002738704236997800 92:50:291079702202355285643818108 92:51:239712695931351411706673736 92:52:189004241022796305384108138 92:53:142644710205884004063477840 92:54:103021179593138447379178440 92:55:71178269537077472734705104 92:56:47028499515569044485430158 92:57:29702210220359396517113784 92:58:17923747546768601346534180 92:59:10328939264239532979358680 92:60:5680916595331743138647274 92:61:2980152968042881646503488 92:62:1490076484021440823251744 92:63:709560230486400392024640 92:64:321519479439150177636165 92:65:138500698835326230366348 92:66:56659376796269821513506 92:67:21987220846313662079868 92:68:8083537075850611058775 92:69:2811665069861082107400 92:70:923832808668641263860 92:71:286258053390283208520 92:72:83491932238832602485 92:73:22874501983241808900 92:74:5873182941643167150 92:75:1409563905994360116 92:76:315297189498738447 92:77:65516299116620976 92:78:12599288291657880 92:79:2232785266876080 92:80:362827605867363 92:81:53752237906276 92:82:7210666060598 92:83:868754947060 92:84:93080887185 92:85:8760554088 92:86:713068356 92:87:49177128 92:88:2794155 92:89:125580 92:90:4186 92:91:92 92:92:1 # binomial(93, k) for 0 <= k <= 93 93:0:1 93:1:93 93:2:4278 93:3:129766 93:4:2919735 93:5:51971283 93:6:762245484 93:7:9473622444 93:8:101841441273 93:9:961835834245 93:10:8079421007658 93:11:60962903966874 93:12:416579843773639 93:13:2595612872743443 93:14:14832073558533960 93:15:78115587408278856 93:16:380813488615359423 93:17:1724861095493098563 93:18:7282746847637527266 93:19:28747684924884976050 93:20:106366434222074411385 93:21:369749985629115811005 93:22:1210090862058924472380 93:23:3735497878529723371260 93:24:10895202145711693166175 93:25:30070757922164273138643 93:26:78646597642583483593374 93:27:195160075631596051879854 93:28:460020178274476408002513 93:29:1031079709925550569660805 93:30:2199636714507841215276384 93:31:4470229452064322469755232 93:32:8661069563374624785150762 93:33:16009855859571276118005954 93:34:28252686811008134325892860 93:35:47625957767127997863647964 93:36:76730709735928441002543942 93:37:118206769052646517220135262 93:38:174199449130215920113883544 93:39:245665889799022451442656280 93:40:331648951228680309447585978 93:41:428716936954147717090781874 93:42:530792398133706697350491844 93:43:629544472205093989880815908 93:44:715391445687606806682745350 93:45:778981796415394078387878270 93:46:812850570172585125274307760 93:47:812850570172585125274307760 93:48:778981796415394078387878270 93:49:715391445687606806682745350 93:50:629544472205093989880815908 93:51:530792398133706697350491844 93:52:428716936954147717090781874 93:53:331648951228680309447585978 93:54:245665889799022451442656280 93:55:174199449130215920113883544 93:56:118206769052646517220135262 93:57:76730709735928441002543942 93:58:47625957767127997863647964 93:59:28252686811008134325892860 93:60:16009855859571276118005954 93:61:8661069563374624785150762 93:62:4470229452064322469755232 93:63:2199636714507841215276384 93:64:1031079709925550569660805 93:65:460020178274476408002513 93:66:195160075631596051879854 93:67:78646597642583483593374 93:68:30070757922164273138643 93:69:10895202145711693166175 93:70:3735497878529723371260 93:71:1210090862058924472380 93:72:369749985629115811005 93:73:106366434222074411385 93:74:28747684924884976050 93:75:7282746847637527266 93:76:1724861095493098563 93:77:380813488615359423 93:78:78115587408278856 93:79:14832073558533960 93:80:2595612872743443 93:81:416579843773639 93:82:60962903966874 93:83:8079421007658 93:84:961835834245 93:85:101841441273 93:86:9473622444 93:87:762245484 93:88:51971283 93:89:2919735 93:90:129766 93:91:4278 93:92:93 93:93:1 # binomial(94, k) for 0 <= k <= 94 94:0:1 94:1:94 94:2:4371 94:3:134044 94:4:3049501 94:5:54891018 94:6:814216767 94:7:10235867928 94:8:111315063717 94:9:1063677275518 94:10:9041256841903 94:11:69042324974532 94:12:477542747740513 94:13:3012192716517082 94:14:17427686431277403 94:15:92947660966812816 94:16:458929076023638279 94:17:2105674584108457986 94:18:9007607943130625829 94:19:36030431772522503316 94:20:135114119146959387435 94:21:476116419851190222390 94:22:1579840847688040283385 94:23:4945588740588647843640 94:24:14630700024241416537435 94:25:40965960067875966304818 94:26:108717355564747756732017 94:27:273806673274179535473228 94:28:655180253906072459882367 94:29:1491099888200026977663318 94:30:3230716424433391784937189 94:31:6669866166572163685031616 94:32:13131299015438947254905994 94:33:24670925422945900903156716 94:34:44262542670579410443898814 94:35:75878644578136132189540824 94:36:124356667503056438866191906 94:37:194937478788574958222679204 94:38:292406218182862437334018806 94:39:419865338929238371556539824 94:40:577314841027702760890242258 94:41:760365888182828026538367852 94:42:959509335087854414441273718 94:43:1160336870338800687231307752 94:44:1344935917892700796563561258 94:45:1494373242103000885070623620 94:46:1591832366587979203662186030 94:47:1625701140345170250548615520 94:48:1591832366587979203662186030 94:49:1494373242103000885070623620 94:50:1344935917892700796563561258 94:51:1160336870338800687231307752 94:52:959509335087854414441273718 94:53:760365888182828026538367852 94:54:577314841027702760890242258 94:55:419865338929238371556539824 94:56:292406218182862437334018806 94:57:194937478788574958222679204 94:58:124356667503056438866191906 94:59:75878644578136132189540824 94:60:44262542670579410443898814 94:61:24670925422945900903156716 94:62:13131299015438947254905994 94:63:6669866166572163685031616 94:64:3230716424433391784937189 94:65:1491099888200026977663318 94:66:655180253906072459882367 94:67:273806673274179535473228 94:68:108717355564747756732017 94:69:40965960067875966304818 94:70:14630700024241416537435 94:71:4945588740588647843640 94:72:1579840847688040283385 94:73:476116419851190222390 94:74:135114119146959387435 94:75:36030431772522503316 94:76:9007607943130625829 94:77:2105674584108457986 94:78:458929076023638279 94:79:92947660966812816 94:80:17427686431277403 94:81:3012192716517082 94:82:477542747740513 94:83:69042324974532 94:84:9041256841903 94:85:1063677275518 94:86:111315063717 94:87:10235867928 94:88:814216767 94:89:54891018 94:90:3049501 94:91:134044 94:92:4371 94:93:94 94:94:1 # binomial(95, k) for 0 <= k <= 95 95:0:1 95:1:95 95:2:4465 95:3:138415 95:4:3183545 95:5:57940519 95:6:869107785 95:7:11050084695 95:8:121550931645 95:9:1174992339235 95:10:10104934117421 95:11:78083581816435 95:12:546585072715045 95:13:3489735464257595 95:14:20439879147794485 95:15:110375347398090219 95:16:551876736990451095 95:17:2564603660132096265 95:18:11113282527239083815 95:19:45038039715653129145 95:20:171144550919481890751 95:21:611230538998149609825 95:22:2055957267539230505775 95:23:6525429588276688127025 95:24:19576288764830064381075 95:25:55596660092117382842253 95:26:149683315632623723036835 95:27:382524028838927292205245 95:28:928986927180251995355595 95:29:2146280142106099437545685 95:30:4721816312633418762600507 95:31:9900582591005555469968805 95:32:19801165182011110939937610 95:33:37802224438384848158062710 95:34:68933468093525311347055530 95:35:120141187248715542633439638 95:36:200235312081192571055732730 95:37:319294146291631397088871110 95:38:487343696971437395556698010 95:39:712271557112100808890558630 95:40:997180179956941132446782082 95:41:1337680729210530787428610110 95:42:1719875223270682440979641570 95:43:2119846205426655101672581470 95:44:2505272788231501483794869010 95:45:2839309159995701681634184878 95:46:3086205608690980088732809650 95:47:3217533506933149454210801550 95:48:3217533506933149454210801550 95:49:3086205608690980088732809650 95:50:2839309159995701681634184878 95:51:2505272788231501483794869010 95:52:2119846205426655101672581470 95:53:1719875223270682440979641570 95:54:1337680729210530787428610110 95:55:997180179956941132446782082 95:56:712271557112100808890558630 95:57:487343696971437395556698010 95:58:319294146291631397088871110 95:59:200235312081192571055732730 95:60:120141187248715542633439638 95:61:68933468093525311347055530 95:62:37802224438384848158062710 95:63:19801165182011110939937610 95:64:9900582591005555469968805 95:65:4721816312633418762600507 95:66:2146280142106099437545685 95:67:928986927180251995355595 95:68:382524028838927292205245 95:69:149683315632623723036835 95:70:55596660092117382842253 95:71:19576288764830064381075 95:72:6525429588276688127025 95:73:2055957267539230505775 95:74:611230538998149609825 95:75:171144550919481890751 95:76:45038039715653129145 95:77:11113282527239083815 95:78:2564603660132096265 95:79:551876736990451095 95:80:110375347398090219 95:81:20439879147794485 95:82:3489735464257595 95:83:546585072715045 95:84:78083581816435 95:85:10104934117421 95:86:1174992339235 95:87:121550931645 95:88:11050084695 95:89:869107785 95:90:57940519 95:91:3183545 95:92:138415 95:93:4465 95:94:95 95:95:1 # binomial(96, k) for 0 <= k <= 96 96:0:1 96:1:96 96:2:4560 96:3:142880 96:4:3321960 96:5:61124064 96:6:927048304 96:7:11919192480 96:8:132601016340 96:9:1296543270880 96:10:11279926456656 96:11:88188515933856 96:12:624668654531480 96:13:4036320536972640 96:14:23929614612052080 96:15:130815226545884704 96:16:662252084388541314 96:17:3116480397122547360 96:18:13677886187371180080 96:19:56151322242892212960 96:20:216182590635135019896 96:21:782375089917631500576 96:22:2667187806537380115600 96:23:8581386855815918632800 96:24:26101718353106752508100 96:25:75172948856947447223328 96:26:205279975724741105879088 96:27:532207344471551015242080 96:28:1311510956019179287560840 96:29:3075267069286351432901280 96:30:6868096454739518200146192 96:31:14622398903638974232569312 96:32:29701747773016666409906415 96:33:57603389620395959098000320 96:34:106735692531910159505118240 96:35:189074655342240853980495168 96:36:320376499329908113689172368 96:37:519529458372823968144603840 96:38:806637843263068792645569120 96:39:1199615254083538204447256640 96:40:1709451737069041941337340712 96:41:2334860909167471919875392192 96:42:3057555952481213228408251680 96:43:3839721428697337542652223040 96:44:4625118993658156585467450480 96:45:5344581948227203165429053888 96:46:5925514768686681770366994528 96:47:6303739115624129542943611200 96:48:6435067013866298908421603100 96:49:6303739115624129542943611200 96:50:5925514768686681770366994528 96:51:5344581948227203165429053888 96:52:4625118993658156585467450480 96:53:3839721428697337542652223040 96:54:3057555952481213228408251680 96:55:2334860909167471919875392192 96:56:1709451737069041941337340712 96:57:1199615254083538204447256640 96:58:806637843263068792645569120 96:59:519529458372823968144603840 96:60:320376499329908113689172368 96:61:189074655342240853980495168 96:62:106735692531910159505118240 96:63:57603389620395959098000320 96:64:29701747773016666409906415 96:65:14622398903638974232569312 96:66:6868096454739518200146192 96:67:3075267069286351432901280 96:68:1311510956019179287560840 96:69:532207344471551015242080 96:70:205279975724741105879088 96:71:75172948856947447223328 96:72:26101718353106752508100 96:73:8581386855815918632800 96:74:2667187806537380115600 96:75:782375089917631500576 96:76:216182590635135019896 96:77:56151322242892212960 96:78:13677886187371180080 96:79:3116480397122547360 96:80:662252084388541314 96:81:130815226545884704 96:82:23929614612052080 96:83:4036320536972640 96:84:624668654531480 96:85:88188515933856 96:86:11279926456656 96:87:1296543270880 96:88:132601016340 96:89:11919192480 96:90:927048304 96:91:61124064 96:92:3321960 96:93:142880 96:94:4560 96:95:96 96:96:1 # binomial(97, k) for 0 <= k <= 97 97:0:1 97:1:97 97:2:4656 97:3:147440 97:4:3464840 97:5:64446024 97:6:988172368 97:7:12846240784 97:8:144520208820 97:9:1429144287220 97:10:12576469727536 97:11:99468442390512 97:12:712857170465336 97:13:4660989191504120 97:14:27965935149024720 97:15:154744841157936784 97:16:793067310934426018 97:17:3778732481511088674 97:18:16794366584493727440 97:19:69829208430263393040 97:20:272333912878027232856 97:21:998557680552766520472 97:22:3449562896455011616176 97:23:11248574662353298748400 97:24:34683105208922671140900 97:25:101274667210054199731428 97:26:280452924581688553102416 97:27:737487320196292121121168 97:28:1843718300490730302802920 97:29:4386778025305530720462120 97:30:9943363524025869633047472 97:31:21490495358378492432715504 97:32:44324146676655640642475727 97:33:87305137393412625507906735 97:34:164339082152306118603118560 97:35:295810347874151013485613408 97:36:509451154672148967669667536 97:37:839905957702732081833776208 97:38:1326167301635892760790172960 97:39:2006253097346606997092825760 97:40:2909066991152580145784597352 97:41:4044312646236513861212732904 97:42:5392416861648685148283643872 97:43:6897277381178550771060474720 97:44:8464840422355494128119673520 97:45:9969700941885359750896504368 97:46:11270096716913884935796048416 97:47:12229253884310811313310605728 97:48:12738806129490428451365214300 97:49:12738806129490428451365214300 97:50:12229253884310811313310605728 97:51:11270096716913884935796048416 97:52:9969700941885359750896504368 97:53:8464840422355494128119673520 97:54:6897277381178550771060474720 97:55:5392416861648685148283643872 97:56:4044312646236513861212732904 97:57:2909066991152580145784597352 97:58:2006253097346606997092825760 97:59:1326167301635892760790172960 97:60:839905957702732081833776208 97:61:509451154672148967669667536 97:62:295810347874151013485613408 97:63:164339082152306118603118560 97:64:87305137393412625507906735 97:65:44324146676655640642475727 97:66:21490495358378492432715504 97:67:9943363524025869633047472 97:68:4386778025305530720462120 97:69:1843718300490730302802920 97:70:737487320196292121121168 97:71:280452924581688553102416 97:72:101274667210054199731428 97:73:34683105208922671140900 97:74:11248574662353298748400 97:75:3449562896455011616176 97:76:998557680552766520472 97:77:272333912878027232856 97:78:69829208430263393040 97:79:16794366584493727440 97:80:3778732481511088674 97:81:793067310934426018 97:82:154744841157936784 97:83:27965935149024720 97:84:4660989191504120 97:85:712857170465336 97:86:99468442390512 97:87:12576469727536 97:88:1429144287220 97:89:144520208820 97:90:12846240784 97:91:988172368 97:92:64446024 97:93:3464840 97:94:147440 97:95:4656 97:96:97 97:97:1 # binomial(98, k) for 0 <= k <= 98 98:0:1 98:1:98 98:2:4753 98:3:152096 98:4:3612280 98:5:67910864 98:6:1052618392 98:7:13834413152 98:8:157366449604 98:9:1573664496040 98:10:14005614014756 98:11:112044912118048 98:12:812325612855848 98:13:5373846361969456 98:14:32626924340528840 98:15:182710776306961504 98:16:947812152092362802 98:17:4571799792445514692 98:18:20573099066004816114 98:19:86623575014757120480 98:20:342163121308290625896 98:21:1270891593430793753328 98:22:4448120577007778136648 98:23:14698137558808310364576 98:24:45931679871275969889300 98:25:135957772418976870872328 98:26:381727591791742752833844 98:27:1017940244777980674223584 98:28:2581205620687022423924088 98:29:6230496325796261023265040 98:30:14330141549331400353509592 98:31:31433858882404362065762976 98:32:65814642035034133075191231 98:33:131629284070068266150382462 98:34:251644219545718744111025295 98:35:460149430026457132088731968 98:36:805261502546299981155280944 98:37:1349357112374881049503443744 98:38:2166073259338624842623949168 98:39:3332420398982499757882998720 98:40:4915320088499187142877423112 98:41:6953379637389094006997330256 98:42:9436729507885199009496376776 98:43:12289694242827235919344118592 98:44:15362117803534044899180148240 98:45:18434541364240853879016177888 98:46:21239797658799244686692552784 98:47:23499350601224696249106654144 98:48:24968060013801239764675820028 98:49:25477612258980856902730428600 98:50:24968060013801239764675820028 98:51:23499350601224696249106654144 98:52:21239797658799244686692552784 98:53:18434541364240853879016177888 98:54:15362117803534044899180148240 98:55:12289694242827235919344118592 98:56:9436729507885199009496376776 98:57:6953379637389094006997330256 98:58:4915320088499187142877423112 98:59:3332420398982499757882998720 98:60:2166073259338624842623949168 98:61:1349357112374881049503443744 98:62:805261502546299981155280944 98:63:460149430026457132088731968 98:64:251644219545718744111025295 98:65:131629284070068266150382462 98:66:65814642035034133075191231 98:67:31433858882404362065762976 98:68:14330141549331400353509592 98:69:6230496325796261023265040 98:70:2581205620687022423924088 98:71:1017940244777980674223584 98:72:381727591791742752833844 98:73:135957772418976870872328 98:74:45931679871275969889300 98:75:14698137558808310364576 98:76:4448120577007778136648 98:77:1270891593430793753328 98:78:342163121308290625896 98:79:86623575014757120480 98:80:20573099066004816114 98:81:4571799792445514692 98:82:947812152092362802 98:83:182710776306961504 98:84:32626924340528840 98:85:5373846361969456 98:86:812325612855848 98:87:112044912118048 98:88:14005614014756 98:89:1573664496040 98:90:157366449604 98:91:13834413152 98:92:1052618392 98:93:67910864 98:94:3612280 98:95:152096 98:96:4753 98:97:98 98:98:1 # binomial(99, k) for 0 <= k <= 99 99:0:1 99:1:99 99:2:4851 99:3:156849 99:4:3764376 99:5:71523144 99:6:1120529256 99:7:14887031544 99:8:171200862756 99:9:1731030945644 99:10:15579278510796 99:11:126050526132804 99:12:924370524973896 99:13:6186171974825304 99:14:38000770702498296 99:15:215337700647490344 99:16:1130522928399324306 99:17:5519611944537877494 99:18:25144898858450330806 99:19:107196674080761936594 99:20:428786696323047746376 99:21:1613054714739084379224 99:22:5719012170438571889976 99:23:19146258135816088501224 99:24:60629817430084280253876 99:25:181889452290252840761628 99:26:517685364210719623706172 99:27:1399667836569723427057428 99:28:3599145865465003098147672 99:29:8811701946483283447189128 99:30:20560637875127661376774632 99:31:45764000431735762419272568 99:32:97248500917438495140954207 99:33:197443926105102399225573693 99:34:383273503615787010261407757 99:35:711793649572175876199757263 99:36:1265410932572757113244012912 99:37:2154618614921181030658724688 99:38:3515430371713505892127392912 99:39:5498493658321124600506947888 99:40:8247740487481686900760421832 99:41:11868699725888281149874753368 99:42:16390109145274293016493707032 99:43:21726423750712434928840495368 99:44:27651812046361280818524266832 99:45:33796659167774898778196326128 99:46:39674339023040098565708730672 99:47:44739148260023940935799206928 99:48:48467410615025936013782474172 99:49:50445672272782096667406248628 99:50:50445672272782096667406248628 99:51:48467410615025936013782474172 99:52:44739148260023940935799206928 99:53:39674339023040098565708730672 99:54:33796659167774898778196326128 99:55:27651812046361280818524266832 99:56:21726423750712434928840495368 99:57:16390109145274293016493707032 99:58:11868699725888281149874753368 99:59:8247740487481686900760421832 99:60:5498493658321124600506947888 99:61:3515430371713505892127392912 99:62:2154618614921181030658724688 99:63:1265410932572757113244012912 99:64:711793649572175876199757263 99:65:383273503615787010261407757 99:66:197443926105102399225573693 99:67:97248500917438495140954207 99:68:45764000431735762419272568 99:69:20560637875127661376774632 99:70:8811701946483283447189128 99:71:3599145865465003098147672 99:72:1399667836569723427057428 99:73:517685364210719623706172 99:74:181889452290252840761628 99:75:60629817430084280253876 99:76:19146258135816088501224 99:77:5719012170438571889976 99:78:1613054714739084379224 99:79:428786696323047746376 99:80:107196674080761936594 99:81:25144898858450330806 99:82:5519611944537877494 99:83:1130522928399324306 99:84:215337700647490344 99:85:38000770702498296 99:86:6186171974825304 99:87:924370524973896 99:88:126050526132804 99:89:15579278510796 99:90:1731030945644 99:91:171200862756 99:92:14887031544 99:93:1120529256 99:94:71523144 99:95:3764376 99:96:156849 99:97:4851 99:98:99 99:99:1 # binomial(100, k) for 0 <= k <= 100 100:0:1 100:1:100 100:2:4950 100:3:161700 100:4:3921225 100:5:75287520 100:6:1192052400 100:7:16007560800 100:8:186087894300 100:9:1902231808400 100:10:17310309456440 100:11:141629804643600 100:12:1050421051106700 100:13:7110542499799200 100:14:44186942677323600 100:15:253338471349988640 100:16:1345860629046814650 100:17:6650134872937201800 100:18:30664510802988208300 100:19:132341572939212267400 100:20:535983370403809682970 100:21:2041841411062132125600 100:22:7332066885177656269200 100:23:24865270306254660391200 100:24:79776075565900368755100 100:25:242519269720337121015504 100:26:699574816500972464467800 100:27:1917353200780443050763600 100:28:4998813702034726525205100 100:29:12410847811948286545336800 100:30:29372339821610944823963760 100:31:66324638306863423796047200 100:32:143012501349174257560226775 100:33:294692427022540894366527900 100:34:580717429720889409486981450 100:35:1095067153187962886461165020 100:36:1977204582144932989443770175 100:37:3420029547493938143902737600 100:38:5670048986634686922786117600 100:39:9013924030034630492634340800 100:40:13746234145802811501267369720 100:41:20116440213369968050635175200 100:42:28258808871162574166368460400 100:43:38116532895986727945334202400 100:44:49378235797073715747364762200 100:45:61448471214136179596720592960 100:46:73470998190814997343905056800 100:47:84413487283064039501507937600 100:48:93206558875049876949581681100 100:49:98913082887808032681188722800 100:50:100891344545564193334812497256 100:51:98913082887808032681188722800 100:52:93206558875049876949581681100 100:53:84413487283064039501507937600 100:54:73470998190814997343905056800 100:55:61448471214136179596720592960 100:56:49378235797073715747364762200 100:57:38116532895986727945334202400 100:58:28258808871162574166368460400 100:59:20116440213369968050635175200 100:60:13746234145802811501267369720 100:61:9013924030034630492634340800 100:62:5670048986634686922786117600 100:63:3420029547493938143902737600 100:64:1977204582144932989443770175 100:65:1095067153187962886461165020 100:66:580717429720889409486981450 100:67:294692427022540894366527900 100:68:143012501349174257560226775 100:69:66324638306863423796047200 100:70:29372339821610944823963760 100:71:12410847811948286545336800 100:72:4998813702034726525205100 100:73:1917353200780443050763600 100:74:699574816500972464467800 100:75:242519269720337121015504 100:76:79776075565900368755100 100:77:24865270306254660391200 100:78:7332066885177656269200 100:79:2041841411062132125600 100:80:535983370403809682970 100:81:132341572939212267400 100:82:30664510802988208300 100:83:6650134872937201800 100:84:1345860629046814650 100:85:253338471349988640 100:86:44186942677323600 100:87:7110542499799200 100:88:1050421051106700 100:89:141629804643600 100:90:17310309456440 100:91:1902231808400 100:92:186087894300 100:93:16007560800 100:94:1192052400 100:95:75287520 100:96:3921225 100:97:161700 100:98:4950 100:99:100 100:100:1 # binomial(101, k) for 0 <= k <= 101 101:0:1 101:1:101 101:2:5050 101:3:166650 101:4:4082925 101:5:79208745 101:6:1267339920 101:7:17199613200 101:8:202095455100 101:9:2088319702700 101:10:19212541264840 101:11:158940114100040 101:12:1192050855750300 101:13:8160963550905900 101:14:51297485177122800 101:15:297525414027312240 101:16:1599199100396803290 101:17:7995995501984016450 101:18:37314645675925410100 101:19:163006083742200475700 101:20:668324943343021950370 101:21:2577824781465941808570 101:22:9373908296239788394800 101:23:32197337191432316660400 101:24:104641345872155029146300 101:25:322295345286237489770604 101:26:942094086221309585483304 101:27:2616928017281415515231400 101:28:6916166902815169575968700 101:29:17409661513983013070541900 101:30:41783187633559231369300560 101:31:95696978128474368620010960 101:32:209337139656037681356273975 101:33:437704928371715151926754675 101:34:875409856743430303853509350 101:35:1675784582908852295948146470 101:36:3072271735332895875904935195 101:37:5397234129638871133346507775 101:38:9090078534128625066688855200 101:39:14683973016669317415420458400 101:40:22760158175837441993901710520 101:41:33862674359172779551902544920 101:42:48375249084532542217003635600 101:43:66375341767149302111702662800 101:44:87494768693060443692698964600 101:45:110826707011209895344085355160 101:46:134919469404951176940625649760 101:47:157884485473879036845412994400 101:48:177620046158113916451089618700 101:49:192119641762857909630770403900 101:50:199804427433372226016001220056 101:51:199804427433372226016001220056 101:52:192119641762857909630770403900 101:53:177620046158113916451089618700 101:54:157884485473879036845412994400 101:55:134919469404951176940625649760 101:56:110826707011209895344085355160 101:57:87494768693060443692698964600 101:58:66375341767149302111702662800 101:59:48375249084532542217003635600 101:60:33862674359172779551902544920 101:61:22760158175837441993901710520 101:62:14683973016669317415420458400 101:63:9090078534128625066688855200 101:64:5397234129638871133346507775 101:65:3072271735332895875904935195 101:66:1675784582908852295948146470 101:67:875409856743430303853509350 101:68:437704928371715151926754675 101:69:209337139656037681356273975 101:70:95696978128474368620010960 101:71:41783187633559231369300560 101:72:17409661513983013070541900 101:73:6916166902815169575968700 101:74:2616928017281415515231400 101:75:942094086221309585483304 101:76:322295345286237489770604 101:77:104641345872155029146300 101:78:32197337191432316660400 101:79:9373908296239788394800 101:80:2577824781465941808570 101:81:668324943343021950370 101:82:163006083742200475700 101:83:37314645675925410100 101:84:7995995501984016450 101:85:1599199100396803290 101:86:297525414027312240 101:87:51297485177122800 101:88:8160963550905900 101:89:1192050855750300 101:90:158940114100040 101:91:19212541264840 101:92:2088319702700 101:93:202095455100 101:94:17199613200 101:95:1267339920 101:96:79208745 101:97:4082925 101:98:166650 101:99:5050 101:100:101 101:101:1 # binomial(102, k) for 0 <= k <= 102 102:0:1 102:1:102 102:2:5151 102:3:171700 102:4:4249575 102:5:83291670 102:6:1346548665 102:7:18466953120 102:8:219295068300 102:9:2290415157800 102:10:21300860967540 102:11:178152655364880 102:12:1350990969850340 102:13:9353014406656200 102:14:59458448728028700 102:15:348822899204435040 102:16:1896724514424115530 102:17:9595194602380819740 102:18:45310641177909426550 102:19:200320729418125885800 102:20:831331027085222426070 102:21:3246149724808963758940 102:22:11951733077705730203370 102:23:41571245487672105055200 102:24:136838683063587345806700 102:25:426936691158392518916904 102:26:1264389431507547075253908 102:27:3559022103502725100714704 102:28:9533094920096585091200100 102:29:24325828416798182646510600 102:30:59192849147542244439842460 102:31:137480165762033599989311520 102:32:305034117784512049976284935 102:33:647042068027752833283028650 102:34:1313114785115145455780264025 102:35:2551194439652282599801655820 102:36:4748056318241748171853081665 102:37:8469505864971767009251442970 102:38:14487312663767496200035362975 102:39:23774051550797942482109313600 102:40:37444131192506759409322168920 102:41:56622832535010221545804255440 102:42:82237923443705321768906180520 102:43:114750590851681844328706298400 102:44:153870110460209745804401627400 102:45:198321475704270339036784319760 102:46:245746176416161072284711004920 102:47:292803954878830213786038644160 102:48:335504531631992953296502613100 102:49:369739687920971826081860022600 102:50:391924069196230135646771623956 102:51:399608854866744452032002440112 102:52:391924069196230135646771623956 102:53:369739687920971826081860022600 102:54:335504531631992953296502613100 102:55:292803954878830213786038644160 102:56:245746176416161072284711004920 102:57:198321475704270339036784319760 102:58:153870110460209745804401627400 102:59:114750590851681844328706298400 102:60:82237923443705321768906180520 102:61:56622832535010221545804255440 102:62:37444131192506759409322168920 102:63:23774051550797942482109313600 102:64:14487312663767496200035362975 102:65:8469505864971767009251442970 102:66:4748056318241748171853081665 102:67:2551194439652282599801655820 102:68:1313114785115145455780264025 102:69:647042068027752833283028650 102:70:305034117784512049976284935 102:71:137480165762033599989311520 102:72:59192849147542244439842460 102:73:24325828416798182646510600 102:74:9533094920096585091200100 102:75:3559022103502725100714704 102:76:1264389431507547075253908 102:77:426936691158392518916904 102:78:136838683063587345806700 102:79:41571245487672105055200 102:80:11951733077705730203370 102:81:3246149724808963758940 102:82:831331027085222426070 102:83:200320729418125885800 102:84:45310641177909426550 102:85:9595194602380819740 102:86:1896724514424115530 102:87:348822899204435040 102:88:59458448728028700 102:89:9353014406656200 102:90:1350990969850340 102:91:178152655364880 102:92:21300860967540 102:93:2290415157800 102:94:219295068300 102:95:18466953120 102:96:1346548665 102:97:83291670 102:98:4249575 102:99:171700 102:100:5151 102:101:102 102:102:1 # binomial(103, k) for 0 <= k <= 103 103:0:1 103:1:103 103:2:5253 103:3:176851 103:4:4421275 103:5:87541245 103:6:1429840335 103:7:19813501785 103:8:237762021420 103:9:2509710226100 103:10:23591276125340 103:11:199453516332420 103:12:1529143625215220 103:13:10704005376506540 103:14:68811463134684900 103:15:408281347932463740 103:16:2245547413628550570 103:17:11491919116804935270 103:18:54905835780290246290 103:19:245631370596035312350 103:20:1031651756503348311870 103:21:4077480751894186185010 103:22:15197882802514693962310 103:23:53522978565377835258570 103:24:178409928551259450861900 103:25:563775374221979864723604 103:26:1691326122665939594170812 103:27:4823411535010272175968612 103:28:13092117023599310191914804 103:29:33858923336894767737710700 103:30:83518677564340427086353060 103:31:196673014909575844429153980 103:32:442514283546545649965596455 103:33:952076185812264883259313585 103:34:1960156853142898289063292675 103:35:3864309224767428055581919845 103:36:7299250757894030771654737485 103:37:13217562183213515181104524635 103:38:22956818528739263209286805945 103:39:38261364214565438682144676575 103:40:61218182743304701891431482520 103:41:94066963727516980955126424360 103:42:138860755978715543314710435960 103:43:196988514295387166097612478920 103:44:268620701311891590133107925800 103:45:352191586164480084841185947160 103:46:444067652120431411321495324680 103:47:538550131294991286070749649080 103:48:628308486510823167082541257260 103:49:705244219552964779378362635700 103:50:761663757117201961728631646556 103:51:791532924062974587678774064068 103:52:791532924062974587678774064068 103:53:761663757117201961728631646556 103:54:705244219552964779378362635700 103:55:628308486510823167082541257260 103:56:538550131294991286070749649080 103:57:444067652120431411321495324680 103:58:352191586164480084841185947160 103:59:268620701311891590133107925800 103:60:196988514295387166097612478920 103:61:138860755978715543314710435960 103:62:94066963727516980955126424360 103:63:61218182743304701891431482520 103:64:38261364214565438682144676575 103:65:22956818528739263209286805945 103:66:13217562183213515181104524635 103:67:7299250757894030771654737485 103:68:3864309224767428055581919845 103:69:1960156853142898289063292675 103:70:952076185812264883259313585 103:71:442514283546545649965596455 103:72:196673014909575844429153980 103:73:83518677564340427086353060 103:74:33858923336894767737710700 103:75:13092117023599310191914804 103:76:4823411535010272175968612 103:77:1691326122665939594170812 103:78:563775374221979864723604 103:79:178409928551259450861900 103:80:53522978565377835258570 103:81:15197882802514693962310 103:82:4077480751894186185010 103:83:1031651756503348311870 103:84:245631370596035312350 103:85:54905835780290246290 103:86:11491919116804935270 103:87:2245547413628550570 103:88:408281347932463740 103:89:68811463134684900 103:90:10704005376506540 103:91:1529143625215220 103:92:199453516332420 103:93:23591276125340 103:94:2509710226100 103:95:237762021420 103:96:19813501785 103:97:1429840335 103:98:87541245 103:99:4421275 103:100:176851 103:101:5253 103:102:103 103:103:1 # binomial(104, k) for 0 <= k <= 104 104:0:1 104:1:104 104:2:5356 104:3:182104 104:4:4598126 104:5:91962520 104:6:1517381580 104:7:21243342120 104:8:257575523205 104:9:2747472247520 104:10:26100986351440 104:11:223044792457760 104:12:1728597141547640 104:13:12233149001721760 104:14:79515468511191440 104:15:477092811067148640 104:16:2653828761561014310 104:17:13737466530433485840 104:18:66397754897095181560 104:19:300537206376325558640 104:20:1277283127099383624220 104:21:5109132508397534496880 104:22:19275363554408880147320 104:23:68720861367892529220880 104:24:231932907116637286120470 104:25:742185302773239315585504 104:26:2255101496887919458894416 104:27:6514737657676211770139424 104:28:17915528558609582367883416 104:29:46951040360494077929625504 104:30:117377600901235194824063760 104:31:280191692473916271515507040 104:32:639187298456121494394750435 104:33:1394590469358810533224910040 104:34:2912233038955163172322606260 104:35:5824466077910326344645212520 104:36:11163559982661458827236657330 104:37:20516812941107545952759262120 104:38:36174380711952778390391330580 104:39:61218182743304701891431482520 104:40:99479546957870140573576159095 104:41:155285146470821682846557906880 104:42:232927719706232524269836860320 104:43:335849270274102709412322914880 104:44:465609215607278756230720404720 104:45:620812287476371674974293872960 104:46:796259238284911496162681271840 104:47:982617783415422697392244973760 104:48:1166858617805814453153290906340 104:49:1333552706063787946460903892960 104:50:1466907976670166741106994282256 104:51:1553196681180176549407405710624 104:52:1583065848125949175357548128136 104:53:1553196681180176549407405710624 104:54:1466907976670166741106994282256 104:55:1333552706063787946460903892960 104:56:1166858617805814453153290906340 104:57:982617783415422697392244973760 104:58:796259238284911496162681271840 104:59:620812287476371674974293872960 104:60:465609215607278756230720404720 104:61:335849270274102709412322914880 104:62:232927719706232524269836860320 104:63:155285146470821682846557906880 104:64:99479546957870140573576159095 104:65:61218182743304701891431482520 104:66:36174380711952778390391330580 104:67:20516812941107545952759262120 104:68:11163559982661458827236657330 104:69:5824466077910326344645212520 104:70:2912233038955163172322606260 104:71:1394590469358810533224910040 104:72:639187298456121494394750435 104:73:280191692473916271515507040 104:74:117377600901235194824063760 104:75:46951040360494077929625504 104:76:17915528558609582367883416 104:77:6514737657676211770139424 104:78:2255101496887919458894416 104:79:742185302773239315585504 104:80:231932907116637286120470 104:81:68720861367892529220880 104:82:19275363554408880147320 104:83:5109132508397534496880 104:84:1277283127099383624220 104:85:300537206376325558640 104:86:66397754897095181560 104:87:13737466530433485840 104:88:2653828761561014310 104:89:477092811067148640 104:90:79515468511191440 104:91:12233149001721760 104:92:1728597141547640 104:93:223044792457760 104:94:26100986351440 104:95:2747472247520 104:96:257575523205 104:97:21243342120 104:98:1517381580 104:99:91962520 104:100:4598126 104:101:182104 104:102:5356 104:103:104 104:104:1 # binomial(105, k) for 0 <= k <= 105 105:0:1 105:1:105 105:2:5460 105:3:187460 105:4:4780230 105:5:96560646 105:6:1609344100 105:7:22760723700 105:8:278818865325 105:9:3005047770725 105:10:28848458598960 105:11:249145778809200 105:12:1951641934005400 105:13:13961746143269400 105:14:91748617512913200 105:15:556608279578340080 105:16:3130921572628162950 105:17:16391295291994500150 105:18:80135221427528667400 105:19:366934961273420740200 105:20:1577820333475709182860 105:21:6386415635496918121100 105:22:24384496062806414644200 105:23:87996224922301409368200 105:24:300653768484529815341350 105:25:974118209889876601705974 105:26:2997286799661158774479920 105:27:8769839154564131229033840 105:28:24430266216285794138022840 105:29:64866568919103660297508920 105:30:164328641261729272753689264 105:31:397569293375151466339570800 105:32:919378990930037765910257475 105:33:2033777767814932027619660475 105:34:4306823508313973705547516300 105:35:8736699116865489516967818780 105:36:16988026060571785171881869850 105:37:31680372923769004779995919450 105:38:56691193653060324343150592700 105:39:97392563455257480281822813100 105:40:160697729701174842465007641615 105:41:254764693428691823420134065975 105:42:388212866177054207116394767200 105:43:568776989980335233682159775200 105:44:801458485881381465643043319600 105:45:1086421503083650431205014277680 105:46:1417071525761283171136975144800 105:47:1778877021700334193554926245600 105:48:2149476401221237150545535880100 105:49:2500411323869602399614194799300 105:50:2800460682733954687567898175216 105:51:3020104657850343290514399992880 105:52:3136262529306125724764953838760 105:53:3136262529306125724764953838760 105:54:3020104657850343290514399992880 105:55:2800460682733954687567898175216 105:56:2500411323869602399614194799300 105:57:2149476401221237150545535880100 105:58:1778877021700334193554926245600 105:59:1417071525761283171136975144800 105:60:1086421503083650431205014277680 105:61:801458485881381465643043319600 105:62:568776989980335233682159775200 105:63:388212866177054207116394767200 105:64:254764693428691823420134065975 105:65:160697729701174842465007641615 105:66:97392563455257480281822813100 105:67:56691193653060324343150592700 105:68:31680372923769004779995919450 105:69:16988026060571785171881869850 105:70:8736699116865489516967818780 105:71:4306823508313973705547516300 105:72:2033777767814932027619660475 105:73:919378990930037765910257475 105:74:397569293375151466339570800 105:75:164328641261729272753689264 105:76:64866568919103660297508920 105:77:24430266216285794138022840 105:78:8769839154564131229033840 105:79:2997286799661158774479920 105:80:974118209889876601705974 105:81:300653768484529815341350 105:82:87996224922301409368200 105:83:24384496062806414644200 105:84:6386415635496918121100 105:85:1577820333475709182860 105:86:366934961273420740200 105:87:80135221427528667400 105:88:16391295291994500150 105:89:3130921572628162950 105:90:556608279578340080 105:91:91748617512913200 105:92:13961746143269400 105:93:1951641934005400 105:94:249145778809200 105:95:28848458598960 105:96:3005047770725 105:97:278818865325 105:98:22760723700 105:99:1609344100 105:100:96560646 105:101:4780230 105:102:187460 105:103:5460 105:104:105 105:105:1 # binomial(106, k) for 0 <= k <= 106 106:0:1 106:1:106 106:2:5565 106:3:192920 106:4:4967690 106:5:101340876 106:6:1705904746 106:7:24370067800 106:8:301579589025 106:9:3283866636050 106:10:31853506369685 106:11:277994237408160 106:12:2200787712814600 106:13:15913388077274800 106:14:105710363656182600 106:15:648356897091253280 106:16:3687529852206503030 106:17:19522216864622663100 106:18:96526516719523167550 106:19:447070182700949407600 106:20:1944755294749129923060 106:21:7964235968972627303960 106:22:30770911698303332765300 106:23:112380720985107824012400 106:24:388649993406831224709550 106:25:1274771978374406417047324 106:26:3971405009551035376185894 106:27:11767125954225290003513760 106:28:33200105370849925367056680 106:29:89296835135389454435531760 106:30:229195210180832933051198184 106:31:561897934636880739093260064 106:32:1316948284305189232249828275 106:33:2953156758744969793529917950 106:34:6340601276128905733167176775 106:35:13043522625179463222515335080 106:36:25724725177437274688849688630 106:37:48668398984340789951877789300 106:38:88371566576829329123146512150 106:39:154083757108317804624973405800 106:40:258090293156432322746830454715 106:41:415462423129866665885141707590 106:42:642977559605746030536528833175 106:43:956989856157389440798554542400 106:44:1370235475861716699325203094800 106:45:1887879988965031896848057597280 106:46:2503493028844933602341989422480 106:47:3195948547461617364691901390400 106:48:3928353422921571344100462125700 106:49:4649887725090839550159730679400 106:50:5300872006603557087182092974516 106:51:5820565340584297978082298168096 106:52:6156367187156469015279353831640 106:53:6272525058612251449529907677520 106:54:6156367187156469015279353831640 106:55:5820565340584297978082298168096 106:56:5300872006603557087182092974516 106:57:4649887725090839550159730679400 106:58:3928353422921571344100462125700 106:59:3195948547461617364691901390400 106:60:2503493028844933602341989422480 106:61:1887879988965031896848057597280 106:62:1370235475861716699325203094800 106:63:956989856157389440798554542400 106:64:642977559605746030536528833175 106:65:415462423129866665885141707590 106:66:258090293156432322746830454715 106:67:154083757108317804624973405800 106:68:88371566576829329123146512150 106:69:48668398984340789951877789300 106:70:25724725177437274688849688630 106:71:13043522625179463222515335080 106:72:6340601276128905733167176775 106:73:2953156758744969793529917950 106:74:1316948284305189232249828275 106:75:561897934636880739093260064 106:76:229195210180832933051198184 106:77:89296835135389454435531760 106:78:33200105370849925367056680 106:79:11767125954225290003513760 106:80:3971405009551035376185894 106:81:1274771978374406417047324 106:82:388649993406831224709550 106:83:112380720985107824012400 106:84:30770911698303332765300 106:85:7964235968972627303960 106:86:1944755294749129923060 106:87:447070182700949407600 106:88:96526516719523167550 106:89:19522216864622663100 106:90:3687529852206503030 106:91:648356897091253280 106:92:105710363656182600 106:93:15913388077274800 106:94:2200787712814600 106:95:277994237408160 106:96:31853506369685 106:97:3283866636050 106:98:301579589025 106:99:24370067800 106:100:1705904746 106:101:101340876 106:102:4967690 106:103:192920 106:104:5565 106:105:106 106:106:1 # binomial(107, k) for 0 <= k <= 107 107:0:1 107:1:107 107:2:5671 107:3:198485 107:4:5160610 107:5:106308566 107:6:1807245622 107:7:26075972546 107:8:325949656825 107:9:3585446225075 107:10:35137373005735 107:11:309847743777845 107:12:2478781950222760 107:13:18114175790089400 107:14:121623751733457400 107:15:754067260747435880 107:16:4335886749297756310 107:17:23209746716829166130 107:18:116048733584145830650 107:19:543596699420472575150 107:20:2391825477450079330660 107:21:9908991263721757227020 107:22:38735147667275960069260 107:23:143151632683411156777700 107:24:501030714391939048721950 107:25:1663421971781237641756874 107:26:5246176987925441793233218 107:27:15738530963776325379699654 107:28:44967231325075215370570440 107:29:122496940506239379802588440 107:30:318492045316222387486729944 107:31:791093144817713672144458248 107:32:1878846218942069971343088339 107:33:4270105043050159025779746225 107:34:9293758034873875526697094725 107:35:19384123901308368955682511855 107:36:38768247802616737911365023710 107:37:74393124161778064640727477930 107:38:137039965561170119075024301450 107:39:242455323685147133748119917950 107:40:412174050264750127371803860515 107:41:673552716286298988631972162305 107:42:1058439982735612696421670540765 107:43:1599967415763135471335083375575 107:44:2327225332019106140123757637200 107:45:3258115464826748596173260692080 107:46:4391373017809965499190047019760 107:47:5699441576306550967033890812880 107:48:7124301970383188708792363516100 107:49:8578241148012410894260192805100 107:50:9950759731694396637341823653916 107:51:11121437347187855065264391142612 107:52:11976932527740766993361651999736 107:53:12428892245768720464809261509160 107:54:12428892245768720464809261509160 107:55:11976932527740766993361651999736 107:56:11121437347187855065264391142612 107:57:9950759731694396637341823653916 107:58:8578241148012410894260192805100 107:59:7124301970383188708792363516100 107:60:5699441576306550967033890812880 107:61:4391373017809965499190047019760 107:62:3258115464826748596173260692080 107:63:2327225332019106140123757637200 107:64:1599967415763135471335083375575 107:65:1058439982735612696421670540765 107:66:673552716286298988631972162305 107:67:412174050264750127371803860515 107:68:242455323685147133748119917950 107:69:137039965561170119075024301450 107:70:74393124161778064640727477930 107:71:38768247802616737911365023710 107:72:19384123901308368955682511855 107:73:9293758034873875526697094725 107:74:4270105043050159025779746225 107:75:1878846218942069971343088339 107:76:791093144817713672144458248 107:77:318492045316222387486729944 107:78:122496940506239379802588440 107:79:44967231325075215370570440 107:80:15738530963776325379699654 107:81:5246176987925441793233218 107:82:1663421971781237641756874 107:83:501030714391939048721950 107:84:143151632683411156777700 107:85:38735147667275960069260 107:86:9908991263721757227020 107:87:2391825477450079330660 107:88:543596699420472575150 107:89:116048733584145830650 107:90:23209746716829166130 107:91:4335886749297756310 107:92:754067260747435880 107:93:121623751733457400 107:94:18114175790089400 107:95:2478781950222760 107:96:309847743777845 107:97:35137373005735 107:98:3585446225075 107:99:325949656825 107:100:26075972546 107:101:1807245622 107:102:106308566 107:103:5160610 107:104:198485 107:105:5671 107:106:107 107:107:1 # binomial(108, k) for 0 <= k <= 108 108:0:1 108:1:108 108:2:5778 108:3:204156 108:4:5359095 108:5:111469176 108:6:1913554188 108:7:27883218168 108:8:352025629371 108:9:3911395881900 108:10:38722819230810 108:11:344985116783580 108:12:2788629694000605 108:13:20592957740312160 108:14:139737927523546800 108:15:875691012480893280 108:16:5089954010045192190 108:17:27545633466126922440 108:18:139258480300974996780 108:19:659645433004618405800 108:20:2935422176870551905810 108:21:12300816741171836557680 108:22:48644138930997717296280 108:23:181886780350687116846960 108:24:644182347075350205499650 108:25:2164452686173176690478824 108:26:6909598959706679434990092 108:27:20984707951701767172932872 108:28:60705762288851540750270094 108:29:167464171831314595173158880 108:30:440988985822461767289318384 108:31:1109585190133936059631188192 108:32:2669939363759783643487546587 108:33:6148951261992228997122834564 108:34:13563863077924034552476840950 108:35:28677881936182244482379606580 108:36:58152371703925106867047535565 108:37:113161371964394802552092501640 108:38:211433089722948183715751779380 108:39:379495289246317252823144219400 108:40:654629373949897261119923778465 108:41:1085726766551049116003776022820 108:42:1731992699021911685053642703070 108:43:2658407398498748167756753916340 108:44:3927192747782241611458841012775 108:45:5585340796845854736297018329280 108:46:7649488482636714095363307711840 108:47:10090814594116516466223937832640 108:48:12823743546689739675826254328980 108:49:15702543118395599603052556321200 108:50:18529000879706807531602016459016 108:51:21072197078882251702606214796528 108:52:23098369874928622058626043142348 108:53:24405824773509487458170913508896 108:54:24857784491537440929618523018320 108:55:24405824773509487458170913508896 108:56:23098369874928622058626043142348 108:57:21072197078882251702606214796528 108:58:18529000879706807531602016459016 108:59:15702543118395599603052556321200 108:60:12823743546689739675826254328980 108:61:10090814594116516466223937832640 108:62:7649488482636714095363307711840 108:63:5585340796845854736297018329280 108:64:3927192747782241611458841012775 108:65:2658407398498748167756753916340 108:66:1731992699021911685053642703070 108:67:1085726766551049116003776022820 108:68:654629373949897261119923778465 108:69:379495289246317252823144219400 108:70:211433089722948183715751779380 108:71:113161371964394802552092501640 108:72:58152371703925106867047535565 108:73:28677881936182244482379606580 108:74:13563863077924034552476840950 108:75:6148951261992228997122834564 108:76:2669939363759783643487546587 108:77:1109585190133936059631188192 108:78:440988985822461767289318384 108:79:167464171831314595173158880 108:80:60705762288851540750270094 108:81:20984707951701767172932872 108:82:6909598959706679434990092 108:83:2164452686173176690478824 108:84:644182347075350205499650 108:85:181886780350687116846960 108:86:48644138930997717296280 108:87:12300816741171836557680 108:88:2935422176870551905810 108:89:659645433004618405800 108:90:139258480300974996780 108:91:27545633466126922440 108:92:5089954010045192190 108:93:875691012480893280 108:94:139737927523546800 108:95:20592957740312160 108:96:2788629694000605 108:97:344985116783580 108:98:38722819230810 108:99:3911395881900 108:100:352025629371 108:101:27883218168 108:102:1913554188 108:103:111469176 108:104:5359095 108:105:204156 108:106:5778 108:107:108 108:108:1 # binomial(109, k) for 0 <= k <= 109 109:0:1 109:1:109 109:2:5886 109:3:209934 109:4:5563251 109:5:116828271 109:6:2025023364 109:7:29796772356 109:8:379908847539 109:9:4263421511271 109:10:42634215112710 109:11:383707936014390 109:12:3133614810784185 109:13:23381587434312765 109:14:160330885263858960 109:15:1015428940004440080 109:16:5965645022526085470 109:17:32635587476172114630 109:18:166804113767101919220 109:19:798903913305593402580 109:20:3595067609875170311610 109:21:15236238918042388463490 109:22:60944955672169553853960 109:23:230530919281684834143240 109:24:826069127426037322346610 109:25:2808635033248526895978474 109:26:9074051645879856125468916 109:27:27894306911408446607922964 109:28:81690470240553307923202966 109:29:228169934120166135923428974 109:30:608453157653776362462477264 109:31:1550574175956397826920506576 109:32:3779524553893719703118734779 109:33:8818890625752012640610381151 109:34:19712814339916263549599675514 109:35:42241745014106279034856447530 109:36:86830253640107351349427142145 109:37:171313743668319909419140037205 109:38:324594461687342986267844281020 109:39:590928378969265436538895998780 109:40:1034124663196214513943067997865 109:41:1740356140500946377123699801285 109:42:2817719465572960801057418725890 109:43:4390400097520659852810396619410 109:44:6585600146280989779215594929115 109:45:9512533544628096347755859342055 109:46:13234829279482568831660326041120 109:47:17740303076753230561587245544480 109:48:22914558140806256142050192161620 109:49:28526286665085339278878810650180 109:50:34231543998102407134654572780216 109:51:39601197958589059234208231255544 109:52:44170566953810873761232257938876 109:53:47504194648438109516796956651244 109:54:49263609265046928387789436527216 109:55:49263609265046928387789436527216 109:56:47504194648438109516796956651244 109:57:44170566953810873761232257938876 109:58:39601197958589059234208231255544 109:59:34231543998102407134654572780216 109:60:28526286665085339278878810650180 109:61:22914558140806256142050192161620 109:62:17740303076753230561587245544480 109:63:13234829279482568831660326041120 109:64:9512533544628096347755859342055 109:65:6585600146280989779215594929115 109:66:4390400097520659852810396619410 109:67:2817719465572960801057418725890 109:68:1740356140500946377123699801285 109:69:1034124663196214513943067997865 109:70:590928378969265436538895998780 109:71:324594461687342986267844281020 109:72:171313743668319909419140037205 109:73:86830253640107351349427142145 109:74:42241745014106279034856447530 109:75:19712814339916263549599675514 109:76:8818890625752012640610381151 109:77:3779524553893719703118734779 109:78:1550574175956397826920506576 109:79:608453157653776362462477264 109:80:228169934120166135923428974 109:81:81690470240553307923202966 109:82:27894306911408446607922964 109:83:9074051645879856125468916 109:84:2808635033248526895978474 109:85:826069127426037322346610 109:86:230530919281684834143240 109:87:60944955672169553853960 109:88:15236238918042388463490 109:89:3595067609875170311610 109:90:798903913305593402580 109:91:166804113767101919220 109:92:32635587476172114630 109:93:5965645022526085470 109:94:1015428940004440080 109:95:160330885263858960 109:96:23381587434312765 109:97:3133614810784185 109:98:383707936014390 109:99:42634215112710 109:100:4263421511271 109:101:379908847539 109:102:29796772356 109:103:2025023364 109:104:116828271 109:105:5563251 109:106:209934 109:107:5886 109:108:109 109:109:1 # binomial(110, k) for 0 <= k <= 110 110:0:1 110:1:110 110:2:5995 110:3:215820 110:4:5773185 110:5:122391522 110:6:2141851635 110:7:31821795720 110:8:409705619895 110:9:4643330358810 110:10:46897636623981 110:11:426342151127100 110:12:3517322746798575 110:13:26515202245096950 110:14:183712472698171725 110:15:1175759825268299040 110:16:6981073962530525550 110:17:38601232498698200100 110:18:199439701243274033850 110:19:965708027072695321800 110:20:4393971523180763714190 110:21:18831306527917558775100 110:22:76181194590211942317450 110:23:291475874953854387997200 110:24:1056600046707722156489850 110:25:3634704160674564218325084 110:26:11882686679128383021447390 110:27:36968358557288302733391880 110:28:109584777151961754531125930 110:29:309860404360719443846631940 110:30:836623091773942498385906238 110:31:2159027333610174189382983840 110:32:5330098729850117530039241355 110:33:12598415179645732343729115930 110:34:28531704965668276190210056665 110:35:61954559354022542584456123044 110:36:129071998654213630384283589675 110:37:258143997308427260768567179350 110:38:495908205355662895686984318225 110:39:915522840656608422806740279800 110:40:1625053042165479950481963996645 110:41:2774480803697160891066767799150 110:42:4558075606073907178181118527175 110:43:7208119563093620653867815345300 110:44:10976000243801649632025991548525 110:45:16098133690909086126971454271170 110:46:22747362824110665179416185383175 110:47:30975132356235799393247571585600 110:48:40654861217559486703637437706100 110:49:51440844805891595420929002811800 110:50:62757830663187746413533383430396 110:51:73832741956691466368862804035760 110:52:83771764912399932995440489194420 110:53:91674761602248983278029214590120 110:54:96767803913485037904586393178460 110:55:98527218530093856775578873054432 110:56:96767803913485037904586393178460 110:57:91674761602248983278029214590120 110:58:83771764912399932995440489194420 110:59:73832741956691466368862804035760 110:60:62757830663187746413533383430396 110:61:51440844805891595420929002811800 110:62:40654861217559486703637437706100 110:63:30975132356235799393247571585600 110:64:22747362824110665179416185383175 110:65:16098133690909086126971454271170 110:66:10976000243801649632025991548525 110:67:7208119563093620653867815345300 110:68:4558075606073907178181118527175 110:69:2774480803697160891066767799150 110:70:1625053042165479950481963996645 110:71:915522840656608422806740279800 110:72:495908205355662895686984318225 110:73:258143997308427260768567179350 110:74:129071998654213630384283589675 110:75:61954559354022542584456123044 110:76:28531704965668276190210056665 110:77:12598415179645732343729115930 110:78:5330098729850117530039241355 110:79:2159027333610174189382983840 110:80:836623091773942498385906238 110:81:309860404360719443846631940 110:82:109584777151961754531125930 110:83:36968358557288302733391880 110:84:11882686679128383021447390 110:85:3634704160674564218325084 110:86:1056600046707722156489850 110:87:291475874953854387997200 110:88:76181194590211942317450 110:89:18831306527917558775100 110:90:4393971523180763714190 110:91:965708027072695321800 110:92:199439701243274033850 110:93:38601232498698200100 110:94:6981073962530525550 110:95:1175759825268299040 110:96:183712472698171725 110:97:26515202245096950 110:98:3517322746798575 110:99:426342151127100 110:100:46897636623981 110:101:4643330358810 110:102:409705619895 110:103:31821795720 110:104:2141851635 110:105:122391522 110:106:5773185 110:107:215820 110:108:5995 110:109:110 110:110:1 # binomial(111, k) for 0 <= k <= 111 111:0:1 111:1:111 111:2:6105 111:3:221815 111:4:5989005 111:5:128164707 111:6:2264243157 111:7:33963647355 111:8:441527415615 111:9:5053035978705 111:10:51540966982791 111:11:473239787751081 111:12:3943664897925675 111:13:30032524991895525 111:14:210227674943268675 111:15:1359472297966470765 111:16:8156833787798824590 111:17:45582306461228725650 111:18:238040933741972233950 111:19:1165147728315969355650 111:20:5359679550253459035990 111:21:23225278051098322489290 111:22:95012501118129501092550 111:23:367657069544066330314650 111:24:1348075921661576544487050 111:25:4691304207382286374814934 111:26:15517390839802947239772474 111:27:48851045236416685754839270 111:28:146553135709250057264517810 111:29:419445181512681198377757870 111:30:1146483496134661942232538178 111:31:2995650425384116687768890078 111:32:7489126063460291719422225195 111:33:17928513909495849873768357285 111:34:41130120145314008533939172595 111:35:90486264319690818774666179709 111:36:191026558008236172968739712719 111:37:387215995962640891152850769025 111:38:754052202664090156455551497575 111:39:1411431046012271318493724598025 111:40:2540575882822088373288704276445 111:41:4399533845862640841548731795795 111:42:7332556409771068069247886326325 111:43:11766195169167527832048933872475 111:44:18184119806895270285893806893825 111:45:27074133934710735758997445819695 111:46:38845496515019751306387639654345 111:47:53722495180346464572663756968775 111:48:71629993573795286096885009291700 111:49:92095706023451082124566440517900 111:50:114198675469079341834462386242196 111:51:136590572619879212782396187466156 111:52:157604506869091399364303293230180 111:53:175446526514648916273469703784540 111:54:188442565515734021182615607768580 111:55:195295022443578894680165266232892 111:56:195295022443578894680165266232892 111:57:188442565515734021182615607768580 111:58:175446526514648916273469703784540 111:59:157604506869091399364303293230180 111:60:136590572619879212782396187466156 111:61:114198675469079341834462386242196 111:62:92095706023451082124566440517900 111:63:71629993573795286096885009291700 111:64:53722495180346464572663756968775 111:65:38845496515019751306387639654345 111:66:27074133934710735758997445819695 111:67:18184119806895270285893806893825 111:68:11766195169167527832048933872475 111:69:7332556409771068069247886326325 111:70:4399533845862640841548731795795 111:71:2540575882822088373288704276445 111:72:1411431046012271318493724598025 111:73:754052202664090156455551497575 111:74:387215995962640891152850769025 111:75:191026558008236172968739712719 111:76:90486264319690818774666179709 111:77:41130120145314008533939172595 111:78:17928513909495849873768357285 111:79:7489126063460291719422225195 111:80:2995650425384116687768890078 111:81:1146483496134661942232538178 111:82:419445181512681198377757870 111:83:146553135709250057264517810 111:84:48851045236416685754839270 111:85:15517390839802947239772474 111:86:4691304207382286374814934 111:87:1348075921661576544487050 111:88:367657069544066330314650 111:89:95012501118129501092550 111:90:23225278051098322489290 111:91:5359679550253459035990 111:92:1165147728315969355650 111:93:238040933741972233950 111:94:45582306461228725650 111:95:8156833787798824590 111:96:1359472297966470765 111:97:210227674943268675 111:98:30032524991895525 111:99:3943664897925675 111:100:473239787751081 111:101:51540966982791 111:102:5053035978705 111:103:441527415615 111:104:33963647355 111:105:2264243157 111:106:128164707 111:107:5989005 111:108:221815 111:109:6105 111:110:111 111:111:1 # binomial(112, k) for 0 <= k <= 112 112:0:1 112:1:112 112:2:6216 112:3:227920 112:4:6210820 112:5:134153712 112:6:2392407864 112:7:36227890512 112:8:475491062970 112:9:5494563394320 112:10:56594002961496 112:11:524780754733872 112:12:4416904685676756 112:13:33976189889821200 112:14:240260199935164200 112:15:1569699972909739440 112:16:9516306085765295355 112:17:53739140249027550240 112:18:283623240203200959600 112:19:1403188662057941589600 112:20:6524827278569428391640 112:21:28584957601351781525280 112:22:118237779169227823581840 112:23:462669570662195831407200 112:24:1715732991205642874801700 112:25:6039380129043862919301984 112:26:20208695047185233614587408 112:27:64368436076219632994611744 112:28:195404180945666743019357080 112:29:565998317221931255642275680 112:30:1565928677647343140610296048 112:31:4142133921518778630001428256 112:32:10484776488844408407191115273 112:33:25417639972956141593190582480 112:34:59058634054809858407707529880 112:35:131616384465004827308605352304 112:36:281512822327926991743405892428 112:37:578242553970877064121590481744 112:38:1141268198626731047608402266600 112:39:2165483248676361474949276095600 112:40:3952006928834359691782428874470 112:41:6940109728684729214837436072240 112:42:11732090255633708910796618122120 112:43:19098751578938595901296820198800 112:44:29950314976062798117942740766300 112:45:45258253741606006044891252713520 112:46:65919630449730487065385085474040 112:47:92567991695366215879051396623120 112:48:125352488754141750669548766260475 112:49:163725699597246368221451449809600 112:50:206294381492530423959028826760096 112:51:250789248088958554616858573708352 112:52:294195079488970612146699480696336 112:53:333051033383740315637772997014720 112:54:363889092030382937456085311553120 112:55:383737587959312915862780874001472 112:56:390590044887157789360330532465784 112:57:383737587959312915862780874001472 112:58:363889092030382937456085311553120 112:59:333051033383740315637772997014720 112:60:294195079488970612146699480696336 112:61:250789248088958554616858573708352 112:62:206294381492530423959028826760096 112:63:163725699597246368221451449809600 112:64:125352488754141750669548766260475 112:65:92567991695366215879051396623120 112:66:65919630449730487065385085474040 112:67:45258253741606006044891252713520 112:68:29950314976062798117942740766300 112:69:19098751578938595901296820198800 112:70:11732090255633708910796618122120 112:71:6940109728684729214837436072240 112:72:3952006928834359691782428874470 112:73:2165483248676361474949276095600 112:74:1141268198626731047608402266600 112:75:578242553970877064121590481744 112:76:281512822327926991743405892428 112:77:131616384465004827308605352304 112:78:59058634054809858407707529880 112:79:25417639972956141593190582480 112:80:10484776488844408407191115273 112:81:4142133921518778630001428256 112:82:1565928677647343140610296048 112:83:565998317221931255642275680 112:84:195404180945666743019357080 112:85:64368436076219632994611744 112:86:20208695047185233614587408 112:87:6039380129043862919301984 112:88:1715732991205642874801700 112:89:462669570662195831407200 112:90:118237779169227823581840 112:91:28584957601351781525280 112:92:6524827278569428391640 112:93:1403188662057941589600 112:94:283623240203200959600 112:95:53739140249027550240 112:96:9516306085765295355 112:97:1569699972909739440 112:98:240260199935164200 112:99:33976189889821200 112:100:4416904685676756 112:101:524780754733872 112:102:56594002961496 112:103:5494563394320 112:104:475491062970 112:105:36227890512 112:106:2392407864 112:107:134153712 112:108:6210820 112:109:227920 112:110:6216 112:111:112 112:112:1 # binomial(113, k) for 0 <= k <= 113 113:0:1 113:1:113 113:2:6328 113:3:234136 113:4:6438740 113:5:140364532 113:6:2526561576 113:7:38620298376 113:8:511718953482 113:9:5970054457290 113:10:62088566355816 113:11:581374757695368 113:12:4941685440410628 113:13:38393094575497956 113:14:274236389824985400 113:15:1809960172844903640 113:16:11086006058675034795 113:17:63255446334792845595 113:18:337362380452228509840 113:19:1686811902261142549200 113:20:7928015940627369981240 113:21:35109784879921209916920 113:22:146822736770579605107120 113:23:580907349831423654989040 113:24:2178402561867838706208900 113:25:7755113120249505794103684 113:26:26248075176229096533889392 113:27:84577131123404866609199152 113:28:259772617021886376013968824 113:29:761402498167597998661632760 113:30:2131926994869274396252571728 113:31:5708062599166121770611724304 113:32:14626910410363187037192543529 113:33:35902416461800550000381697753 113:34:84476274027766000000898112360 113:35:190675018519814685716312882184 113:36:413129206792931819052011244732 113:37:859755376298804055864996374172 113:38:1719510752597608111729992748344 113:39:3306751447303092522557678362200 113:40:6117490177510721166731704970070 113:41:10892116657519088906619864946710 113:42:18672199984318438125634054194360 113:43:30830841834572304812093438320920 113:44:49049066555001394019239560965100 113:45:75208568717668804162833993479820 113:46:111177884191336493110276338187560 113:47:158487622145096702944436482097160 113:48:217920480449507966548600162883595 113:49:289078188351388118891000216070075 113:50:370020081089776792180480276569696 113:51:457083629581488978575887400468448 113:52:544984327577929166763558054404688 113:53:627246112872710927784472477711056 113:54:696940125414123253093858308567840 113:55:747626679989695853318866185554592 113:56:774327632846470705223111406467256 113:57:774327632846470705223111406467256 113:58:747626679989695853318866185554592 113:59:696940125414123253093858308567840 113:60:627246112872710927784472477711056 113:61:544984327577929166763558054404688 113:62:457083629581488978575887400468448 113:63:370020081089776792180480276569696 113:64:289078188351388118891000216070075 113:65:217920480449507966548600162883595 113:66:158487622145096702944436482097160 113:67:111177884191336493110276338187560 113:68:75208568717668804162833993479820 113:69:49049066555001394019239560965100 113:70:30830841834572304812093438320920 113:71:18672199984318438125634054194360 113:72:10892116657519088906619864946710 113:73:6117490177510721166731704970070 113:74:3306751447303092522557678362200 113:75:1719510752597608111729992748344 113:76:859755376298804055864996374172 113:77:413129206792931819052011244732 113:78:190675018519814685716312882184 113:79:84476274027766000000898112360 113:80:35902416461800550000381697753 113:81:14626910410363187037192543529 113:82:5708062599166121770611724304 113:83:2131926994869274396252571728 113:84:761402498167597998661632760 113:85:259772617021886376013968824 113:86:84577131123404866609199152 113:87:26248075176229096533889392 113:88:7755113120249505794103684 113:89:2178402561867838706208900 113:90:580907349831423654989040 113:91:146822736770579605107120 113:92:35109784879921209916920 113:93:7928015940627369981240 113:94:1686811902261142549200 113:95:337362380452228509840 113:96:63255446334792845595 113:97:11086006058675034795 113:98:1809960172844903640 113:99:274236389824985400 113:100:38393094575497956 113:101:4941685440410628 113:102:581374757695368 113:103:62088566355816 113:104:5970054457290 113:105:511718953482 113:106:38620298376 113:107:2526561576 113:108:140364532 113:109:6438740 113:110:234136 113:111:6328 113:112:113 113:113:1 # binomial(114, k) for 0 <= k <= 114 114:0:1 114:1:114 114:2:6441 114:3:240464 114:4:6672876 114:5:146803272 114:6:2666926108 114:7:41146859952 114:8:550339251858 114:9:6481773410772 114:10:68058620813106 114:11:643463324051184 114:12:5523060198105996 114:13:43334780015908584 114:14:312629484400483356 114:15:2084196562669889040 114:16:12895966231519938435 114:17:74341452393467880390 114:18:400617826787021355435 114:19:2024174282713371059040 114:20:9614827842888512530440 114:21:43037800820548579898160 114:22:181932521650500815024040 114:23:727730086602003260096160 114:24:2759309911699262361197940 114:25:9933515682117344500312584 114:26:34003188296478602327993076 114:27:110825206299633963143088544 114:28:344349748145291242623167976 114:29:1021175115189484374675601584 114:30:2893329493036872394914204488 114:31:7839989594035396166864296032 114:32:20334973009529308807804267833 114:33:50529326872163737037574241282 114:34:120378690489566550001279810113 114:35:275151292547580685717210994544 114:36:603804225312746504768324126916 114:37:1272884583091735874917007618904 114:38:2579266128896412167594989122516 114:39:5026262199900700634287671110544 114:40:9424241624813813689289383332270 114:41:17009606835029810073351569916780 114:42:29564316641837527032253919141070 114:43:49503041818890742937727492515280 114:44:79879908389573698831332999286020 114:45:124257635272670198182073554444920 114:46:186386452909005297273110331667380 114:47:269665506336433196054712820284720 114:48:376408102594604669493036644980755 114:49:506998668800896085439600378953670 114:50:659098269441164911071480492639771 114:51:827103710671265770756367677038144 114:52:1002067957159418145339445454873136 114:53:1172230440450640094548030532115744 114:54:1324186238286834180878330786278896 114:55:1444566805403819106412724494122432 114:56:1521954312836166558541977592021848 114:57:1548655265692941410446222812934512 114:58:1521954312836166558541977592021848 114:59:1444566805403819106412724494122432 114:60:1324186238286834180878330786278896 114:61:1172230440450640094548030532115744 114:62:1002067957159418145339445454873136 114:63:827103710671265770756367677038144 114:64:659098269441164911071480492639771 114:65:506998668800896085439600378953670 114:66:376408102594604669493036644980755 114:67:269665506336433196054712820284720 114:68:186386452909005297273110331667380 114:69:124257635272670198182073554444920 114:70:79879908389573698831332999286020 114:71:49503041818890742937727492515280 114:72:29564316641837527032253919141070 114:73:17009606835029810073351569916780 114:74:9424241624813813689289383332270 114:75:5026262199900700634287671110544 114:76:2579266128896412167594989122516 114:77:1272884583091735874917007618904 114:78:603804225312746504768324126916 114:79:275151292547580685717210994544 114:80:120378690489566550001279810113 114:81:50529326872163737037574241282 114:82:20334973009529308807804267833 114:83:7839989594035396166864296032 114:84:2893329493036872394914204488 114:85:1021175115189484374675601584 114:86:344349748145291242623167976 114:87:110825206299633963143088544 114:88:34003188296478602327993076 114:89:9933515682117344500312584 114:90:2759309911699262361197940 114:91:727730086602003260096160 114:92:181932521650500815024040 114:93:43037800820548579898160 114:94:9614827842888512530440 114:95:2024174282713371059040 114:96:400617826787021355435 114:97:74341452393467880390 114:98:12895966231519938435 114:99:2084196562669889040 114:100:312629484400483356 114:101:43334780015908584 114:102:5523060198105996 114:103:643463324051184 114:104:68058620813106 114:105:6481773410772 114:106:550339251858 114:107:41146859952 114:108:2666926108 114:109:146803272 114:110:6672876 114:111:240464 114:112:6441 114:113:114 114:114:1 # binomial(115, k) for 0 <= k <= 115 115:0:1 115:1:115 115:2:6555 115:3:246905 115:4:6913340 115:5:153476148 115:6:2813729380 115:7:43813786060 115:8:591486111810 115:9:7032112662630 115:10:74540394223878 115:11:711521944864290 115:12:6166523522157180 115:13:48857840214014580 115:14:355964264416391940 115:15:2396826047070372396 115:16:14980162794189827475 115:17:87237418624987818825 115:18:474959279180489235825 115:19:2424792109500392414475 115:20:11639002125601883589480 115:21:52652628663437092428600 115:22:224970322471049394922200 115:23:909662608252504075120200 115:24:3487039998301265621294100 115:25:12692825593816606861510524 115:26:43936703978595946828305660 115:27:144828394596112565471081620 115:28:455174954444925205766256520 115:29:1365524863334775617298769560 115:30:3914504608226356769589806072 115:31:10733319087072268561778500520 115:32:28174962603564704974668563865 115:33:70864299881693045845378509115 115:34:170908017361730287038854051395 115:35:395529983037147235718490804657 115:36:878955517860327190485535121460 115:37:1876688808404482379685331745820 115:38:3852150711988148042511996741420 115:39:7605528328797112801882660233060 115:40:14450503824714514323577054442814 115:41:26433848459843623762640953249050 115:42:46573923476867337105605489057850 115:43:79067358460728269969981411656350 115:44:129382950208464441769060491801300 115:45:204137543662243897013406553730940 115:46:310644088181675495455183886112300 115:47:456051959245438493327823151952100 115:48:646073608931037865547749465265475 115:49:883406771395500754932637023934425 115:50:1166096938242060996511080871593441 115:51:1486201980112430681827848169677915 115:52:1829171667830683916095813131911280 115:53:2174298397610058239887475986988880 115:54:2496416678737474275426361318394640 115:55:2768753043690653287291055280401328 115:56:2966521118239985664954702086144280 115:57:3070609578529107968988200404956360 115:58:3070609578529107968988200404956360 115:59:2966521118239985664954702086144280 115:60:2768753043690653287291055280401328 115:61:2496416678737474275426361318394640 115:62:2174298397610058239887475986988880 115:63:1829171667830683916095813131911280 115:64:1486201980112430681827848169677915 115:65:1166096938242060996511080871593441 115:66:883406771395500754932637023934425 115:67:646073608931037865547749465265475 115:68:456051959245438493327823151952100 115:69:310644088181675495455183886112300 115:70:204137543662243897013406553730940 115:71:129382950208464441769060491801300 115:72:79067358460728269969981411656350 115:73:46573923476867337105605489057850 115:74:26433848459843623762640953249050 115:75:14450503824714514323577054442814 115:76:7605528328797112801882660233060 115:77:3852150711988148042511996741420 115:78:1876688808404482379685331745820 115:79:878955517860327190485535121460 115:80:395529983037147235718490804657 115:81:170908017361730287038854051395 115:82:70864299881693045845378509115 115:83:28174962603564704974668563865 115:84:10733319087072268561778500520 115:85:3914504608226356769589806072 115:86:1365524863334775617298769560 115:87:455174954444925205766256520 115:88:144828394596112565471081620 115:89:43936703978595946828305660 115:90:12692825593816606861510524 115:91:3487039998301265621294100 115:92:909662608252504075120200 115:93:224970322471049394922200 115:94:52652628663437092428600 115:95:11639002125601883589480 115:96:2424792109500392414475 115:97:474959279180489235825 115:98:87237418624987818825 115:99:14980162794189827475 115:100:2396826047070372396 115:101:355964264416391940 115:102:48857840214014580 115:103:6166523522157180 115:104:711521944864290 115:105:74540394223878 115:106:7032112662630 115:107:591486111810 115:108:43813786060 115:109:2813729380 115:110:153476148 115:111:6913340 115:112:246905 115:113:6555 115:114:115 115:115:1 # binomial(116, k) for 0 <= k <= 116 116:0:1 116:1:116 116:2:6670 116:3:253460 116:4:7160245 116:5:160389488 116:6:2967205528 116:7:46627515440 116:8:635299897870 116:9:7623598774440 116:10:81572506886508 116:11:786062339088168 116:12:6878045467021470 116:13:55024363736171760 116:14:404822104630406520 116:15:2752790311486764336 116:16:17376988841260199871 116:17:102217581419177646300 116:18:562196697805477054650 116:19:2899751388680881650300 116:20:14063794235102276003955 116:21:64291630789038976018080 116:22:277622951134486487350800 116:23:1134632930723553470042400 116:24:4396702606553769696414300 116:25:16179865592117872482804624 116:26:56629529572412553689816184 116:27:188765098574708512299387280 116:28:600003349041037771237338140 116:29:1820699817779700823065026080 116:30:5280029471561132386888575632 116:31:14647823695298625331368306592 116:32:38908281690636973536447064385 116:33:99039262485257750820047072980 116:34:241772317243423332884232560510 116:35:566438000398877522757344856052 116:36:1274485500897474426204025926117 116:37:2755644326264809570170866867280 116:38:5728839520392630422197328487240 116:39:11457679040785260844394656974480 116:40:22056032153511627125459714675874 116:41:40884352284558138086218007691864 116:42:73007771936710960868246442306900 116:43:125641281937595607075586900714200 116:44:208450308669192711739041903457650 116:45:333520493870708338782467045532240 116:46:514781631843919392468590439843240 116:47:766696047427113988783007038064400 116:48:1102125568176476358875572617217575 116:49:1529480380326538620480386489199900 116:50:2049503709637561751443717895527866 116:51:2652298918354491678338929041271356 116:52:3315373647943114597923661301589195 116:53:4003470065440742155983289118900160 116:54:4670715076347532515313837305383520 116:55:5265169722428127562717416598795968 116:56:5735274161930638952245757366545608 116:57:6037130696769093633942902491100640 116:58:6141219157058215937976400809912720 116:59:6037130696769093633942902491100640 116:60:5735274161930638952245757366545608 116:61:5265169722428127562717416598795968 116:62:4670715076347532515313837305383520 116:63:4003470065440742155983289118900160 116:64:3315373647943114597923661301589195 116:65:2652298918354491678338929041271356 116:66:2049503709637561751443717895527866 116:67:1529480380326538620480386489199900 116:68:1102125568176476358875572617217575 116:69:766696047427113988783007038064400 116:70:514781631843919392468590439843240 116:71:333520493870708338782467045532240 116:72:208450308669192711739041903457650 116:73:125641281937595607075586900714200 116:74:73007771936710960868246442306900 116:75:40884352284558138086218007691864 116:76:22056032153511627125459714675874 116:77:11457679040785260844394656974480 116:78:5728839520392630422197328487240 116:79:2755644326264809570170866867280 116:80:1274485500897474426204025926117 116:81:566438000398877522757344856052 116:82:241772317243423332884232560510 116:83:99039262485257750820047072980 116:84:38908281690636973536447064385 116:85:14647823695298625331368306592 116:86:5280029471561132386888575632 116:87:1820699817779700823065026080 116:88:600003349041037771237338140 116:89:188765098574708512299387280 116:90:56629529572412553689816184 116:91:16179865592117872482804624 116:92:4396702606553769696414300 116:93:1134632930723553470042400 116:94:277622951134486487350800 116:95:64291630789038976018080 116:96:14063794235102276003955 116:97:2899751388680881650300 116:98:562196697805477054650 116:99:102217581419177646300 116:100:17376988841260199871 116:101:2752790311486764336 116:102:404822104630406520 116:103:55024363736171760 116:104:6878045467021470 116:105:786062339088168 116:106:81572506886508 116:107:7623598774440 116:108:635299897870 116:109:46627515440 116:110:2967205528 116:111:160389488 116:112:7160245 116:113:253460 116:114:6670 116:115:116 116:116:1 # binomial(117, k) for 0 <= k <= 117 117:0:1 117:1:117 117:2:6786 117:3:260130 117:4:7413705 117:5:167549733 117:6:3127595016 117:7:49594720968 117:8:681927413310 117:9:8258898672310 117:10:89196105660948 117:11:867634845974676 117:12:7664107806109638 117:13:61902409203193230 117:14:459846468366578280 117:15:3157612416117170856 117:16:20129779152746964207 117:17:119594570260437846171 117:18:664414279224654700950 117:19:3461948086486358704950 117:20:16963545623783157654255 117:21:78355425024141252022035 117:22:341914581923525463368880 117:23:1412255881858039957393200 117:24:5531335537277323166456700 117:25:20576568198671642179218924 117:26:72809395164530426172620808 117:27:245394628147121065989203464 117:28:788768447615746283536725420 117:29:2420703166820738594302364220 117:30:7100729289340833209953601712 117:31:19927853166859757718256882224 117:32:53556105385935598867815370977 117:33:137947544175894724356494137365 117:34:340811579728681083704279633490 117:35:808210317642300855641577416562 117:36:1840923501296351948961370782169 117:37:4030129827162283996374892793397 117:38:8484483846657439992368195354520 117:39:17186518561177891266591985461720 117:40:33513711194296887969854371650354 117:41:62940384438069765211677722367738 117:42:113892124221269098954464449998764 117:43:198649053874306567943833343021100 117:44:334091590606788318814628804171850 117:45:541970802539901050521508948989890 117:46:848302125714627731251057485375480 117:47:1281477679271033381251597477907640 117:48:1868821615603590347658579655281975 117:49:2631605948503014979355959106417475 117:50:3578984089964100371924104384727766 117:51:4701802627992053429782646936799222 117:52:5967672566297606276262590342860551 117:53:7318843713383856753906950420489355 117:54:8674185141788274671297126424283680 117:55:9935884798775660078031253904179488 117:56:11000443884358766514963173965341576 117:57:11772404858699732586188659857646248 117:58:12178349853827309571919303301013360 117:59:12178349853827309571919303301013360 117:60:11772404858699732586188659857646248 117:61:11000443884358766514963173965341576 117:62:9935884798775660078031253904179488 117:63:8674185141788274671297126424283680 117:64:7318843713383856753906950420489355 117:65:5967672566297606276262590342860551 117:66:4701802627992053429782646936799222 117:67:3578984089964100371924104384727766 117:68:2631605948503014979355959106417475 117:69:1868821615603590347658579655281975 117:70:1281477679271033381251597477907640 117:71:848302125714627731251057485375480 117:72:541970802539901050521508948989890 117:73:334091590606788318814628804171850 117:74:198649053874306567943833343021100 117:75:113892124221269098954464449998764 117:76:62940384438069765211677722367738 117:77:33513711194296887969854371650354 117:78:17186518561177891266591985461720 117:79:8484483846657439992368195354520 117:80:4030129827162283996374892793397 117:81:1840923501296351948961370782169 117:82:808210317642300855641577416562 117:83:340811579728681083704279633490 117:84:137947544175894724356494137365 117:85:53556105385935598867815370977 117:86:19927853166859757718256882224 117:87:7100729289340833209953601712 117:88:2420703166820738594302364220 117:89:788768447615746283536725420 117:90:245394628147121065989203464 117:91:72809395164530426172620808 117:92:20576568198671642179218924 117:93:5531335537277323166456700 117:94:1412255881858039957393200 117:95:341914581923525463368880 117:96:78355425024141252022035 117:97:16963545623783157654255 117:98:3461948086486358704950 117:99:664414279224654700950 117:100:119594570260437846171 117:101:20129779152746964207 117:102:3157612416117170856 117:103:459846468366578280 117:104:61902409203193230 117:105:7664107806109638 117:106:867634845974676 117:107:89196105660948 117:108:8258898672310 117:109:681927413310 117:110:49594720968 117:111:3127595016 117:112:167549733 117:113:7413705 117:114:260130 117:115:6786 117:116:117 117:117:1 # binomial(118, k) for 0 <= k <= 118 118:0:1 118:1:118 118:2:6903 118:3:266916 118:4:7673835 118:5:174963438 118:6:3295144749 118:7:52722315984 118:8:731522134278 118:9:8940826085620 118:10:97455004333258 118:11:956830951635624 118:12:8531742652084314 118:13:69566517009302868 118:14:521748877569771510 118:15:3617458884483749136 118:16:23287391568864135063 118:17:139724349413184810378 118:18:784008849485092547121 118:19:4126362365711013405900 118:20:20425493710269516359205 118:21:95318970647924409676290 118:22:420270006947666715390915 118:23:1754170463781565420762080 118:24:6943591419135363123849900 118:25:26107903735948965345675624 118:26:93385963363202068351839732 118:27:318204023311651492161824272 118:28:1034163075762867349525928884 118:29:3209471614436484877839089640 118:30:9521432456161571804255965932 118:31:27028582456200590928210483936 118:32:73483958552795356586072253201 118:33:191503649561830323224309508342 118:34:478759123904575808060773770855 118:35:1149021897370981939345857050052 118:36:2649133818938652804602948198731 118:37:5871053328458635945336263575566 118:38:12514613673819723988743088147917 118:39:25671002407835331258960180816240 118:40:50700229755474779236446357112074 118:41:96454095632366653181532094018092 118:42:176832508659338864166142172366502 118:43:312541178095575666898297793019864 118:44:532740644481094886758462147192950 118:45:876062393146689369336137753161740 118:46:1390272928254528781772566434365370 118:47:2129779804985661112502654963283120 118:48:3150299294874623728910177133189615 118:49:4500427564106605327014538761699450 118:50:6210590038467115351280063491145241 118:51:8280786717956153801706751321526988 118:52:10669475194289659706045237279659773 118:53:13286516279681463030169540763349906 118:54:15993028855172131425204076844773035 118:55:18610069940563934749328380328463168 118:56:20936328683134426592994427869521064 118:57:22772848743058499101151833822987824 118:58:23950754712527042158107963158659608 118:59:24356699707654619143838606602026720 118:60:23950754712527042158107963158659608 118:61:22772848743058499101151833822987824 118:62:20936328683134426592994427869521064 118:63:18610069940563934749328380328463168 118:64:15993028855172131425204076844773035 118:65:13286516279681463030169540763349906 118:66:10669475194289659706045237279659773 118:67:8280786717956153801706751321526988 118:68:6210590038467115351280063491145241 118:69:4500427564106605327014538761699450 118:70:3150299294874623728910177133189615 118:71:2129779804985661112502654963283120 118:72:1390272928254528781772566434365370 118:73:876062393146689369336137753161740 118:74:532740644481094886758462147192950 118:75:312541178095575666898297793019864 118:76:176832508659338864166142172366502 118:77:96454095632366653181532094018092 118:78:50700229755474779236446357112074 118:79:25671002407835331258960180816240 118:80:12514613673819723988743088147917 118:81:5871053328458635945336263575566 118:82:2649133818938652804602948198731 118:83:1149021897370981939345857050052 118:84:478759123904575808060773770855 118:85:191503649561830323224309508342 118:86:73483958552795356586072253201 118:87:27028582456200590928210483936 118:88:9521432456161571804255965932 118:89:3209471614436484877839089640 118:90:1034163075762867349525928884 118:91:318204023311651492161824272 118:92:93385963363202068351839732 118:93:26107903735948965345675624 118:94:6943591419135363123849900 118:95:1754170463781565420762080 118:96:420270006947666715390915 118:97:95318970647924409676290 118:98:20425493710269516359205 118:99:4126362365711013405900 118:100:784008849485092547121 118:101:139724349413184810378 118:102:23287391568864135063 118:103:3617458884483749136 118:104:521748877569771510 118:105:69566517009302868 118:106:8531742652084314 118:107:956830951635624 118:108:97455004333258 118:109:8940826085620 118:110:731522134278 118:111:52722315984 118:112:3295144749 118:113:174963438 118:114:7673835 118:115:266916 118:116:6903 118:117:118 118:118:1 # binomial(119, k) for 0 <= k <= 119 119:0:1 119:1:119 119:2:7021 119:3:273819 119:4:7940751 119:5:182637273 119:6:3470108187 119:7:56017460733 119:8:784244450262 119:9:9672348219898 119:10:106395830418878 119:11:1054285955968882 119:12:9488573603719938 119:13:78098259661387182 119:14:591315394579074378 119:15:4139207762053520646 119:16:26904850453347884199 119:17:163011740982048945441 119:18:923733198898277357499 119:19:4910371215196105953021 119:20:24551856075980529765105 119:21:115744464358193926035495 119:22:515588977595591125067205 119:23:2174440470729232136152995 119:24:8697761882916928544611980 119:25:33051495155084328469525524 119:26:119493867099151033697515356 119:27:411589986674853560513664004 119:28:1352367099074518841687753156 119:29:4243634690199352227365018524 119:30:12730904070598056682095055572 119:31:36550014912362162732466449868 119:32:100512541008995947514282737137 119:33:264987608114625679810381761543 119:34:670262773466406131285083279197 119:35:1627781021275557747406630820907 119:36:3798155716309634743948805248783 119:37:8520187147397288749939211774297 119:38:18385667002278359934079351723483 119:39:38185616081655055247703268964157 119:40:76371232163310110495406537928314 119:41:147154325387841432417978451130166 119:42:273286604291705517347674266384594 119:43:489373686754914531064439965386366 119:44:845281822576670553656759940212814 119:45:1408803037627784256094599900354690 119:46:2266335321401218151108704187527110 119:47:3520052733240189894275221397648490 119:48:5280079099860284841412832096472735 119:49:7650726858981229055924715894889065 119:50:10711017602573720678294602252844691 119:51:14491376756423269152986814812672229 119:52:18950261912245813507751988601186761 119:53:23955991473971122736214778043009679 119:54:29279545134853594455373617608122941 119:55:34603098795736066174532457173236203 119:56:39546398623698361342322808197984232 119:57:43709177426192925694146261692508888 119:58:46723603455585541259259796981647432 119:59:48307454420181661301946569760686328 119:60:48307454420181661301946569760686328 119:61:46723603455585541259259796981647432 119:62:43709177426192925694146261692508888 119:63:39546398623698361342322808197984232 119:64:34603098795736066174532457173236203 119:65:29279545134853594455373617608122941 119:66:23955991473971122736214778043009679 119:67:18950261912245813507751988601186761 119:68:14491376756423269152986814812672229 119:69:10711017602573720678294602252844691 119:70:7650726858981229055924715894889065 119:71:5280079099860284841412832096472735 119:72:3520052733240189894275221397648490 119:73:2266335321401218151108704187527110 119:74:1408803037627784256094599900354690 119:75:845281822576670553656759940212814 119:76:489373686754914531064439965386366 119:77:273286604291705517347674266384594 119:78:147154325387841432417978451130166 119:79:76371232163310110495406537928314 119:80:38185616081655055247703268964157 119:81:18385667002278359934079351723483 119:82:8520187147397288749939211774297 119:83:3798155716309634743948805248783 119:84:1627781021275557747406630820907 119:85:670262773466406131285083279197 119:86:264987608114625679810381761543 119:87:100512541008995947514282737137 119:88:36550014912362162732466449868 119:89:12730904070598056682095055572 119:90:4243634690199352227365018524 119:91:1352367099074518841687753156 119:92:411589986674853560513664004 119:93:119493867099151033697515356 119:94:33051495155084328469525524 119:95:8697761882916928544611980 119:96:2174440470729232136152995 119:97:515588977595591125067205 119:98:115744464358193926035495 119:99:24551856075980529765105 119:100:4910371215196105953021 119:101:923733198898277357499 119:102:163011740982048945441 119:103:26904850453347884199 119:104:4139207762053520646 119:105:591315394579074378 119:106:78098259661387182 119:107:9488573603719938 119:108:1054285955968882 119:109:106395830418878 119:110:9672348219898 119:111:784244450262 119:112:56017460733 119:113:3470108187 119:114:182637273 119:115:7940751 119:116:273819 119:117:7021 119:118:119 119:119:1 # binomial(120, k) for 0 <= k <= 120 120:0:1 120:1:120 120:2:7140 120:3:280840 120:4:8214570 120:5:190578024 120:6:3652745460 120:7:59487568920 120:8:840261910995 120:9:10456592670160 120:10:116068178638776 120:11:1160681786387760 120:12:10542859559688820 120:13:87586833265107120 120:14:669413654240461560 120:15:4730523156632595024 120:16:31044058215401404845 120:17:189916591435396829640 120:18:1086744939880326302940 120:19:5834104414094383310520 120:20:29462227291176635718126 120:21:140296320434174455800600 120:22:631333441953785051102700 120:23:2690029448324823261220200 120:24:10872202353646160680764975 120:25:41749257038001257014137504 120:26:152545362254235362167040880 120:27:531083853774004594211179360 120:28:1763957085749372402201417160 120:29:5596001789273871069052771680 120:30:16974538760797408909460074096 120:31:49280918982960219414561505440 120:32:137062555921358110246749187005 120:33:365500149123621627324664498680 120:34:935250381581031811095465040740 120:35:2298043794741963878691714100104 120:36:5425936737585192491355436069690 120:37:12318342863706923493888017023080 120:38:26905854149675648684018563497780 120:39:56571283083933415181782620687640 120:40:114556848244965165743109806892471 120:41:223525557551151542913384989058480 120:42:420440929679546949765652717514760 120:43:762660291046620048412114231770960 120:44:1334655509331585084721199905599180 120:45:2254084860204454809751359840567504 120:46:3675138359029002407203304087881800 120:47:5786388054641408045383925585175600 120:48:8800131833100474735688053494121225 120:49:12930805958841513897337547991361800 120:50:18361744461554949734219318147733756 120:51:25202394358996989831281417065516920 120:52:33441638668669082660738803413858990 120:53:42906253386216936243966766644196440 120:54:53235536608824717191588395651132620 120:55:63882643930589660629906074781359144 120:56:74149497419434427516855265371220435 120:57:83255576049891287036469069890493120 120:58:90432780881778466953406058674156320 120:59:95031057875767202561206366742333760 120:60:96614908840363322603893139521372656 120:61:95031057875767202561206366742333760 120:62:90432780881778466953406058674156320 120:63:83255576049891287036469069890493120 120:64:74149497419434427516855265371220435 120:65:63882643930589660629906074781359144 120:66:53235536608824717191588395651132620 120:67:42906253386216936243966766644196440 120:68:33441638668669082660738803413858990 120:69:25202394358996989831281417065516920 120:70:18361744461554949734219318147733756 120:71:12930805958841513897337547991361800 120:72:8800131833100474735688053494121225 120:73:5786388054641408045383925585175600 120:74:3675138359029002407203304087881800 120:75:2254084860204454809751359840567504 120:76:1334655509331585084721199905599180 120:77:762660291046620048412114231770960 120:78:420440929679546949765652717514760 120:79:223525557551151542913384989058480 120:80:114556848244965165743109806892471 120:81:56571283083933415181782620687640 120:82:26905854149675648684018563497780 120:83:12318342863706923493888017023080 120:84:5425936737585192491355436069690 120:85:2298043794741963878691714100104 120:86:935250381581031811095465040740 120:87:365500149123621627324664498680 120:88:137062555921358110246749187005 120:89:49280918982960219414561505440 120:90:16974538760797408909460074096 120:91:5596001789273871069052771680 120:92:1763957085749372402201417160 120:93:531083853774004594211179360 120:94:152545362254235362167040880 120:95:41749257038001257014137504 120:96:10872202353646160680764975 120:97:2690029448324823261220200 120:98:631333441953785051102700 120:99:140296320434174455800600 120:100:29462227291176635718126 120:101:5834104414094383310520 120:102:1086744939880326302940 120:103:189916591435396829640 120:104:31044058215401404845 120:105:4730523156632595024 120:106:669413654240461560 120:107:87586833265107120 120:108:10542859559688820 120:109:1160681786387760 120:110:116068178638776 120:111:10456592670160 120:112:840261910995 120:113:59487568920 120:114:3652745460 120:115:190578024 120:116:8214570 120:117:280840 120:118:7140 120:119:120 120:120:1 # binomial(121, k) for 0 <= k <= 121 121:0:1 121:1:121 121:2:7260 121:3:287980 121:4:8495410 121:5:198792594 121:6:3843323484 121:7:63140314380 121:8:899749479915 121:9:11296854581155 121:10:126524771308936 121:11:1276749965026536 121:12:11703541346076580 121:13:98129692824795940 121:14:757000487505568680 121:15:5399936810873056584 121:16:35774581372033999869 121:17:220960649650798234485 121:18:1276661531315723132580 121:19:6920849353974709613460 121:20:35296331705271019028646 121:21:169758547725351091518726 121:22:771629762387959506903300 121:23:3321362890278608312322900 121:24:13562231801970983941985175 121:25:52621459391647417694902479 121:26:194294619292236619181178384 121:27:683629216028239956378220240 121:28:2295040939523376996412596520 121:29:7359958875023243471254188840 121:30:22570540550071279978512845776 121:31:66255457743757628324021579536 121:32:186343474904318329661310692445 121:33:502562705044979737571413685685 121:34:1300750530704653438420129539420 121:35:3233294176322995689787179140844 121:36:7723980532327156370047150169794 121:37:17744279601292115985243453092770 121:38:39224197013382572177906580520860 121:39:83477137233609063865801184185420 121:40:171128131328898580924892427580111 121:41:338082405796116708656494795950951 121:42:643966487230698492679037706573240 121:43:1183101220726166998177766949285720 121:44:2097315800378205133133314137370140 121:45:3588740369536039894472559746166684 121:46:5929223219233457216954663928449304 121:47:9461526413670410452587229673057400 121:48:14586519887741882781071979079296825 121:49:21730937791941988633025601485483025 121:50:31292550420396463631556866139095556 121:51:43564138820551939565500735213250676 121:52:58644033027666072492020220479375910 121:53:76347892054886018904705570058055430 121:54:96141789995041653435555162295329060 121:55:117118180539414377821494470432491764 121:56:138032141350024088146761340152579579 121:57:157405073469325714553324335261713555 121:58:173688356931669753989875128564649440 121:59:185463838757545669514612425416490080 121:60:191645966716130525165099506263706416 121:61:191645966716130525165099506263706416 121:62:185463838757545669514612425416490080 121:63:173688356931669753989875128564649440 121:64:157405073469325714553324335261713555 121:65:138032141350024088146761340152579579 121:66:117118180539414377821494470432491764 121:67:96141789995041653435555162295329060 121:68:76347892054886018904705570058055430 121:69:58644033027666072492020220479375910 121:70:43564138820551939565500735213250676 121:71:31292550420396463631556866139095556 121:72:21730937791941988633025601485483025 121:73:14586519887741882781071979079296825 121:74:9461526413670410452587229673057400 121:75:5929223219233457216954663928449304 121:76:3588740369536039894472559746166684 121:77:2097315800378205133133314137370140 121:78:1183101220726166998177766949285720 121:79:643966487230698492679037706573240 121:80:338082405796116708656494795950951 121:81:171128131328898580924892427580111 121:82:83477137233609063865801184185420 121:83:39224197013382572177906580520860 121:84:17744279601292115985243453092770 121:85:7723980532327156370047150169794 121:86:3233294176322995689787179140844 121:87:1300750530704653438420129539420 121:88:502562705044979737571413685685 121:89:186343474904318329661310692445 121:90:66255457743757628324021579536 121:91:22570540550071279978512845776 121:92:7359958875023243471254188840 121:93:2295040939523376996412596520 121:94:683629216028239956378220240 121:95:194294619292236619181178384 121:96:52621459391647417694902479 121:97:13562231801970983941985175 121:98:3321362890278608312322900 121:99:771629762387959506903300 121:100:169758547725351091518726 121:101:35296331705271019028646 121:102:6920849353974709613460 121:103:1276661531315723132580 121:104:220960649650798234485 121:105:35774581372033999869 121:106:5399936810873056584 121:107:757000487505568680 121:108:98129692824795940 121:109:11703541346076580 121:110:1276749965026536 121:111:126524771308936 121:112:11296854581155 121:113:899749479915 121:114:63140314380 121:115:3843323484 121:116:198792594 121:117:8495410 121:118:287980 121:119:7260 121:120:121 121:121:1 # binomial(122, k) for 0 <= k <= 122 122:0:1 122:1:122 122:2:7381 122:3:295240 122:4:8783390 122:5:207288004 122:6:4042116078 122:7:66983637864 122:8:962889794295 122:9:12196604061070 122:10:137821625890091 122:11:1403274736335472 122:12:12980291311103116 122:13:109833234170872520 122:14:855130180330364620 122:15:6156937298378625264 122:16:41174518182907056453 122:17:256735231022832234354 122:18:1497622180966521367065 122:19:8197510885290432746040 122:20:42217181059245728642106 122:21:205054879430622110547372 122:22:941388310113310598422026 122:23:4092992652666567819226200 122:24:16883594692249592254308075 122:25:66183691193618401636887654 122:26:246916078683884036876080863 122:27:877923835320476575559398624 122:28:2978670155551616952790816760 122:29:9654999814546620467666785360 122:30:29930499425094523449767034616 122:31:88825998293828908302534425312 122:32:252598932648075957985332271981 122:33:688906179949298067232724378130 122:34:1803313235749633175991543225105 122:35:4534044707027649128207308680264 122:36:10957274708650152059834329310638 122:37:25468260133619272355290603262564 122:38:56968476614674688163150033613630 122:39:122701334246991636043707764706280 122:40:254605268562507644790693611765531 122:41:509210537125015289581387223531062 122:42:982048893026815201335532502524191 122:43:1827067707956865490856804655858960 122:44:3280417021104372131311081086655860 122:45:5686056169914245027605873883536824 122:46:9517963588769497111427223674615988 122:47:15390749632903867669541893601506704 122:48:24048046301412293233659208752354225 122:49:36317457679683871414097580564779850 122:50:53023488212338452264582467624578581 122:51:74856689240948403197057601352346232 122:52:102208171848218012057520955692626586 122:53:134991925082552091396725790537431340 122:54:172489682049927672340260732353384490 122:55:213259970534456031257049632727820824 122:56:255150321889438465968255810585071343 122:57:295437214819349802700085675414293134 122:58:331093430400995468543199463826362995 122:59:359152195689215423504487553981139520 122:60:377109805473676194679711931680196496 122:61:383291933432261050330199012527412832 122:62:377109805473676194679711931680196496 122:63:359152195689215423504487553981139520 122:64:331093430400995468543199463826362995 122:65:295437214819349802700085675414293134 122:66:255150321889438465968255810585071343 122:67:213259970534456031257049632727820824 122:68:172489682049927672340260732353384490 122:69:134991925082552091396725790537431340 122:70:102208171848218012057520955692626586 122:71:74856689240948403197057601352346232 122:72:53023488212338452264582467624578581 122:73:36317457679683871414097580564779850 122:74:24048046301412293233659208752354225 122:75:15390749632903867669541893601506704 122:76:9517963588769497111427223674615988 122:77:5686056169914245027605873883536824 122:78:3280417021104372131311081086655860 122:79:1827067707956865490856804655858960 122:80:982048893026815201335532502524191 122:81:509210537125015289581387223531062 122:82:254605268562507644790693611765531 122:83:122701334246991636043707764706280 122:84:56968476614674688163150033613630 122:85:25468260133619272355290603262564 122:86:10957274708650152059834329310638 122:87:4534044707027649128207308680264 122:88:1803313235749633175991543225105 122:89:688906179949298067232724378130 122:90:252598932648075957985332271981 122:91:88825998293828908302534425312 122:92:29930499425094523449767034616 122:93:9654999814546620467666785360 122:94:2978670155551616952790816760 122:95:877923835320476575559398624 122:96:246916078683884036876080863 122:97:66183691193618401636887654 122:98:16883594692249592254308075 122:99:4092992652666567819226200 122:100:941388310113310598422026 122:101:205054879430622110547372 122:102:42217181059245728642106 122:103:8197510885290432746040 122:104:1497622180966521367065 122:105:256735231022832234354 122:106:41174518182907056453 122:107:6156937298378625264 122:108:855130180330364620 122:109:109833234170872520 122:110:12980291311103116 122:111:1403274736335472 122:112:137821625890091 122:113:12196604061070 122:114:962889794295 122:115:66983637864 122:116:4042116078 122:117:207288004 122:118:8783390 122:119:295240 122:120:7381 122:121:122 122:122:1 # binomial(123, k) for 0 <= k <= 123 123:0:1 123:1:123 123:2:7503 123:3:302621 123:4:9078630 123:5:216071394 123:6:4249404082 123:7:71025753942 123:8:1029873432159 123:9:13159493855365 123:10:150018229951161 123:11:1541096362225563 123:12:14383566047438588 123:13:122813525481975636 123:14:964963414501237140 123:15:7012067478708989884 123:16:47331455481285681717 123:17:297909749205739290807 123:18:1754357411989353601419 123:19:9695133066256954113105 123:20:50414691944536161388146 123:21:247272060489867839189478 123:22:1146443189543932708969398 123:23:5034380962779878417648226 123:24:20976587344916160073534275 123:25:83067285885867993891195729 123:26:313099769877502438512968517 123:27:1124839914004360612435479487 123:28:3856593990872093528350215384 123:29:12633669970098237420457602120 123:30:39585499239641143917433819976 123:31:118756497718923431752301459928 123:32:341424930941904866287866697293 123:33:941505112597374025218056650111 123:34:2492219415698931243224267603235 123:35:6337357942777282304198851905369 123:36:15491319415677801188041637990902 123:37:36425534842269424415124932573202 123:38:82436736748293960518440636876194 123:39:179669810861666324206857798319910 123:40:377306602809499280834401376471811 123:41:763815805687522934372080835296593 123:42:1491259430151830490916919726055253 123:43:2809116600983680692192337158383151 123:44:5107484729061237622167885742514820 123:45:8966473191018617158916954970192684 123:46:15204019758683742139033097558152812 123:47:24908713221673364780969117276122692 123:48:39438795934316160903201102353860929 123:49:60365503981096164647756789317134075 123:50:89340945892022323678680048189358431 123:51:127880177453286855461640068976924813 123:52:177064861089166415254578557044972818 123:53:237200096930770103454246746230057926 123:54:307481607132479763736986522890815830 123:55:385749652584383703597310365081205314 123:56:468410292423894497225305443312892167 123:57:550587536708788268668341485999364477 123:58:626530645220345271243285139240656129 123:59:690245626090210892047687017807502515 123:60:736262001162891618184199485661336016 123:61:760401738905937245009910944207609328 123:62:760401738905937245009910944207609328 123:63:736262001162891618184199485661336016 123:64:690245626090210892047687017807502515 123:65:626530645220345271243285139240656129 123:66:550587536708788268668341485999364477 123:67:468410292423894497225305443312892167 123:68:385749652584383703597310365081205314 123:69:307481607132479763736986522890815830 123:70:237200096930770103454246746230057926 123:71:177064861089166415254578557044972818 123:72:127880177453286855461640068976924813 123:73:89340945892022323678680048189358431 123:74:60365503981096164647756789317134075 123:75:39438795934316160903201102353860929 123:76:24908713221673364780969117276122692 123:77:15204019758683742139033097558152812 123:78:8966473191018617158916954970192684 123:79:5107484729061237622167885742514820 123:80:2809116600983680692192337158383151 123:81:1491259430151830490916919726055253 123:82:763815805687522934372080835296593 123:83:377306602809499280834401376471811 123:84:179669810861666324206857798319910 123:85:82436736748293960518440636876194 123:86:36425534842269424415124932573202 123:87:15491319415677801188041637990902 123:88:6337357942777282304198851905369 123:89:2492219415698931243224267603235 123:90:941505112597374025218056650111 123:91:341424930941904866287866697293 123:92:118756497718923431752301459928 123:93:39585499239641143917433819976 123:94:12633669970098237420457602120 123:95:3856593990872093528350215384 123:96:1124839914004360612435479487 123:97:313099769877502438512968517 123:98:83067285885867993891195729 123:99:20976587344916160073534275 123:100:5034380962779878417648226 123:101:1146443189543932708969398 123:102:247272060489867839189478 123:103:50414691944536161388146 123:104:9695133066256954113105 123:105:1754357411989353601419 123:106:297909749205739290807 123:107:47331455481285681717 123:108:7012067478708989884 123:109:964963414501237140 123:110:122813525481975636 123:111:14383566047438588 123:112:1541096362225563 123:113:150018229951161 123:114:13159493855365 123:115:1029873432159 123:116:71025753942 123:117:4249404082 123:118:216071394 123:119:9078630 123:120:302621 123:121:7503 123:122:123 123:123:1 # binomial(124, k) for 0 <= k <= 124 124:0:1 124:1:124 124:2:7626 124:3:310124 124:4:9381251 124:5:225150024 124:6:4465475476 124:7:75275158024 124:8:1100899186101 124:9:14189367287524 124:10:163177723806526 124:11:1691114592176724 124:12:15924662409664151 124:13:137197091529414224 124:14:1087776939983212776 124:15:7977030893210227024 124:16:54343522959994671601 124:17:345241204687024972524 124:18:2052267161195092892226 124:19:11449490478246307714524 124:20:60109825010793115501251 124:21:297686752434404000577624 124:22:1393715250033800548158876 124:23:6180824152323811126617624 124:24:26010968307696038491182501 124:25:104043873230784153964730004 124:26:396167055763370432404164246 124:27:1437939683881863050948448004 124:28:4981433904876454140785694871 124:29:16490263960970330948807817504 124:30:52219169209739381337891422096 124:31:158341996958564575669735279904 124:32:460181428660828298040168157221 124:33:1282930043539278891505923347404 124:34:3433724528296305268442324253346 124:35:8829577358476213547423119508604 124:36:21828677358455083492240489896271 124:37:51916854257947225603166570564104 124:38:118862271590563384933565569449396 124:39:262106547609960284725298435196104 124:40:556976413671165605041259174791721 124:41:1141122408497022215206482211768404 124:42:2255075235839353425289000561351846 124:43:4300376031135511183109256884438404 124:44:7916601330044918314360222900897971 124:45:14073957920079854781084840712707504 124:46:24170492949702359297950052528345496 124:47:40112732980357106920002214834275504 124:48:64347509155989525684170219629983621 124:49:99804299915412325550957891670995004 124:50:149706449873118488326436837506492506 124:51:217221123345309179140320117166283244 124:52:304945038542453270716218626021897631 124:53:414264958019936518708825303275030744 124:54:544681704063249867191233269120873756 124:55:693231259716863467334296887972021144 124:56:854159945008278200822615808394097481 124:57:1018997829132682765893646929312256644 124:58:1177118181929133539911626625240020606 124:59:1316776271310556163290972157048158644 124:60:1426507627253102510231886503468838531 124:61:1496663740068828863194110429868945344 124:62:1520803477811874490019821888415218656 124:63:1496663740068828863194110429868945344 124:64:1426507627253102510231886503468838531 124:65:1316776271310556163290972157048158644 124:66:1177118181929133539911626625240020606 124:67:1018997829132682765893646929312256644 124:68:854159945008278200822615808394097481 124:69:693231259716863467334296887972021144 124:70:544681704063249867191233269120873756 124:71:414264958019936518708825303275030744 124:72:304945038542453270716218626021897631 124:73:217221123345309179140320117166283244 124:74:149706449873118488326436837506492506 124:75:99804299915412325550957891670995004 124:76:64347509155989525684170219629983621 124:77:40112732980357106920002214834275504 124:78:24170492949702359297950052528345496 124:79:14073957920079854781084840712707504 124:80:7916601330044918314360222900897971 124:81:4300376031135511183109256884438404 124:82:2255075235839353425289000561351846 124:83:1141122408497022215206482211768404 124:84:556976413671165605041259174791721 124:85:262106547609960284725298435196104 124:86:118862271590563384933565569449396 124:87:51916854257947225603166570564104 124:88:21828677358455083492240489896271 124:89:8829577358476213547423119508604 124:90:3433724528296305268442324253346 124:91:1282930043539278891505923347404 124:92:460181428660828298040168157221 124:93:158341996958564575669735279904 124:94:52219169209739381337891422096 124:95:16490263960970330948807817504 124:96:4981433904876454140785694871 124:97:1437939683881863050948448004 124:98:396167055763370432404164246 124:99:104043873230784153964730004 124:100:26010968307696038491182501 124:101:6180824152323811126617624 124:102:1393715250033800548158876 124:103:297686752434404000577624 124:104:60109825010793115501251 124:105:11449490478246307714524 124:106:2052267161195092892226 124:107:345241204687024972524 124:108:54343522959994671601 124:109:7977030893210227024 124:110:1087776939983212776 124:111:137197091529414224 124:112:15924662409664151 124:113:1691114592176724 124:114:163177723806526 124:115:14189367287524 124:116:1100899186101 124:117:75275158024 124:118:4465475476 124:119:225150024 124:120:9381251 124:121:310124 124:122:7626 124:123:124 124:124:1 # binomial(125, k) for 0 <= k <= 125 125:0:1 125:1:125 125:2:7750 125:3:317750 125:4:9691375 125:5:234531275 125:6:4690625500 125:7:79740633500 125:8:1176174344125 125:9:15290266473625 125:10:177367091094050 125:11:1854292315983250 125:12:17615777001840875 125:13:153121753939078375 125:14:1224974031512627000 125:15:9064807833193439800 125:16:62320553853204898625 125:17:399584727647019644125 125:18:2397508365882117864750 125:19:13501757639441400606750 125:20:71559315489039423215775 125:21:357796577445197116078875 125:22:1691402002468204548736500 125:23:7574539402357611674776500 125:24:32191792460019849617800125 125:25:130054841538480192455912505 125:26:500210928994154586368894250 125:27:1834106739645233483352612250 125:28:6419373588758317191734142875 125:29:21471697865846785089593512375 125:30:68709433170709712286699239600 125:31:210561166168303957007626702000 125:32:618523425619392873709903437125 125:33:1743111472200107189546091504625 125:34:4716654571835584159948247600750 125:35:12263301886772518815865443761950 125:36:30658254716931297039663609404875 125:37:73745531616402309095407060460375 125:38:170779125848510610536732140013500 125:39:380968819200523669658864004645500 125:40:819082961281125889766557609987825 125:41:1698098822168187820247741386560125 125:42:3396197644336375640495482773120250 125:43:6555451266974864608398257445790250 125:44:12216977361180429497469479785336375 125:45:21990559250124773095445063613605475 125:46:38244450869782214079034893241053000 125:47:64283225930059466217952267362621000 125:48:104460242136346632604172434464259125 125:49:164151809071401851235128111300978625 125:50:249510749788530813877394729177487510 125:51:366927573218427667466756954672775750 125:52:522166161887762449856538743188180875 125:53:719209996562389789425043929296928375 125:54:958946662083186385900058572395904500 125:55:1237912963780113334525530157092894900 125:56:1547391204725141668156912696366118625 125:57:1873157774140960966716262737706354125 125:58:2196116011061816305805273554552277250 125:59:2493894453239689703202598782288179250 125:60:2743283898563658673522858660516997175 125:61:2923171367321931373425996933337783875 125:62:3017467217880703353213932318284164000 125:63:3017467217880703353213932318284164000 125:64:2923171367321931373425996933337783875 125:65:2743283898563658673522858660516997175 125:66:2493894453239689703202598782288179250 125:67:2196116011061816305805273554552277250 125:68:1873157774140960966716262737706354125 125:69:1547391204725141668156912696366118625 125:70:1237912963780113334525530157092894900 125:71:958946662083186385900058572395904500 125:72:719209996562389789425043929296928375 125:73:522166161887762449856538743188180875 125:74:366927573218427667466756954672775750 125:75:249510749788530813877394729177487510 125:76:164151809071401851235128111300978625 125:77:104460242136346632604172434464259125 125:78:64283225930059466217952267362621000 125:79:38244450869782214079034893241053000 125:80:21990559250124773095445063613605475 125:81:12216977361180429497469479785336375 125:82:6555451266974864608398257445790250 125:83:3396197644336375640495482773120250 125:84:1698098822168187820247741386560125 125:85:819082961281125889766557609987825 125:86:380968819200523669658864004645500 125:87:170779125848510610536732140013500 125:88:73745531616402309095407060460375 125:89:30658254716931297039663609404875 125:90:12263301886772518815865443761950 125:91:4716654571835584159948247600750 125:92:1743111472200107189546091504625 125:93:618523425619392873709903437125 125:94:210561166168303957007626702000 125:95:68709433170709712286699239600 125:96:21471697865846785089593512375 125:97:6419373588758317191734142875 125:98:1834106739645233483352612250 125:99:500210928994154586368894250 125:100:130054841538480192455912505 125:101:32191792460019849617800125 125:102:7574539402357611674776500 125:103:1691402002468204548736500 125:104:357796577445197116078875 125:105:71559315489039423215775 125:106:13501757639441400606750 125:107:2397508365882117864750 125:108:399584727647019644125 125:109:62320553853204898625 125:110:9064807833193439800 125:111:1224974031512627000 125:112:153121753939078375 125:113:17615777001840875 125:114:1854292315983250 125:115:177367091094050 125:116:15290266473625 125:117:1176174344125 125:118:79740633500 125:119:4690625500 125:120:234531275 125:121:9691375 125:122:317750 125:123:7750 125:124:125 125:125:1 # binomial(126, k) for 0 <= k <= 126 126:0:1 126:1:126 126:2:7875 126:3:325500 126:4:10009125 126:5:244222650 126:6:4925156775 126:7:84431259000 126:8:1255914977625 126:9:16466440817750 126:10:192657357567675 126:11:2031659407077300 126:12:19470069317824125 126:13:170737530940919250 126:14:1378095785451705375 126:15:10289781864706066800 126:16:71385361686398338425 126:17:461905281500224542750 126:18:2797093093529137508875 126:19:15899266005323518471500 126:20:85061073128480823822525 126:21:429355892934236539294650 126:22:2049198579913401664815375 126:23:9265941404825816223513000 126:24:39766331862377461292576625 126:25:162246633998500042073712630 126:26:630265770532634778824806755 126:27:2334317668639388069721506500 126:28:8253480328403550675086755125 126:29:27891071454605102281327655250 126:30:90181131036556497376292751975 126:31:279270599339013669294325941600 126:32:829084591787696830717530139125 126:33:2361634897819500063255994941750 126:34:6459766044035691349494339105375 126:35:16979956458608102975813691362700 126:36:42921556603703815855529053166825 126:37:104403786333333606135070669865250 126:38:244524657464912919632139200473875 126:39:551747945049034280195596144659000 126:40:1200051780481649559425421614633325 126:41:2517181783449313710014298996547950 126:42:5094296466504563460743224159680375 126:43:9951648911311240248893740218910500 126:44:18772428628155294105867737231126625 126:45:34207536611305202592914543398941850 126:46:60235010119906987174479956854658475 126:47:102527676799841680296987160603674000 126:48:168743468066406098822124701826880125 126:49:268612051207748483839300545765237750 126:50:413662558859932665112522840478466135 126:51:616438323006958481344151683850263260 126:52:889093735106190117323295697860956625 126:53:1241376158450152239281582672485109250 126:54:1678156658645576175325102501692832875 126:55:2196859625863299720425588729488799400 126:56:2785304168505255002682442853459013525 126:57:3420548978866102634873175434072472750 126:58:4069273785202777272521536292258631375 126:59:4690010464301506009007872336840456500 126:60:5237178351803348376725457442805176425 126:61:5666455265885590046948855593854781050 126:62:5940638585202634726639929251621947875 126:63:6034934435761406706427864636568328000 126:64:5940638585202634726639929251621947875 126:65:5666455265885590046948855593854781050 126:66:5237178351803348376725457442805176425 126:67:4690010464301506009007872336840456500 126:68:4069273785202777272521536292258631375 126:69:3420548978866102634873175434072472750 126:70:2785304168505255002682442853459013525 126:71:2196859625863299720425588729488799400 126:72:1678156658645576175325102501692832875 126:73:1241376158450152239281582672485109250 126:74:889093735106190117323295697860956625 126:75:616438323006958481344151683850263260 126:76:413662558859932665112522840478466135 126:77:268612051207748483839300545765237750 126:78:168743468066406098822124701826880125 126:79:102527676799841680296987160603674000 126:80:60235010119906987174479956854658475 126:81:34207536611305202592914543398941850 126:82:18772428628155294105867737231126625 126:83:9951648911311240248893740218910500 126:84:5094296466504563460743224159680375 126:85:2517181783449313710014298996547950 126:86:1200051780481649559425421614633325 126:87:551747945049034280195596144659000 126:88:244524657464912919632139200473875 126:89:104403786333333606135070669865250 126:90:42921556603703815855529053166825 126:91:16979956458608102975813691362700 126:92:6459766044035691349494339105375 126:93:2361634897819500063255994941750 126:94:829084591787696830717530139125 126:95:279270599339013669294325941600 126:96:90181131036556497376292751975 126:97:27891071454605102281327655250 126:98:8253480328403550675086755125 126:99:2334317668639388069721506500 126:100:630265770532634778824806755 126:101:162246633998500042073712630 126:102:39766331862377461292576625 126:103:9265941404825816223513000 126:104:2049198579913401664815375 126:105:429355892934236539294650 126:106:85061073128480823822525 126:107:15899266005323518471500 126:108:2797093093529137508875 126:109:461905281500224542750 126:110:71385361686398338425 126:111:10289781864706066800 126:112:1378095785451705375 126:113:170737530940919250 126:114:19470069317824125 126:115:2031659407077300 126:116:192657357567675 126:117:16466440817750 126:118:1255914977625 126:119:84431259000 126:120:4925156775 126:121:244222650 126:122:10009125 126:123:325500 126:124:7875 126:125:126 126:126:1 # binomial(127, k) for 0 <= k <= 127 127:0:1 127:1:127 127:2:8001 127:3:333375 127:4:10334625 127:5:254231775 127:6:5169379425 127:7:89356415775 127:8:1340346236625 127:9:17722355795375 127:10:209123798385425 127:11:2224316764644975 127:12:21501728724901425 127:13:190207600258743375 127:14:1548833316392624625 127:15:11667877650157772175 127:16:81675143551104405225 127:17:533290643186622881175 127:18:3258998375029362051625 127:19:18696359098852655980375 127:20:100960339133804342294025 127:21:514416966062717363117175 127:22:2478554472847638204110025 127:23:11315139984739217888328375 127:24:49032273267203277516089625 127:25:202012965860877503366289255 127:26:792512404531134820898519385 127:27:2964583439172022848546313255 127:28:10587797997042938744808261625 127:29:36144551783008652956414410375 127:30:118072202491161599657620407225 127:31:369451730375570166670618693575 127:32:1108355191126710500011856080725 127:33:3190719489607196893973525080875 127:34:8821400941855191412750334047125 127:35:23439722502643794325308030468075 127:36:59901513062311918831342744529525 127:37:147325342937037421990599723032075 127:38:348928443798246525767209870339125 127:39:796272602513947199827735345132875 127:40:1751799725530683839621017759292325 127:41:3717233563930963269439720611181275 127:42:7611478249953877170757523156228325 127:43:15045945377815803709636964378590875 127:44:28724077539466534354761477450037125 127:45:52979965239460496698782280630068475 127:46:94442546731212189767394500253600325 127:47:162762686919748667471467117458332475 127:48:271271144866247779119111862430554125 127:49:437355519274154582661425247592117875 127:50:682274610067681148951823386243703885 127:51:1030100881866891146456674524328729395 127:52:1505532058113148598667447381711219885 127:53:2130469893556342356604878370346065875 127:54:2919532817095728414606685174177942125 127:55:3875016284508875895750691231181632275 127:56:4982163794368554723108031582947812925 127:57:6205853147371357637555618287531486275 127:58:7489822764068879907394711726331104125 127:59:8759284249504283281529408629099087875 127:60:9927188816104854385733329779645632925 127:61:10903633617688938423674313036659957475 127:62:11607093851088224773588784845476728925 127:63:11975573020964041433067793888190275875 127:64:11975573020964041433067793888190275875 127:65:11607093851088224773588784845476728925 127:66:10903633617688938423674313036659957475 127:67:9927188816104854385733329779645632925 127:68:8759284249504283281529408629099087875 127:69:7489822764068879907394711726331104125 127:70:6205853147371357637555618287531486275 127:71:4982163794368554723108031582947812925 127:72:3875016284508875895750691231181632275 127:73:2919532817095728414606685174177942125 127:74:2130469893556342356604878370346065875 127:75:1505532058113148598667447381711219885 127:76:1030100881866891146456674524328729395 127:77:682274610067681148951823386243703885 127:78:437355519274154582661425247592117875 127:79:271271144866247779119111862430554125 127:80:162762686919748667471467117458332475 127:81:94442546731212189767394500253600325 127:82:52979965239460496698782280630068475 127:83:28724077539466534354761477450037125 127:84:15045945377815803709636964378590875 127:85:7611478249953877170757523156228325 127:86:3717233563930963269439720611181275 127:87:1751799725530683839621017759292325 127:88:796272602513947199827735345132875 127:89:348928443798246525767209870339125 127:90:147325342937037421990599723032075 127:91:59901513062311918831342744529525 127:92:23439722502643794325308030468075 127:93:8821400941855191412750334047125 127:94:3190719489607196893973525080875 127:95:1108355191126710500011856080725 127:96:369451730375570166670618693575 127:97:118072202491161599657620407225 127:98:36144551783008652956414410375 127:99:10587797997042938744808261625 127:100:2964583439172022848546313255 127:101:792512404531134820898519385 127:102:202012965860877503366289255 127:103:49032273267203277516089625 127:104:11315139984739217888328375 127:105:2478554472847638204110025 127:106:514416966062717363117175 127:107:100960339133804342294025 127:108:18696359098852655980375 127:109:3258998375029362051625 127:110:533290643186622881175 127:111:81675143551104405225 127:112:11667877650157772175 127:113:1548833316392624625 127:114:190207600258743375 127:115:21501728724901425 127:116:2224316764644975 127:117:209123798385425 127:118:17722355795375 127:119:1340346236625 127:120:89356415775 127:121:5169379425 127:122:254231775 127:123:10334625 127:124:333375 127:125:8001 127:126:127 127:127:1 # binomial(128, k) for 0 <= k <= 128 128:0:1 128:1:128 128:2:8128 128:3:341376 128:4:10668000 128:5:264566400 128:6:5423611200 128:7:94525795200 128:8:1429702652400 128:9:19062702032000 128:10:226846154180800 128:11:2433440563030400 128:12:23726045489546400 128:13:211709328983644800 128:14:1739040916651368000 128:15:13216710966550396800 128:16:93343021201262177400 128:17:614965786737727286400 128:18:3792289018215984932800 128:19:21955357473882018032000 128:20:119656698232656998274400 128:21:615377305196521705411200 128:22:2992971438910355567227200 128:23:13793694457586856092438400 128:24:60347413251942495404418000 128:25:251045239128080780882378880 128:26:994525370392012324264808640 128:27:3757095843703157669444832640 128:28:13552381436214961593354574880 128:29:46732349780051591701222672000 128:30:154216754274170252614034817600 128:31:487523932866731766328239100800 128:32:1477806921502280666682474774300 128:33:4299074680733907393985381161600 128:34:12012120431462388306723859128000 128:35:32261123444498985738058364515200 128:36:83341235564955713156650774997600 128:37:207226855999349340821942467561600 128:38:496253786735283947757809593371200 128:39:1145201046312193725594945215472000 128:40:2548072328044631039448753104425200 128:41:5469033289461647109060738370473600 128:42:11328711813884840440197243767409600 128:43:22657423627769680880394487534819200 128:44:43770022917282338064398441828628000 128:45:81704042778927031053543758080105600 128:46:147422511970672686466176780883668800 128:47:257205233650960857238861617711932800 128:48:434033831785996446590578979888886600 128:49:708626664140402361780537110022672000 128:50:1119630129341835731613248633835821760 128:51:1712375491934572295408497910572433280 128:52:2535632939980039745124121906039949280 128:53:3636001951669490955272325752057285760 128:54:5050002710652070771211563544524008000 128:55:6794549101604604310357376405359574400 128:56:8857180078877430618858722814129445200 128:57:11188016941739912360663649870479299200 128:58:13695675911440237544950330013862590400 128:59:16249107013573163188924120355430192000 128:60:18686473065609137667262738408744720800 128:61:20830822433793792809407642816305590400 128:62:22510727468777163197263097882136686400 128:63:23582666872052266206656578733667004800 128:64:23951146041928082866135587776380551750 128:65:23582666872052266206656578733667004800 128:66:22510727468777163197263097882136686400 128:67:20830822433793792809407642816305590400 128:68:18686473065609137667262738408744720800 128:69:16249107013573163188924120355430192000 128:70:13695675911440237544950330013862590400 128:71:11188016941739912360663649870479299200 128:72:8857180078877430618858722814129445200 128:73:6794549101604604310357376405359574400 128:74:5050002710652070771211563544524008000 128:75:3636001951669490955272325752057285760 128:76:2535632939980039745124121906039949280 128:77:1712375491934572295408497910572433280 128:78:1119630129341835731613248633835821760 128:79:708626664140402361780537110022672000 128:80:434033831785996446590578979888886600 128:81:257205233650960857238861617711932800 128:82:147422511970672686466176780883668800 128:83:81704042778927031053543758080105600 128:84:43770022917282338064398441828628000 128:85:22657423627769680880394487534819200 128:86:11328711813884840440197243767409600 128:87:5469033289461647109060738370473600 128:88:2548072328044631039448753104425200 128:89:1145201046312193725594945215472000 128:90:496253786735283947757809593371200 128:91:207226855999349340821942467561600 128:92:83341235564955713156650774997600 128:93:32261123444498985738058364515200 128:94:12012120431462388306723859128000 128:95:4299074680733907393985381161600 128:96:1477806921502280666682474774300 128:97:487523932866731766328239100800 128:98:154216754274170252614034817600 128:99:46732349780051591701222672000 128:100:13552381436214961593354574880 128:101:3757095843703157669444832640 128:102:994525370392012324264808640 128:103:251045239128080780882378880 128:104:60347413251942495404418000 128:105:13793694457586856092438400 128:106:2992971438910355567227200 128:107:615377305196521705411200 128:108:119656698232656998274400 128:109:21955357473882018032000 128:110:3792289018215984932800 128:111:614965786737727286400 128:112:93343021201262177400 128:113:13216710966550396800 128:114:1739040916651368000 128:115:211709328983644800 128:116:23726045489546400 128:117:2433440563030400 128:118:226846154180800 128:119:19062702032000 128:120:1429702652400 128:121:94525795200 128:122:5423611200 128:123:264566400 128:124:10668000 128:125:341376 128:126:8128 128:127:128 128:128:1 # binomial(129, k) for 0 <= k <= 129 129:0:1 129:1:129 129:2:8256 129:3:349504 129:4:11009376 129:5:275234400 129:6:5688177600 129:7:99949406400 129:8:1524228447600 129:9:20492404684400 129:10:245908856212800 129:11:2660286717211200 129:12:26159486052576800 129:13:235435374473191200 129:14:1950750245635012800 129:15:14955751883201764800 129:16:106559732167812574200 129:17:708308807938989463800 129:18:4407254804953712219200 129:19:25747646492098002964800 129:20:141612055706539016306400 129:21:735034003429178703685600 129:22:3608348744106877272638400 129:23:16786665896497211659665600 129:24:74141107709529351496856400 129:25:311392652380023276286796880 129:26:1245570609520093105147187520 129:27:4751621214095169993709641280 129:28:17309477279918119262799407520 129:29:60284731216266553294577246880 129:30:200949104054221844315257489600 129:31:641740687140902018942273918400 129:32:1965330854369012433010713875100 129:33:5776881602236188060667855935900 129:34:16311195112196295700709240289600 129:35:44273243875961374044782223643200 129:36:115602359009454698894709139512800 129:37:290568091564305053978593242559200 129:38:703480642734633288579752060932800 129:39:1641454833047477673352754808843200 129:40:3693273374356824765043698319897200 129:41:8017105617506278148509491474898800 129:42:16797745103346487549257982137883200 129:43:33986135441654521320591731302228800 129:44:66427446545052018944792929363447200 129:45:125474065696209369117942199908733600 129:46:229126554749599717519720538963774400 129:47:404627745621633543705038398595601600 129:48:691239065436957303829440597600819400 129:49:1142660495926398808371116089911558600 129:50:1828256793482238093393785743858493760 129:51:2832005621276408027021746544408255040 129:52:4248008431914612040532619816612382560 129:53:6171634891649530700396447658097235040 129:54:8686004662321561726483889296581293760 129:55:11844551812256675081568939949883582400 129:56:15651729180482034929216099219489019600 129:57:20045197020617342979522372684608744400 129:58:24883692853180149905613979884341889600 129:59:29944782925013400733874450369292782400 129:60:34935580079182300856186858764174912800 129:61:39517295499402930476670381225050311200 129:62:43341549902570956006670740698442276800 129:63:46093394340829429403919676615803691200 129:64:47533812913980349072792166510047556550 129:65:47533812913980349072792166510047556550 129:66:46093394340829429403919676615803691200 129:67:43341549902570956006670740698442276800 129:68:39517295499402930476670381225050311200 129:69:34935580079182300856186858764174912800 129:70:29944782925013400733874450369292782400 129:71:24883692853180149905613979884341889600 129:72:20045197020617342979522372684608744400 129:73:15651729180482034929216099219489019600 129:74:11844551812256675081568939949883582400 129:75:8686004662321561726483889296581293760 129:76:6171634891649530700396447658097235040 129:77:4248008431914612040532619816612382560 129:78:2832005621276408027021746544408255040 129:79:1828256793482238093393785743858493760 129:80:1142660495926398808371116089911558600 129:81:691239065436957303829440597600819400 129:82:404627745621633543705038398595601600 129:83:229126554749599717519720538963774400 129:84:125474065696209369117942199908733600 129:85:66427446545052018944792929363447200 129:86:33986135441654521320591731302228800 129:87:16797745103346487549257982137883200 129:88:8017105617506278148509491474898800 129:89:3693273374356824765043698319897200 129:90:1641454833047477673352754808843200 129:91:703480642734633288579752060932800 129:92:290568091564305053978593242559200 129:93:115602359009454698894709139512800 129:94:44273243875961374044782223643200 129:95:16311195112196295700709240289600 129:96:5776881602236188060667855935900 129:97:1965330854369012433010713875100 129:98:641740687140902018942273918400 129:99:200949104054221844315257489600 129:100:60284731216266553294577246880 129:101:17309477279918119262799407520 129:102:4751621214095169993709641280 129:103:1245570609520093105147187520 129:104:311392652380023276286796880 129:105:74141107709529351496856400 129:106:16786665896497211659665600 129:107:3608348744106877272638400 129:108:735034003429178703685600 129:109:141612055706539016306400 129:110:25747646492098002964800 129:111:4407254804953712219200 129:112:708308807938989463800 129:113:106559732167812574200 129:114:14955751883201764800 129:115:1950750245635012800 129:116:235435374473191200 129:117:26159486052576800 129:118:2660286717211200 129:119:245908856212800 129:120:20492404684400 129:121:1524228447600 129:122:99949406400 129:123:5688177600 129:124:275234400 129:125:11009376 129:126:349504 129:127:8256 129:128:129 129:129:1 # binomial(130, k) for 0 <= k <= 130 130:0:1 130:1:130 130:2:8385 130:3:357760 130:4:11358880 130:5:286243776 130:6:5963412000 130:7:105637584000 130:8:1624177854000 130:9:22016633132000 130:10:266401260897200 130:11:2906195573424000 130:12:28819772769788000 130:13:261594860525768000 130:14:2186185620108204000 130:15:16906502128836777600 130:16:121515484051014339000 130:17:814868540106802038000 130:18:5115563612892701683000 130:19:30154901297051715184000 130:20:167359702198637019271200 130:21:876646059135717719992000 130:22:4343382747536055976324000 130:23:20395014640604088932304000 130:24:90927773606026563156522000 130:25:385533760089552627783653280 130:26:1556963261900116381433984400 130:27:5997191823615263098856828800 130:28:22061098494013289256509048800 130:29:77594208496184672557376654400 130:30:261233835270488397609834736480 130:31:842689791195123863257531408000 130:32:2607071541509914451952987793500 130:33:7742212456605200493678569811000 130:34:22088076714432483761377096225500 130:35:60584438988157669745491463932800 130:36:159875602885416072939491363156000 130:37:406170450573759752873302382072000 130:38:994048734298938342558345303492000 130:39:2344935475782110961932506869776000 130:40:5334728207404302438396453128740400 130:41:11710378991863102913553189794796000 130:42:24814850720852765697767473612782000 130:43:50783880545001008869849713440112000 130:44:100413581986706540265384660665676000 130:45:191901512241261388062735129272180800 130:46:354600620445809086637662738872508000 130:47:633754300371233261224758937559376000 130:48:1095866811058590847534478996196421000 130:49:1833899561363356112200556687512378000 130:50:2970917289408636901764901833770052360 130:51:4660262414758646120415532288266748800 130:52:7080014053191020067554366361020637600 130:53:10419643323564142740929067474709617600 130:54:14857639553971092426880336954678528800 130:55:20530556474578236808052829246464876160 130:56:27496280992738710010785039169372602000 130:57:35696926201099377908738471904097764000 130:58:44928889873797492885136352568950634000 130:59:54828475778193550639488430253634672000 130:60:64880363004195701590061309133467695200 130:61:74452875578585231332857239989225224000 130:62:82858845401973886483341121923492588000 130:63:89434944243400385410590417314245968000 130:64:93627207254809778476711843125851247750 130:65:95067625827960698145584333020095113100 130:66:93627207254809778476711843125851247750 130:67:89434944243400385410590417314245968000 130:68:82858845401973886483341121923492588000 130:69:74452875578585231332857239989225224000 130:70:64880363004195701590061309133467695200 130:71:54828475778193550639488430253634672000 130:72:44928889873797492885136352568950634000 130:73:35696926201099377908738471904097764000 130:74:27496280992738710010785039169372602000 130:75:20530556474578236808052829246464876160 130:76:14857639553971092426880336954678528800 130:77:10419643323564142740929067474709617600 130:78:7080014053191020067554366361020637600 130:79:4660262414758646120415532288266748800 130:80:2970917289408636901764901833770052360 130:81:1833899561363356112200556687512378000 130:82:1095866811058590847534478996196421000 130:83:633754300371233261224758937559376000 130:84:354600620445809086637662738872508000 130:85:191901512241261388062735129272180800 130:86:100413581986706540265384660665676000 130:87:50783880545001008869849713440112000 130:88:24814850720852765697767473612782000 130:89:11710378991863102913553189794796000 130:90:5334728207404302438396453128740400 130:91:2344935475782110961932506869776000 130:92:994048734298938342558345303492000 130:93:406170450573759752873302382072000 130:94:159875602885416072939491363156000 130:95:60584438988157669745491463932800 130:96:22088076714432483761377096225500 130:97:7742212456605200493678569811000 130:98:2607071541509914451952987793500 130:99:842689791195123863257531408000 130:100:261233835270488397609834736480 130:101:77594208496184672557376654400 130:102:22061098494013289256509048800 130:103:5997191823615263098856828800 130:104:1556963261900116381433984400 130:105:385533760089552627783653280 130:106:90927773606026563156522000 130:107:20395014640604088932304000 130:108:4343382747536055976324000 130:109:876646059135717719992000 130:110:167359702198637019271200 130:111:30154901297051715184000 130:112:5115563612892701683000 130:113:814868540106802038000 130:114:121515484051014339000 130:115:16906502128836777600 130:116:2186185620108204000 130:117:261594860525768000 130:118:28819772769788000 130:119:2906195573424000 130:120:266401260897200 130:121:22016633132000 130:122:1624177854000 130:123:105637584000 130:124:5963412000 130:125:286243776 130:126:11358880 130:127:357760 130:128:8385 130:129:130 130:130:1 # binomial(131, k) for 0 <= k <= 131 131:0:1 131:1:131 131:2:8515 131:3:366145 131:4:11716640 131:5:297602656 131:6:6249655776 131:7:111600996000 131:8:1729815438000 131:9:23640810986000 131:10:288417894029200 131:11:3172596834321200 131:12:31725968343212000 131:13:290414633295556000 131:14:2447780480633972000 131:15:19092687748944981600 131:16:138421986179851116600 131:17:936384024157816377000 131:18:5930432152999503721000 131:19:35270464909944416867000 131:20:197514603495688734455200 131:21:1044005761334354739263200 131:22:5220028806671773696316000 131:23:24738397388140144908628000 131:24:111322788246630652088826000 131:25:476461533695579190940175280 131:26:1942497021989669009217637680 131:27:7554155085515379480290813200 131:28:28058290317628552355365877600 131:29:99655306990197961813885703200 131:30:338828043766673070167211390880 131:31:1103923626465612260867366144480 131:32:3449761332705038315210519201500 131:33:10349283998115114945631557604500 131:34:29830289171037684255055666036500 131:35:82672515702590153506868560158300 131:36:220460041873573742684982827088800 131:37:566046053459175825812793745228000 131:38:1400219184872698095431647685564000 131:39:3338984210081049304490852173268000 131:40:7679663683186413400328959998516400 131:41:17045107199267405351949642923536400 131:42:36525229712715868611320663407578000 131:43:75598731265853774567617187052894000 131:44:151197462531707549135234374105788000 131:45:292315094227967928328119789937856800 131:46:546502132687070474700397868144688800 131:47:988354920817042347862421676431884000 131:48:1729621111429824108759237933755797000 131:49:2929766372421946959735035683708799000 131:50:4804816850771993013965458521282430360 131:51:7631179704167283022180434122036801160 131:52:11740276467949666187969898649287386400 131:53:17499657376755162808483433835730255200 131:54:25277282877535235167809404429388146400 131:55:35388196028549329234933166201143404960 131:56:48026837467316946818837868415837478160 131:57:63193207193838087919523511073470366000 131:58:80625816074896870793874824473048398000 131:59:99757365651991043524624782822585306000 131:60:119708838782389252229549739387102367200 131:61:139333238582780932922918549122692919200 131:62:157311720980559117816198361912717812000 131:63:172293789645374271893931539237738556000 131:64:183062151498210163887302260440097215750 131:65:188694833082770476622296176145946360850 131:66:188694833082770476622296176145946360850 131:67:183062151498210163887302260440097215750 131:68:172293789645374271893931539237738556000 131:69:157311720980559117816198361912717812000 131:70:139333238582780932922918549122692919200 131:71:119708838782389252229549739387102367200 131:72:99757365651991043524624782822585306000 131:73:80625816074896870793874824473048398000 131:74:63193207193838087919523511073470366000 131:75:48026837467316946818837868415837478160 131:76:35388196028549329234933166201143404960 131:77:25277282877535235167809404429388146400 131:78:17499657376755162808483433835730255200 131:79:11740276467949666187969898649287386400 131:80:7631179704167283022180434122036801160 131:81:4804816850771993013965458521282430360 131:82:2929766372421946959735035683708799000 131:83:1729621111429824108759237933755797000 131:84:988354920817042347862421676431884000 131:85:546502132687070474700397868144688800 131:86:292315094227967928328119789937856800 131:87:151197462531707549135234374105788000 131:88:75598731265853774567617187052894000 131:89:36525229712715868611320663407578000 131:90:17045107199267405351949642923536400 131:91:7679663683186413400328959998516400 131:92:3338984210081049304490852173268000 131:93:1400219184872698095431647685564000 131:94:566046053459175825812793745228000 131:95:220460041873573742684982827088800 131:96:82672515702590153506868560158300 131:97:29830289171037684255055666036500 131:98:10349283998115114945631557604500 131:99:3449761332705038315210519201500 131:100:1103923626465612260867366144480 131:101:338828043766673070167211390880 131:102:99655306990197961813885703200 131:103:28058290317628552355365877600 131:104:7554155085515379480290813200 131:105:1942497021989669009217637680 131:106:476461533695579190940175280 131:107:111322788246630652088826000 131:108:24738397388140144908628000 131:109:5220028806671773696316000 131:110:1044005761334354739263200 131:111:197514603495688734455200 131:112:35270464909944416867000 131:113:5930432152999503721000 131:114:936384024157816377000 131:115:138421986179851116600 131:116:19092687748944981600 131:117:2447780480633972000 131:118:290414633295556000 131:119:31725968343212000 131:120:3172596834321200 131:121:288417894029200 131:122:23640810986000 131:123:1729815438000 131:124:111600996000 131:125:6249655776 131:126:297602656 131:127:11716640 131:128:366145 131:129:8515 131:130:131 131:131:1 # binomial(132, k) for 0 <= k <= 132 132:0:1 132:1:132 132:2:8646 132:3:374660 132:4:12082785 132:5:309319296 132:6:6547258432 132:7:117850651776 132:8:1841416434000 132:9:25370626424000 132:10:312058705015200 132:11:3461014728350400 132:12:34898565177533200 132:13:322140601638768000 132:14:2738195113929528000 132:15:21540468229578953600 132:16:157514673928796098200 132:17:1074806010337667493600 132:18:6866816177157320098000 132:19:41200897062943920588000 132:20:232785068405633151322200 132:21:1241520364830043473718400 132:22:6264034568006128435579200 132:23:29958426194811918604944000 132:24:136061185634770796997454000 132:25:587784321942209843029001280 132:26:2418958555685248200157812960 132:27:9496652107505048489508450880 132:28:35612445403143931835656690800 132:29:127713597307826514169251580800 132:30:438483350756871031981097094080 132:31:1442751670232285331034577535360 132:32:4553684959170650576077885345980 132:33:13799045330820153260842076806000 132:34:40179573169152799200687223641000 132:35:112502804873627837761924226194800 132:36:303132557576163896191851387247100 132:37:786506095332749568497776572316800 132:38:1966265238331873921244441430792000 132:39:4739203394953747399922499858832000 132:40:11018647893267462704819812171784400 132:41:24724770882453818752278602922052800 132:42:53570336911983273963270306331114400 132:43:112123960978569643178937850460472000 132:44:226796193797561323702851561158682000 132:45:443512556759675477463354164043644800 132:46:838817226915038403028517658082545600 132:47:1534857053504112822562819544576572800 132:48:2717976032246866456621659610187681000 132:49:4659387483851771068494273617464596000 132:50:7734583223193939973700494204991229360 132:51:12435996554939276036145892643319231520 132:52:19371456172116949210150332771324187560 132:53:29239933844704828996453332485017641600 132:54:42776940254290397976292838265118401600 132:55:60665478906084564402742570630531551360 132:56:83415033495866276053771034616980883120 132:57:111220044661155034738361379489307844160 132:58:143819023268734958713398335546518764000 132:59:180383181726887914318499607295633704000 132:60:219466204434380295754174522209687673200 132:61:259042077365170185152468288509795286400 132:62:296644959563340050739116911035410731200 132:63:329605510625933389710129901150456368000 132:64:355355941143584435781233799677835771750 132:65:371756984580980640509598436586043576600 132:66:377389666165540953244592352291892721700 132:67:371756984580980640509598436586043576600 132:68:355355941143584435781233799677835771750 132:69:329605510625933389710129901150456368000 132:70:296644959563340050739116911035410731200 132:71:259042077365170185152468288509795286400 132:72:219466204434380295754174522209687673200 132:73:180383181726887914318499607295633704000 132:74:143819023268734958713398335546518764000 132:75:111220044661155034738361379489307844160 132:76:83415033495866276053771034616980883120 132:77:60665478906084564402742570630531551360 132:78:42776940254290397976292838265118401600 132:79:29239933844704828996453332485017641600 132:80:19371456172116949210150332771324187560 132:81:12435996554939276036145892643319231520 132:82:7734583223193939973700494204991229360 132:83:4659387483851771068494273617464596000 132:84:2717976032246866456621659610187681000 132:85:1534857053504112822562819544576572800 132:86:838817226915038403028517658082545600 132:87:443512556759675477463354164043644800 132:88:226796193797561323702851561158682000 132:89:112123960978569643178937850460472000 132:90:53570336911983273963270306331114400 132:91:24724770882453818752278602922052800 132:92:11018647893267462704819812171784400 132:93:4739203394953747399922499858832000 132:94:1966265238331873921244441430792000 132:95:786506095332749568497776572316800 132:96:303132557576163896191851387247100 132:97:112502804873627837761924226194800 132:98:40179573169152799200687223641000 132:99:13799045330820153260842076806000 132:100:4553684959170650576077885345980 132:101:1442751670232285331034577535360 132:102:438483350756871031981097094080 132:103:127713597307826514169251580800 132:104:35612445403143931835656690800 132:105:9496652107505048489508450880 132:106:2418958555685248200157812960 132:107:587784321942209843029001280 132:108:136061185634770796997454000 132:109:29958426194811918604944000 132:110:6264034568006128435579200 132:111:1241520364830043473718400 132:112:232785068405633151322200 132:113:41200897062943920588000 132:114:6866816177157320098000 132:115:1074806010337667493600 132:116:157514673928796098200 132:117:21540468229578953600 132:118:2738195113929528000 132:119:322140601638768000 132:120:34898565177533200 132:121:3461014728350400 132:122:312058705015200 132:123:25370626424000 132:124:1841416434000 132:125:117850651776 132:126:6547258432 132:127:309319296 132:128:12082785 132:129:374660 132:130:8646 132:131:132 132:132:1 # binomial(133, k) for 0 <= k <= 133 133:0:1 133:1:133 133:2:8778 133:3:383306 133:4:12457445 133:5:321402081 133:6:6856577728 133:7:124397910208 133:8:1959267085776 133:9:27212042858000 133:10:337429331439200 133:11:3773073433365600 133:12:38359579905883600 133:13:357039166816301200 133:14:3060335715568296000 133:15:24278663343508481600 133:16:179055142158375051800 133:17:1232320684266463591800 133:18:7941622187494987591600 133:19:48067713240101240686000 133:20:273985965468577071910200 133:21:1474305433235676625040600 133:22:7505554932836171909297600 133:23:36222460762818047040523200 133:24:166019611829582715602398000 133:25:723845507576980640026455280 133:26:3006742877627458043186814240 133:27:11915610663190296689666263840 133:28:45109097510648980325165141680 133:29:163326042710970446004908271600 133:30:566196948064697546150348674880 133:31:1881235020989156363015674629440 133:32:5996436629402935907112462881340 133:33:18352730289990803836919962151980 133:34:53978618499972952461529300447000 133:35:152682378042780636962611449835800 133:36:415635362449791733953775613441900 133:37:1089638652908913464689627959563900 133:38:2752771333664623489742218003108800 133:39:6705468633285621321166941289624000 133:40:15757851288221210104742312030616400 133:41:35743418775721281457098415093837200 133:42:78295107794437092715548909253167200 133:43:165694297890552917142208156791586400 133:44:338920154776130966881789411619154000 133:45:670308750557236801166205725202326800 133:46:1282329783674713880491871822126190400 133:47:2373674280419151225591337202659118400 133:48:4252833085750979279184479154764253800 133:49:7377363516098637525115933227652277000 133:50:12393970707045711042194767822455825360 133:51:20170579778133216009846386848310460880 133:52:31807452727056225246296225414643419080 133:53:48611390016821778206603665256341829160 133:54:72016874098995226972746170750136043200 133:55:103442419160374962379035408895649952960 133:56:144080512401950840456513605247512434480 133:57:194635078157021310792132414106288727280 133:58:255039067929889993451759715035826608160 133:59:324202204995622873031897942842152468000 133:60:399849386161268210072674129505321377200 133:61:478508281799550480906642810719482959600 133:62:555687036928510235891585199545206017600 133:63:626250470189273440449246812185867099200 133:64:684961451769517825491363700828292139750 133:65:727112925724565076290832236263879348350 133:66:749146650746521593754190788877936298300 133:67:749146650746521593754190788877936298300 133:68:727112925724565076290832236263879348350 133:69:684961451769517825491363700828292139750 133:70:626250470189273440449246812185867099200 133:71:555687036928510235891585199545206017600 133:72:478508281799550480906642810719482959600 133:73:399849386161268210072674129505321377200 133:74:324202204995622873031897942842152468000 133:75:255039067929889993451759715035826608160 133:76:194635078157021310792132414106288727280 133:77:144080512401950840456513605247512434480 133:78:103442419160374962379035408895649952960 133:79:72016874098995226972746170750136043200 133:80:48611390016821778206603665256341829160 133:81:31807452727056225246296225414643419080 133:82:20170579778133216009846386848310460880 133:83:12393970707045711042194767822455825360 133:84:7377363516098637525115933227652277000 133:85:4252833085750979279184479154764253800 133:86:2373674280419151225591337202659118400 133:87:1282329783674713880491871822126190400 133:88:670308750557236801166205725202326800 133:89:338920154776130966881789411619154000 133:90:165694297890552917142208156791586400 133:91:78295107794437092715548909253167200 133:92:35743418775721281457098415093837200 133:93:15757851288221210104742312030616400 133:94:6705468633285621321166941289624000 133:95:2752771333664623489742218003108800 133:96:1089638652908913464689627959563900 133:97:415635362449791733953775613441900 133:98:152682378042780636962611449835800 133:99:53978618499972952461529300447000 133:100:18352730289990803836919962151980 133:101:5996436629402935907112462881340 133:102:1881235020989156363015674629440 133:103:566196948064697546150348674880 133:104:163326042710970446004908271600 133:105:45109097510648980325165141680 133:106:11915610663190296689666263840 133:107:3006742877627458043186814240 133:108:723845507576980640026455280 133:109:166019611829582715602398000 133:110:36222460762818047040523200 133:111:7505554932836171909297600 133:112:1474305433235676625040600 133:113:273985965468577071910200 133:114:48067713240101240686000 133:115:7941622187494987591600 133:116:1232320684266463591800 133:117:179055142158375051800 133:118:24278663343508481600 133:119:3060335715568296000 133:120:357039166816301200 133:121:38359579905883600 133:122:3773073433365600 133:123:337429331439200 133:124:27212042858000 133:125:1959267085776 133:126:124397910208 133:127:6856577728 133:128:321402081 133:129:12457445 133:130:383306 133:131:8778 133:132:133 133:133:1 # binomial(134, k) for 0 <= k <= 134 134:0:1 134:1:134 134:2:8911 134:3:392084 134:4:12840751 134:5:333859526 134:6:7177979809 134:7:131254487936 134:8:2083664995984 134:9:29171309943776 134:10:364641374297200 134:11:4110502764804800 134:12:42132653339249200 134:13:395398746722184800 134:14:3417374882384597200 134:15:27338999059076777600 134:16:203333805501883533400 134:17:1411375826424838643600 134:18:9173942871761451183400 134:19:56009335427596228277600 134:20:322053678708678312596200 134:21:1748291398704253696950800 134:22:8979860366071848534338200 134:23:43728015695654218949820800 134:24:202242072592400762642921200 134:25:889865119406563355628853280 134:26:3730588385204438683213269520 134:27:14922353540817754732853078080 134:28:57024708173839277014831405520 134:29:208435140221619426330073413280 134:30:729522990775667992155256946480 134:31:2447431969053853909166023304320 134:32:7877671650392092270128137510780 134:33:24349166919393739744032425033320 134:34:72331348789963756298449262598980 134:35:206660996542753589424140750282800 134:36:568317740492572370916387063277700 134:37:1505274015358705198643403573005800 134:38:3842409986573536954431845962672700 134:39:9458239966950244810909159292732800 134:40:22463319921506831425909253320240400 134:41:51501270063942491561840727124453600 134:42:114038526570158374172647324347004400 134:43:243989405684990009857757066044753600 134:44:504614452666683884023997568410740400 134:45:1009228905333367768047995136821480800 134:46:1952638534231950681658077547328517200 134:47:3656004064093865106083209024785308800 134:48:6626507366170130504775816357423372200 134:49:11630196601849616804300412382416530800 134:50:19771334223144348567310701050108102360 134:51:32564550485178927052041154670766286240 134:52:51978032505189441256142612262953879960 134:53:80418842743878003452899890670985248240 134:54:120628264115817005179349836006477872360 134:55:175459293259370189351781579645785996160 134:56:247522931562325802835549014143162387440 134:57:338715590558972151248646019353801161760 134:58:449674146086911304243892129142115335440 134:59:579241272925512866483657657877979076160 134:60:724051591156891083104572072347473845200 134:61:878357667960818690979316940224804336800 134:62:1034195318728060716798228010264688977200 134:63:1181937507117783676340832011731073116800 134:64:1311211921958791265940610513014159238950 134:65:1412074377494082901782195937092171488100 134:66:1476259576471086670045023025141815646650 134:67:1498293301493043187508381577755872596600 134:68:1476259576471086670045023025141815646650 134:69:1412074377494082901782195937092171488100 134:70:1311211921958791265940610513014159238950 134:71:1181937507117783676340832011731073116800 134:72:1034195318728060716798228010264688977200 134:73:878357667960818690979316940224804336800 134:74:724051591156891083104572072347473845200 134:75:579241272925512866483657657877979076160 134:76:449674146086911304243892129142115335440 134:77:338715590558972151248646019353801161760 134:78:247522931562325802835549014143162387440 134:79:175459293259370189351781579645785996160 134:80:120628264115817005179349836006477872360 134:81:80418842743878003452899890670985248240 134:82:51978032505189441256142612262953879960 134:83:32564550485178927052041154670766286240 134:84:19771334223144348567310701050108102360 134:85:11630196601849616804300412382416530800 134:86:6626507366170130504775816357423372200 134:87:3656004064093865106083209024785308800 134:88:1952638534231950681658077547328517200 134:89:1009228905333367768047995136821480800 134:90:504614452666683884023997568410740400 134:91:243989405684990009857757066044753600 134:92:114038526570158374172647324347004400 134:93:51501270063942491561840727124453600 134:94:22463319921506831425909253320240400 134:95:9458239966950244810909159292732800 134:96:3842409986573536954431845962672700 134:97:1505274015358705198643403573005800 134:98:568317740492572370916387063277700 134:99:206660996542753589424140750282800 134:100:72331348789963756298449262598980 134:101:24349166919393739744032425033320 134:102:7877671650392092270128137510780 134:103:2447431969053853909166023304320 134:104:729522990775667992155256946480 134:105:208435140221619426330073413280 134:106:57024708173839277014831405520 134:107:14922353540817754732853078080 134:108:3730588385204438683213269520 134:109:889865119406563355628853280 134:110:202242072592400762642921200 134:111:43728015695654218949820800 134:112:8979860366071848534338200 134:113:1748291398704253696950800 134:114:322053678708678312596200 134:115:56009335427596228277600 134:116:9173942871761451183400 134:117:1411375826424838643600 134:118:203333805501883533400 134:119:27338999059076777600 134:120:3417374882384597200 134:121:395398746722184800 134:122:42132653339249200 134:123:4110502764804800 134:124:364641374297200 134:125:29171309943776 134:126:2083664995984 134:127:131254487936 134:128:7177979809 134:129:333859526 134:130:12840751 134:131:392084 134:132:8911 134:133:134 134:134:1 # binomial(135, k) for 0 <= k <= 135 135:0:1 135:1:135 135:2:9045 135:3:400995 135:4:13232835 135:5:346700277 135:6:7511839335 135:7:138432467745 135:8:2214919483920 135:9:31254974939760 135:10:393812684240976 135:11:4475144139102000 135:12:46243156104054000 135:13:437531400061434000 135:14:3812773629106782000 135:15:30756373941461374800 135:16:230672804560960311000 135:17:1614709631926722177000 135:18:10585318698186289827000 135:19:65183278299357679461000 135:20:378063014136274540873800 135:21:2070345077412932009547000 135:22:10728151764776102231289000 135:23:52707876061726067484159000 135:24:245970088288054981592742000 135:25:1092107191998964118271774480 135:26:4620453504611002038842122800 135:27:18652941926022193416066347600 135:28:71947061714657031747684483600 135:29:265459848395458703344904818800 135:30:937958130997287418485330359760 135:31:3176954959829521901321280250800 135:32:10325103619445946179294160815100 135:33:32226838569785832014160562544100 135:34:96680515709357496042481687632300 135:35:278992345332717345722590012881780 135:36:774978737035325960340527813560500 135:37:2073591755851277569559790636283500 135:38:5347684001932242153075249535678500 135:39:13300649953523781765341005255405500 135:40:31921559888457076236818412612973200 135:41:73964589985449322987749980444694000 135:42:165539796634100865734488051471458000 135:43:358027932255148384030404390391758000 135:44:748603858351673893881754634455494000 135:45:1513843358000051652071992705232221200 135:46:2961867439565318449706072684149998000 135:47:5608642598325815787741286572113826000 135:48:10282511430263995610859025382208681000 135:49:18256703968019747309076228739839903000 135:50:31401530824993965371611113432524633160 135:51:52335884708323275619351855720874388600 135:52:84542582990368368308183766933720166200 135:53:132396875249067444709042502933939128200 135:54:201047106859695008632249726677463120600 135:55:296087557375187194531131415652263868520 135:56:422982224821695992187330593788948383600 135:57:586238522121297954084195033496963549200 135:58:788389736645883455492538148495916497200 135:59:1028915419012424170727549787020094411600 135:60:1303292864082403949588229730225452921360 135:61:1602409259117709774083889012572278182000 135:62:1912552986688879407777544950489493314000 135:63:2216132825845844393139060021995762094000 135:64:2493149429076574942281442524745232355750 135:65:2723286299452874167722806450106330727050 135:66:2888333953965169571827218962233987134750 135:67:2974552877964129857553404602897688243250 135:68:2974552877964129857553404602897688243250 135:69:2888333953965169571827218962233987134750 135:70:2723286299452874167722806450106330727050 135:71:2493149429076574942281442524745232355750 135:72:2216132825845844393139060021995762094000 135:73:1912552986688879407777544950489493314000 135:74:1602409259117709774083889012572278182000 135:75:1303292864082403949588229730225452921360 135:76:1028915419012424170727549787020094411600 135:77:788389736645883455492538148495916497200 135:78:586238522121297954084195033496963549200 135:79:422982224821695992187330593788948383600 135:80:296087557375187194531131415652263868520 135:81:201047106859695008632249726677463120600 135:82:132396875249067444709042502933939128200 135:83:84542582990368368308183766933720166200 135:84:52335884708323275619351855720874388600 135:85:31401530824993965371611113432524633160 135:86:18256703968019747309076228739839903000 135:87:10282511430263995610859025382208681000 135:88:5608642598325815787741286572113826000 135:89:2961867439565318449706072684149998000 135:90:1513843358000051652071992705232221200 135:91:748603858351673893881754634455494000 135:92:358027932255148384030404390391758000 135:93:165539796634100865734488051471458000 135:94:73964589985449322987749980444694000 135:95:31921559888457076236818412612973200 135:96:13300649953523781765341005255405500 135:97:5347684001932242153075249535678500 135:98:2073591755851277569559790636283500 135:99:774978737035325960340527813560500 135:100:278992345332717345722590012881780 135:101:96680515709357496042481687632300 135:102:32226838569785832014160562544100 135:103:10325103619445946179294160815100 135:104:3176954959829521901321280250800 135:105:937958130997287418485330359760 135:106:265459848395458703344904818800 135:107:71947061714657031747684483600 135:108:18652941926022193416066347600 135:109:4620453504611002038842122800 135:110:1092107191998964118271774480 135:111:245970088288054981592742000 135:112:52707876061726067484159000 135:113:10728151764776102231289000 135:114:2070345077412932009547000 135:115:378063014136274540873800 135:116:65183278299357679461000 135:117:10585318698186289827000 135:118:1614709631926722177000 135:119:230672804560960311000 135:120:30756373941461374800 135:121:3812773629106782000 135:122:437531400061434000 135:123:46243156104054000 135:124:4475144139102000 135:125:393812684240976 135:126:31254974939760 135:127:2214919483920 135:128:138432467745 135:129:7511839335 135:130:346700277 135:131:13232835 135:132:400995 135:133:9045 135:134:135 135:135:1 # binomial(136, k) for 0 <= k <= 136 136:0:1 136:1:136 136:2:9180 136:3:410040 136:4:13633830 136:5:359933112 136:6:7858539612 136:7:145944307080 136:8:2353351951665 136:9:33469894423680 136:10:425067659180736 136:11:4868956823342976 136:12:50718300243156000 136:13:483774556165488000 136:14:4250305029168216000 136:15:34569147570568156800 136:16:261429178502421685800 136:17:1845382436487682488000 136:18:12200028330113012004000 136:19:75768596997543969288000 136:20:443246292435632220334800 136:21:2448408091549206550420800 136:22:12798496842189034240836000 136:23:63436027826502169715448000 136:24:298677964349781049076901000 136:25:1338077280287019099864516480 136:26:5712560696609966157113897280 136:27:23273395430633195454908470400 136:28:90600003640679225163750831200 136:29:337406910110115735092589302400 136:30:1203417979392746121830235178560 136:31:4114913090826809319806610610560 136:32:13502058579275468080615441065900 136:33:42551942189231778193454723359200 136:34:128907354279143328056642250176400 136:35:375672861042074841765071700514080 136:36:1053971082368043306063117826442280 136:37:2848570492886603529900318449844000 136:38:7421275757783519722635040171962000 136:39:18648333955456023918416254791084000 136:40:45222209841980858002159417868378700 136:41:105886149873906399224568393057667200 136:42:239504386619550188722238031916152000 136:43:523567728889249249764892441863216000 136:44:1106631790606822277912159024847252000 136:45:2262447216351725545953747339687715200 136:46:4475710797565370101778065389382219200 136:47:8570510037891134237447359256263824000 136:48:15891154028589811398600311954322507000 136:49:28539215398283742919935254122048584000 136:50:49658234793013712680687342172364536160 136:51:83737415533317240990962969153399021760 136:52:136878467698691643927535622654594554800 136:53:216939458239435813017226269867659294400 136:54:333443982108762453341292229611402248800 136:55:497134664234882203163381142329726989120 136:56:719069782196883186718462009441212252120 136:57:1009220746942993946271525627285911932800 136:58:1374628258767181409576733181992880046400 136:59:1817305155658307626220087935516010908800 136:60:2332208283094828120315779517245547332960 136:61:2905702123200113723672118742797731103360 136:62:3514962245806589181861433963061771496000 136:63:4128685812534723800916604972485255408000 136:64:4709282254922419335420502546740994449750 136:65:5216435728529449110004248974851563082800 136:66:5611620253418043739550025412340317861800 136:67:5862886831929299429380623565131675378000 136:68:5949105755928259715106809205795376486500 136:69:5862886831929299429380623565131675378000 136:70:5611620253418043739550025412340317861800 136:71:5216435728529449110004248974851563082800 136:72:4709282254922419335420502546740994449750 136:73:4128685812534723800916604972485255408000 136:74:3514962245806589181861433963061771496000 136:75:2905702123200113723672118742797731103360 136:76:2332208283094828120315779517245547332960 136:77:1817305155658307626220087935516010908800 136:78:1374628258767181409576733181992880046400 136:79:1009220746942993946271525627285911932800 136:80:719069782196883186718462009441212252120 136:81:497134664234882203163381142329726989120 136:82:333443982108762453341292229611402248800 136:83:216939458239435813017226269867659294400 136:84:136878467698691643927535622654594554800 136:85:83737415533317240990962969153399021760 136:86:49658234793013712680687342172364536160 136:87:28539215398283742919935254122048584000 136:88:15891154028589811398600311954322507000 136:89:8570510037891134237447359256263824000 136:90:4475710797565370101778065389382219200 136:91:2262447216351725545953747339687715200 136:92:1106631790606822277912159024847252000 136:93:523567728889249249764892441863216000 136:94:239504386619550188722238031916152000 136:95:105886149873906399224568393057667200 136:96:45222209841980858002159417868378700 136:97:18648333955456023918416254791084000 136:98:7421275757783519722635040171962000 136:99:2848570492886603529900318449844000 136:100:1053971082368043306063117826442280 136:101:375672861042074841765071700514080 136:102:128907354279143328056642250176400 136:103:42551942189231778193454723359200 136:104:13502058579275468080615441065900 136:105:4114913090826809319806610610560 136:106:1203417979392746121830235178560 136:107:337406910110115735092589302400 136:108:90600003640679225163750831200 136:109:23273395430633195454908470400 136:110:5712560696609966157113897280 136:111:1338077280287019099864516480 136:112:298677964349781049076901000 136:113:63436027826502169715448000 136:114:12798496842189034240836000 136:115:2448408091549206550420800 136:116:443246292435632220334800 136:117:75768596997543969288000 136:118:12200028330113012004000 136:119:1845382436487682488000 136:120:261429178502421685800 136:121:34569147570568156800 136:122:4250305029168216000 136:123:483774556165488000 136:124:50718300243156000 136:125:4868956823342976 136:126:425067659180736 136:127:33469894423680 136:128:2353351951665 136:129:145944307080 136:130:7858539612 136:131:359933112 136:132:13633830 136:133:410040 136:134:9180 136:135:136 136:136:1 # binomial(137, k) for 0 <= k <= 137 137:0:1 137:1:137 137:2:9316 137:3:419220 137:4:14043870 137:5:373566942 137:6:8218472724 137:7:153802846692 137:8:2499296258745 137:9:35823246375345 137:10:458537553604416 137:11:5294024482523712 137:12:55587257066498976 137:13:534492856408644000 137:14:4734079585333704000 137:15:38819452599736372800 137:16:295998326072989842600 137:17:2106811614990104173800 137:18:14045410766600694492000 137:19:87968625327656981292000 137:20:519014889433176189622800 137:21:2891654383984838770755600 137:22:15246904933738240791256800 137:23:76234524668691203956284000 137:24:362113992176283218792349000 137:25:1636755244636800148941417480 137:26:7050637976896985256978413760 137:27:28985956127243161612022367680 137:28:113873399071312420618659301600 137:29:428006913750794960256340133600 137:30:1540824889502861856922824480960 137:31:5318331070219555441636845789120 137:32:17616971670102277400422051676460 137:33:56054000768507246274070164425100 137:34:171459296468375106250096973535600 137:35:504580215321218169821713950690480 137:36:1429643943410118147828189526956360 137:37:3902541575254646835963436276286280 137:38:10269846250670123252535358621806000 137:39:26069609713239543641051294963046000 137:40:63870543797436881920575672659462700 137:41:151108359715887257226727810926045900 137:42:345390536493456587946806424973819200 137:43:763072115508799438487130473779368000 137:44:1630199519496071527677051466710468000 137:45:3369079006958547823865906364534967200 137:46:6738158013917095647731812729069934400 137:47:13046220835456504339225424645646043200 137:48:24461664066480945636047671210586331000 137:49:44430369426873554318535566076371091000 137:50:78197450191297455600622596294413120160 137:51:133395650326330953671650311325763557920 137:52:220615883232008884918498591807993576560 137:53:353817925938127456944761892522253849200 137:54:550383440348198266358518499479061543200 137:55:830578646343644656504673371941129237920 137:56:1216204446431765389881843151770939241240 137:57:1728290529139877132989987636727124184920 137:58:2383849005710175355848258809278791979200 137:59:3191933414425489035796821117508890955200 137:60:4149513438753135746535867452761558241760 137:61:5237910406294941843987898260043278436320 137:62:6420664369006702905533552705859502599360 137:63:7643648058341312982778038935547026904000 137:64:8837968067457143136337107519226249857750 137:65:9925717983451868445424751521592557532550 137:66:10828055981947492849554274387191880944600 137:67:11474507085347343168930648977471993239800 137:68:11811992587857559144487432770927051864500 137:69:11811992587857559144487432770927051864500 137:70:11474507085347343168930648977471993239800 137:71:10828055981947492849554274387191880944600 137:72:9925717983451868445424751521592557532550 137:73:8837968067457143136337107519226249857750 137:74:7643648058341312982778038935547026904000 137:75:6420664369006702905533552705859502599360 137:76:5237910406294941843987898260043278436320 137:77:4149513438753135746535867452761558241760 137:78:3191933414425489035796821117508890955200 137:79:2383849005710175355848258809278791979200 137:80:1728290529139877132989987636727124184920 137:81:1216204446431765389881843151770939241240 137:82:830578646343644656504673371941129237920 137:83:550383440348198266358518499479061543200 137:84:353817925938127456944761892522253849200 137:85:220615883232008884918498591807993576560 137:86:133395650326330953671650311325763557920 137:87:78197450191297455600622596294413120160 137:88:44430369426873554318535566076371091000 137:89:24461664066480945636047671210586331000 137:90:13046220835456504339225424645646043200 137:91:6738158013917095647731812729069934400 137:92:3369079006958547823865906364534967200 137:93:1630199519496071527677051466710468000 137:94:763072115508799438487130473779368000 137:95:345390536493456587946806424973819200 137:96:151108359715887257226727810926045900 137:97:63870543797436881920575672659462700 137:98:26069609713239543641051294963046000 137:99:10269846250670123252535358621806000 137:100:3902541575254646835963436276286280 137:101:1429643943410118147828189526956360 137:102:504580215321218169821713950690480 137:103:171459296468375106250096973535600 137:104:56054000768507246274070164425100 137:105:17616971670102277400422051676460 137:106:5318331070219555441636845789120 137:107:1540824889502861856922824480960 137:108:428006913750794960256340133600 137:109:113873399071312420618659301600 137:110:28985956127243161612022367680 137:111:7050637976896985256978413760 137:112:1636755244636800148941417480 137:113:362113992176283218792349000 137:114:76234524668691203956284000 137:115:15246904933738240791256800 137:116:2891654383984838770755600 137:117:519014889433176189622800 137:118:87968625327656981292000 137:119:14045410766600694492000 137:120:2106811614990104173800 137:121:295998326072989842600 137:122:38819452599736372800 137:123:4734079585333704000 137:124:534492856408644000 137:125:55587257066498976 137:126:5294024482523712 137:127:458537553604416 137:128:35823246375345 137:129:2499296258745 137:130:153802846692 137:131:8218472724 137:132:373566942 137:133:14043870 137:134:419220 137:135:9316 137:136:137 137:137:1 # binomial(138, k) for 0 <= k <= 138 138:0:1 138:1:138 138:2:9453 138:3:428536 138:4:14463090 138:5:387610812 138:6:8592039666 138:7:162021319416 138:8:2653099105437 138:9:38322542634090 138:10:494360799979761 138:11:5752562036128128 138:12:60881281549022688 138:13:590080113475142976 138:14:5268572441742348000 138:15:43553532185070076800 138:16:334817778672726215400 138:17:2402809941063094016400 138:18:16152222381590798665800 138:19:102014036094257675784000 138:20:606983514760833170914800 138:21:3410669273418014960378400 138:22:18138559317723079562012400 138:23:91481429602429444747540800 138:24:438348516844974422748633000 138:25:1998869236813083367733766480 138:26:8687393221533785405919831240 138:27:36036594104140146869000781440 138:28:142859355198555582230681669280 138:29:541880312822107380874999435200 138:30:1968831803253656817179164614560 138:31:6859155959722417298559670270080 138:32:22935302740321832842058897465580 138:33:73670972438609523674492216101560 138:34:227513297236882352524167137960700 138:35:676039511789593276071810924226080 138:36:1934224158731336317649903477646840 138:37:5332185518664764983791625803242640 138:38:14172387825924770088498794898092280 138:39:36339455963909666893586653584852000 138:40:89940153510676425561626967622508700 138:41:214978903513324139147303483585508600 138:42:496498896209343845173534235899865100 138:43:1108462652002256026433936898753187200 138:44:2393271635004870966164181940489836000 138:45:4999278526454619351542957831245435200 138:46:10107237020875643471597719093604901600 138:47:19784378849373599986957237374715977600 138:48:37507884901937449975273095856232374200 138:49:68892033493354499954583237286957422000 138:50:122627819618171009919158162370784211160 138:51:211593100517628409272272907620176678080 138:52:354011533558339838590148903133757134480 138:53:574433809170136341863260484330247425760 138:54:904201366286325723303280392001315392400 138:55:1380962086691842922863191871420190781120 138:56:2046783092775410046386516523712068479160 138:57:2944494975571642522871830788498063426160 138:58:4112139534850052488838246446005916164120 138:59:5575782420135664391645079926787682934400 138:60:7341446853178624782332688570270449196960 138:61:9387423845048077590523765712804836678080 138:62:11658574775301644749521450965902781035680 138:63:14064312427348015888311591641406529503360 138:64:16481616125798456119115146454773276761750 138:65:18763686050909011581761859040818807390300 138:66:20753773965399361294979025908784438477150 138:67:22302563067294836018484923364663874184400 138:68:23286499673204902313418081748399045104300 138:69:23623985175715118288974865541854103729000 138:70:23286499673204902313418081748399045104300 138:71:22302563067294836018484923364663874184400 138:72:20753773965399361294979025908784438477150 138:73:18763686050909011581761859040818807390300 138:74:16481616125798456119115146454773276761750 138:75:14064312427348015888311591641406529503360 138:76:11658574775301644749521450965902781035680 138:77:9387423845048077590523765712804836678080 138:78:7341446853178624782332688570270449196960 138:79:5575782420135664391645079926787682934400 138:80:4112139534850052488838246446005916164120 138:81:2944494975571642522871830788498063426160 138:82:2046783092775410046386516523712068479160 138:83:1380962086691842922863191871420190781120 138:84:904201366286325723303280392001315392400 138:85:574433809170136341863260484330247425760 138:86:354011533558339838590148903133757134480 138:87:211593100517628409272272907620176678080 138:88:122627819618171009919158162370784211160 138:89:68892033493354499954583237286957422000 138:90:37507884901937449975273095856232374200 138:91:19784378849373599986957237374715977600 138:92:10107237020875643471597719093604901600 138:93:4999278526454619351542957831245435200 138:94:2393271635004870966164181940489836000 138:95:1108462652002256026433936898753187200 138:96:496498896209343845173534235899865100 138:97:214978903513324139147303483585508600 138:98:89940153510676425561626967622508700 138:99:36339455963909666893586653584852000 138:100:14172387825924770088498794898092280 138:101:5332185518664764983791625803242640 138:102:1934224158731336317649903477646840 138:103:676039511789593276071810924226080 138:104:227513297236882352524167137960700 138:105:73670972438609523674492216101560 138:106:22935302740321832842058897465580 138:107:6859155959722417298559670270080 138:108:1968831803253656817179164614560 138:109:541880312822107380874999435200 138:110:142859355198555582230681669280 138:111:36036594104140146869000781440 138:112:8687393221533785405919831240 138:113:1998869236813083367733766480 138:114:438348516844974422748633000 138:115:91481429602429444747540800 138:116:18138559317723079562012400 138:117:3410669273418014960378400 138:118:606983514760833170914800 138:119:102014036094257675784000 138:120:16152222381590798665800 138:121:2402809941063094016400 138:122:334817778672726215400 138:123:43553532185070076800 138:124:5268572441742348000 138:125:590080113475142976 138:126:60881281549022688 138:127:5752562036128128 138:128:494360799979761 138:129:38322542634090 138:130:2653099105437 138:131:162021319416 138:132:8592039666 138:133:387610812 138:134:14463090 138:135:428536 138:136:9453 138:137:138 138:138:1 # binomial(139, k) for 0 <= k <= 139 139:0:1 139:1:139 139:2:9591 139:3:437989 139:4:14891626 139:5:402073902 139:6:8979650478 139:7:170613359082 139:8:2815120424853 139:9:40975641739527 139:10:532683342613851 139:11:6246922836107889 139:12:66633843585150816 139:13:650961395024165664 139:14:5858652555217490976 139:15:48822104626812424800 139:16:378371310857796292200 139:17:2737627719735820231800 139:18:18555032322653892682200 139:19:118166258475848474449800 139:20:708997550855090846698800 139:21:4017652788178848131293200 139:22:21549228591141094522390800 139:23:109619988920152524309553200 139:24:529829946447403867496173800 139:25:2437217753658057790482399480 139:26:10686262458346868773653597720 139:27:44723987325673932274920612680 139:28:178895949302695729099682450720 139:29:684739668020662963105681104480 139:30:2510712116075764198054164049760 139:31:8827987762976074115738834884640 139:32:29794458700044250140618567735660 139:33:96606275178931356516551113567140 139:34:301184269675491876198659354062260 139:35:903552809026475628595978062186780 139:36:2610263670520929593721714401872920 139:37:7266409677396101301441529280889480 139:38:19504573344589535072290420701334920 139:39:50511843789834436982085448482944280 139:40:126279609474586092455213621207360700 139:41:304919057024000564708930451208017300 139:42:711477799722667984320837719485373700 139:43:1604961548211599871607471134653052300 139:44:3501734287007126992598118839243023200 139:45:7392550161459490317707139771735271200 139:46:15106515547330262823140676924850336800 139:47:29891615870249243458554956468320879200 139:48:57292263751311049962230333230948351800 139:49:106399918395291949929856333143189796200 139:50:191519853111525509873741399657741633160 139:51:334220920135799419191431069990960889240 139:52:565604634075968247862421810753933812560 139:53:928445342728476180453409387464004560240 139:54:1478635175456462065166540876331562818160 139:55:2285163452978168646166472263421506173520 139:56:3427745179467252969249708395132259260280 139:57:4991278068347052569258347312210131905320 139:58:7056634510421695011710077234503979590280 139:59:9687921954985716880483326372793599098520 139:60:12917229273314289173977768497058132131360 139:61:16728870698226702372856454283075285875040 139:62:21045998620349722340045216678707617713760 139:63:25722887202649660637833042607309310539040 139:64:30545928553146472007426738096179806265110 139:65:35245302176707467700877005495592084152050 139:66:39517460016308372876740884949603245867450 139:67:43056337032694197313463949273448312661550 139:68:45589062740499738331903005113062919288700 139:69:46910484848920020602392947290253148833300 139:70:46910484848920020602392947290253148833300 139:71:45589062740499738331903005113062919288700 139:72:43056337032694197313463949273448312661550 139:73:39517460016308372876740884949603245867450 139:74:35245302176707467700877005495592084152050 139:75:30545928553146472007426738096179806265110 139:76:25722887202649660637833042607309310539040 139:77:21045998620349722340045216678707617713760 139:78:16728870698226702372856454283075285875040 139:79:12917229273314289173977768497058132131360 139:80:9687921954985716880483326372793599098520 139:81:7056634510421695011710077234503979590280 139:82:4991278068347052569258347312210131905320 139:83:3427745179467252969249708395132259260280 139:84:2285163452978168646166472263421506173520 139:85:1478635175456462065166540876331562818160 139:86:928445342728476180453409387464004560240 139:87:565604634075968247862421810753933812560 139:88:334220920135799419191431069990960889240 139:89:191519853111525509873741399657741633160 139:90:106399918395291949929856333143189796200 139:91:57292263751311049962230333230948351800 139:92:29891615870249243458554956468320879200 139:93:15106515547330262823140676924850336800 139:94:7392550161459490317707139771735271200 139:95:3501734287007126992598118839243023200 139:96:1604961548211599871607471134653052300 139:97:711477799722667984320837719485373700 139:98:304919057024000564708930451208017300 139:99:126279609474586092455213621207360700 139:100:50511843789834436982085448482944280 139:101:19504573344589535072290420701334920 139:102:7266409677396101301441529280889480 139:103:2610263670520929593721714401872920 139:104:903552809026475628595978062186780 139:105:301184269675491876198659354062260 139:106:96606275178931356516551113567140 139:107:29794458700044250140618567735660 139:108:8827987762976074115738834884640 139:109:2510712116075764198054164049760 139:110:684739668020662963105681104480 139:111:178895949302695729099682450720 139:112:44723987325673932274920612680 139:113:10686262458346868773653597720 139:114:2437217753658057790482399480 139:115:529829946447403867496173800 139:116:109619988920152524309553200 139:117:21549228591141094522390800 139:118:4017652788178848131293200 139:119:708997550855090846698800 139:120:118166258475848474449800 139:121:18555032322653892682200 139:122:2737627719735820231800 139:123:378371310857796292200 139:124:48822104626812424800 139:125:5858652555217490976 139:126:650961395024165664 139:127:66633843585150816 139:128:6246922836107889 139:129:532683342613851 139:130:40975641739527 139:131:2815120424853 139:132:170613359082 139:133:8979650478 139:134:402073902 139:135:14891626 139:136:437989 139:137:9591 139:138:139 139:139:1 # binomial(140, k) for 0 <= k <= 140 140:0:1 140:1:140 140:2:9730 140:3:447580 140:4:15329615 140:5:416965528 140:6:9381724380 140:7:179593009560 140:8:2985733783935 140:9:43790762164380 140:10:573658984353378 140:11:6779606178721740 140:12:72880766421258705 140:13:717595238609316480 140:14:6509613950241656640 140:15:54680757182029915776 140:16:427193415484608717000 140:17:3115999030593616524000 140:18:21292660042389712914000 140:19:136721290798502367132000 140:20:827163809330939321148600 140:21:4726650339033938977992000 140:22:25566881379319942653684000 140:23:131169217511293618831944000 140:24:639449935367556391805727000 140:25:2967047700105461657978573280 140:26:13123480212004926564135997200 140:27:55410249784020801048574210400 140:28:223619936628369661374603063400 140:29:863635617323358692205363555200 140:30:3195451784096427161159845154240 140:31:11338699879051838313792998934400 140:32:38622446463020324256357402620300 140:33:126400733878975606657169681302800 140:34:397790544854423232715210467629400 140:35:1204737078701967504794637416249040 140:36:3513816479547405222317692464059700 140:37:9876673347917030895163243682762400 140:38:26770983021985636373731949982224400 140:39:70016417134423972054375869184279200 140:40:176791453264420529437299069690304980 140:41:431198666498586657164144072415378000 140:42:1016396856746668549029768170693391000 140:43:2316439347934267855928308854138426000 140:44:5106695835218726864205589973896075500 140:45:10894284448466617310305258610978294400 140:46:22499065708789753140847816696585608000 140:47:44998131417579506281695633393171216000 140:48:87183879621560293420785289699269231000 140:49:163692182146602999892086666374138148000 140:50:297919771506817459803597732800931429360 140:51:525740773247324929065172469648702522400 140:52:899825554211767667053852880744894701800 140:53:1494049976804444428315831198217938372800 140:54:2407080518184938245619950263795567378400 140:55:3763798628434630711333013139753068991680 140:56:5712908632445421615416180658553765433800 140:57:8419023247814305538508055707342391165600 140:58:12047912578768747580968424546714111495600 140:59:16744556465407411892193403607297578688800 140:60:22605151228300006054461094869851731229880 140:61:29646099971540991546834222780133418006400 140:62:37774869318576424712901670961782903588800 140:63:46768885822999382977878259286016928252800 140:64:56268815755796132645259780703489116804150 140:65:65791230729853939708303743591771890417160 140:66:74762762193015840577617890445195330019500 140:67:82573797049002570190204834223051558529000 140:68:88645399773193935645366954386511231950250 140:69:92499547589419758934295952403316068122000 140:70:93820969697840041204785894580506297666600 140:71:92499547589419758934295952403316068122000 140:72:88645399773193935645366954386511231950250 140:73:82573797049002570190204834223051558529000 140:74:74762762193015840577617890445195330019500 140:75:65791230729853939708303743591771890417160 140:76:56268815755796132645259780703489116804150 140:77:46768885822999382977878259286016928252800 140:78:37774869318576424712901670961782903588800 140:79:29646099971540991546834222780133418006400 140:80:22605151228300006054461094869851731229880 140:81:16744556465407411892193403607297578688800 140:82:12047912578768747580968424546714111495600 140:83:8419023247814305538508055707342391165600 140:84:5712908632445421615416180658553765433800 140:85:3763798628434630711333013139753068991680 140:86:2407080518184938245619950263795567378400 140:87:1494049976804444428315831198217938372800 140:88:899825554211767667053852880744894701800 140:89:525740773247324929065172469648702522400 140:90:297919771506817459803597732800931429360 140:91:163692182146602999892086666374138148000 140:92:87183879621560293420785289699269231000 140:93:44998131417579506281695633393171216000 140:94:22499065708789753140847816696585608000 140:95:10894284448466617310305258610978294400 140:96:5106695835218726864205589973896075500 140:97:2316439347934267855928308854138426000 140:98:1016396856746668549029768170693391000 140:99:431198666498586657164144072415378000 140:100:176791453264420529437299069690304980 140:101:70016417134423972054375869184279200 140:102:26770983021985636373731949982224400 140:103:9876673347917030895163243682762400 140:104:3513816479547405222317692464059700 140:105:1204737078701967504794637416249040 140:106:397790544854423232715210467629400 140:107:126400733878975606657169681302800 140:108:38622446463020324256357402620300 140:109:11338699879051838313792998934400 140:110:3195451784096427161159845154240 140:111:863635617323358692205363555200 140:112:223619936628369661374603063400 140:113:55410249784020801048574210400 140:114:13123480212004926564135997200 140:115:2967047700105461657978573280 140:116:639449935367556391805727000 140:117:131169217511293618831944000 140:118:25566881379319942653684000 140:119:4726650339033938977992000 140:120:827163809330939321148600 140:121:136721290798502367132000 140:122:21292660042389712914000 140:123:3115999030593616524000 140:124:427193415484608717000 140:125:54680757182029915776 140:126:6509613950241656640 140:127:717595238609316480 140:128:72880766421258705 140:129:6779606178721740 140:130:573658984353378 140:131:43790762164380 140:132:2985733783935 140:133:179593009560 140:134:9381724380 140:135:416965528 140:136:15329615 140:137:447580 140:138:9730 140:139:140 140:140:1 # binomial(141, k) for 0 <= k <= 141 141:0:1 141:1:141 141:2:9870 141:3:457310 141:4:15777195 141:5:432295143 141:6:9798689908 141:7:188974733940 141:8:3165326793495 141:9:46776495948315 141:10:617449746517758 141:11:7353265163075118 141:12:79660372599980445 141:13:790476005030575185 141:14:7227209188850973120 141:15:61190371132271572416 141:16:481874172666638632776 141:17:3543192446078225241000 141:18:24408659072983329438000 141:19:158013950840892080046000 141:20:963885100129441688280600 141:21:5553814148364878299140600 141:22:30293531718353881631676000 141:23:156736098890613561485628000 141:24:770619152878850010637671000 141:25:3606497635473018049784300280 141:26:16090527912110388222114570480 141:27:68533729996025727612710207600 141:28:279030186412390462423177273800 141:29:1087255553951728353579966618600 141:30:4059087401419785853365208709440 141:31:14534151663148265474952844088640 141:32:49961146342072162570150401554700 141:33:165023180341995930913527083923100 141:34:524191278733398839372380148932200 141:35:1602527623556390737509847883878440 141:36:4718553558249372727112329880308740 141:37:13390489827464436117480936146822100 141:38:36647656369902667268895193664986800 141:39:96787400156409608428107819166503600 141:40:246807870398844501491674938874584180 141:41:607990119763007186601443142105682980 141:42:1447595523245255206193912243108769000 141:43:3332836204680936404958077024831817000 141:44:7423135183152994720133898828034501500 141:45:16000980283685344174510848584874369900 141:46:33393350157256370451153075307563902400 141:47:67497197126369259422543450089756824000 141:48:132182011039139799702480923092440447000 141:49:250876061768163293312871956073407379000 141:50:461611953653420459695684399175069577360 141:51:823660544754142388868770202449633951760 141:52:1425566327459092596119025350393597224200 141:53:2393875531016212095369684078962833074600 141:54:3901130494989382673935781462013505751200 141:55:6170879146619568956952963403548636370080 141:56:9476707260880052326749193798306834425480 141:57:14131931880259727153924236365896156599400 141:58:20466935826583053119476480254056502661200 141:59:28792469044176159473161828154011690184400 141:60:39349707693707417946654498477149309918680 141:61:52251251199840997601295317649985149236280 141:62:67420969290117416259735893741916321595200 141:63:84543755141575807690779930247799831841600 141:64:103037701578795515623138039989506045056950 141:65:122060046485650072353563524295261007221310 141:66:140553992922869780285921634036967220436660 141:67:157336559242018410767822724668246888548500 141:68:171219196822196505835571788609562790479250 141:69:181144947362613694579662906789827300072250 141:70:186320517287259800139081846983822365788600 141:71:186320517287259800139081846983822365788600 141:72:181144947362613694579662906789827300072250 141:73:171219196822196505835571788609562790479250 141:74:157336559242018410767822724668246888548500 141:75:140553992922869780285921634036967220436660 141:76:122060046485650072353563524295261007221310 141:77:103037701578795515623138039989506045056950 141:78:84543755141575807690779930247799831841600 141:79:67420969290117416259735893741916321595200 141:80:52251251199840997601295317649985149236280 141:81:39349707693707417946654498477149309918680 141:82:28792469044176159473161828154011690184400 141:83:20466935826583053119476480254056502661200 141:84:14131931880259727153924236365896156599400 141:85:9476707260880052326749193798306834425480 141:86:6170879146619568956952963403548636370080 141:87:3901130494989382673935781462013505751200 141:88:2393875531016212095369684078962833074600 141:89:1425566327459092596119025350393597224200 141:90:823660544754142388868770202449633951760 141:91:461611953653420459695684399175069577360 141:92:250876061768163293312871956073407379000 141:93:132182011039139799702480923092440447000 141:94:67497197126369259422543450089756824000 141:95:33393350157256370451153075307563902400 141:96:16000980283685344174510848584874369900 141:97:7423135183152994720133898828034501500 141:98:3332836204680936404958077024831817000 141:99:1447595523245255206193912243108769000 141:100:607990119763007186601443142105682980 141:101:246807870398844501491674938874584180 141:102:96787400156409608428107819166503600 141:103:36647656369902667268895193664986800 141:104:13390489827464436117480936146822100 141:105:4718553558249372727112329880308740 141:106:1602527623556390737509847883878440 141:107:524191278733398839372380148932200 141:108:165023180341995930913527083923100 141:109:49961146342072162570150401554700 141:110:14534151663148265474952844088640 141:111:4059087401419785853365208709440 141:112:1087255553951728353579966618600 141:113:279030186412390462423177273800 141:114:68533729996025727612710207600 141:115:16090527912110388222114570480 141:116:3606497635473018049784300280 141:117:770619152878850010637671000 141:118:156736098890613561485628000 141:119:30293531718353881631676000 141:120:5553814148364878299140600 141:121:963885100129441688280600 141:122:158013950840892080046000 141:123:24408659072983329438000 141:124:3543192446078225241000 141:125:481874172666638632776 141:126:61190371132271572416 141:127:7227209188850973120 141:128:790476005030575185 141:129:79660372599980445 141:130:7353265163075118 141:131:617449746517758 141:132:46776495948315 141:133:3165326793495 141:134:188974733940 141:135:9798689908 141:136:432295143 141:137:15777195 141:138:457310 141:139:9870 141:140:141 141:141:1 # binomial(142, k) for 0 <= k <= 142 142:0:1 142:1:142 142:2:10011 142:3:467180 142:4:16234505 142:5:448072338 142:6:10230985051 142:7:198773423848 142:8:3354301527435 142:9:49941822741810 142:10:664226242466073 142:11:7970714909592876 142:12:87013637763055563 142:13:870136377630555630 142:14:8017685193881548305 142:15:68417580321122545536 142:16:543064543798910205192 142:17:4025066618744863873776 142:18:27951851519061554679000 142:19:182422609913875409484000 142:20:1121899050970333768326600 142:21:6517699248494319987421200 142:22:35847345866718759930816600 142:23:187029630608967443117304000 142:24:927355251769463572123299000 142:25:4377116788351868060421971280 142:26:19697025547583406271898870760 142:27:84624257908136115834824778080 142:28:347563916408416190035887481400 142:29:1366285740364118816003143892400 142:30:5146342955371514206945175328040 142:31:18593239064568051328318052798080 142:32:64495298005220428045103245643340 142:33:214984326684068093483677485477800 142:34:689214459075394770285907232855300 142:35:2126718902289789576882228032810640 142:36:6321081181805763464622177764187180 142:37:18109043385713808844593266027130840 142:38:50038146197367103386376129811808900 142:39:133435056526312275697003012831490400 142:40:343595270555254109919782758041087780 142:41:854797990161851688093118080980267160 142:42:2055585643008262392795355385214451980 142:43:4780431727926191611151989267940586000 142:44:10755971387833931125091975852866318500 142:45:23424115466838338894644747412908871400 142:46:49394330440941714625663923892438272300 142:47:100890547283625629873696525397320726400 142:48:199679208165509059125024373182197271000 142:49:383058072807303093015352879165847826000 142:50:712488015421583753008556355248476956360 142:51:1285272498407562848564454601624703529120 142:52:2249226872213234984987795552843231175960 142:53:3819441858475304691488709429356430298800 142:54:6295006026005594769305465540976338825800 142:55:10072009641608951630888744865562142121280 142:56:15647586407499621283702157201855470795560 142:57:23608639141139779480673430164202991024880 142:58:34598867706842780273400716619952659260600 142:59:49259404870759212592638308408068192845600 142:60:68142176737883577419816326631161000103080 142:61:91600958893548415547949816127134459154960 142:62:119672220489958413861031211391901470831480 142:63:151964724431693223950515823989716153436800 142:64:187581456720371323313917970237305876898550 142:65:225097748064445587976701564284767052278260 142:66:262614039408519852639485158332228227657970 142:67:297890552164888191053744358705214108985160 142:68:328555756064214916603394513277809679027750 142:69:352364144184810200415234695399390090551500 142:70:367465464649873494718744753773649665860850 142:71:372641034574519600278163693967644731577200 142:72:367465464649873494718744753773649665860850 142:73:352364144184810200415234695399390090551500 142:74:328555756064214916603394513277809679027750 142:75:297890552164888191053744358705214108985160 142:76:262614039408519852639485158332228227657970 142:77:225097748064445587976701564284767052278260 142:78:187581456720371323313917970237305876898550 142:79:151964724431693223950515823989716153436800 142:80:119672220489958413861031211391901470831480 142:81:91600958893548415547949816127134459154960 142:82:68142176737883577419816326631161000103080 142:83:49259404870759212592638308408068192845600 142:84:34598867706842780273400716619952659260600 142:85:23608639141139779480673430164202991024880 142:86:15647586407499621283702157201855470795560 142:87:10072009641608951630888744865562142121280 142:88:6295006026005594769305465540976338825800 142:89:3819441858475304691488709429356430298800 142:90:2249226872213234984987795552843231175960 142:91:1285272498407562848564454601624703529120 142:92:712488015421583753008556355248476956360 142:93:383058072807303093015352879165847826000 142:94:199679208165509059125024373182197271000 142:95:100890547283625629873696525397320726400 142:96:49394330440941714625663923892438272300 142:97:23424115466838338894644747412908871400 142:98:10755971387833931125091975852866318500 142:99:4780431727926191611151989267940586000 142:100:2055585643008262392795355385214451980 142:101:854797990161851688093118080980267160 142:102:343595270555254109919782758041087780 142:103:133435056526312275697003012831490400 142:104:50038146197367103386376129811808900 142:105:18109043385713808844593266027130840 142:106:6321081181805763464622177764187180 142:107:2126718902289789576882228032810640 142:108:689214459075394770285907232855300 142:109:214984326684068093483677485477800 142:110:64495298005220428045103245643340 142:111:18593239064568051328318052798080 142:112:5146342955371514206945175328040 142:113:1366285740364118816003143892400 142:114:347563916408416190035887481400 142:115:84624257908136115834824778080 142:116:19697025547583406271898870760 142:117:4377116788351868060421971280 142:118:927355251769463572123299000 142:119:187029630608967443117304000 142:120:35847345866718759930816600 142:121:6517699248494319987421200 142:122:1121899050970333768326600 142:123:182422609913875409484000 142:124:27951851519061554679000 142:125:4025066618744863873776 142:126:543064543798910205192 142:127:68417580321122545536 142:128:8017685193881548305 142:129:870136377630555630 142:130:87013637763055563 142:131:7970714909592876 142:132:664226242466073 142:133:49941822741810 142:134:3354301527435 142:135:198773423848 142:136:10230985051 142:137:448072338 142:138:16234505 142:139:467180 142:140:10011 142:141:142 142:142:1 # binomial(143, k) for 0 <= k <= 143 143:0:1 143:1:143 143:2:10153 143:3:477191 143:4:16701685 143:5:464306843 143:6:10679057389 143:7:209004408899 143:8:3553074951283 143:9:53296124269245 143:10:714168065207883 143:11:8634941152058949 143:12:94984352672648439 143:13:957150015393611193 143:14:8887821571512103935 143:15:76435265515004093841 143:16:611482124120032750728 143:17:4568131162543774078968 143:18:31976918137806418552776 143:19:210374461432936964163000 143:20:1304321660884209177810600 143:21:7639598299464653755747800 143:22:42365045115213079918237800 143:23:222876976475686203048120600 143:24:1114384882378431015240603000 143:25:5304472040121331632545270280 143:26:24074142335935274332320842040 143:27:104321283455719522106723648840 143:28:432188174316552305870712259480 143:29:1713849656772535006039031373800 143:30:6512628695735633022948319220440 143:31:23739582019939565535263228126120 143:32:83088537069788479373421298441420 143:33:279479624689288521528780731121140 143:34:904198785759462863769584718333100 143:35:2815933361365184347168135265665940 143:36:8447800084095553041504405796997820 143:37:24430124567519572309215443791318020 143:38:68147189583080912230969395838939740 143:39:183473202723679379083379142643299300 143:40:477030327081566385616785770872578180 143:41:1198393260717105798012900839021354940 143:42:2910383633170114080888473466194719140 143:43:6836017370934454003947344653155037980 143:44:15536403115760122736243965120806904500 143:45:34180086854672270019736723265775189900 143:46:72818445907780053520308671305347143700 143:47:150284877724567344499360449289758998700 143:48:300569755449134688998720898579517997400 143:49:582737280972812152140377252348045097000 143:50:1095546088228886846023909234414324782360 143:51:1997760513829146601573010956873180485480 143:52:3534499370620797833552250154467934705080 143:53:6068668730688539676476504982199661474760 143:54:10114447884480899460794174970332769124600 143:55:16367015667614546400194210406538480947080 143:56:25719596049108572914590902067417612916840 143:57:39256225548639400764375587366058461820440 143:58:58207506847982559754074146784155650285480 143:59:83858272577601992866039025028020852106200 143:60:117401581608642790012454635039229192948680 143:61:159743135631431992967766142758295459258040 143:62:211273179383506829408981027519035929986440 143:63:271636944921651637811547035381617624268280 143:64:339546181152064547264433794227022030335350 143:65:412679204784816911290619534522072929176810 143:66:487711787472965440616186722616995279936230 143:67:560504591573408043693229517037442336643130 143:68:626446308229103107657138871983023788012910 143:69:680919900249025117018629208677199769579250 143:70:719829608834683695133979449173039756412350 143:71:740106499224393094996908447741294397438050 143:72:740106499224393094996908447741294397438050 143:73:719829608834683695133979449173039756412350 143:74:680919900249025117018629208677199769579250 143:75:626446308229103107657138871983023788012910 143:76:560504591573408043693229517037442336643130 143:77:487711787472965440616186722616995279936230 143:78:412679204784816911290619534522072929176810 143:79:339546181152064547264433794227022030335350 143:80:271636944921651637811547035381617624268280 143:81:211273179383506829408981027519035929986440 143:82:159743135631431992967766142758295459258040 143:83:117401581608642790012454635039229192948680 143:84:83858272577601992866039025028020852106200 143:85:58207506847982559754074146784155650285480 143:86:39256225548639400764375587366058461820440 143:87:25719596049108572914590902067417612916840 143:88:16367015667614546400194210406538480947080 143:89:10114447884480899460794174970332769124600 143:90:6068668730688539676476504982199661474760 143:91:3534499370620797833552250154467934705080 143:92:1997760513829146601573010956873180485480 143:93:1095546088228886846023909234414324782360 143:94:582737280972812152140377252348045097000 143:95:300569755449134688998720898579517997400 143:96:150284877724567344499360449289758998700 143:97:72818445907780053520308671305347143700 143:98:34180086854672270019736723265775189900 143:99:15536403115760122736243965120806904500 143:100:6836017370934454003947344653155037980 143:101:2910383633170114080888473466194719140 143:102:1198393260717105798012900839021354940 143:103:477030327081566385616785770872578180 143:104:183473202723679379083379142643299300 143:105:68147189583080912230969395838939740 143:106:24430124567519572309215443791318020 143:107:8447800084095553041504405796997820 143:108:2815933361365184347168135265665940 143:109:904198785759462863769584718333100 143:110:279479624689288521528780731121140 143:111:83088537069788479373421298441420 143:112:23739582019939565535263228126120 143:113:6512628695735633022948319220440 143:114:1713849656772535006039031373800 143:115:432188174316552305870712259480 143:116:104321283455719522106723648840 143:117:24074142335935274332320842040 143:118:5304472040121331632545270280 143:119:1114384882378431015240603000 143:120:222876976475686203048120600 143:121:42365045115213079918237800 143:122:7639598299464653755747800 143:123:1304321660884209177810600 143:124:210374461432936964163000 143:125:31976918137806418552776 143:126:4568131162543774078968 143:127:611482124120032750728 143:128:76435265515004093841 143:129:8887821571512103935 143:130:957150015393611193 143:131:94984352672648439 143:132:8634941152058949 143:133:714168065207883 143:134:53296124269245 143:135:3553074951283 143:136:209004408899 143:137:10679057389 143:138:464306843 143:139:16701685 143:140:477191 143:141:10153 143:142:143 143:143:1 # binomial(144, k) for 0 <= k <= 144 144:0:1 144:1:144 144:2:10296 144:3:487344 144:4:17178876 144:5:481008528 144:6:11143364232 144:7:219683466288 144:8:3762079360182 144:9:56849199220528 144:10:767464189477128 144:11:9349109217266832 144:12:103619293824707388 144:13:1052134368066259632 144:14:9844971586905715128 144:15:85323087086516197776 144:16:687917389635036844569 144:17:5179613286663806829696 144:18:36545049300350192631744 144:19:242351379570743382715776 144:20:1514696122317146141973600 144:21:8943919960348862933558400 144:22:50004643414677733673985600 144:23:265242021590899282966358400 144:24:1337261858854117218288723600 144:25:6418856922499762647785873280 144:26:29378614376056605964866112320 144:27:128395425791654796439044490880 144:28:536509457772271827977435908320 144:29:2146037831089087311909743633280 144:30:8226478352508168028987350594240 144:31:30252210715675198558211547346560 144:32:106828119089728044908684526567540 144:33:362568161759077000902202029562560 144:34:1183678410448751385298365449454240 144:35:3720132147124647210937719983999040 144:36:11263733445460737388672541062663760 144:37:32877924651615125350719849588315840 144:38:92577314150600484540184839630257760 144:39:251620392306760291314348538482239040 144:40:660503529805245764700164913515877480 144:41:1675423587798672183629686609893933120 144:42:4108776893887219878901374305216074080 144:43:9746401004104568084835818119349757120 144:44:22372420486694576740191309773961942480 144:45:49716489970432392755980688386582094400 144:46:106998532762452323540045394571122333600 144:47:223103323632347398019669120595106142400 144:48:450854633173702033498081347869276996100 144:49:883307036421946841139098150927563094400 144:50:1678283369201698998164286486762369879360 144:51:3093306602058033447596920191287505267840 144:52:5532259884449944435125261111341115190560 144:53:9603168101309337510028755136667596179840 144:54:16183116615169439137270679952532430599360 144:55:26481463552095445860988385376871250071680 144:56:42086611716723119314785112473956093863920 144:57:64975821597747973678966489433476074737280 144:58:97463732396621960518449734150214112105920 144:59:142065779425584552620113171812176502391680 144:60:201259854186244782878493660067250045054880 144:61:277144717240074782980220777797524652206720 144:62:371016315014938822376747170277331389244480 144:63:482910124305158467220528062900653554254720 144:64:611183126073716185075980829608639654603630 144:65:752225385936881458555053328749094959512160 144:66:900390992257782351906806257139068209113040 144:67:1048216379046373484309416239654437616579360 144:68:1186950899802511151350368389020466124656040 144:69:1307366208478128224675768080660223557592160 144:70:1400749509083708812152608657850239525991600 144:71:1459936108059076790130887896914334153850400 144:72:1480212998448786189993816895482588794876100 144:73:1459936108059076790130887896914334153850400 144:74:1400749509083708812152608657850239525991600 144:75:1307366208478128224675768080660223557592160 144:76:1186950899802511151350368389020466124656040 144:77:1048216379046373484309416239654437616579360 144:78:900390992257782351906806257139068209113040 144:79:752225385936881458555053328749094959512160 144:80:611183126073716185075980829608639654603630 144:81:482910124305158467220528062900653554254720 144:82:371016315014938822376747170277331389244480 144:83:277144717240074782980220777797524652206720 144:84:201259854186244782878493660067250045054880 144:85:142065779425584552620113171812176502391680 144:86:97463732396621960518449734150214112105920 144:87:64975821597747973678966489433476074737280 144:88:42086611716723119314785112473956093863920 144:89:26481463552095445860988385376871250071680 144:90:16183116615169439137270679952532430599360 144:91:9603168101309337510028755136667596179840 144:92:5532259884449944435125261111341115190560 144:93:3093306602058033447596920191287505267840 144:94:1678283369201698998164286486762369879360 144:95:883307036421946841139098150927563094400 144:96:450854633173702033498081347869276996100 144:97:223103323632347398019669120595106142400 144:98:106998532762452323540045394571122333600 144:99:49716489970432392755980688386582094400 144:100:22372420486694576740191309773961942480 144:101:9746401004104568084835818119349757120 144:102:4108776893887219878901374305216074080 144:103:1675423587798672183629686609893933120 144:104:660503529805245764700164913515877480 144:105:251620392306760291314348538482239040 144:106:92577314150600484540184839630257760 144:107:32877924651615125350719849588315840 144:108:11263733445460737388672541062663760 144:109:3720132147124647210937719983999040 144:110:1183678410448751385298365449454240 144:111:362568161759077000902202029562560 144:112:106828119089728044908684526567540 144:113:30252210715675198558211547346560 144:114:8226478352508168028987350594240 144:115:2146037831089087311909743633280 144:116:536509457772271827977435908320 144:117:128395425791654796439044490880 144:118:29378614376056605964866112320 144:119:6418856922499762647785873280 144:120:1337261858854117218288723600 144:121:265242021590899282966358400 144:122:50004643414677733673985600 144:123:8943919960348862933558400 144:124:1514696122317146141973600 144:125:242351379570743382715776 144:126:36545049300350192631744 144:127:5179613286663806829696 144:128:687917389635036844569 144:129:85323087086516197776 144:130:9844971586905715128 144:131:1052134368066259632 144:132:103619293824707388 144:133:9349109217266832 144:134:767464189477128 144:135:56849199220528 144:136:3762079360182 144:137:219683466288 144:138:11143364232 144:139:481008528 144:140:17178876 144:141:487344 144:142:10296 144:143:144 144:144:1 # binomial(145, k) for 0 <= k <= 145 145:0:1 145:1:145 145:2:10440 145:3:497640 145:4:17666220 145:5:498187404 145:6:11624372760 145:7:230826830520 145:8:3981762826470 145:9:60611278580710 145:10:824313388697656 145:11:10116573406743960 145:12:112968403041974220 145:13:1155753661890967020 145:14:10897105954971974760 145:15:95168058673421912904 145:16:773240476721553042345 145:17:5867530676298843674265 145:18:41724662587013999461440 145:19:278896428871093575347520 145:20:1757047501887889524689376 145:21:10458616082666009075532000 145:22:58948563375026596607544000 145:23:315246665005577016640344000 145:24:1602503880445016501255082000 145:25:7756118781353879866074596880 145:26:35797471298556368612651985600 145:27:157774040167711402403910603200 145:28:664904883563926624416480399200 145:29:2682547288861359139887179541600 145:30:10372516183597255340897094227520 145:31:38478689068183366587198897940800 145:32:137080329805403243466896073914100 145:33:469396280848805045810886556130100 145:34:1546246572207828386200567479016800 145:35:4903810557573398596236085433453280 145:36:14983865592585384599610261046662800 145:37:44141658097075862739392390650979600 145:38:125455238802215609890904689218573600 145:39:344197706457360775854533378112496800 145:40:912123922112006056014513451998116520 145:41:2335927117603917948329851523409810600 145:42:5784200481685892062531060915110007200 145:43:13855177897991787963737192424565831200 145:44:32118821490799144825027127893311699600 145:45:72088910457126969496171998160544036880 145:46:156715022732884716296026082957704428000 145:47:330101856394799721559714515166228476000 145:48:673957956806049431517750468464383138500 145:49:1334161669595648874637179498796840090500 145:50:2561590405623645839303384637689932973760 145:51:4771589971259732445761206678049875147200 145:52:8625566486507977882722181302628620458400 145:53:15135427985759281945154016248008711370400 145:54:25786284716478776647299435089200026779200 145:55:42664580167264884998259065329403680671040 145:56:68568075268818565175773497850827343935600 145:57:107062433314471092993751601907432168601200 145:58:162439553994369934197416223583690186843200 145:59:239529511822206513138562905962390614497600 145:60:343325633611829335498606831879426547446560 145:61:478404571426319565858714437864774697261600 145:62:648161032255013605356967948074856041451200 145:63:853926439320097289597275233177984943499200 145:64:1094093250378874652296508892509293208858350 145:65:1363408512010597643631034158357734614115790 145:66:1652616378194663810461859585888163168625200 145:67:1948607371304155836216222496793505825692400 145:68:2235167278848884635659784628674903741235400 145:69:2494317108280639376026136469680689682248200 145:70:2708115717561837036828376738510463083583760 145:71:2860685617142785602283496554764573679842000 145:72:2940149106507862980124704792396922948726500 145:73:2940149106507862980124704792396922948726500 145:74:2860685617142785602283496554764573679842000 145:75:2708115717561837036828376738510463083583760 145:76:2494317108280639376026136469680689682248200 145:77:2235167278848884635659784628674903741235400 145:78:1948607371304155836216222496793505825692400 145:79:1652616378194663810461859585888163168625200 145:80:1363408512010597643631034158357734614115790 145:81:1094093250378874652296508892509293208858350 145:82:853926439320097289597275233177984943499200 145:83:648161032255013605356967948074856041451200 145:84:478404571426319565858714437864774697261600 145:85:343325633611829335498606831879426547446560 145:86:239529511822206513138562905962390614497600 145:87:162439553994369934197416223583690186843200 145:88:107062433314471092993751601907432168601200 145:89:68568075268818565175773497850827343935600 145:90:42664580167264884998259065329403680671040 145:91:25786284716478776647299435089200026779200 145:92:15135427985759281945154016248008711370400 145:93:8625566486507977882722181302628620458400 145:94:4771589971259732445761206678049875147200 145:95:2561590405623645839303384637689932973760 145:96:1334161669595648874637179498796840090500 145:97:673957956806049431517750468464383138500 145:98:330101856394799721559714515166228476000 145:99:156715022732884716296026082957704428000 145:100:72088910457126969496171998160544036880 145:101:32118821490799144825027127893311699600 145:102:13855177897991787963737192424565831200 145:103:5784200481685892062531060915110007200 145:104:2335927117603917948329851523409810600 145:105:912123922112006056014513451998116520 145:106:344197706457360775854533378112496800 145:107:125455238802215609890904689218573600 145:108:44141658097075862739392390650979600 145:109:14983865592585384599610261046662800 145:110:4903810557573398596236085433453280 145:111:1546246572207828386200567479016800 145:112:469396280848805045810886556130100 145:113:137080329805403243466896073914100 145:114:38478689068183366587198897940800 145:115:10372516183597255340897094227520 145:116:2682547288861359139887179541600 145:117:664904883563926624416480399200 145:118:157774040167711402403910603200 145:119:35797471298556368612651985600 145:120:7756118781353879866074596880 145:121:1602503880445016501255082000 145:122:315246665005577016640344000 145:123:58948563375026596607544000 145:124:10458616082666009075532000 145:125:1757047501887889524689376 145:126:278896428871093575347520 145:127:41724662587013999461440 145:128:5867530676298843674265 145:129:773240476721553042345 145:130:95168058673421912904 145:131:10897105954971974760 145:132:1155753661890967020 145:133:112968403041974220 145:134:10116573406743960 145:135:824313388697656 145:136:60611278580710 145:137:3981762826470 145:138:230826830520 145:139:11624372760 145:140:498187404 145:141:17666220 145:142:497640 145:143:10440 145:144:145 145:145:1 # binomial(146, k) for 0 <= k <= 146 146:0:1 146:1:146 146:2:10585 146:3:508080 146:4:18163860 146:5:515853624 146:6:12122560164 146:7:242451203280 146:8:4212589656990 146:9:64593041407180 146:10:884924667278366 146:11:10940886795441616 146:12:123084976448718180 146:13:1268722064932941240 146:14:12052859616862941780 146:15:106065164628393887664 146:16:868408535394974955249 146:17:6640771153020396716610 146:18:47592193263312843135705 146:19:320621091458107574808960 146:20:2035943930758983100036896 146:21:12215663584553898600221376 146:22:69407179457692605683076000 146:23:374195228380603613247888000 146:24:1917750545450593517895426000 146:25:9358622661798896367329678880 146:26:43553590079910248478726582480 146:27:193571511466267771016562588800 146:28:822678923731638026820391002400 146:29:3347452172425285764303659940800 146:30:13055063472458614480784273769120 146:31:48851205251780621928095992168320 146:32:175559018873586610054094971854900 146:33:606476610654208289277782630044200 146:34:2015642853056633432011454035146900 146:35:6450057129781226982436652912470080 146:36:19887676150158783195846346480116080 146:37:59125523689661247339002651697642400 146:38:169596896899291472630297079869553200 146:39:469652945259576385745438067331070400 146:40:1256321628569366831869046830110613320 146:41:3248051039715924004344364975407927120 146:42:8120127599289810010860912438519817800 146:43:19639378379677680026268253339675838400 146:44:45973999388790932788764320317877530800 146:45:104207731947926114321199126053855736480 146:46:228803933190011685792198081118248464880 146:47:486816879127684437855740598123932904000 146:48:1004059813200849153077464983630611614500 146:49:2008119626401698306154929967261223229000 146:50:3895752075219294713940564136486773064260 146:51:7333180376883378285064591315739808120960 146:52:13397156457767710328483387980678495605600 146:53:23760994472267259827876197550637331828800 146:54:40921712702238058592453451337208738149600 146:55:68450864883743661645558500418603707450240 146:56:111232655436083450174032563180231024606640 146:57:175630508583289658169525099758259512536800 146:58:269501987308841027191167825491122355444400 146:59:401969065816576447335979129546080801340800 146:60:582855145434035848637169737841817161944160 146:61:821730205038148901357321269744201244708160 146:62:1126565603681333171215682385939630738712800 146:63:1502087471575110894954243181252840984950400 146:64:1948019689698971941893784125687278152357550 146:65:2457501762389472295927543050867027822974140 146:66:3016024890205261454092893744245897782740990 146:67:3601223749498819646678082082681668994317600 146:68:4183774650153040471876007125468409566927800 146:69:4729484387129524011685921098355593423483600 146:70:5202432825842476412854513208191152765831960 146:71:5568801334704622639111873293275036763425760 146:72:5800834723650648582408201347161496628568500 146:73:5880298213015725960249409584793845897453000 146:74:5800834723650648582408201347161496628568500 146:75:5568801334704622639111873293275036763425760 146:76:5202432825842476412854513208191152765831960 146:77:4729484387129524011685921098355593423483600 146:78:4183774650153040471876007125468409566927800 146:79:3601223749498819646678082082681668994317600 146:80:3016024890205261454092893744245897782740990 146:81:2457501762389472295927543050867027822974140 146:82:1948019689698971941893784125687278152357550 146:83:1502087471575110894954243181252840984950400 146:84:1126565603681333171215682385939630738712800 146:85:821730205038148901357321269744201244708160 146:86:582855145434035848637169737841817161944160 146:87:401969065816576447335979129546080801340800 146:88:269501987308841027191167825491122355444400 146:89:175630508583289658169525099758259512536800 146:90:111232655436083450174032563180231024606640 146:91:68450864883743661645558500418603707450240 146:92:40921712702238058592453451337208738149600 146:93:23760994472267259827876197550637331828800 146:94:13397156457767710328483387980678495605600 146:95:7333180376883378285064591315739808120960 146:96:3895752075219294713940564136486773064260 146:97:2008119626401698306154929967261223229000 146:98:1004059813200849153077464983630611614500 146:99:486816879127684437855740598123932904000 146:100:228803933190011685792198081118248464880 146:101:104207731947926114321199126053855736480 146:102:45973999388790932788764320317877530800 146:103:19639378379677680026268253339675838400 146:104:8120127599289810010860912438519817800 146:105:3248051039715924004344364975407927120 146:106:1256321628569366831869046830110613320 146:107:469652945259576385745438067331070400 146:108:169596896899291472630297079869553200 146:109:59125523689661247339002651697642400 146:110:19887676150158783195846346480116080 146:111:6450057129781226982436652912470080 146:112:2015642853056633432011454035146900 146:113:606476610654208289277782630044200 146:114:175559018873586610054094971854900 146:115:48851205251780621928095992168320 146:116:13055063472458614480784273769120 146:117:3347452172425285764303659940800 146:118:822678923731638026820391002400 146:119:193571511466267771016562588800 146:120:43553590079910248478726582480 146:121:9358622661798896367329678880 146:122:1917750545450593517895426000 146:123:374195228380603613247888000 146:124:69407179457692605683076000 146:125:12215663584553898600221376 146:126:2035943930758983100036896 146:127:320621091458107574808960 146:128:47592193263312843135705 146:129:6640771153020396716610 146:130:868408535394974955249 146:131:106065164628393887664 146:132:12052859616862941780 146:133:1268722064932941240 146:134:123084976448718180 146:135:10940886795441616 146:136:884924667278366 146:137:64593041407180 146:138:4212589656990 146:139:242451203280 146:140:12122560164 146:141:515853624 146:142:18163860 146:143:508080 146:144:10585 146:145:146 146:146:1 # binomial(147, k) for 0 <= k <= 147 147:0:1 147:1:147 147:2:10731 147:3:518665 147:4:18671940 147:5:534017484 147:6:12638413788 147:7:254573763444 147:8:4455040860270 147:9:68805631064170 147:10:949517708685546 147:11:11825811462719982 147:12:134025863244159796 147:13:1391807041381659420 147:14:13321581681795883020 147:15:118118024245256829444 147:16:974473700023368842913 147:17:7509179688415371671859 147:18:54232964416333239852315 147:19:368213284721420417944665 147:20:2356565022217090674845856 147:21:14251607515312881700258272 147:22:81622843042246504283297376 147:23:443602407838296218930964000 147:24:2291945773831197131143314000 147:25:11276373207249489885225104880 147:26:52912212741709144846056261360 147:27:237125101546178019495289171280 147:28:1016250435197905797836953591200 147:29:4170131096156923791124050943200 147:30:16402515644883900245087933709920 147:31:61906268724239236408880265937440 147:32:224410224125367231982190964023220 147:33:782035629527794899331877601899100 147:34:2622119463710841721289236665191100 147:35:8465699982837860414448106947616980 147:36:26337733279940010178282999392586160 147:37:79013199839820030534848998177758480 147:38:228722420588952719969299731567195600 147:39:639249842158867858375735147200623600 147:40:1725974573828943217614484897441683720 147:41:4504372668285290836213411805518540440 147:42:11368178639005734015205277413927744920 147:43:27759505978967490037129165778195656200 147:44:65613377768468612815032573657553369200 147:45:150181731336717047109963446371733267280 147:46:333011665137937800113397207172104201360 147:47:715620812317696123647938679242181368880 147:48:1490876692328533590933205581754544518500 147:49:3012179439602547459232394950891834843500 147:50:5903871701620993020095494103747996293260 147:51:11228932452102672999005155452226581185220 147:52:20730336834651088613547979296418303726560 147:53:37158150930034970156359585531315827434400 147:54:64682707174505318420329648887846069978400 147:55:109372577585981720238011951755812445599840 147:56:179683520319827111819591063598834732056880 147:57:286863164019373108343557662938490537143440 147:58:445132495892130685360692925249381867981200 147:59:671471053125417474527146955037203156785200 147:60:984824211250612295973148867387897963284960 147:61:1404585350472184749994491007586018406652320 147:62:1948295808719482072573003655683831983420960 147:63:2628653075256444066169925567192471723663200 147:64:3450107161274082836848027306940119137307950 147:65:4405521452088444237821327176554305975331690 147:66:5473526652594733750020436795112925605715130 147:67:6617248639704081100770975826927566777058590 147:68:7784998399651860118554089208150078561245400 147:69:8913259037282564483561928223824002990411400 147:70:9931917212972000424540434306546746189315560 147:71:10771234160547099051966386501466189529257720 147:72:11369636058355271221520074640436533391994260 147:73:11681132936666374542657610931955342526021500 147:74:11681132936666374542657610931955342526021500 147:75:11369636058355271221520074640436533391994260 147:76:10771234160547099051966386501466189529257720 147:77:9931917212972000424540434306546746189315560 147:78:8913259037282564483561928223824002990411400 147:79:7784998399651860118554089208150078561245400 147:80:6617248639704081100770975826927566777058590 147:81:5473526652594733750020436795112925605715130 147:82:4405521452088444237821327176554305975331690 147:83:3450107161274082836848027306940119137307950 147:84:2628653075256444066169925567192471723663200 147:85:1948295808719482072573003655683831983420960 147:86:1404585350472184749994491007586018406652320 147:87:984824211250612295973148867387897963284960 147:88:671471053125417474527146955037203156785200 147:89:445132495892130685360692925249381867981200 147:90:286863164019373108343557662938490537143440 147:91:179683520319827111819591063598834732056880 147:92:109372577585981720238011951755812445599840 147:93:64682707174505318420329648887846069978400 147:94:37158150930034970156359585531315827434400 147:95:20730336834651088613547979296418303726560 147:96:11228932452102672999005155452226581185220 147:97:5903871701620993020095494103747996293260 147:98:3012179439602547459232394950891834843500 147:99:1490876692328533590933205581754544518500 147:100:715620812317696123647938679242181368880 147:101:333011665137937800113397207172104201360 147:102:150181731336717047109963446371733267280 147:103:65613377768468612815032573657553369200 147:104:27759505978967490037129165778195656200 147:105:11368178639005734015205277413927744920 147:106:4504372668285290836213411805518540440 147:107:1725974573828943217614484897441683720 147:108:639249842158867858375735147200623600 147:109:228722420588952719969299731567195600 147:110:79013199839820030534848998177758480 147:111:26337733279940010178282999392586160 147:112:8465699982837860414448106947616980 147:113:2622119463710841721289236665191100 147:114:782035629527794899331877601899100 147:115:224410224125367231982190964023220 147:116:61906268724239236408880265937440 147:117:16402515644883900245087933709920 147:118:4170131096156923791124050943200 147:119:1016250435197905797836953591200 147:120:237125101546178019495289171280 147:121:52912212741709144846056261360 147:122:11276373207249489885225104880 147:123:2291945773831197131143314000 147:124:443602407838296218930964000 147:125:81622843042246504283297376 147:126:14251607515312881700258272 147:127:2356565022217090674845856 147:128:368213284721420417944665 147:129:54232964416333239852315 147:130:7509179688415371671859 147:131:974473700023368842913 147:132:118118024245256829444 147:133:13321581681795883020 147:134:1391807041381659420 147:135:134025863244159796 147:136:11825811462719982 147:137:949517708685546 147:138:68805631064170 147:139:4455040860270 147:140:254573763444 147:141:12638413788 147:142:534017484 147:143:18671940 147:144:518665 147:145:10731 147:146:147 147:147:1 # binomial(148, k) for 0 <= k <= 148 148:0:1 148:1:148 148:2:10878 148:3:529396 148:4:19190605 148:5:552689424 148:6:13172431272 148:7:267212177232 148:8:4709614623714 148:9:73260671924440 148:10:1018323339749716 148:11:12775329171405528 148:12:145851674706879778 148:13:1525832904625819216 148:14:14713388723177542440 148:15:131439605927052712464 148:16:1092591724268625672357 148:17:8483653388438740514772 148:18:61742144104748611524174 148:19:422446249137753657796980 148:20:2724778306938511092790521 148:21:16608172537529972375104128 148:22:95874450557559385983555648 148:23:525225250880542723214261376 148:24:2735548181669493350074278000 148:25:13568318981080687016368418880 148:26:64188585948958634731281366240 148:27:290037314287887164341345432640 148:28:1253375536744083817332242762480 148:29:5186381531354829588961004534400 148:30:20572646741040824036211984653120 148:31:78308784369123136653968199647360 148:32:286316492849606468391071229960660 148:33:1006445853653162131314068565922320 148:34:3404155093238636620621114267090200 148:35:11087819446548702135737343612808080 148:36:34803433262777870592731106340203140 148:37:105350933119760040713131997570344640 148:38:307735620428772750504148729744954080 148:39:867972262747820578345034878767819200 148:40:2365224415987811075990220044642307320 148:41:6230347242114234053827896702960224160 148:42:15872551307291024851418689219446285360 148:43:39127684617973224052334443192123401120 148:44:93372883747436102852161739435749025400 148:45:215795109105185659924996020029286636480 148:46:483193396474654847223360653543837468640 148:47:1048632477455633923761335886414285570240 148:48:2206497504646229714581144260996725887380 148:49:4503056131931081050165600532646379362000 148:50:8916051141223540479327889054639831136760 148:51:17132804153723666019100649555974577478480 148:52:31959269286753761612553134748644884911780 148:53:57888487764686058769907564827734131160960 148:54:101840858104540288576689234419161897412800 148:55:174055284760487038658341600643658515578240 148:56:289056097905808832057603015354647177656720 148:57:466546684339200220163148726537325269200320 148:58:731995659911503793704250588187872405124640 148:59:1116603549017548159887839880286585024766400 148:60:1656295264376029770500295822425101120070160 148:61:2389409561722797045967639874973916369937280 148:62:3352881159191666822567494663269850390073280 148:63:4576948883975926138742929222876303707084160 148:64:6078760236530526903017952874132590860971150 148:65:7855628613362527074669354483494425112639640 148:66:9879048104683177987841763971667231581046820 148:67:12090775292298814850791412622040492382773720 148:68:14402247039355941219325065035077645338303990 148:69:16698257436934424602116017431974081551656800 148:70:18845176250254564908102362530370749179726960 148:71:20703151373519099476506820808012935718573280 148:72:22140870218902370273486461141902722921251980 148:73:23050768995021645764177685572391875918015760 148:74:23362265873332749085315221863910685052043000 148:75:23050768995021645764177685572391875918015760 148:76:22140870218902370273486461141902722921251980 148:77:20703151373519099476506820808012935718573280 148:78:18845176250254564908102362530370749179726960 148:79:16698257436934424602116017431974081551656800 148:80:14402247039355941219325065035077645338303990 148:81:12090775292298814850791412622040492382773720 148:82:9879048104683177987841763971667231581046820 148:83:7855628613362527074669354483494425112639640 148:84:6078760236530526903017952874132590860971150 148:85:4576948883975926138742929222876303707084160 148:86:3352881159191666822567494663269850390073280 148:87:2389409561722797045967639874973916369937280 148:88:1656295264376029770500295822425101120070160 148:89:1116603549017548159887839880286585024766400 148:90:731995659911503793704250588187872405124640 148:91:466546684339200220163148726537325269200320 148:92:289056097905808832057603015354647177656720 148:93:174055284760487038658341600643658515578240 148:94:101840858104540288576689234419161897412800 148:95:57888487764686058769907564827734131160960 148:96:31959269286753761612553134748644884911780 148:97:17132804153723666019100649555974577478480 148:98:8916051141223540479327889054639831136760 148:99:4503056131931081050165600532646379362000 148:100:2206497504646229714581144260996725887380 148:101:1048632477455633923761335886414285570240 148:102:483193396474654847223360653543837468640 148:103:215795109105185659924996020029286636480 148:104:93372883747436102852161739435749025400 148:105:39127684617973224052334443192123401120 148:106:15872551307291024851418689219446285360 148:107:6230347242114234053827896702960224160 148:108:2365224415987811075990220044642307320 148:109:867972262747820578345034878767819200 148:110:307735620428772750504148729744954080 148:111:105350933119760040713131997570344640 148:112:34803433262777870592731106340203140 148:113:11087819446548702135737343612808080 148:114:3404155093238636620621114267090200 148:115:1006445853653162131314068565922320 148:116:286316492849606468391071229960660 148:117:78308784369123136653968199647360 148:118:20572646741040824036211984653120 148:119:5186381531354829588961004534400 148:120:1253375536744083817332242762480 148:121:290037314287887164341345432640 148:122:64188585948958634731281366240 148:123:13568318981080687016368418880 148:124:2735548181669493350074278000 148:125:525225250880542723214261376 148:126:95874450557559385983555648 148:127:16608172537529972375104128 148:128:2724778306938511092790521 148:129:422446249137753657796980 148:130:61742144104748611524174 148:131:8483653388438740514772 148:132:1092591724268625672357 148:133:131439605927052712464 148:134:14713388723177542440 148:135:1525832904625819216 148:136:145851674706879778 148:137:12775329171405528 148:138:1018323339749716 148:139:73260671924440 148:140:4709614623714 148:141:267212177232 148:142:13172431272 148:143:552689424 148:144:19190605 148:145:529396 148:146:10878 148:147:148 148:148:1 # binomial(149, k) for 0 <= k <= 149 149:0:1 149:1:149 149:2:11026 149:3:540274 149:4:19720001 149:5:571880029 149:6:13725120696 149:7:280384608504 149:8:4976826800946 149:9:77970286548154 149:10:1091584011674156 149:11:13793652511155244 149:12:158627003878285306 149:13:1671684579332698994 149:14:16239221627803361656 149:15:146152994650230254904 149:16:1224031330195678384821 149:17:9576245112707366187129 149:18:70225797493187352038946 149:19:484188393242502269321154 149:20:3147224556076264750587501 149:21:19332950844468483467894649 149:22:112482623095089358358659776 149:23:621099701438102109197817024 149:24:3260773432550036073288539376 149:25:16303867162750180366442696880 149:26:77756904930039321747649785120 149:27:354225900236845799072626798880 149:28:1543412851031970981673588195120 149:29:6439757068098913406293247296880 149:30:25759028272395653625172989187520 149:31:98881431110163960690180184300480 149:32:364625277218729605045039429608020 149:33:1292762346502768599705139795882980 149:34:4410600946891798751935182833012520 149:35:14491974539787338756358457879898280 149:36:45891252709326572728468449953011220 149:37:140154366382537911305863103910547780 149:38:413086553548532791217280727315298720 149:39:1175707883176593328849183608512773280 149:40:3233196678735631654335254923410126520 149:41:8595571658102045129818116747602531480 149:42:22102898549405258905246585922406509520 149:43:55000235925264248903753132411569686480 149:44:132500568365409326904496182627872426520 149:45:309167992852621762777157759465035661880 149:46:698988505579840507148356673573124105120 149:47:1531825873930288770984696539958123038880 149:48:3255129982101863638342480147411011457620 149:49:6709553636577310764746744793643105249380 149:50:13419107273154621529493489587286210498760 149:51:26048855294947206498428538610614408615240 149:52:49092073440477427631653784304619462390260 149:53:89847757051439820382460699576379016072740 149:54:159729345869226347346596799246896028573760 149:55:275896142865027327235030835062820412991040 149:56:463111382666295870715944615998305693234960 149:57:755602782245009052220751741891972446857040 149:58:1198542344250704013867399314725197674324960 149:59:1848599208929051953592090468474457429891040 149:60:2772898813393577930388135702711686144836560 149:61:4045704826098826816467935697399017490007440 149:62:5742290720914463868535134538243766760010560 149:63:7929830043167592961310423886146154097157440 149:64:10655709120506453041760882097008894568055310 149:65:13934388849893053977687307357627015973610790 149:66:17734676718045705062511118455161656693686460 149:67:21969823396981992838633176593707723963820540 149:68:26493022331654756070116477657118137721077710 149:69:31100504476290365821441082467051726889960790 149:70:35543433687188989510218379962344830731383760 149:71:39548327623773664384609183338383684898300240 149:72:42844021592421469749993281949915658639825260 149:73:45191639213924016037664146714294598839267740 149:74:46413034868354394849492907436302560970058760 149:75:46413034868354394849492907436302560970058760 149:76:45191639213924016037664146714294598839267740 149:77:42844021592421469749993281949915658639825260 149:78:39548327623773664384609183338383684898300240 149:79:35543433687188989510218379962344830731383760 149:80:31100504476290365821441082467051726889960790 149:81:26493022331654756070116477657118137721077710 149:82:21969823396981992838633176593707723963820540 149:83:17734676718045705062511118455161656693686460 149:84:13934388849893053977687307357627015973610790 149:85:10655709120506453041760882097008894568055310 149:86:7929830043167592961310423886146154097157440 149:87:5742290720914463868535134538243766760010560 149:88:4045704826098826816467935697399017490007440 149:89:2772898813393577930388135702711686144836560 149:90:1848599208929051953592090468474457429891040 149:91:1198542344250704013867399314725197674324960 149:92:755602782245009052220751741891972446857040 149:93:463111382666295870715944615998305693234960 149:94:275896142865027327235030835062820412991040 149:95:159729345869226347346596799246896028573760 149:96:89847757051439820382460699576379016072740 149:97:49092073440477427631653784304619462390260 149:98:26048855294947206498428538610614408615240 149:99:13419107273154621529493489587286210498760 149:100:6709553636577310764746744793643105249380 149:101:3255129982101863638342480147411011457620 149:102:1531825873930288770984696539958123038880 149:103:698988505579840507148356673573124105120 149:104:309167992852621762777157759465035661880 149:105:132500568365409326904496182627872426520 149:106:55000235925264248903753132411569686480 149:107:22102898549405258905246585922406509520 149:108:8595571658102045129818116747602531480 149:109:3233196678735631654335254923410126520 149:110:1175707883176593328849183608512773280 149:111:413086553548532791217280727315298720 149:112:140154366382537911305863103910547780 149:113:45891252709326572728468449953011220 149:114:14491974539787338756358457879898280 149:115:4410600946891798751935182833012520 149:116:1292762346502768599705139795882980 149:117:364625277218729605045039429608020 149:118:98881431110163960690180184300480 149:119:25759028272395653625172989187520 149:120:6439757068098913406293247296880 149:121:1543412851031970981673588195120 149:122:354225900236845799072626798880 149:123:77756904930039321747649785120 149:124:16303867162750180366442696880 149:125:3260773432550036073288539376 149:126:621099701438102109197817024 149:127:112482623095089358358659776 149:128:19332950844468483467894649 149:129:3147224556076264750587501 149:130:484188393242502269321154 149:131:70225797493187352038946 149:132:9576245112707366187129 149:133:1224031330195678384821 149:134:146152994650230254904 149:135:16239221627803361656 149:136:1671684579332698994 149:137:158627003878285306 149:138:13793652511155244 149:139:1091584011674156 149:140:77970286548154 149:141:4976826800946 149:142:280384608504 149:143:13725120696 149:144:571880029 149:145:19720001 149:146:540274 149:147:11026 149:148:149 149:149:1 # binomial(150, k) for 0 <= k <= 150 150:0:1 150:1:150 150:2:11175 150:3:551300 150:4:20260275 150:5:591600030 150:6:14297000725 150:7:294109729200 150:8:5257211409450 150:9:82947113349100 150:10:1169554298222310 150:11:14885236522829400 150:12:172420656389440550 150:13:1830311583210984300 150:14:17910906207136060650 150:15:162392216278033616560 150:16:1370184324845908639725 150:17:10800276442903044571950 150:18:79802042605894718226075 150:19:554414190735689621360100 150:20:3631412949318767019908655 150:21:22480175400544748218482150 150:22:131815573939557841826554425 150:23:733582324533191467556476800 150:24:3881873133988138182486356400 150:25:19564640595300216439731236256 150:26:94060772092789502114092482000 150:27:431982805166885120820276584000 150:28:1897638751268816780746214994000 150:29:7983169919130884387966835492000 150:30:32198785340494567031466236484400 150:31:124640459382559614315353173488000 150:32:463506708328893565735219613908500 150:33:1657387623721498204750179225491000 150:34:5703363293394567351640322628895500 150:35:18902575486679137508293640712910800 150:36:60383227249113911484826907832909500 150:37:186045619091864484034331553863559000 150:38:553240919931070702523143831225846500 150:39:1588794436725126120066464335828072000 150:40:4408904561912224983184438531922899800 150:41:11828768336837676784153371671012658000 150:42:30698470207507304035064702670009041000 150:43:77103134474669507808999718333976196000 150:44:187500804290673575808249315039442113000 150:45:441668561218031089681653942092908088400 150:46:1008156498432462269925514433038159767000 150:47:2230814379510129278133053213531247144000 150:48:4786955856032152409327176687369134496500 150:49:9964683618679174403089224941054116707000 150:50:20128660909731932294240234380929315748140 150:51:39467962568101828027922028197900619114000 150:52:75140928735424634130082322915233871005500 150:53:138939830491917248014114483880998478463000 150:54:249577102920666167729057498823275044646500 150:55:435625488734253674581627634309716441564800 150:56:739007525531323197950975451061126106226000 150:57:1218714164911304922936696357890278140092000 150:58:1954145126495713066088151056617170121182000 150:59:3047141553179755967459489783199655104216000 150:60:4621498022322629883980226171186143574727600 150:61:6818603639492404746856071400110703634844000 150:62:9787995547013290685003070235642784250018000 150:63:13672120764082056829845558424389920857168000 150:64:18585539163674046003071305983155048665212750 150:65:24590097970399507019448189454635910541666100 150:66:31669065567938759040198425812788672667297250 150:67:39704500115027697901144295048869380657507000 150:68:48462845728636748908749654250825861684898250 150:69:57593526807945121891557560124169864611038500 150:70:66643938163479355331659462429396557621344550 150:71:75091761310962653894827563300728515629684000 150:72:82392349216195134134602465288299343538125500 150:73:88035660806345485787657428664210257479093000 150:74:91604674082278410887157054150597159809326500 150:75:92826069736708789698985814872605121940117520 150:76:91604674082278410887157054150597159809326500 150:77:88035660806345485787657428664210257479093000 150:78:82392349216195134134602465288299343538125500 150:79:75091761310962653894827563300728515629684000 150:80:66643938163479355331659462429396557621344550 150:81:57593526807945121891557560124169864611038500 150:82:48462845728636748908749654250825861684898250 150:83:39704500115027697901144295048869380657507000 150:84:31669065567938759040198425812788672667297250 150:85:24590097970399507019448189454635910541666100 150:86:18585539163674046003071305983155048665212750 150:87:13672120764082056829845558424389920857168000 150:88:9787995547013290685003070235642784250018000 150:89:6818603639492404746856071400110703634844000 150:90:4621498022322629883980226171186143574727600 150:91:3047141553179755967459489783199655104216000 150:92:1954145126495713066088151056617170121182000 150:93:1218714164911304922936696357890278140092000 150:94:739007525531323197950975451061126106226000 150:95:435625488734253674581627634309716441564800 150:96:249577102920666167729057498823275044646500 150:97:138939830491917248014114483880998478463000 150:98:75140928735424634130082322915233871005500 150:99:39467962568101828027922028197900619114000 150:100:20128660909731932294240234380929315748140 150:101:9964683618679174403089224941054116707000 150:102:4786955856032152409327176687369134496500 150:103:2230814379510129278133053213531247144000 150:104:1008156498432462269925514433038159767000 150:105:441668561218031089681653942092908088400 150:106:187500804290673575808249315039442113000 150:107:77103134474669507808999718333976196000 150:108:30698470207507304035064702670009041000 150:109:11828768336837676784153371671012658000 150:110:4408904561912224983184438531922899800 150:111:1588794436725126120066464335828072000 150:112:553240919931070702523143831225846500 150:113:186045619091864484034331553863559000 150:114:60383227249113911484826907832909500 150:115:18902575486679137508293640712910800 150:116:5703363293394567351640322628895500 150:117:1657387623721498204750179225491000 150:118:463506708328893565735219613908500 150:119:124640459382559614315353173488000 150:120:32198785340494567031466236484400 150:121:7983169919130884387966835492000 150:122:1897638751268816780746214994000 150:123:431982805166885120820276584000 150:124:94060772092789502114092482000 150:125:19564640595300216439731236256 150:126:3881873133988138182486356400 150:127:733582324533191467556476800 150:128:131815573939557841826554425 150:129:22480175400544748218482150 150:130:3631412949318767019908655 150:131:554414190735689621360100 150:132:79802042605894718226075 150:133:10800276442903044571950 150:134:1370184324845908639725 150:135:162392216278033616560 150:136:17910906207136060650 150:137:1830311583210984300 150:138:172420656389440550 150:139:14885236522829400 150:140:1169554298222310 150:141:82947113349100 150:142:5257211409450 150:143:294109729200 150:144:14297000725 150:145:591600030 150:146:20260275 150:147:551300 150:148:11175 150:149:150 150:150:1 # binomial(151, k) for 0 <= k <= 151 151:0:1 151:1:151 151:2:11325 151:3:562475 151:4:20811575 151:5:611860305 151:6:14888600755 151:7:308406729925 151:8:5551321138650 151:9:88204324758550 151:10:1252501411571410 151:11:16054790821051710 151:12:187305892912269950 151:13:2002732239600424850 151:14:19741217790347044950 151:15:180303122485169677210 151:16:1532576541123942256285 151:17:12170460767748953211675 151:18:90602319048797762798025 151:19:634216233341584339586175 151:20:4185827140054456641268755 151:21:26111588349863515238390805 151:22:154295749340102590045036575 151:23:865397898472749309383031225 151:24:4615455458521329650042833200 151:25:23446513729288354622217592656 151:26:113625412688089718553823718256 151:27:526043577259674622934369066000 151:28:2329621556435701901566491578000 151:29:9880808670399701168713050486000 151:30:40181955259625451419433071976400 151:31:156839244723054181346819409972400 151:32:588147167711453180050572787396500 151:33:2120894332050391770485398839399500 151:34:7360750917116065556390501854386500 151:35:24605938780073704859933963341806300 151:36:79285802735793048993120548545820300 151:37:246428846340978395519158461696468500 151:38:739286539022935186557475385089405500 151:39:2142035356656196822589608167053918500 151:40:5997698998637351103250902867750971800 151:41:16237672898749901767337810202935557800 151:42:42527238544344980819218074341021699000 151:43:107801604682176811844064421003985237000 151:44:264603938765343083617249033373418309000 151:45:629169365508704665489903257132350201400 151:46:1449825059650493359607168375131067855400 151:47:3238970877942591548058567646569406911000 151:48:7017770235542281687460229900900381640500 151:49:14751639474711326812416401628423251203500 151:50:30093344528411106697329459321983432455140 151:51:59596623477833760322162262578829934862140 151:52:114608891303526462158004351113134490119500 151:53:214080759227341882144196806796232349468500 151:54:388516933412583415743171982704273523109500 151:55:685202591654919842310685133132991486211300 151:56:1174633014265576872532603085370842547790800 151:57:1957721690442628120887671808951404246318000 151:58:3172859291407017989024847414507448261274000 151:59:5001286679675469033547640839816825225398000 151:60:7668639575502385851439715954385798678943600 151:61:11440101661815034630836297571296847209571600 151:62:16606599186505695431859141635753487884862000 151:63:23460116311095347514848628660032705107186000 151:64:32257659927756102832916864407544969522380750 151:65:43175637134073553022519495437790959206878850 151:66:56259163538338266059646615267424583208963350 151:67:71373565682966456941342720861658053324804250 151:68:88167345843664446809893949299695242342405250 151:69:106056372536581870800307214374995726295936750 151:70:124237464971424477223217022553566422232383050 151:71:141735699474442009226487025730125073251028550 151:72:157484110527157788029430028589027859167809500 151:73:170428010022540619922259893952509601017218500 151:74:179640334888623896674814482814807417288419500 151:75:184430743818987200586142869023202281749444020 151:76:184430743818987200586142869023202281749444020 151:77:179640334888623896674814482814807417288419500 151:78:170428010022540619922259893952509601017218500 151:79:157484110527157788029430028589027859167809500 151:80:141735699474442009226487025730125073251028550 151:81:124237464971424477223217022553566422232383050 151:82:106056372536581870800307214374995726295936750 151:83:88167345843664446809893949299695242342405250 151:84:71373565682966456941342720861658053324804250 151:85:56259163538338266059646615267424583208963350 151:86:43175637134073553022519495437790959206878850 151:87:32257659927756102832916864407544969522380750 151:88:23460116311095347514848628660032705107186000 151:89:16606599186505695431859141635753487884862000 151:90:11440101661815034630836297571296847209571600 151:91:7668639575502385851439715954385798678943600 151:92:5001286679675469033547640839816825225398000 151:93:3172859291407017989024847414507448261274000 151:94:1957721690442628120887671808951404246318000 151:95:1174633014265576872532603085370842547790800 151:96:685202591654919842310685133132991486211300 151:97:388516933412583415743171982704273523109500 151:98:214080759227341882144196806796232349468500 151:99:114608891303526462158004351113134490119500 151:100:59596623477833760322162262578829934862140 151:101:30093344528411106697329459321983432455140 151:102:14751639474711326812416401628423251203500 151:103:7017770235542281687460229900900381640500 151:104:3238970877942591548058567646569406911000 151:105:1449825059650493359607168375131067855400 151:106:629169365508704665489903257132350201400 151:107:264603938765343083617249033373418309000 151:108:107801604682176811844064421003985237000 151:109:42527238544344980819218074341021699000 151:110:16237672898749901767337810202935557800 151:111:5997698998637351103250902867750971800 151:112:2142035356656196822589608167053918500 151:113:739286539022935186557475385089405500 151:114:246428846340978395519158461696468500 151:115:79285802735793048993120548545820300 151:116:24605938780073704859933963341806300 151:117:7360750917116065556390501854386500 151:118:2120894332050391770485398839399500 151:119:588147167711453180050572787396500 151:120:156839244723054181346819409972400 151:121:40181955259625451419433071976400 151:122:9880808670399701168713050486000 151:123:2329621556435701901566491578000 151:124:526043577259674622934369066000 151:125:113625412688089718553823718256 151:126:23446513729288354622217592656 151:127:4615455458521329650042833200 151:128:865397898472749309383031225 151:129:154295749340102590045036575 151:130:26111588349863515238390805 151:131:4185827140054456641268755 151:132:634216233341584339586175 151:133:90602319048797762798025 151:134:12170460767748953211675 151:135:1532576541123942256285 151:136:180303122485169677210 151:137:19741217790347044950 151:138:2002732239600424850 151:139:187305892912269950 151:140:16054790821051710 151:141:1252501411571410 151:142:88204324758550 151:143:5551321138650 151:144:308406729925 151:145:14888600755 151:146:611860305 151:147:20811575 151:148:562475 151:149:11325 151:150:151 151:151:1 # binomial(152, k) for 0 <= k <= 152 152:0:1 152:1:152 152:2:11476 152:3:573800 152:4:21374050 152:5:632671880 152:6:15500461060 152:7:323295330680 152:8:5859727868575 152:9:93755645897200 152:10:1340705736329960 152:11:17307292232623120 152:12:203360683733321660 152:13:2190038132512694800 152:14:21743950029947469800 152:15:200044340275516722160 152:16:1712879663609111933495 152:17:13703037308872895467960 152:18:102772779816546716009700 152:19:724818552390382102384200 152:20:4820043373396040980854930 152:21:30297415489917971879659560 152:22:180407337689966105283427380 152:23:1019693647812851899428067800 152:24:5480853356994078959425864425 152:25:28061969187809684272260425856 152:26:137071926417378073176041310912 152:27:639668989947764341488192784256 152:28:2855665133695376524500860644000 152:29:12210430226835403070279542064000 152:30:50062763930025152588146122462400 152:31:197021199982679632766252481948800 152:32:744986412434507361397392197368900 152:33:2709041499761844950535971626796000 152:34:9481645249166457326875900693786000 152:35:31966689697189770416324465196192800 152:36:103891741515866753853054511887626600 152:37:325714649076771444512279010242288800 152:38:985715385363913582076633846785874000 152:39:2881321895679132009147083552143324000 152:40:8139734355293547925840511034804890300 152:41:22235371897387252870588713070686529600 152:42:58764911443094882586555884543957256800 152:43:150328843226521792663282495345006936000 152:44:372405543447519895461313454377403546000 152:45:893773304274047749107152290505768510400 152:46:2078994425159198025097071632263418056800 152:47:4688795937593084907665736021700474766400 152:48:10256741113484873235518797547469788551500 152:49:21769409710253608499876631529323632844000 152:50:44844984003122433509745860950406683658640 152:51:89689968006244867019491721900813367317280 152:52:174205514781360222480166613691964424981640 152:53:328689650530868344302201157909366839588000 152:54:602597692639925297887368789500505872578000 152:55:1073719525067503258053857115837265009320800 152:56:1859835605920496714843288218503834034002100 152:57:3132354704708204993420274894322246794108800 152:58:5130580981849646109912519223458852507592000 152:59:8174145971082487022572488254324273486672000 152:60:12669926255177854884987356794202623904341600 152:61:19108741237317420482276013525682645888515200 152:62:28046700848320730062695439207050335094433600 152:63:40066715497601042946707770295786192992048000 152:64:55717776238851450347765493067577674629566750 152:65:75433297061829655855436359845335928729259600 152:66:99434800672411819082166110705215542415842200 152:67:127632729221304723000989336129082636533767600 152:68:159540911526630903751236670161353295667209500 152:69:194223718380246317610201163674690968638342000 152:70:230293837508006348023524236928562148528319800 152:71:265973164445866486449704048283691495483411600 152:72:299219810001599797255917054319152932418838050 152:73:327912120549698407951689922541537460185028000 152:74:350068344911164516597074376767317018305638000 152:75:364071078707611097260957351838009699037863520 152:76:368861487637974401172285738046404563498888040 152:77:364071078707611097260957351838009699037863520 152:78:350068344911164516597074376767317018305638000 152:79:327912120549698407951689922541537460185028000 152:80:299219810001599797255917054319152932418838050 152:81:265973164445866486449704048283691495483411600 152:82:230293837508006348023524236928562148528319800 152:83:194223718380246317610201163674690968638342000 152:84:159540911526630903751236670161353295667209500 152:85:127632729221304723000989336129082636533767600 152:86:99434800672411819082166110705215542415842200 152:87:75433297061829655855436359845335928729259600 152:88:55717776238851450347765493067577674629566750 152:89:40066715497601042946707770295786192992048000 152:90:28046700848320730062695439207050335094433600 152:91:19108741237317420482276013525682645888515200 152:92:12669926255177854884987356794202623904341600 152:93:8174145971082487022572488254324273486672000 152:94:5130580981849646109912519223458852507592000 152:95:3132354704708204993420274894322246794108800 152:96:1859835605920496714843288218503834034002100 152:97:1073719525067503258053857115837265009320800 152:98:602597692639925297887368789500505872578000 152:99:328689650530868344302201157909366839588000 152:100:174205514781360222480166613691964424981640 152:101:89689968006244867019491721900813367317280 152:102:44844984003122433509745860950406683658640 152:103:21769409710253608499876631529323632844000 152:104:10256741113484873235518797547469788551500 152:105:4688795937593084907665736021700474766400 152:106:2078994425159198025097071632263418056800 152:107:893773304274047749107152290505768510400 152:108:372405543447519895461313454377403546000 152:109:150328843226521792663282495345006936000 152:110:58764911443094882586555884543957256800 152:111:22235371897387252870588713070686529600 152:112:8139734355293547925840511034804890300 152:113:2881321895679132009147083552143324000 152:114:985715385363913582076633846785874000 152:115:325714649076771444512279010242288800 152:116:103891741515866753853054511887626600 152:117:31966689697189770416324465196192800 152:118:9481645249166457326875900693786000 152:119:2709041499761844950535971626796000 152:120:744986412434507361397392197368900 152:121:197021199982679632766252481948800 152:122:50062763930025152588146122462400 152:123:12210430226835403070279542064000 152:124:2855665133695376524500860644000 152:125:639668989947764341488192784256 152:126:137071926417378073176041310912 152:127:28061969187809684272260425856 152:128:5480853356994078959425864425 152:129:1019693647812851899428067800 152:130:180407337689966105283427380 152:131:30297415489917971879659560 152:132:4820043373396040980854930 152:133:724818552390382102384200 152:134:102772779816546716009700 152:135:13703037308872895467960 152:136:1712879663609111933495 152:137:200044340275516722160 152:138:21743950029947469800 152:139:2190038132512694800 152:140:203360683733321660 152:141:17307292232623120 152:142:1340705736329960 152:143:93755645897200 152:144:5859727868575 152:145:323295330680 152:146:15500461060 152:147:632671880 152:148:21374050 152:149:573800 152:150:11476 152:151:152 152:152:1 # binomial(153, k) for 0 <= k <= 153 153:0:1 153:1:153 153:2:11628 153:3:585276 153:4:21947850 153:5:654045930 153:6:16133132940 153:7:338795791740 153:8:6183023199255 153:9:99615373765775 153:10:1434461382227160 153:11:18647997968953080 153:12:220667975965944780 153:13:2393398816246016460 153:14:23933988162460164600 153:15:221788290305464191960 153:16:1912924003884628655655 153:17:15415916972482007401455 153:18:116475817125419611477660 153:19:827591332206928818393900 153:20:5544861925786423083239130 153:21:35117458863314012860514490 153:22:210704753179884077163086940 153:23:1200100985502818004711495180 153:24:6500547004806930858853932225 153:25:33542822544803763231686290281 153:26:165133895605187757448301736768 153:27:776740916365142414664234095168 153:28:3495334123643140865989053428256 153:29:15066095360530779594780402708000 153:30:62273194156860555658425664526400 153:31:247083963912704785354398604411200 153:32:942007612417186994163644679317700 153:33:3454027912196352311933363824164900 153:34:12190686748928302277411872320582000 153:35:41448334946356227743200365889978800 153:36:135858431213056524269378977083819400 153:37:429606390592638198365333522129915400 153:38:1311430034440685026588912857028162800 153:39:3867037281043045591223717398929198000 153:40:11021056250972679934987594586948214300 153:41:30375106252680800796429224105491419900 153:42:81000283340482135457144597614643786400 153:43:209093754669616675249838379888964192800 153:44:522734386674041688124595949722410482000 153:45:1266178847721567644568465744883172056400 153:46:2972767729433245774204223922769186567200 153:47:6767790362752282932762807653963892823200 153:48:14945537051077958143184533569170263317900 153:49:32026150823738481735395429076793421395500 153:50:66614393713376042009622492479730316502640 153:51:134534952009367300529237582851220050975920 153:52:263895482787605089499658335592777792298920 153:53:502895165312228566782367771601331264569640 153:54:931287343170793642189569947409872712166000 153:55:1676317217707428555941225905337770881898800 153:56:2933555130987999972897145334341099043322900 153:57:4992190310628701708263563112826080828110900 153:58:8262935686557851103332794117781099301700800 153:59:13304726952932133132485007477783125994264000 153:60:20844072226260341907559845048526897391013600 153:61:31778667492495275367263370319885269792856800 153:62:47155442085638150544971452732732980982948800 153:63:68113416345921773009403209502836528086481600 153:64:95784491736452493294473263363363867621614750 153:65:131151073300681106203201852912913603358826350 153:66:174868097734241474937602470550551471145101800 153:67:227067529893716542083155446834298178949609800 153:68:287173640747935626752226006290435932200977100 153:69:353764629906877221361437833836044264305551500 153:70:424517555888252665633725400603253117166661800 153:71:496267001953872834473228285212253644011731400 153:72:565192974447466283705621102602844427902249650 153:73:627131930551298205207606976860690392603866050 153:74:677980465460862924548764299308854478490666000 153:75:714139423618775613858031728605326717343501520 153:76:732932566345585498433243089884414262536751560 153:77:732932566345585498433243089884414262536751560 153:78:714139423618775613858031728605326717343501520 153:79:677980465460862924548764299308854478490666000 153:80:627131930551298205207606976860690392603866050 153:81:565192974447466283705621102602844427902249650 153:82:496267001953872834473228285212253644011731400 153:83:424517555888252665633725400603253117166661800 153:84:353764629906877221361437833836044264305551500 153:85:287173640747935626752226006290435932200977100 153:86:227067529893716542083155446834298178949609800 153:87:174868097734241474937602470550551471145101800 153:88:131151073300681106203201852912913603358826350 153:89:95784491736452493294473263363363867621614750 153:90:68113416345921773009403209502836528086481600 153:91:47155442085638150544971452732732980982948800 153:92:31778667492495275367263370319885269792856800 153:93:20844072226260341907559845048526897391013600 153:94:13304726952932133132485007477783125994264000 153:95:8262935686557851103332794117781099301700800 153:96:4992190310628701708263563112826080828110900 153:97:2933555130987999972897145334341099043322900 153:98:1676317217707428555941225905337770881898800 153:99:931287343170793642189569947409872712166000 153:100:502895165312228566782367771601331264569640 153:101:263895482787605089499658335592777792298920 153:102:134534952009367300529237582851220050975920 153:103:66614393713376042009622492479730316502640 153:104:32026150823738481735395429076793421395500 153:105:14945537051077958143184533569170263317900 153:106:6767790362752282932762807653963892823200 153:107:2972767729433245774204223922769186567200 153:108:1266178847721567644568465744883172056400 153:109:522734386674041688124595949722410482000 153:110:209093754669616675249838379888964192800 153:111:81000283340482135457144597614643786400 153:112:30375106252680800796429224105491419900 153:113:11021056250972679934987594586948214300 153:114:3867037281043045591223717398929198000 153:115:1311430034440685026588912857028162800 153:116:429606390592638198365333522129915400 153:117:135858431213056524269378977083819400 153:118:41448334946356227743200365889978800 153:119:12190686748928302277411872320582000 153:120:3454027912196352311933363824164900 153:121:942007612417186994163644679317700 153:122:247083963912704785354398604411200 153:123:62273194156860555658425664526400 153:124:15066095360530779594780402708000 153:125:3495334123643140865989053428256 153:126:776740916365142414664234095168 153:127:165133895605187757448301736768 153:128:33542822544803763231686290281 153:129:6500547004806930858853932225 153:130:1200100985502818004711495180 153:131:210704753179884077163086940 153:132:35117458863314012860514490 153:133:5544861925786423083239130 153:134:827591332206928818393900 153:135:116475817125419611477660 153:136:15415916972482007401455 153:137:1912924003884628655655 153:138:221788290305464191960 153:139:23933988162460164600 153:140:2393398816246016460 153:141:220667975965944780 153:142:18647997968953080 153:143:1434461382227160 153:144:99615373765775 153:145:6183023199255 153:146:338795791740 153:147:16133132940 153:148:654045930 153:149:21947850 153:150:585276 153:151:11628 153:152:153 153:153:1 # binomial(154, k) for 0 <= k <= 154 154:0:1 154:1:154 154:2:11781 154:3:596904 154:4:22533126 154:5:675993780 154:6:16787178870 154:7:354928924680 154:8:6521818990995 154:9:105798396965030 154:10:1534076755992935 154:11:20082459351180240 154:12:239315973934897860 154:13:2614066792211961240 154:14:26327386978706181060 154:15:245722278467924356560 154:16:2134712294190092847615 154:17:17328840976366636057110 154:18:131891734097901618879115 154:19:944067149332348429871560 154:20:6372453257993351901633030 154:21:40662320789100435943753620 154:22:245822212043198090023601430 154:23:1410805738682702081874582120 154:24:7700647990309748863565427405 154:25:40043369549610694090540222506 154:26:198676718149991520679988027049 154:27:941874811970330172112535831936 154:28:4272075040008283280653287523424 154:29:18561429484173920460769456136256 154:30:77339289517391335253206067234400 154:31:309357158069565341012824268937600 154:32:1189091576329891779518043283728900 154:33:4396035524613539306097008503482600 154:34:15644714661124654589345236144746900 154:35:53639021695284530020612238210560800 154:36:177306766159412752012579342973798200 154:37:565464821805694722634712499213734800 154:38:1741036425033323224954246379158078200 154:39:5178467315483730617812630255957360800 154:40:14888093532015725526211311985877412300 154:41:41396162503653480731416818692439634200 154:42:111375389593162936253573821720135206300 154:43:290094038010098810706982977503607979200 154:44:731828141343658363374434329611374674800 154:45:1788913234395609332693061694605582538400 154:46:4238946577154813418772689667652358623600 154:47:9740558092185528706967031576733079390400 154:48:21713327413830241075947341223134156141100 154:49:46971687874816439878579962645963684713400 154:50:98640544537114523745017921556523737898140 154:51:201149345722743342538860075330950367478560 154:52:398430434796972390028895918443997843274840 154:53:766790648099833656282026107194109056868560 154:54:1434182508483022208971937719011203976735640 154:55:2607604560878222198130795852747643594064800 154:56:4609872348695428528838371239678869925221700 154:57:7925745441616701681160708447167179871433800 154:58:13255125997186552811596357230607180129811700 154:59:21567662639489984235817801595564225295964800 154:60:34148799179192475040044852526310023385277600 154:61:52622739718755617274823215368412167183870400 154:62:78934109578133425912234823052618250775805600 154:63:115268858431559923554374662235569509069430400 154:64:163897908082374266303876472866200395708096350 154:65:226935565037133599497675116276277470980441100 154:66:306019171034922581140804323463465074503928150 154:67:401935627627958017020757917384849650094711600 154:68:514241170641652168835381453124734111150586900 154:69:640938270654812848113663840126480196506528600 154:70:778282185795129886995163234439297381472213300 154:71:920784557842125500106953685815506761178393200 154:72:1061459976401339118178849387815098071913981050 154:73:1192324904998764488913228079463534820506115700 154:74:1305112396012161129756371276169544871094532050 154:75:1392119889079638538406796027914181195834167520 154:76:1447071989964361112291274818489740979880253080 154:77:1465865132691170996866486179768828525073503120 154:78:1447071989964361112291274818489740979880253080 154:79:1392119889079638538406796027914181195834167520 154:80:1305112396012161129756371276169544871094532050 154:81:1192324904998764488913228079463534820506115700 154:82:1061459976401339118178849387815098071913981050 154:83:920784557842125500106953685815506761178393200 154:84:778282185795129886995163234439297381472213300 154:85:640938270654812848113663840126480196506528600 154:86:514241170641652168835381453124734111150586900 154:87:401935627627958017020757917384849650094711600 154:88:306019171034922581140804323463465074503928150 154:89:226935565037133599497675116276277470980441100 154:90:163897908082374266303876472866200395708096350 154:91:115268858431559923554374662235569509069430400 154:92:78934109578133425912234823052618250775805600 154:93:52622739718755617274823215368412167183870400 154:94:34148799179192475040044852526310023385277600 154:95:21567662639489984235817801595564225295964800 154:96:13255125997186552811596357230607180129811700 154:97:7925745441616701681160708447167179871433800 154:98:4609872348695428528838371239678869925221700 154:99:2607604560878222198130795852747643594064800 154:100:1434182508483022208971937719011203976735640 154:101:766790648099833656282026107194109056868560 154:102:398430434796972390028895918443997843274840 154:103:201149345722743342538860075330950367478560 154:104:98640544537114523745017921556523737898140 154:105:46971687874816439878579962645963684713400 154:106:21713327413830241075947341223134156141100 154:107:9740558092185528706967031576733079390400 154:108:4238946577154813418772689667652358623600 154:109:1788913234395609332693061694605582538400 154:110:731828141343658363374434329611374674800 154:111:290094038010098810706982977503607979200 154:112:111375389593162936253573821720135206300 154:113:41396162503653480731416818692439634200 154:114:14888093532015725526211311985877412300 154:115:5178467315483730617812630255957360800 154:116:1741036425033323224954246379158078200 154:117:565464821805694722634712499213734800 154:118:177306766159412752012579342973798200 154:119:53639021695284530020612238210560800 154:120:15644714661124654589345236144746900 154:121:4396035524613539306097008503482600 154:122:1189091576329891779518043283728900 154:123:309357158069565341012824268937600 154:124:77339289517391335253206067234400 154:125:18561429484173920460769456136256 154:126:4272075040008283280653287523424 154:127:941874811970330172112535831936 154:128:198676718149991520679988027049 154:129:40043369549610694090540222506 154:130:7700647990309748863565427405 154:131:1410805738682702081874582120 154:132:245822212043198090023601430 154:133:40662320789100435943753620 154:134:6372453257993351901633030 154:135:944067149332348429871560 154:136:131891734097901618879115 154:137:17328840976366636057110 154:138:2134712294190092847615 154:139:245722278467924356560 154:140:26327386978706181060 154:141:2614066792211961240 154:142:239315973934897860 154:143:20082459351180240 154:144:1534076755992935 154:145:105798396965030 154:146:6521818990995 154:147:354928924680 154:148:16787178870 154:149:675993780 154:150:22533126 154:151:596904 154:152:11781 154:153:154 154:154:1 # binomial(155, k) for 0 <= k <= 155 155:0:1 155:1:155 155:2:11935 155:3:608685 155:4:23130030 155:5:698526906 155:6:17463172650 155:7:371716103550 155:8:6876747915675 155:9:112320215956025 155:10:1639875152957965 155:11:21616536107173175 155:12:259398433286078100 155:13:2853382766146859100 155:14:28941453770918142300 155:15:272049665446630537620 155:16:2380434572658017204175 155:17:19463553270556728904725 155:18:149220575074268254936225 155:19:1075958883430250048750675 155:20:7316520407325700331504590 155:21:47034774047093787845386650 155:22:286484532832298525967355050 155:23:1656627950725900171898183550 155:24:9111453728992450945440009525 155:25:47744017539920442954105649911 155:26:238720087699602214770528249555 155:27:1140551530120321692792523858985 155:28:5213949851978613452765823355360 155:29:22833504524182203741422743659680 155:30:95900719001565255713975523370656 155:31:386696447586956676266030336172000 155:32:1498448734399457120530867552666500 155:33:5585127100943431085615051787211500 155:34:20040750185738193895442244648229500 155:35:69283736356409184609957474355307700 155:36:230945787854697282033191581184359000 155:37:742771587965107474647291842187533000 155:38:2306501246839017947588958878371813000 155:39:6919503740517053842766876635115439000 155:40:20066560847499456144023942241834773100 155:41:56284256035669206257628130678317046500 155:42:152771552096816416984990640412574840500 155:43:401469427603261746960556799223743185500 155:44:1021922179353757174081417307114982654000 155:45:2520741375739267696067496024216957213200 155:46:6027859811550422751465751362257941162000 155:47:13979504669340342125739721244385438014000 155:48:31453885506015769782914372799867235531500 155:49:68685015288646680954527303869097840854500 155:50:145612232411930963623597884202487422611540 155:51:299789890259857866283877996887474105376700 155:52:599579780519715732567755993774948210753400 155:53:1165221082896806046310922025638106900143400 155:54:2200973156582855865253963826205313033604200 155:55:4041787069361244407102733571758847570800440 155:56:7217476909573650726969167092426513519286500 155:57:12535617790312130209999079686846049796655500 155:58:21180871438803254492757065677774360001245500 155:59:34822788636676537047414158826171405425776500 155:60:55716461818682459275862654121874248681242400 155:61:86771538897948092314868067894722190569148000 155:62:131556849296889043187058038421030417959676000 155:63:194202968009693349466609485288187759845236000 155:64:279166766513934189858251135101769904777526750 155:65:390833473119507865801551589142477866688537450 155:66:532954736072056180638479439739742545484369250 155:67:707954798662880598161562240848314724598639750 155:68:916176798269610185856139370509583761245298500 155:69:1155179441296465016949045293251214307657115500 155:70:1419220456449942735108827074565777577978741900 155:71:1699066743637255387102116920254804142650606500 155:72:1982244534243464618285803073630604833092374250 155:73:2253784881400103607092077467278632892420096750 155:74:2497437301010925618669599355633079691600647750 155:75:2697232285091799668163167304083726066928699570 155:76:2839191879043999650698070846403922175714420600 155:77:2912937122655532109157760998258569504953756200 155:78:2912937122655532109157760998258569504953756200 155:79:2839191879043999650698070846403922175714420600 155:80:2697232285091799668163167304083726066928699570 155:81:2497437301010925618669599355633079691600647750 155:82:2253784881400103607092077467278632892420096750 155:83:1982244534243464618285803073630604833092374250 155:84:1699066743637255387102116920254804142650606500 155:85:1419220456449942735108827074565777577978741900 155:86:1155179441296465016949045293251214307657115500 155:87:916176798269610185856139370509583761245298500 155:88:707954798662880598161562240848314724598639750 155:89:532954736072056180638479439739742545484369250 155:90:390833473119507865801551589142477866688537450 155:91:279166766513934189858251135101769904777526750 155:92:194202968009693349466609485288187759845236000 155:93:131556849296889043187058038421030417959676000 155:94:86771538897948092314868067894722190569148000 155:95:55716461818682459275862654121874248681242400 155:96:34822788636676537047414158826171405425776500 155:97:21180871438803254492757065677774360001245500 155:98:12535617790312130209999079686846049796655500 155:99:7217476909573650726969167092426513519286500 155:100:4041787069361244407102733571758847570800440 155:101:2200973156582855865253963826205313033604200 155:102:1165221082896806046310922025638106900143400 155:103:599579780519715732567755993774948210753400 155:104:299789890259857866283877996887474105376700 155:105:145612232411930963623597884202487422611540 155:106:68685015288646680954527303869097840854500 155:107:31453885506015769782914372799867235531500 155:108:13979504669340342125739721244385438014000 155:109:6027859811550422751465751362257941162000 155:110:2520741375739267696067496024216957213200 155:111:1021922179353757174081417307114982654000 155:112:401469427603261746960556799223743185500 155:113:152771552096816416984990640412574840500 155:114:56284256035669206257628130678317046500 155:115:20066560847499456144023942241834773100 155:116:6919503740517053842766876635115439000 155:117:2306501246839017947588958878371813000 155:118:742771587965107474647291842187533000 155:119:230945787854697282033191581184359000 155:120:69283736356409184609957474355307700 155:121:20040750185738193895442244648229500 155:122:5585127100943431085615051787211500 155:123:1498448734399457120530867552666500 155:124:386696447586956676266030336172000 155:125:95900719001565255713975523370656 155:126:22833504524182203741422743659680 155:127:5213949851978613452765823355360 155:128:1140551530120321692792523858985 155:129:238720087699602214770528249555 155:130:47744017539920442954105649911 155:131:9111453728992450945440009525 155:132:1656627950725900171898183550 155:133:286484532832298525967355050 155:134:47034774047093787845386650 155:135:7316520407325700331504590 155:136:1075958883430250048750675 155:137:149220575074268254936225 155:138:19463553270556728904725 155:139:2380434572658017204175 155:140:272049665446630537620 155:141:28941453770918142300 155:142:2853382766146859100 155:143:259398433286078100 155:144:21616536107173175 155:145:1639875152957965 155:146:112320215956025 155:147:6876747915675 155:148:371716103550 155:149:17463172650 155:150:698526906 155:151:23130030 155:152:608685 155:153:11935 155:154:155 155:155:1 # binomial(156, k) for 0 <= k <= 156 156:0:1 156:1:156 156:2:12090 156:3:620620 156:4:23738715 156:5:721656936 156:6:18161699556 156:7:389179276200 156:8:7248464019225 156:9:119196963871700 156:10:1752195368913990 156:11:23256411260131140 156:12:281014969393251275 156:13:3112781199432937200 156:14:31794836537065001400 156:15:300991119217548679920 156:16:2652484238104647741795 156:17:21843987843214746108900 156:18:168684128344824983840950 156:19:1225179458504518303686900 156:20:8392479290755950380255265 156:21:54351294454419488176891240 156:22:333519306879392313812741700 156:23:1943112483558198697865538600 156:24:10768081679718351117338193075 156:25:56855471268912893899545659436 156:26:286464105239522657724633899466 156:27:1379271617819923907563052108540 156:28:6354501382098935145558347214345 156:29:28047454376160817194188567015040 156:30:118734223525747459455398267030336 156:31:482597166588521931980005859542656 156:32:1885145181986413796796897888838500 156:33:7083575835342888206145919339878000 156:34:25625877286681624981057296435441000 156:35:89324486542147378505399719003537200 156:36:300229524211106466643149055539666700 156:37:973717375819804756680483423371892000 156:38:3049272834804125422236250720559346000 156:39:9226004987356071790355835513487252000 156:40:26986064588016509986790818876950212100 156:41:76350816883168662401652072920151819600 156:42:209055808132485623242618771090891887000 156:43:554240979700078163945547439636318026000 156:44:1423391606957018921041974106338725839500 156:45:3542663555093024870148913331331939867200 156:46:8548601187289690447533247386474898375200 156:47:20007364480890764877205472606643379176000 156:48:45433390175356111908654094044252673545500 156:49:100138900794662450737441676668965076386000 156:50:214297247700577644578125188071585263466040 156:51:445402122671788829907475881089961527988240 156:52:899369670779573598851633990662422316130100 156:53:1764800863416521778878678019413055110896800 156:54:3366194239479661911564885851843419933747600 156:55:6242760225944100272356697397964160604404640 156:56:11259263978934895134071900664185361090086940 156:57:19753094699885780936968246779272563315942000 156:58:33716489229115384702756145364620409797901000 156:59:56003660075479791540171224503945765427022000 156:60:90539250455358996323276812948045654107018900 156:61:142488000716630551590730722016596439250390400 156:62:218328388194837135501926106315752608528824000 156:63:325759817306582392653667523709218177804912000 156:64:473369734523627539324860620389957664622762750 156:65:670000239633442055659802724244247771466064200 156:66:923788209191564046440031028882220412172906700 156:67:1240909534734936778800041680588057270083009000 156:68:1624131596932490784017701611357898485843938250 156:69:2071356239566075202805184663760798068902414000 156:70:2574399897746407752057872367816991885635857400 156:71:3118287200087198122210943994820581720629348400 156:72:3681311277880720005387919993885408975742980750 156:73:4236029415643568225377880540909237725512471000 156:74:4751222182411029225761676822911712584020744500 156:75:5194669586102725286832766659716805758529347320 156:76:5536424164135799318861238150487648242643120170 156:77:5752129001699531759855831844662491680668176800 156:78:5825874245311064218315521996517139009907512400 156:79:5752129001699531759855831844662491680668176800 156:80:5536424164135799318861238150487648242643120170 156:81:5194669586102725286832766659716805758529347320 156:82:4751222182411029225761676822911712584020744500 156:83:4236029415643568225377880540909237725512471000 156:84:3681311277880720005387919993885408975742980750 156:85:3118287200087198122210943994820581720629348400 156:86:2574399897746407752057872367816991885635857400 156:87:2071356239566075202805184663760798068902414000 156:88:1624131596932490784017701611357898485843938250 156:89:1240909534734936778800041680588057270083009000 156:90:923788209191564046440031028882220412172906700 156:91:670000239633442055659802724244247771466064200 156:92:473369734523627539324860620389957664622762750 156:93:325759817306582392653667523709218177804912000 156:94:218328388194837135501926106315752608528824000 156:95:142488000716630551590730722016596439250390400 156:96:90539250455358996323276812948045654107018900 156:97:56003660075479791540171224503945765427022000 156:98:33716489229115384702756145364620409797901000 156:99:19753094699885780936968246779272563315942000 156:100:11259263978934895134071900664185361090086940 156:101:6242760225944100272356697397964160604404640 156:102:3366194239479661911564885851843419933747600 156:103:1764800863416521778878678019413055110896800 156:104:899369670779573598851633990662422316130100 156:105:445402122671788829907475881089961527988240 156:106:214297247700577644578125188071585263466040 156:107:100138900794662450737441676668965076386000 156:108:45433390175356111908654094044252673545500 156:109:20007364480890764877205472606643379176000 156:110:8548601187289690447533247386474898375200 156:111:3542663555093024870148913331331939867200 156:112:1423391606957018921041974106338725839500 156:113:554240979700078163945547439636318026000 156:114:209055808132485623242618771090891887000 156:115:76350816883168662401652072920151819600 156:116:26986064588016509986790818876950212100 156:117:9226004987356071790355835513487252000 156:118:3049272834804125422236250720559346000 156:119:973717375819804756680483423371892000 156:120:300229524211106466643149055539666700 156:121:89324486542147378505399719003537200 156:122:25625877286681624981057296435441000 156:123:7083575835342888206145919339878000 156:124:1885145181986413796796897888838500 156:125:482597166588521931980005859542656 156:126:118734223525747459455398267030336 156:127:28047454376160817194188567015040 156:128:6354501382098935145558347214345 156:129:1379271617819923907563052108540 156:130:286464105239522657724633899466 156:131:56855471268912893899545659436 156:132:10768081679718351117338193075 156:133:1943112483558198697865538600 156:134:333519306879392313812741700 156:135:54351294454419488176891240 156:136:8392479290755950380255265 156:137:1225179458504518303686900 156:138:168684128344824983840950 156:139:21843987843214746108900 156:140:2652484238104647741795 156:141:300991119217548679920 156:142:31794836537065001400 156:143:3112781199432937200 156:144:281014969393251275 156:145:23256411260131140 156:146:1752195368913990 156:147:119196963871700 156:148:7248464019225 156:149:389179276200 156:150:18161699556 156:151:721656936 156:152:23738715 156:153:620620 156:154:12090 156:155:156 156:156:1 # binomial(157, k) for 0 <= k <= 157 157:0:1 157:1:157 157:2:12246 157:3:632710 157:4:24359335 157:5:745395651 157:6:18883356492 157:7:407340975756 157:8:7637643295425 157:9:126445427890925 157:10:1871392332785690 157:11:25008606629045130 157:12:304271380653382415 157:13:3393796168826188475 157:14:34907617736497938600 157:15:332785955754613681320 157:16:2953475357322196421715 157:17:24496472081319393850695 157:18:190528116188039729949850 157:19:1393863586849343287527850 157:20:9617658749260468683942165 157:21:62743773745175438557146505 157:22:387870601333811801989632940 157:23:2276631790437591011678280300 157:24:12711194163276549815203731675 157:25:67623552948631245016883852511 157:26:343319576508435551624179558902 157:27:1665735723059446565287686008006 157:28:7733772999918859053121399322885 157:29:34401955758259752339746914229385 157:30:146781677901908276649586834045376 157:31:601331390114269391435404126572992 157:32:2367742348574935728776903748381156 157:33:8968721017329302002942817228716500 157:34:32709453122024513187203215775319000 157:35:114950363828829003486457015438978200 157:36:389554010753253845148548774543203900 157:37:1273946900030911223323632478911558700 157:38:4022990210623930178916734143931238000 157:39:12275277822160197212592086234046598000 157:40:36212069575372581777146654390437464100 157:41:103336881471185172388442891797102031700 157:42:285406625015654285644270844011043706600 157:43:763296787832563787188166210727209913000 157:44:1977632586657097084987521545975043865500 157:45:4966055162050043791190887437670665706700 157:46:12091264742382715317682160717806838242400 157:47:28555965668180455324738719993118277551200 157:48:65440754656246876785859566650896052721500 157:49:145572290970018562646095770713217749931500 157:50:314436148495240095315566864740550339852040 157:51:659699370372366474485601069161546791454280 157:52:1344771793451362428759109871752383844118340 157:53:2664170534196095377730312010075477427026900 157:54:5130995102896183690443563871256475044644400 157:55:9608954465423762183921583249807580538152240 157:56:17502024204878995406428598062149521694491580 157:57:31012358678820676071040147443457924406028940 157:58:53469583929001165639724392143892973113843000 157:59:89720149304595176242927369868566175224923000 157:60:146542910530838787863448037451991419534040900 157:61:233027251171989547914007534964642093357409300 157:62:360816388911467687092656828332349047779214400 157:63:544088205501419528155593630024970786333736000 157:64:799129551830209931978528144099175842427674750 157:65:1143369974157069594984663344634205436088826950 157:66:1593788448825006102099833753126468183638970900 157:67:2164697743926500825240072709470277682255915700 157:68:2865041131667427562817743291945955755926947250 157:69:3695487836498565986822886275118696554746352250 157:70:4645756137312482954863057031577789954538271400 157:71:5692687097833605874268816362637573606265205800 157:72:6799598477967918127598863988705990696372329150 157:73:7917340693524288230765800534794646701255451750 157:74:8987251598054597451139557363820950309533215500 157:75:9945891768513754512594443482628518342550091820 157:76:10731093750238524605694004810204454001172467490 157:77:11288553165835331078717069995150139923311296970 157:78:11578003247010595978171353841179630690575689200 157:79:11578003247010595978171353841179630690575689200 157:80:11288553165835331078717069995150139923311296970 157:81:10731093750238524605694004810204454001172467490 157:82:9945891768513754512594443482628518342550091820 157:83:8987251598054597451139557363820950309533215500 157:84:7917340693524288230765800534794646701255451750 157:85:6799598477967918127598863988705990696372329150 157:86:5692687097833605874268816362637573606265205800 157:87:4645756137312482954863057031577789954538271400 157:88:3695487836498565986822886275118696554746352250 157:89:2865041131667427562817743291945955755926947250 157:90:2164697743926500825240072709470277682255915700 157:91:1593788448825006102099833753126468183638970900 157:92:1143369974157069594984663344634205436088826950 157:93:799129551830209931978528144099175842427674750 157:94:544088205501419528155593630024970786333736000 157:95:360816388911467687092656828332349047779214400 157:96:233027251171989547914007534964642093357409300 157:97:146542910530838787863448037451991419534040900 157:98:89720149304595176242927369868566175224923000 157:99:53469583929001165639724392143892973113843000 157:100:31012358678820676071040147443457924406028940 157:101:17502024204878995406428598062149521694491580 157:102:9608954465423762183921583249807580538152240 157:103:5130995102896183690443563871256475044644400 157:104:2664170534196095377730312010075477427026900 157:105:1344771793451362428759109871752383844118340 157:106:659699370372366474485601069161546791454280 157:107:314436148495240095315566864740550339852040 157:108:145572290970018562646095770713217749931500 157:109:65440754656246876785859566650896052721500 157:110:28555965668180455324738719993118277551200 157:111:12091264742382715317682160717806838242400 157:112:4966055162050043791190887437670665706700 157:113:1977632586657097084987521545975043865500 157:114:763296787832563787188166210727209913000 157:115:285406625015654285644270844011043706600 157:116:103336881471185172388442891797102031700 157:117:36212069575372581777146654390437464100 157:118:12275277822160197212592086234046598000 157:119:4022990210623930178916734143931238000 157:120:1273946900030911223323632478911558700 157:121:389554010753253845148548774543203900 157:122:114950363828829003486457015438978200 157:123:32709453122024513187203215775319000 157:124:8968721017329302002942817228716500 157:125:2367742348574935728776903748381156 157:126:601331390114269391435404126572992 157:127:146781677901908276649586834045376 157:128:34401955758259752339746914229385 157:129:7733772999918859053121399322885 157:130:1665735723059446565287686008006 157:131:343319576508435551624179558902 157:132:67623552948631245016883852511 157:133:12711194163276549815203731675 157:134:2276631790437591011678280300 157:135:387870601333811801989632940 157:136:62743773745175438557146505 157:137:9617658749260468683942165 157:138:1393863586849343287527850 157:139:190528116188039729949850 157:140:24496472081319393850695 157:141:2953475357322196421715 157:142:332785955754613681320 157:143:34907617736497938600 157:144:3393796168826188475 157:145:304271380653382415 157:146:25008606629045130 157:147:1871392332785690 157:148:126445427890925 157:149:7637643295425 157:150:407340975756 157:151:18883356492 157:152:745395651 157:153:24359335 157:154:632710 157:155:12246 157:156:157 157:157:1 # binomial(158, k) for 0 <= k <= 158 158:0:1 158:1:158 158:2:12403 158:3:644956 158:4:24992045 158:5:769754986 158:6:19628752143 158:7:426224332248 158:8:8044984271181 158:9:134083071186350 158:10:1997837760676615 158:11:26879998961830820 158:12:329279987282427545 158:13:3698067549479570890 158:14:38301413905324127075 158:15:367693573491111619920 158:16:3286261313076810103035 158:17:27449947438641590272410 158:18:215024588269359123800545 158:19:1584391703037383017477700 158:20:11011522336109811971470015 158:21:72361432494435907241088670 158:22:450614375078987240546779445 158:23:2664502391771402813667913240 158:24:14987825953714140826882011975 158:25:80334747111907794832087584186 158:26:410943129457066796641063411413 158:27:2009055299567882116911865566908 158:28:9399508722978305618409085330891 158:29:42135728758178611392868313552270 158:30:181183633660168028989333748274761 158:31:748113068016177668084990960618368 158:32:2969073738689205120212307874954148 158:33:11336463365904237731719720977097656 158:34:41678174139353815190146033004035500 158:35:147659816950853516673660231214297200 158:36:504504374582082848635005789982182100 158:37:1663500910784165068472181253454762600 158:38:5296937110654841402240366622842796700 158:39:16298268032784127391508820377977836000 158:40:48487347397532778989738740624484062100 158:41:139548951046557754165589546187539495800 158:42:388743506486839458032713735808145738300 158:43:1048703412848218072832437054738253619600 158:44:2740929374489660872175687756702253778500 158:45:6943687748707140876178408983645709572200 158:46:17057319904432759108873048155477503949100 158:47:40647230410563170642420880710925115793600 158:48:93996720324427332110598286644014330272700 158:49:211013045626265439431955337364113802653000 158:50:460008439465258657961662635453768089783540 158:51:974135518867606569801167933902097131306320 158:52:2004471163823728903244710940913930635572620 158:53:4008942327647457806489421881827861271145240 158:54:7795165637092279068173875881331952471671300 158:55:14739949568319945874365147121064055582796640 158:56:27110978670302757590350181311957102232643820 158:57:48514382883699671477468745505607446100520520 158:58:84481942607821841710764539587350897519871940 158:59:143189733233596341882651762012459148338766000 158:60:236263059835433964106375407320557594758963900 158:61:379570161702828335777455572416633512891450200 158:62:593843640083457235006664363296991141136623700 158:63:904904594412887215248250458357319834112950400 158:64:1343217757331629460134121774124146628761410750 158:65:1942499525987279526963191488733381278516501700 158:66:2737158422982075697084497097760673619727797850 158:67:3758486192751506927339906462596745865894886600 158:68:5029738875593928388057816001416233438182862950 158:69:6560528968165993549640629567064652310673299500 158:70:8341243973811048941685943306696486509284623650 158:71:10338443235146088829131873394215363560803477200 158:72:12492285575801524001867680351343564302637534950 158:73:14716939171492206358364664523500637397627780900 158:74:16904592291578885681905357898615597010788667250 158:75:18933143366568351963734000846449468652083307320 158:76:20676985518752279118288448292832972343722559310 158:77:22019646916073855684411074805354593924483764460 158:78:22866556412845927056888423836329770613886986170 158:79:23156006494021191956342707682359261381151378400 158:80:22866556412845927056888423836329770613886986170 158:81:22019646916073855684411074805354593924483764460 158:82:20676985518752279118288448292832972343722559310 158:83:18933143366568351963734000846449468652083307320 158:84:16904592291578885681905357898615597010788667250 158:85:14716939171492206358364664523500637397627780900 158:86:12492285575801524001867680351343564302637534950 158:87:10338443235146088829131873394215363560803477200 158:88:8341243973811048941685943306696486509284623650 158:89:6560528968165993549640629567064652310673299500 158:90:5029738875593928388057816001416233438182862950 158:91:3758486192751506927339906462596745865894886600 158:92:2737158422982075697084497097760673619727797850 158:93:1942499525987279526963191488733381278516501700 158:94:1343217757331629460134121774124146628761410750 158:95:904904594412887215248250458357319834112950400 158:96:593843640083457235006664363296991141136623700 158:97:379570161702828335777455572416633512891450200 158:98:236263059835433964106375407320557594758963900 158:99:143189733233596341882651762012459148338766000 158:100:84481942607821841710764539587350897519871940 158:101:48514382883699671477468745505607446100520520 158:102:27110978670302757590350181311957102232643820 158:103:14739949568319945874365147121064055582796640 158:104:7795165637092279068173875881331952471671300 158:105:4008942327647457806489421881827861271145240 158:106:2004471163823728903244710940913930635572620 158:107:974135518867606569801167933902097131306320 158:108:460008439465258657961662635453768089783540 158:109:211013045626265439431955337364113802653000 158:110:93996720324427332110598286644014330272700 158:111:40647230410563170642420880710925115793600 158:112:17057319904432759108873048155477503949100 158:113:6943687748707140876178408983645709572200 158:114:2740929374489660872175687756702253778500 158:115:1048703412848218072832437054738253619600 158:116:388743506486839458032713735808145738300 158:117:139548951046557754165589546187539495800 158:118:48487347397532778989738740624484062100 158:119:16298268032784127391508820377977836000 158:120:5296937110654841402240366622842796700 158:121:1663500910784165068472181253454762600 158:122:504504374582082848635005789982182100 158:123:147659816950853516673660231214297200 158:124:41678174139353815190146033004035500 158:125:11336463365904237731719720977097656 158:126:2969073738689205120212307874954148 158:127:748113068016177668084990960618368 158:128:181183633660168028989333748274761 158:129:42135728758178611392868313552270 158:130:9399508722978305618409085330891 158:131:2009055299567882116911865566908 158:132:410943129457066796641063411413 158:133:80334747111907794832087584186 158:134:14987825953714140826882011975 158:135:2664502391771402813667913240 158:136:450614375078987240546779445 158:137:72361432494435907241088670 158:138:11011522336109811971470015 158:139:1584391703037383017477700 158:140:215024588269359123800545 158:141:27449947438641590272410 158:142:3286261313076810103035 158:143:367693573491111619920 158:144:38301413905324127075 158:145:3698067549479570890 158:146:329279987282427545 158:147:26879998961830820 158:148:1997837760676615 158:149:134083071186350 158:150:8044984271181 158:151:426224332248 158:152:19628752143 158:153:769754986 158:154:24992045 158:155:644956 158:156:12403 158:157:158 158:158:1 # binomial(159, k) for 0 <= k <= 159 159:0:1 159:1:159 159:2:12561 159:3:657359 159:4:25637001 159:5:794747031 159:6:20398507129 159:7:445853084391 159:8:8471208603429 159:9:142128055457531 159:10:2131920831862965 159:11:28877836722507435 159:12:356159986244258365 159:13:4027347536761998435 159:14:41999481454803697965 159:15:405994987396435746995 159:16:3653954886567921722955 159:17:30736208751718400375445 159:18:242474535708000714072955 159:19:1799416291306742141278245 159:20:12595914039147194988947715 159:21:83372954830545719212558685 159:22:522975807573423147787868115 159:23:3115116766850390054214692685 159:24:17652328345485543640549925215 159:25:95322573065621935658969596161 159:26:491277876568974591473150995599 159:27:2419998429024948913552928978321 159:28:11408564022546187735320950897799 159:29:51535237481156917011277398883161 159:30:223319362418346640382202061827031 159:31:929296701676345697074324708893129 159:32:3717186806705382788297298835572516 159:33:14305537104593442851932028852051804 159:34:53014637505258052921865753981133156 159:35:189337991090207331863806264218332700 159:36:652164191532936365308666021196479300 159:37:2168005285366247917107187043436944700 159:38:6960438021439006470712547876297559300 159:39:21595205143438968793749187000820632700 159:40:64785615430316906381247561002461898100 159:41:188036298444090533155328286812023557900 159:42:528292457533397212198303281995685234100 159:43:1437446919335057530865150790546399357900 159:44:3789632787337878945008124811440507398100 159:45:9684617123196801748354096740347963350700 159:46:24001007653139899985051457139123213521300 159:47:57704550314995929751293928866402619742700 159:48:134643950734990502753019167354939446066300 159:49:305009765950692771542553624008128132925700 159:50:671021485091524097393617972817881892436540 159:51:1434143958332865227762830569355865221089860 159:52:2978606682691335473045878874816027766878940 159:53:6013413491471186709734132822741791906717860 159:54:11804107964739736874663297763159813742816540 159:55:22535115205412224942539023002396008054467940 159:56:41850928238622703464715328433021157815440460 159:57:75625361554002429067818926817564548333164340 159:58:132996325491521513188233285092958343620392460 159:59:227671675841418183593416301599810045858637940 159:60:379452793069030305989027169333016743097729900 159:61:615833221538262299883830979737191107650414100 159:62:973413801786285570784119935713624654028073900 159:63:1498748234496344450254914821654310975249574100 159:64:2248122351744516675382372232481466462874361150 159:65:3285717283318908987097313262857527907277912450 159:66:4679657948969355224047688586494054898244299550 159:67:6495644615733582624424403560357419485622684450 159:68:8788225068345435315397722464012979304077749550 159:69:11590267843759921937698445568480885748856162450 159:70:14901772941977042491326572873761138819957923150 159:71:18679687208957137770817816700911850070088100850 159:72:22830728810947612830999553745558927863441012150 159:73:27209224747293730360232344874844201700265315850 159:74:31621531463071092040270022422116234408416448150 159:75:35837735658147237645639358745065065662871974570 159:76:39610128885320631082022449139282440995805866630 159:77:42696632434826134802699523098187566268206323770 159:78:44886203328919782741299498641684364538370750630 159:79:46022562906867119013231131518689031995038364570 159:80:46022562906867119013231131518689031995038364570 159:81:44886203328919782741299498641684364538370750630 159:82:42696632434826134802699523098187566268206323770 159:83:39610128885320631082022449139282440995805866630 159:84:35837735658147237645639358745065065662871974570 159:85:31621531463071092040270022422116234408416448150 159:86:27209224747293730360232344874844201700265315850 159:87:22830728810947612830999553745558927863441012150 159:88:18679687208957137770817816700911850070088100850 159:89:14901772941977042491326572873761138819957923150 159:90:11590267843759921937698445568480885748856162450 159:91:8788225068345435315397722464012979304077749550 159:92:6495644615733582624424403560357419485622684450 159:93:4679657948969355224047688586494054898244299550 159:94:3285717283318908987097313262857527907277912450 159:95:2248122351744516675382372232481466462874361150 159:96:1498748234496344450254914821654310975249574100 159:97:973413801786285570784119935713624654028073900 159:98:615833221538262299883830979737191107650414100 159:99:379452793069030305989027169333016743097729900 159:100:227671675841418183593416301599810045858637940 159:101:132996325491521513188233285092958343620392460 159:102:75625361554002429067818926817564548333164340 159:103:41850928238622703464715328433021157815440460 159:104:22535115205412224942539023002396008054467940 159:105:11804107964739736874663297763159813742816540 159:106:6013413491471186709734132822741791906717860 159:107:2978606682691335473045878874816027766878940 159:108:1434143958332865227762830569355865221089860 159:109:671021485091524097393617972817881892436540 159:110:305009765950692771542553624008128132925700 159:111:134643950734990502753019167354939446066300 159:112:57704550314995929751293928866402619742700 159:113:24001007653139899985051457139123213521300 159:114:9684617123196801748354096740347963350700 159:115:3789632787337878945008124811440507398100 159:116:1437446919335057530865150790546399357900 159:117:528292457533397212198303281995685234100 159:118:188036298444090533155328286812023557900 159:119:64785615430316906381247561002461898100 159:120:21595205143438968793749187000820632700 159:121:6960438021439006470712547876297559300 159:122:2168005285366247917107187043436944700 159:123:652164191532936365308666021196479300 159:124:189337991090207331863806264218332700 159:125:53014637505258052921865753981133156 159:126:14305537104593442851932028852051804 159:127:3717186806705382788297298835572516 159:128:929296701676345697074324708893129 159:129:223319362418346640382202061827031 159:130:51535237481156917011277398883161 159:131:11408564022546187735320950897799 159:132:2419998429024948913552928978321 159:133:491277876568974591473150995599 159:134:95322573065621935658969596161 159:135:17652328345485543640549925215 159:136:3115116766850390054214692685 159:137:522975807573423147787868115 159:138:83372954830545719212558685 159:139:12595914039147194988947715 159:140:1799416291306742141278245 159:141:242474535708000714072955 159:142:30736208751718400375445 159:143:3653954886567921722955 159:144:405994987396435746995 159:145:41999481454803697965 159:146:4027347536761998435 159:147:356159986244258365 159:148:28877836722507435 159:149:2131920831862965 159:150:142128055457531 159:151:8471208603429 159:152:445853084391 159:153:20398507129 159:154:794747031 159:155:25637001 159:156:657359 159:157:12561 159:158:159 159:159:1 # binomial(160, k) for 0 <= k <= 160 160:0:1 160:1:160 160:2:12720 160:3:669920 160:4:26294360 160:5:820384032 160:6:21193254160 160:7:466251591520 160:8:8917061687820 160:9:150599264060960 160:10:2274048887320496 160:11:31009757554370400 160:12:385037822966765800 160:13:4383507523006256800 160:14:46026828991565696400 160:15:447994468851239444960 160:16:4059949873964357469950 160:17:34390163638286322098400 160:18:273210744459719114448400 160:19:2041890827014742855351200 160:20:14395330330453937130225960 160:21:95968868869692914201506400 160:22:606348762403968867000426800 160:23:3638092574423813202002560800 160:24:20767445112335933694764617900 160:25:112974901411107479299519521376 160:26:586600449634596527132120591760 160:27:2911276305593923505026079973920 160:28:13828562451571136648873879876120 160:29:62943801503703104746598349780960 160:30:274854599899503557393479460710192 160:31:1152616064094692337456526770720160 160:32:4646483508381728485371623544465645 160:33:18022723911298825640229327687624320 160:34:67320174609851495773797782833184960 160:35:242352628595465384785672018199465856 160:36:841502182623143697172472285414812000 160:37:2820169476899184282415853064633424000 160:38:9128443306805254387819734919734504000 160:39:28555643164877975264461734877118192000 160:40:86380820573755875174996748003282530800 160:41:252821913874407439536575847814485456000 160:42:716328755977487745353631568807708792000 160:43:1965739376868454743063454072542084592000 160:44:5227079706672936475873275601986906756000 160:45:13474249910534680693362221551788470748800 160:46:33685624776336701733405553879471176872000 160:47:81705557968135829736345386005525833264000 160:48:192348501049986432504313096221342065809000 160:49:439653716685683274295572791363067578992000 160:50:976031251042216868936171596826010025362240 160:51:2105165443424389325156448542173747113526400 160:52:4412750641024200700808709444171892987968800 160:53:8992020174162522182780011697557819673596800 160:54:17817521456210923584397430585901605649534400 160:55:34339223170151961817202320765555821797284480 160:56:64386043444034928407254351435417165869908400 160:57:117476289792625132532534255250585706148604800 160:58:208621687045523942256052211910522891953556800 160:59:360668001332939696781649586692768389479030400 160:60:607124468910448489582443470932826788956367840 160:61:995286014607292605872858149070207850748144000 160:62:1589247023324547870667950915450815761678488000 160:63:2472162036282630021039034757367935629277648000 160:64:3746870586240861125637287054135777438123935250 160:65:5533839635063425662479685495338994370152273600 160:66:7965375232288264211145001849351582805522212000 160:67:11175302564702937848472092146851474383866984000 160:68:15283869684079017939822126024370398789700434000 160:69:20378492912105357253096168032493865052933912000 160:70:26492040785736964429025018442242024568814085600 160:71:33581460150934180262144389574672988890046024000 160:72:41510416019904750601817370446470777933529113000 160:73:50039953558241343191231898620403129563706328000 160:74:58830756210364822400502367296960436108681764000 160:75:67459267121218329685909381167181300071288422720 160:76:75447864543467868727661807884347506658677841200 160:77:82306761320146765884721972237470007264012190400 160:78:87582835763745917543999021739871930806577074400 160:79:90908766235786901754530630160373396533409115200 160:80:92045125813734238026462263037378063990076729140 160:81:90908766235786901754530630160373396533409115200 160:82:87582835763745917543999021739871930806577074400 160:83:82306761320146765884721972237470007264012190400 160:84:75447864543467868727661807884347506658677841200 160:85:67459267121218329685909381167181300071288422720 160:86:58830756210364822400502367296960436108681764000 160:87:50039953558241343191231898620403129563706328000 160:88:41510416019904750601817370446470777933529113000 160:89:33581460150934180262144389574672988890046024000 160:90:26492040785736964429025018442242024568814085600 160:91:20378492912105357253096168032493865052933912000 160:92:15283869684079017939822126024370398789700434000 160:93:11175302564702937848472092146851474383866984000 160:94:7965375232288264211145001849351582805522212000 160:95:5533839635063425662479685495338994370152273600 160:96:3746870586240861125637287054135777438123935250 160:97:2472162036282630021039034757367935629277648000 160:98:1589247023324547870667950915450815761678488000 160:99:995286014607292605872858149070207850748144000 160:100:607124468910448489582443470932826788956367840 160:101:360668001332939696781649586692768389479030400 160:102:208621687045523942256052211910522891953556800 160:103:117476289792625132532534255250585706148604800 160:104:64386043444034928407254351435417165869908400 160:105:34339223170151961817202320765555821797284480 160:106:17817521456210923584397430585901605649534400 160:107:8992020174162522182780011697557819673596800 160:108:4412750641024200700808709444171892987968800 160:109:2105165443424389325156448542173747113526400 160:110:976031251042216868936171596826010025362240 160:111:439653716685683274295572791363067578992000 160:112:192348501049986432504313096221342065809000 160:113:81705557968135829736345386005525833264000 160:114:33685624776336701733405553879471176872000 160:115:13474249910534680693362221551788470748800 160:116:5227079706672936475873275601986906756000 160:117:1965739376868454743063454072542084592000 160:118:716328755977487745353631568807708792000 160:119:252821913874407439536575847814485456000 160:120:86380820573755875174996748003282530800 160:121:28555643164877975264461734877118192000 160:122:9128443306805254387819734919734504000 160:123:2820169476899184282415853064633424000 160:124:841502182623143697172472285414812000 160:125:242352628595465384785672018199465856 160:126:67320174609851495773797782833184960 160:127:18022723911298825640229327687624320 160:128:4646483508381728485371623544465645 160:129:1152616064094692337456526770720160 160:130:274854599899503557393479460710192 160:131:62943801503703104746598349780960 160:132:13828562451571136648873879876120 160:133:2911276305593923505026079973920 160:134:586600449634596527132120591760 160:135:112974901411107479299519521376 160:136:20767445112335933694764617900 160:137:3638092574423813202002560800 160:138:606348762403968867000426800 160:139:95968868869692914201506400 160:140:14395330330453937130225960 160:141:2041890827014742855351200 160:142:273210744459719114448400 160:143:34390163638286322098400 160:144:4059949873964357469950 160:145:447994468851239444960 160:146:46026828991565696400 160:147:4383507523006256800 160:148:385037822966765800 160:149:31009757554370400 160:150:2274048887320496 160:151:150599264060960 160:152:8917061687820 160:153:466251591520 160:154:21193254160 160:155:820384032 160:156:26294360 160:157:669920 160:158:12720 160:159:160 160:160:1 # binomial(161, k) for 0 <= k <= 161 161:0:1 161:1:161 161:2:12880 161:3:682640 161:4:26964280 161:5:846678392 161:6:22013638192 161:7:487444845680 161:8:9383313279340 161:9:159516325748780 161:10:2424648151381456 161:11:33283806441690896 161:12:416047580521136200 161:13:4768545345973022600 161:14:50410336514571953200 161:15:494021297842805141360 161:16:4507944342815596914910 161:17:38450113512250679568350 161:18:307600908098005436546800 161:19:2315101571474461969799600 161:20:16437221157468679985577160 161:21:110364199200146851331732360 161:22:702317631273661781201933200 161:23:4244441336827782069002987600 161:24:24405537686759746896767178700 161:25:133742346523443412994284139276 161:26:699575351045704006431640113136 161:27:3497876755228520032158200565680 161:28:16739838757165060153899959850040 161:29:76772363955274241395472229657080 161:30:337798401403206662140077810491152 161:31:1427470663994195894850006231430352 161:32:5799099572476420822828150315185805 161:33:22669207419680554125600951232089965 161:34:85342898521150321414027110520809280 161:35:309672803205316880559469801032650816 161:36:1083854811218609081958144303614277856 161:37:3661671659522327979588325350048236000 161:38:11948612783704438670235587984367928000 161:39:37684086471683229652281469796852696000 161:40:114936463738633850439458482880400722800 161:41:339202734448163314711572595817767986800 161:42:969150669851895184890207416622194248000 161:43:2682068132845942488417085641349793384000 161:44:7192819083541391218936729674528991348000 161:45:18701329617207617169235497153775377504800 161:46:47159874686871382426767775431259647620800 161:47:115391182744472531469750939884997010136000 161:48:274054059018122262240658482226867899073000 161:49:632002217735669706799885887584409644801000 161:50:1415684967727900143231744388189077604354240 161:51:3081196694466606194092620138999757138888640 161:52:6517916084448590025965157986345640101495200 161:53:13404770815186722883588721141729712661565600 161:54:26809541630373445767177442283459425323131200 161:55:52156744626362885401599751351457427446818880 161:56:98725266614186890224456672200972987667192880 161:57:181862333236660060939788606686002872018513200 161:58:326097976838149074788586467161108598102161600 161:59:569289688378463639037701798603291281432587200 161:60:967792470243388186364093057625595178435398240 161:61:1602410483517741095455301620003034639704511840 161:62:2584533037931840476540809064521023612426632000 161:63:4061409059607177891706985672818751390956136000 161:64:6219032622523491146676321811503713067401583250 161:65:9280710221304286788116972549474771808276208850 161:66:13499214867351689873624687344690577175674485600 161:67:19140677796991202059617093996203057189389196000 161:68:26459172248781955788294218171221873173567418000 161:69:35662362596184375192918294056864263842634346000 161:70:46870533697842321682121186474735889621747997600 161:71:60073500936671144691169408016915013458860109600 161:72:75091876170838930863961760021143766823575137000 161:73:91550369578146093793049269066873907497235441000 161:74:108870709768606165591734265917363565672388092000 161:75:126290023331583152086411748464141736179970186720 161:76:142907131664686198413571189051528806729966263920 161:77:157754625863614634612383780121817513922690031600 161:78:169889597083892683428720993977341938070589264800 161:79:178491601999532819298529651900245327339986189600 161:80:182953892049521139780992893197751460523485844340 161:81:182953892049521139780992893197751460523485844340 161:82:178491601999532819298529651900245327339986189600 161:83:169889597083892683428720993977341938070589264800 161:84:157754625863614634612383780121817513922690031600 161:85:142907131664686198413571189051528806729966263920 161:86:126290023331583152086411748464141736179970186720 161:87:108870709768606165591734265917363565672388092000 161:88:91550369578146093793049269066873907497235441000 161:89:75091876170838930863961760021143766823575137000 161:90:60073500936671144691169408016915013458860109600 161:91:46870533697842321682121186474735889621747997600 161:92:35662362596184375192918294056864263842634346000 161:93:26459172248781955788294218171221873173567418000 161:94:19140677796991202059617093996203057189389196000 161:95:13499214867351689873624687344690577175674485600 161:96:9280710221304286788116972549474771808276208850 161:97:6219032622523491146676321811503713067401583250 161:98:4061409059607177891706985672818751390956136000 161:99:2584533037931840476540809064521023612426632000 161:100:1602410483517741095455301620003034639704511840 161:101:967792470243388186364093057625595178435398240 161:102:569289688378463639037701798603291281432587200 161:103:326097976838149074788586467161108598102161600 161:104:181862333236660060939788606686002872018513200 161:105:98725266614186890224456672200972987667192880 161:106:52156744626362885401599751351457427446818880 161:107:26809541630373445767177442283459425323131200 161:108:13404770815186722883588721141729712661565600 161:109:6517916084448590025965157986345640101495200 161:110:3081196694466606194092620138999757138888640 161:111:1415684967727900143231744388189077604354240 161:112:632002217735669706799885887584409644801000 161:113:274054059018122262240658482226867899073000 161:114:115391182744472531469750939884997010136000 161:115:47159874686871382426767775431259647620800 161:116:18701329617207617169235497153775377504800 161:117:7192819083541391218936729674528991348000 161:118:2682068132845942488417085641349793384000 161:119:969150669851895184890207416622194248000 161:120:339202734448163314711572595817767986800 161:121:114936463738633850439458482880400722800 161:122:37684086471683229652281469796852696000 161:123:11948612783704438670235587984367928000 161:124:3661671659522327979588325350048236000 161:125:1083854811218609081958144303614277856 161:126:309672803205316880559469801032650816 161:127:85342898521150321414027110520809280 161:128:22669207419680554125600951232089965 161:129:5799099572476420822828150315185805 161:130:1427470663994195894850006231430352 161:131:337798401403206662140077810491152 161:132:76772363955274241395472229657080 161:133:16739838757165060153899959850040 161:134:3497876755228520032158200565680 161:135:699575351045704006431640113136 161:136:133742346523443412994284139276 161:137:24405537686759746896767178700 161:138:4244441336827782069002987600 161:139:702317631273661781201933200 161:140:110364199200146851331732360 161:141:16437221157468679985577160 161:142:2315101571474461969799600 161:143:307600908098005436546800 161:144:38450113512250679568350 161:145:4507944342815596914910 161:146:494021297842805141360 161:147:50410336514571953200 161:148:4768545345973022600 161:149:416047580521136200 161:150:33283806441690896 161:151:2424648151381456 161:152:159516325748780 161:153:9383313279340 161:154:487444845680 161:155:22013638192 161:156:846678392 161:157:26964280 161:158:682640 161:159:12880 161:160:161 161:161:1 # binomial(162, k) for 0 <= k <= 162 162:0:1 162:1:162 162:2:13041 162:3:695520 162:4:27646920 162:5:873642672 162:6:22860316584 162:7:509458483872 162:8:9870758125020 162:9:168899639028120 162:10:2584164477130236 162:11:35708454593072352 162:12:449331386962827096 162:13:5184592926494158800 162:14:55178881860544975800 162:15:544431634357377094560 162:16:5001965640658402056270 162:17:42958057855066276483260 162:18:346051021610256116115150 162:19:2622702479572467406346400 162:20:18752322728943141955376760 162:21:126801420357615531317309520 162:22:812681830473808632533665560 162:23:4946758968101443850204920800 162:24:28649979023587528965770166300 162:25:158147884210203159891051317976 162:26:833317697569147419425924252412 162:27:4197452106274224038589840678816 162:28:20237715512393580186058160415720 162:29:93512202712439301549372189507120 162:30:414570765358480903535550040148232 162:31:1765269065397402556990084041921504 162:32:7226570236470616717678156546616157 162:33:28468306992156974948429101547275770 162:34:108012105940830875539628061752899245 162:35:395015701726467201973496911553460096 162:36:1393527614423925962517614104646928672 162:37:4745526470740937061546469653662513856 162:38:15610284443226766649823913334416164000 162:39:49632699255387668322517057781220624000 162:40:152620550210317080091739952677253418800 162:41:454139198186797165151031078698168709600 162:42:1308353404300058499601780012439962234800 162:43:3651218802697837673307293057971987632000 162:44:9874887216387333707353815315878784732000 162:45:25894148700749008388172226828304368852800 162:46:65861204304078999596003272585035025125600 162:47:162551057431343913896518715316256657756800 162:48:389445241762594793710409422111864909209000 162:49:906056276753791969040544369811277543874000 162:50:2047687185463569850031630275773487249155240 162:51:4496881662194506337324364527188834743242880 162:52:9599112778915196220057778125345397240383840 162:53:19922686899635312909553879128075352763060800 162:54:40214312445560168650766163425189137984696800 162:55:78966286256736331168777193634916852769950080 162:56:150882011240549775626056423552430415114011760 162:57:280587599850846951164245278886975859685706080 162:58:507960310074809135728375073847111470120674800 162:59:895387665216612713826288265764399879534748800 162:60:1537082158621851825401794856228886459867985440 162:61:2570202953761129281819394677628629818139910080 162:62:4186943521449581571996110684524058252131143840 162:63:6645942097539018368247794737339775003382768000 162:64:10280441682130669038383307484322464458357719250 162:65:15499742843827777934793294360978484875677792100 162:66:22779925088655976661741659894165348983950694450 162:67:32639892664342891933241781340893634365063681600 162:68:45599850045773157847911312167424930362956614000 162:69:62121534844966330981212512228086137016201764000 162:70:82532896294026696875039480531600153464382343600 162:71:106944034634513466373290594491650903080608107200 162:72:135165377107510075555131168038058780282435246600 162:73:166642245748985024657011029088017674320810578000 162:74:200421079346752259384783534984237473169623533000 162:75:235160733100189317678146014381505301852358278720 162:76:269197154996269350499982937515670542909936450640 162:77:300661757528300833025954969173346320652656295520 162:78:327644222947507318041104774099159451993279296400 162:79:348381199083425502727250645877587265410575454400 162:80:361445494049053959079522545097996787863472033940 162:81:365907784099042279561985786395502921046971688680 162:82:361445494049053959079522545097996787863472033940 162:83:348381199083425502727250645877587265410575454400 162:84:327644222947507318041104774099159451993279296400 162:85:300661757528300833025954969173346320652656295520 162:86:269197154996269350499982937515670542909936450640 162:87:235160733100189317678146014381505301852358278720 162:88:200421079346752259384783534984237473169623533000 162:89:166642245748985024657011029088017674320810578000 162:90:135165377107510075555131168038058780282435246600 162:91:106944034634513466373290594491650903080608107200 162:92:82532896294026696875039480531600153464382343600 162:93:62121534844966330981212512228086137016201764000 162:94:45599850045773157847911312167424930362956614000 162:95:32639892664342891933241781340893634365063681600 162:96:22779925088655976661741659894165348983950694450 162:97:15499742843827777934793294360978484875677792100 162:98:10280441682130669038383307484322464458357719250 162:99:6645942097539018368247794737339775003382768000 162:100:4186943521449581571996110684524058252131143840 162:101:2570202953761129281819394677628629818139910080 162:102:1537082158621851825401794856228886459867985440 162:103:895387665216612713826288265764399879534748800 162:104:507960310074809135728375073847111470120674800 162:105:280587599850846951164245278886975859685706080 162:106:150882011240549775626056423552430415114011760 162:107:78966286256736331168777193634916852769950080 162:108:40214312445560168650766163425189137984696800 162:109:19922686899635312909553879128075352763060800 162:110:9599112778915196220057778125345397240383840 162:111:4496881662194506337324364527188834743242880 162:112:2047687185463569850031630275773487249155240 162:113:906056276753791969040544369811277543874000 162:114:389445241762594793710409422111864909209000 162:115:162551057431343913896518715316256657756800 162:116:65861204304078999596003272585035025125600 162:117:25894148700749008388172226828304368852800 162:118:9874887216387333707353815315878784732000 162:119:3651218802697837673307293057971987632000 162:120:1308353404300058499601780012439962234800 162:121:454139198186797165151031078698168709600 162:122:152620550210317080091739952677253418800 162:123:49632699255387668322517057781220624000 162:124:15610284443226766649823913334416164000 162:125:4745526470740937061546469653662513856 162:126:1393527614423925962517614104646928672 162:127:395015701726467201973496911553460096 162:128:108012105940830875539628061752899245 162:129:28468306992156974948429101547275770 162:130:7226570236470616717678156546616157 162:131:1765269065397402556990084041921504 162:132:414570765358480903535550040148232 162:133:93512202712439301549372189507120 162:134:20237715512393580186058160415720 162:135:4197452106274224038589840678816 162:136:833317697569147419425924252412 162:137:158147884210203159891051317976 162:138:28649979023587528965770166300 162:139:4946758968101443850204920800 162:140:812681830473808632533665560 162:141:126801420357615531317309520 162:142:18752322728943141955376760 162:143:2622702479572467406346400 162:144:346051021610256116115150 162:145:42958057855066276483260 162:146:5001965640658402056270 162:147:544431634357377094560 162:148:55178881860544975800 162:149:5184592926494158800 162:150:449331386962827096 162:151:35708454593072352 162:152:2584164477130236 162:153:168899639028120 162:154:9870758125020 162:155:509458483872 162:156:22860316584 162:157:873642672 162:158:27646920 162:159:695520 162:160:13041 162:161:162 162:162:1 # binomial(163, k) for 0 <= k <= 163 163:0:1 163:1:163 163:2:13203 163:3:708561 163:4:28342440 163:5:901289592 163:6:23733959256 163:7:532318800456 163:8:10380216608892 163:9:178770397153140 163:10:2753064116158356 163:11:38292619070202588 163:12:485039841555899448 163:13:5633924313456985896 163:14:60363474787039134600 163:15:599610516217922070360 163:16:5546397275015779150830 163:17:47960023495724678539530 163:18:389009079465322392598410 163:19:2968753501182723522461550 163:20:21375025208515609361723160 163:21:145553743086558673272686280 163:22:939483250831424163850975080 163:23:5759440798575252482738586360 163:24:33596737991688972815975087100 163:25:186797863233790688856821484276 163:26:991465581779350579316975570388 163:27:5030769803843371458015764931228 163:28:24435167618667804224648001094536 163:29:113749918224832881735430349922840 163:30:508082968070920205084922229655352 163:31:2179839830755883460525634082069736 163:32:8991839301868019274668240588537661 163:33:35694877228627591666107258093891927 163:34:136480412932987850488057163300175015 163:35:503027807667298077513124973306359341 163:36:1788543316150393164491111016200388768 163:37:6139054085164863024064083758309442528 163:38:20355810913967703711370382988078677856 163:39:65242983698614434972340971115636788000 163:40:202253249465704748414257010458474042800 163:41:606759748397114245242771031375422128400 163:42:1762492602486855664752811091138130944400 163:43:4959572206997896172909073070411949866800 163:44:13526106019085171380661108373850772364000 163:45:35769035917136342095526042144183153584800 163:46:91755353004828007984175499413339393978400 163:47:228412261735422913492521987901291682882400 163:48:551996299193938707606928137428121566965800 163:49:1295501518516386762750953791923142453083000 163:50:2953743462217361819072174645584764793029240 163:51:6544568847658076187355994802962321992398120 163:52:14095994441109702557382142652534231983626720 163:53:29521799678550509129611657253420750003444640 163:54:60136999345195481560320042553264490747757600 163:55:119180598702296499819543357060105990754646880 163:56:229848297497286106794833617187347267883961840 163:57:431469611091396726790301702439406274799717840 163:58:788547909925656086892620352734087329806380880 163:59:1403347975291421849554663339611511349655423600 163:60:2432469823838464539228083121993286339402734240 163:61:4107285112382981107221189533857516278007895520 163:62:6757146475210710853815505362152688070271053920 163:63:10832885618988599940243905421863833255513911840 163:64:16926383779669687406631102221662239461740487250 163:65:25780184525958446973176601845300949334035511350 163:66:38279667932483754596534954255143833859628486550 163:67:55419817752998868594983441235058983349014376050 163:68:78239742710116049781153093508318564728020295600 163:69:107721384890739488829123824395511067379158378000 163:70:144654431138993027856251992759686290480584107600 163:71:189476930928540163248330075023251056544990450800 163:72:242109411742023541928421762529709683363043353800 163:73:301807622856495100212142197126076454603245824600 163:74:367063325095737284041794564072255147490434111000 163:75:435581812446941577062929549365742775021981811720 163:76:504357888096458668178128951897175844762294729360 163:77:569858912524570183525937906689016863562592746160 163:78:628305980475808151067059743272505772645935591920 163:79:676025422030932820768355419976746717403854750800 163:80:709826693132479461806773190975584053274047488340 163:81:727353278148096238641508331493499708910443722620 163:82:727353278148096238641508331493499708910443722620 163:83:709826693132479461806773190975584053274047488340 163:84:676025422030932820768355419976746717403854750800 163:85:628305980475808151067059743272505772645935591920 163:86:569858912524570183525937906689016863562592746160 163:87:504357888096458668178128951897175844762294729360 163:88:435581812446941577062929549365742775021981811720 163:89:367063325095737284041794564072255147490434111000 163:90:301807622856495100212142197126076454603245824600 163:91:242109411742023541928421762529709683363043353800 163:92:189476930928540163248330075023251056544990450800 163:93:144654431138993027856251992759686290480584107600 163:94:107721384890739488829123824395511067379158378000 163:95:78239742710116049781153093508318564728020295600 163:96:55419817752998868594983441235058983349014376050 163:97:38279667932483754596534954255143833859628486550 163:98:25780184525958446973176601845300949334035511350 163:99:16926383779669687406631102221662239461740487250 163:100:10832885618988599940243905421863833255513911840 163:101:6757146475210710853815505362152688070271053920 163:102:4107285112382981107221189533857516278007895520 163:103:2432469823838464539228083121993286339402734240 163:104:1403347975291421849554663339611511349655423600 163:105:788547909925656086892620352734087329806380880 163:106:431469611091396726790301702439406274799717840 163:107:229848297497286106794833617187347267883961840 163:108:119180598702296499819543357060105990754646880 163:109:60136999345195481560320042553264490747757600 163:110:29521799678550509129611657253420750003444640 163:111:14095994441109702557382142652534231983626720 163:112:6544568847658076187355994802962321992398120 163:113:2953743462217361819072174645584764793029240 163:114:1295501518516386762750953791923142453083000 163:115:551996299193938707606928137428121566965800 163:116:228412261735422913492521987901291682882400 163:117:91755353004828007984175499413339393978400 163:118:35769035917136342095526042144183153584800 163:119:13526106019085171380661108373850772364000 163:120:4959572206997896172909073070411949866800 163:121:1762492602486855664752811091138130944400 163:122:606759748397114245242771031375422128400 163:123:202253249465704748414257010458474042800 163:124:65242983698614434972340971115636788000 163:125:20355810913967703711370382988078677856 163:126:6139054085164863024064083758309442528 163:127:1788543316150393164491111016200388768 163:128:503027807667298077513124973306359341 163:129:136480412932987850488057163300175015 163:130:35694877228627591666107258093891927 163:131:8991839301868019274668240588537661 163:132:2179839830755883460525634082069736 163:133:508082968070920205084922229655352 163:134:113749918224832881735430349922840 163:135:24435167618667804224648001094536 163:136:5030769803843371458015764931228 163:137:991465581779350579316975570388 163:138:186797863233790688856821484276 163:139:33596737991688972815975087100 163:140:5759440798575252482738586360 163:141:939483250831424163850975080 163:142:145553743086558673272686280 163:143:21375025208515609361723160 163:144:2968753501182723522461550 163:145:389009079465322392598410 163:146:47960023495724678539530 163:147:5546397275015779150830 163:148:599610516217922070360 163:149:60363474787039134600 163:150:5633924313456985896 163:151:485039841555899448 163:152:38292619070202588 163:153:2753064116158356 163:154:178770397153140 163:155:10380216608892 163:156:532318800456 163:157:23733959256 163:158:901289592 163:159:28342440 163:160:708561 163:161:13203 163:162:163 163:163:1 # binomial(164, k) for 0 <= k <= 164 164:0:1 164:1:164 164:2:13366 164:3:721764 164:4:29051001 164:5:929632032 164:6:24635248848 164:7:556052759712 164:8:10912535409348 164:9:189150613762032 164:10:2931834513311496 164:11:41045683186360944 164:12:523332460626102036 164:13:6118964155012885344 164:14:65997399100496120496 164:15:659973991004961204960 164:16:6146007791233701221190 164:17:53506420770740457690360 164:18:436969102961047071137940 164:19:3357762580648045915059960 164:20:24343778709698332884184710 164:21:166928768295074282634409440 164:22:1085036993917982837123661360 164:23:6698924049406676646589561440 164:24:39356178790264225298713673460 164:25:220394601225479661672796571376 164:26:1178263445013141268173797054664 164:27:6022235385622722037332740501616 164:28:29465937422511175682663766025764 164:29:138185085843500685960078351017376 164:30:621832886295753086820352579578192 164:31:2687922798826803665610556311725088 164:32:11171679132623902735193874670607397 164:33:44686716530495610940775498682429588 164:34:172175290161615442154164421394066942 164:35:639508220600285928001182136606534356 164:36:2291571123817691242004235989506748109 164:37:7927597401315256188555194774509831296 164:38:26494864999132566735434466746388120384 164:39:85598794612582138683711354103715465856 164:40:267496233164319183386597981574110830800 164:41:809012997862818993657028041833896171200 164:42:2369252350883969909995582122513553072800 164:43:6722064809484751837661884161550080811200 164:44:18485678226083067553570181444262722230800 164:45:49295141936221513476187150518033925948800 164:46:127524388921964350079701541557522547563200 164:47:320167614740250921476697487314631076860800 164:48:780408560929361621099450125329413249848200 164:49:1847497817710325470357881929351264020048800 164:50:4249244980733748581823128437507907246112240 164:51:9498312309875438006428169448547086785427360 164:52:20640563288767778744738137455496553976024840 164:53:43617794119660211686993799905954981987071360 164:54:89658799023745990689931699806685240751202240 164:55:179317598047491981379863399613370481502404480 164:56:349028896199582606614376974247453258638608720 164:57:661317908588682833585135319626753542683679680 164:58:1220017521017052813682922055173493604606098720 164:59:2191895885217077936447283692345598679461804480 164:60:3835817799129886388782746461604797689058157840 164:61:6539754936221445646449272655850802617410629760 164:62:10864431587593691961036694896010204348278949440 164:63:17590032094199310794059410784016521325784965760 164:64:27759269398658287346875007643526072717254399090 164:65:42706568305628134379807704066963188795775998600 164:66:64059852458442201569711556100444783193663997900 164:67:93699485685482623191518395490202817208642862600 164:68:133659560463114918376136534743377548077034671650 164:69:185961127600855538610276917903829632107178673600 164:70:252375816029732516685375817155197357859742485600 164:71:334131362067533191104582067782937347025574558400 164:72:431586342670563705176751837552960739908033804600 164:73:543917034598518642140563959655786137966289178400 164:74:668870947952232384253936761198331602093679935600 164:75:802645137542678861104724113437997922512415922720 164:76:939939700543400245241058501262918619784276541080 164:77:1074216800621028851704066858586192708324887475520 164:78:1198164893000378334592997649961522636208528338080 164:79:1304331402506740971835415163249252490049790342720 164:80:1385852115163412282575128610952330770677902239140 164:81:1437179971280575700448281522469083762184491210960 164:82:1454706556296192477283016662986999417820887445240 164:83:1437179971280575700448281522469083762184491210960 164:84:1385852115163412282575128610952330770677902239140 164:85:1304331402506740971835415163249252490049790342720 164:86:1198164893000378334592997649961522636208528338080 164:87:1074216800621028851704066858586192708324887475520 164:88:939939700543400245241058501262918619784276541080 164:89:802645137542678861104724113437997922512415922720 164:90:668870947952232384253936761198331602093679935600 164:91:543917034598518642140563959655786137966289178400 164:92:431586342670563705176751837552960739908033804600 164:93:334131362067533191104582067782937347025574558400 164:94:252375816029732516685375817155197357859742485600 164:95:185961127600855538610276917903829632107178673600 164:96:133659560463114918376136534743377548077034671650 164:97:93699485685482623191518395490202817208642862600 164:98:64059852458442201569711556100444783193663997900 164:99:42706568305628134379807704066963188795775998600 164:100:27759269398658287346875007643526072717254399090 164:101:17590032094199310794059410784016521325784965760 164:102:10864431587593691961036694896010204348278949440 164:103:6539754936221445646449272655850802617410629760 164:104:3835817799129886388782746461604797689058157840 164:105:2191895885217077936447283692345598679461804480 164:106:1220017521017052813682922055173493604606098720 164:107:661317908588682833585135319626753542683679680 164:108:349028896199582606614376974247453258638608720 164:109:179317598047491981379863399613370481502404480 164:110:89658799023745990689931699806685240751202240 164:111:43617794119660211686993799905954981987071360 164:112:20640563288767778744738137455496553976024840 164:113:9498312309875438006428169448547086785427360 164:114:4249244980733748581823128437507907246112240 164:115:1847497817710325470357881929351264020048800 164:116:780408560929361621099450125329413249848200 164:117:320167614740250921476697487314631076860800 164:118:127524388921964350079701541557522547563200 164:119:49295141936221513476187150518033925948800 164:120:18485678226083067553570181444262722230800 164:121:6722064809484751837661884161550080811200 164:122:2369252350883969909995582122513553072800 164:123:809012997862818993657028041833896171200 164:124:267496233164319183386597981574110830800 164:125:85598794612582138683711354103715465856 164:126:26494864999132566735434466746388120384 164:127:7927597401315256188555194774509831296 164:128:2291571123817691242004235989506748109 164:129:639508220600285928001182136606534356 164:130:172175290161615442154164421394066942 164:131:44686716530495610940775498682429588 164:132:11171679132623902735193874670607397 164:133:2687922798826803665610556311725088 164:134:621832886295753086820352579578192 164:135:138185085843500685960078351017376 164:136:29465937422511175682663766025764 164:137:6022235385622722037332740501616 164:138:1178263445013141268173797054664 164:139:220394601225479661672796571376 164:140:39356178790264225298713673460 164:141:6698924049406676646589561440 164:142:1085036993917982837123661360 164:143:166928768295074282634409440 164:144:24343778709698332884184710 164:145:3357762580648045915059960 164:146:436969102961047071137940 164:147:53506420770740457690360 164:148:6146007791233701221190 164:149:659973991004961204960 164:150:65997399100496120496 164:151:6118964155012885344 164:152:523332460626102036 164:153:41045683186360944 164:154:2931834513311496 164:155:189150613762032 164:156:10912535409348 164:157:556052759712 164:158:24635248848 164:159:929632032 164:160:29051001 164:161:721764 164:162:13366 164:163:164 164:164:1 # binomial(165, k) for 0 <= k <= 165 165:0:1 165:1:165 165:2:13530 165:3:735130 165:4:29772765 165:5:958683033 165:6:25564880880 165:7:580688008560 165:8:11468588169060 165:9:200063149171380 165:10:3120985127073528 165:11:43977517699672440 165:12:564378143812462980 165:13:6642296615638987380 165:14:72116363255509005840 165:15:725971390105457325456 165:16:6805981782238662426150 165:17:59652428561974158911550 165:18:490475523731787528828300 165:19:3794731683609092986197900 165:20:27701541290346378799244670 165:21:191272547004772615518594150 165:22:1251965762213057119758070800 165:23:7783961043324659483713222800 165:24:46055102839670901945303234900 165:25:259750780015743886971510244836 165:26:1398658046238620929846593626040 165:27:7200498830635863305506537556280 165:28:35488172808133897719996506527380 165:29:167651023266011861642742117043140 165:30:760017972139253772780430930595568 165:31:3309755685122556752430908891303280 165:32:13859601931450706400804430982332485 165:33:55858395663119513675969373353036985 165:34:216862006692111053094939920076496530 165:35:811683510761901370155346558000601298 165:36:2931079344417977170005418126113282465 165:37:10219168525132947430559430764016579405 165:38:34422462400447822923989661520897951680 165:39:112093659611714705419145820850103586240 165:40:353095027776901322070309335677826296656 165:41:1076509231027138177043626023408007002000 165:42:3178265348746788903652610164347449244000 165:43:9091317160368721747657466284063633884000 165:44:25207743035567819391232065605812803042000 165:45:67780820162304581029757331962296648179600 165:46:176819530858185863555888692075556473512000 165:47:447692003662215271556399028872153624424000 165:48:1100576175669612542576147612644044326709000 165:49:2627906378639687091457332054680677269897000 165:50:6096742798444074052181010366859171266161040 165:51:13747557290609186588251297886054994031539600 165:52:30138875598643216751166306904043640761452200 165:53:64258357408427990431731937361451535963096200 165:54:133276593143406202376925499712640222738273600 165:55:268976397071237972069795099420055722253606720 165:56:528346494247074587994240373860823740141013200 165:57:1010346804788265440199512293874206801322288400 165:58:1881335429605735647268057374800247147289778400 165:59:3411913406234130750130205747519092284067903200 165:60:6027713684346964325230030153950396368519962320 165:61:10375572735351332035232019117455600306468787600 165:62:17404186523815137607485967551861006965689579200 165:63:28454463681793002755096105680026725674063915200 165:64:45349301492857598140934418427542594043039364850 165:65:70465837704286421726682711710489261513030397690 165:66:106766420764070335949519260167407971989439996500 165:67:157759338143924824761229951590647600402306860500 165:68:227359046148597541567654930233580365285677534250 165:69:319620688063970456986413452647207180184213345250 165:70:438336943630588055295652735059026989966921159200 165:71:586507178097265707789957884938134704885317044000 165:72:765717704738096896281333905335898086933608363000 165:73:975503377269082347317315797208746877874322983000 165:74:1212787982550751026394500720854117740059969114000 165:75:1471516085494911245358660874636329524606095858320 165:76:1742584838086079106345782614700916542296692463800 165:77:2014156501164429096945125359849111328109164016600 165:78:2272381693621407186297064508547715344533415813600 165:79:2502496295507119306428412813210775126258318680800 165:80:2690183517670153254410543774201583260727692581860 165:81:2823032086443987983023410133421414532862393450100 165:82:2891886527576768177731298185456083180005378656200 165:83:2891886527576768177731298185456083180005378656200 165:84:2823032086443987983023410133421414532862393450100 165:85:2690183517670153254410543774201583260727692581860 165:86:2502496295507119306428412813210775126258318680800 165:87:2272381693621407186297064508547715344533415813600 165:88:2014156501164429096945125359849111328109164016600 165:89:1742584838086079106345782614700916542296692463800 165:90:1471516085494911245358660874636329524606095858320 165:91:1212787982550751026394500720854117740059969114000 165:92:975503377269082347317315797208746877874322983000 165:93:765717704738096896281333905335898086933608363000 165:94:586507178097265707789957884938134704885317044000 165:95:438336943630588055295652735059026989966921159200 165:96:319620688063970456986413452647207180184213345250 165:97:227359046148597541567654930233580365285677534250 165:98:157759338143924824761229951590647600402306860500 165:99:106766420764070335949519260167407971989439996500 165:100:70465837704286421726682711710489261513030397690 165:101:45349301492857598140934418427542594043039364850 165:102:28454463681793002755096105680026725674063915200 165:103:17404186523815137607485967551861006965689579200 165:104:10375572735351332035232019117455600306468787600 165:105:6027713684346964325230030153950396368519962320 165:106:3411913406234130750130205747519092284067903200 165:107:1881335429605735647268057374800247147289778400 165:108:1010346804788265440199512293874206801322288400 165:109:528346494247074587994240373860823740141013200 165:110:268976397071237972069795099420055722253606720 165:111:133276593143406202376925499712640222738273600 165:112:64258357408427990431731937361451535963096200 165:113:30138875598643216751166306904043640761452200 165:114:13747557290609186588251297886054994031539600 165:115:6096742798444074052181010366859171266161040 165:116:2627906378639687091457332054680677269897000 165:117:1100576175669612542576147612644044326709000 165:118:447692003662215271556399028872153624424000 165:119:176819530858185863555888692075556473512000 165:120:67780820162304581029757331962296648179600 165:121:25207743035567819391232065605812803042000 165:122:9091317160368721747657466284063633884000 165:123:3178265348746788903652610164347449244000 165:124:1076509231027138177043626023408007002000 165:125:353095027776901322070309335677826296656 165:126:112093659611714705419145820850103586240 165:127:34422462400447822923989661520897951680 165:128:10219168525132947430559430764016579405 165:129:2931079344417977170005418126113282465 165:130:811683510761901370155346558000601298 165:131:216862006692111053094939920076496530 165:132:55858395663119513675969373353036985 165:133:13859601931450706400804430982332485 165:134:3309755685122556752430908891303280 165:135:760017972139253772780430930595568 165:136:167651023266011861642742117043140 165:137:35488172808133897719996506527380 165:138:7200498830635863305506537556280 165:139:1398658046238620929846593626040 165:140:259750780015743886971510244836 165:141:46055102839670901945303234900 165:142:7783961043324659483713222800 165:143:1251965762213057119758070800 165:144:191272547004772615518594150 165:145:27701541290346378799244670 165:146:3794731683609092986197900 165:147:490475523731787528828300 165:148:59652428561974158911550 165:149:6805981782238662426150 165:150:725971390105457325456 165:151:72116363255509005840 165:152:6642296615638987380 165:153:564378143812462980 165:154:43977517699672440 165:155:3120985127073528 165:156:200063149171380 165:157:11468588169060 165:158:580688008560 165:159:25564880880 165:160:958683033 165:161:29772765 165:162:735130 165:163:13530 165:164:165 165:165:1 # binomial(166, k) for 0 <= k <= 166 166:0:1 166:1:166 166:2:13695 166:3:748660 166:4:30507895 166:5:988455798 166:6:26523563913 166:7:606252889440 166:8:12049276177620 166:9:211531737340440 166:10:3321048276244908 166:11:47098502826745968 166:12:608355661512135420 166:13:7206674759451450360 166:14:78758659871147993220 166:15:798087753360966331296 166:16:7531953172344119751606 166:17:66458410344212821337700 166:18:550127952293761687739850 166:19:4285207207340880515026200 166:20:31496272973955471785442570 166:21:218974088295118994317838820 166:22:1443238309217829735276664950 166:23:9035926805537716603471293600 166:24:53839063882995561429016457700 166:25:305805882855414788916813479736 166:26:1658408826254364816818103870876 166:27:8599156876874484235353131182320 166:28:42688671638769761025503044083660 166:29:203139196074145759362738623570520 166:30:927668995405265634423173047638708 166:31:4069773657261810525211339821898848 166:32:17169357616573263153235339873635765 166:33:69717997594570220076773804335369470 166:34:272720402355230566770909293429533515 166:35:1028545517454012423250286478077097828 166:36:3742762855179878540160764684113883763 166:37:13150247869550924600564848890129861870 166:38:44641630925580770354549092284914531085 166:39:146516122012162528343135482371001537920 166:40:465188687388616027489455156527929882896 166:41:1429604258804039499113935359085833298656 166:42:4254774579773927080696236187755456246000 166:43:12269582509115510651310076448411083128000 166:44:34299060195936541138889531889876436926000 166:45:92988563197872400420989397568109451221600 166:46:244600351020490444585646024037853121691600 166:47:624511534520401135112287720947710097936000 166:48:1548268179331827814132546641516197951133000 166:49:3728482554309299634033479667324721596606000 166:50:8724649177083761143638342421539848536058040 166:51:19844300089053260640432308252914165297700640 166:52:43886432889252403339417604790098634792991800 166:53:94397233007071207182898244265495176724548400 166:54:197534950551834192808657437074091758701369800 166:55:402252990214644174446720599132695944991880320 166:56:797322891318312560064035473280879462394619920 166:57:1538693299035340028193752667735030541463301600 166:58:2891682234394001087467569668674453948612066800 166:59:5293248835839866397398263122319339431357681600 166:60:9439627090581095075360235901469488652587865520 166:61:16403286419698296360462049271405996674988749920 166:62:27779759259166469642717986669316607272158366800 166:63:45858650205608140362582073231887732639753494400 166:64:73803765174650600896030524107569319717103280050 166:65:115815139197144019867617130138031855556069762540 166:66:177232258468356757676201971877897233502470394190 166:67:264525758907995160710749211758055572391746857000 166:68:385118384292522366328884881824227965687984394750 166:69:546979734212567998554068382880787545469890879500 166:70:757957631694558512282066187706234170151134504450 166:71:1024844121727853763085610619997161694852238203200 166:72:1352224882835362604071291790274032791818925407000 166:73:1741221082007179243598649702544644964807931346000 166:74:2188291359819833373711816518062864617934292097000 166:75:2684304068045662271753161595490447264666064972320 166:76:3214100923580990351704443489337246066902788322120 166:77:3756741339250508203290907974550027870405856480400 166:78:4286538194785836283242189868396826672642579830200 166:79:4774877989128526492725477321758490470791734494400 166:80:5192679813177272560838956587412358386986011262660 166:81:5513215604114141237433953907622997793590086031960 166:82:5714918614020756160754708318877497712867772106300 166:83:5783773055153536355462596370912166360010757312400 166:84:5714918614020756160754708318877497712867772106300 166:85:5513215604114141237433953907622997793590086031960 166:86:5192679813177272560838956587412358386986011262660 166:87:4774877989128526492725477321758490470791734494400 166:88:4286538194785836283242189868396826672642579830200 166:89:3756741339250508203290907974550027870405856480400 166:90:3214100923580990351704443489337246066902788322120 166:91:2684304068045662271753161595490447264666064972320 166:92:2188291359819833373711816518062864617934292097000 166:93:1741221082007179243598649702544644964807931346000 166:94:1352224882835362604071291790274032791818925407000 166:95:1024844121727853763085610619997161694852238203200 166:96:757957631694558512282066187706234170151134504450 166:97:546979734212567998554068382880787545469890879500 166:98:385118384292522366328884881824227965687984394750 166:99:264525758907995160710749211758055572391746857000 166:100:177232258468356757676201971877897233502470394190 166:101:115815139197144019867617130138031855556069762540 166:102:73803765174650600896030524107569319717103280050 166:103:45858650205608140362582073231887732639753494400 166:104:27779759259166469642717986669316607272158366800 166:105:16403286419698296360462049271405996674988749920 166:106:9439627090581095075360235901469488652587865520 166:107:5293248835839866397398263122319339431357681600 166:108:2891682234394001087467569668674453948612066800 166:109:1538693299035340028193752667735030541463301600 166:110:797322891318312560064035473280879462394619920 166:111:402252990214644174446720599132695944991880320 166:112:197534950551834192808657437074091758701369800 166:113:94397233007071207182898244265495176724548400 166:114:43886432889252403339417604790098634792991800 166:115:19844300089053260640432308252914165297700640 166:116:8724649177083761143638342421539848536058040 166:117:3728482554309299634033479667324721596606000 166:118:1548268179331827814132546641516197951133000 166:119:624511534520401135112287720947710097936000 166:120:244600351020490444585646024037853121691600 166:121:92988563197872400420989397568109451221600 166:122:34299060195936541138889531889876436926000 166:123:12269582509115510651310076448411083128000 166:124:4254774579773927080696236187755456246000 166:125:1429604258804039499113935359085833298656 166:126:465188687388616027489455156527929882896 166:127:146516122012162528343135482371001537920 166:128:44641630925580770354549092284914531085 166:129:13150247869550924600564848890129861870 166:130:3742762855179878540160764684113883763 166:131:1028545517454012423250286478077097828 166:132:272720402355230566770909293429533515 166:133:69717997594570220076773804335369470 166:134:17169357616573263153235339873635765 166:135:4069773657261810525211339821898848 166:136:927668995405265634423173047638708 166:137:203139196074145759362738623570520 166:138:42688671638769761025503044083660 166:139:8599156876874484235353131182320 166:140:1658408826254364816818103870876 166:141:305805882855414788916813479736 166:142:53839063882995561429016457700 166:143:9035926805537716603471293600 166:144:1443238309217829735276664950 166:145:218974088295118994317838820 166:146:31496272973955471785442570 166:147:4285207207340880515026200 166:148:550127952293761687739850 166:149:66458410344212821337700 166:150:7531953172344119751606 166:151:798087753360966331296 166:152:78758659871147993220 166:153:7206674759451450360 166:154:608355661512135420 166:155:47098502826745968 166:156:3321048276244908 166:157:211531737340440 166:158:12049276177620 166:159:606252889440 166:160:26523563913 166:161:988455798 166:162:30507895 166:163:748660 166:164:13695 166:165:166 166:166:1 # binomial(167, k) for 0 <= k <= 167 167:0:1 167:1:167 167:2:13861 167:3:762355 167:4:31256555 167:5:1018963693 167:6:27512019711 167:7:632776453353 167:8:12655529067060 167:9:223581013518060 167:10:3532580013585348 167:11:50419551102990876 167:12:655454164338881388 167:13:7815030420963585780 167:14:85965334630599443580 167:15:876846413232114324516 167:16:8330040925705086082902 167:17:73990363516556941089306 167:18:616586362637974509077550 167:19:4835335159634642202766050 167:20:35781480181296352300468770 167:21:250470361269074466103281390 167:22:1662212397512948729594503770 167:23:10479165114755546338747958550 167:24:62874990688533278032487751300 167:25:359644946738410350345829937436 167:26:1964214709109779605734917350612 167:27:10257565703128849052171235053196 167:28:51287828515644245260856175265980 167:29:245827867712915520388241667654180 167:30:1130808191479411393785911671209228 167:31:4997442652667076159634512869537556 167:32:21239131273835073678446679695534613 167:33:86887355211143483230009144209005235 167:34:342438399949800786847683097764902985 167:35:1301265919809242990021195771506631343 167:36:4771308372633890963411051162190981591 167:37:16893010724730803140725613574243745633 167:38:57791878795131694955113941175044392955 167:39:191157752937743298697684574655916069005 167:40:611704809400778555832590638898931420816 167:41:1894792946192655526603390515613763181552 167:42:5684378838577966579810171546841289544656 167:43:16524357088889437732006312636166539374000 167:44:46568642705052051790199608338287520054000 167:45:127287623393808941559878929457985888147600 167:46:337588914218362845006635421605962572913200 167:47:869111885540891579697933744985563219627600 167:48:2172779713852228949244834362463908049069000 167:49:5276750733641127448166026308840919547739000 167:50:12453131731393060777671822088864570132664040 167:51:28568949266137021784070650674454013833758680 167:52:63730732978305663979849913043012800090692440 167:53:138283665896323610522315849055593811517540200 167:54:291932183558905399991555681339586935425918200 167:55:599787940766478367255378036206787703693250120 167:56:1199575881532956734510756072413575407386500240 167:57:2336016190353652588257788141015910003857921520 167:58:4430375533429341115661322336409484490075368400 167:59:8184931070233867484865832790993793379969748400 167:60:14732875926420961472758499023788828083945547120 167:61:25842913510279391435822285172875485327576615440 167:62:44183045678864766003180035940722603947147116720 167:63:73638409464774610005300059901204339911911861200 167:64:119662415380258741258612597339457052356856774450 167:65:189618904371794620763647654245601175273173042590 167:66:293047397665500777543819102015929089058540156730 167:67:441758017376351918386951183635952805894217251190 167:68:649644143200517527039634093582283538079731251750 167:69:932098118505090364882953264705015511157875274250 167:70:1304937365907126510836134570587021715621025383950 167:71:1782801753422412275367676807703395865003372707650 167:72:2377069004563216367156902410271194486671163610200 167:73:3093445964842541847669941492818677756626856753000 167:74:3929512441827012617310466220607509582742223443000 167:75:4872595427865495645464978113553311882600357069320 167:76:5898404991626652623457605084827693331568853294440 167:77:6970842262831498554995351463887273937308644802520 167:78:8043279534036344486533097842946854543048436310600 167:79:9061416183914362775967667190155317143434314324600 167:80:9967557802305799053564433909170848857777745757060 167:81:10705895417291413798272910495035356180576097294620 167:82:11228134218134897398188662226500495506457858138260 167:83:11498691669174292516217304689789664072878529418700 167:84:11498691669174292516217304689789664072878529418700 167:85:11228134218134897398188662226500495506457858138260 167:86:10705895417291413798272910495035356180576097294620 167:87:9967557802305799053564433909170848857777745757060 167:88:9061416183914362775967667190155317143434314324600 167:89:8043279534036344486533097842946854543048436310600 167:90:6970842262831498554995351463887273937308644802520 167:91:5898404991626652623457605084827693331568853294440 167:92:4872595427865495645464978113553311882600357069320 167:93:3929512441827012617310466220607509582742223443000 167:94:3093445964842541847669941492818677756626856753000 167:95:2377069004563216367156902410271194486671163610200 167:96:1782801753422412275367676807703395865003372707650 167:97:1304937365907126510836134570587021715621025383950 167:98:932098118505090364882953264705015511157875274250 167:99:649644143200517527039634093582283538079731251750 167:100:441758017376351918386951183635952805894217251190 167:101:293047397665500777543819102015929089058540156730 167:102:189618904371794620763647654245601175273173042590 167:103:119662415380258741258612597339457052356856774450 167:104:73638409464774610005300059901204339911911861200 167:105:44183045678864766003180035940722603947147116720 167:106:25842913510279391435822285172875485327576615440 167:107:14732875926420961472758499023788828083945547120 167:108:8184931070233867484865832790993793379969748400 167:109:4430375533429341115661322336409484490075368400 167:110:2336016190353652588257788141015910003857921520 167:111:1199575881532956734510756072413575407386500240 167:112:599787940766478367255378036206787703693250120 167:113:291932183558905399991555681339586935425918200 167:114:138283665896323610522315849055593811517540200 167:115:63730732978305663979849913043012800090692440 167:116:28568949266137021784070650674454013833758680 167:117:12453131731393060777671822088864570132664040 167:118:5276750733641127448166026308840919547739000 167:119:2172779713852228949244834362463908049069000 167:120:869111885540891579697933744985563219627600 167:121:337588914218362845006635421605962572913200 167:122:127287623393808941559878929457985888147600 167:123:46568642705052051790199608338287520054000 167:124:16524357088889437732006312636166539374000 167:125:5684378838577966579810171546841289544656 167:126:1894792946192655526603390515613763181552 167:127:611704809400778555832590638898931420816 167:128:191157752937743298697684574655916069005 167:129:57791878795131694955113941175044392955 167:130:16893010724730803140725613574243745633 167:131:4771308372633890963411051162190981591 167:132:1301265919809242990021195771506631343 167:133:342438399949800786847683097764902985 167:134:86887355211143483230009144209005235 167:135:21239131273835073678446679695534613 167:136:4997442652667076159634512869537556 167:137:1130808191479411393785911671209228 167:138:245827867712915520388241667654180 167:139:51287828515644245260856175265980 167:140:10257565703128849052171235053196 167:141:1964214709109779605734917350612 167:142:359644946738410350345829937436 167:143:62874990688533278032487751300 167:144:10479165114755546338747958550 167:145:1662212397512948729594503770 167:146:250470361269074466103281390 167:147:35781480181296352300468770 167:148:4835335159634642202766050 167:149:616586362637974509077550 167:150:73990363516556941089306 167:151:8330040925705086082902 167:152:876846413232114324516 167:153:85965334630599443580 167:154:7815030420963585780 167:155:655454164338881388 167:156:50419551102990876 167:157:3532580013585348 167:158:223581013518060 167:159:12655529067060 167:160:632776453353 167:161:27512019711 167:162:1018963693 167:163:31256555 167:164:762355 167:165:13861 167:166:167 167:167:1 # binomial(168, k) for 0 <= k <= 168 168:0:1 168:1:168 168:2:14028 168:3:776216 168:4:32018910 168:5:1050220248 168:6:28530983404 168:7:660288473064 168:8:13288305520413 168:9:236236542585120 168:10:3756161027103408 168:11:53952131116576224 168:12:705873715441872264 168:13:8470484585302467168 168:14:93780365051563029360 168:15:962811747862713768096 168:16:9206887338937200407418 168:17:82320404442262027172208 168:18:690576726154531450166856 168:19:5451921522272616711843600 168:20:40616815340930994503234820 168:21:286251841450370818403750160 168:22:1912682758782023195697785160 168:23:12141377512268495068342462320 168:24:73354155803288824371235709850 168:25:422519937426943628378317688736 168:26:2323859655848189956080747288048 168:27:12221780412238628657906152403808 168:28:61545394218773094313027410319176 168:29:297115696228559765649097842920160 168:30:1376636059192326914174153338863408 168:31:6128250844146487553420424540746784 168:32:26236573926502149838081192565072169 168:33:108126486484978556908455823904539848 168:34:429325755160944270077692241973908220 168:35:1643704319759043776868878869271534328 168:36:6072574292443133953432246933697612934 168:37:21664319097364694104136664736434727224 168:38:74684889519862498095839554749288138588 168:39:248949631732874993652798515830960461960 168:40:802862562338521854530275213554847489821 168:41:2506497755593434082435981154512694602368 168:42:7579171784770622106413562062455052726208 168:43:22208735927467404311816484183007828918656 168:44:63092999793941489522205920974454059428000 168:45:173856266098860993350078537796273408201600 168:46:464876537612171786566514351063948461060800 168:47:1206700799759254424704569166591525792540800 168:48:3041891599393120528942768107449471268696600 168:49:7449530447493356397410860671304827596808000 168:50:17729882465034188225837848397705489680403040 168:51:41022080997530082561742472763318583966422720 168:52:92299682244442685763920563717466813924451120 168:53:202014398874629274502165762098606611608232640 168:54:430215849455229010513871530395180746943458400 168:55:891720124325383767246933717546374639119168320 168:56:1799363822299435101766134108620363111079750360 168:57:3535592071886609322768544213429485411244421760 168:58:6766391723782993703919110477425394493933289920 168:59:12615306603663208600527155127403277870045116800 168:60:22917806996654828957624331814782621463915295520 168:61:40575789436700352908580784196664313411522162560 168:62:70025959189144157439002321113598089274723732160 168:63:117821455143639376008480095841926943859058977920 168:64:193300824845033351263912657240661392268768635650 168:65:309281319752053362022260251585058227630029817040 168:66:482666302037295398307466756261530264331713199320 168:67:734805415041852695930770285651881894952757407920 168:68:1091402160576869445426585277218236343973948502940 168:69:1581742261705607891922587358287299049237606526000 168:70:2237035484412216875719087835292037226778900658200 168:71:3087739119329538786203811378290417580624398091600 168:72:4159870757985628642524579217974590351674536317850 168:73:5470514969405758214826843903089872243298020363200 168:74:7022958406669554464980407713426187339369080196000 168:75:8802107869692508262775444334160821465342580512320 168:76:10771000419492148268922583198381005214169210363760 168:77:12869247254458151178452956548714967268877498096960 168:78:15014121796867843041528449306834128480357081113120 168:79:17104695717950707262500765033102171686482750635200 168:80:19028973986220161829532101099326166001212060081660 168:81:20673453219597212851837344404206205038353843051680 168:82:21934029635426311196461572721535851687033955432880 168:83:22726825887309189914405966916290159579336387556960 168:84:22997383338348585032434609379579328145757058837400 168:85:22726825887309189914405966916290159579336387556960 168:86:21934029635426311196461572721535851687033955432880 168:87:20673453219597212851837344404206205038353843051680 168:88:19028973986220161829532101099326166001212060081660 168:89:17104695717950707262500765033102171686482750635200 168:90:15014121796867843041528449306834128480357081113120 168:91:12869247254458151178452956548714967268877498096960 168:92:10771000419492148268922583198381005214169210363760 168:93:8802107869692508262775444334160821465342580512320 168:94:7022958406669554464980407713426187339369080196000 168:95:5470514969405758214826843903089872243298020363200 168:96:4159870757985628642524579217974590351674536317850 168:97:3087739119329538786203811378290417580624398091600 168:98:2237035484412216875719087835292037226778900658200 168:99:1581742261705607891922587358287299049237606526000 168:100:1091402160576869445426585277218236343973948502940 168:101:734805415041852695930770285651881894952757407920 168:102:482666302037295398307466756261530264331713199320 168:103:309281319752053362022260251585058227630029817040 168:104:193300824845033351263912657240661392268768635650 168:105:117821455143639376008480095841926943859058977920 168:106:70025959189144157439002321113598089274723732160 168:107:40575789436700352908580784196664313411522162560 168:108:22917806996654828957624331814782621463915295520 168:109:12615306603663208600527155127403277870045116800 168:110:6766391723782993703919110477425394493933289920 168:111:3535592071886609322768544213429485411244421760 168:112:1799363822299435101766134108620363111079750360 168:113:891720124325383767246933717546374639119168320 168:114:430215849455229010513871530395180746943458400 168:115:202014398874629274502165762098606611608232640 168:116:92299682244442685763920563717466813924451120 168:117:41022080997530082561742472763318583966422720 168:118:17729882465034188225837848397705489680403040 168:119:7449530447493356397410860671304827596808000 168:120:3041891599393120528942768107449471268696600 168:121:1206700799759254424704569166591525792540800 168:122:464876537612171786566514351063948461060800 168:123:173856266098860993350078537796273408201600 168:124:63092999793941489522205920974454059428000 168:125:22208735927467404311816484183007828918656 168:126:7579171784770622106413562062455052726208 168:127:2506497755593434082435981154512694602368 168:128:802862562338521854530275213554847489821 168:129:248949631732874993652798515830960461960 168:130:74684889519862498095839554749288138588 168:131:21664319097364694104136664736434727224 168:132:6072574292443133953432246933697612934 168:133:1643704319759043776868878869271534328 168:134:429325755160944270077692241973908220 168:135:108126486484978556908455823904539848 168:136:26236573926502149838081192565072169 168:137:6128250844146487553420424540746784 168:138:1376636059192326914174153338863408 168:139:297115696228559765649097842920160 168:140:61545394218773094313027410319176 168:141:12221780412238628657906152403808 168:142:2323859655848189956080747288048 168:143:422519937426943628378317688736 168:144:73354155803288824371235709850 168:145:12141377512268495068342462320 168:146:1912682758782023195697785160 168:147:286251841450370818403750160 168:148:40616815340930994503234820 168:149:5451921522272616711843600 168:150:690576726154531450166856 168:151:82320404442262027172208 168:152:9206887338937200407418 168:153:962811747862713768096 168:154:93780365051563029360 168:155:8470484585302467168 168:156:705873715441872264 168:157:53952131116576224 168:158:3756161027103408 168:159:236236542585120 168:160:13288305520413 168:161:660288473064 168:162:28530983404 168:163:1050220248 168:164:32018910 168:165:776216 168:166:14028 168:167:168 168:168:1 # binomial(169, k) for 0 <= k <= 169 169:0:1 169:1:169 169:2:14196 169:3:790244 169:4:32795126 169:5:1082239158 169:6:29581203652 169:7:688819456468 169:8:13948593993477 169:9:249524848105533 169:10:3992397569688528 169:11:57708292143679632 169:12:759825846558448488 169:13:9176358300744339432 169:14:102250849636865496528 169:15:1056592112914276797456 169:16:10169699086799914175514 169:17:91527291781199227579626 169:18:772897130596793477339064 169:19:6142498248427148162010456 169:20:46068736863203611215078420 169:21:326868656791301812906984980 169:22:2198934600232394014101535320 169:23:14054060271050518264040247480 169:24:85495533315557319439578172170 169:25:495874093230232452749553398586 169:26:2746379593275133584459064976784 169:27:14545640068086818613986899691856 169:28:73767174631011722970933562722984 169:29:358661090447332859962125253239336 169:30:1673751755420886679823251181783568 169:31:7504886903338814467594577879610192 169:32:32364824770648637391501617105818953 169:33:134363060411480706746537016469612017 169:34:537452241645922826986148065878448068 169:35:2073030074919988046946571111245442548 169:36:7716278612202177730301125802969147262 169:37:27736893389807828057568911670132340158 169:38:96349208617227192199976219485722865812 169:39:323634521252737491748638070580248600548 169:40:1051812194071396848183073729385807951781 169:41:3309360317931955936966256368067542092189 169:42:10085669540364056188849543216967747328576 169:43:29787907712238026418230046245462881644864 169:44:85301735721408893834022405157461888346656 169:45:236949265892802482872284458770727467629600 169:46:638732803711032779916592888860221869262400 169:47:1671577337371426211271083517655474253601600 169:48:4248592399152374953647337274040997061237400 169:49:10491422046886476926353628778754298865504600 169:50:25179412912527544623248709069010317277211040 169:51:58751963462564270787580321161024073646825760 169:52:133321763241972768325663036480785397890873840 169:53:294314081119071960266086325816073425532683760 169:54:632230248329858285016037292493787358551691040 169:55:1321935973780612777760805247941555386062626720 169:56:2691083946624818869013067826166737750198918680 169:57:5334955894186044424534678322049848522324172120 169:58:10301983795669603026687654690854879905177711680 169:59:19381698327446202304446265604828672363978406720 169:60:35533113600318037558151486942185899333960412320 169:61:63493596433355181866205116011446934875437458080 169:62:110601748625844510347583105310262402686245894720 169:63:187847414332783533447482416955525033133782710080 169:64:311122279988672727272392753082588336127827613570 169:65:502582144597086713286172908825719619898798452690 169:66:791947621789348760329727007846588491961743016360 169:67:1217471717079148094238237041913412159284470607240 169:68:1826207575618722141357355562870118238926705910860 169:69:2673144422282477337349172635505535393211555028940 169:70:3818777746117824767641675193579336276016507184200 169:71:5324774603741755661922899213582454807403298749800 169:72:7247609877315167428728390596265007932298934409450 169:73:9630385727391386857351423121064462594972556681050 169:74:12493473376075312679807251616516059582667100559200 169:75:15825066276362062727755852047587008804711660708320 169:76:19573108289184656531698027532541826679511790876080 169:77:23640247673950299447375539747095972483046708460720 169:78:27883369051325994219981405855549095749234579210080 169:79:32118817514818550304029214339936300166839831748320 169:80:36133669704170869092032866132428337687694810716860 169:81:39702427205817374681369445503532371039565903133340 169:82:42607482855023524048298917125742056725387798484560 169:83:44660855522735501110867539637826011266370342989840 169:84:45724209225657774946840576295869487725093446394360 169:85:45724209225657774946840576295869487725093446394360 169:86:44660855522735501110867539637826011266370342989840 169:87:42607482855023524048298917125742056725387798484560 169:88:39702427205817374681369445503532371039565903133340 169:89:36133669704170869092032866132428337687694810716860 169:90:32118817514818550304029214339936300166839831748320 169:91:27883369051325994219981405855549095749234579210080 169:92:23640247673950299447375539747095972483046708460720 169:93:19573108289184656531698027532541826679511790876080 169:94:15825066276362062727755852047587008804711660708320 169:95:12493473376075312679807251616516059582667100559200 169:96:9630385727391386857351423121064462594972556681050 169:97:7247609877315167428728390596265007932298934409450 169:98:5324774603741755661922899213582454807403298749800 169:99:3818777746117824767641675193579336276016507184200 169:100:2673144422282477337349172635505535393211555028940 169:101:1826207575618722141357355562870118238926705910860 169:102:1217471717079148094238237041913412159284470607240 169:103:791947621789348760329727007846588491961743016360 169:104:502582144597086713286172908825719619898798452690 169:105:311122279988672727272392753082588336127827613570 169:106:187847414332783533447482416955525033133782710080 169:107:110601748625844510347583105310262402686245894720 169:108:63493596433355181866205116011446934875437458080 169:109:35533113600318037558151486942185899333960412320 169:110:19381698327446202304446265604828672363978406720 169:111:10301983795669603026687654690854879905177711680 169:112:5334955894186044424534678322049848522324172120 169:113:2691083946624818869013067826166737750198918680 169:114:1321935973780612777760805247941555386062626720 169:115:632230248329858285016037292493787358551691040 169:116:294314081119071960266086325816073425532683760 169:117:133321763241972768325663036480785397890873840 169:118:58751963462564270787580321161024073646825760 169:119:25179412912527544623248709069010317277211040 169:120:10491422046886476926353628778754298865504600 169:121:4248592399152374953647337274040997061237400 169:122:1671577337371426211271083517655474253601600 169:123:638732803711032779916592888860221869262400 169:124:236949265892802482872284458770727467629600 169:125:85301735721408893834022405157461888346656 169:126:29787907712238026418230046245462881644864 169:127:10085669540364056188849543216967747328576 169:128:3309360317931955936966256368067542092189 169:129:1051812194071396848183073729385807951781 169:130:323634521252737491748638070580248600548 169:131:96349208617227192199976219485722865812 169:132:27736893389807828057568911670132340158 169:133:7716278612202177730301125802969147262 169:134:2073030074919988046946571111245442548 169:135:537452241645922826986148065878448068 169:136:134363060411480706746537016469612017 169:137:32364824770648637391501617105818953 169:138:7504886903338814467594577879610192 169:139:1673751755420886679823251181783568 169:140:358661090447332859962125253239336 169:141:73767174631011722970933562722984 169:142:14545640068086818613986899691856 169:143:2746379593275133584459064976784 169:144:495874093230232452749553398586 169:145:85495533315557319439578172170 169:146:14054060271050518264040247480 169:147:2198934600232394014101535320 169:148:326868656791301812906984980 169:149:46068736863203611215078420 169:150:6142498248427148162010456 169:151:772897130596793477339064 169:152:91527291781199227579626 169:153:10169699086799914175514 169:154:1056592112914276797456 169:155:102250849636865496528 169:156:9176358300744339432 169:157:759825846558448488 169:158:57708292143679632 169:159:3992397569688528 169:160:249524848105533 169:161:13948593993477 169:162:688819456468 169:163:29581203652 169:164:1082239158 169:165:32795126 169:166:790244 169:167:14196 169:168:169 169:169:1 # binomial(170, k) for 0 <= k <= 170 170:0:1 170:1:170 170:2:14365 170:3:804440 170:4:33585370 170:5:1115034284 170:6:30663442810 170:7:718400660120 170:8:14637413449945 170:9:263473442099010 170:10:4241922417794061 170:11:61700689713368160 170:12:817534138702128120 170:13:9936184147302787920 170:14:111427207937609835960 170:15:1158842962551142293984 170:16:11226291199714190972970 170:17:101696990867999141755140 170:18:864424422377992704918690 170:19:6915395379023941639349520 170:20:52211235111630759377088876 170:21:372937393654505424122063400 170:22:2525803257023695827008520300 170:23:16252994871282912278141782800 170:24:99549593586607837703618419650 170:25:581369626545789772189131570756 170:26:3242253686505366037208618375370 170:27:17292019661361952198445964668640 170:28:88312814699098541584920462414840 170:29:432428265078344582933058815962320 170:30:2032412845868219539785376435022904 170:31:9178638658759701147417829061393760 170:32:39869711673987451859096194985429145 170:33:166727885182129344138038633575430970 170:34:671815302057403533732685082348060085 170:35:2610482316565910873932719177123890616 170:36:9789308687122165777247696914214589810 170:37:35453172002010005787870037473101487420 170:38:124086102007035020257545131155855205970 170:39:419983729869964683948614290065971466360 170:40:1375446715324134339931711799966056552329 170:41:4361172512003352785149330097453350043970 170:42:13395029858296012125815799585035289420765 170:43:39873577252602082607079589462430628973440 170:44:115089643433646920252252451402924769991520 170:45:322251001614211376706306863928189355976256 170:46:875682069603835262788877347630949336892000 170:47:2310310141082458991187676406515696122864000 170:48:5920169736523801164918420791696471314839000 170:49:14740014446038851880000966052795295926742000 170:50:35670834959414021549602337847764616142715640 170:51:83931376375091815410829030230034390924036800 170:52:192073726704537039113243357641809471537699600 170:53:427635844361044728591749362296858823423557600 170:54:926544329448930245282123618309860784084374800 170:55:1954166222110471062776842540435342744614317760 170:56:4013019920405431646773873074108293136261545400 170:57:8026039840810863293547746148216586272523090800 170:58:15636939689855647451222333012904728427501883800 170:59:29683682123115805331133920295683552269156118400 170:60:54914811927764239862597752547014571697938819040 170:61:99026710033673219424356602953632834209397870400 170:62:174095345059199692213788221321709337561683352800 170:63:298449162958628043795065522265787435820028604800 170:64:498969694321456260719875170038113369261610323650 170:65:813704424585759440558565661908307956026626066260 170:66:1294529766386435473615899916672308111860541469050 170:67:2009419338868496854567964049760000651246213623600 170:68:3043679292697870235595592604783530398211176518100 170:69:4499351997901199478706528198375653632138260939800 170:70:6491922168400302104990847829084871669228062213140 170:71:9143552349859580429564574407161791083419805934000 170:72:12572384481056923090651289809847462739702233159250 170:73:16877995604706554286079813717329470527271491090500 170:74:22123859103466699537158674737580522177639657240250 170:75:28318539652437375407563103664103068387378761267520 170:76:35398174565546719259453879580128835484223451584400 170:77:43213355963134955979073567279637799162558499336800 170:78:51523616725276293667356945602645068232281287670800 170:79:60002186566144544524010620195485395916074410958400 170:80:68252487218989419396062080472364637854534642465180 170:81:75836096909988243773402311635960708727260713850200 170:82:82309910060840898729668362629274427764953701617900 170:83:87268338377759025159166456763568067991758141474400 170:84:90385064748393276057708115933695498991463789384200 170:85:91448418451315549893681152591738975450186892788720 170:86:90385064748393276057708115933695498991463789384200 170:87:87268338377759025159166456763568067991758141474400 170:88:82309910060840898729668362629274427764953701617900 170:89:75836096909988243773402311635960708727260713850200 170:90:68252487218989419396062080472364637854534642465180 170:91:60002186566144544524010620195485395916074410958400 170:92:51523616725276293667356945602645068232281287670800 170:93:43213355963134955979073567279637799162558499336800 170:94:35398174565546719259453879580128835484223451584400 170:95:28318539652437375407563103664103068387378761267520 170:96:22123859103466699537158674737580522177639657240250 170:97:16877995604706554286079813717329470527271491090500 170:98:12572384481056923090651289809847462739702233159250 170:99:9143552349859580429564574407161791083419805934000 170:100:6491922168400302104990847829084871669228062213140 170:101:4499351997901199478706528198375653632138260939800 170:102:3043679292697870235595592604783530398211176518100 170:103:2009419338868496854567964049760000651246213623600 170:104:1294529766386435473615899916672308111860541469050 170:105:813704424585759440558565661908307956026626066260 170:106:498969694321456260719875170038113369261610323650 170:107:298449162958628043795065522265787435820028604800 170:108:174095345059199692213788221321709337561683352800 170:109:99026710033673219424356602953632834209397870400 170:110:54914811927764239862597752547014571697938819040 170:111:29683682123115805331133920295683552269156118400 170:112:15636939689855647451222333012904728427501883800 170:113:8026039840810863293547746148216586272523090800 170:114:4013019920405431646773873074108293136261545400 170:115:1954166222110471062776842540435342744614317760 170:116:926544329448930245282123618309860784084374800 170:117:427635844361044728591749362296858823423557600 170:118:192073726704537039113243357641809471537699600 170:119:83931376375091815410829030230034390924036800 170:120:35670834959414021549602337847764616142715640 170:121:14740014446038851880000966052795295926742000 170:122:5920169736523801164918420791696471314839000 170:123:2310310141082458991187676406515696122864000 170:124:875682069603835262788877347630949336892000 170:125:322251001614211376706306863928189355976256 170:126:115089643433646920252252451402924769991520 170:127:39873577252602082607079589462430628973440 170:128:13395029858296012125815799585035289420765 170:129:4361172512003352785149330097453350043970 170:130:1375446715324134339931711799966056552329 170:131:419983729869964683948614290065971466360 170:132:124086102007035020257545131155855205970 170:133:35453172002010005787870037473101487420 170:134:9789308687122165777247696914214589810 170:135:2610482316565910873932719177123890616 170:136:671815302057403533732685082348060085 170:137:166727885182129344138038633575430970 170:138:39869711673987451859096194985429145 170:139:9178638658759701147417829061393760 170:140:2032412845868219539785376435022904 170:141:432428265078344582933058815962320 170:142:88312814699098541584920462414840 170:143:17292019661361952198445964668640 170:144:3242253686505366037208618375370 170:145:581369626545789772189131570756 170:146:99549593586607837703618419650 170:147:16252994871282912278141782800 170:148:2525803257023695827008520300 170:149:372937393654505424122063400 170:150:52211235111630759377088876 170:151:6915395379023941639349520 170:152:864424422377992704918690 170:153:101696990867999141755140 170:154:11226291199714190972970 170:155:1158842962551142293984 170:156:111427207937609835960 170:157:9936184147302787920 170:158:817534138702128120 170:159:61700689713368160 170:160:4241922417794061 170:161:263473442099010 170:162:14637413449945 170:163:718400660120 170:164:30663442810 170:165:1115034284 170:166:33585370 170:167:804440 170:168:14365 170:169:170 170:170:1 # binomial(171, k) for 0 <= k <= 171 171:0:1 171:1:171 171:2:14535 171:3:818805 171:4:34389810 171:5:1148619654 171:6:31778477094 171:7:749064102930 171:8:15355814110065 171:9:278110855548955 171:10:4505395859893071 171:11:65942612131162221 171:12:879234828415496280 171:13:10753718286004916040 171:14:121363392084912623880 171:15:1270270170488752129944 171:16:12385134162265333266954 171:17:112923282067713332728110 171:18:966121413245991846673830 171:19:7779819801401934344268210 171:20:59126630490654701016438396 171:21:425148628766136183499152276 171:22:2898740650678201251130583700 171:23:18778798128306608105150303100 171:24:115802588457890749981760202450 171:25:680919220132397609892749990406 171:26:3823623313051155809397749946126 171:27:20534273347867318235654583044010 171:28:105604834360460493783366427083480 171:29:520741079777443124517979278377160 171:30:2464841110946564122718435250985224 171:31:11211051504627920687203205496416664 171:32:49048350332747153006514024046822905 171:33:206597596856116795997134828560860115 171:34:838543187239532877870723715923491055 171:35:3282297618623314407665404259471950701 171:36:12399791003688076651180416091338480426 171:37:45242480689132171565117734387316077230 171:38:159539274009045026045415168628956693390 171:39:544069831876999704206159421221826672330 171:40:1795430445194099023880326090032028018689 171:41:5736619227327487125081041897419406596299 171:42:17756202370299364910965129682488639464735 171:43:53268607110898094732895389047465918394205 171:44:154963220686249002859332040865355398964960 171:45:437340645047858296958559315331114125967776 171:46:1197933071218046639495184211559138692868256 171:47:3185992210686294253976553754146645459756000 171:48:8230479877606260156106097198212167437703000 171:49:20660184182562653044919386844491767241581000 171:50:50410849405452873429603303900559912069457640 171:51:119602211334505836960431368077799007066752440 171:52:276005103079628854524072387871843862461736400 171:53:619709571065581767704992719938668294961257200 171:54:1354180173809974973873872980606719607507932400 171:55:2880710551559401308058966158745203528698692560 171:56:5967186142515902709550715614543635880875863160 171:57:12039059761216294940321619222324879408784636200 171:58:23662979530666510744770079161121314700024974600 171:59:45320621812971452782356253308588280696658002200 171:60:84598494050880045193731672842698123967094937440 171:61:153941521961437459286954355500647405907336689440 171:62:273122055092872911638144824275342171771081223200 171:63:472544508017827736008853743587496773381711957600 171:64:797418857280084304514940692303900805081638928450 171:65:1312674118907215701278440831946421325288236389910 171:66:2108234190972194914174465578580616067887167535310 171:67:3303949105254932328183863966432308763106755092650 171:68:5053098631566367090163556654543531049457390141700 171:69:7543031290599069714302120803159184030349437457900 171:70:10991274166301501583697376027460525301366323152940 171:71:15635474518259882534555422236246662752647868147140 171:72:21715936830916503520215864217009253823122039093250 171:73:29450380085763477376731103527176933266973724249750 171:74:39001854708173253823238488454909992704911148330750 171:75:50442398755904074944721778401683590565018418507770 171:76:63716714217984094667016983244231903871602212851920 171:77:78611530528681675238527446859766634646781950921200 171:78:94736972688411249646430512882282867394839787007600 171:79:111525803291420838191367565798130464148355698629200 171:80:128254673785133963920072700667850033770609053423580 171:81:144088584128977663169464392108325346581795356315380 171:82:158146006970829142503070674265235136492214415468100 171:83:169578248438599923888834819392842495756711843092300 171:84:177653403126152301216874572697263566983221930858600 171:85:181833483199708825951389268525434474441650682172920 171:86:181833483199708825951389268525434474441650682172920 171:87:177653403126152301216874572697263566983221930858600 171:88:169578248438599923888834819392842495756711843092300 171:89:158146006970829142503070674265235136492214415468100 171:90:144088584128977663169464392108325346581795356315380 171:91:128254673785133963920072700667850033770609053423580 171:92:111525803291420838191367565798130464148355698629200 171:93:94736972688411249646430512882282867394839787007600 171:94:78611530528681675238527446859766634646781950921200 171:95:63716714217984094667016983244231903871602212851920 171:96:50442398755904074944721778401683590565018418507770 171:97:39001854708173253823238488454909992704911148330750 171:98:29450380085763477376731103527176933266973724249750 171:99:21715936830916503520215864217009253823122039093250 171:100:15635474518259882534555422236246662752647868147140 171:101:10991274166301501583697376027460525301366323152940 171:102:7543031290599069714302120803159184030349437457900 171:103:5053098631566367090163556654543531049457390141700 171:104:3303949105254932328183863966432308763106755092650 171:105:2108234190972194914174465578580616067887167535310 171:106:1312674118907215701278440831946421325288236389910 171:107:797418857280084304514940692303900805081638928450 171:108:472544508017827736008853743587496773381711957600 171:109:273122055092872911638144824275342171771081223200 171:110:153941521961437459286954355500647405907336689440 171:111:84598494050880045193731672842698123967094937440 171:112:45320621812971452782356253308588280696658002200 171:113:23662979530666510744770079161121314700024974600 171:114:12039059761216294940321619222324879408784636200 171:115:5967186142515902709550715614543635880875863160 171:116:2880710551559401308058966158745203528698692560 171:117:1354180173809974973873872980606719607507932400 171:118:619709571065581767704992719938668294961257200 171:119:276005103079628854524072387871843862461736400 171:120:119602211334505836960431368077799007066752440 171:121:50410849405452873429603303900559912069457640 171:122:20660184182562653044919386844491767241581000 171:123:8230479877606260156106097198212167437703000 171:124:3185992210686294253976553754146645459756000 171:125:1197933071218046639495184211559138692868256 171:126:437340645047858296958559315331114125967776 171:127:154963220686249002859332040865355398964960 171:128:53268607110898094732895389047465918394205 171:129:17756202370299364910965129682488639464735 171:130:5736619227327487125081041897419406596299 171:131:1795430445194099023880326090032028018689 171:132:544069831876999704206159421221826672330 171:133:159539274009045026045415168628956693390 171:134:45242480689132171565117734387316077230 171:135:12399791003688076651180416091338480426 171:136:3282297618623314407665404259471950701 171:137:838543187239532877870723715923491055 171:138:206597596856116795997134828560860115 171:139:49048350332747153006514024046822905 171:140:11211051504627920687203205496416664 171:141:2464841110946564122718435250985224 171:142:520741079777443124517979278377160 171:143:105604834360460493783366427083480 171:144:20534273347867318235654583044010 171:145:3823623313051155809397749946126 171:146:680919220132397609892749990406 171:147:115802588457890749981760202450 171:148:18778798128306608105150303100 171:149:2898740650678201251130583700 171:150:425148628766136183499152276 171:151:59126630490654701016438396 171:152:7779819801401934344268210 171:153:966121413245991846673830 171:154:112923282067713332728110 171:155:12385134162265333266954 171:156:1270270170488752129944 171:157:121363392084912623880 171:158:10753718286004916040 171:159:879234828415496280 171:160:65942612131162221 171:161:4505395859893071 171:162:278110855548955 171:163:15355814110065 171:164:749064102930 171:165:31778477094 171:166:1148619654 171:167:34389810 171:168:818805 171:169:14535 171:170:171 171:171:1 # binomial(172, k) for 0 <= k <= 172 172:0:1 172:1:172 172:2:14706 172:3:833340 172:4:35208615 172:5:1183009464 172:6:32927096748 172:7:780842580024 172:8:16104878212995 172:9:293466669659020 172:10:4783506715442026 172:11:70448007991055292 172:12:945177440546658501 172:13:11632953114420412320 172:14:132117110370917539920 172:15:1391633562573664753824 172:16:13655404332754085396898 172:17:125308416229978665995064 172:18:1079044695313705179401940 172:19:8745941214647926190942040 172:20:66906450292056635360706606 172:21:484275259256790884515590672 172:22:3323889279444337434629735976 172:23:21677538778984809356280886800 172:24:134581386586197358086910505550 172:25:796721808590288359874510192856 172:26:4504542533183553419290499936532 172:27:24357896660918474045052332990136 172:28:126139107708327812019021010127490 172:29:626345914137903618301345705460640 172:30:2985582190724007247236414529362384 172:31:13675892615574484809921640747401888 172:32:60259401837375073693717229543239569 172:33:255645947188863949003648852607683020 172:34:1045140784095649673867858544484351170 172:35:4120840805862847285536127975395441756 172:36:15682088622311391058845820350810431127 172:37:57642271692820248216298150478654557656 172:38:204781754698177197610532903016272770620 172:39:703609105886044730251574589850783365720 172:40:2339500277071098728086485511253854691019 172:41:7532049672521586148961367987451434614988 172:42:23492821597626852036046171579908046061034 172:43:71024809481197459643860518729954557858940 172:44:208231827797147097592227429912821317359165 172:45:592303865734107299817891356196469524932736 172:46:1635273716265904936453743526890252818836032 172:47:4383925281904340893471737965705784152624256 172:48:11416472088292554410082650952358812897459000 172:49:28890664060168913201025484042703934679284000 172:50:71071033588015526474522690745051679311038640 172:51:170013060739958710390034671978358919136210080 172:52:395607314414134691484503755949642869528488840 172:53:895714674145210622229065107810512157422993600 172:54:1973889744875556741578865700545387902469189600 172:55:4234890725369376281932839139351923136206624960 172:56:8847896694075304017609681773288839409574555720 172:57:18006245903732197649872334836868515289660499360 172:58:35702039291882805685091698383446194108809610800 172:59:68983601343637963527126332469709595396682976800 172:60:129919115863851497976087926151286404663752939640 172:61:238540016012317504480686028343345529874431626880 172:62:427063577054310370925099179775989577678417912640 172:63:745666563110700647646998567862838945152793180800 172:64:1269963365297912040523794435891397578463350886050 172:65:2110092976187300005793381524250322130369875318360 172:66:3420908309879410615452906410527037393175403925220 172:67:5412183296227127242358329545012924830993922627960 172:68:8357047736821299418347420620975839812564145234350 172:69:12596129922165436804465677457702715079806827599600 172:70:18534305456900571297999496830619709331715760610840 172:71:26626748684561384118252798263707188054014191300080 172:72:37351411349176386054771286453255916575769907240390 172:73:51166316916679980896946967744186187090095763343000 172:74:68452234793936731199969591982086925971884872580500 172:75:89444253464077328767960266856593583269929566838520 172:76:114159112973888169611738761645915494436620631359690 172:77:142328244746665769905544430103998538518384163773120 172:78:173348503217092924884957959742049502041621737928800 172:79:206262775979832087837798078680413331543195485636800 172:80:239780477076554802111440266465980497918964752052780 172:81:272343257914111627089537092776175380352404409738960 172:82:302234591099806805672535066373560483074009771783480 172:83:327724255409429066391905493658077632248926258560400 172:84:347231651564752225105709392090106062739933773950900 172:85:359486886325861127168263841222698041424872613031520 172:86:363666966399417651902778537050868948883301364345840 172:87:359486886325861127168263841222698041424872613031520 172:88:347231651564752225105709392090106062739933773950900 172:89:327724255409429066391905493658077632248926258560400 172:90:302234591099806805672535066373560483074009771783480 172:91:272343257914111627089537092776175380352404409738960 172:92:239780477076554802111440266465980497918964752052780 172:93:206262775979832087837798078680413331543195485636800 172:94:173348503217092924884957959742049502041621737928800 172:95:142328244746665769905544430103998538518384163773120 172:96:114159112973888169611738761645915494436620631359690 172:97:89444253464077328767960266856593583269929566838520 172:98:68452234793936731199969591982086925971884872580500 172:99:51166316916679980896946967744186187090095763343000 172:100:37351411349176386054771286453255916575769907240390 172:101:26626748684561384118252798263707188054014191300080 172:102:18534305456900571297999496830619709331715760610840 172:103:12596129922165436804465677457702715079806827599600 172:104:8357047736821299418347420620975839812564145234350 172:105:5412183296227127242358329545012924830993922627960 172:106:3420908309879410615452906410527037393175403925220 172:107:2110092976187300005793381524250322130369875318360 172:108:1269963365297912040523794435891397578463350886050 172:109:745666563110700647646998567862838945152793180800 172:110:427063577054310370925099179775989577678417912640 172:111:238540016012317504480686028343345529874431626880 172:112:129919115863851497976087926151286404663752939640 172:113:68983601343637963527126332469709595396682976800 172:114:35702039291882805685091698383446194108809610800 172:115:18006245903732197649872334836868515289660499360 172:116:8847896694075304017609681773288839409574555720 172:117:4234890725369376281932839139351923136206624960 172:118:1973889744875556741578865700545387902469189600 172:119:895714674145210622229065107810512157422993600 172:120:395607314414134691484503755949642869528488840 172:121:170013060739958710390034671978358919136210080 172:122:71071033588015526474522690745051679311038640 172:123:28890664060168913201025484042703934679284000 172:124:11416472088292554410082650952358812897459000 172:125:4383925281904340893471737965705784152624256 172:126:1635273716265904936453743526890252818836032 172:127:592303865734107299817891356196469524932736 172:128:208231827797147097592227429912821317359165 172:129:71024809481197459643860518729954557858940 172:130:23492821597626852036046171579908046061034 172:131:7532049672521586148961367987451434614988 172:132:2339500277071098728086485511253854691019 172:133:703609105886044730251574589850783365720 172:134:204781754698177197610532903016272770620 172:135:57642271692820248216298150478654557656 172:136:15682088622311391058845820350810431127 172:137:4120840805862847285536127975395441756 172:138:1045140784095649673867858544484351170 172:139:255645947188863949003648852607683020 172:140:60259401837375073693717229543239569 172:141:13675892615574484809921640747401888 172:142:2985582190724007247236414529362384 172:143:626345914137903618301345705460640 172:144:126139107708327812019021010127490 172:145:24357896660918474045052332990136 172:146:4504542533183553419290499936532 172:147:796721808590288359874510192856 172:148:134581386586197358086910505550 172:149:21677538778984809356280886800 172:150:3323889279444337434629735976 172:151:484275259256790884515590672 172:152:66906450292056635360706606 172:153:8745941214647926190942040 172:154:1079044695313705179401940 172:155:125308416229978665995064 172:156:13655404332754085396898 172:157:1391633562573664753824 172:158:132117110370917539920 172:159:11632953114420412320 172:160:945177440546658501 172:161:70448007991055292 172:162:4783506715442026 172:163:293466669659020 172:164:16104878212995 172:165:780842580024 172:166:32927096748 172:167:1183009464 172:168:35208615 172:169:833340 172:170:14706 172:171:172 172:172:1 # binomial(173, k) for 0 <= k <= 173 173:0:1 173:1:173 173:2:14878 173:3:848046 173:4:36041955 173:5:1218218079 173:6:34110106212 173:7:813769676772 173:8:16885720793019 173:9:309571547872015 173:10:5076973385101046 173:11:75231514706497318 173:12:1015625448537713793 173:13:12578130554967070821 173:14:143750063485337952240 173:15:1523750672944582293744 173:16:15047037895327750150722 173:17:138963820562732751391962 173:18:1204353111543683845397004 173:19:9824985909961631370343980 173:20:75652391506704561551648646 173:21:551181709548847519876297278 173:22:3808164538701128319145326648 173:23:25001428058429146790910622776 173:24:156258925365182167443191392350 173:25:931303195176485717961420698406 173:26:5301264341773841779165010129388 173:27:28862439194102027464342832926668 173:28:150497004369246286064073343117626 173:29:752485021846231430320366715588130 173:30:3611928104861910865537760234823024 173:31:16661474806298492057158055276764272 173:32:73935294452949558503638870290641457 173:33:315905349026239022697366082150922589 173:34:1300786731284513622871507397092034190 173:35:5165981589958496959403986519879792926 173:36:19802929428174238344381948326205872883 173:37:73324360315131639275143970829464988783 173:38:262424026390997445826831053494927328276 173:39:908390860584221927862107492867056136340 173:40:3043109382957143458338060101104638056739 173:41:9871549949592684877047853498705289306007 173:42:31024871270148438185007539567359480676022 173:43:94517631078824311679906690309862603919974 173:44:279256637278344557236087948642775875218105 173:45:800535693531254397410118786109290842291901 173:46:2227577582000012236271634883086722343768768 173:47:6019198998170245829925481492596036971460288 173:48:15800397370196895303554388918064597050083256 173:49:40307136148461467611108134995062747576743000 173:50:99961697648184439675548174787755613990322640 173:51:241084094327974236864557362723410598447248720 173:52:565620375154093401874538427928001788664698920 173:53:1291321988559345313713568863760155026951482440 173:54:2869604419020767363807930808355900059892183200 173:55:6208780470244933023511704839897311038675814560 173:56:13082787419444680299542520912640762545781180680 173:57:26854142597807501667482016610157354699235055080 173:58:53708285195615003334964033220314709398470110160 173:59:104685640635520769212218030853155789505492587600 173:60:198902717207489461503214258620996000060435916440 173:61:368459131876169002456773954494631934538184566520 173:62:665603593066627875405785208119335107552849539520 173:63:1172730140165011018572097747638828522831211093440 173:64:2015629928408612688170793003754236523616144066850 173:65:3380056341485212046317175960141719708833226204410 173:66:5531001286066710621246287934777359523545279243580 173:67:8833091606106537857811235955539962224169326553180 173:68:13769231033048426660705750165988764643558067862310 173:69:20953177658986736222813098078678554892370972833950 173:70:31130435379066008102465174288322424411522588210440 173:71:45161054141461955416252295094326897385729951910920 173:72:63978160033737770173024084716963104629784098540470 173:73:88517728265856366951718254197442103665865670583390 173:74:119618551710616712096916559726273113061980635923500 173:75:157896488258014059967929858838680509241814439419020 173:76:203603366437965498379699028502509077706550198198210 173:77:256487357720553939517283191749914032955004795132810 173:78:315676747963758694790502389846048040560005901701920 173:79:379611279196925012722756038422462833584817223565600 173:80:446043253056386889949238345146393829462160237689580 173:81:512123734990666429200977359242155878271369161791740 173:82:574577849013918432762072159149735863426414181522440 173:83:629958846509235872064440560031638115322936030343880 173:84:674955906974181291497614885748183694988860032511300 173:85:706718537890613352273973233312804104164806386982420 173:86:723153852725278779071042378273566990308173977377360 173:87:723153852725278779071042378273566990308173977377360 173:88:706718537890613352273973233312804104164806386982420 173:89:674955906974181291497614885748183694988860032511300 173:90:629958846509235872064440560031638115322936030343880 173:91:574577849013918432762072159149735863426414181522440 173:92:512123734990666429200977359242155878271369161791740 173:93:446043253056386889949238345146393829462160237689580 173:94:379611279196925012722756038422462833584817223565600 173:95:315676747963758694790502389846048040560005901701920 173:96:256487357720553939517283191749914032955004795132810 173:97:203603366437965498379699028502509077706550198198210 173:98:157896488258014059967929858838680509241814439419020 173:99:119618551710616712096916559726273113061980635923500 173:100:88517728265856366951718254197442103665865670583390 173:101:63978160033737770173024084716963104629784098540470 173:102:45161054141461955416252295094326897385729951910920 173:103:31130435379066008102465174288322424411522588210440 173:104:20953177658986736222813098078678554892370972833950 173:105:13769231033048426660705750165988764643558067862310 173:106:8833091606106537857811235955539962224169326553180 173:107:5531001286066710621246287934777359523545279243580 173:108:3380056341485212046317175960141719708833226204410 173:109:2015629928408612688170793003754236523616144066850 173:110:1172730140165011018572097747638828522831211093440 173:111:665603593066627875405785208119335107552849539520 173:112:368459131876169002456773954494631934538184566520 173:113:198902717207489461503214258620996000060435916440 173:114:104685640635520769212218030853155789505492587600 173:115:53708285195615003334964033220314709398470110160 173:116:26854142597807501667482016610157354699235055080 173:117:13082787419444680299542520912640762545781180680 173:118:6208780470244933023511704839897311038675814560 173:119:2869604419020767363807930808355900059892183200 173:120:1291321988559345313713568863760155026951482440 173:121:565620375154093401874538427928001788664698920 173:122:241084094327974236864557362723410598447248720 173:123:99961697648184439675548174787755613990322640 173:124:40307136148461467611108134995062747576743000 173:125:15800397370196895303554388918064597050083256 173:126:6019198998170245829925481492596036971460288 173:127:2227577582000012236271634883086722343768768 173:128:800535693531254397410118786109290842291901 173:129:279256637278344557236087948642775875218105 173:130:94517631078824311679906690309862603919974 173:131:31024871270148438185007539567359480676022 173:132:9871549949592684877047853498705289306007 173:133:3043109382957143458338060101104638056739 173:134:908390860584221927862107492867056136340 173:135:262424026390997445826831053494927328276 173:136:73324360315131639275143970829464988783 173:137:19802929428174238344381948326205872883 173:138:5165981589958496959403986519879792926 173:139:1300786731284513622871507397092034190 173:140:315905349026239022697366082150922589 173:141:73935294452949558503638870290641457 173:142:16661474806298492057158055276764272 173:143:3611928104861910865537760234823024 173:144:752485021846231430320366715588130 173:145:150497004369246286064073343117626 173:146:28862439194102027464342832926668 173:147:5301264341773841779165010129388 173:148:931303195176485717961420698406 173:149:156258925365182167443191392350 173:150:25001428058429146790910622776 173:151:3808164538701128319145326648 173:152:551181709548847519876297278 173:153:75652391506704561551648646 173:154:9824985909961631370343980 173:155:1204353111543683845397004 173:156:138963820562732751391962 173:157:15047037895327750150722 173:158:1523750672944582293744 173:159:143750063485337952240 173:160:12578130554967070821 173:161:1015625448537713793 173:162:75231514706497318 173:163:5076973385101046 173:164:309571547872015 173:165:16885720793019 173:166:813769676772 173:167:34110106212 173:168:1218218079 173:169:36041955 173:170:848046 173:171:14878 173:172:173 173:173:1 # binomial(174, k) for 0 <= k <= 174 174:0:1 174:1:174 174:2:15051 174:3:862924 174:4:36890001 174:5:1254260034 174:6:35328324291 174:7:847879782984 174:8:17699490469791 174:9:326457268665034 174:10:5386544932973061 174:11:80308488091598364 174:12:1090856963244211111 174:13:13593756003504784614 174:14:156328194040305023061 174:15:1667500736429920245984 174:16:16570788568272332444466 174:17:154010858458060501542684 174:18:1343316932106416596788966 174:19:11029339021505315215740984 174:20:85477377416666192921992626 174:21:626834101055552081427945924 174:22:4359346248249975839021623926 174:23:28809592597130275110055949424 174:24:181260353423611314234102015126 174:25:1087562120541667885404612090756 174:26:6232567536950327497126430827794 174:27:34163703535875869243507843056056 174:28:179359443563348313528416176044294 174:29:902982026215477716384440058705756 174:30:4364413126708142295858126950411154 174:31:20273402911160402922695815511587296 174:32:90596769259248050560796925567405729 174:33:389840643479188581201004952441564046 174:34:1616692080310752645568873479242956779 174:35:6466768321243010582275493916971827116 174:36:24968911018132735303785934846085665809 174:37:93127289743305877619525919155670861666 174:38:335748386706129085101975024324392317059 174:39:1170814886975219373688938546361983464616 174:40:3951500243541365386200167593971694193079 174:41:12914659332549828335385913599809927362746 174:42:40896421219741123062055393066064769982029 174:43:125542502348972749864914229877222084595996 174:44:373774268357168868915994638952638479138079 174:45:1079792330809598954646206734752066717510006 174:46:3028113275531266633681753669196013186060669 174:47:8246776580170258066197116375682759315229056 174:48:21819596368367141133479870410660634021543544 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174:67:14364092892173248479057523890317321747714605796760 174:68:22602322639154964518516986121528726867727394415490 174:69:34722408692035162883518848244667319535929040696260 174:70:52083613038052744325278272367000979303893561044390 174:71:76291489520527963518717469382649321797252540121360 174:72:109139214175199725589276379811290002015514050451390 174:73:152495888299594137124742338914405208295649769123860 174:74:208136279976473079048634813923715216727846306506890 174:75:277515039968630772064846418564953622303795075342520 174:76:361499854695979558347628887341189586948364637617230 174:77:460090724158519437896982220252423110661554993331020 174:78:572164105684312634307785581595962073515010696834730 174:79:695288027160683707513258428268510874144823125267520 174:80:825654532253311902671994383568856663046977461255180 174:81:958166988047053319150215704388549707733529399481320 174:82:1086701584004584861963049518391891741697783343314180 174:83:1204536695523154304826512719181373978749350211866320 174:84:1304914753483417163562055445779821810311796062855180 174:85:1381674444864794643771588119060987799153666419493720 174:86:1429872390615892131345015611586371094472980364359780 174:87:1446307705450557558142084756547133980616347954754720 174:88:1429872390615892131345015611586371094472980364359780 174:89:1381674444864794643771588119060987799153666419493720 174:90:1304914753483417163562055445779821810311796062855180 174:91:1204536695523154304826512719181373978749350211866320 174:92:1086701584004584861963049518391891741697783343314180 174:93:958166988047053319150215704388549707733529399481320 174:94:825654532253311902671994383568856663046977461255180 174:95:695288027160683707513258428268510874144823125267520 174:96:572164105684312634307785581595962073515010696834730 174:97:460090724158519437896982220252423110661554993331020 174:98:361499854695979558347628887341189586948364637617230 174:99:277515039968630772064846418564953622303795075342520 174:100:208136279976473079048634813923715216727846306506890 174:101:152495888299594137124742338914405208295649769123860 174:102:109139214175199725589276379811290002015514050451390 174:103:76291489520527963518717469382649321797252540121360 174:104:52083613038052744325278272367000979303893561044390 174:105:34722408692035162883518848244667319535929040696260 174:106:22602322639154964518516986121528726867727394415490 174:107:14364092892173248479057523890317321747714605796760 174:108:8911057627551922667563463894919079232378505447990 174:109:5395686269893824734487968963895956232449370271260 174:110:3188360068573623706742890751393065046447355160290 174:111:1838333733231638893977882955758163630384060632960 174:112:1034062724942796877862559162613967042091034106040 174:113:567361849083658463959988213115627934598620482960 174:114:303588357843010230715432289474151789565928504040 174:115:158393925831135772547182064073470498903962697760 174:116:80562427793422505002446049830472064097705165240 174:117:39936930017252181967024537522798117245016235760 174:118:19291567889689613323054225752538073584456995240 174:119:9078384889265700387319635648253211098567997760 174:120:4160926407580112677521499672116055086843665640 174:121:1856942363713438715588107291688156815616181360 174:122:806704469482067638739095790651412387111947640 174:123:341045791976158676540105537511166212437571360 174:124:140268833796645907286656309782818361567065640 174:125:56107533518658362914662523913127344626826256 174:126:21819596368367141133479870410660634021543544 174:127:8246776580170258066197116375682759315229056 174:128:3028113275531266633681753669196013186060669 174:129:1079792330809598954646206734752066717510006 174:130:373774268357168868915994638952638479138079 174:131:125542502348972749864914229877222084595996 174:132:40896421219741123062055393066064769982029 174:133:12914659332549828335385913599809927362746 174:134:3951500243541365386200167593971694193079 174:135:1170814886975219373688938546361983464616 174:136:335748386706129085101975024324392317059 174:137:93127289743305877619525919155670861666 174:138:24968911018132735303785934846085665809 174:139:6466768321243010582275493916971827116 174:140:1616692080310752645568873479242956779 174:141:389840643479188581201004952441564046 174:142:90596769259248050560796925567405729 174:143:20273402911160402922695815511587296 174:144:4364413126708142295858126950411154 174:145:902982026215477716384440058705756 174:146:179359443563348313528416176044294 174:147:34163703535875869243507843056056 174:148:6232567536950327497126430827794 174:149:1087562120541667885404612090756 174:150:181260353423611314234102015126 174:151:28809592597130275110055949424 174:152:4359346248249975839021623926 174:153:626834101055552081427945924 174:154:85477377416666192921992626 174:155:11029339021505315215740984 174:156:1343316932106416596788966 174:157:154010858458060501542684 174:158:16570788568272332444466 174:159:1667500736429920245984 174:160:156328194040305023061 174:161:13593756003504784614 174:162:1090856963244211111 174:163:80308488091598364 174:164:5386544932973061 174:165:326457268665034 174:166:17699490469791 174:167:847879782984 174:168:35328324291 174:169:1254260034 174:170:36890001 174:171:862924 174:172:15051 174:173:174 174:174:1 # binomial(175, k) for 0 <= k <= 175 175:0:1 175:1:175 175:2:15225 175:3:877975 175:4:37752925 175:5:1291150035 175:6:36582584325 175:7:883208107275 175:8:18547370252775 175:9:344156759134825 175:10:5713002201638095 175:11:85695033024571425 175:12:1171165451335809475 175:13:14684612966748995725 175:14:169921950043809807675 175:15:1823828930470225269045 175:16:18238289304702252690450 175:17:170581647026332833987150 175:18:1497327790564477098331650 175:19:12372655953611731812529950 175:20:96506716438171508137733610 175:21:712311478472218274349938550 175:22:4986180349305527920449569850 175:23:33168938845380250949077573350 175:24:210069946020741589344157964550 175:25:1268822473965279199638714105882 175:26:7320129657491995382531042918550 175:27:40396271072826196740634273883850 175:28:213523147099224182771924019100350 175:29:1082341469778826029912856234750050 175:30:5267395152923620012242567009116910 175:31:24637816037868545218553942461998450 175:32:110870172170408453483492741078993025 175:33:480437412738436631761801878008969775 175:34:2006532723789941226769878431684520825 175:35:8083460401553763227844367396214783895 175:36:31435679339375745886061428763057492925 175:37:118096200761438612923311854001756527475 175:38:428875676449434962721500943480063178725 175:39:1506563273681348458790913570686375781675 175:40:5122315130516584759889106140333677657695 175:41:16866159576091193721586081193781621555825 175:42:53811080552290951397441306665874697344775 175:43:166438923568713872926969622943286854578025 175:44:499316770706141618780908868829860563734075 175:45:1453566599166767823562201373704705196648085 175:46:4107905606340865588327960403948079903570675 175:47:11274889855701524699878870044878772501289725 175:48:30066372948537399199676986786343393336772600 175:49:77927129887025504048142394323787978648369800 175:50:196376367315304270201318833695945706193891896 175:51:481314625772804583826761847293984574004637000 175:52:1147750261458226315279201328162578599549519000 175:53:2663646833195506354327203082339569202728129000 175:54:6017868771293551393109606963804211902459847000 175:55:13239311296845813064841135320369266185411663400 175:56:28369952778955313710373861400791284683024993000 175:57:59228497906941795290078763275336190829473231000 175:58:120499357810674686969470587353270181342721401000 175:59:238956353624558277549628113903942563001667863000 175:60:461982283674146003262614353547622288469891201800 175:61:870950206926668694675420502589779724164548987000 175:62:1601424574026455341822547375729594976689654589000 175:63:2872396458174435771840442118372130672475094739000 175:64:5026693801805262600720773707151228676831415793250 175:65:8584046338467448441230859715289021278896725431550 175:66:14306743897445747402051432858815035464827875719250 175:67:23275150519725171146620987785236400980093111244750 175:68:36966415531328212997574510011846048615442000212250 175:69:57324731331190127402035834366196046403656435111750 175:70:86806021730087907208797120611668298839822601740650 175:71:128375102558580707843995741749650301101146101165750 175:72:185430703695727689107993849193939323812766590572750 175:73:261635102474793862714018718725695210311163819575250 175:74:360632168276067216173377152838120425023496075630750 175:75:485651319945103851113481232488668839031641381849410 175:76:639014894664610330412475305906143209252159712959750 175:77:821590578854498996244611107593612697609919630948250 175:78:1032254829842832072204767801848385184176565690165750 175:79:1267452132844996341821044009864472947659833822102250 175:80:1520942559413995610185252811837367537191800586522700 175:81:1783821520300365221822210087957406370780506860736500 175:82:2044868572051638181113265222780441449431312742795500 175:83:2291238279527739166789562237573265720447133555180500 175:84:2509451449006571468388568164961195789061146274721500 175:85:2686589198348211807333643564840809609465462482348900 175:86:2811546835480686775116603730647358893626646783853500 175:87:2876180096066449689487100368133505075089328319114500 175:88:2876180096066449689487100368133505075089328319114500 175:89:2811546835480686775116603730647358893626646783853500 175:90:2686589198348211807333643564840809609465462482348900 175:91:2509451449006571468388568164961195789061146274721500 175:92:2291238279527739166789562237573265720447133555180500 175:93:2044868572051638181113265222780441449431312742795500 175:94:1783821520300365221822210087957406370780506860736500 175:95:1520942559413995610185252811837367537191800586522700 175:96:1267452132844996341821044009864472947659833822102250 175:97:1032254829842832072204767801848385184176565690165750 175:98:821590578854498996244611107593612697609919630948250 175:99:639014894664610330412475305906143209252159712959750 175:100:485651319945103851113481232488668839031641381849410 175:101:360632168276067216173377152838120425023496075630750 175:102:261635102474793862714018718725695210311163819575250 175:103:185430703695727689107993849193939323812766590572750 175:104:128375102558580707843995741749650301101146101165750 175:105:86806021730087907208797120611668298839822601740650 175:106:57324731331190127402035834366196046403656435111750 175:107:36966415531328212997574510011846048615442000212250 175:108:23275150519725171146620987785236400980093111244750 175:109:14306743897445747402051432858815035464827875719250 175:110:8584046338467448441230859715289021278896725431550 175:111:5026693801805262600720773707151228676831415793250 175:112:2872396458174435771840442118372130672475094739000 175:113:1601424574026455341822547375729594976689654589000 175:114:870950206926668694675420502589779724164548987000 175:115:461982283674146003262614353547622288469891201800 175:116:238956353624558277549628113903942563001667863000 175:117:120499357810674686969470587353270181342721401000 175:118:59228497906941795290078763275336190829473231000 175:119:28369952778955313710373861400791284683024993000 175:120:13239311296845813064841135320369266185411663400 175:121:6017868771293551393109606963804211902459847000 175:122:2663646833195506354327203082339569202728129000 175:123:1147750261458226315279201328162578599549519000 175:124:481314625772804583826761847293984574004637000 175:125:196376367315304270201318833695945706193891896 175:126:77927129887025504048142394323787978648369800 175:127:30066372948537399199676986786343393336772600 175:128:11274889855701524699878870044878772501289725 175:129:4107905606340865588327960403948079903570675 175:130:1453566599166767823562201373704705196648085 175:131:499316770706141618780908868829860563734075 175:132:166438923568713872926969622943286854578025 175:133:53811080552290951397441306665874697344775 175:134:16866159576091193721586081193781621555825 175:135:5122315130516584759889106140333677657695 175:136:1506563273681348458790913570686375781675 175:137:428875676449434962721500943480063178725 175:138:118096200761438612923311854001756527475 175:139:31435679339375745886061428763057492925 175:140:8083460401553763227844367396214783895 175:141:2006532723789941226769878431684520825 175:142:480437412738436631761801878008969775 175:143:110870172170408453483492741078993025 175:144:24637816037868545218553942461998450 175:145:5267395152923620012242567009116910 175:146:1082341469778826029912856234750050 175:147:213523147099224182771924019100350 175:148:40396271072826196740634273883850 175:149:7320129657491995382531042918550 175:150:1268822473965279199638714105882 175:151:210069946020741589344157964550 175:152:33168938845380250949077573350 175:153:4986180349305527920449569850 175:154:712311478472218274349938550 175:155:96506716438171508137733610 175:156:12372655953611731812529950 175:157:1497327790564477098331650 175:158:170581647026332833987150 175:159:18238289304702252690450 175:160:1823828930470225269045 175:161:169921950043809807675 175:162:14684612966748995725 175:163:1171165451335809475 175:164:85695033024571425 175:165:5713002201638095 175:166:344156759134825 175:167:18547370252775 175:168:883208107275 175:169:36582584325 175:170:1291150035 175:171:37752925 175:172:877975 175:173:15225 175:174:175 175:175:1 # binomial(176, k) for 0 <= k <= 176 176:0:1 176:1:176 176:2:15400 176:3:893200 176:4:38630900 176:5:1328902960 176:6:37873734360 176:7:919790691600 176:8:19430578360050 176:9:362704129387600 176:10:6057158960772920 176:11:91408035226209520 176:12:1256860484360380900 176:13:15855778418084805200 176:14:184606563010558803400 176:15:1993750880514035076720 176:16:20062118235172477959495 176:17:188819936331035086677600 176:18:1667909437590809932318800 176:19:13869983744176208910861600 176:20:108879372391783239950263560 176:21:808818194910389782487672160 176:22:5698491827777746194799508400 176:23:38155119194685778869527143200 176:24:243238884866121840293235537900 176:25:1478892419986020788982872070432 176:26:8588952131457274582169757024432 176:27:47716400730318192123165316802400 176:28:253919418172050379512558292984200 176:29:1295864616878050212684780253850400 176:30:6349736622702446042155423243866960 176:31:29905211190792165230796509471115360 176:32:135507988208276998702046683540991475 176:33:591307584908845085245294619087962800 176:34:2486970136528377858531680309693490600 176:35:10089993125343704454614245827899304720 176:36:39519139740929509113905796159272276820 176:37:149531880100814358809373282764814020400 176:38:546971877210873575644812797481819706200 176:39:1935438950130783421512414514166438960400 176:40:6628878404197933218680019711020053439370 176:41:21988474706607778481475187334115299213520 176:42:70677240128382145119027387859656318900600 176:43:220250004121004824324410929609161551922800 176:44:665755694274855491707878491773147418312100 176:45:1952883369872909442343110242534565760382160 176:46:5561472205507633411890161777652785100218760 176:47:15382795462042390288206830448826852404860400 176:48:41341262804238923899555856831222165838062325 176:49:107993502835562903247819381110131371985142400 176:50:274303497202329774249461228019733684842261696 176:51:677690993088108854028080680989930280198528896 176:52:1629064887231030899105963175456563173554156000 176:53:3811397094653732669606404410502147802277648000 176:54:8681515604489057747436810046143781105187976000 176:55:19257180068139364457950742284173478087871510400 176:56:41609264075801126775214996721160550868436656400 176:57:87598450685897109000452624676127475512498224000 176:58:179727855717616482259549350628606372172194632000 176:59:359455711435232964519098701257212744344389264000 176:60:700938637298704280812242467451564851471559064800 176:61:1332932490600814697938034856137402012634440188800 176:62:2472374780953124036497967878319374700854203576000 176:63:4473821032200891113662989494101725649164749328000 176:64:7899090259979698372561215825523359349306510532250 176:65:13610740140272711041951633422440249955728141224800 176:66:22890790235913195843282292574104056743724601150800 176:67:37581894417170918548672420644051436444920986964000 176:68:60241566051053384144195497797082449595535111457000 176:69:94291146862518340399610344378042095019098435324000 176:70:144130753061278034610832954977864345243479036852400 176:71:215181124288668615052792862361318599940968702906400 176:72:313805806254308396951989590943589624913912691738500 176:73:447065806170521551822012567919634534123930410148000 176:74:622267270750861078887395871563815635334659895206000 176:75:846283488221171067286858385326789264055137457480160 176:76:1124666214609714181525956538394812048283801094809160 176:77:1460605473519109326657086413499755906862079343908000 176:78:1853845408697331068449378909441997881786485321114000 176:79:2299706962687828414025811811712858131836399512268000 176:80:2788394692258991952006296821701840484851634408624950 176:81:3304764079714360832007462899794773907972307447259200 176:82:3828690092352003402935475310737847820211819603532000 176:83:4336106851579377347902827460353707169878446297976000 176:84:4800689728534310635178130402534461509508279829902000 176:85:5196040647354783275722211729802005398526608757070400 176:86:5498136033828898582450247295488168503092109266202400 176:87:5687726931547136464603704098780863968715975102968000 176:88:5752360192132899378974200736267010150178656638229000 176:89:5687726931547136464603704098780863968715975102968000 176:90:5498136033828898582450247295488168503092109266202400 176:91:5196040647354783275722211729802005398526608757070400 176:92:4800689728534310635178130402534461509508279829902000 176:93:4336106851579377347902827460353707169878446297976000 176:94:3828690092352003402935475310737847820211819603532000 176:95:3304764079714360832007462899794773907972307447259200 176:96:2788394692258991952006296821701840484851634408624950 176:97:2299706962687828414025811811712858131836399512268000 176:98:1853845408697331068449378909441997881786485321114000 176:99:1460605473519109326657086413499755906862079343908000 176:100:1124666214609714181525956538394812048283801094809160 176:101:846283488221171067286858385326789264055137457480160 176:102:622267270750861078887395871563815635334659895206000 176:103:447065806170521551822012567919634534123930410148000 176:104:313805806254308396951989590943589624913912691738500 176:105:215181124288668615052792862361318599940968702906400 176:106:144130753061278034610832954977864345243479036852400 176:107:94291146862518340399610344378042095019098435324000 176:108:60241566051053384144195497797082449595535111457000 176:109:37581894417170918548672420644051436444920986964000 176:110:22890790235913195843282292574104056743724601150800 176:111:13610740140272711041951633422440249955728141224800 176:112:7899090259979698372561215825523359349306510532250 176:113:4473821032200891113662989494101725649164749328000 176:114:2472374780953124036497967878319374700854203576000 176:115:1332932490600814697938034856137402012634440188800 176:116:700938637298704280812242467451564851471559064800 176:117:359455711435232964519098701257212744344389264000 176:118:179727855717616482259549350628606372172194632000 176:119:87598450685897109000452624676127475512498224000 176:120:41609264075801126775214996721160550868436656400 176:121:19257180068139364457950742284173478087871510400 176:122:8681515604489057747436810046143781105187976000 176:123:3811397094653732669606404410502147802277648000 176:124:1629064887231030899105963175456563173554156000 176:125:677690993088108854028080680989930280198528896 176:126:274303497202329774249461228019733684842261696 176:127:107993502835562903247819381110131371985142400 176:128:41341262804238923899555856831222165838062325 176:129:15382795462042390288206830448826852404860400 176:130:5561472205507633411890161777652785100218760 176:131:1952883369872909442343110242534565760382160 176:132:665755694274855491707878491773147418312100 176:133:220250004121004824324410929609161551922800 176:134:70677240128382145119027387859656318900600 176:135:21988474706607778481475187334115299213520 176:136:6628878404197933218680019711020053439370 176:137:1935438950130783421512414514166438960400 176:138:546971877210873575644812797481819706200 176:139:149531880100814358809373282764814020400 176:140:39519139740929509113905796159272276820 176:141:10089993125343704454614245827899304720 176:142:2486970136528377858531680309693490600 176:143:591307584908845085245294619087962800 176:144:135507988208276998702046683540991475 176:145:29905211190792165230796509471115360 176:146:6349736622702446042155423243866960 176:147:1295864616878050212684780253850400 176:148:253919418172050379512558292984200 176:149:47716400730318192123165316802400 176:150:8588952131457274582169757024432 176:151:1478892419986020788982872070432 176:152:243238884866121840293235537900 176:153:38155119194685778869527143200 176:154:5698491827777746194799508400 176:155:808818194910389782487672160 176:156:108879372391783239950263560 176:157:13869983744176208910861600 176:158:1667909437590809932318800 176:159:188819936331035086677600 176:160:20062118235172477959495 176:161:1993750880514035076720 176:162:184606563010558803400 176:163:15855778418084805200 176:164:1256860484360380900 176:165:91408035226209520 176:166:6057158960772920 176:167:362704129387600 176:168:19430578360050 176:169:919790691600 176:170:37873734360 176:171:1328902960 176:172:38630900 176:173:893200 176:174:15400 176:175:176 176:176:1 # binomial(177, k) for 0 <= k <= 177 177:0:1 177:1:177 177:2:15576 177:3:908600 177:4:39524100 177:5:1367533860 177:6:39202637320 177:7:957664425960 177:8:20350369051650 177:9:382134707747650 177:10:6419863090160520 177:11:97465194186982440 177:12:1348268519586590420 177:13:17112638902445186100 177:14:200462341428643608600 177:15:2178357443524593880120 177:16:22055869115686513036215 177:17:208882054566207564637095 177:18:1856729373921845018996400 177:19:15537893181767018843180400 177:20:122749356135959448861125160 177:21:917697567302173022437935720 177:22:6507310022688135977287180560 177:23:43853611022463525064326651600 177:24:281394004060807619162762681100 177:25:1722131304852142629276107608332 177:26:10067844551443295371152629094864 177:27:56305352861775466705335073826832 177:28:301635818902368571635723609786600 177:29:1549784035050100592197338546834600 177:30:7645601239580496254840203497717360 177:31:36254947813494611272951932714982320 177:32:165413199399069163932843193012106835 177:33:726815573117122083947341302628954275 177:34:3078277721437222943776974928781453400 177:35:12576963261872082313145926137592795320 177:36:49609132866273213568520041987171581540 177:37:189051019841743867923279078924086297220 177:38:696503757311687934454186080246633726600 177:39:2482410827341656997157227311648258666600 177:40:8564317354328716640192434225186492399770 177:41:28617353110805711700155207045135352652890 177:42:92665714834989923600502575193771618114120 177:43:290927244249386969443438317468817870823400 177:44:886005698395860316032289421382308970234900 177:45:2618639064147764934050988734307713178694260 177:46:7514355575380542854233272020187350860600920 177:47:20944267667550023700096992226479637505079160 177:48:56724058266281314187762687280049018242922725 177:49:149334765639801827147375237941353537823204725 177:50:382297000037892677497280609129865056827404096 177:51:951994490290438628277541909009663965040790592 177:52:2306755880319139753134043856446493453752684896 177:53:5440461981884763568712367585958710975831804000 177:54:12492912699142790417043214456645928907465624000 177:55:27938695672628422205387552330317259193059486400 177:56:60866444143940491233165739005334028956308166800 177:57:129207714761698235775667621397288026380934880400 177:58:267326306403513591260001975304733847684692856000 177:59:539183567152849446778648051885819116516583896000 177:60:1060394348733937245331341168708777595815948328800 177:61:2033871127899518978750277323588966864105999253600 177:62:3805307271553938734436002734456776713488643764800 177:63:6946195813154015150160957372421100350018952904000 177:64:12372911292180589486224205319625084998471259860250 177:65:21509830400252409414512849247963609305034651757050 177:66:36501530376185906885233925996544306699452742375600 177:67:60472684653084114391954713218155493188645588114800 177:68:97823460468224302692867918441133886040456098421000 177:69:154532712913571724543805842175124544614633546781000 177:70:238421899923796375010443299355906440262577472176400 177:71:359311877349946649663625817339182945184447739758800 177:72:528986930542977012004782453304908224854881394644900 177:73:760871612424829948774002158863224159037843101886500 177:74:1069333076921382630709408439483450169458590305354000 177:75:1468550758972032146174254256890604899389797352686160 177:76:1970949702830885248812814923721601312338938552289320 177:77:2585271688128823508183042951894567955145880438717160 177:78:3314450882216440395106465322941753788648564665022000 177:79:4153552371385159482475190721154856013622884833382000 177:80:5088101654946820366032108633414698616688033920892950 177:81:6093158771973352784013759721496614392823941855884150 177:82:7133454172066364234942938210532621728184127050791200 177:83:8164796943931380750838302771091554990090265901508000 177:84:9136796580113687983080957862888168679386726127878000 177:85:9996730375889093910900342132336466908034888586972400 177:86:10694176681183681858172459025290173901618718023272800 177:87:11185862965376035047053951394269032471808084369170400 177:88:11440087123680035843577904835047874118894631741197000 177:89:11440087123680035843577904835047874118894631741197000 177:90:11185862965376035047053951394269032471808084369170400 177:91:10694176681183681858172459025290173901618718023272800 177:92:9996730375889093910900342132336466908034888586972400 177:93:9136796580113687983080957862888168679386726127878000 177:94:8164796943931380750838302771091554990090265901508000 177:95:7133454172066364234942938210532621728184127050791200 177:96:6093158771973352784013759721496614392823941855884150 177:97:5088101654946820366032108633414698616688033920892950 177:98:4153552371385159482475190721154856013622884833382000 177:99:3314450882216440395106465322941753788648564665022000 177:100:2585271688128823508183042951894567955145880438717160 177:101:1970949702830885248812814923721601312338938552289320 177:102:1468550758972032146174254256890604899389797352686160 177:103:1069333076921382630709408439483450169458590305354000 177:104:760871612424829948774002158863224159037843101886500 177:105:528986930542977012004782453304908224854881394644900 177:106:359311877349946649663625817339182945184447739758800 177:107:238421899923796375010443299355906440262577472176400 177:108:154532712913571724543805842175124544614633546781000 177:109:97823460468224302692867918441133886040456098421000 177:110:60472684653084114391954713218155493188645588114800 177:111:36501530376185906885233925996544306699452742375600 177:112:21509830400252409414512849247963609305034651757050 177:113:12372911292180589486224205319625084998471259860250 177:114:6946195813154015150160957372421100350018952904000 177:115:3805307271553938734436002734456776713488643764800 177:116:2033871127899518978750277323588966864105999253600 177:117:1060394348733937245331341168708777595815948328800 177:118:539183567152849446778648051885819116516583896000 177:119:267326306403513591260001975304733847684692856000 177:120:129207714761698235775667621397288026380934880400 177:121:60866444143940491233165739005334028956308166800 177:122:27938695672628422205387552330317259193059486400 177:123:12492912699142790417043214456645928907465624000 177:124:5440461981884763568712367585958710975831804000 177:125:2306755880319139753134043856446493453752684896 177:126:951994490290438628277541909009663965040790592 177:127:382297000037892677497280609129865056827404096 177:128:149334765639801827147375237941353537823204725 177:129:56724058266281314187762687280049018242922725 177:130:20944267667550023700096992226479637505079160 177:131:7514355575380542854233272020187350860600920 177:132:2618639064147764934050988734307713178694260 177:133:886005698395860316032289421382308970234900 177:134:290927244249386969443438317468817870823400 177:135:92665714834989923600502575193771618114120 177:136:28617353110805711700155207045135352652890 177:137:8564317354328716640192434225186492399770 177:138:2482410827341656997157227311648258666600 177:139:696503757311687934454186080246633726600 177:140:189051019841743867923279078924086297220 177:141:49609132866273213568520041987171581540 177:142:12576963261872082313145926137592795320 177:143:3078277721437222943776974928781453400 177:144:726815573117122083947341302628954275 177:145:165413199399069163932843193012106835 177:146:36254947813494611272951932714982320 177:147:7645601239580496254840203497717360 177:148:1549784035050100592197338546834600 177:149:301635818902368571635723609786600 177:150:56305352861775466705335073826832 177:151:10067844551443295371152629094864 177:152:1722131304852142629276107608332 177:153:281394004060807619162762681100 177:154:43853611022463525064326651600 177:155:6507310022688135977287180560 177:156:917697567302173022437935720 177:157:122749356135959448861125160 177:158:15537893181767018843180400 177:159:1856729373921845018996400 177:160:208882054566207564637095 177:161:22055869115686513036215 177:162:2178357443524593880120 177:163:200462341428643608600 177:164:17112638902445186100 177:165:1348268519586590420 177:166:97465194186982440 177:167:6419863090160520 177:168:382134707747650 177:169:20350369051650 177:170:957664425960 177:171:39202637320 177:172:1367533860 177:173:39524100 177:174:908600 177:175:15576 177:176:177 177:177:1 # binomial(178, k) for 0 <= k <= 178 178:0:1 178:1:178 178:2:15753 178:3:924176 178:4:40432700 178:5:1407057960 178:6:40570171180 178:7:996867063280 178:8:21308033477610 178:9:402485076799300 178:10:6801997797908170 178:11:103885057277142960 178:12:1445733713773572860 178:13:18460907422031776520 178:14:217574980331088794700 178:15:2378819784953237488720 178:16:24234226559211106916335 178:17:230937923681894077673310 178:18:2065611428488052583633495 178:19:17394622555688863862176800 178:20:138287249317726467704305560 178:21:1040446923438132471299060880 178:22:7425007589990308999725116280 178:23:50360921045151661041613832160 178:24:325247615083271144227089332700 178:25:2003525308912950248438870289432 178:26:11789975856295438000428736703196 178:27:66373197413218762076487702921696 178:28:357941171764144038341058683613432 178:29:1851419853952469163833062156621200 178:30:9195385274630596847037542044551960 178:31:43900549053075107527792136212699680 178:32:201668147212563775205795125727089155 178:33:892228772516191247880184495641061110 178:34:3805093294554345027724316231410407675 178:35:15655240983309305256922901066374248720 178:36:62186096128145295881665968124764376860 178:37:238660152708017081491799120911257878760 178:38:885554777153431802377465159170720023820 178:39:3178914584653344931611413391894892393200 178:40:11046728181670373637349661536834751066370 178:41:37181670465134428340347641270321845052660 178:42:121283067945795635300657782238906970767010 178:43:383592959084376893043940892662589488937520 178:44:1176932942645247285475727738851126841058300 178:45:3504644762543625250083278155690022148929160 178:46:10132994639528307788284260754495064039295180 178:47:28458623242930566554330264246666988365680080 178:48:77668325933831337887859679506528655748001885 178:49:206058823906083141335137925221402556066127450 178:50:531631765677694504644655847071218594650608821 178:51:1334291490328331305774822518139529021868194688 178:52:3258750370609578381411585765456157418793475488 178:53:7747217862203903321846411442405204429584488896 178:54:17933374681027553985755582042604639883297428000 178:55:40431608371771212622430766786963188100525110400 178:56:88805139816568913438553291335651288149367653200 178:57:190074158905638727008833360402622055337243047200 178:58:396534021165211827035669596702021874065627736400 178:59:806509873556363038038650027190552964201276752000 178:60:1599577915886786692109989220594596712332532224800 178:61:3094265476633456224081618492297744459921947582400 178:62:5839178399453457713186280058045743577594643018400 178:63:10751503084707953884596960106877877063507596668800 178:64:19319107105334604636385162692046185348490212764250 178:65:33882741692432998900737054567588694303505911617300 178:66:58011360776438316299746775244507916004487394132650 178:67:96974215029270021277188639214699799888098330490400 178:68:158296145121308417084822631659289379229101686535800 178:69:252356173381796027236673760616258430655089645202000 178:70:392954612837368099554249141531030984877211018957400 178:71:597733777273743024674069116695089385447025211935200 178:72:888298807892923661668408270644091170039329134403700 178:73:1289858542967806960778784612168132383892724496531400 178:74:1830204689346212579483410598346674328496433407240500 178:75:2537883835893414776883662696374055068848387658040160 178:76:3439500461802917394987069180612206211728735904975480 178:77:4556221390959708756995857875616169267484818991006480 178:78:5899722570345263903289508274836321743794445103739160 178:79:7468003253601599877581656044096609802271449498404000 178:80:9241654026331979848507299354569554630310918754274950 178:81:11181260426920173150045868354911313009511975776777100 178:82:13226612944039717018956697932029236121008068906675350 178:83:15298251115997744985781240981624176718274392952299200 178:84:17301593524045068733919260633979723669476992029386000 178:85:19133526956002781893981299995224635587421614714850400 178:86:20690907057072775769072801157626640809653606610245200 178:87:21880039646559716905226410419559206373426802392443200 178:88:22625950089056070890631856229316906590702716110367400 178:89:22880174247360071687155809670095748237789263482394000 178:90:22625950089056070890631856229316906590702716110367400 178:91:21880039646559716905226410419559206373426802392443200 178:92:20690907057072775769072801157626640809653606610245200 178:93:19133526956002781893981299995224635587421614714850400 178:94:17301593524045068733919260633979723669476992029386000 178:95:15298251115997744985781240981624176718274392952299200 178:96:13226612944039717018956697932029236121008068906675350 178:97:11181260426920173150045868354911313009511975776777100 178:98:9241654026331979848507299354569554630310918754274950 178:99:7468003253601599877581656044096609802271449498404000 178:100:5899722570345263903289508274836321743794445103739160 178:101:4556221390959708756995857875616169267484818991006480 178:102:3439500461802917394987069180612206211728735904975480 178:103:2537883835893414776883662696374055068848387658040160 178:104:1830204689346212579483410598346674328496433407240500 178:105:1289858542967806960778784612168132383892724496531400 178:106:888298807892923661668408270644091170039329134403700 178:107:597733777273743024674069116695089385447025211935200 178:108:392954612837368099554249141531030984877211018957400 178:109:252356173381796027236673760616258430655089645202000 178:110:158296145121308417084822631659289379229101686535800 178:111:96974215029270021277188639214699799888098330490400 178:112:58011360776438316299746775244507916004487394132650 178:113:33882741692432998900737054567588694303505911617300 178:114:19319107105334604636385162692046185348490212764250 178:115:10751503084707953884596960106877877063507596668800 178:116:5839178399453457713186280058045743577594643018400 178:117:3094265476633456224081618492297744459921947582400 178:118:1599577915886786692109989220594596712332532224800 178:119:806509873556363038038650027190552964201276752000 178:120:396534021165211827035669596702021874065627736400 178:121:190074158905638727008833360402622055337243047200 178:122:88805139816568913438553291335651288149367653200 178:123:40431608371771212622430766786963188100525110400 178:124:17933374681027553985755582042604639883297428000 178:125:7747217862203903321846411442405204429584488896 178:126:3258750370609578381411585765456157418793475488 178:127:1334291490328331305774822518139529021868194688 178:128:531631765677694504644655847071218594650608821 178:129:206058823906083141335137925221402556066127450 178:130:77668325933831337887859679506528655748001885 178:131:28458623242930566554330264246666988365680080 178:132:10132994639528307788284260754495064039295180 178:133:3504644762543625250083278155690022148929160 178:134:1176932942645247285475727738851126841058300 178:135:383592959084376893043940892662589488937520 178:136:121283067945795635300657782238906970767010 178:137:37181670465134428340347641270321845052660 178:138:11046728181670373637349661536834751066370 178:139:3178914584653344931611413391894892393200 178:140:885554777153431802377465159170720023820 178:141:238660152708017081491799120911257878760 178:142:62186096128145295881665968124764376860 178:143:15655240983309305256922901066374248720 178:144:3805093294554345027724316231410407675 178:145:892228772516191247880184495641061110 178:146:201668147212563775205795125727089155 178:147:43900549053075107527792136212699680 178:148:9195385274630596847037542044551960 178:149:1851419853952469163833062156621200 178:150:357941171764144038341058683613432 178:151:66373197413218762076487702921696 178:152:11789975856295438000428736703196 178:153:2003525308912950248438870289432 178:154:325247615083271144227089332700 178:155:50360921045151661041613832160 178:156:7425007589990308999725116280 178:157:1040446923438132471299060880 178:158:138287249317726467704305560 178:159:17394622555688863862176800 178:160:2065611428488052583633495 178:161:230937923681894077673310 178:162:24234226559211106916335 178:163:2378819784953237488720 178:164:217574980331088794700 178:165:18460907422031776520 178:166:1445733713773572860 178:167:103885057277142960 178:168:6801997797908170 178:169:402485076799300 178:170:21308033477610 178:171:996867063280 178:172:40570171180 178:173:1407057960 178:174:40432700 178:175:924176 178:176:15753 178:177:178 178:178:1 # binomial(179, k) for 0 <= k <= 179 179:0:1 179:1:179 179:2:15931 179:3:939929 179:4:41356876 179:5:1447490660 179:6:41977229140 179:7:1037437234460 179:8:22304900540890 179:9:423793110276910 179:10:7204482874707470 179:11:110687055075051130 179:12:1549618771050715820 179:13:19906641135805349380 179:14:236035887753120571220 179:15:2596394765284326283420 179:16:26613046344164344405055 179:17:255172150241105184589645 179:18:2296549352169946661306805 179:19:19460233984176916445810295 179:20:155681871873415331566482360 179:21:1178734172755858939003366440 179:22:8465454513428441471024177160 179:23:57785928635141970041338948440 179:24:375608536128422805268703164860 179:25:2328772923996221392665959622132 179:26:13793501165208388248867606992628 179:27:78163173269514200076916439624892 179:28:424314369177362800417546386535128 179:29:2209361025716613202174120840234632 179:30:11046805128583066010870604201173160 179:31:53095934327705704374829678257251640 179:32:245568696265638882733587261939788835 179:33:1093896919728755023085979621368150265 179:34:4697322067070536275604500727051468785 179:35:19460334277863650284647217297784656395 179:36:77841337111454601138588869191138625580 179:37:300846248836162377373465089036022255620 179:38:1124214929861448883869264280081977902580 179:39:4064469361806776733988878551065612417020 179:40:14225642766323718568961074928729643459570 179:41:48228398646804801977697302807156596119030 179:42:158464738410930063641005423509228815819670 179:43:504876027030172528344598674901496459704530 179:44:1560525901729624178519668631513716329995820 179:45:4681577705188872535559005894541148989987460 179:46:13637639402071933038367538910185086188224340 179:47:38591617882458874342614525001162052404975260 179:48:106126949176761904442189943753195644113681965 179:49:283727149839914479222997604727931211814129335 179:50:737690589583777645979793772292621150716736271 179:51:1865923256006025810419478365210747616518803509 179:52:4593041860937909687186408283595686440661670176 179:53:11005968232813481703257997207861361848377964384 179:54:25680592543231457307601993485009844312881916896 179:55:58364983052798766608186348829567827983822538400 179:56:129236748188340126060984058122614476249892763600 179:57:278879298722207640447386651738273343486610700400 179:58:586608180070850554044502957104643929402870783600 179:59:1203043894721574865074319623892574838266904488400 179:60:2406087789443149730148639247785149676533808976800 179:61:4693843392520242916191607712892341172254479807200 179:62:8933443876086913937267898550343488037516590600800 179:63:16590681484161411597783240164923620641102239687200 179:64:30070610190042558520982122798924062411997809433050 179:65:53201848797767603537122217259634879651996124381550 179:66:91894102468871315200483829812096610307993305749950 179:67:154985575805708337576935414459207715892585724623050 179:68:255270360150578438362011270873989179117200017026200 179:69:410652318503104444321496392275547809884191331737800 179:70:645310786219164126790922902147289415532300664159400 179:71:990688390111111124228318258226120370324236230892600 179:72:1486032585166666686342477387339180555486354346338900 179:73:2178157350860730622447192882812223553932053630935100 179:74:3120063232314019540262195210514806712389157903771900 179:75:4368088525239627356367073294720729397344821065280660 179:76:5977384297696332171870731876986261280577123563015640 179:77:7995721852762626151982927056228375479213554895981960 179:78:10455943961304972660285366150452491011279264094745640 179:79:13367725823946863780871164318932931546065894602143160 179:80:16709657279933579726088955398666164432582368252678950 179:81:20422914453252152998553167709480867639822894531052050 179:82:24407873370959890169002566286940549130520044683452450 179:83:28524864060037462004737938913653412839282461858974550 179:84:32599844640042813719700501615603900387751384981685200 179:85:36435120480047850627900560629204359256898606744236400 179:86:39824434013075557663054101152851276397075221325095600 179:87:42570946703632492674299211577185847183080409002688400 179:88:44505989735615787795858266648876112964129518502810600 179:89:45506124336416142577787665899412654828491979592761400 179:90:45506124336416142577787665899412654828491979592761400 179:91:44505989735615787795858266648876112964129518502810600 179:92:42570946703632492674299211577185847183080409002688400 179:93:39824434013075557663054101152851276397075221325095600 179:94:36435120480047850627900560629204359256898606744236400 179:95:32599844640042813719700501615603900387751384981685200 179:96:28524864060037462004737938913653412839282461858974550 179:97:24407873370959890169002566286940549130520044683452450 179:98:20422914453252152998553167709480867639822894531052050 179:99:16709657279933579726088955398666164432582368252678950 179:100:13367725823946863780871164318932931546065894602143160 179:101:10455943961304972660285366150452491011279264094745640 179:102:7995721852762626151982927056228375479213554895981960 179:103:5977384297696332171870731876986261280577123563015640 179:104:4368088525239627356367073294720729397344821065280660 179:105:3120063232314019540262195210514806712389157903771900 179:106:2178157350860730622447192882812223553932053630935100 179:107:1486032585166666686342477387339180555486354346338900 179:108:990688390111111124228318258226120370324236230892600 179:109:645310786219164126790922902147289415532300664159400 179:110:410652318503104444321496392275547809884191331737800 179:111:255270360150578438362011270873989179117200017026200 179:112:154985575805708337576935414459207715892585724623050 179:113:91894102468871315200483829812096610307993305749950 179:114:53201848797767603537122217259634879651996124381550 179:115:30070610190042558520982122798924062411997809433050 179:116:16590681484161411597783240164923620641102239687200 179:117:8933443876086913937267898550343488037516590600800 179:118:4693843392520242916191607712892341172254479807200 179:119:2406087789443149730148639247785149676533808976800 179:120:1203043894721574865074319623892574838266904488400 179:121:586608180070850554044502957104643929402870783600 179:122:278879298722207640447386651738273343486610700400 179:123:129236748188340126060984058122614476249892763600 179:124:58364983052798766608186348829567827983822538400 179:125:25680592543231457307601993485009844312881916896 179:126:11005968232813481703257997207861361848377964384 179:127:4593041860937909687186408283595686440661670176 179:128:1865923256006025810419478365210747616518803509 179:129:737690589583777645979793772292621150716736271 179:130:283727149839914479222997604727931211814129335 179:131:106126949176761904442189943753195644113681965 179:132:38591617882458874342614525001162052404975260 179:133:13637639402071933038367538910185086188224340 179:134:4681577705188872535559005894541148989987460 179:135:1560525901729624178519668631513716329995820 179:136:504876027030172528344598674901496459704530 179:137:158464738410930063641005423509228815819670 179:138:48228398646804801977697302807156596119030 179:139:14225642766323718568961074928729643459570 179:140:4064469361806776733988878551065612417020 179:141:1124214929861448883869264280081977902580 179:142:300846248836162377373465089036022255620 179:143:77841337111454601138588869191138625580 179:144:19460334277863650284647217297784656395 179:145:4697322067070536275604500727051468785 179:146:1093896919728755023085979621368150265 179:147:245568696265638882733587261939788835 179:148:53095934327705704374829678257251640 179:149:11046805128583066010870604201173160 179:150:2209361025716613202174120840234632 179:151:424314369177362800417546386535128 179:152:78163173269514200076916439624892 179:153:13793501165208388248867606992628 179:154:2328772923996221392665959622132 179:155:375608536128422805268703164860 179:156:57785928635141970041338948440 179:157:8465454513428441471024177160 179:158:1178734172755858939003366440 179:159:155681871873415331566482360 179:160:19460233984176916445810295 179:161:2296549352169946661306805 179:162:255172150241105184589645 179:163:26613046344164344405055 179:164:2596394765284326283420 179:165:236035887753120571220 179:166:19906641135805349380 179:167:1549618771050715820 179:168:110687055075051130 179:169:7204482874707470 179:170:423793110276910 179:171:22304900540890 179:172:1037437234460 179:173:41977229140 179:174:1447490660 179:175:41356876 179:176:939929 179:177:15931 179:178:179 179:179:1 # binomial(180, k) for 0 <= k <= 180 180:0:1 180:1:180 180:2:16110 180:3:955860 180:4:42296805 180:5:1488847536 180:6:43424719800 180:7:1079414463600 180:8:23342337775350 180:9:446098010817800 180:10:7628275984984380 180:11:117891537949758600 180:12:1660305826125766950 180:13:21456259906856065200 180:14:255942528888925920600 180:15:2832430653037446854640 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180:40:18290112128130495302949953479795255876590 180:41:62454041413128520546658377735886239578600 180:42:206693137057734865618702726316385411938700 180:43:663340765441102591985604098410725275524200 180:44:2065401928759796706864267306415212789700350 180:45:6242103606918496714078674526054865319983280 180:46:18319217107260805573926544804726235178211800 180:47:52229257284530807380982063911347138593199600 180:48:144718567059220778784804468754357696518657225 180:49:389854099016676383665187548481126855927811300 180:50:1021417739423692125202791377020552362530865606 180:51:2603613845589803456399272137503368767235539780 180:52:6458965116943935497605886648806434057180473685 180:53:15599010093751391390444405491457048289039634560 180:54:36686560776044939010859990692871206161259881280 180:55:84045575596030223915788342314577672296704455296 180:56:187601731241138892669170406952182304233715302000 180:57:408116046910547766508370709860887819736503464000 180:58:865487478793058194491889608842917272889481484000 180:59:1789652074792425419118822580997218767669775272000 180:60:3609131684164724595222958871677724514800713465200 180:61:7099931181963392646340246960677490848788288784000 180:62:13627287268607156853459506263235829209771070408000 180:63:25524125360248325535051138715267108678618830288000 180:64:46661291674203970118765362963847683053100049120250 180:65:83272458987810162058104340058558942063993933814600 180:66:145095951266638918737606047071731489959989430131500 180:67:246879678274579652777419244271304326200579030373000 180:68:410255935956286775938946685333196895009785741649250 180:69:665922678653682882683507663149536989001391348764000 180:70:1055963104722268571112419294422837225416491995897200 180:71:1635999176330275251019241160373409785856536895052000 180:72:2476720975277777810570795645565300925810590577231500 180:73:3664189936027397308789670270151404109418407977274000 180:74:5298220583174750162709388093327030266321211534707000 180:75:7488151757553646896629268505235536109733978969052560 180:76:10345472822935959528237805171706990677921944628296300 180:77:13973106150458958323853658933214636759790678458997600 180:78:18451665814067598812268293206680866490492818990727600 180:79:23823669785251836441156530469385422557345158696888800 180:80:30077383103880443506960119717599095978648262854822110 180:81:37132571733185732724642123108147032072405262783731000 180:82:44830787824212043167555733996421416770342939214504500 180:83:52932737430997352173740505200593961969802506542427000 180:84:61124708700080275724438440529257313227033846840659750 180:85:69034965120090664347601062244808259644649991725921600 180:86:76259554493123408290954661782055635653973828069332000 180:87:82395380716708050337353312730037123580155630327784000 180:88:87076936439248280470157478226061960147209927505499000 180:89:90012114072031930373645932548288767792621498095572000 180:90:91012248672832285155575331798825309656983959185522800 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180:107:3664189936027397308789670270151404109418407977274000 180:108:2476720975277777810570795645565300925810590577231500 180:109:1635999176330275251019241160373409785856536895052000 180:110:1055963104722268571112419294422837225416491995897200 180:111:665922678653682882683507663149536989001391348764000 180:112:410255935956286775938946685333196895009785741649250 180:113:246879678274579652777419244271304326200579030373000 180:114:145095951266638918737606047071731489959989430131500 180:115:83272458987810162058104340058558942063993933814600 180:116:46661291674203970118765362963847683053100049120250 180:117:25524125360248325535051138715267108678618830288000 180:118:13627287268607156853459506263235829209771070408000 180:119:7099931181963392646340246960677490848788288784000 180:120:3609131684164724595222958871677724514800713465200 180:121:1789652074792425419118822580997218767669775272000 180:122:865487478793058194491889608842917272889481484000 180:123:408116046910547766508370709860887819736503464000 180:124:187601731241138892669170406952182304233715302000 180:125:84045575596030223915788342314577672296704455296 180:126:36686560776044939010859990692871206161259881280 180:127:15599010093751391390444405491457048289039634560 180:128:6458965116943935497605886648806434057180473685 180:129:2603613845589803456399272137503368767235539780 180:130:1021417739423692125202791377020552362530865606 180:131:389854099016676383665187548481126855927811300 180:132:144718567059220778784804468754357696518657225 180:133:52229257284530807380982063911347138593199600 180:134:18319217107260805573926544804726235178211800 180:135:6242103606918496714078674526054865319983280 180:136:2065401928759796706864267306415212789700350 180:137:663340765441102591985604098410725275524200 180:138:206693137057734865618702726316385411938700 180:139:62454041413128520546658377735886239578600 180:140:18290112128130495302949953479795255876590 180:141:5188684291668225617858142831147590319600 180:142:1425061178697611261242729369118000158200 180:143:378687585947616978512053958227160881200 180:144:97301671389318251423236086488923281975 180:145:24157656344934186560251718024836125180 180:146:5791218986799291298690480348419619050 180:147:1339465615994393905819566883307939100 180:148:298664630593344587108416940197040475 180:149:64142739456288770385700282458424800 180:150:13256166154299679213044725041407792 180:151:2633675394893976002591667226769760 180:152:502477542446877000494462826160020 180:153:91956674434722588325784046617520 180:154:16122274089204609641533566614760 180:155:2704381460124644197934662786992 180:156:433394464763564775310042113300 180:157:66251383148570411512363125600 180:158:9644188686184300410027543600 180:159:1334416044629274270569848800 180:160:175142105857592248012292655 180:161:21756783336346863107117100 180:162:2551721502411051845896450 180:163:281785196585269528994700 180:164:29209441109448670688475 180:165:2832430653037446854640 180:166:255942528888925920600 180:167:21456259906856065200 180:168:1660305826125766950 180:169:117891537949758600 180:170:7628275984984380 180:171:446098010817800 180:172:23342337775350 180:173:1079414463600 180:174:43424719800 180:175:1488847536 180:176:42296805 180:177:955860 180:178:16110 180:179:180 180:180:1 # binomial(181, k) for 0 <= k <= 181 181:0:1 181:1:181 181:2:16290 181:3:971970 181:4:43252665 181:5:1531144341 181:6:44913567336 181:7:1122839183400 181:8:24421752238950 181:9:469440348593150 181:10:8074373995802180 181:11:125519813934742980 181:12:1778197364075525550 181:13:23116565732981832150 181:14:277398788795781985800 181:15:3088373181926372775240 181:16:32041871762486117543115 181:17:310994637694718199683175 181:18:2833506698996321374891150 181:19:24308504838757914953013550 181:20:196898889193939111119409755 181:21:1509558150486866518582141455 181:22:10978604730813574680597392400 181:23:75895571834754711922390669200 181:24:499645847912135186822405238900 181:25:3137775924888208973244704900292 181:26:18826655549329253839468229401752 181:27:108078948523927197967317613232280 181:28:594434216881599588820246872777540 181:29:3136152937340853003086130052929780 181:30:15889841549193655215636392268177552 181:31:77398905610588449598745007499832592 181:32:362807370049633357494117222655465275 181:33:1638130246587738492927983823504979575 181:34:7130684602793685204510047231727558150 181:35:29948875331733477858942198373255744230 181:36:121459327734252437983487804513759407155 181:37:475989257336935229935290044716084163175 181:38:1803748764645228239754783327345161039400 181:39:6613745470365836879100872200265590477800 181:40:23478796419798720920808096310942846196190 181:41:80744153541259015849608331215681495455190 181:42:269147178470863386165361104052271651517300 181:43:870033902498837457604306824727110687462900 181:44:2728742694200899298849871404825938065224550 181:45:8307505535678293420942941832470078109683630 181:46:24561320714179302288005219330781100498195080 181:47:70548474391791612954908608716073373771411400 181:48:196947824343751586165786532665704835111856825 181:49:534572666075897162449992017235484552446468525 181:50:1411271838440368508867978925501679218458676906 181:51:3625031585013495581602063514523921129766405386 181:52:9062578962533738954005158786309802824416013465 181:53:22057975210695326888050292140263482346220108245 181:54:52285570869796330401304396184328254450299515840 181:55:120732136372075162926648333007448878457964336576 181:56:271647306837169116584958749266759976530419757296 181:57:595717778151686659177541116813070123970218766000 181:58:1273603525703605961000260318703805092625984948000 181:59:2655139553585483613610712189840136040559256756000 181:60:5398783758957150014341781452674943282470488737200 181:61:10709062866128117241563205832355215363589002249200 181:62:20727218450570549499799753223913320058559359192000 181:63:39151412628855482388510644978502937888389900696000 181:64:72185417034452295653816501679114791731718879408250 181:65:129933750662014132176869703022406625117093982934850 181:66:228368410254449080795710387130290432023983363946100 181:67:391975629541218571515025291343035816160568460504500 181:68:657135614230866428716365929604501221210364772022250 181:69:1076178614609969658622454348482733884011177090413250 181:70:1721885783375951453795926957572374214417883344661200 181:71:2691962281052543822131660454796247011273028890949200 181:72:4112720151608053061590036805938710711667127472283500 181:73:6140910911305175119360465915716705035228998554505500 181:74:8962410519202147471499058363478434375739619511981000 181:75:12786372340728397059338656598562566376055190503759560 181:76:17833624580489606424867073676942526787655923597348860 181:77:24318578973394917852091464104921627437712623087293900 181:78:32424771964526557136121952139895503250283497449725200 181:79:42275335599319435253424823676066289047837977687616400 181:80:53901052889132279948116650186984518535993421551710910 181:81:67209954837066176231602242825746128051053525638553110 181:82:81963359557397775892197857104568448842748201998235500 181:83:97763525255209395341296239197015378740145445756931500 181:84:114057446131077627898178945729851275196836353383086750 181:85:130159673820170940072039502774065572871683838566581350 181:86:145294519613214072638555724026863895298623819795253600 181:87:158654935209831458628307974512092759234129458397116000 181:88:169472317155956330807510790956099083727365557833283000 181:89:177089050511280210843803410774350727939831425601071000 181:90:181024362744864215529221264347114077449605457281094800 181:91:181024362744864215529221264347114077449605457281094800 181:92:177089050511280210843803410774350727939831425601071000 181:93:169472317155956330807510790956099083727365557833283000 181:94:158654935209831458628307974512092759234129458397116000 181:95:145294519613214072638555724026863895298623819795253600 181:96:130159673820170940072039502774065572871683838566581350 181:97:114057446131077627898178945729851275196836353383086750 181:98:97763525255209395341296239197015378740145445756931500 181:99:81963359557397775892197857104568448842748201998235500 181:100:67209954837066176231602242825746128051053525638553110 181:101:53901052889132279948116650186984518535993421551710910 181:102:42275335599319435253424823676066289047837977687616400 181:103:32424771964526557136121952139895503250283497449725200 181:104:24318578973394917852091464104921627437712623087293900 181:105:17833624580489606424867073676942526787655923597348860 181:106:12786372340728397059338656598562566376055190503759560 181:107:8962410519202147471499058363478434375739619511981000 181:108:6140910911305175119360465915716705035228998554505500 181:109:4112720151608053061590036805938710711667127472283500 181:110:2691962281052543822131660454796247011273028890949200 181:111:1721885783375951453795926957572374214417883344661200 181:112:1076178614609969658622454348482733884011177090413250 181:113:657135614230866428716365929604501221210364772022250 181:114:391975629541218571515025291343035816160568460504500 181:115:228368410254449080795710387130290432023983363946100 181:116:129933750662014132176869703022406625117093982934850 181:117:72185417034452295653816501679114791731718879408250 181:118:39151412628855482388510644978502937888389900696000 181:119:20727218450570549499799753223913320058559359192000 181:120:10709062866128117241563205832355215363589002249200 181:121:5398783758957150014341781452674943282470488737200 181:122:2655139553585483613610712189840136040559256756000 181:123:1273603525703605961000260318703805092625984948000 181:124:595717778151686659177541116813070123970218766000 181:125:271647306837169116584958749266759976530419757296 181:126:120732136372075162926648333007448878457964336576 181:127:52285570869796330401304396184328254450299515840 181:128:22057975210695326888050292140263482346220108245 181:129:9062578962533738954005158786309802824416013465 181:130:3625031585013495581602063514523921129766405386 181:131:1411271838440368508867978925501679218458676906 181:132:534572666075897162449992017235484552446468525 181:133:196947824343751586165786532665704835111856825 181:134:70548474391791612954908608716073373771411400 181:135:24561320714179302288005219330781100498195080 181:136:8307505535678293420942941832470078109683630 181:137:2728742694200899298849871404825938065224550 181:138:870033902498837457604306824727110687462900 181:139:269147178470863386165361104052271651517300 181:140:80744153541259015849608331215681495455190 181:141:23478796419798720920808096310942846196190 181:142:6613745470365836879100872200265590477800 181:143:1803748764645228239754783327345161039400 181:144:475989257336935229935290044716084163175 181:145:121459327734252437983487804513759407155 181:146:29948875331733477858942198373255744230 181:147:7130684602793685204510047231727558150 181:148:1638130246587738492927983823504979575 181:149:362807370049633357494117222655465275 181:150:77398905610588449598745007499832592 181:151:15889841549193655215636392268177552 181:152:3136152937340853003086130052929780 181:153:594434216881599588820246872777540 181:154:108078948523927197967317613232280 181:155:18826655549329253839468229401752 181:156:3137775924888208973244704900292 181:157:499645847912135186822405238900 181:158:75895571834754711922390669200 181:159:10978604730813574680597392400 181:160:1509558150486866518582141455 181:161:196898889193939111119409755 181:162:24308504838757914953013550 181:163:2833506698996321374891150 181:164:310994637694718199683175 181:165:32041871762486117543115 181:166:3088373181926372775240 181:167:277398788795781985800 181:168:23116565732981832150 181:169:1778197364075525550 181:170:125519813934742980 181:171:8074373995802180 181:172:469440348593150 181:173:24421752238950 181:174:1122839183400 181:175:44913567336 181:176:1531144341 181:177:43252665 181:178:971970 181:179:16290 181:180:181 181:181:1 # binomial(182, k) for 0 <= k <= 182 182:0:1 182:1:182 182:2:16471 182:3:988260 182:4:44224635 182:5:1574397006 182:6:46444711677 182:7:1167752750736 182:8:25544591422350 182:9:493862100832100 182:10:8543814344395330 182:11:133594187930545160 182:12:1903717178010268530 182:13:24894763097057357700 182:14:300515354528763817950 182:15:3365771970722154761040 182:16:35130244944412490318355 182:17:343036509457204317226290 182:18:3144501336691039574574325 182:19:27142011537754236327904700 182:20:221207394032697026072423305 182:21:1706457039680805629701551210 182:22:12488162881300441199179533855 182:23:86874176565568286602988061600 182:24:575541419746889898744795908100 182:25:3637421772800344160067110139192 182:26:21964431474217462812712934302044 182:27:126905604073256451806785842634032 182:28:702513165405526786787564486009820 182:29:3730587154222452591906376925707320 182:30:19025994486534508218722522321107332 182:31:93288747159782104814381399768010144 182:32:440206275660221807092862230155297867 182:33:2000937616637371850422101046160444850 182:34:8768814849381423697438031055232537725 182:35:37079559934527163063452245604983302380 182:36:151408203065985915842430002887015151385 182:37:597448585071187667918777849229843570330 182:38:2279738021982163469690073372061245202575 182:39:8417494235011065118855655527610751517200 182:40:30092541890164557799908968511208436673990 182:41:104222949961057736770416427526624341651380 182:42:349891332012122402014969435267953146972490 182:43:1139181080969700843769667928779382338980200 182:44:3598776596699736756454178229553048752687450 182:45:11036248229879192719792813237296016174908180 182:46:32868826249857595708948161163251178607878710 182:47:95109795105970915242913828046854474269606480 182:48:267496298735543199120695141381778208883268225 182:49:731520490419648748615778549901189387558325350 182:50:1945844504516265671317970942737163770905145431 182:51:5036303423453864090470042440025600348225082292 182:52:12687610547547234535607222300833723954182418851 182:53:31120554173229065842055450926573285170636121710 182:54:74343546080491657289354688324591736796519624085 182:55:173017707241871493327952729191777132908263852416 182:56:392379443209244279511607082274208854988384093872 182:57:867365084988855775762499866079830100500638523296 182:58:1869321303855292620177801435516875216596203714000 182:59:3928743079289089574610972508543941133185241704000 182:60:8053923312542633627952493642515079323029745493200 182:61:16107846625085267255904987285030158646059490986400 182:62:31436281316698666741362959056268535422148361441200 182:63:59878631079426031888310398202416257946949259888000 182:64:111336829663307778042327146657617729620108780104250 182:65:202119167696466427830686204701521416848812862343100 182:66:358302160916463212972580090152697057141077346880950 182:67:620344039795667652310735678473326248184551824450600 182:68:1049111243772085000231391220947537037370933232526750 182:69:1733314228840836087338820278087235105221541862435500 182:70:2798064397985921112418381306055108098429060435074450 182:71:4413848064428495275927587412368621225690912235610400 182:72:6804682432660596883721697260734957722940156363232700 182:73:10253631062913228180950502721655415746896126026789000 182:74:15103321430507322590859524279195139410968618066486500 182:75:21748782859930544530837714962041000751794810015740560 182:76:30619996921218003484205730275505093163711114101108420 182:77:42152203553884524276958537781864154225368546684642760 182:78:56743350937921474988213416244817130687996120537019100 182:79:74700107563845992389546775815961792298121475137341600 182:80:96176388488451715201541473863050807583831399239327310 182:81:121111007726198456179718893012730646587046947190264020 182:82:149173314394463952123800099930314576893801727636788610 182:83:179726884812607171233494096301583827582893647755167000 182:84:211820971386287023239475184926866653936981799140018250 182:85:244217119951248567970218448503916848068520191949668100 182:86:275454193433385012710595226800929468170307658361834950 182:87:303949454823045531266863698538956654532753278192369600 182:88:328127252365787789435818765468191842961495016230399000 182:89:346561367667236541651314201730449811667196983434354000 182:90:358113413256144426373024675121464805389436882882165800 182:91:362048725489728431058442528694228154899210914562189600 182:92:358113413256144426373024675121464805389436882882165800 182:93:346561367667236541651314201730449811667196983434354000 182:94:328127252365787789435818765468191842961495016230399000 182:95:303949454823045531266863698538956654532753278192369600 182:96:275454193433385012710595226800929468170307658361834950 182:97:244217119951248567970218448503916848068520191949668100 182:98:211820971386287023239475184926866653936981799140018250 182:99:179726884812607171233494096301583827582893647755167000 182:100:149173314394463952123800099930314576893801727636788610 182:101:121111007726198456179718893012730646587046947190264020 182:102:96176388488451715201541473863050807583831399239327310 182:103:74700107563845992389546775815961792298121475137341600 182:104:56743350937921474988213416244817130687996120537019100 182:105:42152203553884524276958537781864154225368546684642760 182:106:30619996921218003484205730275505093163711114101108420 182:107:21748782859930544530837714962041000751794810015740560 182:108:15103321430507322590859524279195139410968618066486500 182:109:10253631062913228180950502721655415746896126026789000 182:110:6804682432660596883721697260734957722940156363232700 182:111:4413848064428495275927587412368621225690912235610400 182:112:2798064397985921112418381306055108098429060435074450 182:113:1733314228840836087338820278087235105221541862435500 182:114:1049111243772085000231391220947537037370933232526750 182:115:620344039795667652310735678473326248184551824450600 182:116:358302160916463212972580090152697057141077346880950 182:117:202119167696466427830686204701521416848812862343100 182:118:111336829663307778042327146657617729620108780104250 182:119:59878631079426031888310398202416257946949259888000 182:120:31436281316698666741362959056268535422148361441200 182:121:16107846625085267255904987285030158646059490986400 182:122:8053923312542633627952493642515079323029745493200 182:123:3928743079289089574610972508543941133185241704000 182:124:1869321303855292620177801435516875216596203714000 182:125:867365084988855775762499866079830100500638523296 182:126:392379443209244279511607082274208854988384093872 182:127:173017707241871493327952729191777132908263852416 182:128:74343546080491657289354688324591736796519624085 182:129:31120554173229065842055450926573285170636121710 182:130:12687610547547234535607222300833723954182418851 182:131:5036303423453864090470042440025600348225082292 182:132:1945844504516265671317970942737163770905145431 182:133:731520490419648748615778549901189387558325350 182:134:267496298735543199120695141381778208883268225 182:135:95109795105970915242913828046854474269606480 182:136:32868826249857595708948161163251178607878710 182:137:11036248229879192719792813237296016174908180 182:138:3598776596699736756454178229553048752687450 182:139:1139181080969700843769667928779382338980200 182:140:349891332012122402014969435267953146972490 182:141:104222949961057736770416427526624341651380 182:142:30092541890164557799908968511208436673990 182:143:8417494235011065118855655527610751517200 182:144:2279738021982163469690073372061245202575 182:145:597448585071187667918777849229843570330 182:146:151408203065985915842430002887015151385 182:147:37079559934527163063452245604983302380 182:148:8768814849381423697438031055232537725 182:149:2000937616637371850422101046160444850 182:150:440206275660221807092862230155297867 182:151:93288747159782104814381399768010144 182:152:19025994486534508218722522321107332 182:153:3730587154222452591906376925707320 182:154:702513165405526786787564486009820 182:155:126905604073256451806785842634032 182:156:21964431474217462812712934302044 182:157:3637421772800344160067110139192 182:158:575541419746889898744795908100 182:159:86874176565568286602988061600 182:160:12488162881300441199179533855 182:161:1706457039680805629701551210 182:162:221207394032697026072423305 182:163:27142011537754236327904700 182:164:3144501336691039574574325 182:165:343036509457204317226290 182:166:35130244944412490318355 182:167:3365771970722154761040 182:168:300515354528763817950 182:169:24894763097057357700 182:170:1903717178010268530 182:171:133594187930545160 182:172:8543814344395330 182:173:493862100832100 182:174:25544591422350 182:175:1167752750736 182:176:46444711677 182:177:1574397006 182:178:44224635 182:179:988260 182:180:16471 182:181:182 182:182:1 # binomial(183, k) for 0 <= k <= 183 183:0:1 183:1:183 183:2:16653 183:3:1004731 183:4:45212895 183:5:1618621641 183:6:48019108683 183:7:1214197462413 183:8:26712344173086 183:9:519406692254450 183:10:9037676445227430 183:11:142138002274940490 183:12:2037311365940813690 183:13:26798480275067626230 183:14:325410117625821175650 183:15:3666287325250918578990 183:16:38496016915134645079395 183:17:378166754401616807544645 183:18:3487537846148243891800615 183:19:30286512874445275902479025 183:20:248349405570451262400328005 183:21:1927664433713502655773974515 183:22:14194619920981246828881085065 183:23:99362339446868727802167595455 183:24:662415596312458185347783969700 183:25:4212963192547234058811906047292 183:26:25601853247017806972780044441236 183:27:148870035547473914619498776936076 183:28:829418769478783238594350328643852 183:29:4433100319627979378693941411717140 183:30:22756581640756960810628899246814652 183:31:112314741646316613033103922089117476 183:32:533495022820003911907243629923308011 183:33:2441143892297593657514963276315742717 183:34:10769752466018795547860132101392982575 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183:71:7211912462414416388345968718423729324119972670684850 183:72:11218530497089092159649284673103578948631068598843100 183:73:17058313495573825064672199982390373469836282390021700 183:74:25356952493420550771810027000850555157864744093275500 183:75:36852104290437867121697239241236140162763428082227060 183:76:52368779781148548015043445237546093915505924116848980 183:77:72772200475102527761164268057369247389079660785751180 183:78:98895554491805999265171954026681284913364667221661860 183:79:131443458501767467377760192060778922986117595674360700 183:80:170876496052297707591088249679012599881952874376668910 183:81:217287396214650171381260366875781454170878346429591330 183:82:270284322120662408303518992943045223480848674827052630 183:83:328900199207071123357294196231898404476695375391955610 183:84:391547856198894194472969281228450481519875446895185250 183:85:456038091337535591209693633430783502005501991089686350 183:86:519671313384633580680813675304846316238827850311503050 183:87:579403648256430543977458925339886122703060936554204550 183:88:632076707188833320702682464007148497494248294422768600 183:89:674688620033024331087132967198641654628691999664753000 183:90:704674780923380968024338876851914617056633866316519800 183:91:720162138745872857431467203815692960288647797444355400 183:92:720162138745872857431467203815692960288647797444355400 183:93:704674780923380968024338876851914617056633866316519800 183:94:674688620033024331087132967198641654628691999664753000 183:95:632076707188833320702682464007148497494248294422768600 183:96:579403648256430543977458925339886122703060936554204550 183:97:519671313384633580680813675304846316238827850311503050 183:98:456038091337535591209693633430783502005501991089686350 183:99:391547856198894194472969281228450481519875446895185250 183:100:328900199207071123357294196231898404476695375391955610 183:101:270284322120662408303518992943045223480848674827052630 183:102:217287396214650171381260366875781454170878346429591330 183:103:170876496052297707591088249679012599881952874376668910 183:104:131443458501767467377760192060778922986117595674360700 183:105:98895554491805999265171954026681284913364667221661860 183:106:72772200475102527761164268057369247389079660785751180 183:107:52368779781148548015043445237546093915505924116848980 183:108:36852104290437867121697239241236140162763428082227060 183:109:25356952493420550771810027000850555157864744093275500 183:110:17058313495573825064672199982390373469836282390021700 183:111:11218530497089092159649284673103578948631068598843100 183:112:7211912462414416388345968718423729324119972670684850 183:113:4531378626826757199757201584142343203650602297509950 183:114:2782425472612921087570211499034772142592475094962250 183:115:1669455283567752652542126899420863285555485056977350 183:116:978646200712130865283315768626023305325629171331550 183:117:560421328612929640803266294854218473989890209224050 183:118:313455997359774205873013351359139146468921642447350 183:119:171215460742733809930637544860033987567058039992250 183:120:91314912396124698629673357258684793369097621329200 183:121:47544127941783933997267946341298694068207852427600 183:122:24161769937627900883857480927545237969089236479600 183:123:11982666391831723202563466151059020456214987197200 183:124:5798064383144382194788773944060816349781445418000 183:125:2736686388844148395940301301596705317096842237296 183:126:1259744528198100055274106948354038955489022617168 183:127:565397150451115772839559811465985987896647946288 183:128:247361253322363150617307417516368869704783476501 183:129:105464100253720723131410139251165021967155745795 183:130:43808164720776300377662673227407009124818540561 183:131:17723913971001098626077264740859324302407501143 183:132:6982147927970129761788013382762764119130227723 183:133:2677364994935914419933749492638353158463470781 183:134:999016789155191947736473691282967596441593575 183:135:362606093841514114363608969428632683152874705 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184:120:262530373138858508560310902118718780936155661321450 184:121:138859040337908632626941303599983487437305473756800 184:122:71705897879411834881125427268843932037297088907200 184:123:36144436329459624086420947078604258425304223676800 184:124:17780730774976105397352240095119836805996432615200 184:125:8534750771988530590729075245657521666878287655296 184:126:3996430917042248451214408249950744272585864854464 184:127:1825141678649215828113666759820024943385670563456 184:128:812758403773478923456867228982354857601431422789 184:129:352825353576083873748717556767533891671939222296 184:130:149272264974497023509072812478572031091974286356 184:131:61532078691777399003739937968266333427226041704 184:132:24706061898971228387865278123622088421537728866 184:133:9659512922906044181721762875401117277593698504 184:134:3676381784091106367670223183921320754905064356 184:135:1361622882996706062100082660711600279594468280 184:136:490584715197342625315470958638738336030359895 184:137:171883695835565299380602963610652847660272080 184:138:58540099306315717904987965867396259710382520 184:139:19372982504248367076470837625181496019263280 184:140:6227030090651260846008483522379766577620340 184:141:1943186694955003384570023226841912974576560 184:142:588429773824402433355711258832410266949240 184:143:172825527976397917489090020076651966516560 184:144:49207268382168851507310352938491184910965 184:145:13574418864046579726154580120963085492680 184:146:3626043395190524721370059073407947494620 184:147:937344551137686662667090100608857175480 184:148:234336137784421665666772525152214293870 184:149:56618127249927382308750408761608822680 184:150:13210896358316389205375095377708725292 184:151:2974638915117597569422206906239050728 184:152:645809764466320524940347552012425487 184:153:135071323287073573843732821335932128 184:154:27189681960384940189322840658531792 184:155:5262519089106762617288291740360992 184:156:978288805026257153213849105579928 184:157:174471888794491721592278821377312 184:158:29814816439565041031591950488528 184:159:4875378788859692244159690016992 184:160:761777935759326913149951565155 184:161:113556959367849974631048680520 184:162:16122284354694749484655059580 184:163:2176013839283953918174302520 184:164:278635918444896538302807030 184:165:33774050720593519794279640 184:166:3865704600549860699345260 184:167:416662771316751452624040 184:168:42162304240385563658385 184:169:3991697442876739754640 184:170:352208597900888801880 184:171:28835791641008439920 184:172:2179449368215754180 184:173:151175678720167920 184:174:9557083137481880 184:175:546119036427536 184:176:27926541635499 184:177:1262216571096 184:178:49637730324 184:179:1663834536 184:180:46217626 184:181:1021384 184:182:16836 184:183:184 184:184:1 # binomial(185, k) for 0 <= k <= 185 185:0:1 185:1:185 185:2:17020 185:3:1038220 185:4:47239010 185:5:1710052162 185:6:51301564860 185:7:1311854301420 185:8:29188758206595 185:9:574045578063035 185:10:10103202173909416 185:11:160732761857649800 185:12:2330625046935922100 185:13:31015241009224194100 185:14:381044389541897241800 185:15:4343906040777628556520 185:16:46154001683262303413025 185:17:458825075557137016282425 185:18:4282367371866612151969300 185:19:37639755321143380493624900 185:20:312409969165490058097086670 185:21:2454649757728850456477109550 185:22:18298298193978703402829362100 185:23:129679243722544724115703740100 185:24:875334895127176887781000245675 185:25:5637156724619019157309641582147 185:26:34690195228424733275751640505520 185:27:204286705234056762623870771865840 185:28:1152760693820748874806127926957240 185:29:6240807894133019770502140845940920 185:30:32452201049491702806611132398892784 185:31:162261005247458514033055661994463920 185:32:780881087753394098784080373348357615 185:33:3620448679583918094362554458251476215 185:34:16185535273433986774797302283947776020 185:35:69829023608243771514125504139317547972 185:36:290954265034349047975522933913823116550 185:37:1171680688922108328333862625761071469350 185:38:4563387946328211384037149174016804670100 185:39:17200462259237104447524639194371032987300 185:40:62781687246215431233464933059454270403645 185:41:222032796358566768996400373015143151427525 185:42:761255301800800350844801278909062233465800 185:43:2531616468779405817925734485674323241525800 185:44:8170216785606264230578506749221679552196900 185:45:25600012594899627922479321147561262596883620 185:46:77913081810564084981458803492577755729645800 185:47:230423795141881017285590929478049107370654600 185:48:662468411032907924696073922249391183690631975 185:49:1852207598194048687415553619350338615624828175 185:50:5038004667087812429770305844632921034499532636 185:51:13335894706997150549391986059322438032498762860 185:52:34365574821877272569587040999023205699131427370 185:53:86238140590748627391605216091888421848763770570 185:54:210804343666274422512812750446838364519200328060 185:55:502097618550580897257790369246105922763913508652 185:56:1165583757349562797205584785749888749273370645085 185:57:2637900082422694751570533988802379800987101986245 185:58:5821572595691464279328075009770769215971535417920 185:59:12531181689030779041943483495608265939464152509760 185:60:26315481546964635988081315340777358472874720270496 185:61:53925167104435729483773187173724095231300656292000 185:62:107850334208871458967546374347448190462601312584000 185:63:210564938217320467508066730868827419474602562664000 185:64:401389413476767141187252205718702268373461135078250 185:65:747201831241366524363961798337891914972135343761050 185:66:1358548784075211862479930542432530754494791534111000 185:67:2412944855297764352762861709693599399774331232227000 185:68:4187169013604944023912024731527128370196633608864500 185:69:7099982240460557257937781066502522019029074380248500 185:70:11765684855620352027439751481632750774391037544411800 185:71:19057095188680851875430583385743187874013652360667000 185:72:30173734048744682136098423694093380800521616237722750 185:73:46707286952166425772316738047021260691218392258392750 185:74:70692109981657293060803711638734881046168377472162000 185:75:104624322772852793729989493225327623948329198658799760 185:76:151429940855444833030247950720868929398897524374578600 185:77:214361864327837490912948397773697575382854937101676200 185:78:296808735223159602802543935378965873607029912910013200 185:79:402006767960481993669268368171510740201926590903435600 185:80:532658967547638641611780587827251730767552732947052170 185:81:690483846821013053941197058294585576920901690857289850 185:82:875735610602260458657127976373620731704558242062904200 185:83:1086756239663046111345592548993770305609271071475652200 185:84:1319632576733698849491076666635292513954114872506149100 185:85:1568034002942395103512926392119582869521948260272012460 185:86:1823295352258598957573170223394863801769707279386061000 185:87:2074784366363233296548779909380362257186218628266897000 185:88:2310555317086327989338413989991767059139198017842680750 185:89:2518245682667121516469956820552824772320249525064494750 185:90:2686128728178262950901287275256346423808266160068794400 185:91:2804200320625659124567277924718163849030607529742148000 185:92:2865161197160999540318740488298993497922577258649586000 185:93:2865161197160999540318740488298993497922577258649586000 185:94:2804200320625659124567277924718163849030607529742148000 185:95:2686128728178262950901287275256346423808266160068794400 185:96:2518245682667121516469956820552824772320249525064494750 185:97:2310555317086327989338413989991767059139198017842680750 185:98:2074784366363233296548779909380362257186218628266897000 185:99:1823295352258598957573170223394863801769707279386061000 185:100:1568034002942395103512926392119582869521948260272012460 185:101:1319632576733698849491076666635292513954114872506149100 185:102:1086756239663046111345592548993770305609271071475652200 185:103:875735610602260458657127976373620731704558242062904200 185:104:690483846821013053941197058294585576920901690857289850 185:105:532658967547638641611780587827251730767552732947052170 185:106:402006767960481993669268368171510740201926590903435600 185:107:296808735223159602802543935378965873607029912910013200 185:108:214361864327837490912948397773697575382854937101676200 185:109:151429940855444833030247950720868929398897524374578600 185:110:104624322772852793729989493225327623948329198658799760 185:111:70692109981657293060803711638734881046168377472162000 185:112:46707286952166425772316738047021260691218392258392750 185:113:30173734048744682136098423694093380800521616237722750 185:114:19057095188680851875430583385743187874013652360667000 185:115:11765684855620352027439751481632750774391037544411800 185:116:7099982240460557257937781066502522019029074380248500 185:117:4187169013604944023912024731527128370196633608864500 185:118:2412944855297764352762861709693599399774331232227000 185:119:1358548784075211862479930542432530754494791534111000 185:120:747201831241366524363961798337891914972135343761050 185:121:401389413476767141187252205718702268373461135078250 185:122:210564938217320467508066730868827419474602562664000 185:123:107850334208871458967546374347448190462601312584000 185:124:53925167104435729483773187173724095231300656292000 185:125:26315481546964635988081315340777358472874720270496 185:126:12531181689030779041943483495608265939464152509760 185:127:5821572595691464279328075009770769215971535417920 185:128:2637900082422694751570533988802379800987101986245 185:129:1165583757349562797205584785749888749273370645085 185:130:502097618550580897257790369246105922763913508652 185:131:210804343666274422512812750446838364519200328060 185:132:86238140590748627391605216091888421848763770570 185:133:34365574821877272569587040999023205699131427370 185:134:13335894706997150549391986059322438032498762860 185:135:5038004667087812429770305844632921034499532636 185:136:1852207598194048687415553619350338615624828175 185:137:662468411032907924696073922249391183690631975 185:138:230423795141881017285590929478049107370654600 185:139:77913081810564084981458803492577755729645800 185:140:25600012594899627922479321147561262596883620 185:141:8170216785606264230578506749221679552196900 185:142:2531616468779405817925734485674323241525800 185:143:761255301800800350844801278909062233465800 185:144:222032796358566768996400373015143151427525 185:145:62781687246215431233464933059454270403645 185:146:17200462259237104447524639194371032987300 185:147:4563387946328211384037149174016804670100 185:148:1171680688922108328333862625761071469350 185:149:290954265034349047975522933913823116550 185:150:69829023608243771514125504139317547972 185:151:16185535273433986774797302283947776020 185:152:3620448679583918094362554458251476215 185:153:780881087753394098784080373348357615 185:154:162261005247458514033055661994463920 185:155:32452201049491702806611132398892784 185:156:6240807894133019770502140845940920 185:157:1152760693820748874806127926957240 185:158:204286705234056762623870771865840 185:159:34690195228424733275751640505520 185:160:5637156724619019157309641582147 185:161:875334895127176887781000245675 185:162:129679243722544724115703740100 185:163:18298298193978703402829362100 185:164:2454649757728850456477109550 185:165:312409969165490058097086670 185:166:37639755321143380493624900 185:167:4282367371866612151969300 185:168:458825075557137016282425 185:169:46154001683262303413025 185:170:4343906040777628556520 185:171:381044389541897241800 185:172:31015241009224194100 185:173:2330625046935922100 185:174:160732761857649800 185:175:10103202173909416 185:176:574045578063035 185:177:29188758206595 185:178:1311854301420 185:179:51301564860 185:180:1710052162 185:181:47239010 185:182:1038220 185:183:17020 185:184:185 185:185:1 # binomial(186, k) for 0 <= k <= 186 186:0:1 186:1:186 186:2:17205 186:3:1055240 186:4:48277230 186:5:1757291172 186:6:53011617022 186:7:1363155866280 186:8:30500612508015 186:9:603234336269630 186:10:10677247751972451 186:11:170835964031559216 186:12:2491357808793571900 186:13:33345866056160116200 186:14:412059630551121435900 186:15:4724950430319525798320 186:16:50497907724039931969545 186:17:504979077240399319695450 186:18:4741192447423749168251725 186:19:41922122693009992645594200 186:20:350049724486633438590711570 186:21:2767059726894340514574196220 186:22:20752947951707553859306471650 186:23:147977541916523427518533102200 186:24:1005014138849721611896703985775 186:25:6512491619746196045090641827822 186:26:40327351953043752433061282087667 186:27:238976900462481495899622412371360 186:28:1357047399054805637429998698823080 186:29:7393568587953768645308268772898160 186:30:38693008943624722577113273244833704 186:31:194713206296950216839666794393356704 186:32:943142093000852612817136035342821535 186:33:4401329767337312193146634831599833830 186:34:19805983953017904869159856742199252235 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186:54:297042484257023049904417966538726786367964098630 186:55:712901962216855319770603119692944287283113836712 186:56:1667681375900143694463375154995994672037284153737 186:57:3803483839772257548776118774552268550260472631330 186:58:8459472678114159030898608998573149016958637404165 186:59:18352754284722243321271558505379035155435687927680 186:60:38846663235995415030024798836385624412338872780256 186:61:80240648651400365471854502514501453704175376562496 186:62:161775501313307188451319561521172285693901968876000 186:63:318415272426191926475613105216275609937203875248000 186:64:611954351694087608695318936587529687848063697742250 186:65:1148591244718133665551214004056594183345596478839300 186:66:2105750615316578386843892340770422669466926877872050 186:67:3771493639372976215242792252126130154269122766338000 186:68:6600113868902708376674886441220727769970964841091500 186:69:11287151254065501281849805798029650389225707989113000 186:70:18865667096080909285377532548135272793420111924660300 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186:87:3898079718621832254121950132775226058955925907652958000 186:88:4385339683449561285887193899372129316325416646109577750 186:89:4828800999753449505808370810544591831459447542907175500 186:90:5204374410845384467371244095809171196128515685133289150 186:91:5490329048803922075468565199974510272838873689810942400 186:92:5669361517786658664886018413017157346953184788391734000 186:93:5730322394321999080637480976597986995845154517299172000 186:94:5669361517786658664886018413017157346953184788391734000 186:95:5490329048803922075468565199974510272838873689810942400 186:96:5204374410845384467371244095809171196128515685133289150 186:97:4828800999753449505808370810544591831459447542907175500 186:98:4385339683449561285887193899372129316325416646109577750 186:99:3898079718621832254121950132775226058955925907652958000 186:100:3391329355200994061086096615514446671291655539658073460 186:101:2887666579676093953004003058754875383476063132778161560 186:102:2406388816396744960836669215629062819563385943981801300 186:103:1962491850265306570002720525367391037313829313538556400 186:104:1566219457423273512598325034668206308625459932920194050 186:105:1223142814368651695552977646121837307688454423804342020 186:106:934665735508120635281048955998762470969479323850487770 186:107:698815503183641596471812303550476613808956503813448800 186:108:511170599550997093715492333152663448989884850011689400 186:109:365791805183282323943196348494566504781752461476254800 186:110:256054263628297626760237443946196553347226723033378360 186:111:175316432754510086790793204864062504994497576130961760 186:112:117399396933823718833120449685756141737386769730554750 186:113:76881021000911107908415161741114641491740008496115500 186:114:49230829237425534011529007079836568674535268598389750 186:115:30822780044301203902870334867375938648404689905078800 186:116:18865667096080909285377532548135272793420111924660300 186:117:11287151254065501281849805798029650389225707989113000 186:118:6600113868902708376674886441220727769970964841091500 186:119:3771493639372976215242792252126130154269122766338000 186:120:2105750615316578386843892340770422669466926877872050 186:121:1148591244718133665551214004056594183345596478839300 186:122:611954351694087608695318936587529687848063697742250 186:123:318415272426191926475613105216275609937203875248000 186:124:161775501313307188451319561521172285693901968876000 186:125:80240648651400365471854502514501453704175376562496 186:126:38846663235995415030024798836385624412338872780256 186:127:18352754284722243321271558505379035155435687927680 186:128:8459472678114159030898608998573149016958637404165 186:129:3803483839772257548776118774552268550260472631330 186:130:1667681375900143694463375154995994672037284153737 186:131:712901962216855319770603119692944287283113836712 186:132:297042484257023049904417966538726786367964098630 186:133:120603715412625899961192257090911627547895197940 186:134:47701469528874423118979027058345643731630190230 186:135:18373899374084962979162291903955359066998295496 186:136:6890212265281861117185859463983259650124360811 186:137:2514676009226956612111627541599729799315460150 186:138:892892206174788941981664851727440291061286575 186:139:308336876952445102267049732970626863100300400 186:140:103513094405463712903938124640139018326529420 186:141:33770229380505892153057827896782942149080520 186:142:10701833254385670048504241234896002793722700 186:143:3292871770580206168770535764583385474991600 186:144:983288098159367119841201651924205384893325 186:145:284814483604782200229865306074597421831170 186:146:79982149505452535680989572253825303390945 186:147:21763850205565315831561788368387837657400 186:148:5735068635250319712371011799777876139450 186:149:1462634953956457376309385559674894585900 186:150:360783288642592819489648438053140664522 186:151:86014558881677758288922806423265323992 186:152:19805983953017904869159856742199252235 186:153:4401329767337312193146634831599833830 186:154:943142093000852612817136035342821535 186:155:194713206296950216839666794393356704 186:156:38693008943624722577113273244833704 186:157:7393568587953768645308268772898160 186:158:1357047399054805637429998698823080 186:159:238976900462481495899622412371360 186:160:40327351953043752433061282087667 186:161:6512491619746196045090641827822 186:162:1005014138849721611896703985775 186:163:147977541916523427518533102200 186:164:20752947951707553859306471650 186:165:2767059726894340514574196220 186:166:350049724486633438590711570 186:167:41922122693009992645594200 186:168:4741192447423749168251725 186:169:504979077240399319695450 186:170:50497907724039931969545 186:171:4724950430319525798320 186:172:412059630551121435900 186:173:33345866056160116200 186:174:2491357808793571900 186:175:170835964031559216 186:176:10677247751972451 186:177:603234336269630 186:178:30500612508015 186:179:1363155866280 186:180:53011617022 186:181:1757291172 186:182:48277230 186:183:1055240 186:184:17205 186:185:186 186:186:1 # binomial(187, k) for 0 <= k <= 187 187:0:1 187:1:187 187:2:17391 187:3:1072445 187:4:49332470 187:5:1805568402 187:6:54768908194 187:7:1416167483302 187:8:31863768374295 187:9:633734948777645 187:10:11280482088242081 187:11:181513211783531667 187:12:2662193772825131116 187:13:35837223864953688100 187:14:445405496607281552100 187:15:5137010060870647234220 187:16:55222858154359457767865 187:17:555476984964439251664995 187:18:5246171524664148487947175 187:19:46663315140433741813845925 187:20:391971847179643431236305770 187:21:3117109451380973953164907790 187:22:23520007678601894373880667870 187:23:168730489868230981377839573850 187:24:1152991680766245039415237087975 187:25:7517505758595917656987345813597 187:26:46839843572789948478151923915489 187:27:279304252415525248332683694459027 187:28:1596024299517287133329621111194440 187:29:8750615987008574282738267471721240 187:30:46086577531578491222421542017731864 187:31:233406215240574939416780067638190408 187:32:1137855299297802829656802829736178239 187:33:5344471860338164805963770866942655365 187:34:24207313720355217062306491573799086065 187:35:105820542834695663158082663165464576227 187:36:446797847524270577778571244476405988514 187:37:1823418242599050195799033997728035250422 187:38:7197703589206777088680397359452770725350 187:39:27498918840815635543932800168165713796850 187:40:101745999711017851512551360622213141048345 187:41:364796633110234735910854878328422725222115 187:42:1268102581764149320071066957998802806724495 187:43:4276159868739573288611737416507590859884925 187:44:13994705024965876217274776999479388268714300 187:45:44472062634891562201562069131678944942803220 187:46:137283323785969605056995952536921960475609940 187:47:411849971357908815170987857610765881426829820 187:48:1201229083127234044248714584698067154161586975 187:49:3407568215401745554093292393327170090376746725 187:50:9404888274508817729297487005582989449439820961 187:51:25264111639366824096348151367938618717122656307 187:52:66075368902959386098141318962301002798628485726 187:53:168305184941500323080171284149257271279525388170 187:54:417646199669648949865610223629638413915859296570 187:55:1009944446473878369675021086231671073651077935342 187:56:2380583338116999014233978274688938959320397990449 187:57:5471165215672401243239493929548263222297756785067 187:58:12262956517886416579674727773125417567219110035495 187:59:26812226962836402352170167503952184172394325331845 187:60:57199417520717658351296357341764659567774560707936 187:61:119087311887395780501879301350887078116514249342752 187:62:242016149964707553923174064035673739398077345438496 187:63:480190773739499114926932666737447895631105844124000 187:64:930369624120279535170932041803805297785267572990250 187:65:1760545596412221274246532940644123871193660176581550 187:66:3254341860034712052395106344827016852812523356711350 187:67:5877244254689554602086684592896552823736049644210050 187:68:10371607508275684591917678693346857924240087607429500 187:69:17887265122968209658524692239250378159196672830204500 187:70:30152818350146410567227338346164923182645819913773300 187:71:49688447140382113188247867415511211441824801829739100 187:72:80053609281726737914399341947212507322939958503468550 187:73:126111850238336641919944168820951210166275277094505250 187:74:194280417934734826741535611426870783229126778226670250 187:75:292715829688333805623913654549818646731884345861516510 187:76:431370696382807713551030648810259058341724299164340120 187:77:621846068811579950703433792440763058128979184509633160 187:78:876962404734279417658688681647229953771637311487944200 187:79:1209986102734638690187304636703140062798841353825138200 187:80:1633481238691762231752861259549239084778435827663936570 187:81:2157808549876772330834026602120599778657933747654829790 187:82:2789362271791925208151302680790043616313914356724536070 187:83:3528711307688580082601045560035597345939289246458750450 187:84:4368880666662051530839389740996453856877215257520357700 187:85:5294055396072838913840672274383938203039449076759962860 187:86:6278995934877088014090099674269322054767718672436235020 187:87:7289409073822826315208046748289672730247581447311031460 187:88:8283419402071393540009144032147355375281342553762535750 187:89:9214140683203010791695564709916721147784864189016753250 187:90:10033175410598833973179614906353763027587963228040464650 187:91:10694703459649306542839809295783681468967389374944231550 187:92:11159690566590580740354583612991667619792058478202676400 187:93:11399683912108657745523499389615144342798339305690906000 187:94:11399683912108657745523499389615144342798339305690906000 187:95:11159690566590580740354583612991667619792058478202676400 187:96:10694703459649306542839809295783681468967389374944231550 187:97:10033175410598833973179614906353763027587963228040464650 187:98:9214140683203010791695564709916721147784864189016753250 187:99:8283419402071393540009144032147355375281342553762535750 187:100:7289409073822826315208046748289672730247581447311031460 187:101:6278995934877088014090099674269322054767718672436235020 187:102:5294055396072838913840672274383938203039449076759962860 187:103:4368880666662051530839389740996453856877215257520357700 187:104:3528711307688580082601045560035597345939289246458750450 187:105:2789362271791925208151302680790043616313914356724536070 187:106:2157808549876772330834026602120599778657933747654829790 187:107:1633481238691762231752861259549239084778435827663936570 187:108:1209986102734638690187304636703140062798841353825138200 187:109:876962404734279417658688681647229953771637311487944200 187:110:621846068811579950703433792440763058128979184509633160 187:111:431370696382807713551030648810259058341724299164340120 187:112:292715829688333805623913654549818646731884345861516510 187:113:194280417934734826741535611426870783229126778226670250 187:114:126111850238336641919944168820951210166275277094505250 187:115:80053609281726737914399341947212507322939958503468550 187:116:49688447140382113188247867415511211441824801829739100 187:117:30152818350146410567227338346164923182645819913773300 187:118:17887265122968209658524692239250378159196672830204500 187:119:10371607508275684591917678693346857924240087607429500 187:120:5877244254689554602086684592896552823736049644210050 187:121:3254341860034712052395106344827016852812523356711350 187:122:1760545596412221274246532940644123871193660176581550 187:123:930369624120279535170932041803805297785267572990250 187:124:480190773739499114926932666737447895631105844124000 187:125:242016149964707553923174064035673739398077345438496 187:126:119087311887395780501879301350887078116514249342752 187:127:57199417520717658351296357341764659567774560707936 187:128:26812226962836402352170167503952184172394325331845 187:129:12262956517886416579674727773125417567219110035495 187:130:5471165215672401243239493929548263222297756785067 187:131:2380583338116999014233978274688938959320397990449 187:132:1009944446473878369675021086231671073651077935342 187:133:417646199669648949865610223629638413915859296570 187:134:168305184941500323080171284149257271279525388170 187:135:66075368902959386098141318962301002798628485726 187:136:25264111639366824096348151367938618717122656307 187:137:9404888274508817729297487005582989449439820961 187:138:3407568215401745554093292393327170090376746725 187:139:1201229083127234044248714584698067154161586975 187:140:411849971357908815170987857610765881426829820 187:141:137283323785969605056995952536921960475609940 187:142:44472062634891562201562069131678944942803220 187:143:13994705024965876217274776999479388268714300 187:144:4276159868739573288611737416507590859884925 187:145:1268102581764149320071066957998802806724495 187:146:364796633110234735910854878328422725222115 187:147:101745999711017851512551360622213141048345 187:148:27498918840815635543932800168165713796850 187:149:7197703589206777088680397359452770725350 187:150:1823418242599050195799033997728035250422 187:151:446797847524270577778571244476405988514 187:152:105820542834695663158082663165464576227 187:153:24207313720355217062306491573799086065 187:154:5344471860338164805963770866942655365 187:155:1137855299297802829656802829736178239 187:156:233406215240574939416780067638190408 187:157:46086577531578491222421542017731864 187:158:8750615987008574282738267471721240 187:159:1596024299517287133329621111194440 187:160:279304252415525248332683694459027 187:161:46839843572789948478151923915489 187:162:7517505758595917656987345813597 187:163:1152991680766245039415237087975 187:164:168730489868230981377839573850 187:165:23520007678601894373880667870 187:166:3117109451380973953164907790 187:167:391971847179643431236305770 187:168:46663315140433741813845925 187:169:5246171524664148487947175 187:170:555476984964439251664995 187:171:55222858154359457767865 187:172:5137010060870647234220 187:173:445405496607281552100 187:174:35837223864953688100 187:175:2662193772825131116 187:176:181513211783531667 187:177:11280482088242081 187:178:633734948777645 187:179:31863768374295 187:180:1416167483302 187:181:54768908194 187:182:1805568402 187:183:49332470 187:184:1072445 187:185:17391 187:186:187 187:187:1 # binomial(188, k) for 0 <= k <= 188 188:0:1 188:1:188 188:2:17578 188:3:1089836 188:4:50404915 188:5:1854900872 188:6:56574476596 188:7:1470936391496 188:8:33279935857597 188:9:665598717151940 188:10:11914217037019726 188:11:192793693871773748 188:12:2843706984608662783 188:13:38499417637778819216 188:14:481242720472235240200 188:15:5582415557477928786320 188:16:60359868215230105002085 188:17:610699843118798709432860 188:18:5801648509628587739612170 188:19:51909486665097890301793100 188:20:438635162320077173050151695 188:21:3509081298560617384401213560 188:22:26637117129982868327045575660 188:23:192250497546832875751720241720 188:24:1321722170634476020793076661825 188:25:8670497439362162696402582901572 188:26:54357349331385866135139269729086 188:27:326144095988315196810835618374516 188:28:1875328551932812381662304805653467 188:29:10346640286525861416067888582915680 188:30:54837193518587065505159809489453104 188:31:279492792772153430639201609655922272 188:32:1371261514538377769073582897374368647 188:33:6482327159635967635620573696678833604 188:34:29551785580693381868270262440741741430 188:35:130027856555050880220389154739263662292 188:36:552618390358966240936653907641870564741 188:37:2270216090123320773577605242204441238936 188:38:9021121831805827284479431357180805975772 188:39:34696622430022412632613197527618484522200 188:40:129244918551833487056484160790378854845195 188:41:466542632821252587423406238950635866270460 188:42:1632899214874384055981921836327225531946610 188:43:5544262450503722608682804374506393666609420 188:44:18270864893705449505886514415986979128599225 188:45:58466767659857438418836846131158333211517520 188:46:181755386420861167258558021668600905418413160 188:47:549133295143878420227983810147687841902439760 188:48:1613079054485142859419702442308833035588416795 188:49:4608797298528979598342006978025237244538333700 188:50:12812456489910563283390779398910159539816567686 188:51:34668999913875641825645638373521608166562477268 188:52:91339480542326210194489470330239621515751142033 188:53:234380553844459709178312603111558274078153873896 188:54:585951384611149272945781507778895685195384684740 188:55:1427590646143527319540631309861309487566937231912 188:56:3390527784590877383908999360920610032971475925791 188:57:7851748553789400257473472204237202181618154775516 188:58:17734121733558817822914221702673680789516866820562 188:59:39075183480722818931844895277077601739613435367340 188:60:84011644483554060703466524845716843740168886039781 188:61:176286729408113438853175658692651737684288810050688 188:62:361103461852103334425053365386560817514591594781248 188:63:722206923704206668850106730773121635029183189562496 188:64:1410560397859778650097864708541253193416373417114250 188:65:2690915220532500809417464982447929168978927749571800 188:66:5014887456446933326641639285471140724006183533292900 188:67:9131586114724266654481790937723569676548573000921400 188:68:16248851762965239194004363286243410747976137251639550 188:69:28258872631243894250442370932597236083436760437634000 188:70:48040083473114620225752030585415301341842492743977800 188:71:79841265490528523755475205761676134624470621743512400 188:72:129742056422108851102647209362723718764764760333207650 188:73:206165459520063379834343510768163717489215235597973800 188:74:320392268173071468661479780247821993395402055321175500 188:75:486996247623068632365449265976689429961011124088186760 188:76:724086526071141519174944303360077705073608645025856630 188:77:1053216765194387664254464441251022116470703483673973280 188:78:1498808473545859368362122474087993011900616495997577360 188:79:2086948507468918107845993318350370016570478665313082400 188:80:2843467341426400921940165896252379147577277181489074770 188:81:3791289788568534562586887861669838863436369575318766360 188:82:4947170821668697538985329282910643394971848104379365860 188:83:6318073579480505290752348240825640962253203603183286520 188:84:7897591974350631613440435301032051202816504503979108150 188:85:9662936062734890444680062015380392059916664334280320560 188:86:11573051330949926927930771948653260257807167749196197880 188:87:13568405008699914329298146422558994785015300119747266480 188:88:15572828475894219855217190780437028105528924001073567210 188:89:17497560085274404331704708742064076523066206742779289000 188:90:19247316093801844764875179616270484175372827417057217900 188:91:20727878870248140516019424202137444496555352602984696200 188:92:21854394026239887283194392908775349088759447853146907950 188:93:22559374478699238485878083002606811962590397783893582400 188:94:22799367824217315491046998779230288685596678611381812000 188:95:22559374478699238485878083002606811962590397783893582400 188:96:21854394026239887283194392908775349088759447853146907950 188:97:20727878870248140516019424202137444496555352602984696200 188:98:19247316093801844764875179616270484175372827417057217900 188:99:17497560085274404331704708742064076523066206742779289000 188:100:15572828475894219855217190780437028105528924001073567210 188:101:13568405008699914329298146422558994785015300119747266480 188:102:11573051330949926927930771948653260257807167749196197880 188:103:9662936062734890444680062015380392059916664334280320560 188:104:7897591974350631613440435301032051202816504503979108150 188:105:6318073579480505290752348240825640962253203603183286520 188:106:4947170821668697538985329282910643394971848104379365860 188:107:3791289788568534562586887861669838863436369575318766360 188:108:2843467341426400921940165896252379147577277181489074770 188:109:2086948507468918107845993318350370016570478665313082400 188:110:1498808473545859368362122474087993011900616495997577360 188:111:1053216765194387664254464441251022116470703483673973280 188:112:724086526071141519174944303360077705073608645025856630 188:113:486996247623068632365449265976689429961011124088186760 188:114:320392268173071468661479780247821993395402055321175500 188:115:206165459520063379834343510768163717489215235597973800 188:116:129742056422108851102647209362723718764764760333207650 188:117:79841265490528523755475205761676134624470621743512400 188:118:48040083473114620225752030585415301341842492743977800 188:119:28258872631243894250442370932597236083436760437634000 188:120:16248851762965239194004363286243410747976137251639550 188:121:9131586114724266654481790937723569676548573000921400 188:122:5014887456446933326641639285471140724006183533292900 188:123:2690915220532500809417464982447929168978927749571800 188:124:1410560397859778650097864708541253193416373417114250 188:125:722206923704206668850106730773121635029183189562496 188:126:361103461852103334425053365386560817514591594781248 188:127:176286729408113438853175658692651737684288810050688 188:128:84011644483554060703466524845716843740168886039781 188:129:39075183480722818931844895277077601739613435367340 188:130:17734121733558817822914221702673680789516866820562 188:131:7851748553789400257473472204237202181618154775516 188:132:3390527784590877383908999360920610032971475925791 188:133:1427590646143527319540631309861309487566937231912 188:134:585951384611149272945781507778895685195384684740 188:135:234380553844459709178312603111558274078153873896 188:136:91339480542326210194489470330239621515751142033 188:137:34668999913875641825645638373521608166562477268 188:138:12812456489910563283390779398910159539816567686 188:139:4608797298528979598342006978025237244538333700 188:140:1613079054485142859419702442308833035588416795 188:141:549133295143878420227983810147687841902439760 188:142:181755386420861167258558021668600905418413160 188:143:58466767659857438418836846131158333211517520 188:144:18270864893705449505886514415986979128599225 188:145:5544262450503722608682804374506393666609420 188:146:1632899214874384055981921836327225531946610 188:147:466542632821252587423406238950635866270460 188:148:129244918551833487056484160790378854845195 188:149:34696622430022412632613197527618484522200 188:150:9021121831805827284479431357180805975772 188:151:2270216090123320773577605242204441238936 188:152:552618390358966240936653907641870564741 188:153:130027856555050880220389154739263662292 188:154:29551785580693381868270262440741741430 188:155:6482327159635967635620573696678833604 188:156:1371261514538377769073582897374368647 188:157:279492792772153430639201609655922272 188:158:54837193518587065505159809489453104 188:159:10346640286525861416067888582915680 188:160:1875328551932812381662304805653467 188:161:326144095988315196810835618374516 188:162:54357349331385866135139269729086 188:163:8670497439362162696402582901572 188:164:1321722170634476020793076661825 188:165:192250497546832875751720241720 188:166:26637117129982868327045575660 188:167:3509081298560617384401213560 188:168:438635162320077173050151695 188:169:51909486665097890301793100 188:170:5801648509628587739612170 188:171:610699843118798709432860 188:172:60359868215230105002085 188:173:5582415557477928786320 188:174:481242720472235240200 188:175:38499417637778819216 188:176:2843706984608662783 188:177:192793693871773748 188:178:11914217037019726 188:179:665598717151940 188:180:33279935857597 188:181:1470936391496 188:182:56574476596 188:183:1854900872 188:184:50404915 188:185:1089836 188:186:17578 188:187:188 188:188:1 # binomial(189, k) for 0 <= k <= 189 189:0:1 189:1:189 189:2:17766 189:3:1107414 189:4:51494751 189:5:1905305787 189:6:58429377468 189:7:1527510868092 189:8:34750872249093 189:9:698878653009537 189:10:12579815754171666 189:11:204707910908793474 189:12:3036500678480436531 189:13:41343124622387481999 189:14:519742138110014059416 189:15:6063658277950164026520 189:16:65942283772708033788405 189:17:671059711334028814434945 189:18:6412348352747386449045030 189:19:57711135174726478041405270 189:20:490544648985175063351944795 189:21:3947716460880694557451365255 189:22:30146198428543485711446789220 189:23:218887614676815744078765817380 189:24:1513972668181308896544796903545 189:25:9992219609996638717195659563397 189:26:63027846770748028831541852630658 189:27:380501445319701062945974888103602 189:28:2201472647921127578473140424027983 189:29:12221968838458673797730193388569147 189:30:65183833805112926921227698072368784 189:31:334329986290740496144361419145375376 189:32:1650754307310531199712784507030290919 189:33:7853588674174345404694156594053202251 189:34:36034112740329349503890836137420575034 189:35:159579642135744262088659417180005403722 189:36:682646246914017121157043062381134227033 189:37:2822834480482287014514259149846311803677 189:38:11291337921929148058057036599385247214708 189:39:43717744261828239917092628884799290497972 189:40:163941540981855899689097358317997339367395 189:41:595787551373086074479890399741014721115655 189:42:2099441847695636643405328075277861398217070 189:43:7177161665378106664664726210833619198556030 189:44:23815127344209172114569318790493372795208645 189:45:76737632553562887924723360547145312340116745 189:46:240222154080718605677394867799759238629930680 189:47:730888681564739587486541831816288747320852920 189:48:2162212349629021279647686252456520877490856555 189:49:6221876353014122457761709420334070280126750495 189:50:17421253788439542881732786376935396784354901386 189:51:47481456403786205109036417772431767706379044954 189:52:126008480456201852020135108703761229682313619301 189:53:325720034386785919372802073441797895593905015929 189:54:820331938455608982124094110890453959273538558636 189:55:2013542030754676592486412817640205172762321916652 189:56:4818118430734404703449630670781919520538413157703 189:57:11242276338380277641382471565157812214589630701307 189:58:25585870287348218080387693906910882971135021596078 189:59:56809305214281636754759116979751282529130302187902 189:60:123086827964276879635311420122794445479782321407121 189:61:260298373891667499556642183538368581424457696090469 189:62:537390191260216773278229024079212555198880404831936 189:63:1083310385556310003275160096159682452543774784343744 189:64:2132767321563985318947971439314374828445556606676746 189:65:4101475618392279459515329690989182362395301166686050 189:66:7705802676979434136059104267919069892985111282864700 189:67:14146473571171199981123430223194710400554756534214300 189:68:25380437877689505848486154223966980424524710252560950 189:69:44507724394209133444446734218840646831412897689273550 189:70:76298956104358514476194401518012537425279253181611800 189:71:127881348963643143981227236347091435966313114487490200 189:72:209583321912637374858122415124399853389235382076720050 189:73:335907515942172230936990720130887436253979995931181450 189:74:526557727693134848495823291015985710884617290919149300 189:75:807388515796140101026929046224511423356413179409362260 189:76:1211082773694210151540393569336767135034619769114043390 189:77:1777303291265529183429408744611099821544312128699829910 189:78:2552025238740247032616586915339015128371319979671550640 189:79:3585756981014777476208115792438363028471095161310659760 189:80:4930415848895319029786159214602749164147755846802157170 189:81:6634757129994935484527053757922218011013646756807841130 189:82:8738460610237232101572217144580482258408217679698132220 189:83:11265244401149202829737677523736284357225051707562652380 189:84:14215665553831136904192783541857692165069708107162394670 189:85:17560528037085522058120497316412443262733168838259428710 189:86:21235987393684817372610833964033652317723832083476518440 189:87:25141456339649841257228918371212255042822467868943464360 189:88:29141233484594134184515337202996022890544224120820833690 189:89:33070388561168624186921899522501104628595130743852856210 189:90:36744876179076249096579888358334560698439034159836506900 189:91:39975194964049985280894603818407928671928180020041914100 189:92:42582272896488027799213817110912793585314800456131604150 189:93:44413768504939125769072475911382161051349845637040490350 189:94:45358742302916553976925081781837100648187076395275394400 189:95:45358742302916553976925081781837100648187076395275394400 189:96:44413768504939125769072475911382161051349845637040490350 189:97:42582272896488027799213817110912793585314800456131604150 189:98:39975194964049985280894603818407928671928180020041914100 189:99:36744876179076249096579888358334560698439034159836506900 189:100:33070388561168624186921899522501104628595130743852856210 189:101:29141233484594134184515337202996022890544224120820833690 189:102:25141456339649841257228918371212255042822467868943464360 189:103:21235987393684817372610833964033652317723832083476518440 189:104:17560528037085522058120497316412443262733168838259428710 189:105:14215665553831136904192783541857692165069708107162394670 189:106:11265244401149202829737677523736284357225051707562652380 189:107:8738460610237232101572217144580482258408217679698132220 189:108:6634757129994935484527053757922218011013646756807841130 189:109:4930415848895319029786159214602749164147755846802157170 189:110:3585756981014777476208115792438363028471095161310659760 189:111:2552025238740247032616586915339015128371319979671550640 189:112:1777303291265529183429408744611099821544312128699829910 189:113:1211082773694210151540393569336767135034619769114043390 189:114:807388515796140101026929046224511423356413179409362260 189:115:526557727693134848495823291015985710884617290919149300 189:116:335907515942172230936990720130887436253979995931181450 189:117:209583321912637374858122415124399853389235382076720050 189:118:127881348963643143981227236347091435966313114487490200 189:119:76298956104358514476194401518012537425279253181611800 189:120:44507724394209133444446734218840646831412897689273550 189:121:25380437877689505848486154223966980424524710252560950 189:122:14146473571171199981123430223194710400554756534214300 189:123:7705802676979434136059104267919069892985111282864700 189:124:4101475618392279459515329690989182362395301166686050 189:125:2132767321563985318947971439314374828445556606676746 189:126:1083310385556310003275160096159682452543774784343744 189:127:537390191260216773278229024079212555198880404831936 189:128:260298373891667499556642183538368581424457696090469 189:129:123086827964276879635311420122794445479782321407121 189:130:56809305214281636754759116979751282529130302187902 189:131:25585870287348218080387693906910882971135021596078 189:132:11242276338380277641382471565157812214589630701307 189:133:4818118430734404703449630670781919520538413157703 189:134:2013542030754676592486412817640205172762321916652 189:135:820331938455608982124094110890453959273538558636 189:136:325720034386785919372802073441797895593905015929 189:137:126008480456201852020135108703761229682313619301 189:138:47481456403786205109036417772431767706379044954 189:139:17421253788439542881732786376935396784354901386 189:140:6221876353014122457761709420334070280126750495 189:141:2162212349629021279647686252456520877490856555 189:142:730888681564739587486541831816288747320852920 189:143:240222154080718605677394867799759238629930680 189:144:76737632553562887924723360547145312340116745 189:145:23815127344209172114569318790493372795208645 189:146:7177161665378106664664726210833619198556030 189:147:2099441847695636643405328075277861398217070 189:148:595787551373086074479890399741014721115655 189:149:163941540981855899689097358317997339367395 189:150:43717744261828239917092628884799290497972 189:151:11291337921929148058057036599385247214708 189:152:2822834480482287014514259149846311803677 189:153:682646246914017121157043062381134227033 189:154:159579642135744262088659417180005403722 189:155:36034112740329349503890836137420575034 189:156:7853588674174345404694156594053202251 189:157:1650754307310531199712784507030290919 189:158:334329986290740496144361419145375376 189:159:65183833805112926921227698072368784 189:160:12221968838458673797730193388569147 189:161:2201472647921127578473140424027983 189:162:380501445319701062945974888103602 189:163:63027846770748028831541852630658 189:164:9992219609996638717195659563397 189:165:1513972668181308896544796903545 189:166:218887614676815744078765817380 189:167:30146198428543485711446789220 189:168:3947716460880694557451365255 189:169:490544648985175063351944795 189:170:57711135174726478041405270 189:171:6412348352747386449045030 189:172:671059711334028814434945 189:173:65942283772708033788405 189:174:6063658277950164026520 189:175:519742138110014059416 189:176:41343124622387481999 189:177:3036500678480436531 189:178:204707910908793474 189:179:12579815754171666 189:180:698878653009537 189:181:34750872249093 189:182:1527510868092 189:183:58429377468 189:184:1905305787 189:185:51494751 189:186:1107414 189:187:17766 189:188:189 189:189:1 # binomial(190, k) for 0 <= k <= 190 190:0:1 190:1:190 190:2:17955 190:3:1125180 190:4:52602165 190:5:1956800538 190:6:60334683255 190:7:1585940245560 190:8:36278383117185 190:9:733629525258630 190:10:13278694407181203 190:11:217287726662965140 190:12:3241208589389230005 190:13:44379625300867918530 190:14:561085262732401541415 190:15:6583400416060178085936 190:16:72005942050658197814925 190:17:737001995106736848223350 190:18:7083408064081415263479975 190:19:64123483527473864490450300 190:20:548255784159901541393350065 190:21:4438261109865869620803310050 190:22:34093914889424180268898154475 190:23:249033813105359229790212606600 190:24:1732860282858124640623562720925 190:25:11506192278177947613740456466942 190:26:73020066380744667548737512194055 190:27:443529292090449091777516740734260 190:28:2581974093240828641419115312131585 190:29:14423441486379801376203333812597130 190:30:77405802643571600718957891460937931 190:31:399513820095853423065589117217744160 190:32:1985084293601271695857145926175666295 190:33:9504342981484876604406941101083493170 190:34:43887701414503694908584992731473777285 190:35:195613754876073611592550253317425978756 190:36:842225889049761383245702479561139630755 190:37:3505480727396304135671302212227446030710 190:38:14114172402411435072571295749231559018385 190:39:55009082183757387975149665484184537712680 190:40:207659285243684139606189987202796629865367 190:41:759729092354941974168987758059012060483050 190:42:2695229399068722717885218475018876119332725 190:43:9276603513073743308070054286111480596773100 190:44:30992289009587278779234045001326991993764675 190:45:100552759897772060039292679337638685135325390 190:46:316959786634281493602118228346904550970047425 190:47:971110835645458193163936699616047985950783600 190:48:2893101031193760867134228084272809624811709475 190:49:8384088702643143737409395672790591157617607050 190:50:23643130141453665339494495797269467064481651881 190:51:64902710192225747990769204149367164490733946340 190:52:173489936859988057129171526476192997388692664255 190:53:451728514842987771392937182145559125276218635230 190:54:1146051972842394901496896184332251854867443574565 190:55:2833873969210285574610506928530659132035860475288 190:56:6831660461489081295936043488422124693300735074355 190:57:16060394769114682344832102235939731735128043859010 190:58:36828146625728495721770165472068695185724652297385 190:59:82395175501629854835146810886662165500265323783980 190:60:179896133178558516390070537102545728008912623595023 190:61:383385201855944379191953603661163026904240017497590 190:62:797688565151884272834871207617581136623338100922405 190:63:1620700576816526776553389120238895007742655189175680 190:64:3216077707120295322223131535474057280989331391020490 190:65:6234242939956264778463301130303557190840857773362796 190:66:11807278295371713595574433958908252255380412449550750 190:67:21852276248150634117182534491113780293539867817079000 190:68:39526911448860705829609584447161690825079466786775250 190:69:69888162271898639292932888442807627255937607941834500 190:70:120806680498567647920641135736853184256692150870885350 190:71:204180305068001658457421637865103973391592367669102000 190:72:337464670876280518839349651471491289355548496564210250 190:73:545490837854809605795113135255287289643215378007901500 190:74:862465243635307079432814011146873147138597286850330750 190:75:1333946243489274949522752337240497134241030470328511560 190:76:2018471289490350252567322615561278558391032948523405650 190:77:2988386064959739334969802313947866956578931897813873300 190:78:4329328530005776216045995659950114949915632108371380550 190:79:6137782219755024508824702707777378156842415140982210400 190:80:8516172829910096505994275007041112192618851008112816930 190:81:11565172978890254514313212972524967175161402603609998300 190:82:15373217740232167586099270902502700269421864436505973350 190:83:20003705011386434931309894668316766615633269387260784600 190:84:25480909954980339733930461065593976522294759814725047050 190:85:31776193590916658962313280858270135427802876945421823380 190:86:38796515430770339430731331280446095580457000921735947150 190:87:46377443733334658629839752335245907360546299952419982800 190:88:54282689824243975441744255574208277933366691989764298050 190:89:62211622045762758371437236725497127519139354864673689900 190:90:69815264740244873283501787880835665327034164903689363110 190:91:76720071143126234377474492176742489370367214179878421000 190:92:82557467860538013080108420929320722257242980476173518250 190:93:86996041401427153568286293022294954636664646093172094500 190:94:89772510807855679745997557693219261699536922032315884750 190:95:90717484605833107953850163563674201296374152790550788800 190:96:89772510807855679745997557693219261699536922032315884750 190:97:86996041401427153568286293022294954636664646093172094500 190:98:82557467860538013080108420929320722257242980476173518250 190:99:76720071143126234377474492176742489370367214179878421000 190:100:69815264740244873283501787880835665327034164903689363110 190:101:62211622045762758371437236725497127519139354864673689900 190:102:54282689824243975441744255574208277933366691989764298050 190:103:46377443733334658629839752335245907360546299952419982800 190:104:38796515430770339430731331280446095580457000921735947150 190:105:31776193590916658962313280858270135427802876945421823380 190:106:25480909954980339733930461065593976522294759814725047050 190:107:20003705011386434931309894668316766615633269387260784600 190:108:15373217740232167586099270902502700269421864436505973350 190:109:11565172978890254514313212972524967175161402603609998300 190:110:8516172829910096505994275007041112192618851008112816930 190:111:6137782219755024508824702707777378156842415140982210400 190:112:4329328530005776216045995659950114949915632108371380550 190:113:2988386064959739334969802313947866956578931897813873300 190:114:2018471289490350252567322615561278558391032948523405650 190:115:1333946243489274949522752337240497134241030470328511560 190:116:862465243635307079432814011146873147138597286850330750 190:117:545490837854809605795113135255287289643215378007901500 190:118:337464670876280518839349651471491289355548496564210250 190:119:204180305068001658457421637865103973391592367669102000 190:120:120806680498567647920641135736853184256692150870885350 190:121:69888162271898639292932888442807627255937607941834500 190:122:39526911448860705829609584447161690825079466786775250 190:123:21852276248150634117182534491113780293539867817079000 190:124:11807278295371713595574433958908252255380412449550750 190:125:6234242939956264778463301130303557190840857773362796 190:126:3216077707120295322223131535474057280989331391020490 190:127:1620700576816526776553389120238895007742655189175680 190:128:797688565151884272834871207617581136623338100922405 190:129:383385201855944379191953603661163026904240017497590 190:130:179896133178558516390070537102545728008912623595023 190:131:82395175501629854835146810886662165500265323783980 190:132:36828146625728495721770165472068695185724652297385 190:133:16060394769114682344832102235939731735128043859010 190:134:6831660461489081295936043488422124693300735074355 190:135:2833873969210285574610506928530659132035860475288 190:136:1146051972842394901496896184332251854867443574565 190:137:451728514842987771392937182145559125276218635230 190:138:173489936859988057129171526476192997388692664255 190:139:64902710192225747990769204149367164490733946340 190:140:23643130141453665339494495797269467064481651881 190:141:8384088702643143737409395672790591157617607050 190:142:2893101031193760867134228084272809624811709475 190:143:971110835645458193163936699616047985950783600 190:144:316959786634281493602118228346904550970047425 190:145:100552759897772060039292679337638685135325390 190:146:30992289009587278779234045001326991993764675 190:147:9276603513073743308070054286111480596773100 190:148:2695229399068722717885218475018876119332725 190:149:759729092354941974168987758059012060483050 190:150:207659285243684139606189987202796629865367 190:151:55009082183757387975149665484184537712680 190:152:14114172402411435072571295749231559018385 190:153:3505480727396304135671302212227446030710 190:154:842225889049761383245702479561139630755 190:155:195613754876073611592550253317425978756 190:156:43887701414503694908584992731473777285 190:157:9504342981484876604406941101083493170 190:158:1985084293601271695857145926175666295 190:159:399513820095853423065589117217744160 190:160:77405802643571600718957891460937931 190:161:14423441486379801376203333812597130 190:162:2581974093240828641419115312131585 190:163:443529292090449091777516740734260 190:164:73020066380744667548737512194055 190:165:11506192278177947613740456466942 190:166:1732860282858124640623562720925 190:167:249033813105359229790212606600 190:168:34093914889424180268898154475 190:169:4438261109865869620803310050 190:170:548255784159901541393350065 190:171:64123483527473864490450300 190:172:7083408064081415263479975 190:173:737001995106736848223350 190:174:72005942050658197814925 190:175:6583400416060178085936 190:176:561085262732401541415 190:177:44379625300867918530 190:178:3241208589389230005 190:179:217287726662965140 190:180:13278694407181203 190:181:733629525258630 190:182:36278383117185 190:183:1585940245560 190:184:60334683255 190:185:1956800538 190:186:52602165 190:187:1125180 190:188:17955 190:189:190 190:190:1 # binomial(191, k) for 0 <= k <= 191 191:0:1 191:1:191 191:2:18145 191:3:1143135 191:4:53727345 191:5:2009402703 191:6:62291483793 191:7:1646274928815 191:8:37864323362745 191:9:769907908375815 191:10:14012323932439833 191:11:230566421070146343 191:12:3458496316052195145 191:13:47620833890257148535 191:14:605464888033269459945 191:15:7144485678792579627351 191:16:78589342466718375900861 191:17:809007937157395046038275 191:18:7820410059188152111703325 191:19:71206891591555279753930275 191:20:612379267687375405883800365 191:21:4986516894025771162196660115 191:22:38532175999290049889701464525 191:23:283127727994783410059110761075 191:24:1981894095963483870413775327525 191:25:13239052561036072254364019187867 191:26:84526258658922615162477968660997 191:27:516549358471193759326254252928315 191:28:3025503385331277733196632052865845 191:29:17005415579620630017622449124728715 191:30:91829244129951402095161225273535061 191:31:476919622739425023784547008678682091 191:32:2384598113697125118922735043393410455 191:33:11489427275086148300264087027259159465 191:34:53392044395988571512991933832557270455 191:35:239501456290577306501135246048899756041 191:36:1037839643925834994838252732878565609511 191:37:4347706616446065518917004691788585661465 191:38:17619653129807739208242597961459005049095 191:39:69123254586168823047720961233416096731065 191:40:262668367427441527581339652686981167578047 191:41:967388377598626113775177745261808690348417 191:42:3454958491423664692054206233077888179815775 191:43:11971832912142466025955272761130356716105825 191:44:40268892522661022087304099287438472590537775 191:45:131545048907359338818526724338965677129090065 191:46:417512546532053553641410907684543236105372815 191:47:1288070622279739686766054927962952536920831025 191:48:3864211866839219060298164783888857610762493075 191:49:11277189733836904604543623757063400782429316525 191:50:32027218844096809076903891470060058222099258931 191:51:88545840333679413330263699946636631555215598221 191:52:238392647052213805119940730625560161879426610595 191:53:625218451702975828522108708621752122664911299485 191:54:1597780487685382672889833366477810980143662209795 191:55:3979925942052680476107403112862910986903304049853 191:56:9665534430699366870546550416952783825336595549643 191:57:22892055230603763640768145724361856428428778933365 191:58:52888541394843178066602267708008426920852696156395 191:59:119223322127358350556916976358730860685989976081365 191:60:262291308680188371225217347989207893509177947379003 191:61:563281335034502895582024140763708754913152641092613 191:62:1181073767007828652026824811278744163527578118419995 191:63:2418389141968411049388260327856476144365993290098085 191:64:4836778283936822098776520655712952288731986580196170 191:65:9450320647076560100686432665777614471830189164383286 191:66:18041521235327978374037735089211809446221270222913546 191:67:33659554543522347712756968450022032548920280266629750 191:68:61379187697011339946792118938275471118619334603854250 191:69:109415073720759345122542472889969318081017074728609750 191:70:190694842770466287213574024179660811512629758812719850 191:71:324986985566569306378062773601957157648284518539987350 191:72:541644975944282177296771289336595262747140864233312250 191:73:882955508731090124634462786726778578998763874572111750 191:74:1407956081490116685227927146402160436781812664858232250 191:75:2196411487124582028955566348387370281379627757178842310 191:76:3352417532979625202090074952801775692632063418851917210 191:77:5006857354450089587537124929509145514969964846337278950 191:78:7317714594965515551015797973897981906494564006185253850 191:79:10467110749760800724870698367727493106758047249353590950 191:80:14653955049665121014818977714818490349461266149095027330 191:81:20081345808800351020307487979566079367780253611722815230 191:82:26938390719122422100412483875027667444583267040115971650 191:83:35376922751618602517409165570819466885055133823766757950 191:84:45484614966366774665240355733910743137928029201985831650 191:85:57257103545896998696243741923864111950097636760146870430 191:86:70572709021686998393044612138716231008259877867157770530 191:87:85173959164104998060571083615692002941003300874155929950 191:88:100660133557578634071584007909454185293912991942184280850 191:89:116494311870006733813181492299705405452506046854437987950 191:90:132026886786007631654939024606332792846173519768363053010 191:91:146535335883371107660976280057578154697401379083567784110 191:92:159277539003664247457582913106063211627610194656051939250 191:93:169553509261965166648394713951615676893907626569345612750 191:94:176768552209282833314283850715514216336201568125487979250 191:95:180489995413688787699847721256893462995911074822866673550 191:96:180489995413688787699847721256893462995911074822866673550 191:97:176768552209282833314283850715514216336201568125487979250 191:98:169553509261965166648394713951615676893907626569345612750 191:99:159277539003664247457582913106063211627610194656051939250 191:100:146535335883371107660976280057578154697401379083567784110 191:101:132026886786007631654939024606332792846173519768363053010 191:102:116494311870006733813181492299705405452506046854437987950 191:103:100660133557578634071584007909454185293912991942184280850 191:104:85173959164104998060571083615692002941003300874155929950 191:105:70572709021686998393044612138716231008259877867157770530 191:106:57257103545896998696243741923864111950097636760146870430 191:107:45484614966366774665240355733910743137928029201985831650 191:108:35376922751618602517409165570819466885055133823766757950 191:109:26938390719122422100412483875027667444583267040115971650 191:110:20081345808800351020307487979566079367780253611722815230 191:111:14653955049665121014818977714818490349461266149095027330 191:112:10467110749760800724870698367727493106758047249353590950 191:113:7317714594965515551015797973897981906494564006185253850 191:114:5006857354450089587537124929509145514969964846337278950 191:115:3352417532979625202090074952801775692632063418851917210 191:116:2196411487124582028955566348387370281379627757178842310 191:117:1407956081490116685227927146402160436781812664858232250 191:118:882955508731090124634462786726778578998763874572111750 191:119:541644975944282177296771289336595262747140864233312250 191:120:324986985566569306378062773601957157648284518539987350 191:121:190694842770466287213574024179660811512629758812719850 191:122:109415073720759345122542472889969318081017074728609750 191:123:61379187697011339946792118938275471118619334603854250 191:124:33659554543522347712756968450022032548920280266629750 191:125:18041521235327978374037735089211809446221270222913546 191:126:9450320647076560100686432665777614471830189164383286 191:127:4836778283936822098776520655712952288731986580196170 191:128:2418389141968411049388260327856476144365993290098085 191:129:1181073767007828652026824811278744163527578118419995 191:130:563281335034502895582024140763708754913152641092613 191:131:262291308680188371225217347989207893509177947379003 191:132:119223322127358350556916976358730860685989976081365 191:133:52888541394843178066602267708008426920852696156395 191:134:22892055230603763640768145724361856428428778933365 191:135:9665534430699366870546550416952783825336595549643 191:136:3979925942052680476107403112862910986903304049853 191:137:1597780487685382672889833366477810980143662209795 191:138:625218451702975828522108708621752122664911299485 191:139:238392647052213805119940730625560161879426610595 191:140:88545840333679413330263699946636631555215598221 191:141:32027218844096809076903891470060058222099258931 191:142:11277189733836904604543623757063400782429316525 191:143:3864211866839219060298164783888857610762493075 191:144:1288070622279739686766054927962952536920831025 191:145:417512546532053553641410907684543236105372815 191:146:131545048907359338818526724338965677129090065 191:147:40268892522661022087304099287438472590537775 191:148:11971832912142466025955272761130356716105825 191:149:3454958491423664692054206233077888179815775 191:150:967388377598626113775177745261808690348417 191:151:262668367427441527581339652686981167578047 191:152:69123254586168823047720961233416096731065 191:153:17619653129807739208242597961459005049095 191:154:4347706616446065518917004691788585661465 191:155:1037839643925834994838252732878565609511 191:156:239501456290577306501135246048899756041 191:157:53392044395988571512991933832557270455 191:158:11489427275086148300264087027259159465 191:159:2384598113697125118922735043393410455 191:160:476919622739425023784547008678682091 191:161:91829244129951402095161225273535061 191:162:17005415579620630017622449124728715 191:163:3025503385331277733196632052865845 191:164:516549358471193759326254252928315 191:165:84526258658922615162477968660997 191:166:13239052561036072254364019187867 191:167:1981894095963483870413775327525 191:168:283127727994783410059110761075 191:169:38532175999290049889701464525 191:170:4986516894025771162196660115 191:171:612379267687375405883800365 191:172:71206891591555279753930275 191:173:7820410059188152111703325 191:174:809007937157395046038275 191:175:78589342466718375900861 191:176:7144485678792579627351 191:177:605464888033269459945 191:178:47620833890257148535 191:179:3458496316052195145 191:180:230566421070146343 191:181:14012323932439833 191:182:769907908375815 191:183:37864323362745 191:184:1646274928815 191:185:62291483793 191:186:2009402703 191:187:53727345 191:188:1143135 191:189:18145 191:190:191 191:191:1 # binomial(192, k) for 0 <= k <= 192 192:0:1 192:1:192 192:2:18336 192:3:1161280 192:4:54870480 192:5:2063130048 192:6:64300886496 192:7:1708566412608 192:8:39510598291560 192:9:807772231738560 192:10:14782231840815648 192:11:244578745002586176 192:12:3689062737122341488 192:13:51079330206309343680 192:14:653085721923526608480 192:15:7749950566825849087296 192:16:85733828145510955528212 192:17:887597279624113421939136 192:18:8629417996345547157741600 192:19:79027301650743431865633600 192:20:683586159278930685637730640 192:21:5598896161713146568080460480 192:22:43518692893315821051898124640 192:23:321659903994073459948812225600 192:24:2265021823958267280472886088600 192:25:15220946656999556124777794515392 192:26:97765311219958687416841987848864 192:27:601075617130116374488732221589312 192:28:3542052743802471492522886305794160 192:29:20030918964951907750819081177594560 192:30:108834659709572032112783674398263776 192:31:568748866869376425879708233952217152 192:32:2861517736436550142707282052072092546 192:33:13874025388783273419186822070652569920 192:34:64881471671074719813256020859816429920 192:35:292893500686565878014127179881457026496 192:36:1277341100216412301339387978927465365552 192:37:5385546260371900513755257424667151270976 192:38:21967359746253804727159602653247590710560 192:39:86742907715976562255963559194875101780160 192:40:331791622013610350629060613920397264309112 192:41:1230056745026067641356517397948789857926464 192:42:4422346869022290805829383978339696870164192 192:43:15426791403566130718009478994208244895921600 192:44:52240725434803488113259372048568829306643600 192:45:171813941430020360905830823626404149719627840 192:46:549057595439412892459937632023508913234462880 192:47:1705583168811793240407465835647495773026203840 192:48:5152282489118958747064219711851810147683324100 192:49:15141401600676123664841788540952258393191809600 192:50:43304408577933713681447515227123459004528575456 192:51:120573059177776222407167591416696689777314857152 192:52:326938487385893218450204430572196793434642208816 192:53:863611098755189633642049439247312284544337910080 192:54:2222998939388358501411942075099563102808573509280 192:55:5577706429738063148997236479340721967046966259648 192:56:13645460372752047346653953529815694812239899599496 192:57:32557589661303130511314696141314640253765374483008 192:58:75780596625446941707370413432370283349281475089760 192:59:172111863522201528623519244066739287606842672237760 192:60:381514630807546721782134324347938754195167923460368 192:61:825572643714691266807241488752916648422330588471616 192:62:1744355102042331547608848952042452918440730759512608 192:63:3599462908976239701415085139135220307893571408518080 192:64:7255167425905233148164780983569428433097979870294255 192:65:14287098931013382199462953321490566760562175744579456 192:66:27491841882404538474724167754989423918051459387296832 192:67:51701075778850326086794703539233841995141550489543296 192:68:95038742240533687659549087388297503667539614870484000 192:69:170794261417770685069334591828244789199636409332464000 192:70:300109916491225632336116497069630129593646833541329600 192:71:515681828337035593591636797781617969160914277352707200 192:72:866631961510851483674834062938552420395425382773299600 192:73:1424600484675372301931234076063373841745904738805424000 192:74:2290911590221206809862389933128939015780576539430344000 192:75:3604367568614698714183493494789530718161440422037074560 192:76:5548829020104207231045641301189145974011691176030759520 192:77:8359274887429714789627199882310921207602028265189196160 192:78:12324571949415605138552922903407127421464528852522532800 192:79:17784825344726316275886496341625475013252611255538844800 192:80:25121065799425921739689676082545983456219313398448618280 192:81:34735300858465472035126465694384569717241519760817842560 192:82:47019736527922773120719971854593746812363520651838786880 192:83:62315313470741024617821649445847134329638400863882729600 192:84:80861537717985377182649521304730210022983163025752589600 192:85:102741718512263773361484097657774855088025665962132702080 192:86:127829812567583997089288354062580342958357514627304640960 192:87:155746668185791996453615695754408233949263178741313700480 192:88:185834092721683632132155091525146188234916292816340210800 192:89:217154445427585367884765500209159590746419038796622268800 192:90:248521198656014365468120516906038198298679566622801040960 192:91:278562222669378739315915304663910947543574898851930837120 192:92:305812874887035355118559193163641366325011573739619723360 192:93:328831048265629414105977627057678888521517821225397552000 192:94:346322061471247999962678564667129893230109194694833592000 192:95:357258547622971621014131571972407679332112642948354652800 192:96:360979990827377575399695442513786925991822149645733347100 192:97:357258547622971621014131571972407679332112642948354652800 192:98:346322061471247999962678564667129893230109194694833592000 192:99:328831048265629414105977627057678888521517821225397552000 192:100:305812874887035355118559193163641366325011573739619723360 192:101:278562222669378739315915304663910947543574898851930837120 192:102:248521198656014365468120516906038198298679566622801040960 192:103:217154445427585367884765500209159590746419038796622268800 192:104:185834092721683632132155091525146188234916292816340210800 192:105:155746668185791996453615695754408233949263178741313700480 192:106:127829812567583997089288354062580342958357514627304640960 192:107:102741718512263773361484097657774855088025665962132702080 192:108:80861537717985377182649521304730210022983163025752589600 192:109:62315313470741024617821649445847134329638400863882729600 192:110:47019736527922773120719971854593746812363520651838786880 192:111:34735300858465472035126465694384569717241519760817842560 192:112:25121065799425921739689676082545983456219313398448618280 192:113:17784825344726316275886496341625475013252611255538844800 192:114:12324571949415605138552922903407127421464528852522532800 192:115:8359274887429714789627199882310921207602028265189196160 192:116:5548829020104207231045641301189145974011691176030759520 192:117:3604367568614698714183493494789530718161440422037074560 192:118:2290911590221206809862389933128939015780576539430344000 192:119:1424600484675372301931234076063373841745904738805424000 192:120:866631961510851483674834062938552420395425382773299600 192:121:515681828337035593591636797781617969160914277352707200 192:122:300109916491225632336116497069630129593646833541329600 192:123:170794261417770685069334591828244789199636409332464000 192:124:95038742240533687659549087388297503667539614870484000 192:125:51701075778850326086794703539233841995141550489543296 192:126:27491841882404538474724167754989423918051459387296832 192:127:14287098931013382199462953321490566760562175744579456 192:128:7255167425905233148164780983569428433097979870294255 192:129:3599462908976239701415085139135220307893571408518080 192:130:1744355102042331547608848952042452918440730759512608 192:131:825572643714691266807241488752916648422330588471616 192:132:381514630807546721782134324347938754195167923460368 192:133:172111863522201528623519244066739287606842672237760 192:134:75780596625446941707370413432370283349281475089760 192:135:32557589661303130511314696141314640253765374483008 192:136:13645460372752047346653953529815694812239899599496 192:137:5577706429738063148997236479340721967046966259648 192:138:2222998939388358501411942075099563102808573509280 192:139:863611098755189633642049439247312284544337910080 192:140:326938487385893218450204430572196793434642208816 192:141:120573059177776222407167591416696689777314857152 192:142:43304408577933713681447515227123459004528575456 192:143:15141401600676123664841788540952258393191809600 192:144:5152282489118958747064219711851810147683324100 192:145:1705583168811793240407465835647495773026203840 192:146:549057595439412892459937632023508913234462880 192:147:171813941430020360905830823626404149719627840 192:148:52240725434803488113259372048568829306643600 192:149:15426791403566130718009478994208244895921600 192:150:4422346869022290805829383978339696870164192 192:151:1230056745026067641356517397948789857926464 192:152:331791622013610350629060613920397264309112 192:153:86742907715976562255963559194875101780160 192:154:21967359746253804727159602653247590710560 192:155:5385546260371900513755257424667151270976 192:156:1277341100216412301339387978927465365552 192:157:292893500686565878014127179881457026496 192:158:64881471671074719813256020859816429920 192:159:13874025388783273419186822070652569920 192:160:2861517736436550142707282052072092546 192:161:568748866869376425879708233952217152 192:162:108834659709572032112783674398263776 192:163:20030918964951907750819081177594560 192:164:3542052743802471492522886305794160 192:165:601075617130116374488732221589312 192:166:97765311219958687416841987848864 192:167:15220946656999556124777794515392 192:168:2265021823958267280472886088600 192:169:321659903994073459948812225600 192:170:43518692893315821051898124640 192:171:5598896161713146568080460480 192:172:683586159278930685637730640 192:173:79027301650743431865633600 192:174:8629417996345547157741600 192:175:887597279624113421939136 192:176:85733828145510955528212 192:177:7749950566825849087296 192:178:653085721923526608480 192:179:51079330206309343680 192:180:3689062737122341488 192:181:244578745002586176 192:182:14782231840815648 192:183:807772231738560 192:184:39510598291560 192:185:1708566412608 192:186:64300886496 192:187:2063130048 192:188:54870480 192:189:1161280 192:190:18336 192:191:192 192:192:1 # binomial(193, k) for 0 <= k <= 193 193:0:1 193:1:193 193:2:18528 193:3:1179616 193:4:56031760 193:5:2118000528 193:6:66364016544 193:7:1772867299104 193:8:41219164704168 193:9:847282830030120 193:10:15590004072554208 193:11:259360976843401824 193:12:3933641482124927664 193:13:54768392943431685168 193:14:704165052129835952160 193:15:8403036288749375695776 193:16:93483778712336804615508 193:17:973331107769624377467348 193:18:9517015275969660579680736 193:19:87656719647088979023375200 193:20:762613460929674117503364240 193:21:6282482320992077253718191120 193:22:49117589055028967619978585120 193:23:365178596887389281000710350240 193:24:2586681727952340740421698314200 193:25:17485968480957823405250680603992 193:26:112986257876958243541619782364256 193:27:698840928350075061905574209438176 193:28:4143128360932587867011618527383472 193:29:23572971708754379243341967483388720 193:30:128865578674523939863602755575858336 193:31:677583526578948457992491908350480928 193:32:3430266603305926568586990286024309698 193:33:16735543125219823561894104122724662466 193:34:78755497059857993232442842930468999840 193:35:357774972357640597827383200741273456416 193:36:1570234600902978179353515158808922392048 193:37:6662887360588312815094645403594616636528 193:38:27352906006625705240914860077914741981536 193:39:108710267462230366983123161848122692490720 193:40:418534529729586912885024173115272366089272 193:41:1561848367039677991985578011869187122235576 193:42:5652403614048358447185901376288486728090656 193:43:19849138272588421523838862972547941766085792 193:44:67667516838369618831268851042777074202565200 193:45:224054666864823849019090195674972979026271440 193:46:720871536869433253365768455649913062954090720 193:47:2254640764251206132867403467671004686260666720 193:48:6857865657930751987471685547499305920709527940 193:49:20293684089795082411906008252804068540875133700 193:50:58445810178609837346289303768075717397720385056 193:51:163877467755709936088615106643820148781843432608 193:52:447511546563669440857372021988893483211957065968 193:53:1190549586141082852092253869819509077978980118896 193:54:3086610038143548135053991514346875387352911419360 193:55:7800705369126421650409178554440285069855539768928 193:56:19223166802490110495651190009156416779286865859144 193:57:46203050034055177857968649671130335066005274082504 193:58:108338186286750072218685109573684923603046849572768 193:59:247892460147648470330889657499109570956124147327520 193:60:553626494329748250405653568414678041802010595698128 193:61:1207087274522237988589375813100855402617498511931984 193:62:2569927745757022814416090440795369566863061347984224 193:63:5343818011018571249023934091177673226334302168030688 193:64:10854630334881472849579866122704648740991551278812335 193:65:21542266356918615347627734305059995193660155614873711 193:66:41778940813417920674187121076479990678613635131876288 193:67:79192917661254864561518871294223265913193009876840128 193:68:146739818019384013746343790927531345662681165360027296 193:69:265833003658304372728883679216542292867176024202948000 193:70:470904177908996317405451088897874918793283242873793600 193:71:815791744828261225927753294851248098754561110894036800 193:72:1382313789847887077266470860720170389556339660126006800 193:73:2291232446186223785606068139001926262141330121578723600 193:74:3715512074896579111793624009192312857526481278235768000 193:75:5895279158835905524045883427918469733942016961467418560 193:76:9153196588718905945229134795978676692173131598067834080 193:77:13908103907533922020672841183500067181613719441219955680 193:78:20683846836845319928180122785718048629066557117711728960 193:79:30109397294141921414439419245032602434717140108061377600 193:80:42905891144152238015576172424171458469471924653987463080 193:81:59856366657891393774816141776930553173460833159266460840 193:82:81755037386388245155846437548978316529605040412656629440 193:83:109335049998663797738541621300440881142001921515721516480 193:84:143176851188726401800471170750577344352621563889635319200 193:85:183603256230249150544133618962505065111008828987885291680 193:86:230571531079847770450772451720355198046383180589437343040 193:87:283576480753375993542904049816988576907620693368618341440 193:88:341580760907475628585770787279554422184179471557653911280 193:89:402988538149269000016920591734305778981335331612962479600 193:90:465675644083599733352886017115197789045098605419423309760 193:91:527083421325393104784035821569949145842254465474731878080 193:92:584375097556414094434474497827552313868586472591550560480 193:93:634643923152664769224536820221320254846529394965017275360 193:94:675153109736877414068656191724808781751627015920231144000 193:95:703580609094219620976810136639537572562221837643188244800 193:96:718238538450349196413827014486194605323934792594087999900 193:97:718238538450349196413827014486194605323934792594087999900 193:98:703580609094219620976810136639537572562221837643188244800 193:99:675153109736877414068656191724808781751627015920231144000 193:100:634643923152664769224536820221320254846529394965017275360 193:101:584375097556414094434474497827552313868586472591550560480 193:102:527083421325393104784035821569949145842254465474731878080 193:103:465675644083599733352886017115197789045098605419423309760 193:104:402988538149269000016920591734305778981335331612962479600 193:105:341580760907475628585770787279554422184179471557653911280 193:106:283576480753375993542904049816988576907620693368618341440 193:107:230571531079847770450772451720355198046383180589437343040 193:108:183603256230249150544133618962505065111008828987885291680 193:109:143176851188726401800471170750577344352621563889635319200 193:110:109335049998663797738541621300440881142001921515721516480 193:111:81755037386388245155846437548978316529605040412656629440 193:112:59856366657891393774816141776930553173460833159266460840 193:113:42905891144152238015576172424171458469471924653987463080 193:114:30109397294141921414439419245032602434717140108061377600 193:115:20683846836845319928180122785718048629066557117711728960 193:116:13908103907533922020672841183500067181613719441219955680 193:117:9153196588718905945229134795978676692173131598067834080 193:118:5895279158835905524045883427918469733942016961467418560 193:119:3715512074896579111793624009192312857526481278235768000 193:120:2291232446186223785606068139001926262141330121578723600 193:121:1382313789847887077266470860720170389556339660126006800 193:122:815791744828261225927753294851248098754561110894036800 193:123:470904177908996317405451088897874918793283242873793600 193:124:265833003658304372728883679216542292867176024202948000 193:125:146739818019384013746343790927531345662681165360027296 193:126:79192917661254864561518871294223265913193009876840128 193:127:41778940813417920674187121076479990678613635131876288 193:128:21542266356918615347627734305059995193660155614873711 193:129:10854630334881472849579866122704648740991551278812335 193:130:5343818011018571249023934091177673226334302168030688 193:131:2569927745757022814416090440795369566863061347984224 193:132:1207087274522237988589375813100855402617498511931984 193:133:553626494329748250405653568414678041802010595698128 193:134:247892460147648470330889657499109570956124147327520 193:135:108338186286750072218685109573684923603046849572768 193:136:46203050034055177857968649671130335066005274082504 193:137:19223166802490110495651190009156416779286865859144 193:138:7800705369126421650409178554440285069855539768928 193:139:3086610038143548135053991514346875387352911419360 193:140:1190549586141082852092253869819509077978980118896 193:141:447511546563669440857372021988893483211957065968 193:142:163877467755709936088615106643820148781843432608 193:143:58445810178609837346289303768075717397720385056 193:144:20293684089795082411906008252804068540875133700 193:145:6857865657930751987471685547499305920709527940 193:146:2254640764251206132867403467671004686260666720 193:147:720871536869433253365768455649913062954090720 193:148:224054666864823849019090195674972979026271440 193:149:67667516838369618831268851042777074202565200 193:150:19849138272588421523838862972547941766085792 193:151:5652403614048358447185901376288486728090656 193:152:1561848367039677991985578011869187122235576 193:153:418534529729586912885024173115272366089272 193:154:108710267462230366983123161848122692490720 193:155:27352906006625705240914860077914741981536 193:156:6662887360588312815094645403594616636528 193:157:1570234600902978179353515158808922392048 193:158:357774972357640597827383200741273456416 193:159:78755497059857993232442842930468999840 193:160:16735543125219823561894104122724662466 193:161:3430266603305926568586990286024309698 193:162:677583526578948457992491908350480928 193:163:128865578674523939863602755575858336 193:164:23572971708754379243341967483388720 193:165:4143128360932587867011618527383472 193:166:698840928350075061905574209438176 193:167:112986257876958243541619782364256 193:168:17485968480957823405250680603992 193:169:2586681727952340740421698314200 193:170:365178596887389281000710350240 193:171:49117589055028967619978585120 193:172:6282482320992077253718191120 193:173:762613460929674117503364240 193:174:87656719647088979023375200 193:175:9517015275969660579680736 193:176:973331107769624377467348 193:177:93483778712336804615508 193:178:8403036288749375695776 193:179:704165052129835952160 193:180:54768392943431685168 193:181:3933641482124927664 193:182:259360976843401824 193:183:15590004072554208 193:184:847282830030120 193:185:41219164704168 193:186:1772867299104 193:187:66364016544 193:188:2118000528 193:189:56031760 193:190:1179616 193:191:18528 193:192:193 193:193:1 # binomial(194, k) for 0 <= k <= 194 194:0:1 194:1:194 194:2:18721 194:3:1198144 194:4:57211376 194:5:2174032288 194:6:68482017072 194:7:1839231315648 194:8:42992032003272 194:9:888501994734288 194:10:16437286902584328 194:11:274950980915956032 194:12:4193002458968329488 194:13:58702034425556612832 194:14:758933445073267637328 194:15:9107201340879211647936 194:16:101886815001086180311284 194:17:1066814886481961182082856 194:18:10490346383739284957148084 194:19:97173734923058639603055936 194:20:850270180576763096526739440 194:21:7045095781921751371221555360 194:22:55400071376021044873696776240 194:23:414296185942418248620688935360 194:24:2951860324839730021422408664440 194:25:20072650208910164145672378918192 194:26:130472226357916066946870462968248 194:27:811827186227033305447193991802432 194:28:4841969289282662928917192736821648 194:29:27716100069686967110353586010772192 194:30:152438550383278319106944723059247056 194:31:806449105253472397856094663926339264 194:32:4107850129884875026579482194374790626 194:33:20165809728525750130481094408748972164 194:34:95491040185077816794336947053193662306 194:35:436530469417498591059826043671742456256 194:36:1928009573260618777180898359550195848464 194:37:8233121961491290994448160562403539028576 194:38:34015793367214018056009505481509358618064 194:39:136063173468856072224038021926037434472256 194:40:527244797191817279868147334963395058579992 194:41:1980382896769264904870602184984459488324848 194:42:7214251981088036439171479388157673850326232 194:43:25501541886636779971024764348836428494176448 194:44:87516655110958040355107714015325015968650992 194:45:291722183703193467850359046717750053228836640 194:46:944926203734257102384858651324886041980362160 194:47:2975512301120639386233171923320917749214757440 194:48:9112506422181958120339089015170310606970194660 194:49:27151549747725834399377693800303374461584661640 194:50:78739494268404919758195312020879785938595518756 194:51:222323277934319773434904410411895866179563817664 194:52:611389014319379376945987128632713631993800498576 194:53:1638061132704752292949625891808402561190937184864 194:54:4277159624284630987146245384166384465331891538256 194:55:10887315407269969785463170068787160457208451188288 194:56:27023872171616532146060368563596701849142405628072 194:57:65426216836545288353619839680286751845292139941648 194:58:154541236320805250076653759244815258669052123655272 194:59:356230646434398542549574767072794494559170996900288 194:60:801518954477396720736543225913787612758134743025648 194:61:1760713768851986238995029381515533444419509107630112 194:62:3777015020279260803005466253896224969480559859916208 194:63:7913745756775594063440024531973042793197363516014912 194:64:16198448345900044098603800213882321967325853446843023 194:65:32396896691800088197207600427764643934651706893686046 194:66:63321207170336536021814855381539985872273790746749999 194:67:120971858474672785235705992370703256591806645008716416 194:68:225932735680638878307862662221754611575874175236867424 194:69:412572821677688386475227470144073638529857189562975296 194:70:736737181567300690134334768114417211660459267076741600 194:71:1286695922737257543333204383749123017547844353767830400 194:72:2198105534676148303194224155571418488310900771020043600 194:73:3673546236034110862872538999722096651697669781704730400 194:74:6006744521082802897399692148194239119667811399814491600 194:75:9610791233732484635839507437110782591468498239703186560 194:76:15048475747554811469275018223897146426115148559535252640 194:77:23061300496252827965901975979478743873786851039287789760 194:78:34591950744379241948852963969218115810680276558931684640 194:79:50793244130987241342619542030750651063783697225773106560 194:80:73015288438294159430015591669204060904189064762048840680 194:81:102762257802043631790392314201102011642932757813253923920 194:82:141611404044279638930662579325908869703065873571923090280 194:83:191090087385052042894388058849419197671606961928378145920 194:84:252511901187390199539012792051018225494623485405356835680 194:85:326780107418975552344604789713082409463630392877520610880 194:86:414174787310096920994906070682860263157392009577322634720 194:87:514148011833223763993676501537343774954003873958055684480 194:88:625157241660851622128674837096542999091800164926272252720 194:89:744569299056744628602691379013860201165514803170616390880 194:90:868664182232868733369806608849503568026433937032385789360 194:91:992759065408992838136921838685146934887353070894155187840 194:92:1111458518881807199218510319397501459710840938066282438560 194:93:1219019020709078863659011318048872568715115867556567835840 194:94:1309797032889542183293193011946129036598156410885248419360 194:95:1378733718831097035045466328364346354313848853563419388800 194:96:1421819147544568817390637151125732177886156630237276244700 194:97:1436477076900698392827654028972389210647869585188175999800 194:98:1421819147544568817390637151125732177886156630237276244700 194:99:1378733718831097035045466328364346354313848853563419388800 194:100:1309797032889542183293193011946129036598156410885248419360 194:101:1219019020709078863659011318048872568715115867556567835840 194:102:1111458518881807199218510319397501459710840938066282438560 194:103:992759065408992838136921838685146934887353070894155187840 194:104:868664182232868733369806608849503568026433937032385789360 194:105:744569299056744628602691379013860201165514803170616390880 194:106:625157241660851622128674837096542999091800164926272252720 194:107:514148011833223763993676501537343774954003873958055684480 194:108:414174787310096920994906070682860263157392009577322634720 194:109:326780107418975552344604789713082409463630392877520610880 194:110:252511901187390199539012792051018225494623485405356835680 194:111:191090087385052042894388058849419197671606961928378145920 194:112:141611404044279638930662579325908869703065873571923090280 194:113:102762257802043631790392314201102011642932757813253923920 194:114:73015288438294159430015591669204060904189064762048840680 194:115:50793244130987241342619542030750651063783697225773106560 194:116:34591950744379241948852963969218115810680276558931684640 194:117:23061300496252827965901975979478743873786851039287789760 194:118:15048475747554811469275018223897146426115148559535252640 194:119:9610791233732484635839507437110782591468498239703186560 194:120:6006744521082802897399692148194239119667811399814491600 194:121:3673546236034110862872538999722096651697669781704730400 194:122:2198105534676148303194224155571418488310900771020043600 194:123:1286695922737257543333204383749123017547844353767830400 194:124:736737181567300690134334768114417211660459267076741600 194:125:412572821677688386475227470144073638529857189562975296 194:126:225932735680638878307862662221754611575874175236867424 194:127:120971858474672785235705992370703256591806645008716416 194:128:63321207170336536021814855381539985872273790746749999 194:129:32396896691800088197207600427764643934651706893686046 194:130:16198448345900044098603800213882321967325853446843023 194:131:7913745756775594063440024531973042793197363516014912 194:132:3777015020279260803005466253896224969480559859916208 194:133:1760713768851986238995029381515533444419509107630112 194:134:801518954477396720736543225913787612758134743025648 194:135:356230646434398542549574767072794494559170996900288 194:136:154541236320805250076653759244815258669052123655272 194:137:65426216836545288353619839680286751845292139941648 194:138:27023872171616532146060368563596701849142405628072 194:139:10887315407269969785463170068787160457208451188288 194:140:4277159624284630987146245384166384465331891538256 194:141:1638061132704752292949625891808402561190937184864 194:142:611389014319379376945987128632713631993800498576 194:143:222323277934319773434904410411895866179563817664 194:144:78739494268404919758195312020879785938595518756 194:145:27151549747725834399377693800303374461584661640 194:146:9112506422181958120339089015170310606970194660 194:147:2975512301120639386233171923320917749214757440 194:148:944926203734257102384858651324886041980362160 194:149:291722183703193467850359046717750053228836640 194:150:87516655110958040355107714015325015968650992 194:151:25501541886636779971024764348836428494176448 194:152:7214251981088036439171479388157673850326232 194:153:1980382896769264904870602184984459488324848 194:154:527244797191817279868147334963395058579992 194:155:136063173468856072224038021926037434472256 194:156:34015793367214018056009505481509358618064 194:157:8233121961491290994448160562403539028576 194:158:1928009573260618777180898359550195848464 194:159:436530469417498591059826043671742456256 194:160:95491040185077816794336947053193662306 194:161:20165809728525750130481094408748972164 194:162:4107850129884875026579482194374790626 194:163:806449105253472397856094663926339264 194:164:152438550383278319106944723059247056 194:165:27716100069686967110353586010772192 194:166:4841969289282662928917192736821648 194:167:811827186227033305447193991802432 194:168:130472226357916066946870462968248 194:169:20072650208910164145672378918192 194:170:2951860324839730021422408664440 194:171:414296185942418248620688935360 194:172:55400071376021044873696776240 194:173:7045095781921751371221555360 194:174:850270180576763096526739440 194:175:97173734923058639603055936 194:176:10490346383739284957148084 194:177:1066814886481961182082856 194:178:101886815001086180311284 194:179:9107201340879211647936 194:180:758933445073267637328 194:181:58702034425556612832 194:182:4193002458968329488 194:183:274950980915956032 194:184:16437286902584328 194:185:888501994734288 194:186:42992032003272 194:187:1839231315648 194:188:68482017072 194:189:2174032288 194:190:57211376 194:191:1198144 194:192:18721 194:193:194 194:194:1 # binomial(195, k) for 0 <= k <= 195 195:0:1 195:1:195 195:2:18915 195:3:1216865 195:4:58409520 195:5:2231243664 195:6:70656049360 195:7:1907713332720 195:8:44831263318920 195:9:931494026737560 195:10:17325788897318616 195:11:291388267818540360 195:12:4467953439884285520 195:13:62895036884524942320 195:14:817635479498824250160 195:15:9866134785952479285264 195:16:110994016341965391959220 195:17:1168701701483047362394140 195:18:11557161270221246139230940 195:19:107664081306797924560204020 195:20:947443915499821736129795376 195:21:7895365962498514467748294800 195:22:62445167157942796244918331600 195:23:469696257318439293494385711600 195:24:3366156510782148270043097599800 195:25:23024510533749894167094787582632 195:26:150544876566826231092542841886440 195:27:942299412584949372394064454770680 195:28:5653796475509696234364386728624080 195:29:32558069358969630039270778747593840 195:30:180154650452965286217298309070019248 195:31:958887655636750716963039386985586320 195:32:4914299235138347424435576858301129890 195:33:24273659858410625157060576603123762790 195:34:115656849913603566924818041461942634470 195:35:532021509602576407854162990724936118562 195:36:2364540042678117368240724403221938304720 195:37:10161131534751909771629058921953734877040 195:38:42248915328705309050457666043912897646640 195:39:170078966836070090280047527407546793090320 195:40:663307970660673352092185356889432493052248 195:41:2507627693961082184738749519947854546904840 195:42:9194634877857301344042081573142133338651080 195:43:32715793867724816410196243736994102344502680 195:44:113018196997594820326132478364161444462827440 195:45:379238838814151508205466760733075069197487632 195:46:1236648387437450570235217698042636095209198800 195:47:3920438504854896488618030574645803791195119600 195:48:12088018723302597506572260938491228356184952100 195:49:36264056169907792519716782815473685068554856300 195:50:105891044016130754157573005821183160400180180396 195:51:301062772202724693193099722432775652118159336420 195:52:833712292253699150380891539044609498173364316240 195:53:2249450147024131669895613020441116193184737683440 195:54:5915220756989383280095871275974787026522828723120 195:55:15164475031554600772609415452953544922540342726544 195:56:37911187578886501931523538632383862306350856816360 195:57:92450089008161820499680208243883453694434545569720 195:58:219967453157350538430273598925102010514344263596920 195:59:510771882755203792626228526317609753228223120555560 195:60:1157749600911795263286117992986582107317305739925936 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195:122:5871651770710259166066763155293515140008570552724774000 195:123:3484801457413405846527428539320541505858745124787874000 195:124:2023433104304558233467539151863540229208303620844572000 195:125:1149310003244989076609562238258490850190316456639716896 195:126:638505557358327264783090132365828250105731364799842720 195:127:346904594155311663543568654592457868167680820245583840 195:128:184293065645009321257520847752243242464080435755466415 195:129:95718103862136624219022455809304629806925497640436045 195:130:48595345037700132295811400641646965901977560340529069 195:131:24112194102675638162043824745855364760523216962857935 195:132:11690760777054854866445490785869267762677923375931120 195:133:5537728789131247042000495635411758413900068967546320 195:134:2562232723329382959731572607429321057177643850655760 195:135:1157749600911795263286117992986582107317305739925936 195:136:510771882755203792626228526317609753228223120555560 195:137:219967453157350538430273598925102010514344263596920 195:138:92450089008161820499680208243883453694434545569720 195:139:37911187578886501931523538632383862306350856816360 195:140:15164475031554600772609415452953544922540342726544 195:141:5915220756989383280095871275974787026522828723120 195:142:2249450147024131669895613020441116193184737683440 195:143:833712292253699150380891539044609498173364316240 195:144:301062772202724693193099722432775652118159336420 195:145:105891044016130754157573005821183160400180180396 195:146:36264056169907792519716782815473685068554856300 195:147:12088018723302597506572260938491228356184952100 195:148:3920438504854896488618030574645803791195119600 195:149:1236648387437450570235217698042636095209198800 195:150:379238838814151508205466760733075069197487632 195:151:113018196997594820326132478364161444462827440 195:152:32715793867724816410196243736994102344502680 195:153:9194634877857301344042081573142133338651080 195:154:2507627693961082184738749519947854546904840 195:155:663307970660673352092185356889432493052248 195:156:170078966836070090280047527407546793090320 195:157:42248915328705309050457666043912897646640 195:158:10161131534751909771629058921953734877040 195:159:2364540042678117368240724403221938304720 195:160:532021509602576407854162990724936118562 195:161:115656849913603566924818041461942634470 195:162:24273659858410625157060576603123762790 195:163:4914299235138347424435576858301129890 195:164:958887655636750716963039386985586320 195:165:180154650452965286217298309070019248 195:166:32558069358969630039270778747593840 195:167:5653796475509696234364386728624080 195:168:942299412584949372394064454770680 195:169:150544876566826231092542841886440 195:170:23024510533749894167094787582632 195:171:3366156510782148270043097599800 195:172:469696257318439293494385711600 195:173:62445167157942796244918331600 195:174:7895365962498514467748294800 195:175:947443915499821736129795376 195:176:107664081306797924560204020 195:177:11557161270221246139230940 195:178:1168701701483047362394140 195:179:110994016341965391959220 195:180:9866134785952479285264 195:181:817635479498824250160 195:182:62895036884524942320 195:183:4467953439884285520 195:184:291388267818540360 195:185:17325788897318616 195:186:931494026737560 195:187:44831263318920 195:188:1907713332720 195:189:70656049360 195:190:2231243664 195:191:58409520 195:192:1216865 195:193:18915 195:194:195 195:195:1 # binomial(196, k) for 0 <= k <= 196 196:0:1 196:1:196 196:2:19110 196:3:1235780 196:4:59626385 196:5:2289653184 196:6:72887293024 196:7:1978369382080 196:8:46738976651640 196:9:976325290056480 196:10:18257282924056176 196:11:308714056715858976 196:12:4759341707702825880 196:13:67362990324409227840 196:14:880530516383349192480 196:15:10683770265451303535424 196:16:120860151127917871244484 196:17:1279695717825012754353360 196:18:12725862971704293501625080 196:19:119221242577019170699434960 196:20:1055107996806619660689999396 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196:43:41910428745582117754238325310136235683153760 196:44:145733990865319636736328722101155546807330120 196:45:492257035811746328531599239097236513660315072 196:46:1615887226251602078440684458775711164406686432 196:47:5157086892292347058853248272688439886404318400 196:48:16008457228157493995190291513137032147380071700 196:49:48352074893210390026289043753964913424739808400 196:50:142155100186038546677289788636656845468735036696 196:51:406953816218855447350672728253958812518339516816 196:52:1134775064456423843573991261477385150291523652660 196:53:3083162439277830820276504559485725691358101999680 196:54:8164670904013514949991484296415903219707566406560 196:55:21079695788543984052705286728928331949063171449664 196:56:53075662610441102704132954085337407228891199542904 196:57:130361276587048322431203746876267316000785402386080 196:58:312417542165512358929953807168985464208778809166640 196:59:730739335912554331056502125242711763742567384152480 196:60:1668521483666999055912346519304191860545528860481496 196:61:3719982324241178223017690600415903164494949590581696 196:62:8099961512460630001732068242841079471077712818202080 196:63:17228489566186101908445986421281026176577992343477440 196:64:35802954879730493028489315531724632523201140338789055 196:65:72707539140375770457855225387502330662500777303387004 196:66:144313448899836756514833856450951595708903057980965114 196:67:280011169507145945476543303561547872271005933395902460 196:68:531197659800320984801089502344701110631761256001050255 196:69:985410151513638928326658786958286118273412185045426560 196:70:1787815560603316341392652370624319100296047821439559616 196:71:3172743107549547310077101390122031079398620077484288896 196:72:5508234561717964079994967691184081735067048745632446000 196:73:9356453228123665012594191694614056645867315677512648000 196:74:15551942527827172926338994303209850911374051734243996000 196:75:25297826511932201293511430733221357482501790821036900160 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196:106:2982960022007209612703864203973766969449263708299890823840 196:107:2509031794211671636853717554744289974303119006981216580800 196:108:2067628052637396071110933910854090812157199922419706256400 196:109:1669277693872393158328093432616146710732418285990221564800 196:110:1320246903335438225223128442160043307579276280737720692160 196:111:1022893997178807994317018432664538058124484325616612428160 196:112:776303480001773924258451489075765490540903282834036217800 196:113:577075153275654952546105531702338948720671466885478250400 196:114:420151208086661061941462799397316953893120453960479778800 196:115:299586078809619191993043039570260784515094584563124711840 196:116:209193727444647884064107639699923478842436735772526738440 196:117:143038446115998553206227445948665626558931101382924265600 196:118:95763027484439709349931934152072749984369127197042516800 196:119:62769043225094935540291519864383819317485646398061481600 196:120:40276802736102583638353725246312950728719956438756117360 196:121:25297826511932201293511430733221357482501790821036900160 196:122:15551942527827172926338994303209850911374051734243996000 196:123:9356453228123665012594191694614056645867315677512648000 196:124:5508234561717964079994967691184081735067048745632446000 196:125:3172743107549547310077101390122031079398620077484288896 196:126:1787815560603316341392652370624319100296047821439559616 196:127:985410151513638928326658786958286118273412185045426560 196:128:531197659800320984801089502344701110631761256001050255 196:129:280011169507145945476543303561547872271005933395902460 196:130:144313448899836756514833856450951595708903057980965114 196:131:72707539140375770457855225387502330662500777303387004 196:132:35802954879730493028489315531724632523201140338789055 196:133:17228489566186101908445986421281026176577992343477440 196:134:8099961512460630001732068242841079471077712818202080 196:135:3719982324241178223017690600415903164494949590581696 196:136:1668521483666999055912346519304191860545528860481496 196:137:730739335912554331056502125242711763742567384152480 196:138:312417542165512358929953807168985464208778809166640 196:139:130361276587048322431203746876267316000785402386080 196:140:53075662610441102704132954085337407228891199542904 196:141:21079695788543984052705286728928331949063171449664 196:142:8164670904013514949991484296415903219707566406560 196:143:3083162439277830820276504559485725691358101999680 196:144:1134775064456423843573991261477385150291523652660 196:145:406953816218855447350672728253958812518339516816 196:146:142155100186038546677289788636656845468735036696 196:147:48352074893210390026289043753964913424739808400 196:148:16008457228157493995190291513137032147380071700 196:149:5157086892292347058853248272688439886404318400 196:150:1615887226251602078440684458775711164406686432 196:151:492257035811746328531599239097236513660315072 196:152:145733990865319636736328722101155546807330120 196:153:41910428745582117754238325310136235683153760 196:154:11702262571818383528780831093089987885555920 196:155:3170935664621755536830934876837287039957088 196:156:833386937496743442372232884296979286142568 196:157:212327882164775399330505193451459690736960 196:158:52410046863457218822086724965866632523680 196:159:12525671577430027139869783325175673181760 196:160:2896561552280693776094887393946874423282 196:161:647678359516179974778981032186878753032 196:162:139930509772014192081878618065066397260 196:163:29187959093548972581496153461424892680 196:164:5873186890775098141398616245286716210 196:165:1139042306089716003180337696055605568 196:166:212712719811934916256569087817613088 196:167:38211865834479326273635165476217920 196:168:6596095888094645606758451183394760 196:169:1092844289151775603486607296657120 196:170:173569387100576125259637629469072 196:171:26390667044532042437137885182432 196:172:3835852768100587563537483311400 196:173:532141424476382089739304043200 196:174:70340533120441310712666626400 196:175:8842809877998336203878090176 196:176:1055107996806619660689999396 196:177:119221242577019170699434960 196:178:12725862971704293501625080 196:179:1279695717825012754353360 196:180:120860151127917871244484 196:181:10683770265451303535424 196:182:880530516383349192480 196:183:67362990324409227840 196:184:4759341707702825880 196:185:308714056715858976 196:186:18257282924056176 196:187:976325290056480 196:188:46738976651640 196:189:1978369382080 196:190:72887293024 196:191:2289653184 196:192:59626385 196:193:1235780 196:194:19110 196:195:196 196:196:1 # binomial(197, k) for 0 <= k <= 197 197:0:1 197:1:197 197:2:19306 197:3:1254890 197:4:60862165 197:5:2349279569 197:6:75176946208 197:7:2051256675104 197:8:48717346033720 197:9:1023064266708120 197:10:19233608214112656 197:11:326971339639915152 197:12:5068055764418684856 197:13:72122332032112053720 197:14:947893506707758420320 197:15:11564300781834652727904 197:16:131543921393369174779908 197:17:1400555868952930625597844 197:18:14005558689529306255978440 197:19:131947105548723464201060040 197:20:1174329239383638831389434356 197:21:9897917874804955864568089572 197:22:79183342998439646916544716576 197:23:602481957596823400451970669600 197:24:4367994192576969653276787354600 197:25:30226519812632630000675368493832 197:26:199960054145108167696775514651504 197:27:1266413676252351728746244926126192 197:28:7688940177246421210245058480051880 197:29:44807961722573971880393616659612680 197:30:250924585646414242530204253293831008 197:31:1351755025901650919436906783873218656 197:32:7012229196864814144578953941342321778 197:33:35061145984324070722894769706711608890 197:34:169118468865563164663374771526491289940 197:35:787608869288194166860859650251945150292 197:36:3544239911796873750873868426133753176314 197:37:15422233129710720915964670719122547605042 197:38:64935718440887245961956508291042305705440 197:39:264737929028232618152591918417326323260640 197:40:1045714819661518841702738077748438976879528 197:41:4004322602118498979203167761134266326099656 197:42:14873198236440139065611765969927274925513008 197:43:53612691317400501283019156403226223568709680 197:44:187644419610901754490567047411291782490483880 197:45:637991026677065965267927961198392060467645192 197:46:2108144262063348406972283697872947678067001504 197:47:6772974118543949137293932731464151050811004832 197:48:21165544120449841054043539785825472033784390100 197:49:64360532121367884021479335267101945572119880100 197:50:190507175079248936703578832390621758893474845096 197:51:549108916404893994027962516890615657987074553512 197:52:1541728880675279290924663989731343962809863169476 197:53:4217937503734254663850495820963110841649625652340 197:54:11247833343291345770267988855901628911065668406240 197:55:29244366692557499002696771025344235168770737856224 197:56:74155358398985086756838240814265739177954370992568 197:57:183436939197489425135336700961604723229676601928984 197:58:442778818752560681361157554045252780209564211552720 197:59:1043156878078066689986455932411697227951346193319120 197:60:2399260819579553386968848644546903624288096244633976 197:61:5388503807908177278930037119720095025040478451063192 197:62:11819943836701808224749758843256982635572662408783776 197:63:25328451078646731910178054664122105647655705161679520 197:64:53031444445916594936935301953005658699779132682266495 197:65:108510494020106263486344540919226963185701917642176059 197:66:217020988040212526972689081838453926371403835284352118 197:67:424324618406982701991377160012499467979908991376867574 197:68:811208829307466930277632805906248982902767189396952715 197:69:1516607811313959913127748289302987228905173441046476815 197:70:2773225712116955269719311157582605218569460006484986176 197:71:4960558668152863651469753760746350179694667898923848512 197:72:8680977669267511390072069081306112814465668823116734896 197:73:14864687789841629092589159385798138380934364423145094000 197:74:24908395755950837938933185997823907557241367411756644000 197:75:40849769039759374219850425036431208393875842555280896160 197:76:65574629248034784931865155979534308211221747259793017520 197:77:103045845961197519178645245110696770046205602836817598960 197:78:158532070709534644890223454016456569301854773595103998400 197:79:238801473600438262556159380100738376543300228579966782400 197:80:352232173560646437270335085648589105401367837155451004040 197:81:508779806254267076057150679270184263357531320335651450280 197:82:719737286896280253934505838967577738408215038523604490640 197:83:997226361362316014487568331099655902613791920845958029200 197:84:1353378633277428876804557020778104439261574749719514468200 197:85:1799197477180581918575469921740303548665387608450648645960 197:86:2343140900514246219540146874824581365703760606354333120320 197:87:2989524597207831383551221874776190018311694566727942256960 197:88:3736905746509789229439027343470237522889618208409927821200 197:89:4576659846849067707964651465598380786460318929400922837200 197:90:5491991816218881249557581758718056943752382715281107404640 197:91:6457616750938684546183090639371781241554999456429433981280 197:92:7440297560864136542341387041015313169617716765016521761040 197:93:8400335955814347709095114401146321320536131831470266504400 197:94:9293988717071193210062679762970398056763379898647954430400 197:95:10076640398508767375120589637746852629964506626955150592960 197:96:10706430423415565336065626490106030919337288291139847505020 197:97:11147932708917238133429157479388753843846042447475511319660 197:98:11375441539711467483090977019784442697802084130077052367000 197:99:11375441539711467483090977019784442697802084130077052367000 197:100:11147932708917238133429157479388753843846042447475511319660 197:101:10706430423415565336065626490106030919337288291139847505020 197:102:10076640398508767375120589637746852629964506626955150592960 197:103:9293988717071193210062679762970398056763379898647954430400 197:104:8400335955814347709095114401146321320536131831470266504400 197:105:7440297560864136542341387041015313169617716765016521761040 197:106:6457616750938684546183090639371781241554999456429433981280 197:107:5491991816218881249557581758718056943752382715281107404640 197:108:4576659846849067707964651465598380786460318929400922837200 197:109:3736905746509789229439027343470237522889618208409927821200 197:110:2989524597207831383551221874776190018311694566727942256960 197:111:2343140900514246219540146874824581365703760606354333120320 197:112:1799197477180581918575469921740303548665387608450648645960 197:113:1353378633277428876804557020778104439261574749719514468200 197:114:997226361362316014487568331099655902613791920845958029200 197:115:719737286896280253934505838967577738408215038523604490640 197:116:508779806254267076057150679270184263357531320335651450280 197:117:352232173560646437270335085648589105401367837155451004040 197:118:238801473600438262556159380100738376543300228579966782400 197:119:158532070709534644890223454016456569301854773595103998400 197:120:103045845961197519178645245110696770046205602836817598960 197:121:65574629248034784931865155979534308211221747259793017520 197:122:40849769039759374219850425036431208393875842555280896160 197:123:24908395755950837938933185997823907557241367411756644000 197:124:14864687789841629092589159385798138380934364423145094000 197:125:8680977669267511390072069081306112814465668823116734896 197:126:4960558668152863651469753760746350179694667898923848512 197:127:2773225712116955269719311157582605218569460006484986176 197:128:1516607811313959913127748289302987228905173441046476815 197:129:811208829307466930277632805906248982902767189396952715 197:130:424324618406982701991377160012499467979908991376867574 197:131:217020988040212526972689081838453926371403835284352118 197:132:108510494020106263486344540919226963185701917642176059 197:133:53031444445916594936935301953005658699779132682266495 197:134:25328451078646731910178054664122105647655705161679520 197:135:11819943836701808224749758843256982635572662408783776 197:136:5388503807908177278930037119720095025040478451063192 197:137:2399260819579553386968848644546903624288096244633976 197:138:1043156878078066689986455932411697227951346193319120 197:139:442778818752560681361157554045252780209564211552720 197:140:183436939197489425135336700961604723229676601928984 197:141:74155358398985086756838240814265739177954370992568 197:142:29244366692557499002696771025344235168770737856224 197:143:11247833343291345770267988855901628911065668406240 197:144:4217937503734254663850495820963110841649625652340 197:145:1541728880675279290924663989731343962809863169476 197:146:549108916404893994027962516890615657987074553512 197:147:190507175079248936703578832390621758893474845096 197:148:64360532121367884021479335267101945572119880100 197:149:21165544120449841054043539785825472033784390100 197:150:6772974118543949137293932731464151050811004832 197:151:2108144262063348406972283697872947678067001504 197:152:637991026677065965267927961198392060467645192 197:153:187644419610901754490567047411291782490483880 197:154:53612691317400501283019156403226223568709680 197:155:14873198236440139065611765969927274925513008 197:156:4004322602118498979203167761134266326099656 197:157:1045714819661518841702738077748438976879528 197:158:264737929028232618152591918417326323260640 197:159:64935718440887245961956508291042305705440 197:160:15422233129710720915964670719122547605042 197:161:3544239911796873750873868426133753176314 197:162:787608869288194166860859650251945150292 197:163:169118468865563164663374771526491289940 197:164:35061145984324070722894769706711608890 197:165:7012229196864814144578953941342321778 197:166:1351755025901650919436906783873218656 197:167:250924585646414242530204253293831008 197:168:44807961722573971880393616659612680 197:169:7688940177246421210245058480051880 197:170:1266413676252351728746244926126192 197:171:199960054145108167696775514651504 197:172:30226519812632630000675368493832 197:173:4367994192576969653276787354600 197:174:602481957596823400451970669600 197:175:79183342998439646916544716576 197:176:9897917874804955864568089572 197:177:1174329239383638831389434356 197:178:131947105548723464201060040 197:179:14005558689529306255978440 197:180:1400555868952930625597844 197:181:131543921393369174779908 197:182:11564300781834652727904 197:183:947893506707758420320 197:184:72122332032112053720 197:185:5068055764418684856 197:186:326971339639915152 197:187:19233608214112656 197:188:1023064266708120 197:189:48717346033720 197:190:2051256675104 197:191:75176946208 197:192:2349279569 197:193:60862165 197:194:1254890 197:195:19306 197:196:197 197:197:1 # binomial(198, k) for 0 <= k <= 198 198:0:1 198:1:198 198:2:19503 198:3:1274196 198:4:62117055 198:5:2410141734 198:6:77526225777 198:7:2126433621312 198:8:50768602708824 198:9:1071781612741840 198:10:20256672480820776 198:11:346204947854027808 198:12:5395027104058600008 198:13:77190387796530738576 198:14:1020015838739870474040 198:15:12512194288542411148224 198:16:143108222175203827507812 198:17:1532099790346299800377752 198:18:15406114558482236881576284 198:19:145952664238252770457038480 198:20:1306276344932362295590494396 198:21:11072247114188594695957523928 198:22:89081260873244602781112806148 198:23:681665300595263047368515386176 198:24:4970476150173793053728758024200 198:25:34594514005209599653952155848432 198:26:230186573957740797697450883145336 198:27:1466373730397459896443020440777696 198:28:8955353853498772938991303406178072 198:29:52496901899820393090638675139664560 198:30:295732547368988214410597869953443688 198:31:1602679611548065161967111037167049664 198:32:8363984222766465064015860725215540434 198:33:42073375181188884867473723648053930668 198:34:204179614849887235386269541233202898830 198:35:956727338153757331524234421778436440232 198:36:4331848781085067917734728076385698326606 198:37:18966473041507594666838539145256300781356 198:38:80357951570597966877921179010164853310482 198:39:329673647469119864114548426708368628966080 198:40:1310452748689751459855329996165765300140168 198:41:5050037421780017820905905838882705302979184 198:42:18877520838558638044814933731061541251612664 198:43:68485889553840640348630922373153498494222688 198:44:241257110928302255773586203814518006059193560 198:45:825635446287967719758495008609683842958129072 198:46:2746135288740414372240211659071339738534646696 198:47:8881118380607297544266216429337098728878006336 198:48:27938518238993790191337472517289623084595394932 198:49:85526076241817725075522875052927417605904270200 198:50:254867707200616820725058167657723704465594725196 198:51:739616091484142930731541349281237416880549398608 198:52:2090837797080173284952626506621959620796937722988 198:53:5759666384409533954775159810694454804459488821816 198:54:15465770847025600434118484676864739752715294058580 198:55:40492200035848844772964759881245864079836406262464 198:56:103399725091542585759535011839609974346725108848792 198:57:257592297596474511892174941775870462407630972921552 198:58:626215757950050106496494255006857503439240813481704 198:59:1485935696830627371347613486456950008160910404871840 198:60:3442417697657620076955304576958600852239442437953096 198:61:7787764627487730665898885764266998649328574695697168 198:62:17208447644609985503679795962977077660613140859846968 198:63:37148394915348540134927813507379088283228367570463296 198:64:78359895524563326847113356617127764347434837843946015 198:65:161541938466022858423279842872232621885481050324442554 198:66:325531482060318790459033622757680889557105752926528177 198:67:641345606447195228964066241850953394351312826661219692 198:68:1235533447714449632269009965918748450882676180773820289 198:69:2327816640621426843405381095209236211807940630443429530 198:70:4289833523430915182847059446885592447474633447531462991 198:71:7733784380269818921189064918328955398264127905408834688 198:72:13641536337420375041541822842052462994160336722040583408 198:73:23545665459109140482661228467104251195400033246261828896 198:74:39773083545792467031522345383622045938175731834901738000 198:75:65758164795710212158783611034255115951117209967037540160 198:76:106424398287794159151715581015965516605097589815073913680 198:77:168620475209232304110510401090231078257427350096610616480 198:78:261577916670732164068868699127153339348060376431921597360 198:79:397333544309972907446382834117194945845155002175070780800 198:80:591033647161084699826494465749327481944668065735417786440 198:81:861011979814913513327485764918773368758899157491102454320 198:82:1228517093150547329991656518237762001765746358859255940920 198:83:1716963648258596268422074170067233641022006959369562519840 198:84:2350604994639744891292125351877760341875366670565472497400 198:85:3152576110458010795380026942518407987926962358170163114160 198:86:4142338377694828138115616796564884914369148214804981766280 198:87:5332665497722077603091368749600771384015455173082275377280 198:88:6726430343717620612990249218246427541201312775137870078160 198:89:8313565593358856937403678809068618309349937137810850658400 198:90:10068651663067948957522233224316437730212701644682030241840 198:91:11949608567157565795740672398089838185307382171710541385920 198:92:13897914311802821088524477680387094411172716221445955742320 198:93:15840633516678484251436501442161634490153848596486788265440 198:94:17694324672885540919157794164116719377299511730118220934800 198:95:19370629115579960585183269400717250686727886525603105023360 198:96:20783070821924332711186216127852883549301794918094998097980 198:97:21854363132332803469494783969494784763183330738615358824680 198:98:22523374248628705616520134499173196541648126577552563686660 198:99:22750883079422934966181954039568885395604168260154104734000 198:100:22523374248628705616520134499173196541648126577552563686660 198:101:21854363132332803469494783969494784763183330738615358824680 198:102:20783070821924332711186216127852883549301794918094998097980 198:103:19370629115579960585183269400717250686727886525603105023360 198:104:17694324672885540919157794164116719377299511730118220934800 198:105:15840633516678484251436501442161634490153848596486788265440 198:106:13897914311802821088524477680387094411172716221445955742320 198:107:11949608567157565795740672398089838185307382171710541385920 198:108:10068651663067948957522233224316437730212701644682030241840 198:109:8313565593358856937403678809068618309349937137810850658400 198:110:6726430343717620612990249218246427541201312775137870078160 198:111:5332665497722077603091368749600771384015455173082275377280 198:112:4142338377694828138115616796564884914369148214804981766280 198:113:3152576110458010795380026942518407987926962358170163114160 198:114:2350604994639744891292125351877760341875366670565472497400 198:115:1716963648258596268422074170067233641022006959369562519840 198:116:1228517093150547329991656518237762001765746358859255940920 198:117:861011979814913513327485764918773368758899157491102454320 198:118:591033647161084699826494465749327481944668065735417786440 198:119:397333544309972907446382834117194945845155002175070780800 198:120:261577916670732164068868699127153339348060376431921597360 198:121:168620475209232304110510401090231078257427350096610616480 198:122:106424398287794159151715581015965516605097589815073913680 198:123:65758164795710212158783611034255115951117209967037540160 198:124:39773083545792467031522345383622045938175731834901738000 198:125:23545665459109140482661228467104251195400033246261828896 198:126:13641536337420375041541822842052462994160336722040583408 198:127:7733784380269818921189064918328955398264127905408834688 198:128:4289833523430915182847059446885592447474633447531462991 198:129:2327816640621426843405381095209236211807940630443429530 198:130:1235533447714449632269009965918748450882676180773820289 198:131:641345606447195228964066241850953394351312826661219692 198:132:325531482060318790459033622757680889557105752926528177 198:133:161541938466022858423279842872232621885481050324442554 198:134:78359895524563326847113356617127764347434837843946015 198:135:37148394915348540134927813507379088283228367570463296 198:136:17208447644609985503679795962977077660613140859846968 198:137:7787764627487730665898885764266998649328574695697168 198:138:3442417697657620076955304576958600852239442437953096 198:139:1485935696830627371347613486456950008160910404871840 198:140:626215757950050106496494255006857503439240813481704 198:141:257592297596474511892174941775870462407630972921552 198:142:103399725091542585759535011839609974346725108848792 198:143:40492200035848844772964759881245864079836406262464 198:144:15465770847025600434118484676864739752715294058580 198:145:5759666384409533954775159810694454804459488821816 198:146:2090837797080173284952626506621959620796937722988 198:147:739616091484142930731541349281237416880549398608 198:148:254867707200616820725058167657723704465594725196 198:149:85526076241817725075522875052927417605904270200 198:150:27938518238993790191337472517289623084595394932 198:151:8881118380607297544266216429337098728878006336 198:152:2746135288740414372240211659071339738534646696 198:153:825635446287967719758495008609683842958129072 198:154:241257110928302255773586203814518006059193560 198:155:68485889553840640348630922373153498494222688 198:156:18877520838558638044814933731061541251612664 198:157:5050037421780017820905905838882705302979184 198:158:1310452748689751459855329996165765300140168 198:159:329673647469119864114548426708368628966080 198:160:80357951570597966877921179010164853310482 198:161:18966473041507594666838539145256300781356 198:162:4331848781085067917734728076385698326606 198:163:956727338153757331524234421778436440232 198:164:204179614849887235386269541233202898830 198:165:42073375181188884867473723648053930668 198:166:8363984222766465064015860725215540434 198:167:1602679611548065161967111037167049664 198:168:295732547368988214410597869953443688 198:169:52496901899820393090638675139664560 198:170:8955353853498772938991303406178072 198:171:1466373730397459896443020440777696 198:172:230186573957740797697450883145336 198:173:34594514005209599653952155848432 198:174:4970476150173793053728758024200 198:175:681665300595263047368515386176 198:176:89081260873244602781112806148 198:177:11072247114188594695957523928 198:178:1306276344932362295590494396 198:179:145952664238252770457038480 198:180:15406114558482236881576284 198:181:1532099790346299800377752 198:182:143108222175203827507812 198:183:12512194288542411148224 198:184:1020015838739870474040 198:185:77190387796530738576 198:186:5395027104058600008 198:187:346204947854027808 198:188:20256672480820776 198:189:1071781612741840 198:190:50768602708824 198:191:2126433621312 198:192:77526225777 198:193:2410141734 198:194:62117055 198:195:1274196 198:196:19503 198:197:198 198:198:1 # binomial(199, k) for 0 <= k <= 199 199:0:1 199:1:199 199:2:19701 199:3:1293699 199:4:63391251 199:5:2472258789 199:6:79936367511 199:7:2203959847089 199:8:52895036330136 199:9:1122550215450664 199:10:21328454093562616 199:11:366461620334848584 199:12:5741232051912627816 199:13:82585414900589338584 199:14:1097206226536401212616 199:15:13532210127282281622264 199:16:155620416463746238656036 199:17:1675208012521503627885564 199:18:16938214348828536681954036 199:19:161358778796735007338614764 199:20:1452229009170615066047532876 199:21:12378523459120956991548018324 199:22:100153507987433197477070330076 199:23:770746561468507650149628192324 199:24:5652141450769056101097273410376 199:25:39564990155383392707680913872632 199:26:264781087962950397351403038993768 199:27:1696560304355200694140471323923032 199:28:10421727583896232835434323846955768 199:29:61452255753319166029629978545842632 199:30:348229449268808607501236545093108248 199:31:1898412158917053376377708907120493352 199:32:9966663834314530225982971762382590098 199:33:50437359403955349931489584373269471102 199:34:246252990031076120253743264881256829498 199:35:1160906953003644566910503963011639339062 199:36:5288576119238825249258962498164134766838 199:37:23298321822592662584573267221641999107962 199:38:99324424612105561544759718155421154091838 199:39:410031599039717830992469605718533482276562 199:40:1640126396158871323969878422874133929106248 199:41:6360490170469769280761235835048470603119352 199:42:23927558260338655865720839569944246554591848 199:43:87363410392399278393445856104215039745835352 199:44:309743000482142896122217126187671504553416248 199:45:1066892557216269975532081212424201849017322632 199:46:3571770735028382091998706667681023581492775768 199:47:11627253669347711916506428088408438467412653032 199:48:36819636619601087735603688946626721813473401268 199:49:113464594480811515266860347570217040690499665132 199:50:340393783442434545800581042710651122071498995396 199:51:994483798684759751456599516938961121346144123804 199:52:2830453888564316215684167855903197037677487121596 199:53:7850504181489707239727786317316414425256426544804 199:54:21225437231435134388893644487559194557174782880396 199:55:55957970882874445207083244558110603832551700321044 199:56:143891925127391430532499771720855838426561515111256 199:57:360992022688017097651709953615480436754356081770344 199:58:883808055546524618388669196782727965846871786403256 199:59:2112151454780677477844107741463807511600151218353544 199:60:4928353394488247448302918063415550860400352842824936 199:61:11230182325145350742854190341225599501568017133650264 199:62:24996212272097716169578681727244076309941715555544136 199:63:54356842559958525638607609470356165943841508430310264 199:64:115508290439911866982041170124506852630663205414409311 199:65:239901833990586185270393199489360386232915888168388569 199:66:487073420526341648882313465629913511442586803250970731 199:67:966877088507514019423099864608634283908418579587747869 199:68:1876879054161644861233076207769701845233989007435039981 199:69:3563350088335876475674391061127984662690616811217249819 199:70:6617650164052342026252440542094828659282574077974892521 199:71:12023617903700734104036124365214547845738761352940297679 199:72:21375320717690193962730887760381418392424464627449418096 199:73:37187201796529515524203051309156714189560369968302412304 199:74:63318749004901607514183573850726297133575765081163566896 199:75:105531248341502679190305956417877161889292941801939278160 199:76:172182563083504371310499192050220632556214799782111453840 199:77:275044873497026463262225982106196594862524939911684530160 199:78:430198391879964468179379100217384417605487726528532213840 199:79:658911460980705071515251533244348285193215378606992378160 199:80:988367191471057607272877299866522427789823067910488567240 199:81:1452045626975998213153980230668100850703567223226520240760 199:82:2089529072965460843319142283156535370524645516350358395240 199:83:2945480741409143598413730688304995642787753318228818460760 199:84:4067568642898341159714199521944993982897373629935035017240 199:85:5503181105097755686672152294396168329802329028735635611560 199:86:7294914488152838933495643739083292902296110572975144880440 199:87:9475003875416905741206985546165656298384603387887257143560 199:88:12059095841439698216081617967847198925216767948220145455440 199:89:15039995937076477550393928027315045850551249912948720736560 199:90:18382217256426805894925912033385056039562638782492880900240 199:91:22018260230225514753262905622406275915520083816392571627760 199:92:25847522878960386884265150078476932596480098393156497128240 199:93:29738547828481305339960979122548728901326564817932744007760 199:94:33534958189564025170594295606278353867453360326605009200240 199:95:37064953788465501504341063564833970064027398255721325958160 199:96:40153699937504293296369485528570134236029681443698103121340 199:97:42637433954257136180681000097347668312485125656710356922660 199:98:44377737380961509086014918468667981304831457316167922511340 199:99:45274257328051640582702088538742081937252294837706668420660 199:100:45274257328051640582702088538742081937252294837706668420660 199:101:44377737380961509086014918468667981304831457316167922511340 199:102:42637433954257136180681000097347668312485125656710356922660 199:103:40153699937504293296369485528570134236029681443698103121340 199:104:37064953788465501504341063564833970064027398255721325958160 199:105:33534958189564025170594295606278353867453360326605009200240 199:106:29738547828481305339960979122548728901326564817932744007760 199:107:25847522878960386884265150078476932596480098393156497128240 199:108:22018260230225514753262905622406275915520083816392571627760 199:109:18382217256426805894925912033385056039562638782492880900240 199:110:15039995937076477550393928027315045850551249912948720736560 199:111:12059095841439698216081617967847198925216767948220145455440 199:112:9475003875416905741206985546165656298384603387887257143560 199:113:7294914488152838933495643739083292902296110572975144880440 199:114:5503181105097755686672152294396168329802329028735635611560 199:115:4067568642898341159714199521944993982897373629935035017240 199:116:2945480741409143598413730688304995642787753318228818460760 199:117:2089529072965460843319142283156535370524645516350358395240 199:118:1452045626975998213153980230668100850703567223226520240760 199:119:988367191471057607272877299866522427789823067910488567240 199:120:658911460980705071515251533244348285193215378606992378160 199:121:430198391879964468179379100217384417605487726528532213840 199:122:275044873497026463262225982106196594862524939911684530160 199:123:172182563083504371310499192050220632556214799782111453840 199:124:105531248341502679190305956417877161889292941801939278160 199:125:63318749004901607514183573850726297133575765081163566896 199:126:37187201796529515524203051309156714189560369968302412304 199:127:21375320717690193962730887760381418392424464627449418096 199:128:12023617903700734104036124365214547845738761352940297679 199:129:6617650164052342026252440542094828659282574077974892521 199:130:3563350088335876475674391061127984662690616811217249819 199:131:1876879054161644861233076207769701845233989007435039981 199:132:966877088507514019423099864608634283908418579587747869 199:133:487073420526341648882313465629913511442586803250970731 199:134:239901833990586185270393199489360386232915888168388569 199:135:115508290439911866982041170124506852630663205414409311 199:136:54356842559958525638607609470356165943841508430310264 199:137:24996212272097716169578681727244076309941715555544136 199:138:11230182325145350742854190341225599501568017133650264 199:139:4928353394488247448302918063415550860400352842824936 199:140:2112151454780677477844107741463807511600151218353544 199:141:883808055546524618388669196782727965846871786403256 199:142:360992022688017097651709953615480436754356081770344 199:143:143891925127391430532499771720855838426561515111256 199:144:55957970882874445207083244558110603832551700321044 199:145:21225437231435134388893644487559194557174782880396 199:146:7850504181489707239727786317316414425256426544804 199:147:2830453888564316215684167855903197037677487121596 199:148:994483798684759751456599516938961121346144123804 199:149:340393783442434545800581042710651122071498995396 199:150:113464594480811515266860347570217040690499665132 199:151:36819636619601087735603688946626721813473401268 199:152:11627253669347711916506428088408438467412653032 199:153:3571770735028382091998706667681023581492775768 199:154:1066892557216269975532081212424201849017322632 199:155:309743000482142896122217126187671504553416248 199:156:87363410392399278393445856104215039745835352 199:157:23927558260338655865720839569944246554591848 199:158:6360490170469769280761235835048470603119352 199:159:1640126396158871323969878422874133929106248 199:160:410031599039717830992469605718533482276562 199:161:99324424612105561544759718155421154091838 199:162:23298321822592662584573267221641999107962 199:163:5288576119238825249258962498164134766838 199:164:1160906953003644566910503963011639339062 199:165:246252990031076120253743264881256829498 199:166:50437359403955349931489584373269471102 199:167:9966663834314530225982971762382590098 199:168:1898412158917053376377708907120493352 199:169:348229449268808607501236545093108248 199:170:61452255753319166029629978545842632 199:171:10421727583896232835434323846955768 199:172:1696560304355200694140471323923032 199:173:264781087962950397351403038993768 199:174:39564990155383392707680913872632 199:175:5652141450769056101097273410376 199:176:770746561468507650149628192324 199:177:100153507987433197477070330076 199:178:12378523459120956991548018324 199:179:1452229009170615066047532876 199:180:161358778796735007338614764 199:181:16938214348828536681954036 199:182:1675208012521503627885564 199:183:155620416463746238656036 199:184:13532210127282281622264 199:185:1097206226536401212616 199:186:82585414900589338584 199:187:5741232051912627816 199:188:366461620334848584 199:189:21328454093562616 199:190:1122550215450664 199:191:52895036330136 199:192:2203959847089 199:193:79936367511 199:194:2472258789 199:195:63391251 199:196:1293699 199:197:19701 199:198:199 199:199:1 # binomial(200, k) for 0 <= k <= 200 200:0:1 200:1:200 200:2:19900 200:3:1313400 200:4:64684950 200:5:2535650040 200:6:82408626300 200:7:2283896214600 200:8:55098996177225 200:9:1175445251780800 200:10:22451004309013280 200:11:387790074428411200 200:12:6107693672247476400 200:13:88326646952501966400 200:14:1179791641436990551200 200:15:14629416353818682834880 200:16:169152626591028520278300 200:17:1830828428985249866541600 200:18:18613422361350040309839600 200:19:178296993145563544020568800 200:20:1613587787967350073386147640 200:21:13830752468291572057595551200 200:22:112532031446554154468618348400 200:23:870900069455940847626698522400 200:24:6422888012237563751246901602700 200:25:45217131606152448808778187283008 200:26:304346078118333790059083952866400 200:27:1961341392318151091491874362916800 200:28:12118287888251433529574795170878800 200:29:71873983337215398865064302392798400 200:30:409681705022127773530866523638950880 200:31:2246641608185861983878945452213601600 200:32:11865075993231583602360680669503083450 200:33:60404023238269880157472556135652061200 200:34:296690349435031470185232849254526300600 200:35:1407159943034720687164247227892896168560 200:36:6449483072242469816169466461175774105900 200:37:28586897941831487833832229719806133874800 200:38:122622746434698224129332985377063153199800 200:39:509356023651823392537229323873954636368400 200:40:2050157995198589154962348028592667411382810 200:41:8000616566628640604731114257922604532225600 200:42:30288048430808425146482075404992717157711200 200:43:111290968652737934259166695674159286300427200 200:44:397106410874542174515662982291886544299251600 200:45:1376635557698412871654298338611873353570738880 200:46:4638663292244652067530787880105225430510098400 200:47:15199024404376094008505134756089462048905428800 200:48:48446890288948799652110117035035160280886054300 200:49:150284231100412603002464036516843762503973066400 200:50:453858377923246061067441390280868162761998660528 200:51:1334877582127194297257180559649612243417643119200 200:52:3824937687249075967140767372842158159023631245400 200:53:10680958070054023455411954173219611462933913666400 200:54:29075941412924841628621430804875608982431209425200 200:55:77183408114309579595976889045669798389726483201440 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200:189:387790074428411200 200:190:22451004309013280 200:191:1175445251780800 200:192:55098996177225 200:193:2283896214600 200:194:82408626300 200:195:2535650040 200:196:64684950 200:197:1313400 200:198:19900 200:199:200 200:200:1 Math-BigInt-1.999808/t/author-bpi-mbf.t0000644403072340010010000001176512737516654017634 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 9; use Math::BigFloat; my $pi = { 16 => '3.141592653589793', 40 => '3.141592653589793238462643383279502884197', }; subtest "Called as class method without argument.", sub { plan tests => 5; my $x; my $test = '$x = Math::BigFloat -> bpi()'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {40}, "'$test' gives correct output"); is($x -> {_a}, undef, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; subtest "Called as class method with scalar argument.", sub { plan tests => 5; my $x; my $test = '$x = Math::BigFloat -> bpi(16);'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {16}, "'$test' gives correct output"); is($x -> {_a}, 16, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; subtest "Called as class method with class argument.", sub { plan tests => 5; my ($n, $x); my $test = '$n = Math::BigFloat -> new("16"); ' . '$x = Math::BigFloat -> bpi($n);'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {16}, "'$test' gives correct output"); is($x -> {_a}, 16, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; subtest "Called as instance method without argument.", sub { plan tests => 5; my $x; my $test = '$x = Math::BigFloat -> bnan(); $x -> bpi();'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {40}, "'$test' gives correct output"); is($x -> {_a}, undef, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; subtest "Called as instance method with scalar argument.", sub { plan tests => 5; my $x; my $test = '$x = Math::BigFloat -> bnan(); $x -> bpi(16);'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {16}, "'$test' gives correct output"); is($x -> {_a}, 16, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; subtest "Called as instance method with instance argument.", sub { plan tests => 5; my ($n, $x); my $test = '$n = Math::BigFloat -> new("16"); ' . '$x = Math::BigFloat -> bnan(); ' . '$x -> bpi($n);'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {16}, "'$test' gives correct output"); is($x -> {_a}, 16, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; subtest "Called as function without argument.", sub { plan tests => 5; my $x; my $test = '$x = Math::BigFloat::bpi();'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {40}, "'$test' gives correct output"); is($x -> {_a}, undef, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; subtest "Called as function with scalar argument.", sub { plan tests => 5; my $x; my $test = '$x = Math::BigFloat::bpi(16);'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {16}, "'$test' gives correct output"); is($x -> {_a}, 16, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); }; # The following is an ambiguous case. The argument list to bpi() is ($n), which # is assumed to mean $n->bpi(), since we favour the OO-style. So in the test # below, $n is assigned the value of pi with the default number of digits, and # then $n is assigned to $x. subtest "Called as function with instance argument.", sub { plan tests => 9; my ($n, $x); my $test = '$n = Math::BigFloat -> new("16"); ' . '$x = Math::BigFloat::bpi($n);'; eval $test; is($@, "", "'$test' gives emtpy \$\@"); isa_ok($x, 'Math::BigFloat'); is($x, $pi -> {40}, "'$test' gives correct output"); is($x -> {_a}, undef, "'$test' gives correct accuracy"); is($x -> {_p}, undef, "'$test' gives correct precision"); isa_ok($n, 'Math::BigFloat'); is($n, $pi -> {40}, "'$test' gives correct output"); is($n -> {_a}, undef, "'$test' gives correct accuracy"); is($n -> {_p}, undef, "'$test' gives correct precision"); }; Math-BigInt-1.999808/t/author-btmod-btdiv-mbi.t0000644403072340010010000003003012734616176021257 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 41301;; use Math::BigInt; use Math::Complex; use Scalar::Util; my $inf = Math::Complex::Inf(); my $nan = $inf - $inf; # Return 1 if the input argument is +inf or -inf, and "" otherwise. sub isinf { my $x = shift; return $x == $inf || $x == -$inf; } # Return 1 if the input argument is a nan (Not-a-Number), and "" otherwise. sub isnan { my $x = shift; return !($x <= 0 || $x > 0); } # Convert a Perl scalar to a Math::BigInt object. This function is used for # consistent comparisons. For instance, a Not-a-Number might be stringified to # 'nan', but Math::BigInt uses 'NaN'. sub pl2mbi { my $x = shift; return Math::BigInt -> binf('+') if $x == $inf; return Math::BigInt -> binf('-') if $x == -$inf; return Math::BigInt -> bnan() if isnan($x); return Math::BigInt -> new($x); } # Does a truncated division (T-division). sub tdiv { die "Usage: fdiv X Y\n" if @_ != 2; #no integer; my $x = shift; # numerator my $y = shift; # denominator # Convert Perl strings representing nan, +inf, and -inf into Perl numbers. if ($x =~ /^\s*nan\s*$/i) { $x = $nan; } elsif ($x =~ /^\s*([+-]?)inf(inity)?\s*$/i) { $x = $1 eq '-' ? -$inf : $inf; } if ($y =~ /^\s*nan\s*$/i) { $y = $nan; } elsif ($y =~ /^\s*([+-]?)inf(inity)?\s*$/i) { $y = $1 eq '-' ? -$inf : $inf; } # If any input is nan, the output is nan. if (isnan($x) || isnan($y)) { return wantarray ? ($nan, $nan) : $nan; } # Divide by zero and modulo zero. if ($y == 0) { # Core Perl gives an "Illegal division by zero" error whenever the # denominator is zero. Math::BigInt, however, has a different # convention. my $q = $x < 0 ? -$inf : $x > 0 ? $inf : $nan; my $r = $x; return wantarray ? ($q, $r) : $q; } # Numerator is +/-infinity, and denominator is finite and non-zero. if (isinf($x)) { my $q = int($x / $y); my $r = $x - $y * $q; return wantarray ? ($q, $r) : $q; if (isinf($y)) { return wantarray ? ($nan, $nan) : $nan; } else { if (($x <=> 0) == ($y <=> 0)) { return wantarray ? ($inf, $nan) : $inf; } else { return wantarray ? (-$inf, $nan) : -$inf; } } } # Denominator is +/- infinity, and the numerator is finite. # # Core Perl: 5 % Inf = 5 # -5 % -Inf = -5 # -5 % Inf = -5 # 5 % -Inf = 5 if (isinf($y)) { return wantarray ? (0, $x) : 0; } # Do a truncated division. my $q = int($x / $y); my $r = $x - $y * $q; return wantarray ? ($q, $r) : $q; } # Tests where the invocand and the argument are two different objects. #for my $num (-20 .. 20) { # for my $den (-20 .. -1, 1 .. 20) { for my $num (-$inf, -20 .. 20, $inf, $nan) { for my $den (-$inf, -20 .. 20, $inf, $nan) { # Compute expected output values. my ($quo, $rem) = tdiv($num, $den); ####################################################################### # btdiv() in list context. ####################################################################### { note(qq|\n(\$quo, \$rem) = | . qq|Math::BigInt -> new("$num") -> btdiv("$den")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); my $mbi_den = Math::BigInt -> new("$den"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); my $mbi_den_addr = Scalar::Util::refaddr($mbi_den); # Compute actual output values. my ($mbi_quo, $mbi_rem) = $mbi_num -> btdiv($mbi_den); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_den), 'Math::BigInt', "class of denominator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $den = $quo"); is($mbi_rem, pl2mbi($rem), "$num % $den = $rem"); is($mbi_den, pl2mbi($den), "value of denominator has not change"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); ok($mbi_rem_addr != $mbi_num_addr && $mbi_rem_addr != $mbi_den_addr && $mbi_rem_addr != $mbi_quo_addr, "the remainder object is neither the numerator," . " denominator, nor quotient object"); } ####################################################################### # btdiv() in scalar context. ####################################################################### { note(qq|\n\$quo = | . qq|Math::BigInt -> new("$num") -> btdiv("$den")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); my $mbi_den = Math::BigInt -> new("$den"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); my $mbi_den_addr = Scalar::Util::refaddr($mbi_den); # Compute actual output values. my $mbi_quo = $mbi_num -> btdiv($mbi_den); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_den), 'Math::BigInt', "class of denominator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $den = $quo"); is($mbi_den, pl2mbi($den), "value of numerator has not change"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); } ####################################################################### # btmod() (scalar context only). ####################################################################### { note(qq|\n\$quo = | . qq|Math::BigInt -> new("$num") -> btmod("$den")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); my $mbi_den = Math::BigInt -> new("$den"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); my $mbi_den_addr = Scalar::Util::refaddr($mbi_den); # Compute actual output values. my $mbi_rem = $mbi_num -> btmod($mbi_den); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_den), 'Math::BigInt', "class of denominator is still Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_rem, pl2mbi($rem), "$num % $den = $rem"); is($mbi_den, pl2mbi($den), "value of denominator has not change"); # Check addresses. my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_rem_addr, $mbi_num_addr, "the remainder object is the numerator object"); } } } # Tests where the invocand and the argument is the same object. #for my $num (-$inf, -20 .. 20, $inf, $nan) { for my $num (-$inf, -20 .. -1, 1 .. 20, $inf, $nan) { # Compute expected output values. my ($quo, $rem) = tdiv($num, $num); ####################################################################### # btdiv() in list context. ####################################################################### { note(qq|\n\$x = Math::BigInt -> new("$num"); | . qq|(\$quo, \$rem) = \$x -> btdiv("\$x")\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); # Compute actual output values. my ($mbi_quo, $mbi_rem) = $mbi_num -> btdiv($mbi_num); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $num = $quo"); is($mbi_rem, pl2mbi($rem), "$num % $num = $rem"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); ok($mbi_rem_addr != $mbi_num_addr && $mbi_rem_addr != $mbi_quo_addr, "the remainder object is neither the numerator," . " denominator, nor quotient object"); } ####################################################################### # btdiv() in scalar context. ####################################################################### { note(qq|\n\$x = Math::BigInt -> new("$num"); | . qq|\$quo = \$x -> btdiv(\$x)\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); # Compute actual output values. my $mbi_quo = $mbi_num -> btdiv($mbi_num); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_quo), 'Math::BigInt', "class of quotient is Math::BigInt"); # Check values. is($mbi_quo, pl2mbi($quo), "$num / $num = $quo"); # Check addresses. my $mbi_quo_addr = Scalar::Util::refaddr($mbi_quo); is($mbi_quo_addr, $mbi_num_addr, "the quotient object is the numerator object"); } ####################################################################### # btmod() (scalar context only). ####################################################################### { note(qq|\n\$x = Math::BigInt -> new("$num") | . qq|\$quo = \$x -> btmod(\$x)\n\n|); # Input values as objects. my $mbi_num = Math::BigInt -> new("$num"); # Get addresses for later tests. my $mbi_num_addr = Scalar::Util::refaddr($mbi_num); # Compute actual output values. my $mbi_rem = $mbi_num -> btmod($mbi_num); # Check classes. is(ref($mbi_num), 'Math::BigInt', "class of numerator is still Math::BigInt"); is(ref($mbi_rem), 'Math::BigInt', "class of remainder is Math::BigInt"); # Check values. is($mbi_rem, pl2mbi($rem), "$num % $num = $rem"); # Check addresses. my $mbi_rem_addr = Scalar::Util::refaddr($mbi_rem); is($mbi_rem_addr, $mbi_num_addr, "the remainder object is the numerator object"); } } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_add.dat0000644403072340010010000006535713012340550023650 0ustar ospjadomain users38:95:133 51:582:633 77:3259:3336 77:48939:49016 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2248566248782537066521058:9572688262788075807973484:11821254511570612874494542 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_add.t0000644403072340010010000001212513024051250023323 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 7705; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_add'); my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; my @data; # Small numbers. for (my $x = 0; $x <= 24 ; ++ $x) { for (my $y = 0; $y <= 24 ; ++ $y) { push @data, [ $x, $y, $x + $y ]; } } # 9 + 11, 99 + 101, 999 + 1001, 9999 + 1001, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "9" x $p; my $y = "1" . ("0" x ($p - 1)) . "1"; my $z = "2" . ("0" x $p); push @data, [ $x, $y, $z ]; } # 9 + 9, 99 + 99, 999 + 999, 9999 + 9999, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "9" x $p; my $z = "1" . ("9" x ($p - 1)) . "8"; push @data, [ $x, $x, $z ]; } # Powers of 10. for (my $p = 0; $p <= 24 ; ++ $p) { for (my $q = 0; $q <= 24 ; ++ $q) { my $x = "1" . ("0" x $p); my $y = "1" . ("0" x $q); my ($max, $min) = $p > $q ? ($p, $q) : ($q, $p); my $z = "1" . ("0" x $max); substr($z, -1 - $min, 1) = substr($z, -1 - $min, 1) + 1; push @data, [ $x, $y, $z ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_add(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_add() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_add(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_add() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_div.dat0000644403072340010010000003416313012340550023671 0ustar ospjadomain users9:54:0:9 1:781:0:1 3:4665:0:3 3:12746:0:3 6:401608:0:6 5:4973563:0:5 2:38956011:0:2 5:158697436:0:5 7:7124748164:0:7 8:53946138772:0:8 3:336282406075:0:3 7:5075747178985:0:7 2:12741528190606:0:2 6:534035067908715:0:6 3:4355706918152932:0:3 2:10871312221127208:0:2 8:119865422092255109:0:8 3:7394159221356238406:0:3 8:70181009638469054829:0:8 76:6:12:4 93:70:1:23 98:500:0:98 85:5843:0:85 28:76287:0:28 27:389276:0:27 14:2106171:0:14 43:83817435:0:43 93:709704213:0:93 72:7721474597:0:72 28:21540325401:0:28 73:804764354059:0:73 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15701765108586655113:11977088300936683:1310:11779434359600383 92767908704599648797:317314859219406495:292:111969812532952257 10018105311046654961:4057927198723966611:2:1902250913598721739 86016853985828329221:84443436749010104153:1:1573417236818225068 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_div.t0000644403072340010010000001164613024051250023364 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 3997; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_div'); my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; my @data; # Small numbers. for (my $x = 0; $x <= 24 ; ++ $x) { for (my $y = 1; $y <= 24 ; ++ $y) { push @data, [ $x, $y, int($x / $y), $x % $y ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0, $out1) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_div(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_div() in list context: $test", sub { plan tests => $scalar_util_ok ? 13 : 11; cmp_ok(scalar @got, '==', 2, "'$test' gives two output args"); is(ref($got[0]), $REF, "'$test' first output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' first output arg is valid"); is($LIB->_str($got[0]), $out0, "'$test' first output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' first output arg is not the second input arg") if $scalar_util_ok; SKIP: { skip "$LIB doesn't use real objects", 1 if $LIB eq 'Math::BigInt::FastCalc'; is(ref($got[1]), $REF, "'$test' second output arg is a $REF"); } is($LIB->_check($got[1]), 0, "'$test' second output arg is valid"); is($LIB->_str($got[1]), $out1, "'$test' second output arg has the right value"); isnt(refaddr($got[1]), refaddr($y), "'$test' second output arg is not the second input arg"); is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0, $out1) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_div(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_div() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_gcd.dat0000644403072340010010000004734713012340550023654 0ustar ospjadomain users0:0:0 0:1:1 0:2:2 0:3:3 0:4:4 0:5:5 0:6:6 0:7:7 0:8:8 0:9:9 0:10:10 0:11:11 0:12:12 0:13:13 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48:32:16 48:33:3 48:34:2 48:35:1 48:36:12 48:37:1 48:38:2 48:39:3 48:40:8 48:41:1 48:42:6 48:43:1 48:44:4 48:45:3 48:46:2 48:47:1 48:48:48 48:49:1 48:50:2 49:0:49 49:1:1 49:2:1 49:3:1 49:4:1 49:5:1 49:6:1 49:7:7 49:8:1 49:9:1 49:10:1 49:11:1 49:12:1 49:13:1 49:14:7 49:15:1 49:16:1 49:17:1 49:18:1 49:19:1 49:20:1 49:21:7 49:22:1 49:23:1 49:24:1 49:25:1 49:26:1 49:27:1 49:28:7 49:29:1 49:30:1 49:31:1 49:32:1 49:33:1 49:34:1 49:35:7 49:36:1 49:37:1 49:38:1 49:39:1 49:40:1 49:41:1 49:42:7 49:43:1 49:44:1 49:45:1 49:46:1 49:47:1 49:48:1 49:49:49 49:50:1 50:0:50 50:1:1 50:2:2 50:3:1 50:4:2 50:5:5 50:6:2 50:7:1 50:8:2 50:9:1 50:10:10 50:11:1 50:12:2 50:13:1 50:14:2 50:15:5 50:16:2 50:17:1 50:18:2 50:19:1 50:20:10 50:21:1 50:22:2 50:23:1 50:24:2 50:25:25 50:26:2 50:27:1 50:28:2 50:29:1 50:30:10 50:31:1 50:32:2 50:33:1 50:34:2 50:35:5 50:36:2 50:37:1 50:38:2 50:39:1 50:40:10 50:41:1 50:42:2 50:43:1 50:44:2 50:45:5 50:46:2 50:47:1 50:48:2 50:49:1 50:50:50 # # Two consecutive Fibonacci numbers are a worst case scenario for # Euclid's algorithm. # 420196140727489673:679891637638612258:1 394810887814999156320699623170776339:638817435613190341905763972389505493:1 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_gcd.t0000644403072340010010000001076213024051250023335 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 10413; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_gcd'); my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_gcd(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_gcd() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); my $strx = $LIB->_str($x); ok($strx eq $out0 || $strx eq $in0, "'$test' first input arg has the right value") or diag(" got: $strx\n", " expected: ", $out0 eq $in0 ? $out0 : "$out0 or $in0"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($got); my ($x, $y); my ($xo, $yo); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_gcd(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_gcd() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); my $strx = $LIB->_str($x); ok($strx eq $out0 || $strx eq $in0, "'$test' first input arg has the right value") or diag(" got: $strx\n", " expected: ", $out0 eq $in0 ? $out0 : "$out0 or $in0"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_lcm.dat0000644403072340010010000024572013013577020023672 0ustar ospjadomain users# # Small numbers # 0:1:0 0:2:0 0:3:0 0:4:0 0:5:0 0:6:0 0:7:0 0:8:0 0:9:0 0:10:0 0:11:0 0:12:0 0:13:0 0:14:0 0:15:0 0:16:0 0:17:0 0:18:0 0:19:0 0:20:0 0:21:0 0:22:0 0:23:0 0:24:0 0:25:0 0:26:0 0:27:0 0:28:0 0:29:0 0:30:0 0:31:0 0:32:0 0:33:0 0:34:0 0:35:0 0:36:0 0:37:0 0:38:0 0:39:0 0:40:0 0:41:0 0:42:0 0:43:0 0:44:0 0:45:0 0:46:0 0:47:0 0:48:0 0:49:0 0:50:0 1:1:1 1:2:2 1:3:3 1:4:4 1:5:5 1:6:6 1:7:7 1:8:8 1:9:9 1:10:10 1:11:11 1:12:12 1:13:13 1:14:14 1:15:15 1:16:16 1:17:17 1:18:18 1:19:19 1:20:20 1:21:21 1:22:22 1:23:23 1:24:24 1:25:25 1:26:26 1:27:27 1:28:28 1:29:29 1:30:30 1:31:31 1:32:32 1:33:33 1:34:34 1:35:35 1:36:36 1:37:37 1:38:38 1:39:39 1:40:40 1:41:41 1:42:42 1:43:43 1:44:44 1:45:45 1:46:46 1:47:47 1:48:48 1:49:49 1:50:50 2:1:2 2:2:2 2:3:6 2:4:4 2:5:10 2:6:6 2:7:14 2:8:8 2:9:18 2:10:10 2:11:22 2:12:12 2:13:26 2:14:14 2:15:30 2:16:16 2:17:34 2:18:18 2:19:38 2:20:20 2:21:42 2:22:22 2:23:46 2:24:24 2:25:50 2:26:26 2:27:54 2:28:28 2:29:58 2:30:30 2:31:62 2:32:32 2:33:66 2:34:34 2:35:70 2:36:36 2:37:74 2:38:38 2:39:78 2:40:40 2:41:82 2:42:42 2:43:86 2:44:44 2:45:90 2:46:46 2:47:94 2:48:48 2:49:98 2:50:50 3:1:3 3:2:6 3:3:3 3:4:12 3:5:15 3:6:6 3:7:21 3:8:24 3:9:9 3:10:30 3:11:33 3:12:12 3:13:39 3:14:42 3:15:15 3:16:48 3:17:51 3:18:18 3:19:57 3:20:60 3:21:21 3:22:66 3:23:69 3:24:24 3:25:75 3:26:78 3:27:27 3:28:84 3:29:87 3:30:30 3:31:93 3:32:96 3:33:33 3:34:102 3:35:105 3:36:36 3:37:111 3:38:114 3:39:39 3:40:120 3:41:123 3:42:42 3:43:129 3:44:132 3:45:45 3:46:138 3:47:141 3:48:48 3:49:147 3:50:150 4:1:4 4:2:4 4:3:12 4:4:4 4:5:20 4:6:12 4:7:28 4:8:8 4:9:36 4:10:20 4:11:44 4:12:12 4:13:52 4:14:28 4:15:60 4:16:16 4:17:68 4:18:36 4:19:76 4:20:20 4:21:84 4:22:44 4:23:92 4:24:24 4:25:100 4:26:52 4:27:108 4:28:28 4:29:116 4:30:60 4:31:124 4:32:32 4:33:132 4:34:68 4:35:140 4:36:36 4:37:148 4:38:76 4:39:156 4:40:40 4:41:164 4:42:84 4:43:172 4:44:44 4:45:180 4:46:92 4:47:188 4:48:48 4:49:196 4:50:100 5:1:5 5:2:10 5:3:15 5:4:20 5:5:5 5:6:30 5:7:35 5:8:40 5:9:45 5:10:10 5:11:55 5:12:60 5:13:65 5:14:70 5:15:15 5:16:80 5:17:85 5:18:90 5:19:95 5:20:20 5:21:105 5:22:110 5:23:115 5:24:120 5:25:25 5:26:130 5:27:135 5:28:140 5:29:145 5:30:30 5:31:155 5:32:160 5:33:165 5:34:170 5:35:35 5:36:180 5:37:185 5:38:190 5:39:195 5:40:40 5:41:205 5:42:210 5:43:215 5:44:220 5:45:45 5:46:230 5:47:235 5:48:240 5:49:245 5:50:50 6:1:6 6:2:6 6:3:6 6:4:12 6:5:30 6:6:6 6:7:42 6:8:24 6:9:18 6:10:30 6:11:66 6:12:12 6:13:78 6:14:42 6:15:30 6:16:48 6:17:102 6:18:18 6:19:114 6:20:60 6:21:42 6:22:66 6:23:138 6:24:24 6:25:150 6:26:78 6:27:54 6:28:84 6:29:174 6:30:30 6:31:186 6:32:96 6:33:66 6:34:102 6:35:210 6:36:36 6:37:222 6:38:114 6:39:78 6:40:120 6:41:246 6:42:42 6:43:258 6:44:132 6:45:90 6:46:138 6:47:282 6:48:48 6:49:294 6:50:150 7:1:7 7:2:14 7:3:21 7:4:28 7:5:35 7:6:42 7:7:7 7:8:56 7:9:63 7:10:70 7:11:77 7:12:84 7:13:91 7:14:14 7:15:105 7:16:112 7:17:119 7:18:126 7:19:133 7:20:140 7:21:21 7:22:154 7:23:161 7:24:168 7:25:175 7:26:182 7:27:189 7:28:28 7:29:203 7:30:210 7:31:217 7:32:224 7:33:231 7:34:238 7:35:35 7:36:252 7:37:259 7:38:266 7:39:273 7:40:280 7:41:287 7:42:42 7:43:301 7:44:308 7:45:315 7:46:322 7:47:329 7:48:336 7:49:49 7:50:350 8:1:8 8:2:8 8:3:24 8:4:8 8:5:40 8:6:24 8:7:56 8:8:8 8:9:72 8:10:40 8:11:88 8:12:24 8:13:104 8:14:56 8:15:120 8:16:16 8:17:136 8:18:72 8:19:152 8:20:40 8:21:168 8:22:88 8:23:184 8:24:24 8:25:200 8:26:104 8:27:216 8:28:56 8:29:232 8:30:120 8:31:248 8:32:32 8:33:264 8:34:136 8:35:280 8:36:72 8:37:296 8:38:152 8:39:312 8:40:40 8:41:328 8:42:168 8:43:344 8:44:88 8:45:360 8:46:184 8:47:376 8:48:48 8:49:392 8:50:200 9:1:9 9:2:18 9:3:9 9:4:36 9:5:45 9:6:18 9:7:63 9:8:72 9:9:9 9:10:90 9:11:99 9:12:36 9:13:117 9:14:126 9:15:45 9:16:144 9:17:153 9:18:18 9:19:171 9:20:180 9:21:63 9:22:198 9:23:207 9:24:72 9:25:225 9:26:234 9:27:27 9:28:252 9:29:261 9:30:90 9:31:279 9:32:288 9:33:99 9:34:306 9:35:315 9:36:36 9:37:333 9:38:342 9:39:117 9:40:360 9:41:369 9:42:126 9:43:387 9:44:396 9:45:45 9:46:414 9:47:423 9:48:144 9:49:441 9:50:450 10:1:10 10:2:10 10:3:30 10:4:20 10:5:10 10:6:30 10:7:70 10:8:40 10:9:90 10:10:10 10:11:110 10:12:60 10:13:130 10:14:70 10:15:30 10:16:80 10:17:170 10:18:90 10:19:190 10:20:20 10:21:210 10:22:110 10:23:230 10:24:120 10:25:50 10:26:130 10:27:270 10:28:140 10:29:290 10:30:30 10:31:310 10:32:160 10:33:330 10:34:170 10:35:70 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41:21:861 41:22:902 41:23:943 41:24:984 41:25:1025 41:26:1066 41:27:1107 41:28:1148 41:29:1189 41:30:1230 41:31:1271 41:32:1312 41:33:1353 41:34:1394 41:35:1435 41:36:1476 41:37:1517 41:38:1558 41:39:1599 41:40:1640 41:41:41 41:42:1722 41:43:1763 41:44:1804 41:45:1845 41:46:1886 41:47:1927 41:48:1968 41:49:2009 41:50:2050 42:1:42 42:2:42 42:3:42 42:4:84 42:5:210 42:6:42 42:7:42 42:8:168 42:9:126 42:10:210 42:11:462 42:12:84 42:13:546 42:14:42 42:15:210 42:16:336 42:17:714 42:18:126 42:19:798 42:20:420 42:21:42 42:22:462 42:23:966 42:24:168 42:25:1050 42:26:546 42:27:378 42:28:84 42:29:1218 42:30:210 42:31:1302 42:32:672 42:33:462 42:34:714 42:35:210 42:36:252 42:37:1554 42:38:798 42:39:546 42:40:840 42:41:1722 42:42:42 42:43:1806 42:44:924 42:45:630 42:46:966 42:47:1974 42:48:336 42:49:294 42:50:1050 43:1:43 43:2:86 43:3:129 43:4:172 43:5:215 43:6:258 43:7:301 43:8:344 43:9:387 43:10:430 43:11:473 43:12:516 43:13:559 43:14:602 43:15:645 43:16:688 43:17:731 43:18:774 43:19:817 43:20:860 43:21:903 43:22:946 43:23:989 43:24:1032 43:25:1075 43:26:1118 43:27:1161 43:28:1204 43:29:1247 43:30:1290 43:31:1333 43:32:1376 43:33:1419 43:34:1462 43:35:1505 43:36:1548 43:37:1591 43:38:1634 43:39:1677 43:40:1720 43:41:1763 43:42:1806 43:43:43 43:44:1892 43:45:1935 43:46:1978 43:47:2021 43:48:2064 43:49:2107 43:50:2150 44:1:44 44:2:44 44:3:132 44:4:44 44:5:220 44:6:132 44:7:308 44:8:88 44:9:396 44:10:220 44:11:44 44:12:132 44:13:572 44:14:308 44:15:660 44:16:176 44:17:748 44:18:396 44:19:836 44:20:220 44:21:924 44:22:44 44:23:1012 44:24:264 44:25:1100 44:26:572 44:27:1188 44:28:308 44:29:1276 44:30:660 44:31:1364 44:32:352 44:33:132 44:34:748 44:35:1540 44:36:396 44:37:1628 44:38:836 44:39:1716 44:40:440 44:41:1804 44:42:924 44:43:1892 44:44:44 44:45:1980 44:46:1012 44:47:2068 44:48:528 44:49:2156 44:50:1100 45:1:45 45:2:90 45:3:45 45:4:180 45:5:45 45:6:90 45:7:315 45:8:360 45:9:45 45:10:90 45:11:495 45:12:180 45:13:585 45:14:630 45:15:45 45:16:720 45:17:765 45:18:90 45:19:855 45:20:180 45:21:315 45:22:990 45:23:1035 45:24:360 45:25:225 45:26:1170 45:27:135 45:28:1260 45:29:1305 45:30:90 45:31:1395 45:32:1440 45:33:495 45:34:1530 45:35:315 45:36:180 45:37:1665 45:38:1710 45:39:585 45:40:360 45:41:1845 45:42:630 45:43:1935 45:44:1980 45:45:45 45:46:2070 45:47:2115 45:48:720 45:49:2205 45:50:450 46:1:46 46:2:46 46:3:138 46:4:92 46:5:230 46:6:138 46:7:322 46:8:184 46:9:414 46:10:230 46:11:506 46:12:276 46:13:598 46:14:322 46:15:690 46:16:368 46:17:782 46:18:414 46:19:874 46:20:460 46:21:966 46:22:506 46:23:46 46:24:552 46:25:1150 46:26:598 46:27:1242 46:28:644 46:29:1334 46:30:690 46:31:1426 46:32:736 46:33:1518 46:34:782 46:35:1610 46:36:828 46:37:1702 46:38:874 46:39:1794 46:40:920 46:41:1886 46:42:966 46:43:1978 46:44:1012 46:45:2070 46:46:46 46:47:2162 46:48:1104 46:49:2254 46:50:1150 47:1:47 47:2:94 47:3:141 47:4:188 47:5:235 47:6:282 47:7:329 47:8:376 47:9:423 47:10:470 47:11:517 47:12:564 47:13:611 47:14:658 47:15:705 47:16:752 47:17:799 47:18:846 47:19:893 47:20:940 47:21:987 47:22:1034 47:23:1081 47:24:1128 47:25:1175 47:26:1222 47:27:1269 47:28:1316 47:29:1363 47:30:1410 47:31:1457 47:32:1504 47:33:1551 47:34:1598 47:35:1645 47:36:1692 47:37:1739 47:38:1786 47:39:1833 47:40:1880 47:41:1927 47:42:1974 47:43:2021 47:44:2068 47:45:2115 47:46:2162 47:47:47 47:48:2256 47:49:2303 47:50:2350 48:1:48 48:2:48 48:3:48 48:4:48 48:5:240 48:6:48 48:7:336 48:8:48 48:9:144 48:10:240 48:11:528 48:12:48 48:13:624 48:14:336 48:15:240 48:16:48 48:17:816 48:18:144 48:19:912 48:20:240 48:21:336 48:22:528 48:23:1104 48:24:48 48:25:1200 48:26:624 48:27:432 48:28:336 48:29:1392 48:30:240 48:31:1488 48:32:96 48:33:528 48:34:816 48:35:1680 48:36:144 48:37:1776 48:38:912 48:39:624 48:40:240 48:41:1968 48:42:336 48:43:2064 48:44:528 48:45:720 48:46:1104 48:47:2256 48:48:48 48:49:2352 48:50:1200 49:1:49 49:2:98 49:3:147 49:4:196 49:5:245 49:6:294 49:7:49 49:8:392 49:9:441 49:10:490 49:11:539 49:12:588 49:13:637 49:14:98 49:15:735 49:16:784 49:17:833 49:18:882 49:19:931 49:20:980 49:21:147 49:22:1078 49:23:1127 49:24:1176 49:25:1225 49:26:1274 49:27:1323 49:28:196 49:29:1421 49:30:1470 49:31:1519 49:32:1568 49:33:1617 49:34:1666 49:35:245 49:36:1764 49:37:1813 49:38:1862 49:39:1911 49:40:1960 49:41:2009 49:42:294 49:43:2107 49:44:2156 49:45:2205 49:46:2254 49:47:2303 49:48:2352 49:49:49 49:50:2450 50:1:50 50:2:50 50:3:150 50:4:100 50:5:50 50:6:150 50:7:350 50:8:200 50:9:450 50:10:50 50:11:550 50:12:300 50:13:650 50:14:350 50:15:150 50:16:400 50:17:850 50:18:450 50:19:950 50:20:100 50:21:1050 50:22:550 50:23:1150 50:24:600 50:25:50 50:26:650 50:27:1350 50:28:700 50:29:1450 50:30:150 50:31:1550 50:32:800 50:33:1650 50:34:850 50:35:350 50:36:900 50:37:1850 50:38:950 50:39:1950 50:40:200 50:41:2050 50:42:1050 50:43:2150 50:44:1100 50:45:450 50:46:1150 50:47:2350 50:48:1200 50:49:2450 50:50:50 # # Fibonacci numbers # 0:55:0 0:89:0 0:144:0 0:233:0 0:377:0 0:610:0 0:987:0 0:1597:0 0:2584:0 0:4181:0 0:6765:0 0:10946:0 0:17711:0 0:28657:0 0:46368:0 0:75025:0 0:121393:0 0:196418:0 0:317811:0 0:514229:0 0:832040:0 0:1346269:0 0:2178309:0 0:3524578:0 0:5702887:0 0:9227465:0 0:14930352:0 0:24157817:0 0:39088169:0 0:63245986:0 0:102334155:0 0:165580141:0 0:267914296:0 0:433494437:0 0:701408733:0 0:1134903170:0 0:1836311903:0 0:2971215073:0 0:4807526976:0 0:7778742049:0 0:12586269025:0 1:55:55 1:89:89 1:144:144 1:233:233 1:377:377 1:610:610 1:987:987 1:1597:1597 1:2584:2584 1:4181:4181 1:6765:6765 1:10946:10946 1:17711:17711 1:28657:28657 1:46368:46368 1:75025:75025 1:121393:121393 1:196418:196418 1:317811:317811 1:514229:514229 1:832040:832040 1:1346269:1346269 1:2178309:2178309 1:3524578:3524578 1:5702887:5702887 1:9227465:9227465 1:14930352:14930352 1:24157817:24157817 1:39088169:39088169 1:63245986:63245986 1:102334155:102334155 1:165580141:165580141 1:267914296:267914296 1:433494437:433494437 1:701408733:701408733 1:1134903170:1134903170 1:1836311903:1836311903 1:2971215073:2971215073 1:4807526976:4807526976 1:7778742049:7778742049 1:12586269025:12586269025 1:55:55 1:89:89 1:144:144 1:233:233 1:377:377 1:610:610 1:987:987 1:1597:1597 1:2584:2584 1:4181:4181 1:6765:6765 1:10946:10946 1:17711:17711 1:28657:28657 1:46368:46368 1:75025:75025 1:121393:121393 1:196418:196418 1:317811:317811 1:514229:514229 1:832040:832040 1:1346269:1346269 1:2178309:2178309 1:3524578:3524578 1:5702887:5702887 1:9227465:9227465 1:14930352:14930352 1:24157817:24157817 1:39088169:39088169 1:63245986:63245986 1:102334155:102334155 1:165580141:165580141 1:267914296:267914296 1:433494437:433494437 1:701408733:701408733 1:1134903170:1134903170 1:1836311903:1836311903 1:2971215073:2971215073 1:4807526976:4807526976 1:7778742049:7778742049 1:12586269025:12586269025 2:55:110 2:89:178 2:144:144 2:233:466 2:377:754 2:610:610 2:987:1974 2:1597:3194 2:2584:2584 2:4181:8362 2:6765:13530 2:10946:10946 2:17711:35422 2:28657:57314 2:46368:46368 2:75025:150050 2:121393:242786 2:196418:196418 2:317811:635622 2:514229:1028458 2:832040:832040 2:1346269:2692538 2:2178309:4356618 2:3524578:3524578 2:5702887:11405774 2:9227465:18454930 2:14930352:14930352 2:24157817:48315634 2:39088169:78176338 2:63245986:63245986 2:102334155:204668310 2:165580141:331160282 2:267914296:267914296 2:433494437:866988874 2:701408733:1402817466 2:1134903170:1134903170 2:1836311903:3672623806 2:2971215073:5942430146 2:4807526976:4807526976 2:7778742049:15557484098 2:12586269025:25172538050 3:55:165 3:89:267 3:144:144 3:233:699 3:377:1131 3:610:1830 3:987:987 3:1597:4791 3:2584:7752 3:4181:12543 3:6765:6765 3:10946:32838 3:17711:53133 3:28657:85971 3:46368:46368 3:75025:225075 3:121393:364179 3:196418:589254 3:317811:317811 3:514229:1542687 3:832040:2496120 3:1346269:4038807 3:2178309:2178309 3:3524578:10573734 3:5702887:17108661 3:9227465:27682395 3:14930352:14930352 3:24157817:72473451 3:39088169:117264507 3:63245986:189737958 3:102334155:102334155 3:165580141:496740423 3:267914296:803742888 3:433494437:1300483311 3:701408733:701408733 3:1134903170:3404709510 3:1836311903:5508935709 3:2971215073:8913645219 3:4807526976:4807526976 3:7778742049:23336226147 3:12586269025:37758807075 5:55:55 5:89:445 5:144:720 5:233:1165 5:377:1885 5:610:610 5:987:4935 5:1597:7985 5:2584:12920 5:4181:20905 5:6765:6765 5:10946:54730 5:17711:88555 5:28657:143285 5:46368:231840 5:75025:75025 5:121393:606965 5:196418:982090 5:317811:1589055 5:514229:2571145 5:832040:832040 5:1346269:6731345 5:2178309:10891545 5:3524578:17622890 5:5702887:28514435 5:9227465:9227465 5:14930352:74651760 5:24157817:120789085 5:39088169:195440845 5:63245986:316229930 5:102334155:102334155 5:165580141:827900705 5:267914296:1339571480 5:433494437:2167472185 5:701408733:3507043665 5:1134903170:1134903170 5:1836311903:9181559515 5:2971215073:14856075365 5:4807526976:24037634880 5:7778742049:38893710245 5:12586269025:12586269025 8:55:440 8:89:712 8:144:144 8:233:1864 8:377:3016 8:610:2440 8:987:7896 8:1597:12776 8:2584:2584 8:4181:33448 8:6765:54120 8:10946:43784 8:17711:141688 8:28657:229256 8:46368:46368 8:75025:600200 8:121393:971144 8:196418:785672 8:317811:2542488 8:514229:4113832 8:832040:832040 8:1346269:10770152 8:2178309:17426472 8:3524578:14098312 8:5702887:45623096 8:9227465:73819720 8:14930352:14930352 8:24157817:193262536 8:39088169:312705352 8:63245986:252983944 8:102334155:818673240 8:165580141:1324641128 8:267914296:267914296 8:433494437:3467955496 8:701408733:5611269864 8:1134903170:4539612680 8:1836311903:14690495224 8:2971215073:23769720584 8:4807526976:4807526976 8:7778742049:62229936392 8:12586269025:100690152200 13:55:715 13:89:1157 13:144:1872 13:233:3029 13:377:377 13:610:7930 13:987:12831 13:1597:20761 13:2584:33592 13:4181:54353 13:6765:87945 13:10946:10946 13:17711:230243 13:28657:372541 13:46368:602784 13:75025:975325 13:121393:1578109 13:196418:2553434 13:317811:317811 13:514229:6684977 13:832040:10816520 13:1346269:17501497 13:2178309:28318017 13:3524578:45819514 13:5702887:74137531 13:9227465:9227465 13:14930352:194094576 13:24157817:314051621 13:39088169:508146197 13:63245986:822197818 13:102334155:1330344015 13:165580141:2152541833 13:267914296:267914296 13:433494437:5635427681 13:701408733:9118313529 13:1134903170:14753741210 13:1836311903:23872054739 13:2971215073:38625795949 13:4807526976:62497850688 13:7778742049:7778742049 13:12586269025:163621497325 21:55:1155 21:89:1869 21:144:1008 21:233:4893 21:377:7917 21:610:12810 21:987:987 21:1597:33537 21:2584:54264 21:4181:87801 21:6765:47355 21:10946:229866 21:17711:371931 21:28657:601797 21:46368:46368 21:75025:1575525 21:121393:2549253 21:196418:4124778 21:317811:2224677 21:514229:10798809 21:832040:17472840 21:1346269:28271649 21:2178309:2178309 21:3524578:74016138 21:5702887:119760627 21:9227465:193776765 21:14930352:104512464 21:24157817:507314157 21:39088169:820851549 21:63245986:1328165706 21:102334155:102334155 21:165580141:3477182961 21:267914296:5626200216 21:433494437:9103383177 21:701408733:4909861131 21:1134903170:23832966570 21:1836311903:38562549963 21:2971215073:62395516533 21:4807526976:4807526976 21:7778742049:163353583029 21:12586269025:264311649525 34:55:1870 34:89:3026 34:144:2448 34:233:7922 34:377:12818 34:610:10370 34:987:33558 34:1597:54298 34:2584:2584 34:4181:142154 34:6765:230010 34:10946:186082 34:17711:602174 34:28657:974338 34:46368:788256 34:75025:2550850 34:121393:4127362 34:196418:196418 34:317811:10805574 34:514229:17483786 34:832040:14144680 34:1346269:45773146 34:2178309:74062506 34:3524578:59917826 34:5702887:193898158 34:9227465:313733810 34:14930352:14930352 34:24157817:821365778 34:39088169:1328997746 34:63245986:1075181762 34:102334155:3479361270 34:165580141:5629724794 34:267914296:4554543032 34:433494437:14738810858 34:701408733:23847896922 34:1134903170:1134903170 34:1836311903:62434604702 34:2971215073:101021312482 34:4807526976:81727958592 34:7778742049:264477229666 34:12586269025:427933146850 55:0:0 55:1:55 55:1:55 55:2:110 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12586269025:39088169:491974210728665225 12586269025:63245986:796030994547383650 12586269025:102334155:23418276459564525 12586269025:165580141:2084036199823432525 12586269025:267914296:3372041405099481400 12586269025:433494437:5456077604922913925 12586269025:701408733:8828119010022395325 12586269025:1134903170:2856839322989061850 12586269025:1836311903:23112315624967704575 12586269025:2971215073:37396512239913013825 12586269025:4807526976:60508827864880718400 12586269025:7778742049:97905340104793732225 12586269025:12586269025:12586269025 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_lcm.t0000644403072340010010000001076213024051250023353 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 20205; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_lcm'); my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_lcm(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_lcm() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); my $strx = $LIB->_str($x); ok($strx eq $out0 || $strx eq $in0, "'$test' first input arg has the right value") or diag(" got: $strx\n", " expected: ", $out0 eq $in0 ? $out0 : "$out0 or $in0"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($got); my ($x, $y); my ($xo, $yo); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_lcm(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_lcm() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); my $strx = $LIB->_str($x); ok($strx eq $out0 || $strx eq $in0, "'$test' first input arg has the right value") or diag(" got: $strx\n", " expected: ", $out0 eq $in0 ? $out0 : "$out0 or $in0"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_log_int.t0000644403072340010010000000712513024051250024232 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 22023; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_log_int'); my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; my @data; # Small numbers. for (my $x = 0; $x <= 1000 ; ++ $x) { for (my $y = 0; $y <= 10 ; ++ $y) { if ($x == 0 || $y <= 1) { push @data, [ $x, $y, undef, undef ]; next; } my $z = int(log($x) / log($y)); $z++ while $y ** $z < $x; $z-- while $y ** $z > $x; my $status = $y ** $z == $x ? 1 : 0; push @data, [ $x, $y, $z, $status ]; } } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0, $out1) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_log_int(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_log_int() in list context: $test", sub { unless (defined $out0) { plan tests => 1; is($got[0], $out0, "'$test' output arg has the right value"); return; } plan tests => $scalar_util_ok ? 11 : 10; # Number of input arguments. cmp_ok(scalar @got, '==', 2, "'$test' gives two output args"); # First output argument. is(ref($got[0]), $REF, "'$test' first output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' first output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' first output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); # Second output argument. is(ref($got[1]), "", "'$test' second output arg is a scalar"); is($got[1], $out1, "'$test' second output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_mod.dat0000644403072340010010000207015113012340550023665 0ustar ospjadomain users335:8:7 183:2:1 132:2:0 445:8:5 638:7:1 839:39:20 443:38:25 389:97:1 531:43:15 553:48:25 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429546203091033258121346585579:2437873763135424337895305255068:429546203091033258121346585579 799087100494522910913254814333:8788325478515322259159918974653:799087100494522910913254814333 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_mod.t0000644403072340010010000001054013024051250023351 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 51401; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_mod'); my @data; # Small numbers. for (my $x = 0; $x <= 24 ; ++ $x) { for (my $y = 1; $y <= 24 ; ++ $y) { push @data, [ $x, $y, $x % $y ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_mod(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_mod() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_mod(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_mod() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_modinv.dat0000644403072340010010000122116713012340550024406 0ustar ospjadomain users#1:0:undef:undef:undef:undef 1:1:0:+:0:- 1:2:1:+:1:- 1:3:1:+:2:- 1:4:1:+:3:- 1:5:1:+:4:- 1:6:1:+:5:- 1:7:1:+:6:- 1:8:1:+:7:- 1:9:1:+:8:- 1:10:1:+:9:- 1:11:1:+:10:- 1:12:1:+:11:- 1:13:1:+:12:- 1:14:1:+:13:- 1:15:1:+:14:- 1:16:1:+:15:- 1:17:1:+:16:- 1:18:1:+:17:- 1:19:1:+:18:- 1:20:1:+:19:- 1:21:1:+:20:- 1:22:1:+:21:- 1:23:1:+:22:- 1:24:1:+:23:- 1:25:1:+:24:- 1:26:1:+:25:- 1:27:1:+:26:- 1:28:1:+:27:- 1:29:1:+:28:- 1:30:1:+:29:- 1:31:1:+:30:- 1:32:1:+:31:- 1:33:1:+:32:- 1:34:1:+:33:- 1:35:1:+:34:- 1:36:1:+:35:- 1:37:1:+:36:- 1:38:1:+:37:- 1:39:1:+:38:- 1:40:1:+:39:- 1:41:1:+:40:- 1:42:1:+:41:- 1:43:1:+:42:- 1:44:1:+:43:- 1:45:1:+:44:- 1:46:1:+:45:- 1:47:1:+:46:- 1:48:1:+:47:- 1:49:1:+:48:- 1:50:1:+:49:- #2:0:undef:undef:undef:undef 2:1:0:+:0:- 2:2:undef:undef:undef:undef 2:3:2:+:1:- 2:4:undef:undef:undef:undef 2:5:3:+:2:- 2:6:undef:undef:undef:undef 2:7:4:+:3:- 2:8:undef:undef:undef:undef 2:9:5:+:4:- 2:10:undef:undef:undef:undef 2:11:6:+:5:- 2:12:undef:undef:undef:undef 2:13:7:+:6:- 2:14:undef:undef:undef:undef 2:15:8:+:7:- 2:16:undef:undef:undef:undef 2:17:9:+:8:- 2:18:undef:undef:undef:undef 2:19:10:+:9:- 2:20:undef:undef:undef:undef 2:21:11:+:10:- 2:22:undef:undef:undef:undef 2:23:12:+:11:- 2:24:undef:undef:undef:undef 2:25:13:+:12:- 2:26:undef:undef:undef:undef 2:27:14:+:13:- 2:28:undef:undef:undef:undef 2:29:15:+:14:- 2:30:undef:undef:undef:undef 2:31:16:+:15:- 2:32:undef:undef:undef:undef 2:33:17:+:16:- 2:34:undef:undef:undef:undef 2:35:18:+:17:- 2:36:undef:undef:undef:undef 2:37:19:+:18:- 2:38:undef:undef:undef:undef 2:39:20:+:19:- 2:40:undef:undef:undef:undef 2:41:21:+:20:- 2:42:undef:undef:undef:undef 2:43:22:+:21:- 2:44:undef:undef:undef:undef 2:45:23:+:22:- 2:46:undef:undef:undef:undef 2:47:24:+:23:- 2:48:undef:undef:undef:undef 2:49:25:+:24:- 2:50:undef:undef:undef:undef #3:0:undef:undef:undef:undef 3:1:0:+:0:- 3:2:1:+:1:- 3:3:undef:undef:undef:undef 3:4:3:+:1:- 3:5:2:+:3:- 3:6:undef:undef:undef:undef 3:7:5:+:2:- 3:8:3:+:5:- 3:9:undef:undef:undef:undef 3:10:7:+:3:- 3:11:4:+:7:- 3:12:undef:undef:undef:undef 3:13:9:+:4:- 3:14:5:+:9:- 3:15:undef:undef:undef:undef 3:16:11:+:5:- 3:17:6:+:11:- 3:18:undef:undef:undef:undef 3:19:13:+:6:- 3:20:7:+:13:- 3:21:undef:undef:undef:undef 3:22:15:+:7:- 3:23:8:+:15:- 3:24:undef:undef:undef:undef 3:25:17:+:8:- 3:26:9:+:17:- 3:27:undef:undef:undef:undef 3:28:19:+:9:- 3:29:10:+:19:- 3:30:undef:undef:undef:undef 3:31:21:+:10:- 3:32:11:+:21:- 3:33:undef:undef:undef:undef 3:34:23:+:11:- 3:35:12:+:23:- 3:36:undef:undef:undef:undef 3:37:25:+:12:- 3:38:13:+:25:- 3:39:undef:undef:undef:undef 3:40:27:+:13:- 3:41:14:+:27:- 3:42:undef:undef:undef:undef 3:43:29:+:14:- 3:44:15:+:29:- 3:45:undef:undef:undef:undef 3:46:31:+:15:- 3:47:16:+:31:- 3:48:undef:undef:undef:undef 3:49:33:+:16:- 3:50:17:+:33:- #4:0:undef:undef:undef:undef 4:1:0:+:0:- 4:2:undef:undef:undef:undef 4:3:1:+:2:- 4:4:undef:undef:undef:undef 4:5:4:+:1:- 4:6:undef:undef:undef:undef 4:7:2:+:5:- 4:8:undef:undef:undef:undef 4:9:7:+:2:- 4:10:undef:undef:undef:undef 4:11:3:+:8:- 4:12:undef:undef:undef:undef 4:13:10:+:3:- 4:14:undef:undef:undef:undef 4:15:4:+:11:- 4:16:undef:undef:undef:undef 4:17:13:+:4:- 4:18:undef:undef:undef:undef 4:19:5:+:14:- 4:20:undef:undef:undef:undef 4:21:16:+:5:- 4:22:undef:undef:undef:undef 4:23:6:+:17:- 4:24:undef:undef:undef:undef 4:25:19:+:6:- 4:26:undef:undef:undef:undef 4:27:7:+:20:- 4:28:undef:undef:undef:undef 4:29:22:+:7:- 4:30:undef:undef:undef:undef 4:31:8:+:23:- 4:32:undef:undef:undef:undef 4:33:25:+:8:- 4:34:undef:undef:undef:undef 4:35:9:+:26:- 4:36:undef:undef:undef:undef 4:37:28:+:9:- 4:38:undef:undef:undef:undef 4:39:10:+:29:- 4:40:undef:undef:undef:undef 4:41:31:+:10:- 4:42:undef:undef:undef:undef 4:43:11:+:32:- 4:44:undef:undef:undef:undef 4:45:34:+:11:- 4:46:undef:undef:undef:undef 4:47:12:+:35:- 4:48:undef:undef:undef:undef 4:49:37:+:12:- 4:50:undef:undef:undef:undef #5:0:undef:undef:undef:undef 5:1:0:+:0:- 5:2:1:+:1:- 5:3:2:+:1:- 5:4:1:+:3:- 5:5:undef:undef:undef:undef 5:6:5:+:1:- 5:7:3:+:4:- 5:8:5:+:3:- 5:9:2:+:7:- 5:10:undef:undef:undef:undef 5:11:9:+:2:- 5:12:5:+:7:- 5:13:8:+:5:- 5:14:3:+:11:- 5:15:undef:undef:undef:undef 5:16:13:+:3:- 5:17:7:+:10:- 5:18:11:+:7:- 5:19:4:+:15:- 5:20:undef:undef:undef:undef 5:21:17:+:4:- 5:22:9:+:13:- 5:23:14:+:9:- 5:24:5:+:19:- 5:25:undef:undef:undef:undef 5:26:21:+:5:- 5:27:11:+:16:- 5:28:17:+:11:- 5:29:6:+:23:- 5:30:undef:undef:undef:undef 5:31:25:+:6:- 5:32:13:+:19:- 5:33:20:+:13:- 5:34:7:+:27:- 5:35:undef:undef:undef:undef 5:36:29:+:7:- 5:37:15:+:22:- 5:38:23:+:15:- 5:39:8:+:31:- 5:40:undef:undef:undef:undef 5:41:33:+:8:- 5:42:17:+:25:- 5:43:26:+:17:- 5:44:9:+:35:- 5:45:undef:undef:undef:undef 5:46:37:+:9:- 5:47:19:+:28:- 5:48:29:+:19:- 5:49:10:+:39:- 5:50:undef:undef:undef:undef #6:0:undef:undef:undef:undef 6:1:0:+:0:- 6:2:undef:undef:undef:undef 6:3:undef:undef:undef:undef 6:4:undef:undef:undef:undef 6:5:1:+:4:- 6:6:undef:undef:undef:undef 6:7:6:+:1:- 6:8:undef:undef:undef:undef 6:9:undef:undef:undef:undef 6:10:undef:undef:undef:undef 6:11:2:+:9:- 6:12:undef:undef:undef:undef 6:13:11:+:2:- 6:14:undef:undef:undef:undef 6:15:undef:undef:undef:undef 6:16:undef:undef:undef:undef 6:17:3:+:14:- 6:18:undef:undef:undef:undef 6:19:16:+:3:- 6:20:undef:undef:undef:undef 6:21:undef:undef:undef:undef 6:22:undef:undef:undef:undef 6:23:4:+:19:- 6:24:undef:undef:undef:undef 6:25:21:+:4:- 6:26:undef:undef:undef:undef 6:27:undef:undef:undef:undef 6:28:undef:undef:undef:undef 6:29:5:+:24:- 6:30:undef:undef:undef:undef 6:31:26:+:5:- 6:32:undef:undef:undef:undef 6:33:undef:undef:undef:undef 6:34:undef:undef:undef:undef 6:35:6:+:29:- 6:36:undef:undef:undef:undef 6:37:31:+:6:- 6:38:undef:undef:undef:undef 6:39:undef:undef:undef:undef 6:40:undef:undef:undef:undef 6:41:7:+:34:- 6:42:undef:undef:undef:undef 6:43:36:+:7:- 6:44:undef:undef:undef:undef 6:45:undef:undef:undef:undef 6:46:undef:undef:undef:undef 6:47:8:+:39:- 6:48:undef:undef:undef:undef 6:49:41:+:8:- 6:50:undef:undef:undef:undef #7:0:undef:undef:undef:undef 7:1:0:+:0:- 7:2:1:+:1:- 7:3:1:+:2:- 7:4:3:+:1:- 7:5:3:+:2:- 7:6:1:+:5:- 7:7:undef:undef:undef:undef 7:8:7:+:1:- 7:9:4:+:5:- 7:10:3:+:7:- 7:11:8:+:3:- 7:12:7:+:5:- 7:13:2:+:11:- 7:14:undef:undef:undef:undef 7:15:13:+:2:- 7:16:7:+:9:- 7:17:5:+:12:- 7:18:13:+:5:- 7:19:11:+:8:- 7:20:3:+:17:- 7:21:undef:undef:undef:undef 7:22:19:+:3:- 7:23:10:+:13:- 7:24:7:+:17:- 7:25:18:+:7:- 7:26:15:+:11:- 7:27:4:+:23:- 7:28:undef:undef:undef:undef 7:29:25:+:4:- 7:30:13:+:17:- 7:31:9:+:22:- 7:32:23:+:9:- 7:33:19:+:14:- 7:34:5:+:29:- 7:35:undef:undef:undef:undef 7:36:31:+:5:- 7:37:16:+:21:- 7:38:11:+:27:- 7:39:28:+:11:- 7:40:23:+:17:- 7:41:6:+:35:- 7:42:undef:undef:undef:undef 7:43:37:+:6:- 7:44:19:+:25:- 7:45:13:+:32:- 7:46:33:+:13:- 7:47:27:+:20:- 7:48:7:+:41:- 7:49:undef:undef:undef:undef 7:50:43:+:7:- #8:0:undef:undef:undef:undef 8:1:0:+:0:- 8:2:undef:undef:undef:undef 8:3:2:+:1:- 8:4:undef:undef:undef:undef 8:5:2:+:3:- 8:6:undef:undef:undef:undef 8:7:1:+:6:- 8:8:undef:undef:undef:undef 8:9:8:+:1:- 8:10:undef:undef:undef:undef 8:11:7:+:4:- 8:12:undef:undef:undef:undef 8:13:5:+:8:- 8:14:undef:undef:undef:undef 8:15:2:+:13:- 8:16:undef:undef:undef:undef 8:17:15:+:2:- 8:18:undef:undef:undef:undef 8:19:12:+:7:- 8:20:undef:undef:undef:undef 8:21:8:+:13:- 8:22:undef:undef:undef:undef 8:23:3:+:20:- 8:24:undef:undef:undef:undef 8:25:22:+:3:- 8:26:undef:undef:undef:undef 8:27:17:+:10:- 8:28:undef:undef:undef:undef 8:29:11:+:18:- 8:30:undef:undef:undef:undef 8:31:4:+:27:- 8:32:undef:undef:undef:undef 8:33:29:+:4:- 8:34:undef:undef:undef:undef 8:35:22:+:13:- 8:36:undef:undef:undef:undef 8:37:14:+:23:- 8:38:undef:undef:undef:undef 8:39:5:+:34:- 8:40:undef:undef:undef:undef 8:41:36:+:5:- 8:42:undef:undef:undef:undef 8:43:27:+:16:- 8:44:undef:undef:undef:undef 8:45:17:+:28:- 8:46:undef:undef:undef:undef 8:47:6:+:41:- 8:48:undef:undef:undef:undef 8:49:43:+:6:- 8:50:undef:undef:undef:undef #9:0:undef:undef:undef:undef 9:1:0:+:0:- 9:2:1:+:1:- 9:3:undef:undef:undef:undef 9:4:1:+:3:- 9:5:4:+:1:- 9:6:undef:undef:undef:undef 9:7:4:+:3:- 9:8:1:+:7:- 9:9:undef:undef:undef:undef 9:10:9:+:1:- 9:11:5:+:6:- 9:12:undef:undef:undef:undef 9:13:3:+:10:- 9:14:11:+:3:- 9:15:undef:undef:undef:undef 9:16:9:+:7:- 9:17:2:+:15:- 9:18:undef:undef:undef:undef 9:19:17:+:2:- 9:20:9:+:11:- 9:21:undef:undef:undef:undef 9:22:5:+:17:- 9:23:18:+:5:- 9:24:undef:undef:undef:undef 9:25:14:+:11:- 9:26:3:+:23:- 9:27:undef:undef:undef:undef 9:28:25:+:3:- 9:29:13:+:16:- 9:30:undef:undef:undef:undef 9:31:7:+:24:- 9:32:25:+:7:- 9:33:undef:undef:undef:undef 9:34:19:+:15:- 9:35:4:+:31:- 9:36:undef:undef:undef:undef 9:37:33:+:4:- 9:38:17:+:21:- 9:39:undef:undef:undef:undef 9:40:9:+:31:- 9:41:32:+:9:- 9:42:undef:undef:undef:undef 9:43:24:+:19:- 9:44:5:+:39:- 9:45:undef:undef:undef:undef 9:46:41:+:5:- 9:47:21:+:26:- 9:48:undef:undef:undef:undef 9:49:11:+:38:- 9:50:39:+:11:- #10:0:undef:undef:undef:undef 10:1:0:+:0:- 10:2:undef:undef:undef:undef 10:3:1:+:2:- 10:4:undef:undef:undef:undef 10:5:undef:undef:undef:undef 10:6:undef:undef:undef:undef 10:7:5:+:2:- 10:8:undef:undef:undef:undef 10:9:1:+:8:- 10:10:undef:undef:undef:undef 10:11:10:+:1:- 10:12:undef:undef:undef:undef 10:13:4:+:9:- 10:14:undef:undef:undef:undef 10:15:undef:undef:undef:undef 10:16:undef:undef:undef:undef 10:17:12:+:5:- 10:18:undef:undef:undef:undef 10:19:2:+:17:- 10:20:undef:undef:undef:undef 10:21:19:+:2:- 10:22:undef:undef:undef:undef 10:23:7:+:16:- 10:24:undef:undef:undef:undef 10:25:undef:undef:undef:undef 10:26:undef:undef:undef:undef 10:27:19:+:8:- 10:28:undef:undef:undef:undef 10:29:3:+:26:- 10:30:undef:undef:undef:undef 10:31:28:+:3:- 10:32:undef:undef:undef:undef 10:33:10:+:23:- 10:34:undef:undef:undef:undef 10:35:undef:undef:undef:undef 10:36:undef:undef:undef:undef 10:37:26:+:11:- 10:38:undef:undef:undef:undef 10:39:4:+:35:- 10:40:undef:undef:undef:undef 10:41:37:+:4:- 10:42:undef:undef:undef:undef 10:43:13:+:30:- 10:44:undef:undef:undef:undef 10:45:undef:undef:undef:undef 10:46:undef:undef:undef:undef 10:47:33:+:14:- 10:48:undef:undef:undef:undef 10:49:5:+:44:- 10:50:undef:undef:undef:undef #11:0:undef:undef:undef:undef 11:1:0:+:0:- 11:2:1:+:1:- 11:3:2:+:1:- 11:4:3:+:1:- 11:5:1:+:4:- 11:6:5:+:1:- 11:7:2:+:5:- 11:8:3:+:5:- 11:9:5:+:4:- 11:10:1:+:9:- 11:11:undef:undef:undef:undef 11:12:11:+:1:- 11:13:6:+:7:- 11:14:9:+:5:- 11:15:11:+:4:- 11:16:3:+:13:- 11:17:14:+:3:- 11:18:5:+:13:- 11:19:7:+:12:- 11:20:11:+:9:- 11:21:2:+:19:- 11:22:undef:undef:undef:undef 11:23:21:+:2:- 11:24:11:+:13:- 11:25:16:+:9:- 11:26:19:+:7:- 11:27:5:+:22:- 11:28:23:+:5:- 11:29:8:+:21:- 11:30:11:+:19:- 11:31:17:+:14:- 11:32:3:+:29:- 11:33:undef:undef:undef:undef 11:34:31:+:3:- 11:35:16:+:19:- 11:36:23:+:13:- 11:37:27:+:10:- 11:38:7:+:31:- 11:39:32:+:7:- 11:40:11:+:29:- 11:41:15:+:26:- 11:42:23:+:19:- 11:43:4:+:39:- 11:44:undef:undef:undef:undef 11:45:41:+:4:- 11:46:21:+:25:- 11:47:30:+:17:- 11:48:35:+:13:- 11:49:9:+:40:- 11:50:41:+:9:- #12:0:undef:undef:undef:undef 12:1:0:+:0:- 12:2:undef:undef:undef:undef 12:3:undef:undef:undef:undef 12:4:undef:undef:undef:undef 12:5:3:+:2:- 12:6:undef:undef:undef:undef 12:7:3:+:4:- 12:8:undef:undef:undef:undef 12:9:undef:undef:undef:undef 12:10:undef:undef:undef:undef 12:11:1:+:10:- 12:12:undef:undef:undef:undef 12:13:12:+:1:- 12:14:undef:undef:undef:undef 12:15:undef:undef:undef:undef 12:16:undef:undef:undef:undef 12:17:10:+:7:- 12:18:undef:undef:undef:undef 12:19:8:+:11:- 12:20:undef:undef:undef:undef 12:21:undef:undef:undef:undef 12:22:undef:undef:undef:undef 12:23:2:+:21:- 12:24:undef:undef:undef:undef 12:25:23:+:2:- 12:26:undef:undef:undef:undef 12:27:undef:undef:undef:undef 12:28:undef:undef:undef:undef 12:29:17:+:12:- 12:30:undef:undef:undef:undef 12:31:13:+:18:- 12:32:undef:undef:undef:undef 12:33:undef:undef:undef:undef 12:34:undef:undef:undef:undef 12:35:3:+:32:- 12:36:undef:undef:undef:undef 12:37:34:+:3:- 12:38:undef:undef:undef:undef 12:39:undef:undef:undef:undef 12:40:undef:undef:undef:undef 12:41:24:+:17:- 12:42:undef:undef:undef:undef 12:43:18:+:25:- 12:44:undef:undef:undef:undef 12:45:undef:undef:undef:undef 12:46:undef:undef:undef:undef 12:47:4:+:43:- 12:48:undef:undef:undef:undef 12:49:45:+:4:- 12:50:undef:undef:undef:undef #13:0:undef:undef:undef:undef 13:1:0:+:0:- 13:2:1:+:1:- 13:3:1:+:2:- 13:4:1:+:3:- 13:5:2:+:3:- 13:6:1:+:5:- 13:7:6:+:1:- 13:8:5:+:3:- 13:9:7:+:2:- 13:10:7:+:3:- 13:11:6:+:5:- 13:12:1:+:11:- 13:13:undef:undef:undef:undef 13:14:13:+:1:- 13:15:7:+:8:- 13:16:5:+:11:- 13:17:4:+:13:- 13:18:7:+:11:- 13:19:3:+:16:- 13:20:17:+:3:- 13:21:13:+:8:- 13:22:17:+:5:- 13:23:16:+:7:- 13:24:13:+:11:- 13:25:2:+:23:- 13:26:undef:undef:undef:undef 13:27:25:+:2:- 13:28:13:+:15:- 13:29:9:+:20:- 13:30:7:+:23:- 13:31:12:+:19:- 13:32:5:+:27:- 13:33:28:+:5:- 13:34:21:+:13:- 13:35:27:+:8:- 13:36:25:+:11:- 13:37:20:+:17:- 13:38:3:+:35:- 13:39:undef:undef:undef:undef 13:40:37:+:3:- 13:41:19:+:22:- 13:42:13:+:29:- 13:43:10:+:33:- 13:44:17:+:27:- 13:45:7:+:38:- 13:46:39:+:7:- 13:47:29:+:18:- 13:48:37:+:11:- 13:49:34:+:15:- 13:50:27:+:23:- #14:0:undef:undef:undef:undef 14:1:0:+:0:- 14:2:undef:undef:undef:undef 14:3:2:+:1:- 14:4:undef:undef:undef:undef 14:5:4:+:1:- 14:6:undef:undef:undef:undef 14:7:undef:undef:undef:undef 14:8:undef:undef:undef:undef 14:9:2:+:7:- 14:10:undef:undef:undef:undef 14:11:4:+:7:- 14:12:undef:undef:undef:undef 14:13:1:+:12:- 14:14:undef:undef:undef:undef 14:15:14:+:1:- 14:16:undef:undef:undef:undef 14:17:11:+:6:- 14:18:undef:undef:undef:undef 14:19:15:+:4:- 14:20:undef:undef:undef:undef 14:21:undef:undef:undef:undef 14:22:undef:undef:undef:undef 14:23:5:+:18:- 14:24:undef:undef:undef:undef 14:25:9:+:16:- 14:26:undef:undef:undef:undef 14:27:2:+:25:- 14:28:undef:undef:undef:undef 14:29:27:+:2:- 14:30:undef:undef:undef:undef 14:31:20:+:11:- 14:32:undef:undef:undef:undef 14:33:26:+:7:- 14:34:undef:undef:undef:undef 14:35:undef:undef:undef:undef 14:36:undef:undef:undef:undef 14:37:8:+:29:- 14:38:undef:undef:undef:undef 14:39:14:+:25:- 14:40:undef:undef:undef:undef 14:41:3:+:38:- 14:42:undef:undef:undef:undef 14:43:40:+:3:- 14:44:undef:undef:undef:undef 14:45:29:+:16:- 14:46:undef:undef:undef:undef 14:47:37:+:10:- 14:48:undef:undef:undef:undef 14:49:undef:undef:undef:undef 14:50:undef:undef:undef:undef #15:0:undef:undef:undef:undef 15:1:0:+:0:- 15:2:1:+:1:- 15:3:undef:undef:undef:undef 15:4:3:+:1:- 15:5:undef:undef:undef:undef 15:6:undef:undef:undef:undef 15:7:1:+:6:- 15:8:7:+:1:- 15:9:undef:undef:undef:undef 15:10:undef:undef:undef:undef 15:11:3:+:8:- 15:12:undef:undef:undef:undef 15:13:7:+:6:- 15:14:1:+:13:- 15:15:undef:undef:undef:undef 15:16:15:+:1:- 15:17:8:+:9:- 15:18:undef:undef:undef:undef 15:19:14:+:5:- 15:20:undef:undef:undef:undef 15:21:undef:undef:undef:undef 15:22:3:+:19:- 15:23:20:+:3:- 15:24:undef:undef:undef:undef 15:25:undef:undef:undef:undef 15:26:7:+:19:- 15:27:undef:undef:undef:undef 15:28:15:+:13:- 15:29:2:+:27:- 15:30:undef:undef:undef:undef 15:31:29:+:2:- 15:32:15:+:17:- 15:33:undef:undef:undef:undef 15:34:25:+:9:- 15:35:undef:undef:undef:undef 15:36:undef:undef:undef:undef 15:37:5:+:32:- 15:38:33:+:5:- 15:39:undef:undef:undef:undef 15:40:undef:undef:undef:undef 15:41:11:+:30:- 15:42:undef:undef:undef:undef 15:43:23:+:20:- 15:44:3:+:41:- 15:45:undef:undef:undef:undef 15:46:43:+:3:- 15:47:22:+:25:- 15:48:undef:undef:undef:undef 15:49:36:+:13:- 15:50:undef:undef:undef:undef #16:0:undef:undef:undef:undef 16:1:0:+:0:- 16:2:undef:undef:undef:undef 16:3:1:+:2:- 16:4:undef:undef:undef:undef 16:5:1:+:4:- 16:6:undef:undef:undef:undef 16:7:4:+:3:- 16:8:undef:undef:undef:undef 16:9:4:+:5:- 16:10:undef:undef:undef:undef 16:11:9:+:2:- 16:12:undef:undef:undef:undef 16:13:9:+:4:- 16:14:undef:undef:undef:undef 16:15:1:+:14:- 16:16:undef:undef:undef:undef 16:17:16:+:1:- 16:18:undef:undef:undef:undef 16:19:6:+:13:- 16:20:undef:undef:undef:undef 16:21:4:+:17:- 16:22:undef:undef:undef:undef 16:23:13:+:10:- 16:24:undef:undef:undef:undef 16:25:11:+:14:- 16:26:undef:undef:undef:undef 16:27:22:+:5:- 16:28:undef:undef:undef:undef 16:29:20:+:9:- 16:30:undef:undef:undef:undef 16:31:2:+:29:- 16:32:undef:undef:undef:undef 16:33:31:+:2:- 16:34:undef:undef:undef:undef 16:35:11:+:24:- 16:36:undef:undef:undef:undef 16:37:7:+:30:- 16:38:undef:undef:undef:undef 16:39:22:+:17:- 16:40:undef:undef:undef:undef 16:41:18:+:23:- 16:42:undef:undef:undef:undef 16:43:35:+:8:- 16:44:undef:undef:undef:undef 16:45:31:+:14:- 16:46:undef:undef:undef:undef 16:47:3:+:44:- 16:48:undef:undef:undef:undef 16:49:46:+:3:- 16:50:undef:undef:undef:undef #17:0:undef:undef:undef:undef 17:1:0:+:0:- 17:2:1:+:1:- 17:3:2:+:1:- 17:4:1:+:3:- 17:5:3:+:2:- 17:6:5:+:1:- 17:7:5:+:2:- 17:8:1:+:7:- 17:9:8:+:1:- 17:10:3:+:7:- 17:11:2:+:9:- 17:12:5:+:7:- 17:13:10:+:3:- 17:14:5:+:9:- 17:15:8:+:7:- 17:16:1:+:15:- 17:17:undef:undef:undef:undef 17:18:17:+:1:- 17:19:9:+:10:- 17:20:13:+:7:- 17:21:5:+:16:- 17:22:13:+:9:- 17:23:19:+:4:- 17:24:17:+:7:- 17:25:3:+:22:- 17:26:23:+:3:- 17:27:8:+:19:- 17:28:5:+:23:- 17:29:12:+:17:- 17:30:23:+:7:- 17:31:11:+:20:- 17:32:17:+:15:- 17:33:2:+:31:- 17:34:undef:undef:undef:undef 17:35:33:+:2:- 17:36:17:+:19:- 17:37:24:+:13:- 17:38:9:+:29:- 17:39:23:+:16:- 17:40:33:+:7:- 17:41:29:+:12:- 17:42:5:+:37:- 17:43:38:+:5:- 17:44:13:+:31:- 17:45:8:+:37:- 17:46:19:+:27:- 17:47:36:+:11:- 17:48:17:+:31:- 17:49:26:+:23:- 17:50:3:+:47:- #18:0:undef:undef:undef:undef 18:1:0:+:0:- 18:2:undef:undef:undef:undef 18:3:undef:undef:undef:undef 18:4:undef:undef:undef:undef 18:5:2:+:3:- 18:6:undef:undef:undef:undef 18:7:2:+:5:- 18:8:undef:undef:undef:undef 18:9:undef:undef:undef:undef 18:10:undef:undef:undef:undef 18:11:8:+:3:- 18:12:undef:undef:undef:undef 18:13:8:+:5:- 18:14:undef:undef:undef:undef 18:15:undef:undef:undef:undef 18:16:undef:undef:undef:undef 18:17:1:+:16:- 18:18:undef:undef:undef:undef 18:19:18:+:1:- 18:20:undef:undef:undef:undef 18:21:undef:undef:undef:undef 18:22:undef:undef:undef:undef 18:23:9:+:14:- 18:24:undef:undef:undef:undef 18:25:7:+:18:- 18:26:undef:undef:undef:undef 18:27:undef:undef:undef:undef 18:28:undef:undef:undef:undef 18:29:21:+:8:- 18:30:undef:undef:undef:undef 18:31:19:+:12:- 18:32:undef:undef:undef:undef 18:33:undef:undef:undef:undef 18:34:undef:undef:undef:undef 18:35:2:+:33:- 18:36:undef:undef:undef:undef 18:37:35:+:2:- 18:38:undef:undef:undef:undef 18:39:undef:undef:undef:undef 18:40:undef:undef:undef:undef 18:41:16:+:25:- 18:42:undef:undef:undef:undef 18:43:12:+:31:- 18:44:undef:undef:undef:undef 18:45:undef:undef:undef:undef 18:46:undef:undef:undef:undef 18:47:34:+:13:- 18:48:undef:undef:undef:undef 18:49:30:+:19:- 18:50:undef:undef:undef:undef #19:0:undef:undef:undef:undef 19:1:0:+:0:- 19:2:1:+:1:- 19:3:1:+:2:- 19:4:3:+:1:- 19:5:4:+:1:- 19:6:1:+:5:- 19:7:3:+:4:- 19:8:3:+:5:- 19:9:1:+:8:- 19:10:9:+:1:- 19:11:7:+:4:- 19:12:7:+:5:- 19:13:11:+:2:- 19:14:3:+:11:- 19:15:4:+:11:- 19:16:11:+:5:- 19:17:9:+:8:- 19:18:1:+:17:- 19:19:undef:undef:undef:undef 19:20:19:+:1:- 19:21:10:+:11:- 19:22:7:+:15:- 19:23:17:+:6:- 19:24:19:+:5:- 19:25:4:+:21:- 19:26:11:+:15:- 19:27:10:+:17:- 19:28:3:+:25:- 19:29:26:+:3:- 19:30:19:+:11:- 19:31:18:+:13:- 19:32:27:+:5:- 19:33:7:+:26:- 19:34:9:+:25:- 19:35:24:+:11:- 19:36:19:+:17:- 19:37:2:+:35:- 19:38:undef:undef:undef:undef 19:39:37:+:2:- 19:40:19:+:21:- 19:41:13:+:28:- 19:42:31:+:11:- 19:43:34:+:9:- 19:44:7:+:37:- 19:45:19:+:26:- 19:46:17:+:29:- 19:47:5:+:42:- 19:48:43:+:5:- 19:49:31:+:18:- 19:50:29:+:21:- #20:0:undef:undef:undef:undef 20:1:0:+:0:- 20:2:undef:undef:undef:undef 20:3:2:+:1:- 20:4:undef:undef:undef:undef 20:5:undef:undef:undef:undef 20:6:undef:undef:undef:undef 20:7:6:+:1:- 20:8:undef:undef:undef:undef 20:9:5:+:4:- 20:10:undef:undef:undef:undef 20:11:5:+:6:- 20:12:undef:undef:undef:undef 20:13:2:+:11:- 20:14:undef:undef:undef:undef 20:15:undef:undef:undef:undef 20:16:undef:undef:undef:undef 20:17:6:+:11:- 20:18:undef:undef:undef:undef 20:19:1:+:18:- 20:20:undef:undef:undef:undef 20:21:20:+:1:- 20:22:undef:undef:undef:undef 20:23:15:+:8:- 20:24:undef:undef:undef:undef 20:25:undef:undef:undef:undef 20:26:undef:undef:undef:undef 20:27:23:+:4:- 20:28:undef:undef:undef:undef 20:29:16:+:13:- 20:30:undef:undef:undef:undef 20:31:14:+:17:- 20:32:undef:undef:undef:undef 20:33:5:+:28:- 20:34:undef:undef:undef:undef 20:35:undef:undef:undef:undef 20:36:undef:undef:undef:undef 20:37:13:+:24:- 20:38:undef:undef:undef:undef 20:39:2:+:37:- 20:40:undef:undef:undef:undef 20:41:39:+:2:- 20:42:undef:undef:undef:undef 20:43:28:+:15:- 20:44:undef:undef:undef:undef 20:45:undef:undef:undef:undef 20:46:undef:undef:undef:undef 20:47:40:+:7:- 20:48:undef:undef:undef:undef 20:49:27:+:22:- 20:50:undef:undef:undef:undef #21:0:undef:undef:undef:undef 21:1:0:+:0:- 21:2:1:+:1:- 21:3:undef:undef:undef:undef 21:4:1:+:3:- 21:5:1:+:4:- 21:6:undef:undef:undef:undef 21:7:undef:undef:undef:undef 21:8:5:+:3:- 21:9:undef:undef:undef:undef 21:10:1:+:9:- 21:11:10:+:1:- 21:12:undef:undef:undef:undef 21:13:5:+:8:- 21:14:undef:undef:undef:undef 21:15:undef:undef:undef:undef 21:16:13:+:3:- 21:17:13:+:4:- 21:18:undef:undef:undef:undef 21:19:10:+:9:- 21:20:1:+:19:- 21:21:undef:undef:undef:undef 21:22:21:+:1:- 21:23:11:+:12:- 21:24:undef:undef:undef:undef 21:25:6:+:19:- 21:26:5:+:21:- 21:27:undef:undef:undef:undef 21:28:undef:undef:undef:undef 21:29:18:+:11:- 21:30:undef:undef:undef:undef 21:31:3:+:28:- 21:32:29:+:3:- 21:33:undef:undef:undef:undef 21:34:13:+:21:- 21:35:undef:undef:undef:undef 21:36:undef:undef:undef:undef 21:37:30:+:7:- 21:38:29:+:9:- 21:39:undef:undef:undef:undef 21:40:21:+:19:- 21:41:2:+:39:- 21:42:undef:undef:undef:undef 21:43:41:+:2:- 21:44:21:+:23:- 21:45:undef:undef:undef:undef 21:46:11:+:35:- 21:47:9:+:38:- 21:48:undef:undef:undef:undef 21:49:undef:undef:undef:undef 21:50:31:+:19:- #22:0:undef:undef:undef:undef 22:1:0:+:0:- 22:2:undef:undef:undef:undef 22:3:1:+:2:- 22:4:undef:undef:undef:undef 22:5:3:+:2:- 22:6:undef:undef:undef:undef 22:7:1:+:6:- 22:8:undef:undef:undef:undef 22:9:7:+:2:- 22:10:undef:undef:undef:undef 22:11:undef:undef:undef:undef 22:12:undef:undef:undef:undef 22:13:3:+:10:- 22:14:undef:undef:undef:undef 22:15:13:+:2:- 22:16:undef:undef:undef:undef 22:17:7:+:10:- 22:18:undef:undef:undef:undef 22:19:13:+:6:- 22:20:undef:undef:undef:undef 22:21:1:+:20:- 22:22:undef:undef:undef:undef 22:23:22:+:1:- 22:24:undef:undef:undef:undef 22:25:8:+:17:- 22:26:undef:undef:undef:undef 22:27:16:+:11:- 22:28:undef:undef:undef:undef 22:29:4:+:25:- 22:30:undef:undef:undef:undef 22:31:24:+:7:- 22:32:undef:undef:undef:undef 22:33:undef:undef:undef:undef 22:34:undef:undef:undef:undef 22:35:8:+:27:- 22:36:undef:undef:undef:undef 22:37:32:+:5:- 22:38:undef:undef:undef:undef 22:39:16:+:23:- 22:40:undef:undef:undef:undef 22:41:28:+:13:- 22:42:undef:undef:undef:undef 22:43:2:+:41:- 22:44:undef:undef:undef:undef 22:45:43:+:2:- 22:46:undef:undef:undef:undef 22:47:15:+:32:- 22:48:undef:undef:undef:undef 22:49:29:+:20:- 22:50:undef:undef:undef:undef #23:0:undef:undef:undef:undef 23:1:0:+:0:- 23:2:1:+:1:- 23:3:2:+:1:- 23:4:3:+:1:- 23:5:2:+:3:- 23:6:5:+:1:- 23:7:4:+:3:- 23:8:7:+:1:- 23:9:2:+:7:- 23:10:7:+:3:- 23:11:1:+:10:- 23:12:11:+:1:- 23:13:4:+:9:- 23:14:11:+:3:- 23:15:2:+:13:- 23:16:7:+:9:- 23:17:3:+:14:- 23:18:11:+:7:- 23:19:5:+:14:- 23:20:7:+:13:- 23:21:11:+:10:- 23:22:1:+:21:- 23:23:undef:undef:undef:undef 23:24:23:+:1:- 23:25:12:+:13:- 23:26:17:+:9:- 23:27:20:+:7:- 23:28:11:+:17:- 23:29:24:+:5:- 23:30:17:+:13:- 23:31:27:+:4:- 23:32:7:+:25:- 23:33:23:+:10:- 23:34:3:+:31:- 23:35:32:+:3:- 23:36:11:+:25:- 23:37:29:+:8:- 23:38:5:+:33:- 23:39:17:+:22:- 23:40:7:+:33:- 23:41:25:+:16:- 23:42:11:+:31:- 23:43:15:+:28:- 23:44:23:+:21:- 23:45:2:+:43:- 23:46:undef:undef:undef:undef 23:47:45:+:2:- 23:48:23:+:25:- 23:49:32:+:17:- 23:50:37:+:13:- #24:0:undef:undef:undef:undef 24:1:0:+:0:- 24:2:undef:undef:undef:undef 24:3:undef:undef:undef:undef 24:4:undef:undef:undef:undef 24:5:4:+:1:- 24:6:undef:undef:undef:undef 24:7:5:+:2:- 24:8:undef:undef:undef:undef 24:9:undef:undef:undef:undef 24:10:undef:undef:undef:undef 24:11:6:+:5:- 24:12:undef:undef:undef:undef 24:13:6:+:7:- 24:14:undef:undef:undef:undef 24:15:undef:undef:undef:undef 24:16:undef:undef:undef:undef 24:17:5:+:12:- 24:18:undef:undef:undef:undef 24:19:4:+:15:- 24:20:undef:undef:undef:undef 24:21:undef:undef:undef:undef 24:22:undef:undef:undef:undef 24:23:1:+:22:- 24:24:undef:undef:undef:undef 24:25:24:+:1:- 24:26:undef:undef:undef:undef 24:27:undef:undef:undef:undef 24:28:undef:undef:undef:undef 24:29:23:+:6:- 24:30:undef:undef:undef:undef 24:31:22:+:9:- 24:32:undef:undef:undef:undef 24:33:undef:undef:undef:undef 24:34:undef:undef:undef:undef 24:35:19:+:16:- 24:36:undef:undef:undef:undef 24:37:17:+:20:- 24:38:undef:undef:undef:undef 24:39:undef:undef:undef:undef 24:40:undef:undef:undef:undef 24:41:12:+:29:- 24:42:undef:undef:undef:undef 24:43:9:+:34:- 24:44:undef:undef:undef:undef 24:45:undef:undef:undef:undef 24:46:undef:undef:undef:undef 24:47:2:+:45:- 24:48:undef:undef:undef:undef 24:49:47:+:2:- 24:50:undef:undef:undef:undef #25:0:undef:undef:undef:undef 25:1:0:+:0:- 25:2:1:+:1:- 25:3:1:+:2:- 25:4:1:+:3:- 25:5:undef:undef:undef:undef 25:6:1:+:5:- 25:7:2:+:5:- 25:8:1:+:7:- 25:9:4:+:5:- 25:10:undef:undef:undef:undef 25:11:4:+:7:- 25:12:1:+:11:- 25:13:12:+:1:- 25:14:9:+:5:- 25:15:undef:undef:undef:undef 25:16:9:+:7:- 25:17:15:+:2:- 25:18:13:+:5:- 25:19:16:+:3:- 25:20:undef:undef:undef:undef 25:21:16:+:5:- 25:22:15:+:7:- 25:23:12:+:11:- 25:24:1:+:23:- 25:25:undef:undef:undef:undef 25:26:25:+:1:- 25:27:13:+:14:- 25:28:9:+:19:- 25:29:7:+:22:- 25:30:undef:undef:undef:undef 25:31:5:+:26:- 25:32:9:+:23:- 25:33:4:+:29:- 25:34:15:+:19:- 25:35:undef:undef:undef:undef 25:36:13:+:23:- 25:37:3:+:34:- 25:38:35:+:3:- 25:39:25:+:14:- 25:40:undef:undef:undef:undef 25:41:23:+:18:- 25:42:37:+:5:- 25:43:31:+:12:- 25:44:37:+:7:- 25:45:undef:undef:undef:undef 25:46:35:+:11:- 25:47:32:+:15:- 25:48:25:+:23:- 25:49:2:+:47:- 25:50:undef:undef:undef:undef #26:0:undef:undef:undef:undef 26:1:0:+:0:- 26:2:undef:undef:undef:undef 26:3:2:+:1:- 26:4:undef:undef:undef:undef 26:5:1:+:4:- 26:6:undef:undef:undef:undef 26:7:3:+:4:- 26:8:undef:undef:undef:undef 26:9:8:+:1:- 26:10:undef:undef:undef:undef 26:11:3:+:8:- 26:12:undef:undef:undef:undef 26:13:undef:undef:undef:undef 26:14:undef:undef:undef:undef 26:15:11:+:4:- 26:16:undef:undef:undef:undef 26:17:2:+:15:- 26:18:undef:undef:undef:undef 26:19:11:+:8:- 26:20:undef:undef:undef:undef 26:21:17:+:4:- 26:22:undef:undef:undef:undef 26:23:8:+:15:- 26:24:undef:undef:undef:undef 26:25:1:+:24:- 26:26:undef:undef:undef:undef 26:27:26:+:1:- 26:28:undef:undef:undef:undef 26:29:19:+:10:- 26:30:undef:undef:undef:undef 26:31:6:+:25:- 26:32:undef:undef:undef:undef 26:33:14:+:19:- 26:34:undef:undef:undef:undef 26:35:31:+:4:- 26:36:undef:undef:undef:undef 26:37:10:+:27:- 26:38:undef:undef:undef:undef 26:39:undef:undef:undef:undef 26:40:undef:undef:undef:undef 26:41:30:+:11:- 26:42:undef:undef:undef:undef 26:43:5:+:38:- 26:44:undef:undef:undef:undef 26:45:26:+:19:- 26:46:undef:undef:undef:undef 26:47:38:+:9:- 26:48:undef:undef:undef:undef 26:49:17:+:32:- 26:50:undef:undef:undef:undef #27:0:undef:undef:undef:undef 27:1:0:+:0:- 27:2:1:+:1:- 27:3:undef:undef:undef:undef 27:4:3:+:1:- 27:5:3:+:2:- 27:6:undef:undef:undef:undef 27:7:6:+:1:- 27:8:3:+:5:- 27:9:undef:undef:undef:undef 27:10:3:+:7:- 27:11:9:+:2:- 27:12:undef:undef:undef:undef 27:13:1:+:12:- 27:14:13:+:1:- 27:15:undef:undef:undef:undef 27:16:3:+:13:- 27:17:12:+:5:- 27:18:undef:undef:undef:undef 27:19:12:+:7:- 27:20:3:+:17:- 27:21:undef:undef:undef:undef 27:22:9:+:13:- 27:23:6:+:17:- 27:24:undef:undef:undef:undef 27:25:13:+:12:- 27:26:1:+:25:- 27:27:undef:undef:undef:undef 27:28:27:+:1:- 27:29:14:+:15:- 27:30:undef:undef:undef:undef 27:31:23:+:8:- 27:32:19:+:13:- 27:33:undef:undef:undef:undef 27:34:29:+:5:- 27:35:13:+:22:- 27:36:undef:undef:undef:undef 27:37:11:+:26:- 27:38:31:+:7:- 27:39:undef:undef:undef:undef 27:40:3:+:37:- 27:41:38:+:3:- 27:42:undef:undef:undef:undef 27:43:8:+:35:- 27:44:31:+:13:- 27:45:undef:undef:undef:undef 27:46:29:+:17:- 27:47:7:+:40:- 27:48:undef:undef:undef:undef 27:49:20:+:29:- 27:50:13:+:37:- #28:0:undef:undef:undef:undef 28:1:0:+:0:- 28:2:undef:undef:undef:undef 28:3:1:+:2:- 28:4:undef:undef:undef:undef 28:5:2:+:3:- 28:6:undef:undef:undef:undef 28:7:undef:undef:undef:undef 28:8:undef:undef:undef:undef 28:9:1:+:8:- 28:10:undef:undef:undef:undef 28:11:2:+:9:- 28:12:undef:undef:undef:undef 28:13:7:+:6:- 28:14:undef:undef:undef:undef 28:15:7:+:8:- 28:16:undef:undef:undef:undef 28:17:14:+:3:- 28:18:undef:undef:undef:undef 28:19:17:+:2:- 28:20:undef:undef:undef:undef 28:21:undef:undef:undef:undef 28:22:undef:undef:undef:undef 28:23:14:+:9:- 28:24:undef:undef:undef:undef 28:25:17:+:8:- 28:26:undef:undef:undef:undef 28:27:1:+:26:- 28:28:undef:undef:undef:undef 28:29:28:+:1:- 28:30:undef:undef:undef:undef 28:31:10:+:21:- 28:32:undef:undef:undef:undef 28:33:13:+:20:- 28:34:undef:undef:undef:undef 28:35:undef:undef:undef:undef 28:36:undef:undef:undef:undef 28:37:4:+:33:- 28:38:undef:undef:undef:undef 28:39:7:+:32:- 28:40:undef:undef:undef:undef 28:41:22:+:19:- 28:42:undef:undef:undef:undef 28:43:20:+:23:- 28:44:undef:undef:undef:undef 28:45:37:+:8:- 28:46:undef:undef:undef:undef 28:47:42:+:5:- 28:48:undef:undef:undef:undef 28:49:undef:undef:undef:undef 28:50:undef:undef:undef:undef #29:0:undef:undef:undef:undef 29:1:0:+:0:- 29:2:1:+:1:- 29:3:2:+:1:- 29:4:1:+:3:- 29:5:4:+:1:- 29:6:5:+:1:- 29:7:1:+:6:- 29:8:5:+:3:- 29:9:5:+:4:- 29:10:9:+:1:- 29:11:8:+:3:- 29:12:5:+:7:- 29:13:9:+:4:- 29:14:1:+:13:- 29:15:14:+:1:- 29:16:5:+:11:- 29:17:10:+:7:- 29:18:5:+:13:- 29:19:2:+:17:- 29:20:9:+:11:- 29:21:8:+:13:- 29:22:19:+:3:- 29:23:4:+:19:- 29:24:5:+:19:- 29:25:19:+:6:- 29:26:9:+:17:- 29:27:14:+:13:- 29:28:1:+:27:- 29:29:undef:undef:undef:undef 29:30:29:+:1:- 29:31:15:+:16:- 29:32:21:+:11:- 29:33:8:+:25:- 29:34:27:+:7:- 29:35:29:+:6:- 29:36:5:+:31:- 29:37:23:+:14:- 29:38:21:+:17:- 29:39:35:+:4:- 29:40:29:+:11:- 29:41:17:+:24:- 29:42:29:+:13:- 29:43:3:+:40:- 29:44:41:+:3:- 29:45:14:+:31:- 29:46:27:+:19:- 29:47:13:+:34:- 29:48:5:+:43:- 29:49:22:+:27:- 29:50:19:+:31:- #30:0:undef:undef:undef:undef 30:1:0:+:0:- 30:2:undef:undef:undef:undef 30:3:undef:undef:undef:undef 30:4:undef:undef:undef:undef 30:5:undef:undef:undef:undef 30:6:undef:undef:undef:undef 30:7:4:+:3:- 30:8:undef:undef:undef:undef 30:9:undef:undef:undef:undef 30:10:undef:undef:undef:undef 30:11:7:+:4:- 30:12:undef:undef:undef:undef 30:13:10:+:3:- 30:14:undef:undef:undef:undef 30:15:undef:undef:undef:undef 30:16:undef:undef:undef:undef 30:17:4:+:13:- 30:18:undef:undef:undef:undef 30:19:7:+:12:- 30:20:undef:undef:undef:undef 30:21:undef:undef:undef:undef 30:22:undef:undef:undef:undef 30:23:10:+:13:- 30:24:undef:undef:undef:undef 30:25:undef:undef:undef:undef 30:26:undef:undef:undef:undef 30:27:undef:undef:undef:undef 30:28:undef:undef:undef:undef 30:29:1:+:28:- 30:30:undef:undef:undef:undef 30:31:30:+:1:- 30:32:undef:undef:undef:undef 30:33:undef:undef:undef:undef 30:34:undef:undef:undef:undef 30:35:undef:undef:undef:undef 30:36:undef:undef:undef:undef 30:37:21:+:16:- 30:38:undef:undef:undef:undef 30:39:undef:undef:undef:undef 30:40:undef:undef:undef:undef 30:41:26:+:15:- 30:42:undef:undef:undef:undef 30:43:33:+:10:- 30:44:undef:undef:undef:undef 30:45:undef:undef:undef:undef 30:46:undef:undef:undef:undef 30:47:11:+:36:- 30:48:undef:undef:undef:undef 30:49:18:+:31:- 30:50:undef:undef:undef:undef #31:0:undef:undef:undef:undef 31:1:0:+:0:- 31:2:1:+:1:- 31:3:1:+:2:- 31:4:3:+:1:- 31:5:1:+:4:- 31:6:1:+:5:- 31:7:5:+:2:- 31:8:7:+:1:- 31:9:7:+:2:- 31:10:1:+:9:- 31:11:5:+:6:- 31:12:7:+:5:- 31:13:8:+:5:- 31:14:5:+:9:- 31:15:1:+:14:- 31:16:15:+:1:- 31:17:11:+:6:- 31:18:7:+:11:- 31:19:8:+:11:- 31:20:11:+:9:- 31:21:19:+:2:- 31:22:5:+:17:- 31:23:3:+:20:- 31:24:7:+:17:- 31:25:21:+:4:- 31:26:21:+:5:- 31:27:7:+:20:- 31:28:19:+:9:- 31:29:15:+:14:- 31:30:1:+:29:- 31:31:undef:undef:undef:undef 31:32:31:+:1:- 31:33:16:+:17:- 31:34:11:+:23:- 31:35:26:+:9:- 31:36:7:+:29:- 31:37:6:+:31:- 31:38:27:+:11:- 31:39:34:+:5:- 31:40:31:+:9:- 31:41:4:+:37:- 31:42:19:+:23:- 31:43:25:+:18:- 31:44:27:+:17:- 31:45:16:+:29:- 31:46:3:+:43:- 31:47:44:+:3:- 31:48:31:+:17:- 31:49:19:+:30:- 31:50:21:+:29:- #32:0:undef:undef:undef:undef 32:1:0:+:0:- 32:2:undef:undef:undef:undef 32:3:2:+:1:- 32:4:undef:undef:undef:undef 32:5:3:+:2:- 32:6:undef:undef:undef:undef 32:7:2:+:5:- 32:8:undef:undef:undef:undef 32:9:2:+:7:- 32:10:undef:undef:undef:undef 32:11:10:+:1:- 32:12:undef:undef:undef:undef 32:13:11:+:2:- 32:14:undef:undef:undef:undef 32:15:8:+:7:- 32:16:undef:undef:undef:undef 32:17:8:+:9:- 32:18:undef:undef:undef:undef 32:19:3:+:16:- 32:20:undef:undef:undef:undef 32:21:2:+:19:- 32:22:undef:undef:undef:undef 32:23:18:+:5:- 32:24:undef:undef:undef:undef 32:25:18:+:7:- 32:26:undef:undef:undef:undef 32:27:11:+:16:- 32:28:undef:undef:undef:undef 32:29:10:+:19:- 32:30:undef:undef:undef:undef 32:31:1:+:30:- 32:32:undef:undef:undef:undef 32:33:32:+:1:- 32:34:undef:undef:undef:undef 32:35:23:+:12:- 32:36:undef:undef:undef:undef 32:37:22:+:15:- 32:38:undef:undef:undef:undef 32:39:11:+:28:- 32:40:undef:undef:undef:undef 32:41:9:+:32:- 32:42:undef:undef:undef:undef 32:43:39:+:4:- 32:44:undef:undef:undef:undef 32:45:38:+:7:- 32:46:undef:undef:undef:undef 32:47:25:+:22:- 32:48:undef:undef:undef:undef 32:49:23:+:26:- 32:50:undef:undef:undef:undef #33:0:undef:undef:undef:undef 33:1:0:+:0:- 33:2:1:+:1:- 33:3:undef:undef:undef:undef 33:4:1:+:3:- 33:5:2:+:3:- 33:6:undef:undef:undef:undef 33:7:3:+:4:- 33:8:1:+:7:- 33:9:undef:undef:undef:undef 33:10:7:+:3:- 33:11:undef:undef:undef:undef 33:12:undef:undef:undef:undef 33:13:2:+:11:- 33:14:3:+:11:- 33:15:undef:undef:undef:undef 33:16:1:+:15:- 33:17:16:+:1:- 33:18:undef:undef:undef:undef 33:19:15:+:4:- 33:20:17:+:3:- 33:21:undef:undef:undef:undef 33:22:undef:undef:undef:undef 33:23:7:+:16:- 33:24:undef:undef:undef:undef 33:25:22:+:3:- 33:26:15:+:11:- 33:27:undef:undef:undef:undef 33:28:17:+:11:- 33:29:22:+:7:- 33:30:undef:undef:undef:undef 33:31:16:+:15:- 33:32:1:+:31:- 33:33:undef:undef:undef:undef 33:34:33:+:1:- 33:35:17:+:18:- 33:36:undef:undef:undef:undef 33:37:9:+:28:- 33:38:15:+:23:- 33:39:undef:undef:undef:undef 33:40:17:+:23:- 33:41:5:+:36:- 33:42:undef:undef:undef:undef 33:43:30:+:13:- 33:44:undef:undef:undef:undef 33:45:undef:undef:undef:undef 33:46:7:+:39:- 33:47:10:+:37:- 33:48:undef:undef:undef:undef 33:49:3:+:46:- 33:50:47:+:3:- #34:0:undef:undef:undef:undef 34:1:0:+:0:- 34:2:undef:undef:undef:undef 34:3:1:+:2:- 34:4:undef:undef:undef:undef 34:5:4:+:1:- 34:6:undef:undef:undef:undef 34:7:6:+:1:- 34:8:undef:undef:undef:undef 34:9:4:+:5:- 34:10:undef:undef:undef:undef 34:11:1:+:10:- 34:12:undef:undef:undef:undef 34:13:5:+:8:- 34:14:undef:undef:undef:undef 34:15:4:+:11:- 34:16:undef:undef:undef:undef 34:17:undef:undef:undef:undef 34:18:undef:undef:undef:undef 34:19:14:+:5:- 34:20:undef:undef:undef:undef 34:21:13:+:8:- 34:22:undef:undef:undef:undef 34:23:21:+:2:- 34:24:undef:undef:undef:undef 34:25:14:+:11:- 34:26:undef:undef:undef:undef 34:27:4:+:23:- 34:28:undef:undef:undef:undef 34:29:6:+:23:- 34:30:undef:undef:undef:undef 34:31:21:+:10:- 34:32:undef:undef:undef:undef 34:33:1:+:32:- 34:34:undef:undef:undef:undef 34:35:34:+:1:- 34:36:undef:undef:undef:undef 34:37:12:+:25:- 34:38:undef:undef:undef:undef 34:39:31:+:8:- 34:40:undef:undef:undef:undef 34:41:35:+:6:- 34:42:undef:undef:undef:undef 34:43:19:+:24:- 34:44:undef:undef:undef:undef 34:45:4:+:41:- 34:46:undef:undef:undef:undef 34:47:18:+:29:- 34:48:undef:undef:undef:undef 34:49:13:+:36:- 34:50:undef:undef:undef:undef #35:0:undef:undef:undef:undef 35:1:0:+:0:- 35:2:1:+:1:- 35:3:2:+:1:- 35:4:3:+:1:- 35:5:undef:undef:undef:undef 35:6:5:+:1:- 35:7:undef:undef:undef:undef 35:8:3:+:5:- 35:9:8:+:1:- 35:10:undef:undef:undef:undef 35:11:6:+:5:- 35:12:11:+:1:- 35:13:3:+:10:- 35:14:undef:undef:undef:undef 35:15:undef:undef:undef:undef 35:16:11:+:5:- 35:17:1:+:16:- 35:18:17:+:1:- 35:19:6:+:13:- 35:20:undef:undef:undef:undef 35:21:undef:undef:undef:undef 35:22:17:+:5:- 35:23:2:+:21:- 35:24:11:+:13:- 35:25:undef:undef:undef:undef 35:26:3:+:23:- 35:27:17:+:10:- 35:28:undef:undef:undef:undef 35:29:5:+:24:- 35:30:undef:undef:undef:undef 35:31:8:+:23:- 35:32:11:+:21:- 35:33:17:+:16:- 35:34:1:+:33:- 35:35:undef:undef:undef:undef 35:36:35:+:1:- 35:37:18:+:19:- 35:38:25:+:13:- 35:39:29:+:10:- 35:40:undef:undef:undef:undef 35:41:34:+:7:- 35:42:undef:undef:undef:undef 35:43:16:+:27:- 35:44:39:+:5:- 35:45:undef:undef:undef:undef 35:46:25:+:21:- 35:47:43:+:4:- 35:48:11:+:37:- 35:49:undef:undef:undef:undef 35:50:undef:undef:undef:undef #36:0:undef:undef:undef:undef 36:1:0:+:0:- 36:2:undef:undef:undef:undef 36:3:undef:undef:undef:undef 36:4:undef:undef:undef:undef 36:5:1:+:4:- 36:6:undef:undef:undef:undef 36:7:1:+:6:- 36:8:undef:undef:undef:undef 36:9:undef:undef:undef:undef 36:10:undef:undef:undef:undef 36:11:4:+:7:- 36:12:undef:undef:undef:undef 36:13:4:+:9:- 36:14:undef:undef:undef:undef 36:15:undef:undef:undef:undef 36:16:undef:undef:undef:undef 36:17:9:+:8:- 36:18:undef:undef:undef:undef 36:19:9:+:10:- 36:20:undef:undef:undef:undef 36:21:undef:undef:undef:undef 36:22:undef:undef:undef:undef 36:23:16:+:7:- 36:24:undef:undef:undef:undef 36:25:16:+:9:- 36:26:undef:undef:undef:undef 36:27:undef:undef:undef:undef 36:28:undef:undef:undef:undef 36:29:25:+:4:- 36:30:undef:undef:undef:undef 36:31:25:+:6:- 36:32:undef:undef:undef:undef 36:33:undef:undef:undef:undef 36:34:undef:undef:undef:undef 36:35:1:+:34:- 36:36:undef:undef:undef:undef 36:37:36:+:1:- 36:38:undef:undef:undef:undef 36:39:undef:undef:undef:undef 36:40:undef:undef:undef:undef 36:41:8:+:33:- 36:42:undef:undef:undef:undef 36:43:6:+:37:- 36:44:undef:undef:undef:undef 36:45:undef:undef:undef:undef 36:46:undef:undef:undef:undef 36:47:17:+:30:- 36:48:undef:undef:undef:undef 36:49:15:+:34:- 36:50:undef:undef:undef:undef #37:0:undef:undef:undef:undef 37:1:0:+:0:- 37:2:1:+:1:- 37:3:1:+:2:- 37:4:1:+:3:- 37:5:3:+:2:- 37:6:1:+:5:- 37:7:4:+:3:- 37:8:5:+:3:- 37:9:1:+:8:- 37:10:3:+:7:- 37:11:3:+:8:- 37:12:1:+:11:- 37:13:6:+:7:- 37:14:11:+:3:- 37:15:13:+:2:- 37:16:13:+:3:- 37:17:6:+:11:- 37:18:1:+:17:- 37:19:18:+:1:- 37:20:13:+:7:- 37:21:4:+:17:- 37:22:3:+:19:- 37:23:5:+:18:- 37:24:13:+:11:- 37:25:23:+:2:- 37:26:19:+:7:- 37:27:19:+:8:- 37:28:25:+:3:- 37:29:11:+:18:- 37:30:13:+:17:- 37:31:26:+:5:- 37:32:13:+:19:- 37:33:25:+:8:- 37:34:23:+:11:- 37:35:18:+:17:- 37:36:1:+:35:- 37:37:undef:undef:undef:undef 37:38:37:+:1:- 37:39:19:+:20:- 37:40:13:+:27:- 37:41:10:+:31:- 37:42:25:+:17:- 37:43:7:+:36:- 37:44:25:+:19:- 37:45:28:+:17:- 37:46:5:+:41:- 37:47:14:+:33:- 37:48:13:+:35:- 37:49:4:+:45:- 37:50:23:+:27:- #38:0:undef:undef:undef:undef 38:1:0:+:0:- 38:2:undef:undef:undef:undef 38:3:2:+:1:- 38:4:undef:undef:undef:undef 38:5:2:+:3:- 38:6:undef:undef:undef:undef 38:7:5:+:2:- 38:8:undef:undef:undef:undef 38:9:5:+:4:- 38:10:undef:undef:undef:undef 38:11:9:+:2:- 38:12:undef:undef:undef:undef 38:13:12:+:1:- 38:14:undef:undef:undef:undef 38:15:2:+:13:- 38:16:undef:undef:undef:undef 38:17:13:+:4:- 38:18:undef:undef:undef:undef 38:19:undef:undef:undef:undef 38:20:undef:undef:undef:undef 38:21:5:+:16:- 38:22:undef:undef:undef:undef 38:23:20:+:3:- 38:24:undef:undef:undef:undef 38:25:2:+:23:- 38:26:undef:undef:undef:undef 38:27:5:+:22:- 38:28:undef:undef:undef:undef 38:29:13:+:16:- 38:30:undef:undef:undef:undef 38:31:9:+:22:- 38:32:undef:undef:undef:undef 38:33:20:+:13:- 38:34:undef:undef:undef:undef 38:35:12:+:23:- 38:36:undef:undef:undef:undef 38:37:1:+:36:- 38:38:undef:undef:undef:undef 38:39:38:+:1:- 38:40:undef:undef:undef:undef 38:41:27:+:14:- 38:42:undef:undef:undef:undef 38:43:17:+:26:- 38:44:undef:undef:undef:undef 38:45:32:+:13:- 38:46:undef:undef:undef:undef 38:47:26:+:21:- 38:48:undef:undef:undef:undef 38:49:40:+:9:- 38:50:undef:undef:undef:undef #39:0:undef:undef:undef:undef 39:1:0:+:0:- 39:2:1:+:1:- 39:3:undef:undef:undef:undef 39:4:3:+:1:- 39:5:4:+:1:- 39:6:undef:undef:undef:undef 39:7:2:+:5:- 39:8:7:+:1:- 39:9:undef:undef:undef:undef 39:10:9:+:1:- 39:11:2:+:9:- 39:12:undef:undef:undef:undef 39:13:undef:undef:undef:undef 39:14:9:+:5:- 39:15:undef:undef:undef:undef 39:16:7:+:9:- 39:17:7:+:10:- 39:18:undef:undef:undef:undef 39:19:1:+:18:- 39:20:19:+:1:- 39:21:undef:undef:undef:undef 39:22:13:+:9:- 39:23:13:+:10:- 39:24:undef:undef:undef:undef 39:25:9:+:16:- 39:26:undef:undef:undef:undef 39:27:undef:undef:undef:undef 39:28:23:+:5:- 39:29:3:+:26:- 39:30:undef:undef:undef:undef 39:31:4:+:27:- 39:32:23:+:9:- 39:33:undef:undef:undef:undef 39:34:7:+:27:- 39:35:9:+:26:- 39:36:undef:undef:undef:undef 39:37:19:+:18:- 39:38:1:+:37:- 39:39:undef:undef:undef:undef 39:40:39:+:1:- 39:41:20:+:21:- 39:42:undef:undef:undef:undef 39:43:32:+:11:- 39:44:35:+:9:- 39:45:undef:undef:undef:undef 39:46:13:+:33:- 39:47:41:+:6:- 39:48:undef:undef:undef:undef 39:49:44:+:5:- 39:50:9:+:41:- #40:0:undef:undef:undef:undef 40:1:0:+:0:- 40:2:undef:undef:undef:undef 40:3:1:+:2:- 40:4:undef:undef:undef:undef 40:5:undef:undef:undef:undef 40:6:undef:undef:undef:undef 40:7:3:+:4:- 40:8:undef:undef:undef:undef 40:9:7:+:2:- 40:10:undef:undef:undef:undef 40:11:8:+:3:- 40:12:undef:undef:undef:undef 40:13:1:+:12:- 40:14:undef:undef:undef:undef 40:15:undef:undef:undef:undef 40:16:undef:undef:undef:undef 40:17:3:+:14:- 40:18:undef:undef:undef:undef 40:19:10:+:9:- 40:20:undef:undef:undef:undef 40:21:10:+:11:- 40:22:undef:undef:undef:undef 40:23:19:+:4:- 40:24:undef:undef:undef:undef 40:25:undef:undef:undef:undef 40:26:undef:undef:undef:undef 40:27:25:+:2:- 40:28:undef:undef:undef:undef 40:29:8:+:21:- 40:30:undef:undef:undef:undef 40:31:7:+:24:- 40:32:undef:undef:undef:undef 40:33:19:+:14:- 40:34:undef:undef:undef:undef 40:35:undef:undef:undef:undef 40:36:undef:undef:undef:undef 40:37:25:+:12:- 40:38:undef:undef:undef:undef 40:39:1:+:38:- 40:40:undef:undef:undef:undef 40:41:40:+:1:- 40:42:undef:undef:undef:undef 40:43:14:+:29:- 40:44:undef:undef:undef:undef 40:45:undef:undef:undef:undef 40:46:undef:undef:undef:undef 40:47:20:+:27:- 40:48:undef:undef:undef:undef 40:49:38:+:11:- 40:50:undef:undef:undef:undef #41:0:undef:undef:undef:undef 41:1:0:+:0:- 41:2:1:+:1:- 41:3:2:+:1:- 41:4:1:+:3:- 41:5:1:+:4:- 41:6:5:+:1:- 41:7:6:+:1:- 41:8:1:+:7:- 41:9:2:+:7:- 41:10:1:+:9:- 41:11:7:+:4:- 41:12:5:+:7:- 41:13:7:+:6:- 41:14:13:+:1:- 41:15:11:+:4:- 41:16:9:+:7:- 41:17:5:+:12:- 41:18:11:+:7:- 41:19:13:+:6:- 41:20:1:+:19:- 41:21:20:+:1:- 41:22:7:+:15:- 41:23:9:+:14:- 41:24:17:+:7:- 41:25:11:+:14:- 41:26:7:+:19:- 41:27:2:+:25:- 41:28:13:+:15:- 41:29:17:+:12:- 41:30:11:+:19:- 41:31:28:+:3:- 41:32:25:+:7:- 41:33:29:+:4:- 41:34:5:+:29:- 41:35:6:+:29:- 41:36:29:+:7:- 41:37:28:+:9:- 41:38:13:+:25:- 41:39:20:+:19:- 41:40:1:+:39:- 41:41:undef:undef:undef:undef 41:42:41:+:1:- 41:43:21:+:22:- 41:44:29:+:15:- 41:45:11:+:34:- 41:46:9:+:37:- 41:47:39:+:8:- 41:48:41:+:7:- 41:49:6:+:43:- 41:50:11:+:39:- #42:0:undef:undef:undef:undef 42:1:0:+:0:- 42:2:undef:undef:undef:undef 42:3:undef:undef:undef:undef 42:4:undef:undef:undef:undef 42:5:3:+:2:- 42:6:undef:undef:undef:undef 42:7:undef:undef:undef:undef 42:8:undef:undef:undef:undef 42:9:undef:undef:undef:undef 42:10:undef:undef:undef:undef 42:11:5:+:6:- 42:12:undef:undef:undef:undef 42:13:9:+:4:- 42:14:undef:undef:undef:undef 42:15:undef:undef:undef:undef 42:16:undef:undef:undef:undef 42:17:15:+:2:- 42:18:undef:undef:undef:undef 42:19:5:+:14:- 42:20:undef:undef:undef:undef 42:21:undef:undef:undef:undef 42:22:undef:undef:undef:undef 42:23:17:+:6:- 42:24:undef:undef:undef:undef 42:25:3:+:22:- 42:26:undef:undef:undef:undef 42:27:undef:undef:undef:undef 42:28:undef:undef:undef:undef 42:29:9:+:20:- 42:30:undef:undef:undef:undef 42:31:17:+:14:- 42:32:undef:undef:undef:undef 42:33:undef:undef:undef:undef 42:34:undef:undef:undef:undef 42:35:undef:undef:undef:undef 42:36:undef:undef:undef:undef 42:37:15:+:22:- 42:38:undef:undef:undef:undef 42:39:undef:undef:undef:undef 42:40:undef:undef:undef:undef 42:41:1:+:40:- 42:42:undef:undef:undef:undef 42:43:42:+:1:- 42:44:undef:undef:undef:undef 42:45:undef:undef:undef:undef 42:46:undef:undef:undef:undef 42:47:28:+:19:- 42:48:undef:undef:undef:undef 42:49:undef:undef:undef:undef 42:50:undef:undef:undef:undef #43:0:undef:undef:undef:undef 43:1:0:+:0:- 43:2:1:+:1:- 43:3:1:+:2:- 43:4:3:+:1:- 43:5:2:+:3:- 43:6:1:+:5:- 43:7:1:+:6:- 43:8:3:+:5:- 43:9:4:+:5:- 43:10:7:+:3:- 43:11:10:+:1:- 43:12:7:+:5:- 43:13:10:+:3:- 43:14:1:+:13:- 43:15:7:+:8:- 43:16:3:+:13:- 43:17:2:+:15:- 43:18:13:+:5:- 43:19:4:+:15:- 43:20:7:+:13:- 43:21:1:+:20:- 43:22:21:+:1:- 43:23:15:+:8:- 43:24:19:+:5:- 43:25:7:+:18:- 43:26:23:+:3:- 43:27:22:+:5:- 43:28:15:+:13:- 43:29:27:+:2:- 43:30:7:+:23:- 43:31:13:+:18:- 43:32:3:+:29:- 43:33:10:+:23:- 43:34:19:+:15:- 43:35:22:+:13:- 43:36:31:+:5:- 43:37:31:+:6:- 43:38:23:+:15:- 43:39:10:+:29:- 43:40:27:+:13:- 43:41:21:+:20:- 43:42:1:+:41:- 43:43:undef:undef:undef:undef 43:44:43:+:1:- 43:45:22:+:23:- 43:46:15:+:31:- 43:47:35:+:12:- 43:48:19:+:29:- 43:49:8:+:41:- 43:50:7:+:43:- #44:0:undef:undef:undef:undef 44:1:0:+:0:- 44:2:undef:undef:undef:undef 44:3:2:+:1:- 44:4:undef:undef:undef:undef 44:5:4:+:1:- 44:6:undef:undef:undef:undef 44:7:4:+:3:- 44:8:undef:undef:undef:undef 44:9:8:+:1:- 44:10:undef:undef:undef:undef 44:11:undef:undef:undef:undef 44:12:undef:undef:undef:undef 44:13:8:+:5:- 44:14:undef:undef:undef:undef 44:15:14:+:1:- 44:16:undef:undef:undef:undef 44:17:12:+:5:- 44:18:undef:undef:undef:undef 44:19:16:+:3:- 44:20:undef:undef:undef:undef 44:21:11:+:10:- 44:22:undef:undef:undef:undef 44:23:11:+:12:- 44:24:undef:undef:undef:undef 44:25:4:+:21:- 44:26:undef:undef:undef:undef 44:27:8:+:19:- 44:28:undef:undef:undef:undef 44:29:2:+:27:- 44:30:undef:undef:undef:undef 44:31:12:+:19:- 44:32:undef:undef:undef:undef 44:33:undef:undef:undef:undef 44:34:undef:undef:undef:undef 44:35:4:+:31:- 44:36:undef:undef:undef:undef 44:37:16:+:21:- 44:38:undef:undef:undef:undef 44:39:8:+:31:- 44:40:undef:undef:undef:undef 44:41:14:+:27:- 44:42:undef:undef:undef:undef 44:43:1:+:42:- 44:44:undef:undef:undef:undef 44:45:44:+:1:- 44:46:undef:undef:undef:undef 44:47:31:+:16:- 44:48:undef:undef:undef:undef 44:49:39:+:10:- 44:50:undef:undef:undef:undef #45:0:undef:undef:undef:undef 45:1:0:+:0:- 45:2:1:+:1:- 45:3:undef:undef:undef:undef 45:4:1:+:3:- 45:5:undef:undef:undef:undef 45:6:undef:undef:undef:undef 45:7:5:+:2:- 45:8:5:+:3:- 45:9:undef:undef:undef:undef 45:10:undef:undef:undef:undef 45:11:1:+:10:- 45:12:undef:undef:undef:undef 45:13:11:+:2:- 45:14:5:+:9:- 45:15:undef:undef:undef:undef 45:16:5:+:11:- 45:17:14:+:3:- 45:18:undef:undef:undef:undef 45:19:11:+:8:- 45:20:undef:undef:undef:undef 45:21:undef:undef:undef:undef 45:22:1:+:21:- 45:23:22:+:1:- 45:24:undef:undef:undef:undef 45:25:undef:undef:undef:undef 45:26:11:+:15:- 45:27:undef:undef:undef:undef 45:28:5:+:23:- 45:29:20:+:9:- 45:30:undef:undef:undef:undef 45:31:20:+:11:- 45:32:5:+:27:- 45:33:undef:undef:undef:undef 45:34:31:+:3:- 45:35:undef:undef:undef:undef 45:36:undef:undef:undef:undef 45:37:14:+:23:- 45:38:11:+:27:- 45:39:undef:undef:undef:undef 45:40:undef:undef:undef:undef 45:41:31:+:10:- 45:42:undef:undef:undef:undef 45:43:22:+:21:- 45:44:1:+:43:- 45:45:undef:undef:undef:undef 45:46:45:+:1:- 45:47:23:+:24:- 45:48:undef:undef:undef:undef 45:49:12:+:37:- 45:50:undef:undef:undef:undef #46:0:undef:undef:undef:undef 46:1:0:+:0:- 46:2:undef:undef:undef:undef 46:3:1:+:2:- 46:4:undef:undef:undef:undef 46:5:1:+:4:- 46:6:undef:undef:undef:undef 46:7:2:+:5:- 46:8:undef:undef:undef:undef 46:9:1:+:8:- 46:10:undef:undef:undef:undef 46:11:6:+:5:- 46:12:undef:undef:undef:undef 46:13:2:+:11:- 46:14:undef:undef:undef:undef 46:15:1:+:14:- 46:16:undef:undef:undef:undef 46:17:10:+:7:- 46:18:undef:undef:undef:undef 46:19:12:+:7:- 46:20:undef:undef:undef:undef 46:21:16:+:5:- 46:22:undef:undef:undef:undef 46:23:undef:undef:undef:undef 46:24:undef:undef:undef:undef 46:25:6:+:19:- 46:26:undef:undef:undef:undef 46:27:10:+:17:- 46:28:undef:undef:undef:undef 46:29:12:+:17:- 46:30:undef:undef:undef:undef 46:31:29:+:2:- 46:32:undef:undef:undef:undef 46:33:28:+:5:- 46:34:undef:undef:undef:undef 46:35:16:+:19:- 46:36:undef:undef:undef:undef 46:37:33:+:4:- 46:38:undef:undef:undef:undef 46:39:28:+:11:- 46:40:undef:undef:undef:undef 46:41:33:+:8:- 46:42:undef:undef:undef:undef 46:43:29:+:14:- 46:44:undef:undef:undef:undef 46:45:1:+:44:- 46:46:undef:undef:undef:undef 46:47:46:+:1:- 46:48:undef:undef:undef:undef 46:49:16:+:33:- 46:50:undef:undef:undef:undef #47:0:undef:undef:undef:undef 47:1:0:+:0:- 47:2:1:+:1:- 47:3:2:+:1:- 47:4:3:+:1:- 47:5:3:+:2:- 47:6:5:+:1:- 47:7:3:+:4:- 47:8:7:+:1:- 47:9:5:+:4:- 47:10:3:+:7:- 47:11:4:+:7:- 47:12:11:+:1:- 47:13:5:+:8:- 47:14:3:+:11:- 47:15:8:+:7:- 47:16:15:+:1:- 47:17:4:+:13:- 47:18:5:+:13:- 47:19:17:+:2:- 47:20:3:+:17:- 47:21:17:+:4:- 47:22:15:+:7:- 47:23:1:+:22:- 47:24:23:+:1:- 47:25:8:+:17:- 47:26:5:+:21:- 47:27:23:+:4:- 47:28:3:+:25:- 47:29:21:+:8:- 47:30:23:+:7:- 47:31:2:+:29:- 47:32:15:+:17:- 47:33:26:+:7:- 47:34:21:+:13:- 47:35:3:+:32:- 47:36:23:+:13:- 47:37:26:+:11:- 47:38:17:+:21:- 47:39:5:+:34:- 47:40:23:+:17:- 47:41:7:+:34:- 47:42:17:+:25:- 47:43:11:+:32:- 47:44:15:+:29:- 47:45:23:+:22:- 47:46:1:+:45:- 47:47:undef:undef:undef:undef 47:48:47:+:1:- 47:49:24:+:25:- 47:50:33:+:17:- #48:0:undef:undef:undef:undef 48:1:0:+:0:- 48:2:undef:undef:undef:undef 48:3:undef:undef:undef:undef 48:4:undef:undef:undef:undef 48:5:2:+:3:- 48:6:undef:undef:undef:undef 48:7:6:+:1:- 48:8:undef:undef:undef:undef 48:9:undef:undef:undef:undef 48:10:undef:undef:undef:undef 48:11:3:+:8:- 48:12:undef:undef:undef:undef 48:13:3:+:10:- 48:14:undef:undef:undef:undef 48:15:undef:undef:undef:undef 48:16:undef:undef:undef:undef 48:17:11:+:6:- 48:18:undef:undef:undef:undef 48:19:2:+:17:- 48:20:undef:undef:undef:undef 48:21:undef:undef:undef:undef 48:22:undef:undef:undef:undef 48:23:12:+:11:- 48:24:undef:undef:undef:undef 48:25:12:+:13:- 48:26:undef:undef:undef:undef 48:27:undef:undef:undef:undef 48:28:undef:undef:undef:undef 48:29:26:+:3:- 48:30:undef:undef:undef:undef 48:31:11:+:20:- 48:32:undef:undef:undef:undef 48:33:undef:undef:undef:undef 48:34:undef:undef:undef:undef 48:35:27:+:8:- 48:36:undef:undef:undef:undef 48:37:27:+:10:- 48:38:undef:undef:undef:undef 48:39:undef:undef:undef:undef 48:40:undef:undef:undef:undef 48:41:6:+:35:- 48:42:undef:undef:undef:undef 48:43:26:+:17:- 48:44:undef:undef:undef:undef 48:45:undef:undef:undef:undef 48:46:undef:undef:undef:undef 48:47:1:+:46:- 48:48:undef:undef:undef:undef 48:49:48:+:1:- 48:50:undef:undef:undef:undef #49:0:undef:undef:undef:undef 49:1:0:+:0:- 49:2:1:+:1:- 49:3:1:+:2:- 49:4:1:+:3:- 49:5:4:+:1:- 49:6:1:+:5:- 49:7:undef:undef:undef:undef 49:8:1:+:7:- 49:9:7:+:2:- 49:10:9:+:1:- 49:11:9:+:2:- 49:12:1:+:11:- 49:13:4:+:9:- 49:14:undef:undef:undef:undef 49:15:4:+:11:- 49:16:1:+:15:- 49:17:8:+:9:- 49:18:7:+:11:- 49:19:7:+:12:- 49:20:9:+:11:- 49:21:undef:undef:undef:undef 49:22:9:+:13:- 49:23:8:+:15:- 49:24:1:+:23:- 49:25:24:+:1:- 49:26:17:+:9:- 49:27:16:+:11:- 49:28:undef:undef:undef:undef 49:29:16:+:13:- 49:30:19:+:11:- 49:31:19:+:12:- 49:32:17:+:15:- 49:33:31:+:2:- 49:34:25:+:9:- 49:35:undef:undef:undef:undef 49:36:25:+:11:- 49:37:34:+:3:- 49:38:7:+:31:- 49:39:4:+:35:- 49:40:9:+:31:- 49:41:36:+:5:- 49:42:undef:undef:undef:undef 49:43:36:+:7:- 49:44:9:+:35:- 49:45:34:+:11:- 49:46:31:+:15:- 49:47:24:+:23:- 49:48:1:+:47:- 49:49:undef:undef:undef:undef 49:50:49:+:1:- #50:0:undef:undef:undef:undef 50:1:0:+:0:- 50:2:undef:undef:undef:undef 50:3:2:+:1:- 50:4:undef:undef:undef:undef 50:5:undef:undef:undef:undef 50:6:undef:undef:undef:undef 50:7:1:+:6:- 50:8:undef:undef:undef:undef 50:9:2:+:7:- 50:10:undef:undef:undef:undef 50:11:2:+:9:- 50:12:undef:undef:undef:undef 50:13:6:+:7:- 50:14:undef:undef:undef:undef 50:15:undef:undef:undef:undef 50:16:undef:undef:undef:undef 50:17:16:+:1:- 50:18:undef:undef:undef:undef 50:19:8:+:11:- 50:20:undef:undef:undef:undef 50:21:8:+:13:- 50:22:undef:undef:undef:undef 50:23:6:+:17:- 50:24:undef:undef:undef:undef 50:25:undef:undef:undef:undef 50:26:undef:undef:undef:undef 50:27:20:+:7:- 50:28:undef:undef:undef:undef 50:29:18:+:11:- 50:30:undef:undef:undef:undef 50:31:18:+:13:- 50:32:undef:undef:undef:undef 50:33:2:+:31:- 50:34:undef:undef:undef:undef 50:35:undef:undef:undef:undef 50:36:undef:undef:undef:undef 50:37:20:+:17:- 50:38:undef:undef:undef:undef 50:39:32:+:7:- 50:40:undef:undef:undef:undef 50:41:32:+:9:- 50:42:undef:undef:undef:undef 50:43:37:+:6:- 50:44:undef:undef:undef:undef 50:45:undef:undef:undef:undef 50:46:undef:undef:undef:undef 50:47:16:+:31:- 50:48:undef:undef:undef:undef 50:49:1:+:48:- 50:50:undef:undef:undef:undef 741:620:41:+:579:- 461:109:48:+:61:- 278:869:422:+:447:- 561:3498:undef:undef:undef:undef 499:7109:5086:+:2023:- 741:9439:2968:+:6471:- 486:56136:undef:undef:undef:undef 200:10526:undef:undef:undef:undef 672:99812:undef:undef:undef:undef 780:424148:undef:undef:undef:undef 310:384332:undef:undef:undef:undef 225:215820:undef:undef:undef:undef 852:2247541:2054970:+:192571:- 113:8887520:7235857:+:1651663:- 844:7780525:175154:+:7605371:- 687:87465920:509263:+:86956657:- 493:71478351:60459376:+:11018975:- 173:99310988:37313377:+:61997611:- 816:792935352:undef:undef:undef:undef 979:616918181:undef:undef:undef:undef 958:737059268:undef:undef:undef:undef 895:5476284944:3218464671:+:2257820273:- 754:5245579447:3095865854:+:2149713593:- 498:5270898300:undef:undef:undef:undef 413:85194219513:35686682750:+:49507536763:- 184:92943057805:9597380969:+:83345676836:- 282:22116244877:21253554474:+:862690403:- 103:813169626911:623693208990:+:189476417921:- 332:204877945268:undef:undef:undef:undef 305:812044920168:567100222937:+:244944697231:- 874:2233888446784:undef:undef:undef:undef 851:9628562470715:1595331737216:+:8033230733499:- 170:9512424802829:7330162642180:+:2182262160649:- 416:35895309054277:20967692548532:+:14927616505745:- 693:87114971000787:undef:undef:undef:undef 263:15549801355396:10405950716919:+:5143850638477:- 598:670464274337475:595345367346487:+:75118906990988:- 416:417977295301500:undef:undef:undef:undef 281:907403927404997:826674040625193:+:80729886779804:- 696:8403134065908435:undef:undef:undef:undef 277:5812153971708647:1279932824094684:+:4532221147613963:- 658:1133283530973375:undef:undef:undef:undef 632:57996916095727080:undef:undef:undef:undef 819:51981115048676576:undef:undef:undef:undef 549:83015466364372240:undef:undef:undef:undef 531:416202594816372687:undef:undef:undef:undef 664:541037245817077417:299037152432029235:+:242000093385048182:- 631:183722828206333148:92298156167048507:+:91424672039284641:- 175:3611383264044105956:undef:undef:undef:undef 743:2992271347936814844:2492888242762972259:+:499383105173842585:- 602:6134448393502267660:undef:undef:undef:undef 959:53075414038512161512:42283228702214068191:+:10792185336298093321:- 815:56860682801097897246:56093238002555471639:+:767444798542425607:- 886:30009839291014751598:undef:undef:undef:undef 609:273888409952105295020:98941625926868907889:+:174946784025236387131:- 340:181380165037918172099:139235950220284243876:+:42144214817633928223:- 827:229247399647470621945:92308807838703406418:+:136938591808767215527:- 952:5562674809482089173316:undef:undef:undef:undef 901:8309818972650860479311:3532364779717291413514:+:4777454192933569065797:- 265:7701488832510420831126:6945871060264115391091:+:755617772246305440035:- 164:75587116320128057813999:44707013921051351268036:+:30880102399076706545963:- 631:40162982059806098053891:6683222054325895872676:+:33479760005480202181215:- 733:10084115533658671195588:4705003427709775646509:+:5379112105948895549079:- 535:151412058327435602200854:141789609760832218135753:+:9622448566603384065101:- 757:423342299553291085429917:166093346059877744217550:+:257248953493413341212367:- 665:686959841032017875475019:434902395600721091090200:+:252057445431296784384819:- 740:6484819730382801901410848:undef:undef:undef:undef 793:2799159372693769837012668:1295449545748566872867149:+:1503709826945202964145519:- 282:3962201441710282457113977:undef:undef:undef:undef 905:460:undef:undef:undef:undef 828:265:257:+:8:- 542:455:68:+:387:- 756:4964:undef:undef:undef:undef 563:1031:738:+:293:- 224:9957:2267:+:7690:- 252:48856:undef:undef:undef:undef 373:74860:68237:+:6623:- 355:28550:undef:undef:undef:undef 982:348479:5323:+:343156:- 774:300613:undef:undef:undef:undef 854:749913:81665:+:668248:- 306:6065146:undef:undef:undef:undef 271:8099488:2480655:+:5618833:- 841:1638213:714892:+:923321:- 648:11588613:undef:undef:undef:undef 874:23241017:undef:undef:undef:undef 933:12110426:4646873:+:7463553:- 197:574608277:297512915:+:277095362:- 450:885355929:undef:undef:undef:undef 619:814593211:327679660:+:486913551:- 650:4156795794:undef:undef:undef:undef 701:2471540985:1815754076:+:655786909:- 813:5143260312:undef:undef:undef:undef 301:97232678386:15182511243:+:82050167143:- 804:76241122652:undef:undef:undef:undef 476:50715793663:33775013847:+:16940779816:- 407:417193419964:129155702495:+:288037717469:- 577:795565949538:42742711327:+:752823238211:- 113:344037305215:225298766247:+:118738538968:- 909:1781264483287:662340368923:+:1118924114364:- 815:7913809756884:4864808206379:+:3049001550505:- 675:7474109839958:1140493797801:+:6333616042157:- 932:13929482409261:941585184317:+:12987897224944:- 924:15097021630041:undef:undef:undef:undef 499:69768376838141:61239577264741:+:8528799573400:- 722:348476274304903:313242523578784:+:35233750726119:- 854:570193568728738:undef:undef:undef:undef 974:631143898362428:undef:undef:undef:undef 754:5981951447667815:2657763574229069:+:3324187873438746:- 175:7994366069894641:5207758468388509:+:2786607601506132:- 955:8179320935952497:7554095356555081:+:625225579397416:- 880:90993972189730180:undef:undef:undef:undef 332:60642153726739477:22466822013219746:+:38175331713519731:- 146:70480374924497094:undef:undef:undef:undef 785:477376881780158621:11554344909328680:+:465822536870829941:- 509:162367878429460773:115475779943938703:+:46892098485522070:- 277:415929677871336479:252260598853373749:+:163669079017962730:- 116:1152802064631144665:109317437163298201:+:1043484627467846464:- 414:3669698500253122270:undef:undef:undef:undef 272:6975835460709376364:undef:undef:undef:undef 584:76202968713931261880:undef:undef:undef:undef 113:65885331225240062100:46644482283355796177:+:19240848941884265923:- 610:93003648713173191624:undef:undef:undef:undef 194:145142945088276683997:117461043189997110245:+:27681901898279573752:- 563:486532793763280035361:366411908624566136755:+:120120885138713898606:- 738:587662254685605130728:undef:undef:undef:undef 708:8269459575943308522945:undef:undef:undef:undef 784:8119601286270879363659:3614465368505786859588:+:4505135917765092504071:- 174:4176304658042170923312:undef:undef:undef:undef 600:50583901482508562794984:undef:undef:undef:undef 484:87546738364851249507102:undef:undef:undef:undef 584:52635317924212427610338:undef:undef:undef:undef 479:702282439563863762476945:313754576339596754008489:+:388527863224267008468456:- 666:482137212775320246977754:undef:undef:undef:undef 642:591902125029057638793071:166875832757413446451006:+:425026292271644192342065:- 250:1013925362727886106592930:undef:undef:undef:undef 182:6031034047937231309336424:undef:undef:undef:undef 449:7224623463853020688795424:1946947525893575731278945:+:5277675937959444957516479:- 329:681:296:+:385:- 160:481:478:+:3:- 924:628:undef:undef:undef:undef 966:4261:3939:+:322:- 602:3792:undef:undef:undef:undef 503:2192:1303:+:889:- 840:18943:16079:+:2864:- 636:46667:11520:+:35147:- 565:92522:35535:+:56987:- 879:538061:42849:+:495212:- 402:504269:497997:+:6272:- 355:506944:379851:+:127093:- 335:2007636:1162631:+:845005:- 790:2462861:2428568:+:34293:- 917:9664847:5775721:+:3889126:- 475:72334904:54213107:+:18121797:- 819:59111784:undef:undef:undef:undef 294:81023337:undef:undef:undef:undef 572:497201929:398978471:+:98223458:- 421:314772904:216826941:+:97945963:- 765:505227632:450412085:+:54815547:- 237:5278294795:3652490913:+:1625803882:- 847:3110199153:2173834591:+:936364562:- 842:9546719867:5748440585:+:3798279282:- 801:14754617256:undef:undef:undef:undef 115:57978141981:7058208589:+:50919933392:- 214:71768884179:43262551678:+:28506332501:- 202:550042438570:undef:undef:undef:undef 461:856614524249:211830923567:+:644783600682:- 895:801644784874:81508017233:+:720136767641:- 963:3683793693096:undef:undef:undef:undef 334:5630552472673:994618550562:+:4635933922111:- 960:8963131336150:undef:undef:undef:undef 317:22868890215137:8079860265285:+:14789029949852:- 845:83064873649555:undef:undef:undef:undef 730:14582563081721:3775485510199:+:10807077571522:- 587:661031387460777:349096644144533:+:311934743316244:- 874:977093718206815:408054012752274:+:569039705454541:- 125:570801727061713:447508554016383:+:123293173045330:- 256:6743588830453320:undef:undef:undef:undef 162:8916030369222247:7870323103696181:+:1045707265526066:- 626:3338443153918406:undef:undef:undef:undef 737:33673341242625817:14712097530699475:+:18961243711926342:- 480:99211735204558346:undef:undef:undef:undef 440:77720969306266697:57760811279884568:+:19960158026382129:- 183:482260407343311656:287248002188092735:+:195012405155218921:- 786:118688797853185388:undef:undef:undef:undef 334:363171309873152983:undef:undef:undef:undef 571:1366803214546890149:428472461302790432:+:938330753244099717:- 117:6884129668418219012:2530064749931482201:+:4354064918486736811:- 385:8434614983431042942:5630379352576046847:+:2804235630854996095:- 542:93375752200055958358:undef:undef:undef:undef 751:68477372401862025252:45681975463825399003:+:22795396938036626249:- 903:89808109291803554851:81652777108051737024:+:8155332183751817827:- 669:737962127669032713396:undef:undef:undef:undef 254:994853266335556274523:646262948603806241324:+:348590317731750033199:- 327:339366039539626505616:undef:undef:undef:undef 145:5078756999763081840786:1716269606816489725507:+:3362487392946592115279:- 575:5593304214000287175400:undef:undef:undef:undef 839:7737339391509936330092:5053709161558337436103:+:2683630229951598893989:- 322:36517404451080131558649:34589466949004472439093:+:1927937502075659119556:- 810:13908484214268344873541:undef:undef:undef:undef 801:21640894049142413495911:21613876703263334328001:+:27017345879079167910:- 915:898597966959467815355730:undef:undef:undef:undef 440:271572327421957489228719:undef:undef:undef:undef 618:786639168038543887861103:31821972817093199347132:+:754817195221450688513971:- 643:1630290425961246373482606:831625598313046361589883:+:798664827648200011892723:- 935:5065034764752521759691908:124594438063431016548571:+:4940440326689090743143337:- 376:9530592457891569296396161:5855231004715299221988067:+:3675361453176270074408094:- 2946:548:undef:undef:undef:undef 9546:582:undef:undef:undef:undef 6294:153:undef:undef:undef:undef 6436:3798:undef:undef:undef:undef 8678:5609:1389:+:4220:- 4332:9737:5599:+:4138:- 6597:54650:29483:+:25167:- 6349:10623:1285:+:9338:- 8892:10489:4302:+:6187:- 3855:989920:undef:undef:undef:undef 9019:913324:1519:+:911805:- 7251:360052:37043:+:323009:- 9964:5492175:4888609:+:603566:- 9417:7462279:undef:undef:undef:undef 1089:1050423:undef:undef:undef:undef 1407:59792572:undef:undef:undef:undef 7163:46140182:33972263:+:12167919:- 8481:30580067:5271555:+:25308512:- 5584:401476541:18046313:+:383430228:- 1165:491274830:undef:undef:undef:undef 6904:560666466:undef:undef:undef:undef 4693:3443998487:847606702:+:2596391785:- 6277:6375048996:3427718713:+:2947330283:- 1715:2942734466:undef:undef:undef:undef 8402:28571614496:undef:undef:undef:undef 7407:66623347625:59157790918:+:7465556707:- 4097:30072612468:undef:undef:undef:undef 2337:355259397238:340513928033:+:14745469205:- 6577:424150081323:416346803257:+:7803278066:- 8560:318232114571:271724126799:+:46507987772:- 3979:1575914452553:1087575040641:+:488339411912:- 4510:3133369785360:undef:undef:undef:undef 8169:9194251869504:undef:undef:undef:undef 1575:99239191800263:32953712578754:+:66285479221509:- 9369:76312182615150:undef:undef:undef:undef 7693:60744018497638:undef:undef:undef:undef 3727:559162992969877:533957899645772:+:25205093324105:- 1260:681065359017028:undef:undef:undef:undef 3976:685441805727949:70854271165540:+:614587534562409:- 2504:9777800420084735:3658865412787299:+:6118935007297436:- 2762:7873030137588740:undef:undef:undef:undef 6635:7120473956972563:5224184961950631:+:1896288995021932:- 6228:92523947758884024:undef:undef:undef:undef 1304:22925758948775355:10355269954623224:+:12570488994152131:- 9088:86212918824513679:68160191654283757:+:18052727170229922:- 2520:185463029536171412:undef:undef:undef:undef 3577:997340379048801521:958584350900134087:+:38756028148667434:- 2514:162930369528348634:undef:undef:undef:undef 6648:9039445301791270496:undef:undef:undef:undef 9344:8136175292609130143:6938910627868381647:+:1197264664740748496:- 4953:9282031734931944828:undef:undef:undef:undef 3404:26167213577484844372:undef:undef:undef:undef 6557:63575943463035229143:31114107453542786384:+:32461836009492442759:- 5223:17950137655576050657:undef:undef:undef:undef 2998:792868168700507108633:593725496575262994957:+:199142672125244113676:- 3279:388960509706685596867:220517715018215469526:+:168442794688470127341:- 5927:732286607095088984945:384119969876603957178:+:348166637218485027767:- 6777:5490119563688280724837:5421260162343511083165:+:68859401344769641672:- 1497:6395281394987040837127:6275663573303916492812:+:119617821683124344315:- 7491:4664361048026575632196:31133100040225441411:+:4633227947986350190785:- 4033:19196592307972606406454:undef:undef:undef:undef 7071:43562844464026628340476:29577883788967874793187:+:13984960675058753547289:- 4100:57686517973164004591283:24664503904135731719151:+:33022014069028272872132:- 1894:487293779128619555993093:313113267792782470772753:+:174180511335837085220340:- 9154:858190558799326056846033:83906549063294387248984:+:774284009736031669597049:- 9225:781770620562905148078069:undef:undef:undef:undef 8061:4216203196128056053943703:undef:undef:undef:undef 5411:4282833094817001580138184:3275247338080346061469563:+:1007585756736655518668621:- 7175:8104779479452384950607078:undef:undef:undef:undef 5951:205:171:+:34:- 6069:424:373:+:51:- 6371:623:190:+:433:- 5082:3488:undef:undef:undef:undef 1678:3946:undef:undef:undef:undef 4793:9662:7755:+:1907:- 5048:92330:undef:undef:undef:undef 8094:69507:undef:undef:undef:undef 4396:99770:undef:undef:undef:undef 1681:501362:133617:+:367745:- 3664:615286:undef:undef:undef:undef 4915:143405:undef:undef:undef:undef 2529:8023778:488597:+:7535181:- 9060:5117142:undef:undef:undef:undef 3287:4585543:4199113:+:386430:- 3059:41109383:undef:undef:undef:undef 6509:68600092:46889201:+:21710891:- 5765:29503680:undef:undef:undef:undef 6410:988541422:undef:undef:undef:undef 5705:492883670:undef:undef:undef:undef 9837:622709937:undef:undef:undef:undef 3655:3592150238:3034900119:+:557250119:- 1952:4255266825:3642700238:+:612566587:- 2461:4785405085:2286727501:+:2498677584:- 5954:78088441558:undef:undef:undef:undef 8762:33007375700:undef:undef:undef:undef 9542:54551528885:6077161518:+:48474367367:- 9293:309538103946:61654474379:+:247883629567:- 2401:520030780193:107428266129:+:412602514064:- 1860:781528831498:undef:undef:undef:undef 7396:3527877963446:undef:undef:undef:undef 7279:8941549468508:211285411263:+:8730264057245:- 9389:6577806996740:1553200352729:+:5024606644011:- 1296:70387974951888:undef:undef:undef:undef 8023:45356649307727:32761034867042:+:12595614440685:- 4902:68896698482573:64525651312422:+:4371047170151:- 7991:275848275979438:248094301021677:+:27753974957761:- 5367:165924172274849:66808670819070:+:99115501455779:- 9289:888834843323870:73296101839389:+:815538741484481:- 4115:6569146182612215:undef:undef:undef:undef 7306:9909468711518116:undef:undef:undef:undef 4152:6781397856986327:6547838152374322:+:233559704612005:- 3568:47113880300487202:undef:undef:undef:undef 5809:87547803467030994:75611521775537011:+:11936281691493983:- 1787:13054054533808260:9832544713209803:+:3221509820598457:- 9514:605665049151906828:undef:undef:undef:undef 4853:713499000242966379:399459465003119648:+:314039535239846731:- 6452:427694734457904864:undef:undef:undef:undef 4239:8304859947096906141:undef:undef:undef:undef 3544:1969023207138603883:1313978522822459984:+:655044684316143899:- 6911:5031564641665892104:4523384621425291223:+:508180020240600881:- 9912:75163604212370372554:undef:undef:undef:undef 7130:11987974730099950013:11118720461451748869:+:869254268648201144:- 4939:23055485714643712760:8827277482565551899:+:14228208232078160861:- 1121:921401851199540927726:169320946785999492517:+:752080904413541435209:- 9040:872620802022659606426:undef:undef:undef:undef 8213:625934818692447812846:529068490364418935441:+:96866328328028877405:- 4433:4991433139403445570483:2540192457138320145953:+:2451240682265125424530:- 9508:6901625217196528232233:3753502734341948621043:+:3148122482854579611190:- 8595:2091945626639426717509:90298060207472636672:+:2001647566431954080837:- 6813:47447476046608773092632:1476422269467350637845:+:45971053777141422454787:- 3152:95873769198955185999171:50278978580543439865682:+:45594790618411746133489:- 2460:65845398973149003429799:13945306042687248287368:+:51900092930461755142431:- 3269:430088193330985030042478:37496217528091383775499:+:392591975802893646266979:- 5070:416813042846919276362941:105970811090666459020085:+:310842231756252817342856:- 5412:756139458478911579084896:undef:undef:undef:undef 2908:5303962871253938770973780:undef:undef:undef:undef 1379:7714259532129843754371131:2791454319458152308507030:+:4922805212671691445864101:- 2517:8085066861806460985962354:undef:undef:undef:undef 1532:417:371:+:46:- 2057:951:362:+:589:- 2802:257:185:+:72:- 8893:1116:829:+:287:- 4051:3111:1486:+:1625:- 1660:5374:undef:undef:undef:undef 7951:83731:73158:+:10573:- 4076:13977:1862:+:12115:- 3504:20428:undef:undef:undef:undef 1463:331516:330383:+:1133:- 7658:131185:43597:+:87588:- 8748:562512:undef:undef:undef:undef 3593:2809956:452033:+:2357923:- 2453:4643104:3638013:+:1005091:- 2136:4937753:349064:+:4588689:- 4575:12331589:4288428:+:8043161:- 2609:58309024:14728113:+:43580911:- 8325:89728602:undef:undef:undef:undef 5146:730730138:undef:undef:undef:undef 3767:641508965:50237628:+:591271337:- 6344:157295950:undef:undef:undef:undef 4106:4244559109:962417080:+:3282142029:- 8341:7745917746:4524410893:+:3221506853:- 3341:2504453707:1836549411:+:667904296:- 4654:23766898879:117455667:+:23649443212:- 4312:83083937372:undef:undef:undef:undef 6336:62487818477:897473403:+:61590345074:- 2767:105927028089:92336823907:+:13590204182:- 1984:976324738344:undef:undef:undef:undef 4735:414765902842:151715848727:+:263050054115:- 9389:3721921612503:2853777152882:+:868144459621:- 6021:1665187728854:1191711330947:+:473476397907:- 1934:8103149503392:undef:undef:undef:undef 1612:25738933245053:20230290584046:+:5508642661007:- 3540:63939152728664:undef:undef:undef:undef 4766:89000380393717:86591431784655:+:2408948609062:- 6562:806718572406385:57166128645073:+:749552443761312:- 5363:647761086861909:576982045858538:+:70779041003371:- 9985:312364388137023:44359809952759:+:268004578184264:- 9865:3083352379674899:2746105829480351:+:337246550194548:- 3486:5262233541080355:undef:undef:undef:undef 9897:2795886360449468:2246992029000209:+:548894331449259:- 1543:71685648832402483:45204236107535720:+:26481412724866763:- 5059:12149284758431196:10636327771316815:+:1512956987114381:- 9027:98514417733518139:9974762136749261:+:88539655596768878:- 1590:599286719846714674:undef:undef:undef:undef 2067:720695304468239807:500337572284433538:+:220357732183806269:- 9965:268446875052372025:undef:undef:undef:undef 7586:4753743199700456611:3858264814204549348:+:895478385495907263:- 9659:8337920883000826883:606849402707276250:+:7731071480293550633:- 4760:7642033057354407992:undef:undef:undef:undef 2094:89134575223756225143:undef:undef:undef:undef 3687:57937973605915838098:50285195426886542423:+:7652778179029295675:- 9497:73534290861324791607:57460037115077527484:+:16074253746247264123:- 5009:265940345835402303529:234350306751340740223:+:31590039084061563306:- 5625:724160736203734346852:622713863291993428573:+:101446872911740918279:- 7897:768215104928952954817:722007408988563863575:+:46207695940389091242:- 4290:2763058195260869468638:undef:undef:undef:undef 8843:5262665301247273597054:2180527610965736792899:+:3082137690281536804155:- 2817:4746510420518800349358:undef:undef:undef:undef 3575:89260603841583214022691:18451352794106292353222:+:70809251047476921669469:- 1990:83046096926822537014298:undef:undef:undef:undef 5184:94679474023243818818404:undef:undef:undef:undef 6657:650530555659617020407876:undef:undef:undef:undef 8387:775792776185367363844787:492836999107623383160251:+:282955777077743980684536:- 1221:574277496439098265859120:28690358134959045223101:+:545587138304139220636019:- 9454:8404675808910978281111357:7889940533539764358458144:+:514735275371213922653213:- 1843:7644754921502272571178185:1385430354737796548439237:+:6259324566764476022738948:- 3570:5516588796955727027671455:undef:undef:undef:undef 98949:410:59:+:351:- 13266:325:11:+:314:- 98861:589:233:+:356:- 48974:7575:4499:+:3076:- 91546:8701:undef:undef:undef:undef 99273:7134:undef:undef:undef:undef 22509:43674:undef:undef:undef:undef 37299:79911:undef:undef:undef:undef 47076:84931:72773:+:12158:- 42659:475702:169109:+:306593:- 77892:898781:259704:+:639077:- 73077:561447:undef:undef:undef:undef 27369:1403052:undef:undef:undef:undef 83396:2539666:undef:undef:undef:undef 85442:8955594:undef:undef:undef:undef 37950:52345351:31447211:+:20898140:- 72300:76337550:undef:undef:undef:undef 44240:64947945:undef:undef:undef:undef 56331:182321412:undef:undef:undef:undef 21225:238197444:undef:undef:undef:undef 91326:886827301:765746233:+:121081068:- 27120:5634335935:undef:undef:undef:undef 54438:1056390251:931361367:+:125028884:- 53176:4885961849:2775504919:+:2110456930:- 81663:84970728505:14283006872:+:70687721633:- 31590:19301069967:undef:undef:undef:undef 77888:82857346995:7290229547:+:75567117448:- 34574:295082156509:257776548072:+:37305608437:- 99202:196413828823:137338412898:+:59075415925:- 45629:890530580343:775986672389:+:114543907954:- 51796:4593971131457:3315276216749:+:1278694914708:- 36264:8469175155749:2952674318722:+:5516500837027:- 41163:2034818270362:939428282923:+:1095389987439:- 87168:21499737076344:undef:undef:undef:undef 67323:83794068985826:81674417462827:+:2119651522999:- 35696:71793903618027:undef:undef:undef:undef 38329:576830177680735:81417497488919:+:495412680191816:- 98430:153932887634885:undef:undef:undef:undef 44287:961212849119997:329252352183493:+:631960496936504:- 80114:2073377669411928:undef:undef:undef:undef 21985:1142628526143325:undef:undef:undef:undef 95702:3519719893062649:2345732111130685:+:1173987781931964:- 36683:36240802656077687:36121261257571965:+:119541398505722:- 57437:63961527822744327:56295543221672336:+:7665984601071991:- 82822:31431824267977187:17745534651980697:+:13686289615996490:- 80688:582438795398887924:undef:undef:undef:undef 42150:505083778882003806:undef:undef:undef:undef 28531:552597772997540668:275049629327330799:+:277548143670209869:- 95246:2285477974569930952:undef:undef:undef:undef 72972:5744301120023747275:389581568861995358:+:5354719551161751917:- 55924:9699425614779400010:undef:undef:undef:undef 38810:71247342879162927174:undef:undef:undef:undef 73531:23761524533664966739:12588298652390403766:+:11173225881274562973:- 87047:64580830908918491764:31801869299468001763:+:32778961609450490001:- 88987:188928485915225434897:177983894627812811515:+:10944591287412623382:- 13937:422277203317703208772:undef:undef:undef:undef 71839:958335971287091697434:636613945374554072091:+:321722025912537625343:- 14192:8193234122196675355090:undef:undef:undef:undef 12907:6092668016938878540380:2807243875163516749023:+:3285424141775361791357:- 40341:1713352207648418574849:undef:undef:undef:undef 74188:29876754952189326524545:19276845706804961621157:+:10599909245384364903388:- 83314:41298418475555864250535:21018998471073232731779:+:20279420004482631518756:- 13233:70540662004411377734367:undef:undef:undef:undef 73726:783349644379794061043009:436406694295245659186983:+:346942950084548401856026:- 44560:574722775454549706194083:458810890737089243681376:+:115911884717460462512707:- 14607:101779793656446637398062:47374602387223980808477:+:54405191269222656589585:- 71137:4450203389539795390387819:undef:undef:undef:undef 80078:6660533485970888552376949:831672548343151859876834:+:5828860937627736692500115:- 13608:9440367365941748799297120:undef:undef:undef:undef 50921:401:334:+:67:- 97877:451:406:+:45:- 19409:830:549:+:281:- 16269:3792:undef:undef:undef:undef 70989:2774:2075:+:699:- 65551:3621:1495:+:2126:- 83741:83707:2462:+:81245:- 31113:54174:undef:undef:undef:undef 66345:51476:4961:+:46515:- 48935:342063:185225:+:156838:- 42414:875110:undef:undef:undef:undef 12980:776423:402747:+:373676:- 60246:4483256:undef:undef:undef:undef 64256:3644966:undef:undef:undef:undef 93314:9976772:undef:undef:undef:undef 51611:45112350:14680241:+:30432109:- 43979:87221209:29022833:+:58198376:- 54687:55376443:20701739:+:34674704:- 70901:189511063:135820583:+:53690480:- 54163:378435914:343997079:+:34438835:- 78792:595879530:undef:undef:undef:undef 10294:7336496613:6104244559:+:1232252054:- 56674:5083165310:undef:undef:undef:undef 34634:9572355226:undef:undef:undef:undef 21086:61069971786:undef:undef:undef:undef 58811:81915555957:31578947555:+:50336608402:- 98975:79653570706:53279969639:+:26373601067:- 73167:689028842678:328773558511:+:360255284167:- 15032:304619675359:57572145935:+:247047529424:- 62170:562667586156:undef:undef:undef:undef 86350:5600213062628:undef:undef:undef:undef 57494:9614681701251:8800442211854:+:814239489397:- 65855:8108371810902:4947393456923:+:3160978353979:- 44721:78314548293886:13305470314549:+:65009077979337:- 14231:37307879463486:13220689771229:+:24087189692257:- 58181:40167230101095:20870307591071:+:19296922510024:- 39497:178283607402271:144917214361848:+:33366393040423:- 89106:613175635644377:116729494169142:+:496446141475235:- 24062:687079804792199:260160589371695:+:426919215420504:- 36662:3412808637818018:undef:undef:undef:undef 38271:4993604904186131:4843813719476934:+:149791184709197:- 61833:3395224137472925:2258485986421472:+:1136738151051453:- 42304:95477492302360853:36984438028526553:+:58493054273834300:- 85694:35600816286320844:undef:undef:undef:undef 56273:35448665629382790:25707259177038407:+:9741406452344383:- 56222:410518276617429503:225382726412262041:+:185135550205167462:- 61680:646852640607786873:undef:undef:undef:undef 56894:101601632777376973:56090373042933057:+:45511259734443916:- 24811:4362474477594006202:2954266098606847455:+:1408208378987158747:- 47260:7683273992890237308:undef:undef:undef:undef 40228:7165125207818969985:573345382419440797:+:6591779825399529188:- 80803:84606033017234785607:45169358295242644658:+:39436674721992140949:- 35633:67853495818823395226:undef:undef:undef:undef 44976:89501753171236978693:23280883367802859608:+:66220869803434119085:- 20341:525528354368398409736:391620805049711572429:+:133907549318686837307:- 17454:448296269669821284323:6498164101436048180:+:441798105568385236143:- 18266:855807357200009516963:484876291452036488068:+:370931065747973028895:- 74379:2064661858057186460708:1503575931425880447851:+:561085926631306012857:- 66166:4921748401007848145616:undef:undef:undef:undef 45793:9514243759286877591576:6189982406054068178233:+:3324261353232809413343:- 18732:94295295764660778831004:undef:undef:undef:undef 82599:83255979511964457472937:67862508415380707130600:+:15393471096583750342337:- 97795:87545737247545873294574:65770978693332408168369:+:21774758554213465126205:- 54745:550261459492542921785157:10976080258760742909661:+:539285379233782178875496:- 42622:681641273645333525479165:337782021976047332167553:+:343859251669286193311612:- 42088:741827036299760514271235:570171136600954021957807:+:171655899698806492313428:- 67498:6550918562528418654558104:undef:undef:undef:undef 56270:8864972916949669226442287:7835741211486150672037676:+:1029231705463518554404611:- 52707:7920325982802298747009841:1379636724687572899165146:+:6540689258114725847844695:- 83286:303:undef:undef:undef:undef 62219:403:326:+:77:- 60122:999:752:+:247:- 79471:5910:1741:+:4169:- 28644:8905:7834:+:1071:- 40773:6832:5085:+:1747:- 57803:67038:21683:+:45355:- 28648:62012:undef:undef:undef:undef 86481:90641:40113:+:50528:- 44257:164383:26:+:164357:- 43288:441496:undef:undef:undef:undef 15300:173438:undef:undef:undef:undef 64389:2402832:undef:undef:undef:undef 49675:1431753:310792:+:1120961:- 27031:2443360:1937351:+:506009:- 15690:68340859:20040554:+:48300305:- 77840:58531451:442896:+:58088555:- 13208:31527760:undef:undef:undef:undef 17562:495099648:undef:undef:undef:undef 93813:548117276:192831085:+:355286191:- 55647:398926417:318807064:+:80119353:- 53915:1711432114:1161513725:+:549918389:- 78834:6272337255:undef:undef:undef:undef 79562:3645096056:undef:undef:undef:undef 95905:23848163250:undef:undef:undef:undef 77158:35981680866:undef:undef:undef:undef 75958:66383765408:undef:undef:undef:undef 22357:539401373296:236948646381:+:302452726915:- 25771:735738107887:438513730051:+:297224377836:- 83354:666169508427:662517140630:+:3652367797:- 69929:5323662781011:1777320300383:+:3546342480628:- 14762:4661504054560:undef:undef:undef:undef 75358:4516377948158:undef:undef:undef:undef 90004:29675392756153:23274695014106:+:6400697742047:- 88499:56864787868687:2552197622735:+:54312590245952:- 11845:42409240189444:38904077999029:+:3505162190415:- 95443:801932046386432:45153471886683:+:756778574499749:- 83076:612586904946862:undef:undef:undef:undef 13643:518127002856406:370622401295585:+:147504601560821:- 75247:2235081278093313:661699544594266:+:1573381733499047:- 43709:2933526052767664:1612301731122597:+:1321224321645067:- 39412:7098306893331081:4543514361059149:+:2554792532271932:- 57928:66909947699599886:undef:undef:undef:undef 91436:24155884090393154:undef:undef:undef:undef 74343:86765416480816093:25222111235313568:+:61543305245502525:- 78742:857311748410562755:211077987178831883:+:646233761231730872:- 32733:746784599719552847:608004447576637747:+:138780152142915100:- 56396:418839627671856927:295503403529248799:+:123336224142608128:- 19339:6708040388345093314:3615730544914900083:+:3092309843430193231:- 52591:7788956835575156606:209271472469960569:+:7579685363105196037:- 39431:6266184931331947233:1341879880301462363:+:4924305051030484870:- 41048:47417513058902087166:undef:undef:undef:undef 21660:51830240670458603260:undef:undef:undef:undef 44649:51877712731989144474:undef:undef:undef:undef 73019:331734891948663182211:76656251548909104116:+:255078640399754078095:- 34440:864789807931877675606:undef:undef:undef:undef 64259:703927794690955719008:168163145649650029451:+:535764649041305689557:- 60359:3488776244569618305291:1284094386079269707423:+:2204681858490348597868:- 52349:3248466374539030291737:1839901965750678105599:+:1408564408788352186138:- 74472:9121556428179600114232:undef:undef:undef:undef 17120:82426360062482705699251:69662792274769992334256:+:12763567787712713364995:- 81472:39443110493482443636332:undef:undef:undef:undef 19672:83904640536249669184777:15520993641287746348282:+:68383646894961922836495:- 68032:119800381755879704745542:undef:undef:undef:undef 14671:954262899852278932582327:402168053287890439653502:+:552094846564388492928825:- 36253:443839688788582885696215:76811579937096765091387:+:367028108851486120604828:- 47442:7740282115972000012107365:6537358545273851618505333:+:1202923570698148393602032:- 57997:8939664203212718558761393:144121006776279667093848:+:8795543196436438891667545:- 17258:7760906177749602734444441:4751969844725927227655256:+:3008936333023675506789185:- 382831:106:31:+:75:- 717117:103:10:+:93:- 419761:407:342:+:65:- 684662:4655:3198:+:1457:- 556811:2962:1843:+:1119:- 626426:7825:7476:+:349:- 112655:18932:16467:+:2465:- 157265:49416:undef:undef:undef:undef 291654:90355:26274:+:64081:- 807757:623431:443710:+:179721:- 442546:568999:43215:+:525784:- 289219:924202:640281:+:283921:- 833993:2659795:1234522:+:1425273:- 999098:6219865:628207:+:5591658:- 505319:2755392:2469143:+:286249:- 764906:12242940:undef:undef:undef:undef 918854:73975799:65188187:+:8787612:- 936006:30713686:undef:undef:undef:undef 389728:795593461:758821597:+:36771864:- 410283:741247715:651515627:+:89732088:- 863639:585548132:571731827:+:13816305:- 125309:6615586655:286091694:+:6329494961:- 480278:4014177658:undef:undef:undef:undef 925749:4780108001:4121162366:+:658945635:- 475705:24893120028:14124512401:+:10768607627:- 473425:87402742205:undef:undef:undef:undef 162850:42138962711:8101496982:+:34037465729:- 369524:695913039381:20096361923:+:675816677458:- 444258:292213659559:20466098567:+:271747560992:- 884807:457111564133:undef:undef:undef:undef 281219:1590542162352:961144031675:+:629398130677:- 804856:2407803162606:undef:undef:undef:undef 822000:3350634512904:undef:undef:undef:undef 598343:67175827791178:58266885156747:+:8908942634431:- 937636:75374900754845:66856561699511:+:8518339055334:- 280101:27516849888005:2272956383086:+:25243893504919:- 765769:444946424695660:378358060297849:+:66588364397811:- 487005:487216452554724:undef:undef:undef:undef 855715:384585362270430:undef:undef:undef:undef 698372:7908658805163105:3462498457802783:+:4446160347360322:- 632229:2511136767015791:609202751199510:+:1901934015816281:- 208970:8888361715251666:undef:undef:undef:undef 401349:36108675628456296:undef:undef:undef:undef 925300:55356712541430465:undef:undef:undef:undef 303003:41761421281752209:40610443802572423:+:1150977479179786:- 635914:981321060783996848:undef:undef:undef:undef 190581:427930897683537197:221145120715371477:+:206785776968165720:- 549281:748948330472277438:663033772526420579:+:85914557945856859:- 354269:5893703143293242918:3442303672061807981:+:2451399471231434937:- 710612:6918684676947796782:undef:undef:undef:undef 853751:7927181203332586141:3677177121636871590:+:4250004081695714551:- 592571:66770693307736120675:undef:undef:undef:undef 745402:59943273086564553698:undef:undef:undef:undef 773173:96349752291182430150:86164883892055274887:+:10184868399127155263:- 530230:287836166439751422245:undef:undef:undef:undef 454814:922181329183811692864:undef:undef:undef:undef 518268:574756602784127806156:undef:undef:undef:undef 247355:7418956658440683711794:921569656110644408759:+:6497387002330039303035:- 823678:2873948921091979292348:undef:undef:undef:undef 283466:1575257888013435070365:216211322165405086616:+:1359046565848029983749:- 408360:21006006664466201784742:undef:undef:undef:undef 213820:41933472515487093544690:undef:undef:undef:undef 273073:25637866891571493627319:25536938909279434889731:+:100927982292058737588:- 805921:583528496246165735568236:236979959866886837238733:+:346548536379278898329503:- 704630:708614124591982597303827:252969299062968432232499:+:455644825529014165071328:- 477264:311205711857391112764521:11178298632143333346161:+:300027413225247779418360:- 349453:6763935493186266387995961:5787300886587669600619369:+:976634606598596787376592:- 643778:4147884835388304212949000:undef:undef:undef:undef 572752:9821905182359163933880667:5602470606793029472376784:+:4219434575566134461503883:- 632767:177:22:+:155:- 742290:747:undef:undef:undef:undef 746580:605:undef:undef:undef:undef 514793:4052:3173:+:879:- 768150:2466:undef:undef:undef:undef 740768:3437:undef:undef:undef:undef 694815:56911:29751:+:27160:- 715166:51131:23805:+:27326:- 808376:62553:19547:+:43006:- 147052:984361:738659:+:245702:- 498692:851983:88690:+:763293:- 494188:397185:350032:+:47153:- 272826:2788180:undef:undef:undef:undef 773723:7532270:564957:+:6967313:- 395098:7545730:undef:undef:undef:undef 699345:89927315:undef:undef:undef:undef 224792:67285618:undef:undef:undef:undef 697669:81520153:71513539:+:10006614:- 324805:481692647:421692582:+:60000065:- 428617:402652709:152198754:+:250453955:- 514180:510342810:undef:undef:undef:undef 395725:3398841176:2718806685:+:680034491:- 806085:5698228763:410003:+:5697818760:- 758866:4322509093:3687865242:+:634643851:- 538156:77259565152:undef:undef:undef:undef 861626:99725953338:undef:undef:undef:undef 941426:32855708545:11253729141:+:21601979404:- 512447:458023172924:315051535387:+:142971637537:- 307841:665601770687:110657232214:+:554944538473:- 941029:327506810106:36185080963:+:291321729143:- 718771:3597435030808:1809635880947:+:1787799149861:- 298877:6228183425854:2054437603389:+:4173745822465:- 657362:8896035441363:3819304751975:+:5076730689388:- 983132:15337674725688:undef:undef:undef:undef 572519:51599947378070:42955598189789:+:8644349188281:- 783869:46509794992104:4158041615693:+:42351753376411:- 168841:686165777373698:598973171587469:+:87192605786229:- 559479:682137073335004:300596599238539:+:381540474096465:- 942932:437113917060902:undef:undef:undef:undef 338412:3686202417377629:2487433949830201:+:1198768467547428:- 306985:8677250419071127:8352671476900683:+:324578942170444:- 322580:5187869531140500:undef:undef:undef:undef 591139:57010140644545818:1961324206807753:+:55048816437738065:- 122341:67475431753406564:53020783553757393:+:14454648199649171:- 273725:19134232963006239:12319796699728496:+:6814436263277743:- 620624:826910793389445439:345313174179453558:+:481597619209991881:- 944479:710937883202665508:505322096958990307:+:205615786243675201:- 451792:937349094102674468:undef:undef:undef:undef 147549:8477810633609011265:6028278458317959694:+:2449532175291051571:- 616918:8411386103591141220:undef:undef:undef:undef 942364:4699569402055856939:3771772934590336405:+:927796467465520534:- 162166:27766221702807353760:undef:undef:undef:undef 637904:37231375489384578801:17213464532214448682:+:20017910957170130119:- 954541:76734375969851776738:7952619752917398747:+:68781756216934377991:- 624837:272605072424432719366:10291017414697783557:+:262314055009734935809:- 121192:122487450191181185805:75788553926712188758:+:46698896264468997047:- 268360:981854519563685868649:56604081354038545513:+:925250438209647323136:- 916836:6637592345059956856520:undef:undef:undef:undef 441129:2647896397994030451970:undef:undef:undef:undef 823605:2802945094980419491281:undef:undef:undef:undef 139047:19381283931542615172863:11766735182585488990505:+:7614548748957126182358:- 120641:50372794116225478202470:31694847156227514687321:+:18677946959997963515149:- 953271:47209627946576472296148:undef:undef:undef:undef 775455:392255910173754346925186:85612860244627669513693:+:306643049929126677411493:- 140559:135415313275231958248312:78792118585183771265719:+:56623194690048186982593:- 215908:497422538654129493080626:undef:undef:undef:undef 577226:4521763030457479977050766:undef:undef:undef:undef 336483:2232566503385192143558853:1124361370699712245359616:+:1108205132685479898199237:- 981167:6843711597542215307891114:4611346410900401562549859:+:2232365186641813745341255:- 384131:622:453:+:169:- 181105:423:319:+:104:- 570259:281:23:+:258:- 329944:7089:5047:+:2042:- 561533:4250:3947:+:303:- 405819:1903:448:+:1455:- 336386:76290:undef:undef:undef:undef 867738:34849:1659:+:33190:- 714000:98618:undef:undef:undef:undef 619328:981451:311307:+:670144:- 786505:117946:undef:undef:undef:undef 435392:830764:undef:undef:undef:undef 651818:8574777:5674496:+:2900281:- 480257:3059661:2685206:+:374455:- 353610:5297044:undef:undef:undef:undef 910137:56231142:undef:undef:undef:undef 355928:58325778:undef:undef:undef:undef 724522:69346199:44096622:+:25249577:- 499739:330788839:172319791:+:158469048:- 327111:939191164:684228431:+:254962733:- 472957:732312861:30862129:+:701450732:- 315354:7945494854:undef:undef:undef:undef 171166:5793356868:undef:undef:undef:undef 673466:5926567000:undef:undef:undef:undef 542169:34068655996:14872302481:+:19196353515:- 488992:55628620336:undef:undef:undef:undef 529192:71983604434:undef:undef:undef:undef 667352:547530454020:undef:undef:undef:undef 538746:688567179180:undef:undef:undef:undef 691318:310492895010:undef:undef:undef:undef 971750:4971972745075:undef:undef:undef:undef 177937:1728934359308:1206222653517:+:522711705791:- 953866:3223373361009:2536471972639:+:686901388370:- 649883:25735972780719:14691272721566:+:11044700059153:- 487790:51361382665588:undef:undef:undef:undef 805205:60948831728458:5404747153715:+:55544084574743:- 825454:803153870451243:680008099016782:+:123145771434461:- 501634:295744879767085:undef:undef:undef:undef 723977:656459776539322:361057093443225:+:295402683096097:- 482314:7295333069242471:1144969516419692:+:6150363552822779:- 540249:4402023467326955:1658366105693214:+:2743657361633741:- 893695:4825358999012802:3596130116908447:+:1229228882104355:- 101240:16095502213089530:undef:undef:undef:undef 609077:17767089769624938:5993257331516477:+:11773832438108461:- 703613:78880725431326108:62187266924516805:+:16693458506809303:- 605705:347210793890707535:undef:undef:undef:undef 238251:240645097627324140:undef:undef:undef:undef 174861:876902513002318198:153630074664024671:+:723272438338293527:- 517381:7043969400121315143:39713980103934772:+:7004255420017380371:- 771785:4487637387894239639:3695517362608124501:+:792120025286115138:- 447938:7834219846849074810:undef:undef:undef:undef 209346:19255366498759217994:undef:undef:undef:undef 317635:58737738345751323480:undef:undef:undef:undef 760038:46133404113582846836:undef:undef:undef:undef 822994:802960977149957178156:undef:undef:undef:undef 241095:362329256848889171494:87752826216485151549:+:274576430632404019945:- 139743:633877051500154062148:206089535489133621431:+:427787516011020440717:- 887511:7138089737316897145151:4236747582041654894125:+:2901342155275242251026:- 282482:1626761793485259811961:978578285630835749064:+:648183507854424062897:- 674434:7454296133153187786883:3122345988973533496578:+:4331950144179654290305:- 512730:35662057354117934011677:undef:undef:undef:undef 909680:42958046596782067778330:undef:undef:undef:undef 215104:21641846102796689784700:undef:undef:undef:undef 858399:385948280960999152058926:132497673940625236188007:+:253450607020373915870919:- 749618:151346969987709476166566:undef:undef:undef:undef 775387:985944457205300862827049:629593437408311280197449:+:356351019796989582629600:- 634377:9780181173730606721674489:4342718216046817939156301:+:5437462957683788782518188:- 396769:4651478410441148680581255:133752176164778662891384:+:4517726234276370017689871:- 580645:2030126568350526726340113:1174794871183466290528789:+:855331697167060435811324:- 5655726:650:undef:undef:undef:undef 3608982:289:52:+:237:- 3994088:988:undef:undef:undef:undef 7408347:5829:undef:undef:undef:undef 6570293:5046:4895:+:151:- 2890506:9077:4893:+:4184:- 6086931:77051:63685:+:13366:- 9725532:81184:undef:undef:undef:undef 3784159:39899:19579:+:20320:- 2339493:174015:undef:undef:undef:undef 6826489:275682:220681:+:55001:- 2169905:760478:194359:+:566119:- 7222334:6672310:undef:undef:undef:undef 8569540:8430670:undef:undef:undef:undef 6237287:1702120:undef:undef:undef:undef 1349592:35915708:undef:undef:undef:undef 6392461:75985359:69538849:+:6446510:- 1446994:73189513:47624214:+:25565299:- 7813298:350360055:33907847:+:316452208:- 9584516:362140747:99892152:+:262248595:- 5570997:148703918:123670023:+:25033895:- 6112527:8040634747:290170592:+:7750464155:- 3461395:8025326446:639087155:+:7386239291:- 4897564:8970391267:1434894011:+:7535497256:- 9607393:32750238212:28034434321:+:4715803891:- 3832850:78792881419:undef:undef:undef:undef 8851804:22858007922:undef:undef:undef:undef 1926904:516326307131:423786215980:+:92540091151:- 3263965:248639556344:137406136765:+:111233419579:- 7603082:530885166191:87600135089:+:443285031102:- 4656704:1435763396658:undef:undef:undef:undef 7148411:6170426462326:5267412128309:+:903014334017:- 3370569:7383771232117:1931141415391:+:5452629816726:- 7335959:18179577148530:undef:undef:undef:undef 4618936:79311665961500:undef:undef:undef:undef 5696694:83331248251003:48001187101587:+:35330061149416:- 2580167:497964663022384:240219396188711:+:257745266833673:- 5051426:589883351073091:313902297734522:+:275981053338569:- 2013014:429904889194083:317067920484407:+:112836968709676:- 4325378:9363324821601336:undef:undef:undef:undef 9951937:9472111213174491:5831893583579347:+:3640217629595144:- 2421719:3874308727618692:2231865566641979:+:1642443160976713:- 3441677:43388202854410561:24971926384476198:+:18416276469934363:- 5341718:48133956794968491:15711141966571814:+:32422814828396677:- 1084162:52310224670223110:undef:undef:undef:undef 8615182:454607533478095087:416897856881371116:+:37709676596723971:- 6803890:848484711729563233:791753912200782239:+:56730799528780994:- 5493160:854968170156028301:558889627922417266:+:296078542233611035:- 2399932:6737630109030661791:3929904292027376668:+:2807725817003285123:- 3278186:5488017662014808795:3320998121828418196:+:2167019540186390599:- 2489290:8830356345749585901:3752975054234879683:+:5077381291514706218:- 4328469:40513947193980502625:36865597299144041004:+:3648349894836461621:- 9173561:98904160883542453015:19208950310268847476:+:79695210573273605539:- 9826877:90940744520365774570:78006721019280311133:+:12934023501085463437:- 3769503:127891799836486803766:55249179630612139173:+:72642620205874664593:- 6521895:240621606922309617823:86451695485634236377:+:154169911436675381446:- 2622185:738592398848526776969:636218095841266628964:+:102374303007260148005:- 9815218:7848804102470473986906:undef:undef:undef:undef 3703032:8465216333795486974630:undef:undef:undef:undef 8496388:5415092488122079939709:3682290399540579299418:+:1732802088581500640291:- 8007665:19690434466885834488861:6482289419367856225613:+:13208145047517978263248:- 7422032:39714283117701951853164:undef:undef:undef:undef 8439818:62331767931472602549127:31523309711269149029452:+:30808458220203453519675:- 9210966:223916956320044777640909:undef:undef:undef:undef 2026494:739643382110251162682367:undef:undef:undef:undef 6855455:307340164166749910577130:undef:undef:undef:undef 8977941:7108747225126491549407356:4383611100263026771996661:+:2725136124863464777410695:- 7889075:3965408073830288016838065:undef:undef:undef:undef 2525554:1897650533385450917294537:1637642278474554210721833:+:260008254910896706572704:- 5584060:299:14:+:285:- 6799080:658:undef:undef:undef:undef 7990684:358:undef:undef:undef:undef 5335427:1930:183:+:1747:- 9523579:4713:4642:+:71:- 6177948:9370:undef:undef:undef:undef 1119747:22709:7601:+:15108:- 7600932:81364:undef:undef:undef:undef 8958647:92225:56283:+:35942:- 8029198:716576:undef:undef:undef:undef 3641727:184417:179614:+:4803:- 3652069:825338:810557:+:14781:- 5128081:2848667:1763517:+:1085150:- 7750798:8077812:undef:undef:undef:undef 4455239:7339175:5178109:+:2161066:- 3093378:96932285:24946657:+:71985628:- 3825375:94728039:undef:undef:undef:undef 5134480:55790850:undef:undef:undef:undef 5843118:950902156:undef:undef:undef:undef 3543179:948720653:792525692:+:156194961:- 8278923:856949252:505624635:+:351324617:- 4948912:8043341398:undef:undef:undef:undef 4717992:7074562270:undef:undef:undef:undef 4439344:5053238197:undef:undef:undef:undef 6478431:33174024118:32766110109:+:407914009:- 8260320:41943574978:undef:undef:undef:undef 4469287:74392333598:30916793407:+:43475540191:- 6277695:934317508471:undef:undef:undef:undef 4749423:896523624157:undef:undef:undef:undef 7669479:775568096961:undef:undef:undef:undef 6421484:6712822863626:undef:undef:undef:undef 3985051:7259653372363:undef:undef:undef:undef 3828425:2858016031505:undef:undef:undef:undef 9566141:48779533187481:42537945834266:+:6241587353215:- 3649295:92721133556283:90728590685468:+:1992542870815:- 3016054:88025249075383:41144908998232:+:46880340077151:- 9766358:617052500212228:undef:undef:undef:undef 5082051:886792609787086:102690844943809:+:784101764843277:- 2498957:347103253520820:52182225902933:+:294921027617887:- 8334307:1284959991449047:945037226306456:+:339922765142591:- 8894360:3906581887521471:3236072401706495:+:670509485814976:- 6870726:4772488827481455:undef:undef:undef:undef 6184958:28454121310901697:19411404559686758:+:9042716751214939:- 3522143:41612053000600739:36317506394217007:+:5294546606383732:- 4304441:70048374385642233:4114415889902438:+:65933958495739795:- 1652881:514683315419730432:117278086647786097:+:397405228771944335:- 9213401:482079779283727026:4241102336677031:+:477838676947049995:- 8691976:894513960165746060:undef:undef:undef:undef 4229372:6011409689055449759:4869306775314314947:+:1142102913741134812:- 4912254:3199406486470045574:undef:undef:undef:undef 8498841:2229300887748970359:undef:undef:undef:undef 8954335:41184289836022375422:815339321994470671:+:40368950514027904751:- 1009461:34001895483077710264:15301006226029382829:+:18700889257048327435:- 8668636:47774777508019969258:undef:undef:undef:undef 3109154:702540636028380576948:undef:undef:undef:undef 7565133:791565463176335885267:132203547745301788704:+:659361915431034096563:- 5564293:200450660661470063226:115111052230699148713:+:85339608430770914513:- 5062883:9745337553843068528744:2388361600719070882011:+:7356975953123997646733:- 5544874:9122407409577669572139:8597591364840157589749:+:524816044737511982390:- 2369312:3743304529754686176140:undef:undef:undef:undef 5655057:58509875238574917147632:23592319989945361249697:+:34917555248629555897935:- 2793401:67557641498214083216043:18386269656782813948450:+:49171371841431269267593:- 8818345:81496249819128302370245:undef:undef:undef:undef 6760979:888850306283185647734787:106482125846531978903816:+:782368180436653668830971:- 1318857:644102268401771887439494:354656547596101115368515:+:289445720805670772070979:- 1469734:736040113380453948588461:266608425089174045948582:+:469431688291279902639879:- 5121285:9601561590963161796090882:undef:undef:undef:undef 6927156:9229182964914688893546290:undef:undef:undef:undef 4640276:7976308977153836912623731:429005357782839459364463:+:7547303619370997453259268:- 7101148:854:undef:undef:undef:undef 6076771:264:139:+:125:- 6612600:848:undef:undef:undef:undef 2678598:9076:undef:undef:undef:undef 2156938:5262:undef:undef:undef:undef 6044361:9080:8321:+:759:- 3755070:59427:undef:undef:undef:undef 7735501:78797:32160:+:46637:- 3448279:39227:24871:+:14356:- 9588069:712170:undef:undef:undef:undef 8113600:452368:undef:undef:undef:undef 6544638:958299:undef:undef:undef:undef 6256630:2225256:undef:undef:undef:undef 5319614:4376179:3700276:+:675903:- 6275684:7465629:4048277:+:3417352:- 5938383:13804321:12046313:+:1758008:- 8892727:55320736:28785159:+:26535577:- 9281954:65094277:18752273:+:46342004:- 1822497:634656245:436628893:+:198027352:- 4517402:190358780:undef:undef:undef:undef 3949561:577176744:28746889:+:548429855:- 1075019:7220797529:undef:undef:undef:undef 9765271:7472577100:5173287231:+:2299289869:- 7565124:6576126932:undef:undef:undef:undef 6195215:87608631649:49129286286:+:38479345363:- 2447144:57536659087:34830154668:+:22706504419:- 3180977:98414048530:37379850253:+:61034198277:- 1104803:627059414840:270402746227:+:356656668613:- 1028368:257664539394:undef:undef:undef:undef 5133914:532298581860:undef:undef:undef:undef 5853706:5308776986855:2036306624481:+:3272470362374:- 6678336:6754726066067:undef:undef:undef:undef 8137003:6288209136044:5914276052907:+:373933083137:- 8436713:31744903237494:7106441987477:+:24638461250017:- 7379836:94035085081621:12551834893859:+:81483250187762:- 3428625:29877201406682:16619274704349:+:13257926702333:- 1437480:790119172411982:undef:undef:undef:undef 1978104:694886646181275:undef:undef:undef:undef 8626883:932583923685966:484268741787419:+:448315181898547:- 1843744:7728826487085202:undef:undef:undef:undef 1689669:7974776447223703:271922352975847:+:7702854094247856:- 5269097:1674442003893203:72130290476655:+:1602311713416548:- 4512971:28048666850403499:12739645886036889:+:15309020964366610:- 6716203:23390901946343390:11884782341961187:+:11506119604382203:- 9534275:45530591224539792:21921635799229163:+:23608955425310629:- 8013020:607750740458714954:undef:undef:undef:undef 5465320:549924104241758990:undef:undef:undef:undef 3828169:244572837794246744:240557944291503305:+:4014893502743439:- 2448215:2989639008883957686:1784429392382961449:+:1205209616500996237:- 4637181:2697623441723276177:2145171492485141412:+:552451949238134765:- 1498569:2252044799094634508:337652908604795485:+:1914391890489839023:- 1380733:27425035229245696125:20551759084815034522:+:6873276144430661603:- 7603533:10700369469374182322:4099510685967669067:+:6600858783406513255:- 3886222:47109075684322880926:undef:undef:undef:undef 6032858:556129359492489860272:undef:undef:undef:undef 5373365:640028922314168705131:45795824408434801950:+:594233097905733903181:- 4150394:633337905137269963366:undef:undef:undef:undef 1284277:2697754260575630665152:2186331303494684794525:+:511422957080945870627:- 9220237:8625984232394676377002:2602723732815164808861:+:6023260499579511568141:- 2645470:3898425419316240609841:1107558831692846248005:+:2790866587623394361836:- 5943212:87514893265709129839109:78741613611104386601400:+:8773279654604743237709:- 6994617:95912407644838149138781:undef:undef:undef:undef 4123100:30621985707378546077387:27976341504075325728784:+:2645644203303220348603:- 1505190:409057326086093205277094:undef:undef:undef:undef 5424393:365190044696996042947277:203545037635732495106077:+:161645007061263547841200:- 7579644:179553099975924754129516:undef:undef:undef:undef 4271192:9144689425720996342066606:undef:undef:undef:undef 5188945:3290122276906155297402712:567929059386448031616777:+:2722193217519707265785935:- 6444628:6249631352793282715425626:undef:undef:undef:undef 56815526:805:556:+:249:- 90755503:770:587:+:183:- 98439727:596:379:+:217:- 22474430:7378:undef:undef:undef:undef 19289674:4871:3857:+:1014:- 24509397:4030:1543:+:2487:- 62030412:23206:undef:undef:undef:undef 39217788:39034:undef:undef:undef:undef 56069302:84818:undef:undef:undef:undef 66324788:522304:undef:undef:undef:undef 18530567:582397:398855:+:183542:- 96798560:876003:530969:+:345034:- 81179764:6155531:123354:+:6032177:- 63326339:5290241:146387:+:5143854:- 29147342:5033996:undef:undef:undef:undef 18752415:10348213:6999909:+:3348304:- 52539894:19551663:undef:undef:undef:undef 27015317:61739495:41344143:+:20395352:- 84708377:919281123:868102370:+:51178753:- 85864590:297826256:undef:undef:undef:undef 35996649:819414809:584307755:+:235107054:- 75229591:2171426792:1109087967:+:1062338825:- 25718182:3110493853:536539944:+:2573953909:- 69461724:2669625813:undef:undef:undef:undef 72299495:90382180578:50819402375:+:39562778203:- 35203700:45524408629:undef:undef:undef:undef 54591713:59746606706:35317455319:+:24429151387:- 43725049:897870100804:688219771993:+:209650328811:- 59904750:347591214047:166475835265:+:181115378782:- 92814462:673437958045:517000080073:+:156437877972:- 67134428:3133662607307:479768789758:+:2653893817549:- 46510172:4008823306740:undef:undef:undef:undef 25893646:8170858852029:4390167435961:+:3780691416068:- 36410306:44715644560484:undef:undef:undef:undef 27419780:76275048350081:67131869367827:+:9143178982254:- 94170424:23254328710960:undef:undef:undef:undef 69450890:670439220834333:531417036196232:+:139022184638101:- 77976966:424569969701461:56050148124895:+:368519821576566:- 62440990:417130014208565:undef:undef:undef:undef 41343049:5637228499975107:3927317711174689:+:1709910788800418:- 95394679:3335484783591393:2850482859880636:+:485001923710757:- 42456309:5000937112814486:2846015824723787:+:2154921288090699:- 36127570:91149105559390967:2657395901697198:+:88491709657693769:- 12708835:36869763976600725:undef:undef:undef:undef 68949250:55721346766041169:40523938526553788:+:15197408239487381:- 23759782:493183027582267096:undef:undef:undef:undef 10985807:697493548323858106:107841850761271717:+:589651697562586389:- 30775812:640402397676048683:572039585948725382:+:68362811727323301:- 87602261:2111576025521252285:293865054674215696:+:1817710970847036589:- 59453561:9177486117054954593:8218160518851317534:+:959325598203637059:- 86666776:8568099406660577220:undef:undef:undef:undef 85488759:73641354847375916419:2582651606311777307:+:71058703241064139112:- 43486359:80562029236780559201:49577781407057245623:+:30984247829723313578:- 68562931:63822926861777136415:56596271446531244161:+:7226655415245892254:- 57516930:109556882616719282073:undef:undef:undef:undef 91054524:571273987348229732390:undef:undef:undef:undef 81528288:913437482584784518797:undef:undef:undef:undef 99911660:4950141751120231252285:undef:undef:undef:undef 13990875:8928299170359766356217:3977166213122118507721:+:4951132957237647848496:- 77450552:9633447200737521109817:7123597353372759571338:+:2509849847364761538479:- 99849234:62351929593531206742747:undef:undef:undef:undef 26192122:35144124563841590669403:9796592434889558819329:+:25347532128952031850074:- 53708361:62566467497821534152201:undef:undef:undef:undef 67777625:232717097222397862001502:31281896235547296178715:+:201435200986850565822787:- 31161293:323231468822941819103669:229611918826305543073306:+:93619549996636276030363:- 91110241:329106458814843970800581:28089579166305214489675:+:301016879648538756310906:- 51474694:3053822587493552051244323:1218446859834630780166504:+:1835375727658921271077819:- 27447303:4971868109554611327522578:3450168475006847962477095:+:1521699634547763365045483:- 76652381:8637884770632064105237081:2085070691702722033835788:+:6552814078929342071401293:- 48521962:694:undef:undef:undef:undef 48596127:856:839:+:17:- 84146878:427:184:+:243:- 62798715:9134:541:+:8593:- 25834783:1043:858:+:185:- 55793751:4869:undef:undef:undef:undef 81639641:29032:841:+:28191:- 59623450:99705:undef:undef:undef:undef 84135497:64036:689:+:63347:- 77151548:419165:141702:+:277463:- 44441096:156109:124268:+:31841:- 58134604:305586:undef:undef:undef:undef 18068112:7937375:2644548:+:5292827:- 49222480:7678482:undef:undef:undef:undef 18825853:7656298:5500627:+:2155671:- 65199433:64629347:38476889:+:26152458:- 15281900:60343996:undef:undef:undef:undef 20666769:18272977:8181257:+:10091720:- 41141537:677379590:447495573:+:229884017:- 18679281:845663650:421949571:+:423714079:- 50105911:621004816:18234343:+:602770473:- 18791786:9798565996:undef:undef:undef:undef 40518921:1877096876:134204697:+:1742892179:- 33212177:1482811828:1044348377:+:438463451:- 36035592:37291748667:undef:undef:undef:undef 84032327:94198644633:28947543821:+:65251100812:- 52509174:65971297521:undef:undef:undef:undef 47385209:322740096521:104496652436:+:218243444085:- 37318176:170793088515:undef:undef:undef:undef 60574438:512852464945:171278522527:+:341573942418:- 36400188:5484916608000:undef:undef:undef:undef 83223321:3664681424027:1458958901295:+:2205722522732:- 44722194:1760869789814:undef:undef:undef:undef 94352998:10900374499523:6185481313898:+:4714893185625:- 68109005:10840226656418:10112021763371:+:728204893047:- 94059901:39993251959655:28615749964046:+:11377501995609:- 27315027:402965754303983:311724543018810:+:91241211285173:- 12864333:778107077930471:375050121352547:+:403056956577924:- 59053655:102905122720754:60686680699083:+:42218442021671:- 51804535:9307919041555425:undef:undef:undef:undef 76195770:5466923835123176:undef:undef:undef:undef 93471761:6345935241859625:2083865459463966:+:4262069782395659:- 33570183:61185607853401404:undef:undef:undef:undef 35499121:75849646070631348:22479829913500069:+:53369816157131279:- 37200756:51814119082729596:undef:undef:undef:undef 93259441:567384336938641594:202917177634233729:+:364467159304407865:- 70802854:193319754475168628:undef:undef:undef:undef 20752886:905606253856984890:undef:undef:undef:undef 11467604:9218626987938898390:undef:undef:undef:undef 88185572:4669885828161683495:2328817213802521173:+:2341068614359162322:- 80790660:6445566315406924693:2833016907261817062:+:3612549408145107631:- 50627714:11088833353032449016:undef:undef:undef:undef 92324997:15664530676890811099:9884176997121608512:+:5780353679769202587:- 54831892:64935749703708330568:undef:undef:undef:undef 68138945:943461738383586835873:609569461046503699945:+:333892277337083135928:- 93166751:697894432631572005262:149812410202525239179:+:548082022429046766083:- 46484870:990801754101308640954:undef:undef:undef:undef 10553539:1171463360891161974574:607894828392506981503:+:563568532498654993071:- 10033196:1088007293491080230421:1024060976396162358788:+:63946317094917871633:- 47228752:7879205525885164834759:2560001167724755786448:+:5319204358160409048311:- 16708238:93659694480091921619067:24815547177835449180566:+:68844147302256472438501:- 37601284:15633449594452509144565:6692113211069073883384:+:8941336383383435261181:- 21481753:90038249629096778504710:88025878736918119975657:+:2012370892178658529053:- 45900111:400941147310599293692930:118358291678862165481571:+:282582855631737128211359:- 68810788:937888432093836684889312:undef:undef:undef:undef 32925170:539819639305432274019558:undef:undef:undef:undef 72237529:6139984266288987531023882:3896023742342755757318091:+:2243960523946231773705791:- 66055160:9322487012180571255660365:undef:undef:undef:undef 82241635:4861039800604203190504430:undef:undef:undef:undef 23739681:563:409:+:154:- 36893166:776:undef:undef:undef:undef 39554904:759:undef:undef:undef:undef 49258679:9607:6468:+:3139:- 99371686:3376:undef:undef:undef:undef 33369757:1684:161:+:1523:- 70264152:42138:undef:undef:undef:undef 33462000:57276:undef:undef:undef:undef 62361299:91188:58235:+:32953:- 85650721:845680:213681:+:631999:- 24277050:699841:644439:+:55402:- 25711842:413055:undef:undef:undef:undef 12447729:9919240:193529:+:9725711:- 96556227:6470183:2254031:+:4216152:- 28835465:4283301:1398572:+:2884729:- 80132637:42185681:29908304:+:12277377:- 35241370:33161806:undef:undef:undef:undef 89140386:64631484:undef:undef:undef:undef 30989165:596273032:309718157:+:286554875:- 12388482:842375810:undef:undef:undef:undef 68707400:161250250:undef:undef:undef:undef 13664862:9339533245:8347657963:+:991875282:- 79612588:5972694959:undef:undef:undef:undef 66729477:7299675050:5159351763:+:2140323287:- 49708234:68920434697:51294094315:+:17626340382:- 45613873:58147238900:35290164137:+:22857074763:- 43782671:74825659679:36217014252:+:38608645427:- 61002269:853269225033:828966503642:+:24302721391:- 26251544:751403385332:undef:undef:undef:undef 27722269:543551590424:71001340461:+:472550249963:- 78851606:2179596451570:undef:undef:undef:undef 25804423:4696530713654:2916148860253:+:1780381853401:- 71387805:7058973347511:undef:undef:undef:undef 64119687:19348771492733:2313296638554:+:17035474854179:- 28098583:71828271534611:18138890128088:+:53689381406523:- 17848938:31866503137897:12681264431078:+:19185238706819:- 63271259:968668422083848:331156433419067:+:637511988664781:- 99865602:671719468975839:undef:undef:undef:undef 89880032:193972817975472:undef:undef:undef:undef 39570681:4002837545604292:1256786106665245:+:2746051438939047:- 66051058:5329069590288729:3491143915437145:+:1837925674851584:- 48195503:3267457073288160:772598110702127:+:2494858962586033:- 27442817:17417928150703441:10140048125476522:+:7277880025226919:- 92153106:43772581597012442:undef:undef:undef:undef 77455337:49755332999608758:47739668468093075:+:2015664531515683:- 56212328:739660843721507256:undef:undef:undef:undef 66664067:186610646714807957:75155845224497067:+:111454801490310890:- 44142123:632473348084377463:330456029987885838:+:302017318096491625:- 41947281:6781341911666311815:undef:undef:undef:undef 77968394:3147167955135818645:2452530167309821539:+:694637787825997106:- 51368235:5383330098873455117:1540477274307520826:+:3842852824565934291:- 70685715:73978236652582036893:undef:undef:undef:undef 14029506:78383232893824454701:53764550254066435351:+:24618682639758019350:- 93017914:70937671158770576199:46305934243943565133:+:24631736914827011066:- 66353995:373480850604532194044:147356150678966755799:+:226124699925565438245:- 92938084:529689654952902920374:undef:undef:undef:undef 13412084:568384516281716860412:undef:undef:undef:undef 10071012:6330063941759886362600:undef:undef:undef:undef 51134181:1467192954784541197545:undef:undef:undef:undef 93121244:1427440391992557419063:916159427193218712485:+:511280964799338706578:- 41309652:67974030334244637655409:18567750682028200174479:+:49406279652216437480930:- 46116880:21275837137442429987308:undef:undef:undef:undef 82356374:12923467939382709352430:undef:undef:undef:undef 55366450:600506763374829419654035:undef:undef:undef:undef 34104424:220304456393449755266475:202200524540913547152799:+:18103931852536208113676:- 88038969:165677913359742976790445:undef:undef:undef:undef 63638993:4416974696703510241845051:1626003509190049054350461:+:2790971187513461187494590:- 88880457:6160127441683330345303948:3698331872350914226543417:+:2461795569332416118760531:- 22224266:3813357357407726021795654:undef:undef:undef:undef 883429905:239:131:+:108:- 843095866:601:235:+:366:- 197243366:182:undef:undef:undef:undef 154911512:5141:2551:+:2590:- 684843161:2221:1874:+:347:- 559491181:6435:3946:+:2489:- 121572434:83486:undef:undef:undef:undef 600400316:13111:12330:+:781:- 282716255:78439:53238:+:25201:- 288197999:101271:48194:+:53077:- 747532114:200228:undef:undef:undef:undef 431794237:930383:401484:+:528899:- 572708906:1842080:undef:undef:undef:undef 668180136:5909173:1403896:+:4505277:- 928079954:2330078:undef:undef:undef:undef 497337562:95933091:70951108:+:24981983:- 867263390:30144015:undef:undef:undef:undef 467930791:81260280:68031631:+:13228649:- 496061871:725410310:8978471:+:716431839:- 742700902:666139481:470001762:+:196137719:- 772610806:708497394:undef:undef:undef:undef 122392073:8252960557:5849450680:+:2403509877:- 748036066:9581456115:4389559126:+:5191896989:- 219508248:4210771028:undef:undef:undef:undef 593716482:21247936917:undef:undef:undef:undef 182449347:72475225103:64456164892:+:8019060211:- 314053899:31780217662:31189936465:+:590281197:- 200687800:521954653261:376627763655:+:145326889606:- 806215853:619611194613:4447405922:+:615163788691:- 625519048:932638846045:543707677862:+:388931168183:- 196373726:9669217505235:7762184472341:+:1907033032894:- 539566454:8865581563953:1085126661689:+:7780454902264:- 417298561:2311840425971:1005455288483:+:1306385137488:- 989243073:49832606587910:19083371313907:+:30749235274003:- 195957819:38364918117450:undef:undef:undef:undef 651199163:37681701261540:27078920707607:+:10602780553933:- 278027839:914043394179692:328502168026287:+:585541226153405:- 133110730:626224446433740:undef:undef:undef:undef 968325625:686344396032962:244300368685131:+:442044027347831:- 621285390:4311519283585095:undef:undef:undef:undef 767336537:9664107805517444:183460288872889:+:9480647516644555:- 588276529:3156955752166072:3154282686556065:+:2673065610007:- 935073468:43435916971067865:undef:undef:undef:undef 837523391:97280820491028275:82436855807677536:+:14843964683350739:- 568799219:51493119182065471:15334878988945222:+:36158240193120249:- 514230474:654095868247719919:2589149033732265:+:651506719213987654:- 188386003:120128586539588092:106977377324885299:+:13151209214702793:- 205028107:525637628572920391:82186297870224597:+:443451330702695794:- 994054000:2954713543860708334:undef:undef:undef:undef 774885303:4313366464358728081:21573498071706015:+:4291792966287022066:- 112043498:1731101813308863889:455029004039469849:+:1276072809269394040:- 208594103:31068771392561577293:28597068752221188318:+:2471702640340388975:- 488372701:66266215069889121202:64842385366783436653:+:1423829703105684549:- 343220148:77369409024585464276:undef:undef:undef:undef 314029158:196307421458445448775:116762791499706896597:+:79544629958738552178:- 441075525:474301702458929835745:undef:undef:undef:undef 109418169:800946160289866122897:undef:undef:undef:undef 236632924:3573718583127829454612:undef:undef:undef:undef 468200740:5411564248590924938866:undef:undef:undef:undef 350222056:6113166483154822185796:undef:undef:undef:undef 132461946:52328655294364796336187:undef:undef:undef:undef 887479370:44059129839001500314381:21422904208429019151527:+:22636225630572481162854:- 678448686:66904770167813977388667:undef:undef:undef:undef 768427425:377674300515566506794817:104210228506052186013696:+:273464072009514320781121:- 922098288:847269837350122098564638:undef:undef:undef:undef 284720405:365794083952128062573197:210438918605672507200620:+:155355165346455555372577:- 827723531:8794759148138489090701004:7161760586670868724155111:+:1632998561467620366545893:- 379286755:6081091408847129199173575:undef:undef:undef:undef 417201678:8698548455087166099684761:1521259314471452587502494:+:7177289140615713512182267:- 397240908:862:undef:undef:undef:undef 818752762:270:undef:undef:undef:undef 616478520:825:undef:undef:undef:undef 512448691:8994:7057:+:1937:- 603784315:3860:undef:undef:undef:undef 892788622:9782:undef:undef:undef:undef 401991616:47678:undef:undef:undef:undef 923404619:90679:58655:+:32024:- 700137231:40836:undef:undef:undef:undef 203888384:359764:undef:undef:undef:undef 751199018:566530:undef:undef:undef:undef 191600433:935701:717710:+:217991:- 567383547:1535201:17819:+:1517382:- 562383132:8474308:undef:undef:undef:undef 862029053:7876601:5631926:+:2244675:- 893044074:32229142:undef:undef:undef:undef 644296137:18925602:undef:undef:undef:undef 475626379:31691232:21285187:+:10406045:- 832425608:392739855:250568597:+:142171258:- 199889416:704265601:504331320:+:199934281:- 978604540:175889777:36296563:+:139593214:- 585503092:9057799712:undef:undef:undef:undef 119547941:3126207405:2618647346:+:507560059:- 447424949:3275147317:2530241497:+:744905820:- 568796741:65694710980:34397263201:+:31297447779:- 551197335:51642549256:1541173463:+:50101375793:- 223879560:78950562873:undef:undef:undef:undef 453508623:931147937349:undef:undef:undef:undef 142990845:919406050212:undef:undef:undef:undef 224065099:387468429387:82364691298:+:305103738089:- 792365981:7219430403941:365505214194:+:6853925189747:- 776748101:2064245743332:141791386961:+:1922454356371:- 688232162:4633958434134:undef:undef:undef:undef 905496526:11817098263685:undef:undef:undef:undef 771720261:57836008919288:42607669787677:+:15228339131611:- 497096496:65107756330432:undef:undef:undef:undef 410626572:410139631372933:19416226973289:+:390723404399644:- 786408518:763792281184323:264967407556100:+:498824873628223:- 421657879:756550457103685:588112140809899:+:168438316293786:- 523604004:2877758465549810:undef:undef:undef:undef 461669517:8226793504589051:6374450896711752:+:1852342607877299:- 300181504:1271686476051532:undef:undef:undef:undef 267974301:78005629279493273:46438072854390167:+:31567556425103106:- 807818917:95314908522294362:88808816494546789:+:6506092027747573:- 243884885:51346056252266544:36834699562686797:+:14511356689579747:- 532188782:405217730483088308:undef:undef:undef:undef 459877643:282147288320933817:57329522679596804:+:224817765641337013:- 933891523:394787651615513793:22070377672822048:+:372717273942691745:- 862611446:1161250948291856543:1047150244829279363:+:114100703462577180:- 484619574:8487857715230530978:undef:undef:undef:undef 788426737:8217278190616588126:7893048959187923123:+:324229231428665003:- 547779268:11630002460638849613:6370733863555851967:+:5259268597082997646:- 251766220:26251400866817952811:7412420530729632086:+:18838980336088320725:- 494752719:48622894393070478957:undef:undef:undef:undef 767049336:791436666159935219053:275809336137758774997:+:515627330022176444056:- 408628141:843545915132174213949:529481510616827615566:+:314064404515346598383:- 469417077:263709255549230772677:141522049232505946297:+:122187206316724826380:- 264889274:2926560323119362796564:undef:undef:undef:undef 221419267:1296410333062937556900:445468159442430327403:+:850942173620507229497:- 833792033:1942668528859952362009:899026270786294210099:+:1043642258073658151910:- 101973304:58568850938011564432796:undef:undef:undef:undef 934999765:59753345065693175459502:55083047173673608414957:+:4670297892019567044545:- 416919865:75043519171027116644197:47078094509079366710526:+:27965424661947749933671:- 791615775:521385005581184676834827:324988247498802464958060:+:196396758082382211876767:- 374008119:627922933681359783670244:330482369196042981914591:+:297440564485316801755653:- 822807197:453606953810968114941347:186748831783759526348418:+:266858122027208588592929:- 746891368:7864903400761016410253577:1356599359297693796570143:+:6508304041463322613683434:- 370047092:1704498463364560756156428:undef:undef:undef:undef 737742518:1901258092485545089338212:undef:undef:undef:undef 506705415:994:993:+:1:- 647593796:796:undef:undef:undef:undef 708815998:578:undef:undef:undef:undef 887052376:7673:5229:+:2444:- 413081226:5919:undef:undef:undef:undef 994599722:3531:2:+:3529:- 844373423:58384:35327:+:23057:- 375626762:21319:10623:+:10696:- 733265627:12164:8663:+:3501:- 499242851:339102:157175:+:181927:- 864779327:705006:544085:+:160921:- 752228722:537523:undef:undef:undef:undef 499232435:8551224:7184171:+:1367053:- 236982396:1458728:undef:undef:undef:undef 922436254:2071793:1884658:+:187135:- 894766270:68651174:undef:undef:undef:undef 366692807:63905637:22375706:+:41529931:- 849438794:13148065:9581384:+:3566681:- 591001640:618251727:15141515:+:603110212:- 397862927:837051460:undef:undef:undef:undef 675795839:532564056:135517367:+:397046689:- 417639477:4398363060:undef:undef:undef:undef 526369373:8135902330:1620141147:+:6515761183:- 183218716:9006603417:7049158309:+:1957445108:- 923980750:94755069959:undef:undef:undef:undef 789387451:88149024058:77991872869:+:10157151189:- 571127906:19710998757:15037240280:+:4673758477:- 698103737:216920098357:49831269842:+:167088828515:- 549591836:854066180146:undef:undef:undef:undef 419115188:325856763873:164933077910:+:160923685963:- 481478216:9086744572620:undef:undef:undef:undef 420189227:5739435696720:5155886189363:+:583549507357:- 517419356:8498426682596:undef:undef:undef:undef 352005764:48729341538714:undef:undef:undef:undef 702795815:37160297152533:20096402711606:+:17063894440927:- 227099978:58256460576380:undef:undef:undef:undef 376171310:258548466583650:undef:undef:undef:undef 690017593:377080886496272:251226246773641:+:125854639722631:- 186948188:495279019989700:undef:undef:undef:undef 283798239:1965974385993344:1568211290271775:+:397763095721569:- 969096348:6261312907103392:undef:undef:undef:undef 244593320:5059802746358925:undef:undef:undef:undef 815483678:80083787497801525:16119100382694517:+:63964687115107008:- 814203759:59760202907132217:undef:undef:undef:undef 514083401:97091120171649058:undef:undef:undef:undef 360819549:407324746421774172:undef:undef:undef:undef 157695487:194647209998605218:8161180096324747:+:186486029902280471:- 602578029:169480079856106820:101728567280015629:+:67751512576091191:- 405802569:2383778357087955189:undef:undef:undef:undef 447687990:4185778187887997142:undef:undef:undef:undef 538054734:5746384560506186737:undef:undef:undef:undef 426428011:27300739414594875836:25196216475851450539:+:2104522938743425297:- 432205094:76077990467750523935:31388757444103673189:+:44689233023646850746:- 573307801:73779071715843531734:41321002245477783309:+:32458069470365748425:- 679318375:580705898398364048906:200463993861723162803:+:380241904536640886103:- 361893779:860225730293714521997:undef:undef:undef:undef 655461048:706633758700058821654:undef:undef:undef:undef 129404401:4096953153424413604662:3124320859969723095787:+:972632293454690508875:- 341535500:7645731931898181634664:undef:undef:undef:undef 383154445:1012521510194606626450:undef:undef:undef:undef 795321088:93567180722814566931139:undef:undef:undef:undef 275485768:89210350122218304999307:60063107723796901221898:+:29147242398421403777409:- 229108471:55226631269097392735299:13501243239809771791200:+:41725388029287620944099:- 709485417:915954855215312179597360:906244704064186120927673:+:9710151151126058669687:- 723607178:687376702919933236090565:275933469823503454396497:+:411443233096429781694068:- 531519039:268884822594147934201480:30542663603937076757759:+:238342158990210857443721:- 972630944:2862969356276619196048571:1021373465545458735386152:+:1841595890731160460662419:- 861332012:6636614088896377972141106:undef:undef:undef:undef 296143212:3225291872114536173673964:undef:undef:undef:undef 5148123445:914:421:+:493:- 2156188712:536:undef:undef:undef:undef 8291499958:895:857:+:38:- 4253844263:4155:1292:+:2863:- 1358421452:7367:1673:+:5694:- 9730117517:9295:3233:+:6062:- 4743334107:21543:undef:undef:undef:undef 1101209189:37171:753:+:36418:- 1511883525:59689:46903:+:12786:- 7831509333:801926:16723:+:785203:- 1901678424:628922:undef:undef:undef:undef 7582083726:553752:undef:undef:undef:undef 2814121196:6720204:undef:undef:undef:undef 9041977165:3574257:1209775:+:2364482:- 4665349605:1741859:undef:undef:undef:undef 9654885508:11320405:5070547:+:6249858:- 8544595875:81826780:undef:undef:undef:undef 4491577979:44839325:37909494:+:6929831:- 5894419727:209676047:undef:undef:undef:undef 3422175244:200901170:undef:undef:undef:undef 9073863612:285704419:undef:undef:undef:undef 3010456331:1575223721:358803466:+:1216420255:- 3675209249:1238920469:348052350:+:890868119:- 3076955755:2044728121:819483755:+:1225244366:- 5532449106:11804864757:undef:undef:undef:undef 2178321516:72446432820:undef:undef:undef:undef 8141624878:24177169161:12669591040:+:11507578121:- 4373829532:361530049790:undef:undef:undef:undef 6510438062:221919090285:118395549053:+:103523541232:- 2923624068:928301613177:undef:undef:undef:undef 6422616650:1821551105905:undef:undef:undef:undef 3920819292:3609657590139:undef:undef:undef:undef 8529302041:8171890540911:6330113830732:+:1841776710179:- 8283075058:99249682083240:undef:undef:undef:undef 7714159938:42279030272060:undef:undef:undef:undef 8830465691:94598224923192:1238025432947:+:93360199490245:- 6503804316:893134882044913:595341231988876:+:297793650056037:- 3020967744:692332434884097:undef:undef:undef:undef 5707972016:416981172056363:319046936750814:+:97934235305549:- 7802276257:5121005781327377:1006470380725860:+:4114535400601517:- 8488092258:5898469708005668:undef:undef:undef:undef 5719273281:6621050033188944:undef:undef:undef:undef 4269820845:97690537236763468:83725800953243273:+:13964736283520195:- 4890136257:67781149490980209:undef:undef:undef:undef 1249614077:13434251636315727:8033650483878155:+:5400601152437572:- 7567169928:209400997888616374:undef:undef:undef:undef 2892092078:809180780834786061:459957472215866399:+:349223308618919662:- 5059477571:225235022670459161:188872579792036573:+:36362442878422588:- 3296846539:3419541167968110901:3375814864108936545:+:43726303859174356:- 3755465778:5985810828658626985:3396977572175897167:+:2588833256482729818:- 8440375029:7500789156286352849:740815062674890403:+:6759974093611462446:- 7200372756:67154895069447055956:undef:undef:undef:undef 1129552307:47029208094293947604:7082422936839559503:+:39946785157454388101:- 2149757725:67859417827284636751:46371390131760805747:+:21488027695523831004:- 9142316269:430441115080170066523:160600796982128766071:+:269840318098041300452:- 3787820619:404407421001507234094:314994134692265924347:+:89413286309241309747:- 1783571232:759228725504543081212:undef:undef:undef:undef 5259924308:8647842759402242582039:2573478635201018217649:+:6074364124201224364390:- 7549596943:9126835586456198292095:5602555267454219862537:+:3524280319001978429558:- 5502628004:1921833832195605113404:undef:undef:undef:undef 2734794642:20341260710298800232522:undef:undef:undef:undef 6649682442:20588599858934853156107:6112141034906005902861:+:14476458824028847253246:- 7945061400:80888029696624048552137:undef:undef:undef:undef 5318739090:371043970435050967481651:undef:undef:undef:undef 7813005156:625486598641910843913099:undef:undef:undef:undef 7596209423:838237546042044839786955:592126700174737059178067:+:246110845867307780608888:- 5542001838:4371473048465980598505528:undef:undef:undef:undef 9215909038:4418497062287071779597132:undef:undef:undef:undef 9088238948:6385259025471575663888098:undef:undef:undef:undef 7141106533:421:64:+:357:- 4608309022:353:267:+:86:- 3215543482:147:79:+:68:- 5960988438:4252:undef:undef:undef:undef 7407872116:9905:4691:+:5214:- 1707352681:5638:1339:+:4299:- 2628785609:94072:46265:+:47807:- 6960760204:83288:undef:undef:undef:undef 1420175176:10837:5726:+:5111:- 4471827497:750478:19619:+:730859:- 1058033319:745141:79035:+:666106:- 4707692720:459142:undef:undef:undef:undef 6872130879:7596812:3927615:+:3669197:- 7337043892:6212023:4023595:+:2188428:- 6562355347:6847846:769323:+:6078523:- 7414460013:35105897:20727442:+:14378455:- 2431585113:94138027:11221501:+:82916526:- 8926085180:67232734:undef:undef:undef:undef 2696422432:384919346:undef:undef:undef:undef 2518225632:701394234:undef:undef:undef:undef 4582392418:484897725:332579557:+:152318168:- 1593126296:8704586019:4313576687:+:4391009332:- 5576970406:5468430807:undef:undef:undef:undef 8122724503:5592354812:407232599:+:5185122213:- 7223414134:97520329077:69882438535:+:27637890542:- 4483962895:50989493417:22740942054:+:28248551363:- 5920178769:92950702035:undef:undef:undef:undef 2000396391:775202780024:474916861247:+:300285918777:- 9068883969:512247505350:undef:undef:undef:undef 8726799433:501767727686:365378905449:+:136388822237:- 4162671941:8271806934045:2346236556626:+:5925570377419:- 9810813468:2254470979839:undef:undef:undef:undef 6945957450:7134739113826:undef:undef:undef:undef 5419725549:77513920051398:undef:undef:undef:undef 3295597344:51067657361328:undef:undef:undef:undef 7797262227:23985104215078:8462208296939:+:15522895918139:- 9200570839:665110102190379:582850578047767:+:82259524142612:- 4054467081:444097977689960:35609249338001:+:408488728351959:- 2328973673:134392175876030:133853800850287:+:538375025743:- 9707764065:9353285118262517:8693519242135388:+:659765876127129:- 5251765881:6585119250077577:undef:undef:undef:undef 4958537228:3685944437151997:2359687219399978:+:1326257217752019:- 4975107553:23849725039900792:21463622386830961:+:2386102653069831:- 8053531898:48866091437980762:undef:undef:undef:undef 1989915545:37444679715007743:27086022928847654:+:10358656786160089:- 2274266940:380230297405974554:undef:undef:undef:undef 7338671999:237032697192956945:114810539536337184:+:122222157656619761:- 2672076311:710161125077350588:321797615692800887:+:388363509384549701:- 8556132773:4273339019207528078:4068075955799074695:+:205263063408453383:- 1323128849:4987603262857552256:261890174330778097:+:4725713088526774159:- 9331227869:7559757703317873620:3503205231111896789:+:4056552472205976831:- 8306683275:56040420057499208079:undef:undef:undef:undef 4923726787:32491667952172724505:undef:undef:undef:undef 6004565244:39053779102790486024:undef:undef:undef:undef 9180567367:292488594180822005393:43500015152127356759:+:248988579028694648634:- 2420974275:787720949136879886353:undef:undef:undef:undef 3831811701:973713277862130004663:798753610573946524675:+:174959667288183479988:- 3116728212:5194005128166435062520:undef:undef:undef:undef 3748674459:8253306548305148592778:6985466021063217658211:+:1267840527241930934567:- 7726337119:1711126095512018755532:1472383168750974544079:+:238742926761044211453:- 9859039295:99630480228978284598204:22064746749929907191903:+:77565733479048377406301:- 1792896124:78644699454890690955397:5831488120861206829374:+:72813211334029484126023:- 9010729274:34056143941643853006739:6606395455177648232830:+:27449748486466204773909:- 8936492080:555179115685053102546996:undef:undef:undef:undef 8938045036:158058717726679139758931:134184101055217884924706:+:23874616671461254834225:- 3500736605:306848482537996666861469:27823706542582270505843:+:279024775995414396355626:- 2570452638:8186554279070548480048270:undef:undef:undef:undef 9208061087:2701158110687268893701976:212687115087574009549807:+:2488470995599694884152169:- 3532767804:9850603484307820118068443:undef:undef:undef:undef 3292630474:213:61:+:152:- 1177035926:343:124:+:219:- 5064628398:613:600:+:13:- 5420258143:2333:715:+:1618:- 2548536092:5414:undef:undef:undef:undef 9049476761:1324:901:+:423:- 7468130895:73550:undef:undef:undef:undef 3069055502:31332:undef:undef:undef:undef 4586171713:73361:33095:+:40266:- 2813493595:433822:182311:+:251511:- 3293589659:537694:159753:+:377941:- 9787848035:981797:213028:+:768769:- 1211767981:8865597:6153958:+:2711639:- 7527077162:7316748:undef:undef:undef:undef 2070631145:7877295:undef:undef:undef:undef 5645876442:89643311:44878003:+:44765308:- 2975863384:95054744:undef:undef:undef:undef 2450125441:59716025:25381411:+:34334614:- 9328387451:347474581:22697295:+:324777286:- 7276736230:578768518:undef:undef:undef:undef 8097844197:917805224:557826189:+:359979035:- 5542614594:6263902233:undef:undef:undef:undef 5588307923:1304223418:957834829:+:346388589:- 2722553554:1785897687:undef:undef:undef:undef 5846164789:30892076600:12826419709:+:18065656891:- 9270685632:43883358098:undef:undef:undef:undef 2907786447:99699869702:58350311387:+:41349558315:- 4116050874:917931378901:551387474688:+:366543904213:- 8014825660:693906835721:293375057978:+:400531777743:- 2663764664:228156532609:81691276315:+:146465256294:- 2216340909:1830341637693:undef:undef:undef:undef 3316192213:9424145394847:6989463246321:+:2434682148526:- 6416738464:3780072063461:2897533443094:+:882538620367:- 6398251523:31846913227394:9077643971549:+:22769269255845:- 6774543830:15485228438096:undef:undef:undef:undef 9139588413:85631225260902:undef:undef:undef:undef 2646660555:520978488306377:481168766170461:+:39809722135916:- 1708166460:687677804741176:undef:undef:undef:undef 8068783734:576077966548200:undef:undef:undef:undef 7391778815:8793490006282730:undef:undef:undef:undef 4425797098:2649756886789703:982517753185920:+:1667239133603783:- 1927668536:4517684294149869:2094599833025534:+:2423084461124335:- 8846194493:89458969050968238:88473476513555807:+:985492537412431:- 1356247734:57708536612380408:undef:undef:undef:undef 9283400862:60164628617545143:undef:undef:undef:undef 7134997642:970590878828337637:11475370761699700:+:959115508066637937:- 2448044081:497521607705096257:169690938174749282:+:327830669530346975:- 6630294043:355118381517905481:296879341228857643:+:58239040289047838:- 9048703865:6775156322220288085:undef:undef:undef:undef 3360043023:1552463462349220474:1359694808020382509:+:192768654328837965:- 6322110489:2929628186953843343:768202880076132022:+:2161425306877711321:- 1952190995:34944557910816697735:undef:undef:undef:undef 1752383842:47799193299118514504:undef:undef:undef:undef 2591178285:20716078546776381544:542167759790812421:+:20173910786985569123:- 8122148705:719406089648357733188:66006084391585545997:+:653400005256772187191:- 9694973346:719872599872040467710:undef:undef:undef:undef 7651220450:199587106552578178892:undef:undef:undef:undef 2042227136:9977487099852483689869:5552448050932507152839:+:4425039048919976537030:- 7678908931:2066109744744204323008:1080949980017941914603:+:985159764726262408405:- 6776427617:5565961119662384144160:3174002324552687900033:+:2391958795109696244127:- 5506956101:91373598288783887124420:52538003723684051988161:+:38835594565099835136259:- 7750135453:82335349859501196087584:19437141841512928708533:+:62898208017988267379051:- 8167436712:29797131824570137765228:undef:undef:undef:undef 9607370311:121631427998360740391950:116991644172432396453041:+:4639783825928343938909:- 8423935365:390669097503232686224283:undef:undef:undef:undef 7679416321:812057216216967914616590:97719265386820648344381:+:714337950830147266272209:- 6616861234:7124598459490387096368946:undef:undef:undef:undef 8037474856:4394869798590543002227680:undef:undef:undef:undef 8489232501:1079711269233988143651568:696154355808976351663373:+:383556913425011791988195:- 19619863951:640:111:+:529:- 85774558372:870:undef:undef:undef:undef 68692077395:768:731:+:37:- 18817191633:1247:undef:undef:undef:undef 41607799272:4043:undef:undef:undef:undef 91664653876:1953:1228:+:725:- 30295176945:65091:undef:undef:undef:undef 68580059047:31143:31099:+:44:- 18531360333:62597:5961:+:56636:- 64931971582:770747:224390:+:546357:- 76273168395:550050:undef:undef:undef:undef 12687319250:219475:undef:undef:undef:undef 59300897639:4792393:3288541:+:1503852:- 18756681129:2651540:260449:+:2391091:- 11621386352:9988923:9327119:+:661804:- 11671142180:50629990:undef:undef:undef:undef 71178649986:68816970:undef:undef:undef:undef 74013301662:71022147:undef:undef:undef:undef 23241107541:263070580:undef:undef:undef:undef 48817631495:693874447:559839348:+:134035099:- 27002573153:991130369:406278786:+:584851583:- 30110051854:5633080520:undef:undef:undef:undef 81689406704:9011232668:undef:undef:undef:undef 79230938200:2105447195:undef:undef:undef:undef 19365367706:75075911763:24226164476:+:50849747287:- 81083049942:58913389052:undef:undef:undef:undef 51257009494:45938599459:23115072005:+:22823527454:- 42158677183:461384086321:266329865164:+:195054221157:- 39442909636:102294989999:3097205854:+:99197784145:- 57275117957:625569596710:26729474233:+:598840122477:- 46504908030:4891760428228:undef:undef:undef:undef 73684339754:1844138927702:undef:undef:undef:undef 74088481666:4699906983901:3721697754973:+:978209228928:- 26129624873:18411432449513:11761232099671:+:6650200349842:- 19345524820:32205951498816:undef:undef:undef:undef 72054302316:43379703428064:undef:undef:undef:undef 15616222576:848488993596498:undef:undef:undef:undef 69547304804:514984536664451:202506076568533:+:312478460095918:- 12293860148:265512282165446:undef:undef:undef:undef 81199025845:5621389577199773:1852579536987082:+:3768810040212691:- 19058227448:4631815971859621:2500260977776959:+:2131554994082662:- 25706178209:2852697247397245:1094513648549039:+:1758183598848206:- 84487466920:92135420088227056:undef:undef:undef:undef 83614464584:41550747062790023:10299015965969792:+:31251731096820231:- 59989677087:48741797004563563:45861780904575978:+:2880016099987585:- 98582067675:315525240004800411:undef:undef:undef:undef 64232583500:425410208124592332:undef:undef:undef:undef 76934972176:727225029234317401:291112039937901025:+:436112989296416376:- 61795142851:5908241486766574299:1531764824706643039:+:4376476662059931260:- 17457170535:3166396673218459506:undef:undef:undef:undef 17204815290:7640687601245950106:undef:undef:undef:undef 13967589922:24620673542453299190:undef:undef:undef:undef 18996604311:10500459771152570191:3463067987556565681:+:7037391783596004510:- 99529301459:57003647317599090016:52933805965895779835:+:4069841351703310181:- 21766161947:523274541742761821127:450482897901685064168:+:72791643841076756959:- 16942826435:591722373918366385353:524166819689054326493:+:67555554229312058860:- 16804448482:991556680669357611557:313610950653156070248:+:677945730016201541309:- 81417123102:8626004426690250806770:undef:undef:undef:undef 57810478745:1158648995310485169745:undef:undef:undef:undef 42914795809:6665983779754125038980:4126687974584465643489:+:2539295805169659395491:- 36093280350:40741055983857332591795:undef:undef:undef:undef 23163546490:56263620282139603069750:undef:undef:undef:undef 52441622976:91907271791271848630774:undef:undef:undef:undef 73971752879:404396346841326960342107:22483415704898398667030:+:381912931136428561675077:- 27383552312:807536823690462158322754:undef:undef:undef:undef 42968002345:415025458708440421452321:172637226598767276175501:+:242388232109673145276820:- 56637065473:5574917704969584786035494:3393062316543458531439975:+:2181855388426126254595519:- 54752779821:1020499444245376121307585:undef:undef:undef:undef 27299076726:6195794248399897805538700:undef:undef:undef:undef 55988303440:634:undef:undef:undef:undef 46289482707:161:20:+:141:- 34475152213:652:401:+:251:- 24163728134:8820:undef:undef:undef:undef 78921381692:8895:5813:+:3082:- 36157304038:1699:1458:+:241:- 12383420501:12298:10209:+:2089:- 54189087986:77426:undef:undef:undef:undef 30993698782:93964:undef:undef:undef:undef 11005868465:704848:445329:+:259519:- 97908567288:287127:undef:undef:undef:undef 96142337868:537820:undef:undef:undef:undef 48033736196:8356003:6621839:+:1734164:- 14258068690:3307074:undef:undef:undef:undef 98242695686:4794491:1781294:+:3013197:- 98332246156:40701738:undef:undef:undef:undef 40762113568:82218554:undef:undef:undef:undef 72222947107:43372717:29069642:+:14303075:- 78858771447:705940446:undef:undef:undef:undef 22845209534:511457632:undef:undef:undef:undef 79202751925:496736846:288940043:+:207796803:- 44015419886:1370027108:undef:undef:undef:undef 14740617678:3671326471:644054363:+:3027272108:- 51283387001:5035534773:82346837:+:4953187936:- 67754140782:44107492775:9159793518:+:34947699257:- 11450645657:38008624524:2221092461:+:35787532063:- 93908675218:35502305764:undef:undef:undef:undef 84530484757:938890630219:731105383278:+:207785246941:- 96222678102:738162054175:465387276063:+:272774778112:- 31749891953:251063841485:101595824997:+:149468016488:- 87542080948:4505635455016:undef:undef:undef:undef 54977683045:2773383989258:2493438831321:+:279945157937:- 40569027555:3615108721226:2518147895043:+:1096960826183:- 96291110886:28425070691517:undef:undef:undef:undef 90612281235:85629366724855:undef:undef:undef:undef 72510178601:17727060776225:12348745682926:+:5378315093299:- 81306457060:235145400944969:180271187967402:+:54874212977567:- 77551956070:152737902472109:115292749343806:+:37445153128303:- 18362092979:592849786460608:477159064023803:+:115690722436805:- 12568366235:9296831581308712:5572180343877843:+:3724651237430869:- 32759208696:6898093370301786:undef:undef:undef:undef 86487216018:1356322070287283:1033263875860896:+:323058194426387:- 43914979501:57851110256120623:26951290016793684:+:30899820239326939:- 69218213150:33753764914433418:undef:undef:undef:undef 21903718070:22400970582554760:undef:undef:undef:undef 76550114186:169590921694397453:5275067267806340:+:164315854426591113:- 70700648633:927920898274164342:809756760862902311:+:118164137411262031:- 50954298786:439015263921052931:312517981376514752:+:126497282544538179:- 14627845587:2683727529903671189:2626648958035451369:+:57078571868219820:- 60001277877:4213480590674859045:undef:undef:undef:undef 52726275559:2418314281060146017:1713693942213228018:+:704620338846917999:- 70956433758:45183728941930903369:6737839567038249981:+:38445889374892653388:- 84333137725:76868163100446856378:43511485431239100287:+:33356677669207756091:- 46154315150:66357754943455880708:undef:undef:undef:undef 27492026281:461493792779773393753:273687143887649719341:+:187806648892123674412:- 23028559122:780782875393389511867:183222780259840839928:+:597560095133548671939:- 20879898887:289240418968940471885:50011166837551006998:+:239229252131389464887:- 33866533095:5430286568999498031613:4587703373107517096426:+:842583195891980935187:- 72490997240:2853832777203682859457:557816804946260305562:+:2296015972257422553895:- 58220508034:6960755318661979297176:undef:undef:undef:undef 16773993745:82309308062191131745025:undef:undef:undef:undef 90780122928:47914764005555535189608:undef:undef:undef:undef 63272632392:14598393722836057045170:undef:undef:undef:undef 67616722802:523323411117586836682950:undef:undef:undef:undef 27385890062:753331857256691046762753:143202707642973498385235:+:610129149613717548377518:- 46682532055:909883549673243508446865:undef:undef:undef:undef 56316904954:4264791344244348532158840:undef:undef:undef:undef 86843264136:6475134836481391542091695:undef:undef:undef:undef 85244758659:1704360995315663471149471:1375716319199516032741418:+:328644676116147438408053:- 24288217979:353:280:+:73:- 66458437156:386:undef:undef:undef:undef 19718646513:263:106:+:157:- 95474310552:3437:1683:+:1754:- 38871356282:4851:undef:undef:undef:undef 75182558334:4501:3035:+:1466:- 74796843655:36032:4343:+:31689:- 36050059224:23891:17103:+:6788:- 19863094194:89750:undef:undef:undef:undef 19905915706:975620:undef:undef:undef:undef 71406378496:659897:96547:+:563350:- 43322859235:411789:410749:+:1040:- 54974583785:3916040:undef:undef:undef:undef 81903616712:2458455:undef:undef:undef:undef 59628024735:5215309:2878549:+:2336760:- 28705160170:49545545:undef:undef:undef:undef 67752993660:52948818:undef:undef:undef:undef 66859909995:35372569:9054285:+:26318284:- 67527342817:655522510:538008753:+:117513757:- 15698643693:766331281:174247520:+:592083761:- 47450816662:410707617:49859089:+:360848528:- 75603025144:4189222864:undef:undef:undef:undef 73542271399:3273988801:501635612:+:2772353189:- 45694664349:8734878798:undef:undef:undef:undef 66595291204:11729868098:undef:undef:undef:undef 69501488320:85284086864:undef:undef:undef:undef 36661815348:89160068445:undef:undef:undef:undef 92705945126:470374778708:undef:undef:undef:undef 69447267027:560775857202:undef:undef:undef:undef 91303815250:359828355259:191892328492:+:167936026767:- 88976813390:5090743771836:undef:undef:undef:undef 94356842579:7970259562466:6140210284291:+:1830049278175:- 14492287394:5950877408494:undef:undef:undef:undef 27377195044:42999393154994:undef:undef:undef:undef 69047709710:28449727256942:undef:undef:undef:undef 10410308560:63997569964861:13451003143715:+:50546566821146:- 15409058311:251828247387937:14973162977052:+:236855084410885:- 10493672545:954153415958701:232340346578521:+:721813069380180:- 45989252217:996320980569464:767378780584985:+:228942199984479:- 96873617454:5297182065317071:3240764072557170:+:2056417992759901:- 57978276673:6703901945872064:5953616472118145:+:750285473753919:- 59366938953:2908760366126304:undef:undef:undef:undef 57388386219:84252041112507045:undef:undef:undef:undef 28368803324:53635056952793524:undef:undef:undef:undef 74853209254:18038062502188903:13709777410524861:+:4328285091664042:- 94418480790:763270562490260143:378221230890785994:+:385049331599474149:- 32960652072:514712124794857785:undef:undef:undef:undef 23965240606:111896153469198055:96865110870983806:+:15031042598214249:- 92890852933:4317209390559678089:3232811696386326621:+:1084397694173351468:- 66083051517:7484014451845132056:undef:undef:undef:undef 95548308792:8571649108925026632:undef:undef:undef:undef 61587506973:75655998703340740251:undef:undef:undef:undef 36492167113:64830970919116544035:34452121223046558792:+:30378849696069985243:- 47414170431:66283011233668339228:19945104413754249579:+:46337906819914089649:- 83952874484:379577007442534770606:undef:undef:undef:undef 13453938845:627742400476848768996:55527279406551179597:+:572215121070297589399:- 57271608113:500351574761368549681:222800521860369745774:+:277551052900998803907:- 75522487555:3299190756552280864693:36819551463387917873:+:3262371205088892946820:- 27300549379:1326735055393879199770:573991737436460673979:+:752743317957418525791:- 54911657319:5008374103159935107694:undef:undef:undef:undef 88672660086:62868971409272686179217:13131443217355368132150:+:49737528191917318047067:- 27721936547:61710975468863072396278:5078284672196140324593:+:56632690796666932071685:- 76420567898:80335752099127143873694:undef:undef:undef:undef 88462594363:373377635745075437414215:293799652323092890492982:+:79577983421982546921233:- 87117815521:446513595128302477101979:136577511334768668327783:+:309936083793533808774196:- 71148729807:125512385439385059891171:undef:undef:undef:undef 51232114548:8590143757101949690560324:undef:undef:undef:undef 81326725359:9593507402105112306658329:undef:undef:undef:undef 22023900520:4971687822738244653894775:undef:undef:undef:undef 801813494781:678:undef:undef:undef:undef 614649489779:680:339:+:341:- 582713490936:534:undef:undef:undef:undef 138606539624:3468:undef:undef:undef:undef 386646887249:9695:undef:undef:undef:undef 992742944667:2311:1570:+:741:- 991566673011:94751:70371:+:24380:- 934470329536:63740:undef:undef:undef:undef 735070146288:48146:undef:undef:undef:undef 499441086171:764408:481699:+:282709:- 736447819242:890416:undef:undef:undef:undef 410744422180:431391:289234:+:142157:- 872858999230:2932636:undef:undef:undef:undef 464130848993:4486986:undef:undef:undef:undef 801198442388:1478327:98963:+:1379364:- 834528120443:22957683:4097378:+:18860305:- 839083962592:88971800:undef:undef:undef:undef 531999704660:91700683:20060210:+:71640473:- 951291519081:903005862:undef:undef:undef:undef 406295209764:191808480:undef:undef:undef:undef 767630672948:285294076:undef:undef:undef:undef 396206089628:2380922308:undef:undef:undef:undef 864084658545:9876586333:7807255949:+:2069330384:- 629351403044:1233285831:904356758:+:328929073:- 917873706628:10214454505:6101416017:+:4113038488:- 450336168952:47050406832:undef:undef:undef:undef 327961264819:46354078350:43277401879:+:3076676471:- 278152160238:754274017268:undef:undef:undef:undef 334541849439:476377132358:5307918097:+:471069214261:- 780640258206:789810965956:undef:undef:undef:undef 212461885210:5797066227880:undef:undef:undef:undef 358408720871:2519755171595:1684455160376:+:835300011219:- 788432904683:4182666982493:4130571200403:+:52095782090:- 549268238393:19442212278951:undef:undef:undef:undef 299139446754:85037920015177:4498991335615:+:80538928679562:- 585454695380:25115210430725:undef:undef:undef:undef 254753561822:408768593967668:undef:undef:undef:undef 966499320594:561141265883477:376004264706584:+:185137001176893:- 680059330643:339509077857030:283334972558237:+:56174105298793:- 239462108548:4528624397365167:715439292109942:+:3813185105255225:- 609935772510:6892067195528656:undef:undef:undef:undef 112362176049:9796890405922436:7452815293824665:+:2344075112097771:- 257709487380:21971416237355067:undef:undef:undef:undef 908934155940:68186412126027786:undef:undef:undef:undef 354247575039:21510025228683664:undef:undef:undef:undef 119319075259:879239967878656841:177736259493621362:+:701503708385035479:- 804254523797:494089498623257412:386906269134652865:+:107183229488604547:- 543221015155:733108339586390616:602413514390930539:+:130694825195460077:- 568086994695:5769435733689987503:973755647218364807:+:4795680086471622696:- 799727942309:8979693967765833002:2415278824207885017:+:6564415143557947985:- 262366830869:9917829171066368767:8908431466306839038:+:1009397704759529729:- 801958327711:75230504966207135247:505610354521913512:+:74724894611685221735:- 782629705679:34606782233158928567:29884919549816155087:+:4721862683342773480:- 652996323722:68540063885331894960:undef:undef:undef:undef 618053685018:736741605628135241112:undef:undef:undef:undef 406188625527:883406927340539746609:314635529675945416790:+:568771397664594329819:- 961813236447:385820578449172054833:undef:undef:undef:undef 519982801173:4684227705145691031760:896467670168264582477:+:3787760034977426449283:- 611688941091:4157999422802404413994:2207749577029259571213:+:1950249845773144842781:- 730284254238:3480969249312179218785:undef:undef:undef:undef 962781074516:38324004299157166567680:undef:undef:undef:undef 466950241209:26172428851429591731402:undef:undef:undef:undef 596945181824:72614887504841250169861:49703032847455033134280:+:22911854657386217035581:- 180618611008:244105423934601423461897:204271227432580695863257:+:39834196502020727598640:- 795860848202:245855528325337206180642:undef:undef:undef:undef 352183699793:582097768277589867216208:530299208567115343858145:+:51798559710474523358063:- 723063138545:1534932171795810802951721:1170330456803857815612608:+:364601714991952987339113:- 325553416597:3379566852740653736562254:364983928274271006821517:+:3014582924466382729740737:- 731090681506:4019669485829341860348651:undef:undef:undef:undef 539838998545:507:7:+:500:- 170374512797:247:161:+:86:- 424990958887:145:98:+:47:- 108807278437:5932:2521:+:3411:- 233178939657:5653:2715:+:2938:- 807027977703:2472:undef:undef:undef:undef 976598436356:98616:undef:undef:undef:undef 988230847568:44612:undef:undef:undef:undef 470364205892:15544:undef:undef:undef:undef 302425071635:563277:319988:+:243289:- 219475754879:216142:161539:+:54603:- 699147054562:562075:172348:+:389727:- 829675206608:8793826:undef:undef:undef:undef 589355140011:9099979:1109186:+:7990793:- 392952480622:8491184:undef:undef:undef:undef 890224064397:88284845:66381333:+:21903512:- 933681679825:22982808:20235145:+:2747663:- 782012973700:51684539:50010492:+:1674047:- 197248910099:873744194:94469581:+:779274613:- 845643881183:710460352:53055455:+:657404897:- 202542417637:738541112:706082709:+:32458403:- 661052617861:4115902967:2324341310:+:1791561657:- 344531027219:9317694786:7166878709:+:2150816077:- 394613663847:5654080162:4999665219:+:654414943:- 484541465210:33438466317:16660420985:+:16778045332:- 125383494408:23161568367:undef:undef:undef:undef 444600126192:99689925705:undef:undef:undef:undef 173574844181:932314550107:579904335202:+:352410214905:- 969975211838:270079957135:27981089787:+:242098867348:- 122749761441:399795628752:undef:undef:undef:undef 242192263334:6476490046110:undef:undef:undef:undef 524444428681:5071522667390:4569120426681:+:502402240709:- 178409154818:4375991059484:undef:undef:undef:undef 614830537503:30539577929795:4585805722412:+:25953772207383:- 735071268099:66368563915236:undef:undef:undef:undef 532875829676:12877186055234:undef:undef:undef:undef 437988491749:737381170127270:645693715044929:+:91687455082341:- 481846189288:359568635873405:270518854521647:+:89049781351758:- 458103515841:515501956010102:160770845332143:+:354731110677959:- 508366057145:9372236974262244:7974731481400649:+:1397505492861595:- 120232323906:4447604417367689:2894149251255209:+:1553455166112480:- 876848598384:1685318971853925:undef:undef:undef:undef 138479501588:32578168424815627:31166212113160317:+:1411956311655310:- 533666642770:89068727957463288:undef:undef:undef:undef 479439297147:15922726166951385:undef:undef:undef:undef 638497067661:972469011671173991:416750023327742201:+:555718988343431790:- 691022108095:930027344334722104:576090462433909527:+:353936881900812577:- 742847282780:283642538218216660:undef:undef:undef:undef 782713557290:5984673682556848052:undef:undef:undef:undef 797082615787:2591352534815129064:1377191795208135163:+:1214160739606993901:- 142147996405:7537086787316841635:undef:undef:undef:undef 991358285792:91466066258249912028:undef:undef:undef:undef 874948329633:14393999125077889850:8683795833169725347:+:5710203291908164503:- 772007967276:49324783064443875324:undef:undef:undef:undef 605080207724:966301645828029386288:undef:undef:undef:undef 112771167321:835668669621252857343:undef:undef:undef:undef 571031238297:231760969553061898185:undef:undef:undef:undef 316861472933:8755918478458246353336:5302141659834143239253:+:3453776818624103114083:- 711694537086:5504077889510662473729:undef:undef:undef:undef 635580457016:3051056699952132842912:undef:undef:undef:undef 939251853436:49421899701983410182541:14799618160338254984383:+:34622281541645155198158:- 888292517231:68887410489854961995824:20504636833150226385823:+:48382773656704735610001:- 964362919556:15768924368455017921710:undef:undef:undef:undef 664102667876:194250347475587692617411:153400360282828944863537:+:40849987192758747753874:- 628159632643:156250197014367830057358:49621189973332877595865:+:106629007041034952461493:- 924459152964:755408685432182186988710:undef:undef:undef:undef 795212888341:4749615418256194201950885:3589927199807610352267411:+:1159688218448583849683474:- 969306949612:3526700003112794244981402:undef:undef:undef:undef 435130827079:2289524153226895212844946:466605775871864438867941:+:1822918377355030773977005:- 592023096465:674:443:+:231:- 858771784505:189:122:+:67:- 483521220209:100:89:+:11:- 512353038734:5427:1358:+:4069:- 460292553468:3641:undef:undef:undef:undef 924385840680:3549:undef:undef:undef:undef 622797518286:11295:undef:undef:undef:undef 728830918974:68279:36546:+:31733:- 179031377630:83507:54019:+:29488:- 714861405363:749881:194966:+:554915:- 126498673205:306460:undef:undef:undef:undef 433396611768:456306:undef:undef:undef:undef 347938737984:6561022:undef:undef:undef:undef 267433286769:2185923:undef:undef:undef:undef 299888302428:9021353:undef:undef:undef:undef 944411807076:60730977:undef:undef:undef:undef 656857562869:52710527:8028730:+:44681797:- 175039832667:53058033:undef:undef:undef:undef 600321209741:876570444:148325921:+:728244523:- 410801666277:284543609:222814218:+:61729391:- 934740036637:787608667:186849586:+:600759081:- 236251494131:1982052282:677355641:+:1304696641:- 404959025398:1835550551:770382556:+:1065167995:- 870672061651:8280586756:7288456715:+:992130041:- 572275112907:54558901682:6459971709:+:48098929973:- 310335763983:31560369965:12580055557:+:18980314408:- 963607527071:66865319675:undef:undef:undef:undef 533277562731:594926647034:214370455925:+:380556191109:- 125436023478:260253445336:undef:undef:undef:undef 733358546590:106351570723:96439581950:+:9911988773:- 840320962822:4147586246170:undef:undef:undef:undef 960532701335:6973956365960:undef:undef:undef:undef 940977431443:1369840828496:undef:undef:undef:undef 184865250154:55595929368115:33676359108719:+:21919570259396:- 557735659133:35419485572251:6061027410573:+:29358458161678:- 379969274283:88031094139616:38462907988099:+:49568186151517:- 156962092805:192152126661625:undef:undef:undef:undef 878028583425:409543286706155:undef:undef:undef:undef 723236876934:466911911788602:undef:undef:undef:undef 838452683171:5034250413598108:3149945721189243:+:1884304692408865:- 539963468802:3504260435362874:undef:undef:undef:undef 822428386557:7975273187941436:75155367835073:+:7900117820106363:- 620025888923:72077595277040803:41727007177332291:+:30350588099708512:- 887089341627:97437220182961738:15191900082606955:+:82245320100354783:- 550152697503:28685896999083677:27775086852710002:+:910810146373675:- 907736859418:495594698307592668:undef:undef:undef:undef 844532449421:226525458486119867:92675357026312623:+:133850101459807244:- 290030108234:888870145425067508:undef:undef:undef:undef 223122478973:4881707225380243751:2311386379376493401:+:2570320846003750350:- 838180527233:4519190109670626723:468414027727324931:+:4050776081943301792:- 503051187421:2986323539257458540:2714589881726022901:+:271733657531435639:- 438195809002:20686076842979970998:undef:undef:undef:undef 928756754537:21351950083797573408:16808974269714514361:+:4542975814083059047:- 778766734206:73769662894814226457:40320347784044131633:+:33449315110770094824:- 404444348596:402652786177066040565:63723374664283980286:+:338929411512782060279:- 405709159924:476722172728050310518:undef:undef:undef:undef 123809934304:467789418272878823578:undef:undef:undef:undef 483364523636:8434115723329816871422:undef:undef:undef:undef 702997471346:6291500282469527412753:4760928087614525369936:+:1530572194855002042817:- 864677216967:4548263631270988546497:undef:undef:undef:undef 332643775867:76365755420873705024515:28669607070400315778498:+:47696148350473389246017:- 113763860947:98151136623085544064307:25867928408202816739980:+:72283208214882727324327:- 765104930615:98441551806993047906760:undef:undef:undef:undef 286058050022:728576305264353758098427:139752879596817105465930:+:588823425667536652632497:- 716047877999:607838965660317020098603:278584770701658770655661:+:329254194958658249442942:- 510369088451:857801163425997715664873:444460478417136686526255:+:413340685008861029138618:- 307360985951:3503288763328136255311097:2510688541034734103910912:+:992600222293402151400185:- 853276639479:8130173718146949584851816:4601270129124500684525999:+:3528903589022448900325817:- 178828950235:7207199066268548234950097:643719687732055328545714:+:6563479378536492906404383:- 1291023501350:388:undef:undef:undef:undef 8914519194391:964:535:+:429:- 3785490447532:442:undef:undef:undef:undef 1032797957148:3713:523:+:3190:- 8646717950722:5093:867:+:4226:- 7822123404306:7646:undef:undef:undef:undef 4626583585009:89356:87537:+:1819:- 9079556803019:46195:38574:+:7621:- 2390480680998:28534:undef:undef:undef:undef 5307875865096:638454:undef:undef:undef:undef 2604054585447:177301:162624:+:14677:- 9572431315314:829208:undef:undef:undef:undef 6524154613882:4271176:undef:undef:undef:undef 9214492721347:7906028:4237191:+:3668837:- 8988524600670:3354387:undef:undef:undef:undef 3128419233235:10999230:undef:undef:undef:undef 8739744811748:38164520:undef:undef:undef:undef 1698185551761:22414225:6134666:+:16279559:- 5166608725100:209812397:189480138:+:20332259:- 9292163213106:262047604:undef:undef:undef:undef 1223198833954:887505231:473355643:+:414149588:- 8070337179394:4970712133:3360508129:+:1610204004:- 8860537314530:3630643209:357969473:+:3272673736:- 3693132479260:6257550507:4061260069:+:2196290438:- 4172184476851:14363746781:1024378027:+:13339368754:- 9244406947072:68288755668:undef:undef:undef:undef 2081206100866:57695940124:undef:undef:undef:undef 8385576125971:787175603543:787169964879:+:5638664:- 2096667056251:328912581229:114625079406:+:214287501823:- 7323424288731:422111613028:undef:undef:undef:undef 1017580745432:9034837121298:undef:undef:undef:undef 7645405808411:4957960004916:4038709268207:+:919250736709:- 6396169306920:5326727362238:undef:undef:undef:undef 4034431934314:12003416056125:2532698405959:+:9470717650166:- 6333772770664:99793158203172:undef:undef:undef:undef 5419535907787:93637078631846:11094563055647:+:82542515576199:- 3403537814936:624399885047144:undef:undef:undef:undef 9442583388055:335098122909596:307031628652663:+:28066494256933:- 1625334867595:375831378054052:111425698331335:+:264405679722717:- 5363358779615:2507135305833967:75469955465205:+:2431665350368762:- 3001290883323:2722405776932955:undef:undef:undef:undef 5995623250285:2273699468043640:undef:undef:undef:undef 5430258233860:14879327902807915:undef:undef:undef:undef 2009480371111:81569778835077261:undef:undef:undef:undef 8060818778656:80340194042593541:undef:undef:undef:undef 1719916888552:100724926236645251:74547915463096332:+:26177010773548919:- 1710393744862:697076608870176893:541373352472864689:+:155703256397312204:- 4976335389286:793446964186858903:407020962169288668:+:386426002017570235:- 9782344892477:3843112971736180016:3233061258089819973:+:610051713646360043:- 6141658962310:5041879609625351659:23875356626025458:+:5018004252999326201:- 8551740568066:9472573456559108878:undef:undef:undef:undef 6333648282514:67511201167143917000:undef:undef:undef:undef 6698692394389:50026755934259056845:24830640442883066374:+:25196115491375990471:- 9555899774433:26907301042095664279:7787227396742833305:+:19120073645352830974:- 1059030629353:838525276893929711862:129056494743262042681:+:709468782150667669181:- 7528923048127:927075578586380555211:209297471402655112759:+:717778107183725442452:- 8063887169054:958171120653854059763:795387894419027240468:+:162783226234826819295:- 3208049129896:7976366831585787172767:3233233486633041748939:+:4743133344952745423828:- 6309040341427:9674362189053499006488:8552983429862063253715:+:1121378759191435752773:- 9749623155818:9719287505851380685775:8115263141371657388732:+:1604024364479723297043:- 4433943870539:89196508447902402325671:35275960523801223402428:+:53920547924101178923243:- 9876556694758:69976866439984982154930:undef:undef:undef:undef 6515639707808:28009617813979201035332:undef:undef:undef:undef 1074197197298:559875578462144208815527:394558243659367487946171:+:165317334802776720869356:- 8640760683747:477993359537634559273174:436327965906789379436615:+:41665393630845179836559:- 2888779880078:803738423244008874013738:undef:undef:undef:undef 1908619457359:8138382794657404423762001:undef:undef:undef:undef 7054234893560:1056608545958678939471428:undef:undef:undef:undef 7106767104199:2917558549771734775363859:203288873615993146732340:+:2714269676155741628631519:- 1030380160791:234:undef:undef:undef:undef 2258390333510:990:undef:undef:undef:undef 7024855777816:932:undef:undef:undef:undef 5493786002265:1409:1124:+:285:- 5928014438306:4399:940:+:3459:- 9896217023290:5514:undef:undef:undef:undef 1910244733179:78949:425:+:78524:- 6828469218904:79823:78501:+:1322:- 6405863332370:47400:undef:undef:undef:undef 9804063740054:374439:130571:+:243868:- 8313560070776:748383:156935:+:591448:- 5061435378822:128685:undef:undef:undef:undef 9883247622927:2333038:1370789:+:962249:- 4979734023742:5031402:undef:undef:undef:undef 5976191364757:6606892:4625289:+:1981603:- 9434394919019:71904598:44074559:+:27830039:- 5744906695193:97046797:76432966:+:20613831:- 1823025036284:23306578:undef:undef:undef:undef 1174132474849:342456025:249863524:+:92592501:- 4435724095908:705167838:undef:undef:undef:undef 5077520244148:563870137:401183334:+:162686803:- 9711203545679:4902171334:2336745527:+:2565425807:- 5878184522319:7498448356:6651061083:+:847387273:- 4744078864603:5023138454:2239998055:+:2783140399:- 5420081302707:26416299072:undef:undef:undef:undef 5971439306304:39672411949:11649453037:+:28022958912:- 5016596778254:16223684920:undef:undef:undef:undef 5712064772630:679792609931:368221620260:+:311570989671:- 8403824194300:220717020448:undef:undef:undef:undef 1977375942491:659702846061:319492565066:+:340210280995:- 3435584516591:1982999650351:1913477914278:+:69521736073:- 5941331658929:2673352465796:2604118111353:+:69234354443:- 8249577104639:1338703943813:756011906196:+:582692037617:- 4581747637252:24729639181141:21747782363449:+:2981856817692:- 2214350672483:42902804752313:32059610779969:+:10843193972344:- 7715587643575:61460743575338:33111498021069:+:28349245554269:- 5009695000489:433000119308412:263235766091857:+:169764353216555:- 2780831705629:185208281993624:69043791644877:+:116164490348747:- 7672825582131:783604471358360:739393030548611:+:44211440809749:- 8156222205180:3109219503077603:2997452198829590:+:111767304248013:- 1611962821695:7753482891122737:4217262153111896:+:3536220738010841:- 1344055558642:5791429807975789:5112620760498172:+:678809047477617:- 4156214896181:87433200209380821:4036022290114826:+:83397177919265995:- 8791183056533:17266888371263604:14832887253985193:+:2434001117278411:- 2839215467930:15333716803930859:341925618428854:+:14991791185502005:- 9031332797533:772530159158786604:402766106248262089:+:369764052910524515:- 2245892394672:284589341468628386:undef:undef:undef:undef 6628793050257:918609146713656399:undef:undef:undef:undef 6888105415513:7118362515738178674:6967784838104010145:+:150577677634168529:- 7206964244227:3639346422097103707:undef:undef:undef:undef 4933299662870:6579052994026192680:undef:undef:undef:undef 4398085936722:66388421222434399522:undef:undef:undef:undef 6175959807798:76779693447599364073:14857859458457959606:+:61921833989141404467:- 6354148141102:66813618696883914548:undef:undef:undef:undef 9044150524871:389568594988388272031:143314042521346984622:+:246254552467041287409:- 4814210746040:433732095415239717640:undef:undef:undef:undef 9332634314099:670452109194680918419:248334238592552688857:+:422117870602128229562:- 5736492543705:3417271280284106866398:undef:undef:undef:undef 8631249657919:4733409781476931748466:undef:undef:undef:undef 6094039989815:3369611319342579140308:undef:undef:undef:undef 2583722297996:81431725479896681304979:80871272679086793096342:+:560452800809888208637:- 5052888472673:98441868147600474128263:65698019907280289160744:+:32743848240320184967519:- 8460071803145:27471057113022476057946:23026358277427942455881:+:4444698835594533602065:- 7132691709237:826698072835415700701165:69199391036873572813993:+:757498681798542127887172:- 2583208598211:141965554366100683592394:undef:undef:undef:undef 2952268207666:929365864320562368929665:515267089928966547880216:+:414098774391595821049449:- 9914834185011:4152022126245706552477635:undef:undef:undef:undef 1095175494003:2854286084007478686356058:undef:undef:undef:undef 4146822388736:4652366122252896909889132:undef:undef:undef:undef 2667542060084:638:undef:undef:undef:undef 2619119100856:489:286:+:203:- 5471150765644:370:undef:undef:undef:undef 5422654770852:7372:undef:undef:undef:undef 6365483515997:1073:1054:+:19:- 1710773704709:4129:3900:+:229:- 6510241656717:32085:undef:undef:undef:undef 6235004204836:27246:undef:undef:undef:undef 1732986290243:93180:69947:+:23233:- 5052128210619:435359:169861:+:265498:- 7399143702223:313670:undef:undef:undef:undef 9220140871626:972167:606304:+:365863:- 6284334576066:5895034:undef:undef:undef:undef 4896160553553:9274979:6807596:+:2467383:- 8779608519310:1592172:undef:undef:undef:undef 3157760648638:66068639:7197898:+:58870741:- 4203379869707:59797957:50656115:+:9141842:- 2971463108306:81421624:undef:undef:undef:undef 5328039225959:852041219:427109386:+:424931833:- 7223208263787:908347961:490453814:+:417894147:- 6927677824560:729677136:undef:undef:undef:undef 3140617177719:7406264281:2914743811:+:4491520470:- 2686879345811:3583132633:3327906441:+:255226192:- 6080468876608:2170360246:undef:undef:undef:undef 9098349290101:71600559760:13452198141:+:58148361619:- 7604498372334:48716148153:undef:undef:undef:undef 8325583873372:37640609809:30787652453:+:6852957356:- 6221232427758:290437631553:undef:undef:undef:undef 8821824668483:702144063403:691600211398:+:10543852005:- 4687867113852:264453784429:127080233520:+:137373550909:- 9644890486005:5477732202644:2493098621109:+:2984633581535:- 8125551631964:5575596507948:undef:undef:undef:undef 5773855716888:1760621459038:undef:undef:undef:undef 2559983729582:69365648684953:60871322159710:+:8494326525243:- 1924351727803:33553112408704:31625736998899:+:1927375409805:- 2644362096267:65724220634548:47791138766439:+:17933081868109:- 8355484245824:824562588638974:undef:undef:undef:undef 7037413211838:812311386088899:undef:undef:undef:undef 1070483870636:435794905825191:181215486509786:+:254579419315405:- 6491531242222:5633823079615786:undef:undef:undef:undef 6668820087505:9628109909302839:7654626150035173:+:1973483759267666:- 2839652215339:8815014773976322:5149003288847161:+:3666011485129161:- 1932220292086:77170485402188702:undef:undef:undef:undef 9997825576413:10618337018321008:10616517158266469:+:1819860054539:- 7106293740130:50737737820648492:undef:undef:undef:undef 3392977621608:655251102893400214:undef:undef:undef:undef 4223389353572:811417685730993197:220842614198112902:+:590575071532880295:- 5652380780383:583349107691936260:509221536673843367:+:74127571018092893:- 5791577032799:8251416945259750553:7794291602965443924:+:457125342294306629:- 1247512998393:2249359443414575445:undef:undef:undef:undef 6971618691212:9207833474645285898:undef:undef:undef:undef 8900153629539:94334836519360477366:85183123065866489989:+:9151713453493987377:- 4311417354546:78262827216046020061:8386019697177381088:+:69876807518868638973:- 3243037981184:45832612841302700965:42601922870979784739:+:3230689970322916226:- 3712620993619:285041594277832457479:158237595076864455834:+:126803999200968001645:- 1270319397242:498708369749383154597:317894219152632299589:+:180814150596750855008:- 6492783513938:964467096458786966285:251995148231274439117:+:712471948227512527168:- 1289041366441:4239769176510963802726:4080966709529097254761:+:158802466981866547965:- 6731947997059:7768652953268121670028:519938904794059922027:+:7248714048474061748001:- 6729581797199:8021542434360932073457:2755387615898763075605:+:5266154818462168997852:- 4299998412201:69471492938697161449273:2763651428718504669975:+:66707841509978656779298:- 4113635691355:68134614028318691720941:13795117835105828764729:+:54339496193212862956212:- 9124584228095:95599165172048776463126:71149298633605346150427:+:24449866538443430312699:- 5850631452640:912906823809690438386863:441622011063435797449167:+:471284812746254640937696:- 6628780837241:391171427042986582844518:207555674057408922921767:+:183615752985577659922751:- 7096926793765:930894536386130236782553:513250363597403962327949:+:417644172788726274454604:- 1055155853749:1924931603880980247666996:1384901126682163985304925:+:540030477198816262362071:- 3752660520486:9280906580842118223224343:undef:undef:undef:undef 9412962478799:3024215647789167411218260:1715638284602927466244319:+:1308577363186239944973941:- 35522923200296:634:undef:undef:undef:undef 57181270785364:924:undef:undef:undef:undef 76194815537582:639:458:+:181:- 57257650734160:1125:undef:undef:undef:undef 98865799357931:6643:3684:+:2959:- 25718494339513:4073:2064:+:2009:- 49753535089119:36834:undef:undef:undef:undef 37945280665304:39827:13107:+:26720:- 53807078108355:40771:9745:+:31026:- 16620349380813:752697:undef:undef:undef:undef 15854681659924:496080:undef:undef:undef:undef 62312826385242:196766:undef:undef:undef:undef 31323145663904:2045813:2010384:+:35429:- 36156678006696:7555621:5504458:+:2051163:- 76415920596621:3553394:2702601:+:850793:- 83602933541468:52389986:undef:undef:undef:undef 47453343443465:34489920:undef:undef:undef:undef 77665007544214:30973837:5162437:+:25811400:- 60564969964988:859177652:undef:undef:undef:undef 45395992446778:327338644:undef:undef:undef:undef 99031887544217:307576697:305015535:+:2561162:- 57295457423213:2486969440:2396147237:+:90822203:- 98649419506113:4506438861:undef:undef:undef:undef 61132782749273:7844700626:7010480255:+:834220371:- 33969051339731:38805798647:26908457725:+:11897340922:- 32618134075507:34593650870:30599815763:+:3993835107:- 72421520865615:90742668228:undef:undef:undef:undef 96783030974133:104550552917:62241397572:+:42309155345:- 77999419290164:135426628833:117198185558:+:18228443275:- 47711493019423:485606779719:54673548769:+:430933230950:- 14938571358248:1780359622360:undef:undef:undef:undef 62467611171369:2764235263583:750922106125:+:2013313157458:- 68728690999516:7456448281341:4108753780990:+:3347694500351:- 94480261537162:13098773973314:undef:undef:undef:undef 62873473876449:85609346453306:19685023095043:+:65924323358263:- 26103183795343:93952702106289:30739840730893:+:63212861375396:- 97983301053655:266833113684459:245564128428442:+:21268985256017:- 89251925892490:721161704476919:565332285977250:+:155829418499669:- 86847836348596:840288898954459:589599776643864:+:250689122310595:- 58241943230420:5504902549178745:undef:undef:undef:undef 50902392027610:8641986133070199:5995234828175812:+:2646751304894387:- 91175131571309:4884072656666332:2138825994995657:+:2745246661670675:- 75706177722760:41408791837793839:941029647325324:+:40467762190468515:- 82706784759336:50049258979149354:undef:undef:undef:undef 95384977735233:31297080808196148:undef:undef:undef:undef 84076015185718:756239335951243682:undef:undef:undef:undef 13285524212026:663940549353818532:undef:undef:undef:undef 33712258527320:840503203547687032:undef:undef:undef:undef 51891629158085:4370330596001964501:2180700326615269670:+:2189630269386694831:- 58932044552732:1761724527436715359:1307433128356703706:+:454291399080011653:- 82491579726244:3648839307908675837:1655976001686484090:+:1992863306222191747:- 11221487332062:93961837036880203288:undef:undef:undef:undef 15464856220914:85283438058602475019:73460515785035729101:+:11822922273566745918:- 80414717590454:54422406546783016738:undef:undef:undef:undef 75390041825046:618735112504432132321:1669799685651933460:+:617065312818780198861:- 81298287836368:922512690650405753225:133292741494556687407:+:789219949155849065818:- 30462189008225:129860946115201329643:107650202575816188306:+:22210743539385141337:- 28053152938183:6968699673997304528683:4807205285550532186073:+:2161494388446772342610:- 62645469470883:3485795550924374448267:undef:undef:undef:undef 36290345952627:2138411031242920520721:undef:undef:undef:undef 74017734891718:40545327342300947909872:undef:undef:undef:undef 49645250489728:18644884920602335124413:7529551137874837234352:+:11115333782727497890061:- 32074696561708:71779094711734976333290:undef:undef:undef:undef 75924008296972:448662231159554055843685:64762263832345101252333:+:383899967327208954591352:- 62913244261984:593448552354897276206101:154500242057264055861278:+:438948310297633220344823:- 96188784659388:818759232259998368516563:65412096483544929731036:+:753347135776453438785527:- 27368960718596:3412858882021757767890963:undef:undef:undef:undef 37415765084909:2386539707005775650785383:2248794086512464352265461:+:137745620493311298519922:- 10183062115420:5081386526381887802183289:4350480488116397730436354:+:730906038265490071746935:- 15478786464823:121:undef:undef:undef:undef 69202720470006:890:undef:undef:undef:undef 10076631913576:613:11:+:602:- 84467299324713:9960:undef:undef:undef:undef 26777117410898:2778:undef:undef:undef:undef 16293134047963:1431:70:+:1361:- 79997372098343:64456:undef:undef:undef:undef 55274002702722:82872:undef:undef:undef:undef 39204575417309:10137:undef:undef:undef:undef 46262550860337:662232:undef:undef:undef:undef 49622887012954:712204:undef:undef:undef:undef 62495623205097:764266:666811:+:97455:- 45600410054637:4704823:2793824:+:1910999:- 78485464217166:1407140:undef:undef:undef:undef 37901952633099:5559379:1876249:+:3683130:- 89628527454331:75726584:17647363:+:58079221:- 49284217709259:43584686:26429033:+:17155653:- 79252304262143:27000409:2147127:+:24853282:- 78679736100653:860466736:233681989:+:626784747:- 69938203931346:763747995:undef:undef:undef:undef 59053772922835:851644177:406222145:+:445422032:- 25262621201509:9296982356:9164624697:+:132357659:- 38892359871000:2005094152:undef:undef:undef:undef 35968793342881:9553127583:2635314922:+:6917812661:- 53503037458531:21245707669:15903255320:+:5342452349:- 75039198250851:92214128066:16875246345:+:75338881721:- 93356499049629:61738594247:undef:undef:undef:undef 73152497007636:810778180972:undef:undef:undef:undef 19888336877773:290420286146:162449503279:+:127970782867:- 51380179088400:359070650016:undef:undef:undef:undef 13882131384395:4335262478819:113048699900:+:4222213778919:- 48141505872497:6045088167525:876096864833:+:5168991302692:- 94483053473371:3051995424067:1883219118933:+:1168776305134:- 75385622497079:73663124732334:34092563581913:+:39570561150421:- 96110129825183:97306846551413:5561886685972:+:91744959865441:- 55861927240666:31084766799463:8999171473735:+:22085595325728:- 23805795533287:570574994774361:279309427250035:+:291265567524326:- 70544666574231:200438009622566:121452680322985:+:78985329299581:- 98002873595613:643891331744488:529287010314549:+:114604321429939:- 82024307286205:3154950660790085:undef:undef:undef:undef 30156458638523:3954237661640143:218476896058202:+:3735760765581941:- 89154615402438:9373998638475323:7833220469452852:+:1540778169022471:- 51677124964654:81828106705748927:71983096814493461:+:9845009891255466:- 70373931226237:95577751560012759:7598618561661202:+:87979132998351557:- 25853195971451:65661000088735369:8755222804092063:+:56905777284643306:- 74401344682269:499939076031484377:undef:undef:undef:undef 45755932107022:708219472599773786:undef:undef:undef:undef 92740092264260:752301923628377165:undef:undef:undef:undef 16712726948182:7739389375423089033:2483047104668307367:+:5256342270754781666:- 43445532135970:9881057663450000596:undef:undef:undef:undef 29185876416348:4558945063955143416:undef:undef:undef:undef 25742934549156:63115445089321475348:undef:undef:undef:undef 74265457520547:22432569711930017104:10561278554179141067:+:11871291157750876037:- 89954227929484:65835987116620817046:undef:undef:undef:undef 36842296827474:160339718277210969776:undef:undef:undef:undef 11158763341091:657674011792350918256:337809588750180521579:+:319864423042170396677:- 82534997560542:351216201673829805012:undef:undef:undef:undef 44588024637775:6543928690426153292118:4788206348026011488803:+:1755722342400141803315:- 43368203998572:6702826515429349604423:4870302567904153372278:+:1832523947525196232145:- 83844596013205:2110617338012926982867:538050524574304865895:+:1572566813438622116972:- 76517645663653:87048326902813598728276:8802008007711028789509:+:78246318895102569938767:- 48253056282531:14379620566404380515792:7001061341764986492843:+:7378559224639394022949:- 35287846873702:71066164085887300909249:32864407347397594925174:+:38201756738489705984075:- 44013785910309:287676955041574608229925:243543647669102542710664:+:44133307372472065519261:- 13311054472398:993326004301248447933156:undef:undef:undef:undef 52012500961213:246616861226633860548023:111661413119811442889609:+:134955448106822417658414:- 84952659316024:2903823002995793605530535:1677137118898306857690389:+:1226685884097486747840146:- 41377984223283:9816325603455103199788018:1640445767889877784027285:+:8175879835565225415760733:- 71305632950429:3746272423411191331790060:1187896005842721883233049:+:2558376417568469448557011:- 12144440849326:694:undef:undef:undef:undef 63224563667168:706:undef:undef:undef:undef 24660746795804:528:undef:undef:undef:undef 72271763373199:5445:5344:+:101:- 32794764412772:8213:7772:+:441:- 62099092734896:9331:undef:undef:undef:undef 52651721479808:74274:undef:undef:undef:undef 14581506804904:17592:undef:undef:undef:undef 51600239269306:31817:541:+:31276:- 86943330130438:934959:170518:+:764441:- 46700657000396:328978:undef:undef:undef:undef 24799002341989:779689:177382:+:602307:- 63825906516702:2095626:undef:undef:undef:undef 27823593285985:7314358:6658063:+:656295:- 57693736785324:8154066:undef:undef:undef:undef 38359515045221:77221858:49871569:+:27350289:- 69200745303265:14113655:undef:undef:undef:undef 40924348891630:42764546:undef:undef:undef:undef 19776709873877:765952147:405977045:+:359975102:- 26756608309567:458794160:310011023:+:148783137:- 13671318203145:418146403:302620867:+:115525536:- 98729740497908:3490559723:2218516640:+:1272043083:- 78935686496777:5693467235:1905288438:+:3788178797:- 29892280324571:5358168457:3546413190:+:1811755267:- 72113122274020:98464011846:undef:undef:undef:undef 13810533889434:47743368423:undef:undef:undef:undef 17001604103084:22525430362:undef:undef:undef:undef 46203005217917:788036447607:64269889838:+:723766557769:- 96096266258815:135042354904:33205856455:+:101836498449:- 45067379118683:982044126422:306909434363:+:675134692059:- 95598050428116:8630619044485:8055656402216:+:574962642269:- 93840260317516:3817032862846:undef:undef:undef:undef 23642234946698:4264111985069:2770400979324:+:1493711005745:- 41590295481973:48109020285470:42442789016117:+:5666231269353:- 75596253364904:77847224731850:undef:undef:undef:undef 73291951484542:73456311925517:45371300315810:+:28085011609707:- 47844443558790:654992051455722:undef:undef:undef:undef 19822382386128:700726841128307:undef:undef:undef:undef 83140469194618:443285708887785:362208934498087:+:81076774389698:- 41986141058217:1309503449525957:87377812597529:+:1222125636928428:- 68086073022664:9438221220738143:3364254420680274:+:6073966800057869:- 68860587219274:2799565853421436:undef:undef:undef:undef 14112751551213:97700637856663653:undef:undef:undef:undef 53215249099174:75869584615332213:71616742920601924:+:4252841694730289:- 18942243091954:79906960076612625:17417111870851519:+:62489848205761106:- 12937685838708:213686491127509264:undef:undef:undef:undef 94182247860110:327530032088390401:76440536440212626:+:251089495648177775:- 17515210008222:226697714661821283:undef:undef:undef:undef 47248923796198:3406249671011508599:431548213597605730:+:2974701457413902869:- 23728195750197:8354575163725872138:undef:undef:undef:undef 28252506367128:3123655340235727687:489811028863659851:+:2633844311372067836:- 77653981760712:43991897778268523136:undef:undef:undef:undef 62307307596337:23442770455100318240:6827114837377337073:+:16615655617722981167:- 76809170128864:81693945209882598091:18774983500429406701:+:62918961709453191390:- 74323251803879:133043135358710188075:112128269782191698219:+:20914865576518489856:- 39496821921800:215308441099663738264:undef:undef:undef:undef 75573123679526:970321956738426006273:262260002784602944181:+:708061953953823062092:- 64093396075742:1365145810073714971279:805497561843790363488:+:559648248229924607791:- 85129728895176:5850060330326795500815:undef:undef:undef:undef 35086336179273:7710824089175799143499:undef:undef:undef:undef 93991134779567:21910482078489229886991:14068711299867429042908:+:7841770778621800844083:- 22130693305836:33594622107208782150353:2821416032919768547346:+:30773206074289013603007:- 94186900049380:96267224445464823607976:undef:undef:undef:undef 59947414409568:160897712459335661945221:16183766426439062840578:+:144713946032896599104643:- 98161517078501:803561610903872263163737:608137181322884490803533:+:195424429580987772360204:- 87444547802757:594531976734977402236119:undef:undef:undef:undef 82252341906866:8613650423884889815427258:undef:undef:undef:undef 38518751231172:4704718701508252893230437:1066402185034851361727231:+:3638316516473401531503206:- 13808805428541:3856291955818964279110506:undef:undef:undef:undef 728558154702269:800:629:+:171:- 464126645687857:852:505:+:347:- 828854899023291:603:undef:undef:undef:undef 451826920243478:8054:undef:undef:undef:undef 400396011204960:3821:1021:+:2800:- 952450704249276:1319:672:+:647:- 439231300155720:69505:undef:undef:undef:undef 915305722830579:85907:78073:+:7834:- 162854590664408:49073:36243:+:12830:- 698863581755521:127475:123031:+:4444:- 642338998656189:956766:undef:undef:undef:undef 168778341895385:795281:274560:+:520721:- 574895215447259:1375717:undef:undef:undef:undef 512674070748493:8571273:2349844:+:6221429:- 878899446069318:9324712:undef:undef:undef:undef 791083719725767:22094285:19813748:+:2280537:- 570756210425841:46381368:undef:undef:undef:undef 898958442946843:75532446:73343251:+:2189195:- 497436694227405:715732297:276875204:+:438857093:- 176320278021766:954529903:265774473:+:688755430:- 651156419179418:398850990:undef:undef:undef:undef 662525530661225:1872470885:undef:undef:undef:undef 150375630839847:8367667643:445582338:+:7922085305:- 485276826894726:3161393037:undef:undef:undef:undef 639746323359247:33476357254:20058950403:+:13417406851:- 898461573421918:14651432363:7946527006:+:6704905357:- 758059448910712:31720372410:undef:undef:undef:undef 148600376943573:355805151168:undef:undef:undef:undef 523765514002023:745726111068:undef:undef:undef:undef 889123837797237:686267994099:undef:undef:undef:undef 778353850567149:8758800120077:4810219581550:+:3948580538527:- 994676759240856:6073282694990:undef:undef:undef:undef 167077198294565:8436015139306:2634527274591:+:5801487864715:- 122942443916326:51867756638506:undef:undef:undef:undef 503648283021282:75341352806966:undef:undef:undef:undef 357042275147092:13854855417377:4119720892229:+:9735134525148:- 387428611281261:978461194785577:70380344239530:+:908080850546047:- 590637516453151:517988597383851:29123128536475:+:488865468847376:- 363957878598332:551009901339132:undef:undef:undef:undef 876925159115759:7728142602922191:4725588992540147:+:3002553610382044:- 372041367672818:8649545762904626:undef:undef:undef:undef 130876807071190:4126047455634965:undef:undef:undef:undef 827754262395037:66423460111476884:2442002818599613:+:63981457292877271:- 215104066403004:71126165636485512:undef:undef:undef:undef 139217178178097:17346395103766437:7031634868342013:+:10314760235424424:- 692121964657925:821180962822219363:688475176928695354:+:132705785893524009:- 743933453191688:209297748571284886:undef:undef:undef:undef 920668259954788:105668935327519891:87129027262339903:+:18539908065179988:- 922608205845945:6381152885416389547:6100863487063038969:+:280289398353350578:- 598127451365057:5210051178482495530:1838263852770669933:+:3371787325711825597:- 973059395746071:2391326952815458926:undef:undef:undef:undef 497437518925867:33763405035422198600:9871450367394101803:+:23891954668028096797:- 837384153487360:88845487132310477084:undef:undef:undef:undef 753204798523917:12255085936084066306:600794244795188349:+:11654291691288877957:- 859752729764405:341385704218391874826:97665052096579287355:+:243720652121812587471:- 708381549066076:871632851879985471526:undef:undef:undef:undef 258845104926756:355238975171811067393:116908861803386810426:+:238330113368424256967:- 244738239777262:1880933364665171731293:1604652583038687012967:+:276280781626484718326:- 242338695153972:5435020953653204364897:undef:undef:undef:undef 162988507230936:7974386155679607949418:undef:undef:undef:undef 399269657134096:68875130562375605561821:undef:undef:undef:undef 128296916274203:46901748031625432160348:45996912318870318468071:+:904835712755113692277:- 981575687027652:34353291424459284018378:undef:undef:undef:undef 554103357629250:445294027509035399641464:undef:undef:undef:undef 160435825129644:823828482782605416128899:245958859306361599986982:+:577869623476243816141917:- 444177994509049:568708736268692931683715:517927728060377863545229:+:50781008208315068138486:- 444937587409290:4908956687382877797141677:4823180930450345201886187:+:85775756932532595255490:- 913793666016334:5450644045501142443741177:5013731754224549302771058:+:436912291276593140970119:- 579802512972038:2085058098904137287038830:undef:undef:undef:undef 715911434981904:187:129:+:58:- 332736424184517:894:undef:undef:undef:undef 981574328739004:969:undef:undef:undef:undef 880697100457990:5976:undef:undef:undef:undef 486624229079888:9768:undef:undef:undef:undef 469187261898117:1586:965:+:621:- 983467908051667:68987:2434:+:66553:- 757970591261065:59118:34855:+:24263:- 948158568176614:88043:18296:+:69747:- 422670273116456:320058:undef:undef:undef:undef 931018826865212:121689:88433:+:33256:- 818294658294244:387049:381512:+:5537:- 903560862243716:4144922:undef:undef:undef:undef 428970194413039:6218606:3397747:+:2820859:- 723257278504514:9247641:undef:undef:undef:undef 205397214361397:38166234:15398477:+:22767757:- 842300760053495:22670897:13779898:+:8890999:- 965681766127293:34236330:undef:undef:undef:undef 592720380098190:202701236:undef:undef:undef:undef 718847304283852:418109440:undef:undef:undef:undef 817672608493880:927123966:undef:undef:undef:undef 719591658582369:2028016095:undef:undef:undef:undef 215874954109024:4157287849:1570213756:+:2587074093:- 819138328010671:3485070453:1045319641:+:2439750812:- 151920083837769:59467974618:undef:undef:undef:undef 603224040433396:50439368172:undef:undef:undef:undef 549692484550264:81386440341:6249633904:+:75136806437:- 134070785664296:365581284525:283802609531:+:81778674994:- 460438814476451:866179741904:597218689659:+:268961052245:- 792458135509027:782035187480:428336130763:+:353699056717:- 385901173964821:3780311463428:1421276769769:+:2359034693659:- 347939279865051:8758092615194:2058526876923:+:6699565738271:- 857918347348662:3974305146414:undef:undef:undef:undef 921847342945342:32554291867765:14903637464063:+:17650654403702:- 565444013144174:30586732591123:8468488097634:+:22118244493489:- 153031033393395:80125937028483:undef:undef:undef:undef 711618124841181:831566900079115:691188416580386:+:140378483498729:- 185743949720747:284469960212964:166602940494707:+:117867019718257:- 624806234522595:667778408413465:undef:undef:undef:undef 396350849418865:5229741379867891:3691173607831774:+:1538567772036117:- 536609586389447:6933344567517833:6115121525232572:+:818223042285261:- 640365357334723:3309146204415845:2706148829787972:+:602997374627873:- 769367720700040:40233546164517412:undef:undef:undef:undef 326761876649725:83887642608393153:49006631462026837:+:34881011146366316:- 148158890027982:92503371428660592:undef:undef:undef:undef 764105966947642:916714062142845646:undef:undef:undef:undef 324411392601170:822844408365620350:undef:undef:undef:undef 427017250104314:269173258905422307:166809313859067443:+:102363945046354864:- 132974813548680:9229205610959882644:undef:undef:undef:undef 934096205871812:9118680270515409406:undef:undef:undef:undef 985630651877363:9143354659111431661:2377475095296831814:+:6765879563814599847:- 989845308705999:92030848977492782807:51457680329979932029:+:40573168647512850778:- 430064650133347:15355343148660519499:13416021071649725094:+:1939322077010794405:- 619557857254736:77545737319476500074:undef:undef:undef:undef 218945363906535:676713962769435763274:346918529941699251683:+:329795432827736511591:- 282130808835865:790620812865593519104:732120673458091814185:+:58500139407501704919:- 149805682361961:969147018920702335581:undef:undef:undef:undef 354317847225915:7314426746402852687593:163083638291320521322:+:7151343108111532166271:- 389725010387360:1941712073448008324395:undef:undef:undef:undef 950524184574372:5730085870463179120596:undef:undef:undef:undef 642356121518562:66986769556535658760400:undef:undef:undef:undef 404056517578608:48761566533789456022980:undef:undef:undef:undef 157708137861456:76771721727489630223374:undef:undef:undef:undef 146627476330735:964616757317813692905317:921602805273860892026693:+:43013952043952800878624:- 255143799489242:895923090101259738008181:739189755690376890893765:+:156733334410882847114416:- 881102836724883:183566843564327650574472:undef:undef:undef:undef 934000689096342:7363029663629414997603260:undef:undef:undef:undef 351320917059615:7728531259260561630240891:undef:undef:undef:undef 451167462642105:9141347212428985458916014:undef:undef:undef:undef 241214003377902:841:162:+:679:- 427079406739933:453:196:+:257:- 841900355547148:294:undef:undef:undef:undef 163146089159841:5330:1201:+:4129:- 963041775217155:9777:undef:undef:undef:undef 661865536781762:2306:undef:undef:undef:undef 608749614195670:85957:66475:+:19482:- 787355359758778:96064:undef:undef:undef:undef 963689771922466:74185:undef:undef:undef:undef 614717016286331:872171:188397:+:683774:- 521063024189600:586592:undef:undef:undef:undef 807924026323012:573662:undef:undef:undef:undef 397360318799844:6712777:1155783:+:5556994:- 499880900313875:8662194:868271:+:7793923:- 216450114480327:1498733:1302693:+:196040:- 852611438938913:70060304:16670929:+:53389375:- 189823641207200:13191458:undef:undef:undef:undef 254481947407399:78125347:52493008:+:25632339:- 534682821367598:112069120:undef:undef:undef:undef 818475334073039:368877254:84827487:+:284049767:- 352007947510866:605982493:296118753:+:309863740:- 661549466684476:4041233872:undef:undef:undef:undef 749556657504038:8099417582:undef:undef:undef:undef 934047687493198:6400700322:undef:undef:undef:undef 869132340045482:33495198313:20165334044:+:13329864269:- 901625380674965:25995346949:5202076067:+:20793270882:- 451272130822722:47055246763:43208138777:+:3847107986:- 206554877479417:240244417406:68703374267:+:171541043139:- 267200655705298:937800002840:undef:undef:undef:undef 425863686876990:774212142077:84123297752:+:690088844325:- 725729932518632:5203835733772:undef:undef:undef:undef 263926451543558:9193184075151:5185979756057:+:4007204319094:- 254447932163603:3036974297897:932235242973:+:2104739054924:- 842211852400734:30719555272008:undef:undef:undef:undef 276164810898707:96110227539335:56753597346538:+:39356630192797:- 162715711213793:88751979337820:58035344000837:+:30716635336983:- 554581292527349:468349414859331:215127040567859:+:253222374291472:- 612791909857160:135020014513187:56585290882146:+:78434723631041:- 289199213896943:924305534896479:157842916806773:+:766462618089706:- 503869881485078:4800010919333887:3140185984823498:+:1659824934510389:- 659680353075218:2097024323473941:20602134879752:+:2076422188594189:- 470784801980157:2476052524555393:undef:undef:undef:undef 894922164807617:60407445781263412:undef:undef:undef:undef 653410693030439:44777476635867404:29701641839615783:+:15075834796251621:- 588636543349631:46135952075961245:12667424830166556:+:33468527245794689:- 154719537347498:199086978372671745:100135796120568362:+:98951182252103383:- 417015921098265:711616325104127328:undef:undef:undef:undef 391231816921489:183270715416106255:172739572636566099:+:10531142779540156:- 956671474096354:8295046921461418170:undef:undef:undef:undef 616583070423927:9586228385320636171:5184584451123408737:+:4401643934197227434:- 313155285471313:8546200735889453539:5244509552992436149:+:3301691182897017390:- 608289805916728:30380994068504548938:undef:undef:undef:undef 987550572927545:54043735960667076091:52700703858091094555:+:1343032102575981536:- 798625597564455:18902638090583917869:undef:undef:undef:undef 355287564736527:597169124005858900121:270356251715215075618:+:326812872290643824503:- 289265282559714:756347326025791628412:undef:undef:undef:undef 856754322007345:272853476611015715005:undef:undef:undef:undef 849739954855848:9097970213053493174975:6453634815733827946962:+:2644335397319665228013:- 103330312951346:5969872342459466427239:undef:undef:undef:undef 237161257529439:3040738115300583471479:1732267520191015033519:+:1308470595109568437960:- 747025873355636:64871520523658055568359:20583893666269089829250:+:44287626857388965739109:- 662026139719676:41436790906600971440603:11712120460003299559599:+:29724670446597671881004:- 108078521265698:40382412037231818681053:25499384608130553402996:+:14883027429101265278057:- 873836509482432:572596344320415113555830:undef:undef:undef:undef 125090228626031:781069136077556352291021:468704975588583405932048:+:312364160488972946358973:- 253266233816303:511817951361180120499987:357320460229348718117195:+:154497491131831402382792:- 424218954387871:6953182487296273053267924:4487279150880027164222503:+:2465903336416245889045421:- 996317219483882:4127334798153728372804394:undef:undef:undef:undef 374405555416380:8090627742427721530205458:undef:undef:undef:undef 2296100806546680:482:undef:undef:undef:undef 8990668541567382:179:14:+:165:- 5369330375253586:678:undef:undef:undef:undef 1387424364200409:2287:11:+:2276:- 9539300859734009:5142:2261:+:2881:- 6502309117825082:9940:undef:undef:undef:undef 5141171473510589:41562:10601:+:30961:- 5934801348466359:76254:undef:undef:undef:undef 8800672002350256:52637:24356:+:28281:- 7114439731398992:790994:undef:undef:undef:undef 7135836022821261:831523:undef:undef:undef:undef 6680671401216078:921102:undef:undef:undef:undef 3248703399031394:8117938:undef:undef:undef:undef 6377739796473143:5893992:4767167:+:1126825:- 4828893941429366:2950897:1756182:+:1194715:- 5818354736846205:81982339:3035299:+:78947040:- 4366419423202610:96942126:undef:undef:undef:undef 5330308258626952:69473030:undef:undef:undef:undef 3082450128488293:963764090:913758847:+:50005243:- 2295392651181664:950310540:undef:undef:undef:undef 1065742832284893:475717780:95199837:+:380517943:- 4976794163983255:5641938370:undef:undef:undef:undef 3955413616942016:2366101734:undef:undef:undef:undef 5919605937875613:6051466481:3333751546:+:2717714935:- 4731608691402900:98641022322:undef:undef:undef:undef 4237495572454343:72726048114:40709739179:+:32016308935:- 1519861672373688:12767354767:6446909511:+:6320445256:- 1349036664930107:487330589634:329287204973:+:158043384661:- 1842501412723930:938497614268:undef:undef:undef:undef 2546060418383441:606459256656:472037543729:+:134421712927:- 8736212324777843:9538131510559:3935089324317:+:5603042186242:- 1649988281047475:2121808819461:1301744592224:+:820064227237:- 3973415545901119:6948601071998:6039678765841:+:908922306157:- 8524391936585790:44206527396290:undef:undef:undef:undef 7563164769588885:97928554162493:16210956057842:+:81717598104651:- 7171634508132405:26259389961855:undef:undef:undef:undef 7453570996643310:295105698618570:undef:undef:undef:undef 3570131435763195:450557402111635:undef:undef:undef:undef 6696042263628457:396558386049185:140198438218823:+:256359947830362:- 5270879993601338:8444838168545319:2266979145398090:+:6177859023147229:- 1211454394312078:3080860357892989:undef:undef:undef:undef 3834772719664095:4215592934273504:2521819004808095:+:1693773929465409:- 1403486848403189:74680649374182208:44822756274939421:+:29857893099242787:- 2968277358196048:35608432869668028:undef:undef:undef:undef 6322017324503710:22026771251580386:undef:undef:undef:undef 2481168182967910:927846725122061651:734573589836815650:+:193273135285246001:- 9957373657060941:779792952792779814:undef:undef:undef:undef 1605162297576641:823241499841774776:276975755139852929:+:546265744701921847:- 7974553150568464:1735510718049430472:undef:undef:undef:undef 8874979501320214:9041249077872672307:8338498465617729306:+:702750612254943001:- 8583197108993201:5975127255501002620:5315703533685977401:+:659423721815025219:- 9856850544334706:17433626303890314648:undef:undef:undef:undef 6959391254749324:33602975982510249138:undef:undef:undef:undef 9785423193903433:36985105942242854090:20775945342498576787:+:16209160599744277303:- 3694690974295843:263485535295909942016:98133919574328704395:+:165351615721581237621:- 8006969377987831:474204533872797068679:141345134014628282437:+:332859399858168786242:- 9736206842405079:299629567956354200420:119971381510323446239:+:179658186446030754181:- 6136393788182856:4718050169797768460290:undef:undef:undef:undef 2095849202085294:5937478645524533313660:undef:undef:undef:undef 9850431017173080:5322798488018258941986:undef:undef:undef:undef 6817146566058406:97727103830740484537545:65106630151047140926946:+:32620473679693343610599:- 5911041853532198:41773629251629380463493:22590767187395589445390:+:19182862064233791018103:- 6249032151315502:43926039570209325153490:undef:undef:undef:undef 7468428261650680:305649431589140241616132:undef:undef:undef:undef 5089583892821482:473652824251288859352559:204541253053982878897775:+:269111571197305980454784:- 8361210624654015:924937241207478801535706:340538030354554535421091:+:584399210852924266114615:- 2238808446683188:5541231369181077700600015:4570022510913942981377462:+:971208858267134719222553:- 6131847748931781:4577283379657311368838244:1240321299518111321938849:+:3336962080139200046899395:- 5571401864223170:8995232292746528277772637:5040571643708551462640031:+:3954660649037976815132606:- 5488728064061426:774:undef:undef:undef:undef 8718720402635804:819:176:+:643:- 9376608867284021:137:54:+:83:- 8015720109507858:1200:undef:undef:undef:undef 9496173251938585:7348:6241:+:1107:- 2002481152019333:8088:5765:+:2323:- 2395082373480034:18209:6466:+:11743:- 6255018896569153:79813:70605:+:9208:- 4871280884607389:44470:23239:+:21231:- 9540373576019272:391839:undef:undef:undef:undef 9006188315065533:265131:undef:undef:undef:undef 8954758129680836:203389:65767:+:137622:- 5701432136512144:4459584:undef:undef:undef:undef 1275302325247675:9289453:4201078:+:5088375:- 4119440556543504:5793912:undef:undef:undef:undef 1345249960261091:38339028:10133891:+:28205137:- 5210565711407721:92833603:51903318:+:40930285:- 9156553227188736:10930657:7490062:+:3440595:- 7605750152773616:166050708:undef:undef:undef:undef 5112120248906878:347690512:undef:undef:undef:undef 8325756032907520:897414928:undef:undef:undef:undef 4297166330140605:8451124687:1879043015:+:6572081672:- 4052795866210958:6719393806:undef:undef:undef:undef 5599942494884300:5254913589:3675016142:+:1579897447:- 4294165001010270:65299208227:41060667946:+:24238540281:- 3521876006123819:51505483973:27929516537:+:23575967436:- 2975686350001438:68975719872:undef:undef:undef:undef 9987578698637948:933580676654:undef:undef:undef:undef 4478813995882420:899559579484:undef:undef:undef:undef 5165858021681371:944871700984:681251258947:+:263620442037:- 6631110211690658:5509199572787:4542974354898:+:966225217889:- 3200516254001157:4170270691953:undef:undef:undef:undef 4725488680646020:7454286358510:undef:undef:undef:undef 7995124056621538:44736024134162:undef:undef:undef:undef 6504162480158739:76831874868831:undef:undef:undef:undef 5542455301035590:24098329599047:16785730155033:+:7312599444014:- 6920823137206661:407442625236757:63252097226088:+:344190528010669:- 8037980967696072:851234068131819:undef:undef:undef:undef 9219091854501731:974598538761173:214133199093150:+:760465339668023:- 5898645543617277:1702267099774624:345956751806965:+:1356310347967659:- 5427394238177464:1617335287837212:undef:undef:undef:undef 7858414408880449:1370997827861660:494231516045669:+:876766311815991:- 4307965389980085:45999514731450247:33865094732954127:+:12134419998496120:- 3506104261251482:43601776461059844:undef:undef:undef:undef 1190203419512405:25126719871266670:undef:undef:undef:undef 4557460955130067:101730316098224713:44158272895555038:+:57572043202669675:- 2489098116741103:541191016580188961:undef:undef:undef:undef 2348212366514288:942563318071885939:313053493374155951:+:629509824697729988:- 2830409913735330:7114495355770228431:undef:undef:undef:undef 1035772148392020:3452915168200802716:undef:undef:undef:undef 3460827696752293:4050339818955672472:2049422512624877061:+:2000917306330795411:- 8963229771220449:22270265754077222943:undef:undef:undef:undef 8313155627789908:64065344162590490500:undef:undef:undef:undef 3363443326421517:73970563228805828520:undef:undef:undef:undef 8923845510217141:385542532463723478331:15517894406759966535:+:370024638056963511796:- 6397366318806880:574475474744016411405:undef:undef:undef:undef 8675397679844558:562564176023446123792:undef:undef:undef:undef 2910301871886134:3955964756594770607877:2631050206050423008834:+:1324914550544347599043:- 1584670627015036:6273088882766402366721:3622531239479413500850:+:2650557643286988865871:- 5363220656008849:2586623903413614439911:782911984926818975497:+:1803711918486795464414:- 6917209535561867:40256744895225904319995:36867327456178728083643:+:3389417439047176236352:- 1269024503328432:25294841853669594580214:undef:undef:undef:undef 7432100573870595:54567896453627810319112:23203612842302240123459:+:31364283611325570195653:- 1608747248547618:275565079805161504581379:34887313788098803213992:+:240677766017062701367387:- 3404549828233218:825396479228178239259671:66024141064239540183677:+:759372338163938699075994:- 3774208778004648:138650287251389136814825:26999089498391943065487:+:111651197752997193749338:- 4238577793752036:9699877545727099583035941:undef:undef:undef:undef 1929923068567981:5918633631450380694017363:5890956102390179715255422:+:27677529060200978761941:- 1680477580056962:7214912248517969194342092:undef:undef:undef:undef 1841496083602801:730:551:+:179:- 8434627776439561:601:302:+:299:- 2792920109380107:107:81:+:26:- 3732100459735904:8358:undef:undef:undef:undef 8168579180718854:5142:undef:undef:undef:undef 8391127774917141:6694:4409:+:2285:- 5582017437205135:52680:undef:undef:undef:undef 8474984865860137:15181:14622:+:559:- 8002292586438596:68277:27491:+:40786:- 9108699884108801:872777:199191:+:673586:- 2594412923170703:834457:248085:+:586372:- 4382993700983297:886259:746683:+:139576:- 4689917420119983:8773750:6780147:+:1993603:- 8843943989430193:6007841:undef:undef:undef:undef 4033114285249838:5188322:undef:undef:undef:undef 8878559192189492:37892910:undef:undef:undef:undef 2171021458249957:55548527:18532842:+:37015685:- 9374733837743972:73016043:10924895:+:62091148:- 6085111030150088:739954615:215570147:+:524384468:- 9836471563372734:624803391:undef:undef:undef:undef 4334547062456505:477326192:273113609:+:204212583:- 5641861306250880:8832758427:undef:undef:undef:undef 9282577429917227:8706626761:7153121728:+:1553505033:- 8782255279233126:4479378289:122614048:+:4356764241:- 4565103207928964:16631468392:undef:undef:undef:undef 9321957127607023:20100023226:12040783975:+:8059239251:- 3625564843880550:41923217660:undef:undef:undef:undef 7900401309225411:161107386415:125105233316:+:36002153099:- 4427656535510813:487927814719:404683134565:+:83244680154:- 7812718803048309:602566056314:308458485965:+:294107570349:- 7571221341805542:6030702615909:undef:undef:undef:undef 2948534915241316:5252720022991:4758572766630:+:494147256361:- 5845669995935470:4629995023092:undef:undef:undef:undef 3579525232544162:39313951359940:undef:undef:undef:undef 6208071235675697:17256859470592:9001694712785:+:8255164757807:- 8493489755607416:38581143900936:undef:undef:undef:undef 8104547175255898:566187098341508:undef:undef:undef:undef 8498106976520476:649272916882489:537412539637276:+:111860377245213:- 6056449049580070:987620164921142:undef:undef:undef:undef 9200405987416644:1630468931967993:undef:undef:undef:undef 1854670925859374:9513627892986071:5360708176851304:+:4152919716134767:- 8660834948899312:5061850505225302:undef:undef:undef:undef 1932762741080270:64945331340406576:undef:undef:undef:undef 7639232039301626:92678803159372555:67941230624187431:+:24737572535185124:- 8308435541995600:81464543657213580:undef:undef:undef:undef 6416383750046724:692978472836400494:undef:undef:undef:undef 4333088713722114:736729240226843093:625765443124600165:+:110963797102242928:- 4069245031083072:989837201369577923:200648032759061798:+:789189168610516125:- 5464948308777659:3773246659761710346:484043589062912105:+:3289203070698798241:- 9052755996308153:5935018747613414191:3253842088745672734:+:2681176658867741457:- 4767195926080263:2387490215566551629:987310242747406583:+:1400179972819145046:- 3637936503902920:38490091045627145932:undef:undef:undef:undef 2765129188212842:73182047176467825082:undef:undef:undef:undef 6657932056404472:42189316897298808093:29263584725413709680:+:12925732171885098413:- 6139779049542261:762726188214699430665:undef:undef:undef:undef 3792903888814328:489339261115434009811:220070108379020419069:+:269269152736413590742:- 3211142574336455:858751535436865059100:undef:undef:undef:undef 3450677913282617:5403793078611106749350:5391783316670651866803:+:12009761940454882547:- 6771447806101866:6085905690697813072939:4774799916319955714716:+:1311105774377857358223:- 6822331428246822:8359862518235964521832:undef:undef:undef:undef 6317960530647740:68474265611971391082695:undef:undef:undef:undef 3318554932316905:80985070024981863847822:66850108520564448472131:+:14134961504417415375691:- 8729037402547222:84561621551432649225705:52418781236523067498273:+:32142840314909581727432:- 8118655713195858:515319522134590484525849:331192994432869448052106:+:184126527701721036473743:- 2421322609601039:326679188338412179275138:116479631956383766942685:+:210199556382028412332453:- 3286634122049957:838886646676329892591495:714196563700843058381753:+:124690082975486834209742:- 6803870184899314:9739554545089514248279854:undef:undef:undef:undef 8987447912806144:8608890406656831323180183:4626658738937045520188853:+:3982231667719785802991330:- 1772711180643221:9902314582961863026124704:7468954682706445423572029:+:2433359900255417602552675:- 18777857878295360:790:undef:undef:undef:undef 75809979679217995:986:889:+:97:- 22866702148073916:490:undef:undef:undef:undef 73483902338991005:3586:2819:+:767:- 38687357866460274:4227:undef:undef:undef:undef 90142743294164177:2535:1883:+:652:- 87704257155547192:10969:8917:+:2052:- 11903610773811161:86735:33566:+:53169:- 28543095733854604:37908:undef:undef:undef:undef 71749918282618630:164346:undef:undef:undef:undef 76418739681053999:637604:282331:+:355273:- 11129705518878901:121644:46081:+:75563:- 20938080520482539:6383818:1513541:+:4870277:- 12247604817875019:4813387:4337813:+:475574:- 63266108551418800:4329325:undef:undef:undef:undef 41749736061008654:64644113:26583203:+:38060910:- 86995843522210495:28427580:undef:undef:undef:undef 13713199587315799:82855577:61085180:+:21770397:- 78214750687323511:989749048:48537759:+:941211289:- 86774105870039829:237940128:undef:undef:undef:undef 34792635512106973:484742319:448157953:+:36584366:- 46681416697256434:7231958622:undef:undef:undef:undef 59828077309201612:3826217637:372734563:+:3453483074:- 51754287857029799:7930068950:7660819649:+:269249301:- 31885903829433215:29175165805:undef:undef:undef:undef 10969315709785573:90850620535:63749809002:+:27100811533:- 66299953094060171:71343248352:47297687459:+:24045560893:- 82840724271832395:898974512616:undef:undef:undef:undef 56497251668256360:563757295049:undef:undef:undef:undef 45662002402811719:453066329892:234727412767:+:218338917125:- 88181393350160099:6874242621875:5723406976774:+:1150835645101:- 44200929083488529:2580710783209:249745227798:+:2330965555411:- 41911412061920578:9843998117854:undef:undef:undef:undef 72089859535700392:31728830349092:undef:undef:undef:undef 67073616480032418:19358252185659:undef:undef:undef:undef 25282244918188492:80954568589902:undef:undef:undef:undef 69144384761784052:698148087605375:635940041908613:+:62208045696762:- 33028935026922694:662899485291916:undef:undef:undef:undef 75948842502745139:524597987228022:173554320236693:+:351043666991329:- 85678624148787208:4349995716057139:2531559180051487:+:1818436536005652:- 71044090148500051:7531275038393232:4686035531424811:+:2845239506968421:- 68329207483625307:5059503112707484:3690126846012331:+:1369376266695153:- 85881840717946907:77579074192953116:24957019494399099:+:52622054698554017:- 56637960107128459:43484382926479372:39973370574620979:+:3511012351858393:- 12255016666047012:51046491176991341:37825247893004932:+:13221243283986409:- 80237919448700297:444882530036463174:436653873114780869:+:8228656921682305:- 20214002634696644:317311849929769996:undef:undef:undef:undef 75139735869521946:547956235353110173:255528464812415228:+:292427770540694945:- 96217068708656452:8294875925040936662:undef:undef:undef:undef 88992764620505470:4745194956805966064:undef:undef:undef:undef 76681052104470570:4667476501948157920:undef:undef:undef:undef 63428953609896758:86816220069575834171:18124155556302065384:+:68692064513273768787:- 53958167650448494:49842513027450179446:undef:undef:undef:undef 80805749044540444:96560693615440661618:undef:undef:undef:undef 99885150542851309:461313333329818830769:20947175510113906213:+:440366157819704924556:- 49540759584744708:208932018246435390606:undef:undef:undef:undef 55304493965245217:651391776487117112825:undef:undef:undef:undef 58260781049175593:9190941834165116577345:1339420552484048939222:+:7851521281681067638123:- 99399663376107221:1302994212129995067117:905852763300789383981:+:397141448829205683136:- 51599644923328960:5569963733400718975396:undef:undef:undef:undef 47319956365139740:84608481430016788558747:4371117020818448105223:+:80237364409198340453524:- 82393401545267769:72126010140224372341807:1640917274925737984283:+:70485092865298634357524:- 36300969153089991:38561723767761932802970:31789799375515886901271:+:6771924392246045901699:- 38573357102206622:964784204136472709553052:undef:undef:undef:undef 11756151567175068:972615649806262488701593:142546357347680838302455:+:830069292458581650399138:- 26126361201409438:210132523018916975469125:170574254286856108724877:+:39558268732060866744248:- 19280435812491806:9160872983744441808454832:undef:undef:undef:undef 30476572854480239:3010773395760369439421178:1120729230046912514768309:+:1890044165713456924652869:- 16489348319896622:1960616646574107167388815:1614843307003134955986738:+:345773339570972211402077:- 56796852737757856:324:undef:undef:undef:undef 14224883309563304:320:undef:undef:undef:undef 49614531212136907:621:37:+:584:- 72027941762888670:3457:781:+:2676:- 31909303812382508:7567:5272:+:2295:- 43605089878314626:2166:undef:undef:undef:undef 25955086048492185:16242:undef:undef:undef:undef 41753708575470861:44361:undef:undef:undef:undef 26632877646544846:71627:9472:+:62155:- 12715461500422472:566189:296100:+:270089:- 33449055928920850:793335:undef:undef:undef:undef 40164270998180646:859691:242295:+:617396:- 29446347330124339:5033393:3531313:+:1502080:- 40061495291417857:8680501:8596333:+:84168:- 44274952327461512:7556750:undef:undef:undef:undef 96948602606349469:91315196:67529537:+:23785659:- 33176426245472427:32431159:30803912:+:1627247:- 43430641679126806:51532151:32282919:+:19249232:- 33301494630792380:171270740:undef:undef:undef:undef 90570682784220861:924188063:679831166:+:244356897:- 79430639328556982:512662150:undef:undef:undef:undef 57470169462146327:1470589749:687908813:+:782680936:- 68483406845364308:9466550523:4027821677:+:5438728846:- 70010934239091688:4341140166:undef:undef:undef:undef 49819436279160535:85904509902:79882082971:+:6022426931:- 93939925474315091:54581759721:39754230431:+:14827529290:- 24918572925189973:52105238375:27182117787:+:24923120588:- 39130177022959274:790758679262:undef:undef:undef:undef 51488393012386966:186208945027:17629775407:+:168579169620:- 72347642047909278:371269622185:279395670457:+:91873951728:- 61743127891697265:9191136040714:7147317599809:+:2043818440905:- 94530977048044534:6094678504209:5593753359589:+:500925144620:- 96854619031136879:6295728848074:1461398441715:+:4834330406359:- 68333595487310252:25375601707162:undef:undef:undef:undef 38442808642087038:77260027424346:undef:undef:undef:undef 41229185348028335:87463519154924:21667283325847:+:65796235829077:- 88413445336742945:679619497367754:604690101318311:+:74929396049443:- 77766978202972850:532019189388375:undef:undef:undef:undef 98496978178709531:776203931382008:15332536063739:+:760871395318269:- 12135128519994193:4455847532999167:1996975354881579:+:2458872178117588:- 70050719911666950:6737065618201523:5420064790711085:+:1317000827490438:- 99816374601370079:8074615437393557:3874990223148846:+:4199625214244711:- 80053567320567819:33266399295159331:2437650441594990:+:30828748853564341:- 29279386548565787:71796696258651927:16338945935201333:+:55457750323450594:- 15326228583724151:98553224075843632:28034415758903719:+:70518808316939913:- 89875622639855292:795874069109127227:211788693953700046:+:584085375155427181:- 32932645784696979:265173237301416015:undef:undef:undef:undef 23468588393511838:388700173410724183:43606211513805393:+:345093961896918790:- 17030761113179844:3522642303698597018:undef:undef:undef:undef 25443256387461272:4263945185892889838:undef:undef:undef:undef 54666575539893269:7153721776751992625:3928884116985042204:+:3224837659766950421:- 74986511551012014:89202256674285665390:undef:undef:undef:undef 66006984685142039:98345273285790752900:undef:undef:undef:undef 60227434648331826:80447948867125964627:64805254089895456604:+:15642694777230508023:- 83197999838331470:206439239170170931186:undef:undef:undef:undef 33095050621963840:479700065997411479690:undef:undef:undef:undef 94992065168886975:623038807404702315030:undef:undef:undef:undef 92232428828688029:8693752964100314956043:3383560292666666143290:+:5310192671433648812753:- 88811946643767688:7182545366144332727506:undef:undef:undef:undef 52846113871395631:5946343277588065327048:1997347915674367576591:+:3948995361913697750457:- 36472330863434829:29832888877450801264149:undef:undef:undef:undef 96006517877528028:22882643548120125836573:14983780620872265870535:+:7898862927247859966038:- 34816311294894820:65235726487604145294478:undef:undef:undef:undef 85238927115324946:497428028366600978783321:210338557119241795225303:+:287089471247359183558018:- 42232182027548668:584846812665652023573192:undef:undef:undef:undef 19774138567763467:978868828272500398176932:404217494869292525731887:+:574651333403207872445045:- 10834206747351019:1297741647746812329275159:134217273110843180903028:+:1163524374635969148372131:- 79991570797862058:4098378704356382612531249:2897909065962736070033105:+:1200469638393646542498144:- 20160765916820901:9688953547468938268099867:4894015327897760918003740:+:4794938219571177350096127:- 99345310811005534:522:undef:undef:undef:undef 24449021684080449:376:313:+:63:- 27217112835537620:998:undef:undef:undef:undef 97266343556972814:2659:295:+:2364:- 78416890282886204:1454:undef:undef:undef:undef 53173514583689642:8157:647:+:7510:- 57630912489621447:37888:15863:+:22025:- 81145454762535477:53895:undef:undef:undef:undef 15553323637705201:17102:2899:+:14203:- 90462265847168301:519864:undef:undef:undef:undef 32784389531362850:354724:undef:undef:undef:undef 61814294669743836:130494:undef:undef:undef:undef 14952225604902141:4552749:undef:undef:undef:undef 66472449232349347:8123031:7843594:+:279437:- 70964495787965198:6859465:6343177:+:516288:- 92239078565249821:22113845:16215346:+:5898499:- 32249467834212541:38978711:5664011:+:33314700:- 58782909107539147:46231972:42798131:+:3433841:- 20948767694083693:317341273:280940801:+:36400472:- 98088779243778558:812664342:undef:undef:undef:undef 17955727324816081:546925088:85189617:+:461735471:- 13916230920273454:5430982456:undef:undef:undef:undef 57085192554647291:6331757284:2850368415:+:3481388869:- 73644026390874905:5198544666:undef:undef:undef:undef 75754675227551541:50984810352:undef:undef:undef:undef 49227526928437872:14437584861:undef:undef:undef:undef 41633344583414913:94364328454:73401686181:+:20962642273:- 23304947805992190:264077616045:undef:undef:undef:undef 84404676686237561:731416658233:135112311368:+:596304346865:- 58424978869604137:284169430556:210441825417:+:73727605139:- 85282171878110428:7079991708223:3326310725558:+:3753680982665:- 33273670046160765:6471656773786:5655031918089:+:816624855697:- 48432794051350399:5520561444669:2635417198198:+:2885144246471:- 70248691197431409:58766651880244:28749872541449:+:30016779338795:- 16182915488102705:25353442103060:undef:undef:undef:undef 11459182784692556:32862757434317:25337085262452:+:7525672171865:- 52475419230856735:290741912888882:197418482050273:+:93323430838609:- 36232260761342188:562683970264838:undef:undef:undef:undef 47746526812211988:227532097988679:undef:undef:undef:undef 12988437213394599:2317426182778187:552294338258473:+:1765131844519714:- 73906096263761408:4459047733371868:undef:undef:undef:undef 61516014387199789:4346955324090562:4308724219827691:+:38231104262871:- 25476538467650465:40268304727221926:28241984461230661:+:12026320265991265:- 32945929373304579:28101680114954157:undef:undef:undef:undef 50702148816902914:31061406078158976:undef:undef:undef:undef 44339949843554039:535985615359619194:27119109581542179:+:508866505778077015:- 26876110452581283:362923925759693879:136882351792173550:+:226041573967520329:- 72762877934098067:501865071020908804:58650312943382271:+:443214758077526533:- 29949957083929573:9550336519238088976:9479389239358049309:+:70947279880039667:- 20546840597400853:8880476186490221101:5034762524290054635:+:3845713662200166466:- 97362418054391373:9437709569383448836:4154069307426224253:+:5283640261957224583:- 20347662375082835:29164011715132253926:15426087777382241245:+:13737923937750012681:- 60082481508459472:46452247849437497581:9699944804131926489:+:36752303045305571092:- 46285048364241342:27750201480751298416:undef:undef:undef:undef 49885308189279803:965742941017439487231:879257486593763460761:+:86485454423676026470:- 45947044455251118:200533374427872344590:undef:undef:undef:undef 77040110939061271:952699824074496863977:701129178619309401078:+:251570645455187462899:- 12628364659709876:7747580791379386393485:undef:undef:undef:undef 42048102653710734:8754132400302543755518:undef:undef:undef:undef 16931849022276291:2019447833554034747657:657894404027592104454:+:1361553429526442643203:- 21371712853616022:65228568521673389873709:undef:undef:undef:undef 52799363362779200:68781782093587525271926:undef:undef:undef:undef 11750725372935264:43166802878916533044335:undef:undef:undef:undef 81914829780139643:973371029532900522325220:600317512899566983461187:+:373053516633333538864033:- 30765282927580498:256467839165483949215717:25007602924652017154434:+:231460236240831932061283:- 77604538819261036:955126528879719986642845:127263043096979276099311:+:827863485782740710543534:- 54342840099349701:4207206876558598048853326:1878047670533526928050519:+:2329159206025071120802807:- 39810143463392715:2015449810352967156851317:528654547790948124880307:+:1486795262562019031971010:- 68616251362946099:3368537671378563823558444:1958114403431963337122839:+:1410423267946600486435605:- 739944222209625484:205:39:+:166:- 312146567644044979:871:534:+:337:- 234995735919927648:852:undef:undef:undef:undef 881263226289251457:6810:undef:undef:undef:undef 671005619467629815:4721:1281:+:3440:- 163036409710514668:3303:2920:+:383:- 285780624801101379:27576:undef:undef:undef:undef 896090930958559824:42740:undef:undef:undef:undef 796712777144708071:51620:16891:+:34729:- 908228407756368610:354237:77929:+:276308:- 372770406414583885:114473:8911:+:105562:- 666604792063950635:780404:708391:+:72013:- 828469453953096645:7368623:6984403:+:384220:- 750429865401289746:4106755:3408661:+:698094:- 242743961663778672:6691039:5467072:+:1223967:- 833148929164023225:59659076:43404625:+:16254451:- 202481921150250925:16681346:6835463:+:9845883:- 906071778290951527:46253994:29208679:+:17045315:- 901537238852563081:608953684:586427557:+:22526127:- 664522182923427217:120340172:79717233:+:40622939:- 311780644074700991:557325991:159256188:+:398069803:- 562157116867638256:8808712614:undef:undef:undef:undef 827027313006382025:7617649399:855597065:+:6762052334:- 724765870787062032:4129441951:1691471417:+:2437970534:- 105336833433113634:36131529918:undef:undef:undef:undef 834962892482436839:14998237399:8997276447:+:6000960952:- 996997075327497658:74951986703:49403107751:+:25548878952:- 829857708777346295:277636091705:undef:undef:undef:undef 797219364501072188:707978536108:undef:undef:undef:undef 877139979032848018:119112975165:28481990677:+:90630984488:- 841028034609677137:2247069051237:1676672153338:+:570396897899:- 733175820093125946:4116968796869:3995611623895:+:121357172974:- 506257543138215883:2419221598350:421374220447:+:1997847377903:- 678435520652452835:21710927384035:undef:undef:undef:undef 751013114453216196:36101413264893:undef:undef:undef:undef 113935549303883901:86443507710429:undef:undef:undef:undef 205886532494178305:146795182999040:undef:undef:undef:undef 546381004536017022:863110789314293:457137213828287:+:405973575486006:- 344688333778363286:475024385790495:71687016663251:+:403337369127244:- 187225701806494142:9330595506627888:undef:undef:undef:undef 985627526044453786:3476940225646923:undef:undef:undef:undef 125063969759197129:1016025397327886:282306028375647:+:733719368952239:- 614276562355001110:86173070944037787:10915320915553978:+:75257750028483809:- 435319051869297529:63518065647358657:24665703564912947:+:38852362082445710:- 773110844108090999:16325920136436508:12311461352358555:+:4014458784077953:- 806251846239181595:937484240885930727:undef:undef:undef:undef 508800826806954868:915873656971571794:undef:undef:undef:undef 704457075023099246:304998104112998959:209859717777732123:+:95138386335266836:- 623450091203253565:8334627439350300264:1033517460058994245:+:7301109979291306019:- 198202865519155748:8301375918345092606:undef:undef:undef:undef 950569878122459278:6034426742841068379:802248276552555118:+:5232178466288513261:- 439288797376507004:11850021366498989698:undef:undef:undef:undef 611857385566830500:50683866719365423530:undef:undef:undef:undef 453818827428727132:27375762610446687060:undef:undef:undef:undef 806668777608681027:190692192811013315445:undef:undef:undef:undef 764528714166777851:498893044164425465619:243872188860218207678:+:255020855304207257941:- 347976294384733771:222068335639062180905:11023291776468980576:+:211045043862593200329:- 838880478747206996:7042454656162207372364:undef:undef:undef:undef 519647266407412226:4042951395655889924327:1011531208527057271429:+:3031420187128832652898:- 429463306387728577:2904919838953885426448:1265294687955296659681:+:1639625150998588766767:- 454739260236677400:43435723260864921208620:undef:undef:undef:undef 235055100449954428:70371026613122378003611:26636398490735166000447:+:43734628122387212003164:- 357907530028599162:24884942866930377270334:undef:undef:undef:undef 601819786309569269:481586911497552481526182:114490489137964602805827:+:367096422359587878720355:- 187307474587651239:647953927486869640668748:268953788893571607167967:+:379000138593298033500781:- 967433485832737001:855829779915639694093261:619444618765346526822032:+:236385161150293167271229:- 602385516947039571:8687594336791008251491315:905831341305032267415096:+:7781762995485975984076219:- 797797541031493478:3214522432583205161683305:1506836251244780383860047:+:1707686181338424777823258:- 116746909123726496:3835311690391940719271108:undef:undef:undef:undef 681967180982108189:821:611:+:210:- 107708843072655783:164:95:+:69:- 766842904621101824:436:undef:undef:undef:undef 203539646202080784:1049:158:+:891:- 140781008874299874:5198:undef:undef:undef:undef 277082549150592603:6761:4674:+:2087:- 974530190267616268:23621:undef:undef:undef:undef 257651217367991702:31708:undef:undef:undef:undef 773577518971720767:91090:43333:+:47757:- 492531976782122034:162901:8440:+:154461:- 670962596278515952:620130:undef:undef:undef:undef 840568880311046680:604775:undef:undef:undef:undef 649351362475117207:9694565:3205168:+:6489397:- 357938805759032260:8042113:4693011:+:3349102:- 913722984348387908:8971139:1045654:+:7925485:- 933649370374162764:46218886:undef:undef:undef:undef 349410753181637707:98529556:1380271:+:97149285:- 706053457495316397:51382718:28180947:+:23201771:- 405201683720718793:977977364:489251489:+:488725875:- 664598253138890656:967862390:undef:undef:undef:undef 285292835017340308:347819476:undef:undef:undef:undef 872960570171611437:6979466832:undef:undef:undef:undef 542659342768117580:3110573897:322682024:+:2787891873:- 924391825063557497:2217960093:1570985099:+:646974994:- 992370052861293406:57201833091:undef:undef:undef:undef 108901810098555137:70441428908:28156960021:+:42284468887:- 702803944438852101:26812164169:19755973306:+:7056190863:- 273678061334705784:432982040733:undef:undef:undef:undef 807261622685427355:641090349479:569863472112:+:71226877367:- 113016841865081910:314323641274:undef:undef:undef:undef 174152365943648881:3588495242914:3345820006915:+:242675235999:- 435583662090633735:6380155943484:undef:undef:undef:undef 486859494777425717:7928718633119:822566729725:+:7106151903394:- 176963388197987622:55068405765753:undef:undef:undef:undef 325811567662029162:40058509885462:undef:undef:undef:undef 955218985760083130:62518232745635:undef:undef:undef:undef 443394278944930332:560762322993187:253844818353906:+:306917504639281:- 396430035471051157:289019885467962:149311996773481:+:139707888694481:- 167903502160975244:968908013604743:710639578903369:+:258268434701374:- 774406386680166576:9013385182875468:undef:undef:undef:undef 237662527672279155:1067553702374636:102195736886563:+:965357965488073:- 598317780188527430:6048355888957008:undef:undef:undef:undef 104201624575868217:73162203170505428:33472178232043165:+:39690024938462263:- 249800345918568560:24994938428560314:undef:undef:undef:undef 696656966910637972:25434496018832672:undef:undef:undef:undef 955673121757712411:145050266275280522:85614369228848305:+:59435897046432217:- 438970498459641004:624631386113542505:547290084930384659:+:77341301183157846:- 909709124056023317:614703065809376721:398478752261875130:+:216224313547501591:- 100155560151327465:7725277750251013137:undef:undef:undef:undef 206948033775177015:5757364081707158095:undef:undef:undef:undef 924103301676368290:4965215709746283461:4206883590964444248:+:758332118781839213:- 413249971255617621:53186082903358573681:37536987354766582631:+:15649095548591991050:- 349742873878469555:47010285173518596928:35377126292235048059:+:11633158881283548869:- 572830987853789903:17723955576530834788:2970324334779977787:+:14753631241750857001:- 373768487580965325:673733890110850740007:537313447996159520532:+:136420442114691219475:- 416360599486706613:213562464926973212977:145572025736250100053:+:67990439190723112924:- 255307733534768887:384491114741614726983:130140816678638446828:+:254350298062976280155:- 243721910486372067:2806740610389779702552:2570038985185034779307:+:236701625204744923245:- 182047561156981598:5901886460385054914320:undef:undef:undef:undef 879512730478938210:6776533573818022764915:undef:undef:undef:undef 334553986324389684:12517524758678396786266:undef:undef:undef:undef 222461442037222140:81066691159855854800883:undef:undef:undef:undef 581029766120709406:38912538998426697192431:7658465458579874902537:+:31254073539846822289894:- 818243846439592136:885970918883970733985059:2159774719225611754611:+:883811144164745122230448:- 282348932273257360:873329456614643181381202:undef:undef:undef:undef 983316489831539150:924557337165720132867116:undef:undef:undef:undef 809733838473777658:9547866968610146713102477:2103383893146127986438468:+:7444483075464018726664009:- 396887650469626882:7845327974301986160954536:undef:undef:undef:undef 452170280517345885:3958421076582645546044178:undef:undef:undef:undef 781570723018926424:573:274:+:299:- 401460158878978629:281:181:+:100:- 814035689715571067:945:68:+:877:- 615182183410788580:8509:3126:+:5383:- 450845433131669747:4703:4623:+:80:- 520181838750492251:3924:3887:+:37:- 603769251917303493:94838:66131:+:28707:- 524068448833342303:73325:66567:+:6758:- 713183549787548521:71889:65626:+:6263:- 538945463990590912:282376:undef:undef:undef:undef 217847128784696569:264652:47833:+:216819:- 304998980781206559:621589:84973:+:536616:- 295808426943965107:5849600:4018043:+:1831557:- 302407358774745669:3870624:undef:undef:undef:undef 637390987317561085:2868477:1447483:+:1420994:- 277457178799143027:28997888:3910587:+:25087301:- 965362079672929927:50215844:29758271:+:20457573:- 408923169530392581:62881687:49533335:+:13348352:- 297018840451809570:951778007:194894641:+:756883366:- 687051036050103995:609840170:undef:undef:undef:undef 975142143309314227:785715963:333198112:+:452517851:- 595844632862035773:5572417854:undef:undef:undef:undef 138891110547373115:5257258377:3150032390:+:2107225987:- 129272977679931354:5770902820:undef:undef:undef:undef 348788865116431918:36403464432:undef:undef:undef:undef 156759481853855521:71405067820:28926835741:+:42478232079:- 391580558298948898:14260350331:8358043865:+:5902306466:- 530357894657488407:432523414763:324599665371:+:107923749392:- 249041103039299643:661116835748:496697677755:+:164419157993:- 169454863252672806:955769873770:undef:undef:undef:undef 677740582607616370:4148582049178:undef:undef:undef:undef 194650133663085218:1087812926910:undef:undef:undef:undef 426959158065157441:1557729832601:531111368478:+:1026618464123:- 190672481619374176:16096133890936:undef:undef:undef:undef 278274975276226306:20769753482723:undef:undef:undef:undef 208631368712440107:40338347057249:13869691113085:+:26468655944164:- 759149066424119080:758448226173320:undef:undef:undef:undef 576796718957654618:713615321673676:undef:undef:undef:undef 359107963616755855:110804624649059:65768022066249:+:45036602582810:- 817707147713057474:6705651369913227:4763638317195305:+:1942013052717922:- 217164771621955380:2119786950821631:undef:undef:undef:undef 876211027396924498:7853424764924686:undef:undef:undef:undef 126024995196609433:71949677735730773:27391852143934070:+:44557825591796703:- 568489518079846089:40014513832833130:31300447427736299:+:8714066405096831:- 378749987539961063:49011317327263342:31588616004329097:+:17422701322934245:- 988405027394582532:878496535058181987:undef:undef:undef:undef 487986828231244840:449692011945969628:undef:undef:undef:undef 741797012196571282:354477086056442934:undef:undef:undef:undef 377939215180915447:4624077780967689522:903350705581036663:+:3720727075386652859:- 819081125992993587:4336987717545056996:2191187164402886183:+:2145800553142170813:- 799453706990126977:4894371558723396340:413347913747964413:+:4481023644975431927:- 382073959201430754:10460268036197608613:3452921976051216067:+:7007346060146392546:- 986493188904723921:87991746103938340989:undef:undef:undef:undef 360535197098755374:13703441983875248176:undef:undef:undef:undef 554283788405629254:228029444267508694299:undef:undef:undef:undef 408600700542481702:514782742742567080966:undef:undef:undef:undef 557909193473357941:788947974209609807720:555556151725042736741:+:233391822484567070979:- 966604974334974413:5247166898169513860747:989441682954964698031:+:4257725215214549162716:- 496097348904246929:4459949637246120562889:3679432768956948299354:+:780516868289172263535:- 854760067450811302:1503265939223096493078:undef:undef:undef:undef 138102303449697062:96976926875209370458041:53510673241205013589481:+:43466253634004356868560:- 497287993109626163:25527001065555344710667:1448754456114687695008:+:24078246609440657015659:- 754654415391807184:11213201593707236420256:undef:undef:undef:undef 127839986224423631:391440363732623081688995:4998112259978992816456:+:386442251472644088872539:- 914422954312915524:518484039461842977734501:62755222915605946629997:+:455728816546237031104504:- 772042681914295890:293468854128160349285647:undef:undef:undef:undef 336906895227122849:6150064384880127516000952:3313036846330875581646049:+:2837027538549251934354903:- 537510234731606550:6512033009943876747349376:undef:undef:undef:undef 788488983290930009:9365796751401681143367208:4064642308214254655177825:+:5301154443187426488189383:- 5448173866963093566:198:undef:undef:undef:undef 5626552865051956686:469:32:+:437:- 8844549949362314628:608:undef:undef:undef:undef 3623799778646548779:7815:undef:undef:undef:undef 8628457260539462895:4010:undef:undef:undef:undef 2664743947353612834:8409:undef:undef:undef:undef 4809163749754529116:77040:undef:undef:undef:undef 4744875047838478076:40985:24331:+:16654:- 9344645368969109121:27004:23901:+:3103:- 5418453597269350704:494622:undef:undef:undef:undef 4010929013500180628:252290:undef:undef:undef:undef 9992195769786221117:652192:undef:undef:undef:undef 1955843684678499850:8254980:undef:undef:undef:undef 4736927720398569783:6801993:undef:undef:undef:undef 9155006367212001183:3018592:687807:+:2330785:- 9061226290832319071:27696258:2533391:+:25162867:- 9147638239352792546:82423164:undef:undef:undef:undef 4738795568626172051:91457180:42998451:+:48458729:- 9287223749894998697:245435479:150775619:+:94659860:- 7255752505198100882:765852934:undef:undef:undef:undef 9904436455324333688:900933712:undef:undef:undef:undef 1249544648362921831:9705356674:7277503733:+:2427852941:- 7196170494797459408:8373178478:undef:undef:undef:undef 9743990719967973392:4150941207:undef:undef:undef:undef 8074792978161064512:90393665248:undef:undef:undef:undef 8541174566187552818:87918344383:65440641746:+:22477702637:- 3185909761563379232:31066224510:undef:undef:undef:undef 1006727285366483587:239599373796:122556894835:+:117042478961:- 9373734684234844634:196249443160:undef:undef:undef:undef 3712396208939996372:867924429910:undef:undef:undef:undef 3405670761495453193:7702020584968:4264334595097:+:3437685989871:- 4901432356373401795:8472270718856:7524037348139:+:948233370717:- 8877006335445963248:3590372267056:undef:undef:undef:undef 9730381735068725265:95449423461666:undef:undef:undef:undef 6164417305227538002:28407893087177:22815825827166:+:5592067260011:- 7413523847819625113:92210926245534:21097866040955:+:71113060204579:- 3269116376004401800:127456922737043:95024721542228:+:32432201194815:- 1101728946185933565:459179937515481:undef:undef:undef:undef 4554970054606176284:308186106580785:228230383621229:+:79955722959556:- 9310384178045855211:6941935164343581:undef:undef:undef:undef 4041250076577508689:8932613984478794:6915067118291143:+:2017546866187651:- 7266015999377986715:1369712936560330:undef:undef:undef:undef 9008744802515783871:56914691917734237:undef:undef:undef:undef 7926719021619035830:82183578741373077:64482557139893398:+:17701021601479679:- 5898101775487729681:55480822048150809:21570130812543448:+:33910691235607361:- 9196558534885709345:988185475736060653:621168793129643451:+:367016682606417202:- 9188753782593948808:387155367537118647:193351359362986828:+:193804008174131819:- 4217008802705181449:291051868262979217:172438056620684766:+:118613811642294451:- 6820766057705886577:5388719502563758847:216616594899447119:+:5172102907664311728:- 6305086134997371300:7035502515840337479:undef:undef:undef:undef 5716337401051138538:3817375918432559946:undef:undef:undef:undef 2763937994289694220:70731898559598880586:undef:undef:undef:undef 7461855625767535825:63704830200758262008:7119019657265108433:+:56585810543493153575:- 9613386648453534877:77155869512940628721:71404197921773050383:+:5751671591167578338:- 8951383421844972996:521099367803755574860:undef:undef:undef:undef 9567233495930763385:257004462353212219037:211429861860381768670:+:45574600492830450367:- 2168523422606789919:891913243586160114659:861630333218234939544:+:30282910367925175115:- 3643763662144608026:6727303485053239520154:undef:undef:undef:undef 6002861169078744685:9166581210783568350951:2618802327003930536296:+:6547778883779637814655:- 5393437481956112107:1979102385661736166438:1950613801588957870483:+:28488584072778295955:- 5399509697337357717:70814675311828912627499:26755069261624775973382:+:44059606050204136654117:- 6927847530195110149:38283403948446528887618:27764883748909001141163:+:10518520199537527746455:- 6667280153176934172:80895026716156273177393:331915533654595403876:+:80563111182501677773517:- 4233621628053581113:126808305418686159640763:110850054981717865349431:+:15958250436968294291332:- 6401286551523446042:997259473905914752330176:undef:undef:undef:undef 8972007663863237687:851660195089842549606652:231529237590737392064471:+:620130957499105157542181:- 5389046411588702144:7205541982448809562947385:4067066950894471209763624:+:3138475031554338353183761:- 8124252037458168726:2286778277199655241503982:undef:undef:undef:undef 8516215065787083501:6417936479562093736275105:undef:undef:undef:undef 3065523349613036690:620:undef:undef:undef:undef 8306382339859482579:899:871:+:28:- 4860617544234617750:568:undef:undef:undef:undef 5090257266754386675:9453:undef:undef:undef:undef 3367423518511333491:6119:2572:+:3547:- 6996209650374220107:2292:undef:undef:undef:undef 5855899806188408280:98471:962:+:97509:- 6401993991565462070:99190:undef:undef:undef:undef 9706585245534245701:55772:48889:+:6883:- 1565570476055387203:629969:28308:+:601661:- 4769942733196684720:153871:108882:+:44989:- 1042763237745969617:158402:102641:+:55761:- 7975881035620518669:2182936:1394333:+:788603:- 2680926520844559603:8581761:undef:undef:undef:undef 6970188437727975076:6866619:5089609:+:1777010:- 5549806680971370420:90137113:39141756:+:50995357:- 8716166226473048974:46346204:undef:undef:undef:undef 9350592971859709706:45138319:37954372:+:7183947:- 1639402770835011157:449867518:197126555:+:252740963:- 7521785855492311392:870452270:undef:undef:undef:undef 8812149904791132347:578855601:212216261:+:366639340:- 6958378802516079809:5763165515:1046735134:+:4716430381:- 9890902379368941639:7822877001:undef:undef:undef:undef 5249510675034473457:9370189955:817337543:+:8552852412:- 8772801806075805990:72019801735:undef:undef:undef:undef 9313467579288609372:62688828112:undef:undef:undef:undef 4279668364907224623:37467857144:1782463703:+:35685393441:- 7553809826693826247:405533147246:17728364577:+:387804782669:- 8570293656475393812:831231225217:123432702182:+:707798523035:- 3619084243249684081:694148734761:144886104112:+:549262630649:- 2369509599983841938:8709689883065:1765634884707:+:6944054998358:- 3080733753805442465:4719681895089:2617546970141:+:2102134924948:- 4801665454365901469:5443128482436:2365943229101:+:3077185253335:- 6112756636749875159:30005476471584:11093841373031:+:18911635098553:- 8806746401804528823:74302552452888:undef:undef:undef:undef 5687414053979184578:63632413679677:52496199046942:+:11136214632735:- 1840344372984393536:837341716040386:undef:undef:undef:undef 9482222461939037668:672744888046075:undef:undef:undef:undef 9695683815909489915:292599927233375:undef:undef:undef:undef 1415138377029554275:4009577933417269:3401269432701818:+:608308500715451:- 5888404401316808209:4036658896152703:3317494155637996:+:719164740514707:- 6942833732907272122:9743400054533101:8164550826554946:+:1578849227978155:- 9717708795931525358:72053956013729420:undef:undef:undef:undef 6582348512202792422:33755335119606601:4492775817545638:+:29262559302060963:- 5155666533126432283:69555632783017899:17863502986964359:+:51692129796053540:- 6985210945345982579:913324878308717984:841607061696321307:+:71717816612396677:- 8375221505998524132:724480770491387959:90481261615420356:+:633999508875967603:- 9072823084550399269:758031584000131338:216658116489462793:+:541373467510668545:- 4932466339189191043:3295201322235013921:2739050028819134549:+:556151293415879372:- 2356452818252697176:9488228729534580564:undef:undef:undef:undef 2304254304633448451:5452748589427307273:3250545675915538597:+:2202202913511768676:- 7514451896924355224:17556331117486108458:undef:undef:undef:undef 4548941382646167160:35602314977054818218:undef:undef:undef:undef 7051212729091818245:74928412779502426150:undef:undef:undef:undef 3313933993707905913:801719369573166726028:566351258493548552685:+:235368111079618173343:- 9272117437976823355:690843850884584415096:545082808905604106731:+:145761041978980308365:- 9562917074684303997:911171765733045164670:undef:undef:undef:undef 4989924714734957482:2198969013359987883735:250182823716485124868:+:1948786189643502758867:- 7265269837080583723:9172917856075230649859:3702708422187558431958:+:5470209433887672217901:- 2433561876722672864:1817705008267167849334:undef:undef:undef:undef 2346030710822656329:40656876790623791255601:undef:undef:undef:undef 7046502790432066299:65675373902114747816834:39688692327013345799943:+:25986681575101402016891:- 6969037389688816872:48556302414998898518720:undef:undef:undef:undef 2936326423379124322:602392853346664031849482:undef:undef:undef:undef 7768365159183464099:259430460287091923448420:12831573804754944220559:+:246598886482336979227861:- 2186324313808946191:705039031976974274631006:692017541944871573720911:+:13021490032102700910095:- 3080338669254049541:9906211956245336448271844:4828217586339530665403657:+:5077994369905805782868187:- 8163349292473669206:2506221618997046734322168:undef:undef:undef:undef 7710938455222536338:1654999180969921064463025:913424550512163886905752:+:741574630457757177557273:- 1449125440551018814:418:undef:undef:undef:undef 1180425457879471042:771:217:+:554:- 8762218623935859817:543:244:+:299:- 1706629204118241372:8325:undef:undef:undef:undef 7200145922001829912:7506:undef:undef:undef:undef 1492112777320608725:4449:4235:+:214:- 7740757251349921623:13714:8853:+:4861:- 9425031130176876563:32230:3417:+:28813:- 5527905398868180751:61243:48648:+:12595:- 1929655749378553473:479644:78557:+:401087:- 1609285305393394824:181287:undef:undef:undef:undef 5018529168328673017:561616:52409:+:509207:- 4993644871368927553:6119402:4137735:+:1981667:- 3316286154395967166:6729121:2025318:+:4703803:- 2105576075449062143:1457644:1210955:+:246689:- 8515618481677365669:67330780:61147429:+:6183351:- 8265229186665773676:17457776:undef:undef:undef:undef 1677880394698816077:45121759:33660791:+:11460968:- 6696915734591804044:353128979:161887755:+:191241224:- 7429533860845705174:713619309:322157422:+:391461887:- 6009477148440735886:473127457:282877950:+:190249507:- 9921392484388140720:1359685882:undef:undef:undef:undef 1448907897028625534:3714128596:undef:undef:undef:undef 1899003317012142802:6654305303:3205121979:+:3449183324:- 6380555198798231772:43614361908:undef:undef:undef:undef 1291921350621370005:72595509192:undef:undef:undef:undef 5265643183925379118:33205880447:13480150536:+:19725729911:- 5987271878627401697:446527174222:114288074743:+:332239099479:- 6955654866092365663:145410633354:85561229893:+:59849403461:- 2748302997171522319:937365185383:503595108468:+:433770076915:- 8967012175797788268:4871790758800:undef:undef:undef:undef 8371339168022183376:5976200702539:4904264529568:+:1071936172971:- 9619355007613567631:6539355882985:2696000329191:+:3843355553794:- 9262877733901374048:80620440478460:undef:undef:undef:undef 2785801868543753045:84437649958065:undef:undef:undef:undef 9820166988823584534:60295729627587:undef:undef:undef:undef 1434236144978788988:501754630079604:undef:undef:undef:undef 5810003431892748125:353765087523659:17984014907156:+:335781072616503:- 7374028998587274907:990459681584086:359290898482947:+:631168783101139:- 6312070709154296785:4496171410831509:1639082991085543:+:2857088419745966:- 3715279024145237137:9358531756069836:7563334171619449:+:1795197584450387:- 2266754630561007976:8844066375829252:undef:undef:undef:undef 3376019828524691356:98141644440557575:21428141138750221:+:76713503301807354:- 5975796260964159737:10412389744143263:5109185392477894:+:5303204351665369:- 2737407364224756266:86641646422153357:1598589906881323:+:85043056515272034:- 3015449228104975064:959593442068943298:undef:undef:undef:undef 1383647670662464924:324194857059321114:undef:undef:undef:undef 1662503303353151331:303892103931214966:294272434834624717:+:9619669096590249:- 6712189048842419756:9934192423700934208:undef:undef:undef:undef 1957842687473622213:9589335233754972015:undef:undef:undef:undef 3375308887587659207:7314731278830612523:5630280529808663672:+:1684450749021948851:- 1586861085871588412:19434873977171446864:undef:undef:undef:undef 4521729656744422917:82332965956825118638:2857004060038618913:+:79475961896786499725:- 4477759746972627213:70281394355653629787:24014606677319182186:+:46266787678334447601:- 9161598336328369277:847370223383575150056:515585225302969568213:+:331784998080605581843:- 7089578514359716534:394614120413547335681:82738690718590095537:+:311875429694957240144:- 6472978798464192476:131697362135188478826:undef:undef:undef:undef 4130596427326321640:3297666698115364240806:undef:undef:undef:undef 7136290921555859713:5708147921150992988005:1897963106503388945692:+:3810184814647604042313:- 4154957570807193159:4943308095378955227884:1258863207598302862427:+:3684444887780652365457:- 4432460974930394926:29422123339937705613566:undef:undef:undef:undef 3691088856394500051:90213967387896800631767:61023391617308782686391:+:29190575770588017945376:- 4224462774862066164:88114549923841889276368:undef:undef:undef:undef 6406375846626212729:826621026757959485831094:390792714921488253944171:+:435828311836471231886923:- 5707437463253243893:398525466049959600054214:88702073824539740267341:+:309823392225419859786873:- 5012307955498599460:975452538310655614854802:undef:undef:undef:undef 6781824302030669833:5566512192195578180155312:4358897486917519275351001:+:1207614705278058904804311:- 5055894495817134993:5522962606175021879338109:undef:undef:undef:undef 9308443400001553821:3724695440957550662113836:undef:undef:undef:undef 65945991213204890847:204:undef:undef:undef:undef 19866565006617268624:214:undef:undef:undef:undef 44596122854757256800:274:undef:undef:undef:undef 30166592425882860047:9432:3143:+:6289:- 48991470123312661313:7037:3386:+:3651:- 49090169881417935666:9347:8279:+:1068:- 78133959647979267180:67337:30562:+:36775:- 95250113272756947329:43177:35195:+:7982:- 21039588865012358106:29900:undef:undef:undef:undef 96464985230576016288:836282:undef:undef:undef:undef 73290865868497500193:128415:92242:+:36173:- 77210429299142699641:126095:116871:+:9224:- 65582662087471040943:2721939:undef:undef:undef:undef 77640672487126560621:3646365:undef:undef:undef:undef 53682198675385872456:1020090:undef:undef:undef:undef 81285668159830907013:22076699:19865011:+:2211688:- 74746330071661391467:77414662:72475597:+:4939065:- 46135031822273704678:27657599:26298839:+:1358760:- 65983939524749700259:551151359:53000039:+:498151320:- 43265363823293623123:972194110:834855117:+:137338993:- 49606443837224188635:413018824:312772499:+:100246325:- 84505366567384883344:8773028304:undef:undef:undef:undef 94411643650191658216:1802819526:undef:undef:undef:undef 21939722735812456158:5330629561:3020182248:+:2310447313:- 77159705760144316536:80381467881:undef:undef:undef:undef 89688722969251515869:60026317116:52164843617:+:7861473499:- 47796217965838355638:39148820458:undef:undef:undef:undef 18701145256503491765:428827374364:203522591341:+:225304783023:- 13695494018186666793:863178927428:827822621653:+:35356305775:- 71311307240519389474:999521386406:undef:undef:undef:undef 20196369352893294126:7535800913611:2620662801295:+:4915138112316:- 22327794192630190124:4987061654329:1095095756232:+:3891965898097:- 97505949331755737713:3655260923838:2795894972149:+:859365951689:- 81168726060639764185:59146227614183:29339559296420:+:29806668317763:- 21438529551744336416:39604778815542:undef:undef:undef:undef 20506856196020922701:66397844992012:8009924340077:+:58387920651935:- 70650729854558925775:446329783474015:undef:undef:undef:undef 96903831905734248315:762842259674870:undef:undef:undef:undef 44379700912124803378:417251673799802:undef:undef:undef:undef 49361226414687520109:2023977413086132:undef:undef:undef:undef 33379824487931091092:8225753677269070:undef:undef:undef:undef 18056101304636256097:9700430732642833:1770086510414302:+:7930344222228531:- 52751413516809606599:10138449139304722:3174045258731741:+:6964403880572981:- 51710303527953483179:98990907325787861:84941248010662599:+:14049659315125262:- 26902820019667140284:24710392154790510:undef:undef:undef:undef 33644083994414338915:204399273991317551:175838937808422988:+:28560336182894563:- 40672698099579916087:993732842307398621:118489092428769842:+:875243749878628779:- 79717107052801255992:133191092168715947:68123992401842017:+:65067099766873930:- 62554026621020364041:1500172073409749306:335514973458885799:+:1164657099950863507:- 20202632832726888532:4061077904654993151:1294318068108275488:+:2766759836546717663:- 13901826652799979397:5149291532563775598:1499424369338580931:+:3649867163225194667:- 28350448504789639876:21301209119966633798:undef:undef:undef:undef 57480661924784609343:33911397809037139321:undef:undef:undef:undef 11888103051844324713:64183670610140171114:39168446924499486709:+:25015223685640684405:- 47012445569229975752:798581077517867064901:undef:undef:undef:undef 65189061446460154986:292729448997892561727:129633294455255154591:+:163096154542637407136:- 75341507163211208588:840827640856266609486:undef:undef:undef:undef 61991393935622218271:8427993161410846046919:5094852781148136436823:+:3333140380262709610096:- 78245834682792553272:4096183516412255838475:2370750317121257152483:+:1725433199290998685992:- 16506278899127456285:3011957008479515396402:1546124667667761460571:+:1465832340811753935831:- 78351316753060139110:55728919792312918092203:48107330999462651299175:+:7621588792850266793028:- 88500675569676929526:13059961957729276551431:12679142581317193587153:+:380819376412082964278:- 86257467828761493761:66156491428686006660393:23868112201866059588624:+:42288379226819947071769:- 54133831431937114201:317093783084916181469766:188520508698733037716057:+:128573274386183143753709:- 74349127312018094958:673977959974935696853380:undef:undef:undef:undef 62731774589890391908:879508403938361856714471:undef:undef:undef:undef 49492354380681370078:6796280817290774038958873:696137463659245842927018:+:6100143353631528196031855:- 88511415076089135776:1473407891016654772160205:876801576841124996595356:+:596606314175529775564849:- 38616070928009757689:1700720679351975508746184:789724350841378793310985:+:910996328510596715435199:- 31588674115720665522:710:undef:undef:undef:undef 27538038041454067801:165:136:+:29:- 24240007512225159518:157:15:+:142:- 29170439392366862745:1575:undef:undef:undef:undef 75778239191410335325:1571:1279:+:292:- 25708902861742200324:8047:4156:+:3891:- 21731253119972777800:60375:undef:undef:undef:undef 34949430091056991736:42598:undef:undef:undef:undef 98376557863110171421:42134:19847:+:22287:- 24814450973163941320:916456:undef:undef:undef:undef 14778853216608621879:374386:278083:+:96303:- 98594183691549491114:119378:undef:undef:undef:undef 95077421268681236866:9291865:1127496:+:8164369:- 36965582977497604857:6456041:6306616:+:149425:- 47293432736157877219:3115870:1346699:+:1769171:- 91862174977150184929:24089944:13346041:+:10743903:- 19398534456299426760:61885150:undef:undef:undef:undef 92289313430297360564:58231246:undef:undef:undef:undef 46310441999104400020:191266486:undef:undef:undef:undef 39877042933901922814:606307455:undef:undef:undef:undef 97753488968893252706:333877984:undef:undef:undef:undef 83139703716215099431:9590068332:6008542219:+:3581526113:- 63780557421068123036:8061512977:3317763271:+:4743749706:- 50060597971211550087:7642450509:undef:undef:undef:undef 45166290048158830105:88309931022:37757978485:+:50551952537:- 13133582014405751453:17181115594:7802845433:+:9378270161:- 26316135309996093363:79484544404:63099834595:+:16384709809:- 14123787692392568201:869456811552:488504903609:+:380951907943:- 68235447576890798937:772093620127:414556602434:+:357537017693:- 68945702183551101666:491041441088:undef:undef:undef:undef 87113191772051761440:8724507843726:undef:undef:undef:undef 71660345672099809426:7601282071772:undef:undef:undef:undef 33794029746006109262:7207718100663:6683032880225:+:524685220438:- 50812863669362851904:54626320732533:5270191857800:+:49356128874733:- 17269056079114501387:99507020903726:32252063000243:+:67254957903483:- 36105829025038056918:61325443211096:undef:undef:undef:undef 87503584793550020752:808978605382759:107904997492669:+:701073607890090:- 18005279671900622042:835934610515518:undef:undef:undef:undef 84540458353176014085:172265776726936:13003975140909:+:159261801586027:- 29908775267456274463:9154602903715007:2984385636413608:+:6170217267301399:- 40033326276534794210:9072363631383844:undef:undef:undef:undef 72145153883025189496:1273132873363654:undef:undef:undef:undef 59786846033000007735:73293973887942099:undef:undef:undef:undef 80212857983382052219:43906734328798378:8014149190586465:+:35892585138211913:- 83103542125540553773:82937437843016227:75979313349769473:+:6958124493246754:- 46307865779017573030:615840531903755490:undef:undef:undef:undef 91439934055342327935:935321499539922298:552354121831852385:+:382967377708069913:- 81897580657324592477:873679720044479978:810161066852210273:+:63518653192269705:- 35783429166206739722:8817460755801437601:8561730235625088044:+:255730520176349557:- 37774747291999788193:2719007411145293505:317005635182467012:+:2402001775962826493:- 36889916154925832052:7697594947450658323:7665728366872146114:+:31866580578512209:- 74150851609144084776:32280035327789426432:undef:undef:undef:undef 23255383858328353037:45398576381144711433:2538484923275749964:+:42860091457868961469:- 83091194375321980091:29170133994733611672:20270898659107993979:+:8899235335625617693:- 78603066077259805724:144253799380198774946:undef:undef:undef:undef 22795654032814824747:923828670580177932656:465458158791993953091:+:458370511788183979565:- 35967663277143186267:444623028883266070585:183034422912171150833:+:261588605971094919752:- 29633709462946584558:1215959123152496923130:undef:undef:undef:undef 54519513617443438062:8883240371247671639754:undef:undef:undef:undef 44864838295842013874:6934008075047176809482:undef:undef:undef:undef 96380934085721426669:33033406990345707279550:23089822432827598436929:+:9943584557518108842621:- 34438706394518033877:55539350337602159117062:5482482178339893933651:+:50056868159262265183411:- 88632402955359853039:93147944788718228257117:70467753699090970406057:+:22680191089627257851060:- 58889845808828043516:506211071344721308205211:undef:undef:undef:undef 72389378381131767278:924606984469978292837632:undef:undef:undef:undef 58909151720975083642:347184061533561775782630:undef:undef:undef:undef 40385436710002299924:6823252581001428084242241:undef:undef:undef:undef 81815397407819983904:5779312326029839882850083:2748831057887968964589574:+:3030481268141870918260509:- 85889138654042523621:7360070437556045379745779:undef:undef:undef:undef 87790611342649174424:188:undef:undef:undef:undef 23534106003531578853:458:355:+:103:- 79868451341737109298:455:undef:undef:undef:undef 56708851661719914845:4008:undef:undef:undef:undef 92163217766292217257:3340:1633:+:1707:- 49726951837761690952:1994:undef:undef:undef:undef 11437454083374469986:16065:undef:undef:undef:undef 33554502168069243829:81033:3688:+:77345:- 88821853932908263052:59975:11138:+:48837:- 80555830734527655261:926526:undef:undef:undef:undef 91606409763376132974:257632:undef:undef:undef:undef 88660586233055346834:971054:undef:undef:undef:undef 12221208436868245934:5130606:undef:undef:undef:undef 26482535875953791070:8580086:undef:undef:undef:undef 48196625155219968662:8953413:2036435:+:6916978:- 41731711296621812847:46701208:35537383:+:11163825:- 94523039370408491776:31838227:1105751:+:30732476:- 77743673842056461602:15771270:undef:undef:undef:undef 16466906528690752489:734434720:705582809:+:28851911:- 68465450456942785923:316968708:undef:undef:undef:undef 65392130925573284591:926060302:258250569:+:667809733:- 85879814100995419744:7195807062:undef:undef:undef:undef 40730550095500965700:6581982304:undef:undef:undef:undef 13613425094810954136:7040255550:undef:undef:undef:undef 84558037063027249911:95727168307:14051562878:+:81675605429:- 24582907976090389833:17391432744:undef:undef:undef:undef 17983991072762776981:49776896976:1389560269:+:48387336707:- 79909265464113501017:842936459789:477340797479:+:365595662310:- 85060691455987313035:184749153601:undef:undef:undef:undef 71310833888561341837:313803320021:145654272504:+:168149047517:- 39706576208339090356:8497212273539:4189678911533:+:4307533362006:- 48435768266342554324:8918208417974:undef:undef:undef:undef 52544894345511982837:2882527360004:2506010554261:+:376516805743:- 15586883229686058364:25606213251829:18484476014188:+:7121737237641:- 10651167848689667227:15483233236016:8785345224771:+:6697888011245:- 89196524014965301510:15629235365953:4400138969768:+:11229096396185:- 12704381502722002866:158817739933491:undef:undef:undef:undef 61767182596646198539:871200529495247:undef:undef:undef:undef 49342061106770162722:501489922729467:491825582889973:+:9664339839494:- 74205595140138789767:2608727101717786:598743334599451:+:2009983767118335:- 20391493069524616184:9053534660142694:undef:undef:undef:undef 60999161958516409519:6021728310972274:2190881185853917:+:3830847125118357:- 76276141168010495855:62366470421142679:undef:undef:undef:undef 91457074188709709760:58473181589704646:undef:undef:undef:undef 41041540565288490193:54094779733351756:47546705059553477:+:6548074673798279:- 78118877476556488666:154832038781162811:102137334163824898:+:52694704617337913:- 44332318372906253527:578874559212403005:485066814500176333:+:93807744712226672:- 16818998993557434547:564662139472425361:188032874588039478:+:376629264884385883:- 50389581687467027683:5381581176332710699:5366663807030343873:+:14917369302366826:- 31720612552940720105:2576250042346811812:105338714928503861:+:2470911327418307951:- 10507407984047313574:6451596453688652146:undef:undef:undef:undef 82899913481838374642:15509608123512847831:6194724560719373552:+:9314883562793474279:- 88012984245237832199:69692115042440083889:30727235749983398219:+:38964879292456685670:- 61142339689521878862:61936718113107612596:undef:undef:undef:undef 24123604907850369381:798294788364375137063:177368967937016813072:+:620925820427358323991:- 42971940021131267364:827838469721395961351:747159044213086724166:+:80679425508309237185:- 26577447064831626393:888672988413581760646:33493868639718137397:+:855179119773863623249:- 36492357751976942083:4209777394815747978019:2625233922838779668894:+:1584543471976968309125:- 23685505310309526675:7390045029377930500091:1372714656312073244306:+:6017330373065857255785:- 95030497992770995618:5990939932188379455423:4580150725622865453994:+:1410789206565514001429:- 81530050420941357365:89841197082616526161313:18630634103931508011248:+:71210562978685018150065:- 93448375776546688118:32606636837174817011141:19426977077049506834826:+:13179659760125310176315:- 39940476544127344116:31450697486458938110409:undef:undef:undef:undef 25002960888279105365:430965158107824804848291:167875417109799884479328:+:263089740998024920368963:- 81254428092262572594:416596986441224768298834:undef:undef:undef:undef 60522508616508323045:222707578815472695623399:129209177477290705634376:+:93498401338181989989023:- 79211386782320561419:6239951755913447507748181:1968606591109268698716747:+:4271345164804178809031434:- 16585453138970304465:6829983832539893975466119:4315087231050262073489169:+:2514896601489631901976950:- 78362615121605322406:9879452272202434354667378:undef:undef:undef:undef 222469273614121370217:751:653:+:98:- 203634259890618385015:171:94:+:77:- 130866933947358320020:963:388:+:575:- 219313555731993193999:7893:6277:+:1616:- 625385082668408967648:4699:1809:+:2890:- 409887159711255864014:7828:undef:undef:undef:undef 860763130251743758247:56651:25518:+:31133:- 423529667755119235600:34702:undef:undef:undef:undef 547245488569503903717:30439:25897:+:4542:- 666663468221531572697:302883:293165:+:9718:- 942327832300373347805:167309:93189:+:74120:- 510926018221359857509:141157:140949:+:208:- 425025031462462377635:8783206:undef:undef:undef:undef 152968810020455707904:7130868:undef:undef:undef:undef 110272593913604615453:5383912:4181349:+:1202563:- 599636362817393649434:69060688:undef:undef:undef:undef 900236734177671489859:99757274:6414493:+:93342781:- 745687287582016348136:81728322:undef:undef:undef:undef 196132010240399107249:859646990:406352899:+:453294091:- 985571012670637714692:631441957:377458877:+:253983080:- 774405996384028041205:674395070:undef:undef:undef:undef 571564888467356993871:6392456657:1314167970:+:5078288687:- 782561657150052663359:2403784742:14423781:+:2389360961:- 205594183931768043041:4107599642:1850961197:+:2256638445:- 908551033023370529948:97820429454:undef:undef:undef:undef 666477636927229378021:29038358625:4653694006:+:24384664619:- 814747954018195190408:72605082098:undef:undef:undef:undef 924022178560272772741:148043328791:47468964426:+:100574364365:- 985376807931579715383:910512997799:647069982721:+:263443015078:- 840011014058371981307:112993972565:77748946818:+:35245025747:- 511791505538248062554:5630847376129:2887957363651:+:2742890012478:- 813547382132353986829:6180385717462:685474808685:+:5494910908777:- 664727386068519163279:1723355339674:1272576299323:+:450779040351:- 198230064705953949120:18138770238456:undef:undef:undef:undef 970971533215001803608:71320320120120:undef:undef:undef:undef 372979404736410940773:63288681918830:38842670586957:+:24446011331873:- 141361696359391040778:370944208398327:undef:undef:undef:undef 216458624417870919251:666441141732925:293805924050801:+:372635217682124:- 526130860016988910262:491234051258510:undef:undef:undef:undef 215210838958019289699:9769448239969307:1573698167037500:+:8195750072931807:- 438094602187949311474:7289964881683573:1387623964950234:+:5902340916733339:- 263932597475260367880:7663911191863600:undef:undef:undef:undef 326006499397541597466:32422506223659498:undef:undef:undef:undef 715774866656243342395:17520801656458809:3796451785129939:+:13724349871328870:- 129833955791040492408:12159854736877069:4792204795088353:+:7367649941788716:- 195484130008172790738:596797942779792628:undef:undef:undef:undef 923272428840406522860:459912669156287377:undef:undef:undef:undef 502220893025293895270:891889900797980406:undef:undef:undef:undef 265959331276855024136:5925951228390605973:5583964349149869677:+:341986879240736296:- 323547371196221379385:3195045479742245202:1462624001781123397:+:1732421477961121805:- 405874848728728351726:1593917318053558261:167217762731197497:+:1426699555322360764:- 286903803879848390926:79840612734995026445:11396598275279182936:+:68444014459715843509:- 408837954033388993493:55661255038618604811:18486467603553598133:+:37174787435065006678:- 439046389517191274835:61353005519691272463:undef:undef:undef:undef 287002150826635652446:568631611262167491083:258391403036836348689:+:310240208225331142394:- 694654600666740389922:989621481379620028648:undef:undef:undef:undef 635178478562571012680:170675841782350896168:undef:undef:undef:undef 912558166831638956058:2211336056718762891436:undef:undef:undef:undef 900043918152616577260:4798529103099259303551:758771188883683666498:+:4039757914215575637053:- 113829831167694075883:5204630965541897885143:undef:undef:undef:undef 148788686053754525278:25732414550861361433949:18335005157611944235776:+:7397409393249417198173:- 762574956170933342733:48608980217093415137381:37009681437506950304791:+:11599298779586464832590:- 890689100314339904536:67048428073618522154219:64142352182094985652942:+:2906075891523536501277:- 928487171439374260178:887005181253909781817443:638550320306924159343871:+:248454860946985622473572:- 734630026451254820840:428445787696974804720142:undef:undef:undef:undef 816426024260962583892:649610741413494399438795:undef:undef:undef:undef 173947869583086596243:4456555004847206714613624:3830883416722679131090163:+:625671588124527583523461:- 228547162640874074084:7370228099394320654347879:6336669903258825231999399:+:1033558196135495422348480:- 917354889755992125162:3728655370119549475667266:undef:undef:undef:undef 864282471803349087486:854:undef:undef:undef:undef 483094066243361231311:277:100:+:177:- 434847472789877804609:555:254:+:301:- 578439464591811164390:1282:undef:undef:undef:undef 554967806147021936604:7098:undef:undef:undef:undef 865812929167476811648:2549:278:+:2271:- 482213761104336078352:98782:undef:undef:undef:undef 142858277354770352091:93556:86907:+:6649:- 463587017449333463622:70267:4483:+:65784:- 107689072720974842699:519842:285421:+:234421:- 845670961208214778452:979141:880428:+:98713:- 522576555284244809351:745935:144656:+:601279:- 387424439216006491614:7796906:undef:undef:undef:undef 372576414558585433790:1515956:undef:undef:undef:undef 971819654249713886165:4300376:2975741:+:1324635:- 743194650173160351419:80802592:27873363:+:52929229:- 850073890809711137361:94749305:58790796:+:35958509:- 682755474406485007421:94904510:75758691:+:19145819:- 444882942356056887917:842466962:720890469:+:121576493:- 333327753516826636614:861944556:undef:undef:undef:undef 520384425224477655307:138240499:75137917:+:63102582:- 787296883677099455549:7388582467:2248954177:+:5139628290:- 127826412736867950796:5922195878:undef:undef:undef:undef 887317823706046475638:8766644457:461149990:+:8305494467:- 530274912592266434537:95245420324:20971470361:+:74273949963:- 208929399679301267651:39367653420:2728663931:+:36638989489:- 374408131607850444852:19891063744:undef:undef:undef:undef 218903475380797195929:520661585956:136098939977:+:384562645979:- 824875176169814561239:298265922655:27160319659:+:271105602996:- 557360651447408528168:452953609593:271028623937:+:181924985656:- 968732963725397958973:1694313430148:907177707033:+:787135723115:- 704854677395044855806:8859752439997:6122895248601:+:2736857191396:- 912988335156065638463:2970676443389:2924445915787:+:46230527602:- 178929761314785787205:95304782728960:undef:undef:undef:undef 684263934134108222359:74675525587295:58894842336199:+:15780683251096:- 572806267296935748328:34440239444090:undef:undef:undef:undef 354532605347075444984:738211673187192:undef:undef:undef:undef 316881165575535670422:940813427149173:undef:undef:undef:undef 581469655070483145017:873004208528979:198472725832886:+:674531482696093:- 168211535098214994482:7941090336121803:7699922063598152:+:241168272523651:- 744831709272018951145:6609693267390188:5504241459051065:+:1105451808339123:- 387804381536381851751:5212780591410542:2496391364101219:+:2716389227309323:- 719125792603167632036:31519078401126722:undef:undef:undef:undef 952235639878375409557:13095810636721129:11230472275767474:+:1865338360953655:- 673833984925568838072:83791118488390902:undef:undef:undef:undef 934248307467496556957:892961774735345943:139251591001665620:+:753710183733680323:- 199200624819079763043:680117829986528062:24215979789505393:+:655901850197022669:- 570885094635743887859:951049501557169076:32439246166420979:+:918610255390748097:- 934092731964824984329:8998355057754525233:8398913182060315874:+:599441875694209359:- 474529933667997096936:9199403804858679746:undef:undef:undef:undef 271216540185860263251:5319075856055213102:1492189709757765353:+:3826886146297447749:- 557545405188674147030:10584899779916419092:undef:undef:undef:undef 810380252431166322413:41537831863935596037:32700061654662334799:+:8837770209273261238:- 704028938366407125297:37582074119019486321:undef:undef:undef:undef 605353823566371564615:653419650926468676710:undef:undef:undef:undef 529671606734149621121:252794376542150731807:113674614332322336367:+:139119762209828395440:- 771966864669214785259:828635520350272196565:371192199409764223714:+:457443320940507972851:- 833159968112829191390:8036830723554606690872:undef:undef:undef:undef 305484802079956355571:3556406777045134624284:undef:undef:undef:undef 426709424821294632874:8172335118588729648573:504302074553747651791:+:7668033044034981996782:- 363534486403992559766:98596001856328465852536:undef:undef:undef:undef 595412749467829261308:92726428055250457287643:64980251172884704480653:+:27746176882365752806990:- 628373134655347175754:40452954900035573828928:undef:undef:undef:undef 404498830382790889356:288917922391344374800634:undef:undef:undef:undef 163199713008892684058:383129996874859371297778:undef:undef:undef:undef 296870268425103667661:171431006013867368563219:27597956278877507901229:+:143833049734989860661990:- 262334092254534542567:2436317799249906261905168:1581507882081057857356215:+:854809917168848404548953:- 223843803529649713447:9469028158815732242471019:8091238404266646525020707:+:1377789754549085717450312:- 826688228783243144161:9832764636492408278853761:6595836856424819321090377:+:3236927780067588957763384:- 839235939125266130991:929:281:+:648:- 523974141875285108869:463:441:+:22:- 472658157902996626781:330:undef:undef:undef:undef 967969937069874016335:6803:3900:+:2903:- 378751207167767239626:2174:undef:undef:undef:undef 714764454372656757269:7907:634:+:7273:- 261779102500173851997:95593:6873:+:88720:- 778457729874074437676:59312:undef:undef:undef:undef 780243418096937554532:15419:8570:+:6849:- 617311850530168828207:855488:622031:+:233457:- 436191596284235151048:678870:undef:undef:undef:undef 101479008125634803930:149693:75924:+:73769:- 328657677524683600017:2416028:2156545:+:259483:- 254453987712116790854:9626488:undef:undef:undef:undef 742761089109272965522:1505121:143596:+:1361525:- 778051446159165750393:12302376:undef:undef:undef:undef 641992834004740604311:80017626:74702923:+:5314703:- 629665106590431072909:85763321:56746577:+:29016744:- 663008084318467030160:575920312:undef:undef:undef:undef 304733746913720050282:498453749:3614020:+:494839729:- 699672428123124089582:249674064:undef:undef:undef:undef 838035423626190008867:1747181820:1659583943:+:87597877:- 712448899005842831011:7768732395:5734681561:+:2034050834:- 274286531021346345358:4652186853:474303538:+:4177883315:- 380541437366807442998:64450010130:undef:undef:undef:undef 947490796549861256400:44959341145:undef:undef:undef:undef 812266523403261470532:42268119004:undef:undef:undef:undef 376976105498629839115:802061815381:542321464851:+:259740350530:- 444470829262735060386:649427279067:undef:undef:undef:undef 872318051808524143827:861335970044:106746111343:+:754589858701:- 352138991239759812765:9809521853776:9516558483109:+:292963370667:- 666340642191029548992:6408072751043:1174016493169:+:5234056257874:- 327118262063651566875:3101776656344:547433561067:+:2554343095277:- 941299096972080404562:79234428109872:undef:undef:undef:undef 673118480874795407365:31435862908850:undef:undef:undef:undef 525335482136900098790:23576225880980:undef:undef:undef:undef 904170783971713586897:871200333326529:554263814855588:+:316936518470941:- 502063977885606752781:341788036709129:230633709677039:+:111154327032090:- 969395205194360889449:349923067452781:113014477980339:+:236908589472442:- 177543606622200487953:6294627299166699:undef:undef:undef:undef 595715096515837512563:9506607556217870:5313087695823347:+:4193519860394523:- 264864492099650858087:9069744683063336:6049986938395367:+:3019757744667969:- 153972113229710269812:61809964733729308:undef:undef:undef:undef 876937857924627817761:53312132267747526:undef:undef:undef:undef 429439103372129420988:31312320477872090:undef:undef:undef:undef 564371379321778406709:167170860365795723:42499406418721917:+:124671453947073806:- 452893687594722447878:655193298640920221:undef:undef:undef:undef 887247887959222465184:398242535840301959:352180872188486501:+:46061663651815458:- 314022811651945537154:2312814397291594590:undef:undef:undef:undef 156163742339527257523:2921116891223151554:1603591896829753321:+:1317524994393398233:- 290859518526072027409:2372179029485459905:520972281441725419:+:1851206748043734486:- 652372848654248729872:25388608524517493773:11753175005930331171:+:13635433518587162602:- 743433096978462896864:90718735349484900946:undef:undef:undef:undef 755864689787364640209:69286108626235960796:10839070930602053229:+:58447037695633907567:- 624952422221039892644:213048291459562022462:undef:undef:undef:undef 848639585727996439433:909644378828487243258:364771783311627285179:+:544872595516859958079:- 658298202456916737457:107143436381224433348:89249108318278665641:+:17894328062945767707:- 171312241382061258089:9682322644912295622509:136307076623448469379:+:9546015568288847153130:- 209331895956729452737:9894212683454380426945:3936778819111613268758:+:5957433864342767158187:- 964468791709638582035:7663822327008331068066:6407738910810002277893:+:1256083416198328790173:- 519070974498218343914:59005148874057505268376:undef:undef:undef:undef 744400406698297176208:96610848845054035782672:undef:undef:undef:undef 796756082956100130115:64997134522693781592465:undef:undef:undef:undef 575523597543795682321:857541250499537109686933:69848570961008160906359:+:787692679538528948780574:- 701148158120604566210:199055962554917694384725:undef:undef:undef:undef 656184178113079519971:625463465629301951178747:undef:undef:undef:undef 173042295743171271672:1959628452171208119618211:635402454158230428614445:+:1324225998012977691003766:- 492423370848411359061:9323231027933281949392062:undef:undef:undef:undef 996379792997849980955:2035229017542911689468619:1957987668026256978163703:+:77241349516654711304916:- 1839850204584165132145:142:105:+:37:- 6934496594486882514370:844:undef:undef:undef:undef 5692187749797167864750:455:undef:undef:undef:undef 2439575037659688433574:4185:3629:+:556:- 6047484087653889031313:6772:6765:+:7:- 6243859452971106645160:8238:undef:undef:undef:undef 6023121424848063073801:56900:51701:+:5199:- 6971825260004492400682:32721:undef:undef:undef:undef 6888926907943664599670:36470:undef:undef:undef:undef 1745055266386378223395:496053:367264:+:128789:- 4114306336189268952246:522556:undef:undef:undef:undef 7377674484138559602586:863719:undef:undef:undef:undef 2365960864270336898146:5794525:4563756:+:1230769:- 7256177064299722592694:8208532:undef:undef:undef:undef 9163024430187329416057:7534317:undef:undef:undef:undef 6316457727921483460785:41731857:undef:undef:undef:undef 5683986432809029021922:40905834:undef:undef:undef:undef 2778978385244133663022:38071751:3001285:+:35070466:- 3238052242588630599868:758144778:undef:undef:undef:undef 9314124521255823715890:894490575:undef:undef:undef:undef 5534400580796363580709:498257232:463995229:+:34262003:- 7603660466434916850235:2800725124:1633407283:+:1167317841:- 9597172479248228320144:9789982112:undef:undef:undef:undef 3477096603833768348024:7019662580:undef:undef:undef:undef 5248208475367671664104:64851110623:32321382173:+:32529728450:- 5750120784031910049527:57716101172:8789306215:+:48926794957:- 4375721449892938563155:69879051741:43946999936:+:25932051805:- 5980259112557379772472:517887444420:undef:undef:undef:undef 4232530025454664222776:145233849543:undef:undef:undef:undef 1543179602908149553106:809563411171:367870571395:+:441692839776:- 8266358264532765351255:7300442880970:undef:undef:undef:undef 1775722667588063596665:9312238368885:undef:undef:undef:undef 9590724812502212461888:8965525014790:undef:undef:undef:undef 5229211330494937364381:10625410975518:1575761292251:+:9049649683267:- 2431975366336788160139:21156702607124:8621261028043:+:12535441579081:- 9852236962511759235543:39993404718693:undef:undef:undef:undef 7150474159723516578288:244084324068302:undef:undef:undef:undef 9320481827418168997405:385840063054852:185550613097257:+:200289449957595:- 6984792045907820536602:753576448955570:undef:undef:undef:undef 2699392565376452052409:9890243867976939:5162567670851074:+:4727676197125865:- 7682145606332975581697:3845937244304682:3844381199028251:+:1556045276431:- 9335267552861727896855:2371953145618717:1983544593911048:+:388408551707669:- 7258393773822832844455:16460557759675278:15308057335246975:+:1152500424428303:- 8342066539617509476723:83197599892717094:4421890425489971:+:78775709467227123:- 6957220954774008543359:98070056578244222:81972969789857221:+:16097086788387001:- 2306705894433864582719:151620398549773044:17290715609128223:+:134329682940644821:- 6288284318883180440044:934729989281010135:784171973458543309:+:150558015822466826:- 9572088847439282028035:950700976816506549:848348037146528981:+:102352939669977568:- 4849771553093551527886:2427239388537311293:1172999191066544373:+:1254240197470766920:- 8348750284793466712833:8480512216413168101:579181618029798723:+:7901330598383369378:- 6887809555658216357795:4835683327338132062:3358554271170263195:+:1477129056167868867:- 5458870256593658332064:91958564052486527484:undef:undef:undef:undef 3532006205604657078281:43406946313495475179:10387071739263531111:+:33019874574231944068:- 1042167215746232554641:64875304849081830618:undef:undef:undef:undef 3859369749253894536047:548737564541670811849:371755153618532834951:+:176982410923137976898:- 2899485998209405322484:295410054329514266269:56863124488379288040:+:238546929841134978229:- 9272247721625756784959:634249966763061343068:359383982017080814799:+:274865984745980528269:- 1617773355509011607636:5384785757685627478751:4568549050237931109777:+:816236707447696368974:- 6513864342977071834081:9948659543586545483751:7935119641263792097147:+:2013539902322753386604:- 4296022100245925255030:3766238437621586504580:undef:undef:undef:undef 9795654957441755830749:71707597527997962541614:undef:undef:undef:undef 3379410904600974576844:60939201545394304173074:undef:undef:undef:undef 4591890088982211743550:87323802548511328733146:undef:undef:undef:undef 2426611503980499776682:149381630065812724333057:79426065378497101719467:+:69955564687315622613590:- 3443845316095039693295:606649762182609389419893:339576397037487755983490:+:267073365145121633436403:- 5495248395484902216980:528915195078449567501040:undef:undef:undef:undef 8471502510358951657290:8333239668531474842694667:5031469633845788741848737:+:3301770034685686100845930:- 5558113585238071056468:9761568318069654811375806:undef:undef:undef:undef 4891365839792787235204:7701450039486196814583243:1328346739110727609880281:+:6373103300375469204702962:- 5092729372120582936854:258:undef:undef:undef:undef 3828828920718451791694:655:414:+:241:- 4170083076902276183594:270:undef:undef:undef:undef 6261956069770028968282:9661:2880:+:6781:- 4870009061739792812747:4449:1646:+:2803:- 8477354147441096345918:8983:7452:+:1531:- 9148415847187615394287:51570:16063:+:35507:- 9789579618591570165680:47681:6886:+:40795:- 8013933040719989152209:45577:6404:+:39173:- 7420903221006723393430:327107:179708:+:147399:- 8507634999641223445756:556498:undef:undef:undef:undef 1795704365788211211684:552687:undef:undef:undef:undef 4903068472977289910501:3920850:1703651:+:2217199:- 8419562673383589276724:3691014:undef:undef:undef:undef 1076953781209780850369:6136198:5849481:+:286717:- 9865807717925889834881:94343069:46123396:+:48219673:- 8113339496805836715934:89650004:undef:undef:undef:undef 1732297142788054879035:91553491:29200636:+:62352855:- 7606662944165165543646:499354289:203014688:+:296339601:- 3328911390812249765346:101655701:80743225:+:20912476:- 4396306620476765013629:700201801:667601778:+:32600023:- 5320923774284522092207:7060318785:2151260773:+:4909058012:- 1453745318240153550502:2447183667:102390130:+:2344793537:- 4768869271115535010327:9873596409:348332080:+:9525264329:- 3020396247151335827355:52703901248:42988977427:+:9714923821:- 4667689000730773521087:34070119707:undef:undef:undef:undef 2206811938760176420328:69966185273:54647508757:+:15318676516:- 8444698846282531878047:550604444262:130030132499:+:420574311763:- 3487459000638845029301:254791933841:197925583871:+:56866349970:- 4517125068586980645227:921827614468:918161384003:+:3666230465:- 4421752257227474753166:9750964956909:undef:undef:undef:undef 9051476746644240654700:8397122186598:undef:undef:undef:undef 9736326304721217773340:1331810185523:253006595880:+:1078803589643:- 1124928610727608933131:73723030301326:56811420796097:+:16911609505229:- 6591862305825300587752:61601479084751:58750921006762:+:2850558077989:- 5432387990288423051426:49333295635243:27364594462982:+:21968701172261:- 9830865303836212171105:234884106040418:53596541139477:+:181287564900941:- 7787606534616060689721:320355840021647:219531586825890:+:100824253195757:- 9648783398976927659324:297960953889690:undef:undef:undef:undef 9227902213572054824818:9720446483433158:undef:undef:undef:undef 3462926876094537530480:2574937802020480:undef:undef:undef:undef 9457427306463260972168:9418502842830975:7130638537118882:+:2287864305712093:- 1660533730534356942658:76444769176196220:undef:undef:undef:undef 3620302516016020700097:86612568107498304:undef:undef:undef:undef 2931417437711703212621:22758504088523325:8912029597098281:+:13846474491425044:- 3046915016997963694897:259340307336030107:123220057238174932:+:136120250097855175:- 4448448443707697480329:249908228336071142:1907096413910979:+:248001131922160163:- 7812893010168527738415:271153566221059698:undef:undef:undef:undef 1544990484276641899519:3006429639091094575:2470263009561938279:+:536166629529156296:- 1192389794119904167289:8357749089458300900:5292066782423513609:+:3065682307034787291:- 6388434119838448553491:6727713394198264322:2030082226651365897:+:4697631167546898425:- 3716846380578841154646:56493333331807523303:38433721668493223767:+:18059611663314299536:- 4086936601392542350175:12993092317524002002:10781075565330930691:+:2212016752193071311:- 7756826809499740894890:13630419473839181412:undef:undef:undef:undef 7799352049212187293381:754665542213801703886:627062957195215946277:+:127602585018585757609:- 4006015832469367619167:578547324740373465982:468007861874886642005:+:110539462865486823977:- 4221206949096676295898:590610716833518748924:undef:undef:undef:undef 5753938527912127276024:5133482441256109715188:undef:undef:undef:undef 5506207331967874360652:4512388179691757249605:2664015360427888638153:+:1848372819263868611452:- 7166785920987004498828:2740128254235414853280:undef:undef:undef:undef 7531777126692273252450:75549677566006276884881:54185845350578886750719:+:21363832215427390134162:- 4225247981950998099020:30749002023250648659603:6022926981284457099830:+:24726075041966191559773:- 4319562633454669319677:97995545015472199252676:74736050044966539661589:+:23259494970505659591087:- 2537070910191961600896:772462965982135185534304:undef:undef:undef:undef 2698749785802992529208:190020076654053782681067:120404333979494185175410:+:69615742674559597505657:- 8491055145358622945626:647441786171857002296709:32830929819484338894886:+:614610856352372663401823:- 5460001551504418775235:3646253845151233422312019:1608440579291760161891194:+:2037813265859473260420825:- 9407913112559656150356:5620951308692779298843831:2597395277630197001933864:+:3023556031062582296909967:- 3357802138194603213386:7461188232862554481380180:undef:undef:undef:undef 3575011542974564009241:266:29:+:237:- 3002047794987575695002:830:undef:undef:undef:undef 4918856892985336505429:403:114:+:289:- 7750622764021180827828:7918:undef:undef:undef:undef 2725633235355203119157:2074:1643:+:431:- 3123412075700516057895:8607:undef:undef:undef:undef 9686481719098763453527:82203:1807:+:80396:- 7980343316280326035226:41116:undef:undef:undef:undef 4080694656944024838090:72713:21685:+:51028:- 4543716215679952372443:903548:205423:+:698125:- 3683541662014826785795:399080:undef:undef:undef:undef 4357103684637018974727:590817:undef:undef:undef:undef 7246469542416755573756:8038531:7487485:+:551046:- 8614206368349551708945:4782512:3498801:+:1283711:- 2456069606182945176019:7203718:2951783:+:4251935:- 3250688164866423912143:62914602:27817901:+:35096701:- 1254962429834545453295:53865093:32901731:+:20963362:- 6971504891168330605617:62044880:39814513:+:22230367:- 3795588657286113707043:736494918:undef:undef:undef:undef 4643113205071476682302:870749653:53354525:+:817395128:- 4364354391278282795898:236685594:undef:undef:undef:undef 3346189067585829738085:6328379808:2325914221:+:4002465587:- 8703280249357838619967:5913141415:5123205223:+:789936192:- 6580494188519761221661:5844645846:4367761165:+:1476884681:- 8291252866155104652120:42171890144:undef:undef:undef:undef 7010722100907584939383:12987894143:undef:undef:undef:undef 6916473269361729195347:78242066121:39945057125:+:38297008996:- 9982489393403309412559:954234520874:563660750889:+:390573769985:- 7174185876323170063366:877697436224:undef:undef:undef:undef 6311036972687349556678:680661792942:undef:undef:undef:undef 1058274454130136873418:5442236752118:undef:undef:undef:undef 4581810117928278052484:3844711748532:undef:undef:undef:undef 6841409898573512612653:7124428927710:135498912577:+:6988930015133:- 2118344330640610678823:69268332628997:48997836580594:+:20270496048403:- 4308930338606419865761:15806567405363:10217267422814:+:5589299982549:- 6120290225995005358116:91905943552020:undef:undef:undef:undef 6121702826878713662143:398908118950444:71248521474927:+:327659597475517:- 9637687609145294608506:274502458397158:undef:undef:undef:undef 8876007271682114799533:624572847558681:624234760077812:+:338087480869:- 4127547034011543930796:8698843313545464:undef:undef:undef:undef 5249452300394296618070:3767815078124467:2311523892722541:+:1456291185401926:- 2154832440468520679385:5750488679173761:undef:undef:undef:undef 2139341531554656892665:76257659651164788:undef:undef:undef:undef 1412978914201696258549:36540442026846730:32594403769272869:+:3946038257573861:- 1419602346418396189427:18555372006665476:10574818964975195:+:7980553041690281:- 9527289940162145851527:842649885783789032:345795597885112239:+:496854287898676793:- 4622110026844068407312:835436330997561120:undef:undef:undef:undef 5778925857947895116202:564896863387490001:undef:undef:undef:undef 3152841552483974753325:7686805599689267192:1271517839910611757:+:6415287759778655435:- 4569981307889660427099:5225541739657557593:2108880192529718034:+:3116661547127839559:- 6387668328365321786530:1764659485689974621:1341694360853154064:+:422965124836820557:- 1687413314020679257168:89876650301408267308:undef:undef:undef:undef 1232470857547167281956:66788832090488432750:undef:undef:undef:undef 3892164248576509370467:35381650754347142230:32418836648955654903:+:2962814105391487327:- 8624058046969657518849:746248599384453112654:undef:undef:undef:undef 7134421961181730172892:643186897854385150471:346778774574543064508:+:296408123279842085963:- 4439333632535749546384:308198309378221372904:undef:undef:undef:undef 7999695553452878566308:4660402892993960651728:undef:undef:undef:undef 6560820596761192994173:8591323771687685641418:1811967085204785316871:+:6779356686482900324547:- 9198403049364373498442:3740226977806557519011:510227065462374181353:+:3229999912344183337658:- 9572658747105082416395:11991183502499154269091:8054315899216581816245:+:3936867603282572452846:- 1267378080879707738179:30663322734694680665159:undef:undef:undef:undef 5785772173486615785829:78115269268447223522794:49317058575529130804595:+:28798210692918092718199:- 2602821491625501235190:244424982416549482870039:243280043091832552773019:+:1144939324716930097020:- 7595898988159172526221:265353152656109197643545:67359826980341363649771:+:197993325675767833993774:- 4940085938042913688801:848262978758248483228144:589151869344474235044353:+:259111109413774248183791:- 7068231036981475667918:9135929693390387404977861:434637668689909974396674:+:8701292024700477430581187:- 7783103855135276210352:7324361342309366816874017:7119970704057816381511710:+:204390638251550435362307:- 1571095741282499839450:9066288738399053654512098:undef:undef:undef:undef 31827748528677574059460:323:129:+:194:- 68130555795364141468392:599:287:+:312:- 65103013164930796195464:660:undef:undef:undef:undef 97065601613447899809171:9659:7144:+:2515:- 28035457170305099398900:8951:4588:+:4363:- 33221467406768362730414:3062:undef:undef:undef:undef 82778393390177910966120:74559:undef:undef:undef:undef 15762166792325613515903:78653:23001:+:55652:- 85827435022753855564498:47519:8098:+:39421:- 67034508104527773915296:756614:undef:undef:undef:undef 65299738271866793265346:742988:undef:undef:undef:undef 34385482385342915969876:248558:undef:undef:undef:undef 66275300382962440863726:9745572:undef:undef:undef:undef 99712475568816557798282:7232398:undef:undef:undef:undef 39349312681549317176956:9715311:9175795:+:539516:- 57480642105541657834678:44306742:undef:undef:undef:undef 32625484737511546557912:87546575:15954523:+:71592052:- 35208401567020466162610:75307571:30773360:+:44534211:- 22824265018757483694082:663657217:175068291:+:488588926:- 63578939823476281522509:185437488:undef:undef:undef:undef 60490684179748142274988:357271665:304691197:+:52580468:- 80427131525630523437139:8171930468:530972591:+:7640957877:- 84299225076408046769183:3077412139:1135698375:+:1941713764:- 17878952481618810721674:4559165565:undef:undef:undef:undef 89004545574326412531116:42810851955:29502025616:+:13308826339:- 43489813979730336691430:27074074877:6935876468:+:20138198409:- 56050995158598842214705:28091178636:undef:undef:undef:undef 32062714258314191532809:561322493931:116518045781:+:444804448150:- 97100902847288182142313:869373818910:undef:undef:undef:undef 69983764206964929567473:278120062436:246440511197:+:31679551239:- 69580337339742274441532:7662535843930:undef:undef:undef:undef 59839511252980668636066:6594701177494:undef:undef:undef:undef 30459468542352240629860:6407453372858:undef:undef:undef:undef 61250089224658097776631:60258461958713:59149423247614:+:1109038711099:- 12776319084086731390933:68968749906796:58928449266525:+:10040300640271:- 18171434192722220675493:36026778187496:23012460187973:+:13014317999523:- 17322211173226296588714:302257913922052:undef:undef:undef:undef 62527742538401589376333:895074585832651:undef:undef:undef:undef 33424383937819028614690:256080252530417:45035940631086:+:211044311899331:- 16775481034366281796186:5459701512725206:undef:undef:undef:undef 88241767176746591034347:5866935010508119:4814759053581641:+:1052175956926478:- 79086963307459852713001:4245740559885541:2780679683461726:+:1465060876423815:- 74441925600479450179952:81137046166939366:undef:undef:undef:undef 96753060085533547276050:58929624701153932:undef:undef:undef:undef 15081778507283420474218:75563265057607567:52537376008624379:+:23025889048983188:- 79455637996551165199269:414288791040675242:373509065303900125:+:40779725736775117:- 55410240370111916976086:109430081632318887:23477573261090666:+:85952508371228221:- 12603985700297490194334:973836837150783641:276294864346525217:+:697541972804258424:- 41200653521598718148369:2502409121272787556:108723306934489085:+:2393685814338298471:- 46110484348535280031138:9037061699398364373:1222210310644505359:+:7814851388753859014:- 33887344068701194007225:3015554987029259978:1252620467914731507:+:1762934519114528471:- 60973312139906780967285:95265204474688082094:undef:undef:undef:undef 70303735436072392247862:59119679913582544020:undef:undef:undef:undef 35231423872204072728891:93107884939908589434:undef:undef:undef:undef 55098583830819809515511:524860059899952433934:150956120188195290189:+:373903939711757143745:- 79129846760456441736554:741099439573701793909:undef:undef:undef:undef 71370244672885904629021:792581575637158421497:442334646097599490453:+:350246929539558931044:- 62382913438237357910974:8036820378180898616664:undef:undef:undef:undef 26565340352873893298208:5788861009672744197952:undef:undef:undef:undef 87741510877750881136885:2328374905170813666090:undef:undef:undef:undef 64030832752071357402135:90785844432151635631626:undef:undef:undef:undef 23345931807586772721137:18954499656271057168665:7779145136895581592518:+:11175354519375475576147:- 29916081472610117283189:11123269663551540120469:326843131778596466643:+:10796426531772943653826:- 53460053968960153995009:309217493858113798393815:undef:undef:undef:undef 84589026915315410189097:113757022264077646042350:undef:undef:undef:undef 32660194479607446882679:233436018899921166720479:188685500727965412258075:+:44750518171955754462404:- 76069909534299757593737:3086405985400965233313607:1736359014973542706258518:+:1350046970427422527055089:- 34472832926901111132525:6465147265402039673191130:undef:undef:undef:undef 52431210273771446692039:1564764648262925981859887:768564436078172956384577:+:796200212184753025475310:- 18586701600829575529448:460:undef:undef:undef:undef 63229924979706873620692:312:undef:undef:undef:undef 31996954602482607100491:663:undef:undef:undef:undef 21362058576767321716724:8329:7952:+:377:- 37157384617179862363735:2363:1693:+:670:- 80082682147456943718004:9557:6455:+:3102:- 25468052732395570807573:25159:13042:+:12117:- 58735220169865632294941:83336:53781:+:29555:- 95608888017552921494871:34884:undef:undef:undef:undef 40865571926388465583702:493174:undef:undef:undef:undef 65233699349092548925462:815312:undef:undef:undef:undef 89884425685254515283822:321352:undef:undef:undef:undef 45660949768202546527506:7212508:undef:undef:undef:undef 91214396723204404174472:6125147:2799606:+:3325541:- 65085047163118010380539:3666760:2954019:+:712741:- 11593388659505242865577:49840323:undef:undef:undef:undef 24417960854897463154147:48365376:15684811:+:32680565:- 51450080189135324185470:96171864:undef:undef:undef:undef 86775541391838644485635:544405109:334872834:+:209532275:- 19385177748120957985119:945000847:252084283:+:692916564:- 62168125262245427899584:983933265:undef:undef:undef:undef 53491067439481711592366:2828511019:502439625:+:2326071394:- 78388944898480228875500:5860209170:undef:undef:undef:undef 78611678405406648394963:4349777464:2273791363:+:2075986101:- 21505338285442557819631:72096904362:55955903641:+:16141000721:- 99691844204606349482462:69938263567:17620493466:+:52317770101:- 11914783833511848421815:67065264027:undef:undef:undef:undef 73175187931117189650439:100493423395:20662249924:+:79831173471:- 88856866939027959235810:938012583849:245013639781:+:692998944068:- 58954174155822620365071:100947212702:undef:undef:undef:undef 61524225824306974456835:4123849744980:undef:undef:undef:undef 84242417288750291540032:4629337836093:745156804558:+:3884181031535:- 33353419720411607192383:7437722982763:3599651499995:+:3838071482768:- 58561983660017740648278:33057365036189:undef:undef:undef:undef 89945463298399799006041:53678204485224:37693999559065:+:15984204926159:- 89062490909819429128407:38669427295764:undef:undef:undef:undef 12827963036081961760555:639346925698116:160982233838947:+:478364691859169:- 15993569381119190962082:432914612826770:undef:undef:undef:undef 88280067025401417570721:742356056185723:432361488972683:+:309994567213040:- 92839619468720349621981:8124016328463847:4127339068096834:+:3996677260367013:- 36413443402796077638920:5467730994033932:undef:undef:undef:undef 75161842869113372533537:1836917409340579:1813784944790043:+:23132464550536:- 30068849792299829842701:38899823588943365:35696047940414971:+:3203775648528394:- 69107186882279310245288:57716810186408499:46714250475636455:+:11002559710772044:- 61445415328143823314111:69114246541841591:60648522310053432:+:8465724231788159:- 76877388622089734923055:273792677029720872:192391781751976247:+:81400895277744625:- 97061544508572729126834:820263099257987460:undef:undef:undef:undef 85229278420154167201180:479985529541060959:324719401564084366:+:155266127976976593:- 71728109405552987965978:6279939313759678420:undef:undef:undef:undef 42866023983607689846818:5455960434159745302:undef:undef:undef:undef 87269646661294853780466:3777125223388918113:undef:undef:undef:undef 91060217711166228531495:78944026683900079467:undef:undef:undef:undef 49418251336856010001937:64867861139204403277:34154341399403373168:+:30713519739801030109:- 31391108403739303030302:83421022167521449600:undef:undef:undef:undef 93867316695741297791620:621276551885397637919:204091579801566774455:+:417184972083830863464:- 26990915155479675938042:964559948370367634432:undef:undef:undef:undef 48490104784413415094805:727112958937659456268:111723665135302863709:+:615389293802356592559:- 93942015462568640755536:5678901058154739567216:undef:undef:undef:undef 45473802761706396552439:1348525642778066996455:1258568326226430478879:+:89957316551636517576:- 33435314644248146833548:4632474782320500718842:undef:undef:undef:undef 51020306728556862044254:32088874890601663804885:13946409393587184367094:+:18142465497014479437791:- 66353044627958121040340:34389638700152322239657:21510743947489600764987:+:12878894752662721474670:- 39148519604475820040747:21454789281464276741806:17735064239337672929299:+:3719725042126603812507:- 40609083152011441312446:687024763203945469837762:undef:undef:undef:undef 98749349353910550055922:639294304483696901854867:487559902590827129020277:+:151734401892869772834590:- 78829503302916560219849:838353213310689124405054:245629094715793215131339:+:592724118594895909273715:- 12194383708849070263291:6787894226588938163693699:2157777058863685470135464:+:4630117167725252693558235:- 43480371835169636731790:3678488408260467192472700:undef:undef:undef:undef 95334501737544164378205:5443853764717660491532873:4284022501485004383708208:+:1159831263232656107824665:- 19572334068170620221956:289:167:+:122:- 55592113192041441857518:956:undef:undef:undef:undef 67510069015780155945021:930:undef:undef:undef:undef 43913290110343105557261:4710:undef:undef:undef:undef 39833063624006444918074:1097:1061:+:36:- 62382189144113206964024:5015:4049:+:966:- 93720297262645286954550:22205:undef:undef:undef:undef 64325281564324663533166:24882:undef:undef:undef:undef 24516692387459780701696:65413:34428:+:30985:- 85465971442118171138825:636391:363774:+:272617:- 96301239389292360814497:864511:165590:+:698921:- 35293320442037798131200:435842:undef:undef:undef:undef 59339197072027282931374:3674820:undef:undef:undef:undef 86593758584242059975917:6440990:5438353:+:1002637:- 49969888366788653507563:5723729:undef:undef:undef:undef 78337676305285831454419:34176566:24527583:+:9648983:- 12815781626186844573260:48426430:undef:undef:undef:undef 48120930663737526680658:67053522:undef:undef:undef:undef 16800852908706125887652:880676760:undef:undef:undef:undef 28410984064057250050661:973100901:188887220:+:784213681:- 29566935373665536204465:284123521:38078432:+:246045089:- 28103689516585978867696:1808705773:1057623115:+:751082658:- 76941074612252446961551:9958132506:4921648741:+:5036483765:- 18222157607437546023455:8788012092:8191393307:+:596618785:- 50052175730458899895168:39530909850:undef:undef:undef:undef 64610332334449079933744:80850417388:undef:undef:undef:undef 78664266675487346272320:77720207932:undef:undef:undef:undef 61177563312132952894145:742727632276:158166194801:+:584561437475:- 16804560093146747675158:311897504368:undef:undef:undef:undef 55662497696345991662659:130152354070:72565715189:+:57586638881:- 21885463595330223614713:6404750884027:4841028517827:+:1563722366200:- 43354018455135492400870:8948375676946:undef:undef:undef:undef 62595974808706697358516:4844468396795:2088941532551:+:2755526864244:- 10556643094525018913664:99960042542636:undef:undef:undef:undef 27667861726326031846795:20309520896711:1177687835426:+:19131833061285:- 71726486267704076938918:67736883635279:3989524525991:+:63747359109288:- 65130537628778271127452:168490690542227:4192506174550:+:164298184367677:- 55518357035320369610646:431909232560604:undef:undef:undef:undef 70915454260448943180269:864197881396380:743148462239429:+:121049419156951:- 14782779233262435814008:4339986828598729:2467394286356535:+:1872592542242194:- 91727676723328405473009:1223874760331318:191580826209369:+:1032293934121949:- 66153625239884964926525:5841108444700162:3942145353860341:+:1898963090839821:- 48324180831824630962073:42347932028372647:3840809782593912:+:38507122245778735:- 48713498804586142612904:91097188958350630:undef:undef:undef:undef 95818298401702543419654:92139430970158792:undef:undef:undef:undef 68451432397442735310658:777183803845062581:483449611234469835:+:293734192610592746:- 66361342661382655022885:888800464709346329:undef:undef:undef:undef 22768485351905464248412:711005869723783719:203827711517667280:+:507178158206116439:- 99806372206985713374300:5052967339775896691:4424382065419286032:+:628585274356610659:- 10468867024611350563111:4606230531973305864:1596558236506810735:+:3009672295466495129:- 71384655193963866935626:4243994795246118358:undef:undef:undef:undef 94372511278029924560987:35838181597052249518:34250975068387496183:+:1587206528664753335:- 46230710252167124864676:61975866776340683548:undef:undef:undef:undef 15901289350410354243171:83928518227550380384:undef:undef:undef:undef 71387297706391011847731:353371600932869565103:250745627286414167826:+:102625973646455397277:- 86191745316589548906444:425926724179751012630:undef:undef:undef:undef 47362062453366722592870:871230917343112644135:undef:undef:undef:undef 81322237214500514970980:9706388089694071148936:undef:undef:undef:undef 15983452370574578294633:1671398538485916646199:484503398225959992825:+:1186895140259956653374:- 72060774562606935712611:1734846790535446095654:undef:undef:undef:undef 80828350502651299464085:54670584089428058387697:16941546868193973380038:+:37729037221234085007659:- 53589089805800380719939:92923369905362019814937:11784099439554493793541:+:81139270465807526021396:- 97627343358295622087781:84148028432651306932462:69281290733648343016473:+:14866737699002963915989:- 40744363981826236507495:347036573768244689888991:56303003858013388470532:+:290733569910231301418459:- 49100131751740530290551:606507647222932859824643:290249496162059629117412:+:316258151060873230707231:- 45595477716178922598527:931823431457210728444196:369745434213549154935595:+:562077997243661573508601:- 37577684802555632494675:1543246522681766656502903:944618705187086642282002:+:598627817494680014220901:- 39776284731012307189658:7463349581745165925534624:undef:undef:undef:undef 19020265631909290125583:7903039893520121749491308:6750903244034718201262607:+:1152136649485403548228701:- 820097982427154321532606:690:undef:undef:undef:undef 739823242558269779279482:515:393:+:122:- 255662956653376742016745:574:529:+:45:- 502970892308546824114302:1339:350:+:989:- 389302651464611038824842:7519:undef:undef:undef:undef 931132813579743540884936:8702:undef:undef:undef:undef 257194178638699996652876:36390:undef:undef:undef:undef 290212803356672334835941:42449:undef:undef:undef:undef 686978764254942520290318:90109:48431:+:41678:- 632142436897866419497450:794274:undef:undef:undef:undef 155015693713782159194002:814878:undef:undef:undef:undef 808283578764644977119837:726046:126447:+:599599:- 494636210381528377305081:4352579:1015050:+:3337529:- 641012595860961598876830:1451215:undef:undef:undef:undef 986901886972146838011813:8640729:undef:undef:undef:undef 780528497148609360158530:12099702:undef:undef:undef:undef 943633274622801043237132:87304710:undef:undef:undef:undef 178229208511395463331569:39069646:undef:undef:undef:undef 859005433056921169904592:183789660:undef:undef:undef:undef 782721530851908594178769:395671436:158989397:+:236682039:- 162559665393294563859166:537533377:191896182:+:345637195:- 669402900347611185300363:6050161198:2541199043:+:3508962155:- 163461137016253993481244:8470125123:undef:undef:undef:undef 951876797881774425799846:4227282573:2168539510:+:2058743063:- 733087925382323875261589:76902527844:54158858909:+:22743668935:- 373945312922482597869297:79297733522:16617706107:+:62680027415:- 943537646931585332544224:30645097570:undef:undef:undef:undef 729816643977177240032673:691894668088:179718504929:+:512176163159:- 737508322354006012277788:902422486884:undef:undef:undef:undef 411839604354128128190872:684611667817:28219452190:+:656392215627:- 774736145439723276036358:5344405545250:undef:undef:undef:undef 928475480637145488901363:5431979861507:4996051283158:+:435928578349:- 457513888017287326710618:8159869706508:undef:undef:undef:undef 152597111480264996908418:60408276357653:28991596912536:+:31416679445117:- 487669286812443686260118:93237213918994:undef:undef:undef:undef 647825349481322648701912:17671666781480:undef:undef:undef:undef 230318980306829353932155:939011591104562:867903811859965:+:71107779244597:- 634175150417627985364005:610579659015150:undef:undef:undef:undef 628901884903566401419103:504503472698354:407894069557901:+:96609403140453:- 158525826203876893206682:6893760730635719:4667553423914370:+:2226207306721349:- 810249684820806807849569:1438907458826514:947085940241501:+:491821518585013:- 475177611823133016131322:8319567191376515:3085995240091748:+:5233571951284767:- 861236406834460631636295:94270346569311166:33919285628608373:+:60351060940702793:- 731487911065190217596939:23775982180587263:22912109195162332:+:863872985424931:- 958139810611566583073870:33989301896271528:undef:undef:undef:undef 259383033845094387824421:767030348440353734:281288721052560915:+:485741627387792819:- 299971314342690914135600:366810493054114974:undef:undef:undef:undef 310670570650509857699918:614216295424975146:undef:undef:undef:undef 881151124366874677721862:6121134327078652543:4423590291124397790:+:1697544035954254753:- 974240647234201900832216:2397882747091804378:undef:undef:undef:undef 263382548136660766085523:4768311041423937899:undef:undef:undef:undef 894231930819119464433089:19190912766773833789:13748742539904728616:+:5442170226869105173:- 970276548818540222340729:87796125232550799933:undef:undef:undef:undef 750777926807799638664697:44430717993959223276:41542203772533554113:+:2888514221425669163:- 145037632240579178412750:447142343559481975683:undef:undef:undef:undef 726503721540109881290073:553860405500161218224:277249524860453165321:+:276610880639708052903:- 537818243886036501318447:785218629345111118864:451751622708893623199:+:333467006636217495665:- 108174662773249932222988:1517757617648107292193:473173525436100219241:+:1044584092212007072952:- 512226177132536988088725:7362166180698803265738:undef:undef:undef:undef 783777470063501339497325:6217817744880057080618:3861307790477481971421:+:2356509954402575109197:- 729976838311165279743095:69850272431944834943320:undef:undef:undef:undef 625096602518762576367061:46190905020843330846109:10979604194206685530770:+:35211300826636645315339:- 683396443560009229302344:48058984022861929216441:22187921079575037221310:+:25871062943286891995131:- 396277720501534599332679:916273281835814623095204:undef:undef:undef:undef 369514467276877326468657:531213785332089045791147:249796556865280147358180:+:281417228466808898432967:- 470034048772490729525082:194937140903245354354004:undef:undef:undef:undef 927623749343114861034679:7367649270875306870127558:5829739876375899620149153:+:1537909394499407249978405:- 298765618640349494148457:2200420207143751332374124:1323570253581711764700781:+:876849953562039567673343:- 599198399491320750543826:5200333087156216207731082:undef:undef:undef:undef 847223780401083877051197:166:139:+:27:- 407438111032638444701338:922:undef:undef:undef:undef 128243241585057752884789:622:223:+:399:- 470224724971084134055086:3206:undef:undef:undef:undef 263106154966624972009395:4606:2637:+:1969:- 306176201989939817603025:7780:undef:undef:undef:undef 318938098195095211136576:29514:undef:undef:undef:undef 137379744821636365146681:16818:undef:undef:undef:undef 260436758087876389998472:93103:15931:+:77172:- 837489783234868803403883:135339:50042:+:85297:- 275974820836139492296806:195884:undef:undef:undef:undef 754958177909432939234165:275390:undef:undef:undef:undef 385604109882579567774293:7557528:5494877:+:2062651:- 546352384662051732397503:4352437:589563:+:3762874:- 734121918330216324727195:8165224:2461107:+:5704117:- 700614020790900074791294:44628222:undef:undef:undef:undef 708365427972893386410294:64551038:undef:undef:undef:undef 544937695479233032815523:98850949:80404628:+:18446321:- 385025364503459755988429:549859691:60811016:+:489048675:- 528846176519396280977100:688821985:undef:undef:undef:undef 850826172165523602592293:771748927:519487190:+:252261737:- 227934632726641988128357:3386218011:2019744931:+:1366473080:- 475527872870558045444767:9665512855:186535673:+:9478977182:- 382212773543933875209992:2305855638:undef:undef:undef:undef 613357942506429609360416:93095827870:undef:undef:undef:undef 931701096890372860230259:69688993607:47518947805:+:22170045802:- 864696353974067323293307:20517943755:3846940333:+:16671003422:- 196231056201443534648768:701750661214:undef:undef:undef:undef 359624131532739560214259:464775678901:41202189068:+:423573489833:- 789602151436083080859506:663325864257:203109220175:+:460216644082:- 855285483917505149819281:2333005926359:1788591313015:+:544414613344:- 635108159678215348912640:2790279792126:undef:undef:undef:undef 100486921962645605089879:5402237411260:5305003846999:+:97233564261:- 346265900384224100633437:87032195867399:31135053447991:+:55897142419408:- 343984486661892942720025:55027047139392:51172393661929:+:3854653477463:- 142589971492936571773862:69658485423583:undef:undef:undef:undef 664838994936002404532830:651776087852085:undef:undef:undef:undef 255481849874108698131100:705396004837901:536390293208221:+:169005711629680:- 833137238796809541326632:619722749916314:undef:undef:undef:undef 410743094983762039548008:3246897320779598:undef:undef:undef:undef 170570930716075798843642:1579979469606229:272368369046200:+:1307611100560029:- 736160467339746382316756:8184677621075861:1422356152398362:+:6762321468677499:- 592023090947554103184576:27669966231775803:undef:undef:undef:undef 821240872810962217909257:73087984210599046:58113588138918105:+:14974396071680941:- 409896918267349516016030:50244890758751280:undef:undef:undef:undef 969050834772904636420851:236014698941248497:undef:undef:undef:undef 737075905086625366124238:959447252210515455:undef:undef:undef:undef 379286967145392217720924:965964379562850602:undef:undef:undef:undef 224732376964583201872193:1379050590524311214:43032750584536505:+:1336017839939774709:- 271606582283315198887108:6124774640106070681:4394322499097633735:+:1730452141008436946:- 910404069682458590755703:3539057073984257707:3278269367056635052:+:260787706927622655:- 147804160454550991250539:18053376887104528064:14564446948727781251:+:3488929938376746813:- 631742272868624352618518:50802383542292451313:39016081357541364456:+:11786302184751086857:- 447353796451513618583853:20234640903112196500:14763662569229765017:+:5470978333882431483:- 196665228284440403989646:201838432697041024339:31562547896145885223:+:170275884800895139116:- 770512056045392282934056:977236173897559409645:683947713530830595796:+:293288460366728813849:- 974676012677575831761369:245562834952318098971:undef:undef:undef:undef 511796266261247784187472:7730317045507913978216:undef:undef:undef:undef 354454469750200416534075:5595854094948121339802:2613057421853047755937:+:2982796673095073583865:- 890594365083920413293519:9821368076067612939444:undef:undef:undef:undef 145019290237641298384331:10879514788109352095001:189017061236553701291:+:10690497726872798393710:- 734199494018070027002667:17811168765541058358530:17187725167151970918553:+:623443598389087439977:- 130147086581042982015613:66488767968268089619970:29108225899411571610767:+:37380542068856518009203:- 550811529855935663241769:919500853629313843071187:831066978213189465381967:+:88433875416124377689220:- 144532255770003433481190:576779754705724833151101:undef:undef:undef:undef 959718179540650807099792:201517595114281546041688:undef:undef:undef:undef 307460428420924405327070:1132936530861531418052670:undef:undef:undef:undef 578222716636430984297583:3416303657199483318184501:1241961727645381390705435:+:2174341929554101927479066:- 845366848751844019577477:7701553792187984709646852:6001346891031091437194013:+:1700206901156893272452839:- 609401619590114745798467:341:84:+:257:- 158676386684561065636379:667:499:+:168:- 739559676569406957189960:358:undef:undef:undef:undef 831198460883639147740203:1919:736:+:1183:- 386008372405096069854525:8342:1601:+:6741:- 854920204441434068238361:2637:1324:+:1313:- 352747988943091644353092:69019:20552:+:48467:- 992918670308023426472518:30583:7671:+:22912:- 997173824019160124268644:16809:3347:+:13462:- 887429470491606971721699:216755:11944:+:204811:- 619178332960478750267488:183665:122987:+:60678:- 428649352623008502090812:977163:215054:+:762109:- 673982187872938103741206:9336632:undef:undef:undef:undef 100033818279722771914839:8888646:undef:undef:undef:undef 370047487183860740733557:6369436:4262313:+:2107123:- 678123335030884303196067:95791084:undef:undef:undef:undef 415514234477237315719585:38712903:21235717:+:17477186:- 466321327754690473790549:93889154:47860813:+:46028341:- 112915968172603142234272:698961997:148404404:+:550557593:- 242507847403715539726947:609536867:421742610:+:187794257:- 740624899306385542190690:349648917:83547251:+:266101666:- 822421111126799465635363:7425754494:779723689:+:6646030805:- 992462931170332059153357:9699319238:6301141815:+:3398177423:- 125897810797877273242445:7956188805:undef:undef:undef:undef 967063570027466833822241:33920337664:1582024161:+:32338313503:- 636385357417751788167557:34089263104:1757359949:+:32331903155:- 665475133886206812589750:75520177834:undef:undef:undef:undef 895077810131096800730144:889863882577:124742398607:+:765121483970:- 303264420232966670807409:991725671434:702004536151:+:289721135283:- 475075046155244572216662:556518988302:undef:undef:undef:undef 394133247007115236955375:1967780311398:180467355251:+:1787312956147:- 628225545257722449580673:5184391541174:644539353347:+:4539852187827:- 684861216294210069891354:7273210915592:undef:undef:undef:undef 576514408645259039489632:33209123521845:5657780990638:+:27551342531207:- 488133672773697753133262:81019844846651:49511799005053:+:31508045841598:- 938775049978899083023174:63832991091014:undef:undef:undef:undef 553642316401107355029714:821390545102460:undef:undef:undef:undef 895474865627496173343768:247606062782553:undef:undef:undef:undef 109306137382231472614875:268677332547913:87451590059078:+:181225742488835:- 144048458866107032987772:3619940548136499:undef:undef:undef:undef 154063936621984218265901:5728198325719460:364919530740041:+:5363278794979419:- 654404072605172742702726:9812091043664116:undef:undef:undef:undef 145380533532786059416169:45236241482866540:21409191840518189:+:23827049642348351:- 836078401044031746236462:33414289604016478:undef:undef:undef:undef 635944355407754083456819:27100866379886370:22405471121921809:+:4695395257964561:- 894091066852154813342207:641337728215411403:613738054950172923:+:27599673265238480:- 481089093178284178924681:556094214187072904:191065487785479073:+:365028726401593831:- 469317574512921501466100:928969427668446578:undef:undef:undef:undef 783719070289521145299092:1745377744795410338:undef:undef:undef:undef 347687109610734334778482:9449672370594210635:7773052424851581238:+:1676619945742629397:- 777063762229045363729442:1187879651204371064:undef:undef:undef:undef 390014319475461149042166:76855974323230023107:17279572690354178626:+:59576401632875844481:- 141759729595065453849969:64073071728921106196:38187918566749869457:+:25885153162171236739:- 168914319068785242251728:53899984050855461982:undef:undef:undef:undef 293796898072546351765460:412596296820157746574:undef:undef:undef:undef 493039104190669720707527:540114106394556905040:178122968686811915303:+:361991137707744989737:- 399375832539596041502351:568323270277385985962:449319203996833841841:+:119004066280552144121:- 907956090014432360247383:9952433870966270033859:6870286224492154609556:+:3082147646474115424303:- 530529064155784837261748:4915053629775376373827:1448480742033418370471:+:3466572887741958003356:- 488840775159579154386872:6907061502257128169513:4757436614130063074620:+:2149624888127065094893:- 148050873328826216346818:58579573770601188514166:undef:undef:undef:undef 987640026958174561293015:98914944661953458005836:undef:undef:undef:undef 414880490365578965042424:49268435694975108019703:31173904512242695646882:+:18094531182732412372821:- 462606034572395439053367:815046973010413195606422:undef:undef:undef:undef 265638486403213058517673:393831816654373868782106:108522812066684922262199:+:285309004587688946519907:- 759491522794956576600550:101924952303207833168285:undef:undef:undef:undef 217118915218362949208097:4976009853745062094137873:undef:undef:undef:undef 397870340202660993254240:4743301426966512091321828:undef:undef:undef:undef 808703651429004918537717:3079820635185050190105088:1901586945982039092886621:+:1178233689203011097218467:- 9317736453305381928079158:919:356:+:563:- 5739588937057488577399940:176:undef:undef:undef:undef 9380519955894076196579667:173:109:+:64:- 8170118894054335233137800:6324:undef:undef:undef:undef 7834625191844925746503021:3206:undef:undef:undef:undef 1311741365649120492356910:9008:undef:undef:undef:undef 8087218843366809132892466:78412:undef:undef:undef:undef 5047686355101370666121945:36618:23897:+:12721:- 3214866273602577370178601:48466:27611:+:20855:- 5173793381815540802456592:569615:334733:+:234882:- 7665969893761618129770298:754159:103387:+:650772:- 4734207027938738856268237:802087:420877:+:381210:- 7091192102026300077894805:2195560:undef:undef:undef:undef 1315307056771362262092664:6230917:undef:undef:undef:undef 4846151777618298101900464:9540392:undef:undef:undef:undef 2224906245599026265004897:82371985:71961938:+:10410047:- 9398285294755498570929232:18013348:undef:undef:undef:undef 1032541918047187848173228:85695541:67862324:+:17833217:- 2719505786839802571199560:441502939:200047793:+:241455146:- 6450435047666499437288863:953672170:865339487:+:88332683:- 9008371076943797808589103:940292680:370615687:+:569676993:- 4023332769927442020698555:9464836993:3062562552:+:6402274441:- 4786110109041388517454022:9230168853:3551339395:+:5678829458:- 1593946037312439376314600:4892432622:undef:undef:undef:undef 3619197808694129211572231:30668079149:22592397200:+:8075681949:- 7967164303514491286210699:25267887350:13541902799:+:11725984551:- 4219014156022437055628215:94975551369:35915058565:+:59060492804:- 3250215373045582094486962:422040376168:undef:undef:undef:undef 2524365962731804144987890:801616571313:undef:undef:undef:undef 9628977459968111122721783:397681520655:347645050772:+:50036469883:- 7730023417886887234965909:1101305373052:50934227837:+:1050371145215:- 4488444724105399142350554:9590314431792:undef:undef:undef:undef 3456649593507893273063799:5439455514377:5132762506020:+:306693008357:- 6116664815898831791680451:77707358266018:72840239132567:+:4867119133451:- 1649025486620957797865176:40682652695578:undef:undef:undef:undef 3665726501468923190845877:48978801703534:10171689654553:+:38807112048981:- 8437772258543153152748665:714351613126053:178332001339537:+:536019611786516:- 2965460170547740614019150:420107245399249:57756803886519:+:362350441512730:- 1151351831030328105545584:930338679172561:824532009250269:+:105806669922292:- 7770194080666378229911728:2103290573563058:undef:undef:undef:undef 6920242025540177756851195:2492080406595031:1607874629226350:+:884205777368681:- 3570343495385695757049287:8238501910987862:6238116357060739:+:2000385553927123:- 4700573357045150591129124:76749368334228616:undef:undef:undef:undef 5106976737294222503291001:34599738772442239:24066658705399616:+:10533080067042623:- 1141859342339472415876811:15093503687052486:10001878681996601:+:5091625005055885:- 9199964243436686133273982:289927616133301140:undef:undef:undef:undef 5499487122697409016816343:231532659550290934:194647214244324027:+:36885445305966907:- 6671764327345318757427523:383280119887579837:64540781866328034:+:318739338021251803:- 1160188966425519922649272:5086927426831121626:undef:undef:undef:undef 6615891324437526289441729:5740741848777113750:2337289283104579619:+:3403452565672534131:- 2226513737834012247583466:4027475693119198238:undef:undef:undef:undef 9587108098367604941239171:33720655685669415971:15897980193220182743:+:17822675492449233228:- 7925082218346569257913610:16265365411330268492:undef:undef:undef:undef 5725831354815276072553392:28740707117525676027:undef:undef:undef:undef 3110129577646927912317399:620797030510993480598:447908236728056588245:+:172888793782936892353:- 5364602437914966316036180:765514598129553250823:undef:undef:undef:undef 6708623181753027761526065:949030543953759360570:undef:undef:undef:undef 1440480948951891392737103:2831090035165529229601:2691659821261391929800:+:139430213904137299801:- 1981467235582861345941789:5374894143132820205644:5313430200623387999525:+:61463942509432206119:- 7913653686656536686854178:7215612861955802734665:undef:undef:undef:undef 1784118503161975677450334:77518343078520526988940:undef:undef:undef:undef 7442145953264330757180957:77435376881535196004053:11920377786102263932444:+:65514999095432932071609:- 6130028411861449467930940:68458330961277517836862:undef:undef:undef:undef 5095110078878125964186650:426626569285439732348202:undef:undef:undef:undef 7389866522441823648508547:831656833499105992532448:349665759190364595860267:+:481991074308741396672181:- 1726440660013588750134729:960750123062601488327858:undef:undef:undef:undef 3153734587364641998900979:8467972074803429498615434:6562806519482536353978921:+:1905165555320893144636513:- 9754478909976587344788394:7616828586627157450636718:undef:undef:undef:undef 4524422103736733506307551:1985796003852724692831481:917076766779247421280030:+:1068719237073477271551451:- 6471234331070895029215007:444:371:+:73:- 8162744910009756393434558:594:undef:undef:undef:undef 2984896306349942103433598:493:164:+:329:- 1980217166391360154739419:3425:2629:+:796:- 2508646044783168042376965:4157:2970:+:1187:- 1431458164264555100023190:9052:undef:undef:undef:undef 6719706795742063732503172:16818:undef:undef:undef:undef 8596258856676274559258713:49817:43385:+:6432:- 8678473632173225064135444:31430:undef:undef:undef:undef 5260030108109241472100951:268761:20414:+:248347:- 8011131369007802062281143:229711:117077:+:112634:- 3670208861508983100162101:540361:48157:+:492204:- 8717584600724585150988815:2990191:2796867:+:193324:- 2716387285225161380442794:4236203:2220697:+:2015506:- 1519649347369671620114497:8096730:3424513:+:4672217:- 4067227754291382211412539:14271502:undef:undef:undef:undef 3802543398908877736771978:95711698:undef:undef:undef:undef 6981424390525239137459076:76238906:undef:undef:undef:undef 2490040883080788093870716:461167885:108110191:+:353057694:- 7335088584879412842894310:510215709:66039187:+:444176522:- 1015447258250187583008991:754582165:322999791:+:431582374:- 1616533581066783501211997:9469627355:7221034338:+:2248593017:- 3163537073351404881232275:8103273044:5655087871:+:2448185173:- 7260220016661664831795186:7207104211:2555548138:+:4651556073:- 3916542850359391090049508:64558034559:undef:undef:undef:undef 2599545042154170925415943:99538361190:undef:undef:undef:undef 7411140646491865602930584:29848073409:27571361105:+:2276712304:- 5637875495664695856540322:307232798631:70527401311:+:236705397320:- 6476143878746052649173709:968367340434:760702264783:+:207665075651:- 2786735093809363470602520:433986768965:undef:undef:undef:undef 2049426689499601214769090:9662929928587:3718437027034:+:5944492901553:- 7088668040244573311025001:4936615383409:3440335895516:+:1496279487893:- 7501080195731773015057344:3296854200397:2780681465301:+:516172735096:- 2646210077143808398618794:91949632808323:52050886845818:+:39898745962505:- 6670038400096791047702316:12877158837159:undef:undef:undef:undef 3688342936416950137953304:94780313967501:66195866621626:+:28584447345875:- 2101678965089806481118436:528784694402149:524036712699846:+:4747981702303:- 4006542217171850981748385:162214568499679:40211756431585:+:122002812068094:- 8852162033221727637873769:384609249025877:124202136917641:+:260407112108236:- 3564072442333575601678913:2296635808822245:143731162707707:+:2152904646114538:- 3089128196016451311736699:4092462621490379:3789359759016406:+:303102862473973:- 9385371999690302471963669:9267789673919593:7739789783963722:+:1527999889955871:- 4230115811148827220911398:42036024525772508:undef:undef:undef:undef 3582508514080071180906488:42376958311964080:undef:undef:undef:undef 5086919200739908200333366:32427158226747102:undef:undef:undef:undef 8458875544184932090630316:198564860004088489:146612540434329412:+:51952319569759077:- 6593967901465180658499730:963757894010413445:undef:undef:undef:undef 4768405200763469263412236:287164110685459682:undef:undef:undef:undef 8843354549562023373238584:5321670442494936772:undef:undef:undef:undef 3482527184203025284509002:7089254303435144489:4642121523626173875:+:2447132779808970614:- 8183894181866978653110786:7699414630826032366:undef:undef:undef:undef 6648762682672335441428527:77832912267799081479:22877580838673527714:+:54955331429125553765:- 9288309183605316607212790:18207079007393251929:8823880467106598386:+:9383198540286653543:- 9952755731668891447177991:74781889282712854604:7053007174291860363:+:67728882108420994241:- 8435050849560261333912511:588804065295944744886:254536017646284456061:+:334268047649660288825:- 4682427537197600297886716:325907846458788606438:undef:undef:undef:undef 3623142110303962424318910:553272998305307069094:undef:undef:undef:undef 5307727110155784093261493:7192051445801504992939:891344782606092845654:+:6300706663195412147285:- 1039147841469479475590567:4297225734210346362646:1249283897630411684161:+:3047941836579934678485:- 5679474914611408283006122:3457132840190982966199:1503315668162734485553:+:1953817172028248480646:- 8456656318378623098421062:20396825817464359137528:undef:undef:undef:undef 5658294224334920994455317:12904545162613371427011:1248998882685267877567:+:11655546279928103549444:- 3808491221777706807345049:90220236594626894253995:31351651030923707787299:+:58868585563703186466696:- 2606421541588691862064831:357634449571210816302232:77250403867421361031223:+:280384045703789455271009:- 5341387724806038796445531:245777637246256827128370:200249248397865707533811:+:45528388848391119594559:- 9819041733148374840331513:869050111448037176812486:206492080309048217379859:+:662558031138988959432627:- 4536896725457399131526600:1100273252658502666204811:undef:undef:undef:undef 4529685478839375589943314:1371745558150361629227655:1129081371176014891638829:+:242664186974346737588826:- 6277399887254419655061605:2746274189505701524300581:2218590552541321056488789:+:527683636964380467811792:- 9114849943935438597295458:255:undef:undef:undef:undef 2392550500952560939506089:842:143:+:699:- 7550551161740227058350422:706:undef:undef:undef:undef 8952930739943535727261233:6892:161:+:6731:- 4884118571210619630752696:2872:undef:undef:undef:undef 7630427402446440638453497:7901:2046:+:5855:- 7328761789703239043887699:92765:4414:+:88351:- 3291334465854095590507219:87409:60742:+:26667:- 4161018991669490866480300:39421:15656:+:23765:- 6924998632846504865805472:626164:undef:undef:undef:undef 7324045267647673505203849:335646:18523:+:317123:- 1328119757668335709268919:252062:89919:+:162143:- 8456938356401308167653881:6858628:1843505:+:5015123:- 3511941568882462234380235:4557543:1980145:+:2577398:- 2219790616453362838998211:5347927:2057515:+:3290412:- 6010730254593049878855359:40463154:24985781:+:15477373:- 1041484368970393377943348:13712205:13606162:+:106043:- 6466641270199985156947357:34567957:2733445:+:31834512:- 4331513546632376831131999:398053587:338199199:+:59854388:- 8099092496202297903103271:490901688:241606559:+:249295129:- 1108557909998163913819886:975369269:145446241:+:829923028:- 9152695665203419906875304:2709899488:undef:undef:undef:undef 2945301932620832753468542:8197449449:undef:undef:undef:undef 8194403897696393806373671:1428131916:52556263:+:1375575653:- 4392335627454828267631890:60477881046:undef:undef:undef:undef 3761844482815778862698427:62373859921:36125426841:+:26248433080:- 4041951110505829516754901:43584168986:25336461029:+:18247707957:- 7404517239669051427971493:692060527797:425693743327:+:266366784470:- 9471224588912134751642364:567584326187:231701042939:+:335883283248:- 5613970811194291119427806:481460080223:393297452241:+:88162627982:- 9145969185420620229965603:5032508433154:4890250861167:+:142257571987:- 1607684120767321232755179:5989941159009:undef:undef:undef:undef 9816125870946106319992491:5084036885360:130740886851:+:4953295998509:- 3914836415614592914995718:45019999023667:42600250110639:+:2419748913028:- 5736045116501829498149914:72068667311843:4280294215948:+:67788373095895:- 8302367624936167378978059:45828923401792:8075027828387:+:37753895573405:- 7090361086101095567395051:641023903291315:475949685444601:+:165074217846714:- 3915709617053890253781158:657992273250892:undef:undef:undef:undef 9324301051319002976064588:995685901722482:undef:undef:undef:undef 1478705477798155051284289:1179475145902641:1007302295174116:+:172172850728525:- 6180995943012226291946376:1754316715397958:undef:undef:undef:undef 6560603815413685472335497:2443613158246161:undef:undef:undef:undef 7698705757793769711701612:72711202020016389:3251702982055631:+:69459499037960758:- 2178824648174913625649065:75542183877590442:65624069459985157:+:9918114417605285:- 4045446414444027577088529:16270530308567893:14634459909661635:+:1636070398906258:- 7707184705208325610465797:302979673030861794:undef:undef:undef:undef 8647005446316867027981694:789159007922878140:undef:undef:undef:undef 6482706285559587636153780:825509340769610344:undef:undef:undef:undef 9093161669990617254411002:5053075625405783120:undef:undef:undef:undef 2314314959490348198197448:6637404590507564016:undef:undef:undef:undef 4866713974569788800136849:3122574852104245283:1489195220323606794:+:1633379631780638489:- 2999459069753195744252239:87396880394360362662:64189850988690461617:+:23207029405669901045:- 5251750512714252770115663:54688199142721100866:35485172691485513123:+:19203026451235587743:- 2304786397984607120410467:94474508285302549272:undef:undef:undef:undef 9996642661832606868371436:855219411655640533847:332208911741705850371:+:523010499913934683476:- 3306645619353697934006100:177124673540188426602:undef:undef:undef:undef 4273078771505913169450266:740014918990865987017:623538230614438842133:+:116476688376427144884:- 1302837288326744178471685:1072901090995328315405:undef:undef:undef:undef 5667359248811268333339207:9000504074723389312420:1795019218538481413823:+:7205484856184907898597:- 4876812155640947833014323:4912637141287119828780:1263504820461301816967:+:3649132320825818011813:- 3307536909590040567032921:47455737591053000806796:30858735241169364481513:+:16597002349883636325283:- 8447319723342936563578969:15068165777941084653887:undef:undef:undef:undef 8121614101707514230436484:17643950446354870523376:undef:undef:undef:undef 3893939987778225832770180:958659204342321003696714:undef:undef:undef:undef 7628349602295113034298274:777391374791185294549706:undef:undef:undef:undef 4494762906498012086071364:678854691792117721059220:undef:undef:undef:undef 6586163039712296939663435:2722668263032887829140667:269093987195562415070289:+:2453574275837325414070378:- 2741545528274165461648463:4996833048198676901975232:278042837635206017391407:+:4718790210563470884583825:- 3486318671215238622957708:7755318133423599013903404:undef:undef:undef:undef Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_modinv.t0000644403072340010010000000663713024051250024102 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 14523; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_modinv'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0, $out1, $out2, $out3) = @{ $data[$i] }; my ($x, $m, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$m = $LIB->_new("$in1"); | . qq|\@got = $LIB->_modinv(\$x, \$m);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_modinv() in list context: $test", sub { if ($out0 eq "undef") { plan tests => 3; cmp_ok(scalar @got, "==", 2, "'$test' gives two output args"); is($got[0], undef, "'$test' first output arg is undef"); is($got[1], undef, "'$test' second output arg is undef"); } else { plan tests => $scalar_util_ok ? 7 : 6; cmp_ok(scalar @got, "==", 2, "'$test' gives two output args"); is(ref($got[0]), $REF, "'$test' first output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' first output arg is valid"); isnt(refaddr($got[0]), refaddr($m), "'$test' first output arg is not the second input arg") if $scalar_util_ok; is(ref($got[1]), "", "'$test' second output arg is a scalar"); like($got[1], qr/^[+-]\z/, "'$test' second output arg is valid"); my $got = $got[1] . $LIB->_str($got[0]); # prepend sign to value my $alt0 = $out1 . $out0; my $alt1 = $out3 . $out2; ok($got eq $alt0 || $got eq $alt1, "'$test' output args have the right value"); } }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_mul.dat0000644403072340010010000007137713012340550023714 0ustar ospjadomain users37:35:1295 30:590:17700 34:1037:35258 48:98897:4747056 83:828399:68757117 17:6150734:104562478 30:71775210:2153256300 70:550910104:38563707280 75:6044687079:453351530925 86:95833913267:8241716540962 68:946393902563:64354785374284 85:5592090106878:475327659084630 15:79336198786253:1190042981793795 39:994178929580831:38772978253652409 39:1317507036758568:51382774433584152 20:31698055782798918:633961115655978360 38:215949268356886127:8206072197561672826 28:4823970127923114802:135071163581847214456 43:50693696519413137750:2179828950334764923250 23:609743690719070434751:14024104886538619999273 51:4711818582087548081480:240302747686464952155480 46:56462851053735358484582:2597291148471826490290772 34:587970146931945954347789:19990984995686162447824826 666:59:39294 177:197:34869 442:7401:3271242 120:54693:6563160 170:302941:51499970 114:5596785:638033490 908:23147867:21018263236 186:259728669:48309532434 513:5531826885:2837827192005 669:33946156771:22709978879799 378:650536343217:245902737736026 421:1796733377354:756424751866034 387:56828437856727:21992605450553349 836:462338057305251:386514615907189836 618:9305951694357628:5751078147113014104 762:58668765356586059:44705599201718576958 412:501073761224490564:206442389624490112368 607:4142056922420948817:2514228551909515931919 473:95324319954471539074:45088403338465037982002 700:393554009008959521319:275487806306271664923300 788:9849531625834100406992:7761430921157271120709696 567:31023922833513744590415:17590564246602293182765305 182:334051087604083449080600:60797297943943187732669200 1580:27:42660 1139:189:215271 7595:1241:9425395 6894:90594:624555036 6682:102819:687036558 9783:8212178:80339737374 6066:30931555:187630812630 8122:263972950:2143988299900 8112:4592856108:37257248748096 5104:72521200673:370148208234992 5406:448078619369:2422313016308814 6220:9527334318776:59260019462786720 7885:13276466446109:104684937927569465 8561:507330640969791:4343257617342380751 8367:8707238885454274:72853467754595910558 7588:56214338654283540:426554401708703501520 8224:533493520377688707:4387450711586111926368 3280:5738714730609105884:18822984316397867299520 8136:28641385984018317914:233026316365973034548304 3525:522483517779899214559:1841754400174144731320475 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879462582861135078775:691586538:608224482981470543880359530950 153346366209058026219:7292881595:1118336891786169201699572539305 561082234919789413732:84112956396:47194285560378475514742119629872 628199390935398842055:462308279748:290421779762085583268718207202140 163443033149978925040:7969223274771:1302514023877980160596903132165840 763960376318207411693:51346210884471:39226470589814502586886461157519403 510208279950857299137:113307903067107:57810630328707130660119360484186659 375794085192061295829:8821355591142423:3315013254527241941771163075874853667 690397243896706351657:45228415144218675:31225573161384627744313560555056594475 597665234631398017445:725690056193076217:433719717704307309172998745549580605565 915274778985286277519:6551049784225626209:5996010643378717386094772015472333895471 886245380034734690435:26908910693440506485:23847897783828917860071006477846084970975 163519512573947937463:185933063340830680107:30403683888873620696371852824524194148541 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866763631599988517909811:9751:8451812171731488038138567061 488507157189170641306188:58205:28433559084195677177226672540 587056271656377297348857:693829:407316665907072603842260103453 136806881520563038647626:3569592:488344749820749658252256588592 460222903238080690354908:98081778:45139480625912911417476827666424 664977582916897262676267:849271850:564746742052361734533009226183950 270282162669248254861476:6656140161:1799035957744718268862633895337636 405395341521743600434481:62412978050:25301930551968836931645233116142050 878846103724802957457260:887843871649:780278127314667697778499154843221740 284213049936187279021947:5169787155810:1469320975073687135210374259698562070 492616370832257120272687:13187240918407:6496250762516297673685553972157649609 370673675784115570554876:909004850722070:336944169322740947668335805179159313320 229650101674094467614912:7642488986762618:1755098372853182431508993224062780959616 827456040532595888792004:25409784898971678:21025480003288051722316582410385228862712 343969557718545057269512:440369486454872322:151473697488625250954363175572637903246864 635345482877615290350732:4491658345189766182:2853754840245862419140094791573219852545224 137505429192722190108240:12541762225568128394:1724560397659816147472335067588357077366560 590614060935402432985390:618152896748830221976:365089792627809141227768948278780058064930640 881148098425404326931218:2212257061392494626076:1949326102874169597442596997508278865481240568 147236945849167605303264:71030747513813763514778:10458350325317293608074381667119633545235635392 241687167921054996755172:130391714433519082368574:31514004181808176972566532338958068566144764728 # # Big and small numbers: # 0:31415926535897932384626433832795028841:0 1:31415926535897932384626433832795028841:31415926535897932384626433832795028841 2:31415926535897932384626433832795028841:62831853071795864769252867665590057682 31415926535897932384626433832795028841:0:0 31415926535897932384626433832795028841:1:31415926535897932384626433832795028841 31415926535897932384626433832795028841:2:62831853071795864769252867665590057682 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_mul.t0000644403072340010010000001176013024051250023374 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 7541; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_mul'); my @data; # Small numbers. for (my $x = 0; $x <= 24 ; ++ $x) { for (my $y = 0; $y <= 24 ; ++ $y) { push @data, [ $x, $y, $x * $y ]; } } # 9 * 11, 99 * 101, 999 * 1001, 9999 * 1001, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "9" x $p; my $y = "1" . ("0" x ($p - 1)) . "1"; my $z = "9" x (2 * $p); push @data, [ $x, $y, $z ]; } # 9 * 9, 99 * 99, 999 * 999, 9999 * 9999, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "9" x $p; my $z = "9" x ($p - 1) . "8" . "0" x ($p - 1) . "1"; push @data, [ $x, $x, $z ]; } # Powers of 10. for (my $p = 0; $p <= 24 ; ++ $p) { for (my $q = 0; $q <= 24 ; ++ $q) { my $x = "1" . ("0" x $p); my $y = "1" . ("0" x $q); my $z = "1" . ("0" x ($p + $q)); push @data, [ $x, $y, $z ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_mul(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_mul() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_mul(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_mul() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_nok.dat0000644403072340010010000273044413022541212023704 0ustar ospjadomain users# binomial(0, k) for 0 <= k <= 0 0:0:1 # binomial(1, k) for 0 <= k <= 1 1:0:1 1:1:1 # binomial(2, k) for 0 <= k <= 2 2:0:1 2:1:2 2:2:1 # binomial(3, k) for 0 <= k <= 3 3:0:1 3:1:3 3:2:3 3:3:1 # binomial(4, k) for 0 <= k <= 4 4:0:1 4:1:4 4:2:6 4:3:4 4:4:1 # binomial(5, k) for 0 <= k <= 5 5:0:1 5:1:5 5:2:10 5:3:10 5:4:5 5:5:1 # binomial(6, k) for 0 <= k <= 6 6:0:1 6:1:6 6:2:15 6:3:20 6:4:15 6:5:6 6:6:1 # binomial(7, k) for 0 <= k <= 7 7:0:1 7:1:7 7:2:21 7:3:35 7:4:35 7:5:21 7:6:7 7:7:1 # binomial(8, k) for 0 <= k <= 8 8:0:1 8:1:8 8:2:28 8:3:56 8:4:70 8:5:56 8:6:28 8:7:8 8:8:1 # binomial(9, k) for 0 <= k <= 9 9:0:1 9:1:9 9:2:36 9:3:84 9:4:126 9:5:126 9:6:84 9:7:36 9:8:9 9:9:1 # binomial(10, k) for 0 <= k <= 10 10:0:1 10:1:10 10:2:45 10:3:120 10:4:210 10:5:252 10:6:210 10:7:120 10:8:45 10:9:10 10:10:1 # binomial(11, k) for 0 <= k <= 11 11:0:1 11:1:11 11:2:55 11:3:165 11:4:330 11:5:462 11:6:462 11:7:330 11:8:165 11:9:55 11:10:11 11:11:1 # binomial(12, k) for 0 <= k <= 12 12:0:1 12:1:12 12:2:66 12:3:220 12:4:495 12:5:792 12:6:924 12:7:792 12:8:495 12:9:220 12:10:66 12:11:12 12:12:1 # binomial(13, k) for 0 <= k <= 13 13:0:1 13:1:13 13:2:78 13:3:286 13:4:715 13:5:1287 13:6:1716 13:7:1716 13:8:1287 13:9:715 13:10:286 13:11:78 13:12:13 13:13:1 # binomial(14, k) for 0 <= k <= 14 14:0:1 14:1:14 14:2:91 14:3:364 14:4:1001 14:5:2002 14:6:3003 14:7:3432 14:8:3003 14:9:2002 14:10:1001 14:11:364 14:12:91 14:13:14 14:14:1 # binomial(15, k) for 0 <= k <= 15 15:0:1 15:1:15 15:2:105 15:3:455 15:4:1365 15:5:3003 15:6:5005 15:7:6435 15:8:6435 15:9:5005 15:10:3003 15:11:1365 15:12:455 15:13:105 15:14:15 15:15:1 # binomial(16, k) for 0 <= k <= 16 16:0:1 16:1:16 16:2:120 16:3:560 16:4:1820 16:5:4368 16:6:8008 16:7:11440 16:8:12870 16:9:11440 16:10:8008 16:11:4368 16:12:1820 16:13:560 16:14:120 16:15:16 16:16:1 # binomial(17, k) for 0 <= k <= 17 17:0:1 17:1:17 17:2:136 17:3:680 17:4:2380 17:5:6188 17:6:12376 17:7:19448 17:8:24310 17:9:24310 17:10:19448 17:11:12376 17:12:6188 17:13:2380 17:14:680 17:15:136 17:16:17 17:17:1 # binomial(18, k) for 0 <= k <= 18 18:0:1 18:1:18 18:2:153 18:3:816 18:4:3060 18:5:8568 18:6:18564 18:7:31824 18:8:43758 18:9:48620 18:10:43758 18:11:31824 18:12:18564 18:13:8568 18:14:3060 18:15:816 18:16:153 18:17:18 18:18:1 # binomial(19, k) for 0 <= k <= 19 19:0:1 19:1:19 19:2:171 19:3:969 19:4:3876 19:5:11628 19:6:27132 19:7:50388 19:8:75582 19:9:92378 19:10:92378 19:11:75582 19:12:50388 19:13:27132 19:14:11628 19:15:3876 19:16:969 19:17:171 19:18:19 19:19:1 # binomial(20, k) for 0 <= k <= 20 20:0:1 20:1:20 20:2:190 20:3:1140 20:4:4845 20:5:15504 20:6:38760 20:7:77520 20:8:125970 20:9:167960 20:10:184756 20:11:167960 20:12:125970 20:13:77520 20:14:38760 20:15:15504 20:16:4845 20:17:1140 20:18:190 20:19:20 20:20:1 # binomial(21, k) for 0 <= k <= 21 21:0:1 21:1:21 21:2:210 21:3:1330 21:4:5985 21:5:20349 21:6:54264 21:7:116280 21:8:203490 21:9:293930 21:10:352716 21:11:352716 21:12:293930 21:13:203490 21:14:116280 21:15:54264 21:16:20349 21:17:5985 21:18:1330 21:19:210 21:20:21 21:21:1 # binomial(22, k) for 0 <= k <= 22 22:0:1 22:1:22 22:2:231 22:3:1540 22:4:7315 22:5:26334 22:6:74613 22:7:170544 22:8:319770 22:9:497420 22:10:646646 22:11:705432 22:12:646646 22:13:497420 22:14:319770 22:15:170544 22:16:74613 22:17:26334 22:18:7315 22:19:1540 22:20:231 22:21:22 22:22:1 # binomial(23, k) for 0 <= k <= 23 23:0:1 23:1:23 23:2:253 23:3:1771 23:4:8855 23:5:33649 23:6:100947 23:7:245157 23:8:490314 23:9:817190 23:10:1144066 23:11:1352078 23:12:1352078 23:13:1144066 23:14:817190 23:15:490314 23:16:245157 23:17:100947 23:18:33649 23:19:8855 23:20:1771 23:21:253 23:22:23 23:23:1 # binomial(24, k) for 0 <= k <= 24 24:0:1 24:1:24 24:2:276 24:3:2024 24:4:10626 24:5:42504 24:6:134596 24:7:346104 24:8:735471 24:9:1307504 24:10:1961256 24:11:2496144 24:12:2704156 24:13:2496144 24:14:1961256 24:15:1307504 24:16:735471 24:17:346104 24:18:134596 24:19:42504 24:20:10626 24:21:2024 24:22:276 24:23:24 24:24:1 # binomial(25, k) for 0 <= k <= 25 25:0:1 25:1:25 25:2:300 25:3:2300 25:4:12650 25:5:53130 25:6:177100 25:7:480700 25:8:1081575 25:9:2042975 25:10:3268760 25:11:4457400 25:12:5200300 25:13:5200300 25:14:4457400 25:15:3268760 25:16:2042975 25:17:1081575 25:18:480700 25:19:177100 25:20:53130 25:21:12650 25:22:2300 25:23:300 25:24:25 25:25:1 # binomial(26, k) for 0 <= k <= 26 26:0:1 26:1:26 26:2:325 26:3:2600 26:4:14950 26:5:65780 26:6:230230 26:7:657800 26:8:1562275 26:9:3124550 26:10:5311735 26:11:7726160 26:12:9657700 26:13:10400600 26:14:9657700 26:15:7726160 26:16:5311735 26:17:3124550 26:18:1562275 26:19:657800 26:20:230230 26:21:65780 26:22:14950 26:23:2600 26:24:325 26:25:26 26:26:1 # binomial(27, k) for 0 <= k <= 27 27:0:1 27:1:27 27:2:351 27:3:2925 27:4:17550 27:5:80730 27:6:296010 27:7:888030 27:8:2220075 27:9:4686825 27:10:8436285 27:11:13037895 27:12:17383860 27:13:20058300 27:14:20058300 27:15:17383860 27:16:13037895 27:17:8436285 27:18:4686825 27:19:2220075 27:20:888030 27:21:296010 27:22:80730 27:23:17550 27:24:2925 27:25:351 27:26:27 27:27:1 # binomial(28, k) for 0 <= k <= 28 28:0:1 28:1:28 28:2:378 28:3:3276 28:4:20475 28:5:98280 28:6:376740 28:7:1184040 28:8:3108105 28:9:6906900 28:10:13123110 28:11:21474180 28:12:30421755 28:13:37442160 28:14:40116600 28:15:37442160 28:16:30421755 28:17:21474180 28:18:13123110 28:19:6906900 28:20:3108105 28:21:1184040 28:22:376740 28:23:98280 28:24:20475 28:25:3276 28:26:378 28:27:28 28:28:1 # binomial(29, k) for 0 <= k <= 29 29:0:1 29:1:29 29:2:406 29:3:3654 29:4:23751 29:5:118755 29:6:475020 29:7:1560780 29:8:4292145 29:9:10015005 29:10:20030010 29:11:34597290 29:12:51895935 29:13:67863915 29:14:77558760 29:15:77558760 29:16:67863915 29:17:51895935 29:18:34597290 29:19:20030010 29:20:10015005 29:21:4292145 29:22:1560780 29:23:475020 29:24:118755 29:25:23751 29:26:3654 29:27:406 29:28:29 29:29:1 # binomial(30, k) for 0 <= k <= 30 30:0:1 30:1:30 30:2:435 30:3:4060 30:4:27405 30:5:142506 30:6:593775 30:7:2035800 30:8:5852925 30:9:14307150 30:10:30045015 30:11:54627300 30:12:86493225 30:13:119759850 30:14:145422675 30:15:155117520 30:16:145422675 30:17:119759850 30:18:86493225 30:19:54627300 30:20:30045015 30:21:14307150 30:22:5852925 30:23:2035800 30:24:593775 30:25:142506 30:26:27405 30:27:4060 30:28:435 30:29:30 30:30:1 # binomial(31, k) for 0 <= k <= 31 31:0:1 31:1:31 31:2:465 31:3:4495 31:4:31465 31:5:169911 31:6:736281 31:7:2629575 31:8:7888725 31:9:20160075 31:10:44352165 31:11:84672315 31:12:141120525 31:13:206253075 31:14:265182525 31:15:300540195 31:16:300540195 31:17:265182525 31:18:206253075 31:19:141120525 31:20:84672315 31:21:44352165 31:22:20160075 31:23:7888725 31:24:2629575 31:25:736281 31:26:169911 31:27:31465 31:28:4495 31:29:465 31:30:31 31:31:1 # binomial(32, k) for 0 <= k <= 32 32:0:1 32:1:32 32:2:496 32:3:4960 32:4:35960 32:5:201376 32:6:906192 32:7:3365856 32:8:10518300 32:9:28048800 32:10:64512240 32:11:129024480 32:12:225792840 32:13:347373600 32:14:471435600 32:15:565722720 32:16:601080390 32:17:565722720 32:18:471435600 32:19:347373600 32:20:225792840 32:21:129024480 32:22:64512240 32:23:28048800 32:24:10518300 32:25:3365856 32:26:906192 32:27:201376 32:28:35960 32:29:4960 32:30:496 32:31:32 32:32:1 # binomial(33, k) for 0 <= k <= 33 33:0:1 33:1:33 33:2:528 33:3:5456 33:4:40920 33:5:237336 33:6:1107568 33:7:4272048 33:8:13884156 33:9:38567100 33:10:92561040 33:11:193536720 33:12:354817320 33:13:573166440 33:14:818809200 33:15:1037158320 33:16:1166803110 33:17:1166803110 33:18:1037158320 33:19:818809200 33:20:573166440 33:21:354817320 33:22:193536720 33:23:92561040 33:24:38567100 33:25:13884156 33:26:4272048 33:27:1107568 33:28:237336 33:29:40920 33:30:5456 33:31:528 33:32:33 33:33:1 # binomial(34, k) for 0 <= k <= 34 34:0:1 34:1:34 34:2:561 34:3:5984 34:4:46376 34:5:278256 34:6:1344904 34:7:5379616 34:8:18156204 34:9:52451256 34:10:131128140 34:11:286097760 34:12:548354040 34:13:927983760 34:14:1391975640 34:15:1855967520 34:16:2203961430 34:17:2333606220 34:18:2203961430 34:19:1855967520 34:20:1391975640 34:21:927983760 34:22:548354040 34:23:286097760 34:24:131128140 34:25:52451256 34:26:18156204 34:27:5379616 34:28:1344904 34:29:278256 34:30:46376 34:31:5984 34:32:561 34:33:34 34:34:1 # binomial(35, k) for 0 <= k <= 35 35:0:1 35:1:35 35:2:595 35:3:6545 35:4:52360 35:5:324632 35:6:1623160 35:7:6724520 35:8:23535820 35:9:70607460 35:10:183579396 35:11:417225900 35:12:834451800 35:13:1476337800 35:14:2319959400 35:15:3247943160 35:16:4059928950 35:17:4537567650 35:18:4537567650 35:19:4059928950 35:20:3247943160 35:21:2319959400 35:22:1476337800 35:23:834451800 35:24:417225900 35:25:183579396 35:26:70607460 35:27:23535820 35:28:6724520 35:29:1623160 35:30:324632 35:31:52360 35:32:6545 35:33:595 35:34:35 35:35:1 # binomial(36, k) for 0 <= k <= 36 36:0:1 36:1:36 36:2:630 36:3:7140 36:4:58905 36:5:376992 36:6:1947792 36:7:8347680 36:8:30260340 36:9:94143280 36:10:254186856 36:11:600805296 36:12:1251677700 36:13:2310789600 36:14:3796297200 36:15:5567902560 36:16:7307872110 36:17:8597496600 36:18:9075135300 36:19:8597496600 36:20:7307872110 36:21:5567902560 36:22:3796297200 36:23:2310789600 36:24:1251677700 36:25:600805296 36:26:254186856 36:27:94143280 36:28:30260340 36:29:8347680 36:30:1947792 36:31:376992 36:32:58905 36:33:7140 36:34:630 36:35:36 36:36:1 # binomial(37, k) for 0 <= k <= 37 37:0:1 37:1:37 37:2:666 37:3:7770 37:4:66045 37:5:435897 37:6:2324784 37:7:10295472 37:8:38608020 37:9:124403620 37:10:348330136 37:11:854992152 37:12:1852482996 37:13:3562467300 37:14:6107086800 37:15:9364199760 37:16:12875774670 37:17:15905368710 37:18:17672631900 37:19:17672631900 37:20:15905368710 37:21:12875774670 37:22:9364199760 37:23:6107086800 37:24:3562467300 37:25:1852482996 37:26:854992152 37:27:348330136 37:28:124403620 37:29:38608020 37:30:10295472 37:31:2324784 37:32:435897 37:33:66045 37:34:7770 37:35:666 37:36:37 37:37:1 # binomial(38, k) for 0 <= k <= 38 38:0:1 38:1:38 38:2:703 38:3:8436 38:4:73815 38:5:501942 38:6:2760681 38:7:12620256 38:8:48903492 38:9:163011640 38:10:472733756 38:11:1203322288 38:12:2707475148 38:13:5414950296 38:14:9669554100 38:15:15471286560 38:16:22239974430 38:17:28781143380 38:18:33578000610 38:19:35345263800 38:20:33578000610 38:21:28781143380 38:22:22239974430 38:23:15471286560 38:24:9669554100 38:25:5414950296 38:26:2707475148 38:27:1203322288 38:28:472733756 38:29:163011640 38:30:48903492 38:31:12620256 38:32:2760681 38:33:501942 38:34:73815 38:35:8436 38:36:703 38:37:38 38:38:1 # binomial(39, k) for 0 <= k <= 39 39:0:1 39:1:39 39:2:741 39:3:9139 39:4:82251 39:5:575757 39:6:3262623 39:7:15380937 39:8:61523748 39:9:211915132 39:10:635745396 39:11:1676056044 39:12:3910797436 39:13:8122425444 39:14:15084504396 39:15:25140840660 39:16:37711260990 39:17:51021117810 39:18:62359143990 39:19:68923264410 39:20:68923264410 39:21:62359143990 39:22:51021117810 39:23:37711260990 39:24:25140840660 39:25:15084504396 39:26:8122425444 39:27:3910797436 39:28:1676056044 39:29:635745396 39:30:211915132 39:31:61523748 39:32:15380937 39:33:3262623 39:34:575757 39:35:82251 39:36:9139 39:37:741 39:38:39 39:39:1 # binomial(40, k) for 0 <= k <= 40 40:0:1 40:1:40 40:2:780 40:3:9880 40:4:91390 40:5:658008 40:6:3838380 40:7:18643560 40:8:76904685 40:9:273438880 40:10:847660528 40:11:2311801440 40:12:5586853480 40:13:12033222880 40:14:23206929840 40:15:40225345056 40:16:62852101650 40:17:88732378800 40:18:113380261800 40:19:131282408400 40:20:137846528820 40:21:131282408400 40:22:113380261800 40:23:88732378800 40:24:62852101650 40:25:40225345056 40:26:23206929840 40:27:12033222880 40:28:5586853480 40:29:2311801440 40:30:847660528 40:31:273438880 40:32:76904685 40:33:18643560 40:34:3838380 40:35:658008 40:36:91390 40:37:9880 40:38:780 40:39:40 40:40:1 # binomial(41, k) for 0 <= k <= 41 41:0:1 41:1:41 41:2:820 41:3:10660 41:4:101270 41:5:749398 41:6:4496388 41:7:22481940 41:8:95548245 41:9:350343565 41:10:1121099408 41:11:3159461968 41:12:7898654920 41:13:17620076360 41:14:35240152720 41:15:63432274896 41:16:103077446706 41:17:151584480450 41:18:202112640600 41:19:244662670200 41:20:269128937220 41:21:269128937220 41:22:244662670200 41:23:202112640600 41:24:151584480450 41:25:103077446706 41:26:63432274896 41:27:35240152720 41:28:17620076360 41:29:7898654920 41:30:3159461968 41:31:1121099408 41:32:350343565 41:33:95548245 41:34:22481940 41:35:4496388 41:36:749398 41:37:101270 41:38:10660 41:39:820 41:40:41 41:41:1 # binomial(42, k) for 0 <= k <= 42 42:0:1 42:1:42 42:2:861 42:3:11480 42:4:111930 42:5:850668 42:6:5245786 42:7:26978328 42:8:118030185 42:9:445891810 42:10:1471442973 42:11:4280561376 42:12:11058116888 42:13:25518731280 42:14:52860229080 42:15:98672427616 42:16:166509721602 42:17:254661927156 42:18:353697121050 42:19:446775310800 42:20:513791607420 42:21:538257874440 42:22:513791607420 42:23:446775310800 42:24:353697121050 42:25:254661927156 42:26:166509721602 42:27:98672427616 42:28:52860229080 42:29:25518731280 42:30:11058116888 42:31:4280561376 42:32:1471442973 42:33:445891810 42:34:118030185 42:35:26978328 42:36:5245786 42:37:850668 42:38:111930 42:39:11480 42:40:861 42:41:42 42:42:1 # binomial(43, k) for 0 <= k <= 43 43:0:1 43:1:43 43:2:903 43:3:12341 43:4:123410 43:5:962598 43:6:6096454 43:7:32224114 43:8:145008513 43:9:563921995 43:10:1917334783 43:11:5752004349 43:12:15338678264 43:13:36576848168 43:14:78378960360 43:15:151532656696 43:16:265182149218 43:17:421171648758 43:18:608359048206 43:19:800472431850 43:20:960566918220 43:21:1052049481860 43:22:1052049481860 43:23:960566918220 43:24:800472431850 43:25:608359048206 43:26:421171648758 43:27:265182149218 43:28:151532656696 43:29:78378960360 43:30:36576848168 43:31:15338678264 43:32:5752004349 43:33:1917334783 43:34:563921995 43:35:145008513 43:36:32224114 43:37:6096454 43:38:962598 43:39:123410 43:40:12341 43:41:903 43:42:43 43:43:1 # binomial(44, k) for 0 <= k <= 44 44:0:1 44:1:44 44:2:946 44:3:13244 44:4:135751 44:5:1086008 44:6:7059052 44:7:38320568 44:8:177232627 44:9:708930508 44:10:2481256778 44:11:7669339132 44:12:21090682613 44:13:51915526432 44:14:114955808528 44:15:229911617056 44:16:416714805914 44:17:686353797976 44:18:1029530696964 44:19:1408831480056 44:20:1761039350070 44:21:2012616400080 44:22:2104098963720 44:23:2012616400080 44:24:1761039350070 44:25:1408831480056 44:26:1029530696964 44:27:686353797976 44:28:416714805914 44:29:229911617056 44:30:114955808528 44:31:51915526432 44:32:21090682613 44:33:7669339132 44:34:2481256778 44:35:708930508 44:36:177232627 44:37:38320568 44:38:7059052 44:39:1086008 44:40:135751 44:41:13244 44:42:946 44:43:44 44:44:1 # binomial(45, k) for 0 <= k <= 45 45:0:1 45:1:45 45:2:990 45:3:14190 45:4:148995 45:5:1221759 45:6:8145060 45:7:45379620 45:8:215553195 45:9:886163135 45:10:3190187286 45:11:10150595910 45:12:28760021745 45:13:73006209045 45:14:166871334960 45:15:344867425584 45:16:646626422970 45:17:1103068603890 45:18:1715884494940 45:19:2438362177020 45:20:3169870830126 45:21:3773655750150 45:22:4116715363800 45:23:4116715363800 45:24:3773655750150 45:25:3169870830126 45:26:2438362177020 45:27:1715884494940 45:28:1103068603890 45:29:646626422970 45:30:344867425584 45:31:166871334960 45:32:73006209045 45:33:28760021745 45:34:10150595910 45:35:3190187286 45:36:886163135 45:37:215553195 45:38:45379620 45:39:8145060 45:40:1221759 45:41:148995 45:42:14190 45:43:990 45:44:45 45:45:1 # binomial(46, k) for 0 <= k <= 46 46:0:1 46:1:46 46:2:1035 46:3:15180 46:4:163185 46:5:1370754 46:6:9366819 46:7:53524680 46:8:260932815 46:9:1101716330 46:10:4076350421 46:11:13340783196 46:12:38910617655 46:13:101766230790 46:14:239877544005 46:15:511738760544 46:16:991493848554 46:17:1749695026860 46:18:2818953098830 46:19:4154246671960 46:20:5608233007146 46:21:6943526580276 46:22:7890371113950 46:23:8233430727600 46:24:7890371113950 46:25:6943526580276 46:26:5608233007146 46:27:4154246671960 46:28:2818953098830 46:29:1749695026860 46:30:991493848554 46:31:511738760544 46:32:239877544005 46:33:101766230790 46:34:38910617655 46:35:13340783196 46:36:4076350421 46:37:1101716330 46:38:260932815 46:39:53524680 46:40:9366819 46:41:1370754 46:42:163185 46:43:15180 46:44:1035 46:45:46 46:46:1 # binomial(47, k) for 0 <= k <= 47 47:0:1 47:1:47 47:2:1081 47:3:16215 47:4:178365 47:5:1533939 47:6:10737573 47:7:62891499 47:8:314457495 47:9:1362649145 47:10:5178066751 47:11:17417133617 47:12:52251400851 47:13:140676848445 47:14:341643774795 47:15:751616304549 47:16:1503232609098 47:17:2741188875414 47:18:4568648125690 47:19:6973199770790 47:20:9762479679106 47:21:12551759587422 47:22:14833897694226 47:23:16123801841550 47:24:16123801841550 47:25:14833897694226 47:26:12551759587422 47:27:9762479679106 47:28:6973199770790 47:29:4568648125690 47:30:2741188875414 47:31:1503232609098 47:32:751616304549 47:33:341643774795 47:34:140676848445 47:35:52251400851 47:36:17417133617 47:37:5178066751 47:38:1362649145 47:39:314457495 47:40:62891499 47:41:10737573 47:42:1533939 47:43:178365 47:44:16215 47:45:1081 47:46:47 47:47:1 # binomial(48, k) for 0 <= k <= 48 48:0:1 48:1:48 48:2:1128 48:3:17296 48:4:194580 48:5:1712304 48:6:12271512 48:7:73629072 48:8:377348994 48:9:1677106640 48:10:6540715896 48:11:22595200368 48:12:69668534468 48:13:192928249296 48:14:482320623240 48:15:1093260079344 48:16:2254848913647 48:17:4244421484512 48:18:7309837001104 48:19:11541847896480 48:20:16735679449896 48:21:22314239266528 48:22:27385657281648 48:23:30957699535776 48:24:32247603683100 48:25:30957699535776 48:26:27385657281648 48:27:22314239266528 48:28:16735679449896 48:29:11541847896480 48:30:7309837001104 48:31:4244421484512 48:32:2254848913647 48:33:1093260079344 48:34:482320623240 48:35:192928249296 48:36:69668534468 48:37:22595200368 48:38:6540715896 48:39:1677106640 48:40:377348994 48:41:73629072 48:42:12271512 48:43:1712304 48:44:194580 48:45:17296 48:46:1128 48:47:48 48:48:1 # binomial(49, k) for 0 <= k <= 49 49:0:1 49:1:49 49:2:1176 49:3:18424 49:4:211876 49:5:1906884 49:6:13983816 49:7:85900584 49:8:450978066 49:9:2054455634 49:10:8217822536 49:11:29135916264 49:12:92263734836 49:13:262596783764 49:14:675248872536 49:15:1575580702584 49:16:3348108992991 49:17:6499270398159 49:18:11554258485616 49:19:18851684897584 49:20:28277527346376 49:21:39049918716424 49:22:49699896548176 49:23:58343356817424 49:24:63205303218876 49:25:63205303218876 49:26:58343356817424 49:27:49699896548176 49:28:39049918716424 49:29:28277527346376 49:30:18851684897584 49:31:11554258485616 49:32:6499270398159 49:33:3348108992991 49:34:1575580702584 49:35:675248872536 49:36:262596783764 49:37:92263734836 49:38:29135916264 49:39:8217822536 49:40:2054455634 49:41:450978066 49:42:85900584 49:43:13983816 49:44:1906884 49:45:211876 49:46:18424 49:47:1176 49:48:49 49:49:1 # binomial(50, k) for 0 <= k <= 50 50:0:1 50:1:50 50:2:1225 50:3:19600 50:4:230300 50:5:2118760 50:6:15890700 50:7:99884400 50:8:536878650 50:9:2505433700 50:10:10272278170 50:11:37353738800 50:12:121399651100 50:13:354860518600 50:14:937845656300 50:15:2250829575120 50:16:4923689695575 50:17:9847379391150 50:18:18053528883775 50:19:30405943383200 50:20:47129212243960 50:21:67327446062800 50:22:88749815264600 50:23:108043253365600 50:24:121548660036300 50:25:126410606437752 50:26:121548660036300 50:27:108043253365600 50:28:88749815264600 50:29:67327446062800 50:30:47129212243960 50:31:30405943383200 50:32:18053528883775 50:33:9847379391150 50:34:4923689695575 50:35:2250829575120 50:36:937845656300 50:37:354860518600 50:38:121399651100 50:39:37353738800 50:40:10272278170 50:41:2505433700 50:42:536878650 50:43:99884400 50:44:15890700 50:45:2118760 50:46:230300 50:47:19600 50:48:1225 50:49:50 50:50:1 # binomial(51, k) for 0 <= k <= 51 51:0:1 51:1:51 51:2:1275 51:3:20825 51:4:249900 51:5:2349060 51:6:18009460 51:7:115775100 51:8:636763050 51:9:3042312350 51:10:12777711870 51:11:47626016970 51:12:158753389900 51:13:476260169700 51:14:1292706174900 51:15:3188675231420 51:16:7174519270695 51:17:14771069086725 51:18:27900908274925 51:19:48459472266975 51:20:77535155627160 51:21:114456658306760 51:22:156077261327400 51:23:196793068630200 51:24:229591913401900 51:25:247959266474052 51:26:247959266474052 51:27:229591913401900 51:28:196793068630200 51:29:156077261327400 51:30:114456658306760 51:31:77535155627160 51:32:48459472266975 51:33:27900908274925 51:34:14771069086725 51:35:7174519270695 51:36:3188675231420 51:37:1292706174900 51:38:476260169700 51:39:158753389900 51:40:47626016970 51:41:12777711870 51:42:3042312350 51:43:636763050 51:44:115775100 51:45:18009460 51:46:2349060 51:47:249900 51:48:20825 51:49:1275 51:50:51 51:51:1 # binomial(52, k) for 0 <= k <= 52 52:0:1 52:1:52 52:2:1326 52:3:22100 52:4:270725 52:5:2598960 52:6:20358520 52:7:133784560 52:8:752538150 52:9:3679075400 52:10:15820024220 52:11:60403728840 52:12:206379406870 52:13:635013559600 52:14:1768966344600 52:15:4481381406320 52:16:10363194502115 52:17:21945588357420 52:18:42671977361650 52:19:76360380541900 52:20:125994627894135 52:21:191991813933920 52:22:270533919634160 52:23:352870329957600 52:24:426384982032100 52:25:477551179875952 52:26:495918532948104 52:27:477551179875952 52:28:426384982032100 52:29:352870329957600 52:30:270533919634160 52:31:191991813933920 52:32:125994627894135 52:33:76360380541900 52:34:42671977361650 52:35:21945588357420 52:36:10363194502115 52:37:4481381406320 52:38:1768966344600 52:39:635013559600 52:40:206379406870 52:41:60403728840 52:42:15820024220 52:43:3679075400 52:44:752538150 52:45:133784560 52:46:20358520 52:47:2598960 52:48:270725 52:49:22100 52:50:1326 52:51:52 52:52:1 # binomial(53, k) for 0 <= k <= 53 53:0:1 53:1:53 53:2:1378 53:3:23426 53:4:292825 53:5:2869685 53:6:22957480 53:7:154143080 53:8:886322710 53:9:4431613550 53:10:19499099620 53:11:76223753060 53:12:266783135710 53:13:841392966470 53:14:2403979904200 53:15:6250347750920 53:16:14844575908435 53:17:32308782859535 53:18:64617565719070 53:19:119032357903550 53:20:202355008436035 53:21:317986441828055 53:22:462525733568080 53:23:623404249591760 53:24:779255311989700 53:25:903936161908052 53:26:973469712824056 53:27:973469712824056 53:28:903936161908052 53:29:779255311989700 53:30:623404249591760 53:31:462525733568080 53:32:317986441828055 53:33:202355008436035 53:34:119032357903550 53:35:64617565719070 53:36:32308782859535 53:37:14844575908435 53:38:6250347750920 53:39:2403979904200 53:40:841392966470 53:41:266783135710 53:42:76223753060 53:43:19499099620 53:44:4431613550 53:45:886322710 53:46:154143080 53:47:22957480 53:48:2869685 53:49:292825 53:50:23426 53:51:1378 53:52:53 53:53:1 # binomial(54, k) for 0 <= k <= 54 54:0:1 54:1:54 54:2:1431 54:3:24804 54:4:316251 54:5:3162510 54:6:25827165 54:7:177100560 54:8:1040465790 54:9:5317936260 54:10:23930713170 54:11:95722852680 54:12:343006888770 54:13:1108176102180 54:14:3245372870670 54:15:8654327655120 54:16:21094923659355 54:17:47153358767970 54:18:96926348578605 54:19:183649923622620 54:20:321387366339585 54:21:520341450264090 54:22:780512175396135 54:23:1085929983159840 54:24:1402659561581460 54:25:1683191473897752 54:26:1877405874732108 54:27:1946939425648112 54:28:1877405874732108 54:29:1683191473897752 54:30:1402659561581460 54:31:1085929983159840 54:32:780512175396135 54:33:520341450264090 54:34:321387366339585 54:35:183649923622620 54:36:96926348578605 54:37:47153358767970 54:38:21094923659355 54:39:8654327655120 54:40:3245372870670 54:41:1108176102180 54:42:343006888770 54:43:95722852680 54:44:23930713170 54:45:5317936260 54:46:1040465790 54:47:177100560 54:48:25827165 54:49:3162510 54:50:316251 54:51:24804 54:52:1431 54:53:54 54:54:1 # binomial(55, k) for 0 <= k <= 55 55:0:1 55:1:55 55:2:1485 55:3:26235 55:4:341055 55:5:3478761 55:6:28989675 55:7:202927725 55:8:1217566350 55:9:6358402050 55:10:29248649430 55:11:119653565850 55:12:438729741450 55:13:1451182990950 55:14:4353548972850 55:15:11899700525790 55:16:29749251314475 55:17:68248282427325 55:18:144079707346575 55:19:280576272201225 55:20:505037289962205 55:21:841728816603675 55:22:1300853625660225 55:23:1866442158555975 55:24:2488589544741300 55:25:3085851035479212 55:26:3560597348629860 55:27:3824345300380220 55:28:3824345300380220 55:29:3560597348629860 55:30:3085851035479212 55:31:2488589544741300 55:32:1866442158555975 55:33:1300853625660225 55:34:841728816603675 55:35:505037289962205 55:36:280576272201225 55:37:144079707346575 55:38:68248282427325 55:39:29749251314475 55:40:11899700525790 55:41:4353548972850 55:42:1451182990950 55:43:438729741450 55:44:119653565850 55:45:29248649430 55:46:6358402050 55:47:1217566350 55:48:202927725 55:49:28989675 55:50:3478761 55:51:341055 55:52:26235 55:53:1485 55:54:55 55:55:1 # binomial(56, k) for 0 <= k <= 56 56:0:1 56:1:56 56:2:1540 56:3:27720 56:4:367290 56:5:3819816 56:6:32468436 56:7:231917400 56:8:1420494075 56:9:7575968400 56:10:35607051480 56:11:148902215280 56:12:558383307300 56:13:1889912732400 56:14:5804731963800 56:15:16253249498640 56:16:41648951840265 56:17:97997533741800 56:18:212327989773900 56:19:424655979547800 56:20:785613562163430 56:21:1346766106565880 56:22:2142582442263900 56:23:3167295784216200 56:24:4355031703297275 56:25:5574440580220512 56:26:6646448384109072 56:27:7384942649010080 56:28:7648690600760440 56:29:7384942649010080 56:30:6646448384109072 56:31:5574440580220512 56:32:4355031703297275 56:33:3167295784216200 56:34:2142582442263900 56:35:1346766106565880 56:36:785613562163430 56:37:424655979547800 56:38:212327989773900 56:39:97997533741800 56:40:41648951840265 56:41:16253249498640 56:42:5804731963800 56:43:1889912732400 56:44:558383307300 56:45:148902215280 56:46:35607051480 56:47:7575968400 56:48:1420494075 56:49:231917400 56:50:32468436 56:51:3819816 56:52:367290 56:53:27720 56:54:1540 56:55:56 56:56:1 # binomial(57, k) for 0 <= k <= 57 57:0:1 57:1:57 57:2:1596 57:3:29260 57:4:395010 57:5:4187106 57:6:36288252 57:7:264385836 57:8:1652411475 57:9:8996462475 57:10:43183019880 57:11:184509266760 57:12:707285522580 57:13:2448296039700 57:14:7694644696200 57:15:22057981462440 57:16:57902201338905 57:17:139646485582065 57:18:310325523515700 57:19:636983969321700 57:20:1210269541711230 57:21:2132379668729310 57:22:3489348548829780 57:23:5309878226480100 57:24:7522327487513475 57:25:9929472283517787 57:26:12220888964329584 57:27:14031391033119152 57:28:15033633249770520 57:29:15033633249770520 57:30:14031391033119152 57:31:12220888964329584 57:32:9929472283517787 57:33:7522327487513475 57:34:5309878226480100 57:35:3489348548829780 57:36:2132379668729310 57:37:1210269541711230 57:38:636983969321700 57:39:310325523515700 57:40:139646485582065 57:41:57902201338905 57:42:22057981462440 57:43:7694644696200 57:44:2448296039700 57:45:707285522580 57:46:184509266760 57:47:43183019880 57:48:8996462475 57:49:1652411475 57:50:264385836 57:51:36288252 57:52:4187106 57:53:395010 57:54:29260 57:55:1596 57:56:57 57:57:1 # binomial(58, k) for 0 <= k <= 58 58:0:1 58:1:58 58:2:1653 58:3:30856 58:4:424270 58:5:4582116 58:6:40475358 58:7:300674088 58:8:1916797311 58:9:10648873950 58:10:52179482355 58:11:227692286640 58:12:891794789340 58:13:3155581562280 58:14:10142940735900 58:15:29752626158640 58:16:79960182801345 58:17:197548686920970 58:18:449972009097765 58:19:947309492837400 58:20:1847253511032930 58:21:3342649210440540 58:22:5621728217559090 58:23:8799226775309880 58:24:12832205713993575 58:25:17451799771031262 58:26:22150361247847371 58:27:26252279997448736 58:28:29065024282889672 58:29:30067266499541040 58:30:29065024282889672 58:31:26252279997448736 58:32:22150361247847371 58:33:17451799771031262 58:34:12832205713993575 58:35:8799226775309880 58:36:5621728217559090 58:37:3342649210440540 58:38:1847253511032930 58:39:947309492837400 58:40:449972009097765 58:41:197548686920970 58:42:79960182801345 58:43:29752626158640 58:44:10142940735900 58:45:3155581562280 58:46:891794789340 58:47:227692286640 58:48:52179482355 58:49:10648873950 58:50:1916797311 58:51:300674088 58:52:40475358 58:53:4582116 58:54:424270 58:55:30856 58:56:1653 58:57:58 58:58:1 # binomial(59, k) for 0 <= k <= 59 59:0:1 59:1:59 59:2:1711 59:3:32509 59:4:455126 59:5:5006386 59:6:45057474 59:7:341149446 59:8:2217471399 59:9:12565671261 59:10:62828356305 59:11:279871768995 59:12:1119487075980 59:13:4047376351620 59:14:13298522298180 59:15:39895566894540 59:16:109712808959985 59:17:277508869722315 59:18:647520696018735 59:19:1397281501935165 59:20:2794563003870330 59:21:5189902721473470 59:22:8964377427999630 59:23:14420954992868970 59:24:21631432489303455 59:25:30284005485024837 59:26:39602161018878633 59:27:48402641245296107 59:28:55317304280338408 59:29:59132290782430712 59:30:59132290782430712 59:31:55317304280338408 59:32:48402641245296107 59:33:39602161018878633 59:34:30284005485024837 59:35:21631432489303455 59:36:14420954992868970 59:37:8964377427999630 59:38:5189902721473470 59:39:2794563003870330 59:40:1397281501935165 59:41:647520696018735 59:42:277508869722315 59:43:109712808959985 59:44:39895566894540 59:45:13298522298180 59:46:4047376351620 59:47:1119487075980 59:48:279871768995 59:49:62828356305 59:50:12565671261 59:51:2217471399 59:52:341149446 59:53:45057474 59:54:5006386 59:55:455126 59:56:32509 59:57:1711 59:58:59 59:59:1 # binomial(60, k) for 0 <= k <= 60 60:0:1 60:1:60 60:2:1770 60:3:34220 60:4:487635 60:5:5461512 60:6:50063860 60:7:386206920 60:8:2558620845 60:9:14783142660 60:10:75394027566 60:11:342700125300 60:12:1399358844975 60:13:5166863427600 60:14:17345898649800 60:15:53194089192720 60:16:149608375854525 60:17:387221678682300 60:18:925029565741050 60:19:2044802197953900 60:20:4191844505805495 60:21:7984465725343800 60:22:14154280149473100 60:23:23385332420868600 60:24:36052387482172425 60:25:51915437974328292 60:26:69886166503903470 60:27:88004802264174740 60:28:103719945525634515 60:29:114449595062769120 60:30:118264581564861424 60:31:114449595062769120 60:32:103719945525634515 60:33:88004802264174740 60:34:69886166503903470 60:35:51915437974328292 60:36:36052387482172425 60:37:23385332420868600 60:38:14154280149473100 60:39:7984465725343800 60:40:4191844505805495 60:41:2044802197953900 60:42:925029565741050 60:43:387221678682300 60:44:149608375854525 60:45:53194089192720 60:46:17345898649800 60:47:5166863427600 60:48:1399358844975 60:49:342700125300 60:50:75394027566 60:51:14783142660 60:52:2558620845 60:53:386206920 60:54:50063860 60:55:5461512 60:56:487635 60:57:34220 60:58:1770 60:59:60 60:60:1 # binomial(61, k) for 0 <= k <= 61 61:0:1 61:1:61 61:2:1830 61:3:35990 61:4:521855 61:5:5949147 61:6:55525372 61:7:436270780 61:8:2944827765 61:9:17341763505 61:10:90177170226 61:11:418094152866 61:12:1742058970275 61:13:6566222272575 61:14:22512762077400 61:15:70539987842520 61:16:202802465047245 61:17:536830054536825 61:18:1312251244423350 61:19:2969831763694950 61:20:6236646703759395 61:21:12176310231149295 61:22:22138745874816900 61:23:37539612570341700 61:24:59437719903041025 61:25:87967825456500717 61:26:121801604478231762 61:27:157890968768078210 61:28:191724747789809255 61:29:218169540588403635 61:30:232714176627630544 61:31:232714176627630544 61:32:218169540588403635 61:33:191724747789809255 61:34:157890968768078210 61:35:121801604478231762 61:36:87967825456500717 61:37:59437719903041025 61:38:37539612570341700 61:39:22138745874816900 61:40:12176310231149295 61:41:6236646703759395 61:42:2969831763694950 61:43:1312251244423350 61:44:536830054536825 61:45:202802465047245 61:46:70539987842520 61:47:22512762077400 61:48:6566222272575 61:49:1742058970275 61:50:418094152866 61:51:90177170226 61:52:17341763505 61:53:2944827765 61:54:436270780 61:55:55525372 61:56:5949147 61:57:521855 61:58:35990 61:59:1830 61:60:61 61:61:1 # binomial(62, k) for 0 <= k <= 62 62:0:1 62:1:62 62:2:1891 62:3:37820 62:4:557845 62:5:6471002 62:6:61474519 62:7:491796152 62:8:3381098545 62:9:20286591270 62:10:107518933731 62:11:508271323092 62:12:2160153123141 62:13:8308281242850 62:14:29078984349975 62:15:93052749919920 62:16:273342452889765 62:17:739632519584070 62:18:1849081298960175 62:19:4282083008118300 62:20:9206478467454345 62:21:18412956934908690 62:22:34315056105966195 62:23:59678358445158600 62:24:96977332473382725 62:25:147405545359541742 62:26:209769429934732479 62:27:279692573246309972 62:28:349615716557887465 62:29:409894288378212890 62:30:450883717216034179 62:31:465428353255261088 62:32:450883717216034179 62:33:409894288378212890 62:34:349615716557887465 62:35:279692573246309972 62:36:209769429934732479 62:37:147405545359541742 62:38:96977332473382725 62:39:59678358445158600 62:40:34315056105966195 62:41:18412956934908690 62:42:9206478467454345 62:43:4282083008118300 62:44:1849081298960175 62:45:739632519584070 62:46:273342452889765 62:47:93052749919920 62:48:29078984349975 62:49:8308281242850 62:50:2160153123141 62:51:508271323092 62:52:107518933731 62:53:20286591270 62:54:3381098545 62:55:491796152 62:56:61474519 62:57:6471002 62:58:557845 62:59:37820 62:60:1891 62:61:62 62:62:1 # binomial(63, k) for 0 <= k <= 63 63:0:1 63:1:63 63:2:1953 63:3:39711 63:4:595665 63:5:7028847 63:6:67945521 63:7:553270671 63:8:3872894697 63:9:23667689815 63:10:127805525001 63:11:615790256823 63:12:2668424446233 63:13:10468434365991 63:14:37387265592825 63:15:122131734269895 63:16:366395202809685 63:17:1012974972473835 63:18:2588713818544245 63:19:6131164307078475 63:20:13488561475572645 63:21:27619435402363035 63:22:52728013040874885 63:23:93993414551124795 63:24:156655690918541325 63:25:244382877832924467 63:26:357174975294274221 63:27:489462003181042451 63:28:629308289804197437 63:29:759510004936100355 63:30:860778005594247069 63:31:916312070471295267 63:32:916312070471295267 63:33:860778005594247069 63:34:759510004936100355 63:35:629308289804197437 63:36:489462003181042451 63:37:357174975294274221 63:38:244382877832924467 63:39:156655690918541325 63:40:93993414551124795 63:41:52728013040874885 63:42:27619435402363035 63:43:13488561475572645 63:44:6131164307078475 63:45:2588713818544245 63:46:1012974972473835 63:47:366395202809685 63:48:122131734269895 63:49:37387265592825 63:50:10468434365991 63:51:2668424446233 63:52:615790256823 63:53:127805525001 63:54:23667689815 63:55:3872894697 63:56:553270671 63:57:67945521 63:58:7028847 63:59:595665 63:60:39711 63:61:1953 63:62:63 63:63:1 # binomial(64, k) for 0 <= k <= 64 64:0:1 64:1:64 64:2:2016 64:3:41664 64:4:635376 64:5:7624512 64:6:74974368 64:7:621216192 64:8:4426165368 64:9:27540584512 64:10:151473214816 64:11:743595781824 64:12:3284214703056 64:13:13136858812224 64:14:47855699958816 64:15:159518999862720 64:16:488526937079580 64:17:1379370175283520 64:18:3601688791018080 64:19:8719878125622720 64:20:19619725782651120 64:21:41107996877935680 64:22:80347448443237920 64:23:146721427591999680 64:24:250649105469666120 64:25:401038568751465792 64:26:601557853127198688 64:27:846636978475316672 64:28:1118770292985239888 64:29:1388818294740297792 64:30:1620288010530347424 64:31:1777090076065542336 64:32:1832624140942590534 64:33:1777090076065542336 64:34:1620288010530347424 64:35:1388818294740297792 64:36:1118770292985239888 64:37:846636978475316672 64:38:601557853127198688 64:39:401038568751465792 64:40:250649105469666120 64:41:146721427591999680 64:42:80347448443237920 64:43:41107996877935680 64:44:19619725782651120 64:45:8719878125622720 64:46:3601688791018080 64:47:1379370175283520 64:48:488526937079580 64:49:159518999862720 64:50:47855699958816 64:51:13136858812224 64:52:3284214703056 64:53:743595781824 64:54:151473214816 64:55:27540584512 64:56:4426165368 64:57:621216192 64:58:74974368 64:59:7624512 64:60:635376 64:61:41664 64:62:2016 64:63:64 64:64:1 # binomial(65, k) for 0 <= k <= 65 65:0:1 65:1:65 65:2:2080 65:3:43680 65:4:677040 65:5:8259888 65:6:82598880 65:7:696190560 65:8:5047381560 65:9:31966749880 65:10:179013799328 65:11:895068996640 65:12:4027810484880 65:13:16421073515280 65:14:60992558771040 65:15:207374699821536 65:16:648045936942300 65:17:1867897112363100 65:18:4981058966301600 65:19:12321566916640800 65:20:28339603908273840 65:21:60727722660586800 65:22:121455445321173600 65:23:227068876035237600 65:24:397370533061665800 65:25:651687674221131912 65:26:1002596421878664480 65:27:1448194831602515360 65:28:1965407271460556560 65:29:2507588587725537680 65:30:3009106305270645216 65:31:3397378086595889760 65:32:3609714217008132870 65:33:3609714217008132870 65:34:3397378086595889760 65:35:3009106305270645216 65:36:2507588587725537680 65:37:1965407271460556560 65:38:1448194831602515360 65:39:1002596421878664480 65:40:651687674221131912 65:41:397370533061665800 65:42:227068876035237600 65:43:121455445321173600 65:44:60727722660586800 65:45:28339603908273840 65:46:12321566916640800 65:47:4981058966301600 65:48:1867897112363100 65:49:648045936942300 65:50:207374699821536 65:51:60992558771040 65:52:16421073515280 65:53:4027810484880 65:54:895068996640 65:55:179013799328 65:56:31966749880 65:57:5047381560 65:58:696190560 65:59:82598880 65:60:8259888 65:61:677040 65:62:43680 65:63:2080 65:64:65 65:65:1 # binomial(66, k) for 0 <= k <= 66 66:0:1 66:1:66 66:2:2145 66:3:45760 66:4:720720 66:5:8936928 66:6:90858768 66:7:778789440 66:8:5743572120 66:9:37014131440 66:10:210980549208 66:11:1074082795968 66:12:4922879481520 66:13:20448884000160 66:14:77413632286320 66:15:268367258592576 66:16:855420636763836 66:17:2515943049305400 66:18:6848956078664700 66:19:17302625882942400 66:20:40661170824914640 66:21:89067326568860640 66:22:182183167981760400 66:23:348524321356411200 66:24:624439409096903400 66:25:1049058207282797712 66:26:1654284096099796392 66:27:2450791253481179840 66:28:3413602103063071920 66:29:4472995859186094240 66:30:5516694892996182896 66:31:6406484391866534976 66:32:7007092303604022630 66:33:7219428434016265740 66:34:7007092303604022630 66:35:6406484391866534976 66:36:5516694892996182896 66:37:4472995859186094240 66:38:3413602103063071920 66:39:2450791253481179840 66:40:1654284096099796392 66:41:1049058207282797712 66:42:624439409096903400 66:43:348524321356411200 66:44:182183167981760400 66:45:89067326568860640 66:46:40661170824914640 66:47:17302625882942400 66:48:6848956078664700 66:49:2515943049305400 66:50:855420636763836 66:51:268367258592576 66:52:77413632286320 66:53:20448884000160 66:54:4922879481520 66:55:1074082795968 66:56:210980549208 66:57:37014131440 66:58:5743572120 66:59:778789440 66:60:90858768 66:61:8936928 66:62:720720 66:63:45760 66:64:2145 66:65:66 66:66:1 # binomial(67, k) for 0 <= k <= 67 67:0:1 67:1:67 67:2:2211 67:3:47905 67:4:766480 67:5:9657648 67:6:99795696 67:7:869648208 67:8:6522361560 67:9:42757703560 67:10:247994680648 67:11:1285063345176 67:12:5996962277488 67:13:25371763481680 67:14:97862516286480 67:15:345780890878896 67:16:1123787895356412 67:17:3371363686069236 67:18:9364899127970100 67:19:24151581961607100 67:20:57963796707857040 67:21:129728497393775280 67:22:271250494550621040 67:23:530707489338171600 67:24:972963730453314600 67:25:1673497616379701112 67:26:2703342303382594104 67:27:4105075349580976232 67:28:5864393356544251760 67:29:7886597962249166160 67:30:9989690752182277136 67:31:11923179284862717872 67:32:13413576695470557606 67:33:14226520737620288370 67:34:14226520737620288370 67:35:13413576695470557606 67:36:11923179284862717872 67:37:9989690752182277136 67:38:7886597962249166160 67:39:5864393356544251760 67:40:4105075349580976232 67:41:2703342303382594104 67:42:1673497616379701112 67:43:972963730453314600 67:44:530707489338171600 67:45:271250494550621040 67:46:129728497393775280 67:47:57963796707857040 67:48:24151581961607100 67:49:9364899127970100 67:50:3371363686069236 67:51:1123787895356412 67:52:345780890878896 67:53:97862516286480 67:54:25371763481680 67:55:5996962277488 67:56:1285063345176 67:57:247994680648 67:58:42757703560 67:59:6522361560 67:60:869648208 67:61:99795696 67:62:9657648 67:63:766480 67:64:47905 67:65:2211 67:66:67 67:67:1 # binomial(68, k) for 0 <= k <= 68 68:0:1 68:1:68 68:2:2278 68:3:50116 68:4:814385 68:5:10424128 68:6:109453344 68:7:969443904 68:8:7392009768 68:9:49280065120 68:10:290752384208 68:11:1533058025824 68:12:7282025622664 68:13:31368725759168 68:14:123234279768160 68:15:443643407165376 68:16:1469568786235308 68:17:4495151581425648 68:18:12736262814039336 68:19:33516481089577200 68:20:82115378669464140 68:21:187692294101632320 68:22:400978991944396320 68:23:801957983888792640 68:24:1503671219791486200 68:25:2646461346833015712 68:26:4376839919762295216 68:27:6808417652963570336 68:28:9969468706125227992 68:29:13750991318793417920 68:30:17876288714431443296 68:31:21912870037044995008 68:32:25336755980333275478 68:33:27640097433090845976 68:34:28453041475240576740 68:35:27640097433090845976 68:36:25336755980333275478 68:37:21912870037044995008 68:38:17876288714431443296 68:39:13750991318793417920 68:40:9969468706125227992 68:41:6808417652963570336 68:42:4376839919762295216 68:43:2646461346833015712 68:44:1503671219791486200 68:45:801957983888792640 68:46:400978991944396320 68:47:187692294101632320 68:48:82115378669464140 68:49:33516481089577200 68:50:12736262814039336 68:51:4495151581425648 68:52:1469568786235308 68:53:443643407165376 68:54:123234279768160 68:55:31368725759168 68:56:7282025622664 68:57:1533058025824 68:58:290752384208 68:59:49280065120 68:60:7392009768 68:61:969443904 68:62:109453344 68:63:10424128 68:64:814385 68:65:50116 68:66:2278 68:67:68 68:68:1 # binomial(69, k) for 0 <= k <= 69 69:0:1 69:1:69 69:2:2346 69:3:52394 69:4:864501 69:5:11238513 69:6:119877472 69:7:1078897248 69:8:8361453672 69:9:56672074888 69:10:340032449328 69:11:1823810410032 69:12:8815083648488 69:13:38650751381832 69:14:154603005527328 69:15:566877686933536 69:16:1913212193400684 69:17:5964720367660956 69:18:17231414395464984 69:19:46252743903616536 69:20:115631859759041340 69:21:269807672771096460 69:22:588671286046028640 69:23:1202936975833188960 69:24:2305629203680278840 69:25:4150132566624501912 69:26:7023301266595310928 69:27:11185257572725865552 69:28:16777886359088798328 69:29:23720460024918645912 69:30:31627280033224861216 69:31:39789158751476438304 69:32:47249626017378270486 69:33:52976853413424121454 69:34:56093138908331422716 69:35:56093138908331422716 69:36:52976853413424121454 69:37:47249626017378270486 69:38:39789158751476438304 69:39:31627280033224861216 69:40:23720460024918645912 69:41:16777886359088798328 69:42:11185257572725865552 69:43:7023301266595310928 69:44:4150132566624501912 69:45:2305629203680278840 69:46:1202936975833188960 69:47:588671286046028640 69:48:269807672771096460 69:49:115631859759041340 69:50:46252743903616536 69:51:17231414395464984 69:52:5964720367660956 69:53:1913212193400684 69:54:566877686933536 69:55:154603005527328 69:56:38650751381832 69:57:8815083648488 69:58:1823810410032 69:59:340032449328 69:60:56672074888 69:61:8361453672 69:62:1078897248 69:63:119877472 69:64:11238513 69:65:864501 69:66:52394 69:67:2346 69:68:69 69:69:1 # binomial(70, k) for 0 <= k <= 70 70:0:1 70:1:70 70:2:2415 70:3:54740 70:4:916895 70:5:12103014 70:6:131115985 70:7:1198774720 70:8:9440350920 70:9:65033528560 70:10:396704524216 70:11:2163842859360 70:12:10638894058520 70:13:47465835030320 70:14:193253756909160 70:15:721480692460864 70:16:2480089880334220 70:17:7877932561061640 70:18:23196134763125940 70:19:63484158299081520 70:20:161884603662657876 70:21:385439532530137800 70:22:858478958817125100 70:23:1791608261879217600 70:24:3508566179513467800 70:25:6455761770304780752 70:26:11173433833219812840 70:27:18208558839321176480 70:28:27963143931814663880 70:29:40498346384007444240 70:30:55347740058143507128 70:31:71416438784701299520 70:32:87038784768854708790 70:33:100226479430802391940 70:34:109069992321755544170 70:35:112186277816662845432 70:36:109069992321755544170 70:37:100226479430802391940 70:38:87038784768854708790 70:39:71416438784701299520 70:40:55347740058143507128 70:41:40498346384007444240 70:42:27963143931814663880 70:43:18208558839321176480 70:44:11173433833219812840 70:45:6455761770304780752 70:46:3508566179513467800 70:47:1791608261879217600 70:48:858478958817125100 70:49:385439532530137800 70:50:161884603662657876 70:51:63484158299081520 70:52:23196134763125940 70:53:7877932561061640 70:54:2480089880334220 70:55:721480692460864 70:56:193253756909160 70:57:47465835030320 70:58:10638894058520 70:59:2163842859360 70:60:396704524216 70:61:65033528560 70:62:9440350920 70:63:1198774720 70:64:131115985 70:65:12103014 70:66:916895 70:67:54740 70:68:2415 70:69:70 70:70:1 # binomial(71, k) for 0 <= k <= 71 71:0:1 71:1:71 71:2:2485 71:3:57155 71:4:971635 71:5:13019909 71:6:143218999 71:7:1329890705 71:8:10639125640 71:9:74473879480 71:10:461738052776 71:11:2560547383576 71:12:12802736917880 71:13:58104729088840 71:14:240719591939480 71:15:914734449370024 71:16:3201570572795084 71:17:10358022441395860 71:18:31074067324187580 71:19:86680293062207460 71:20:225368761961739396 71:21:547324136192795676 71:22:1243918491347262900 71:23:2650087220696342700 71:24:5300174441392685400 71:25:9964327949818248552 71:26:17629195603524593592 71:27:29381992672540989320 71:28:46171702771135840360 71:29:68461490315822108120 71:30:95846086442150951368 71:31:126764178842844806648 71:32:158455223553556008310 71:33:187265264199657100730 71:34:209296471752557936110 71:35:221256270138418389602 71:36:221256270138418389602 71:37:209296471752557936110 71:38:187265264199657100730 71:39:158455223553556008310 71:40:126764178842844806648 71:41:95846086442150951368 71:42:68461490315822108120 71:43:46171702771135840360 71:44:29381992672540989320 71:45:17629195603524593592 71:46:9964327949818248552 71:47:5300174441392685400 71:48:2650087220696342700 71:49:1243918491347262900 71:50:547324136192795676 71:51:225368761961739396 71:52:86680293062207460 71:53:31074067324187580 71:54:10358022441395860 71:55:3201570572795084 71:56:914734449370024 71:57:240719591939480 71:58:58104729088840 71:59:12802736917880 71:60:2560547383576 71:61:461738052776 71:62:74473879480 71:63:10639125640 71:64:1329890705 71:65:143218999 71:66:13019909 71:67:971635 71:68:57155 71:69:2485 71:70:71 71:71:1 # binomial(72, k) for 0 <= k <= 72 72:0:1 72:1:72 72:2:2556 72:3:59640 72:4:1028790 72:5:13991544 72:6:156238908 72:7:1473109704 72:8:11969016345 72:9:85113005120 72:10:536211932256 72:11:3022285436352 72:12:15363284301456 72:13:70907466006720 72:14:298824321028320 72:15:1155454041309504 72:16:4116305022165108 72:17:13559593014190944 72:18:41432089765583440 72:19:117754360386395040 72:20:312049055023946856 72:21:772692898154535072 72:22:1791242627540058576 72:23:3894005712043605600 72:24:7950261662089028100 72:25:15264502391210933952 72:26:27593523553342842144 72:27:47011188276065582912 72:28:75553695443676829680 72:29:114633193086957948480 72:30:164307576757973059488 72:31:222610265284995758016 72:32:285219402396400814958 72:33:345720487753213109040 72:34:396561735952215036840 72:35:430552741890976325712 72:36:442512540276836779204 72:37:430552741890976325712 72:38:396561735952215036840 72:39:345720487753213109040 72:40:285219402396400814958 72:41:222610265284995758016 72:42:164307576757973059488 72:43:114633193086957948480 72:44:75553695443676829680 72:45:47011188276065582912 72:46:27593523553342842144 72:47:15264502391210933952 72:48:7950261662089028100 72:49:3894005712043605600 72:50:1791242627540058576 72:51:772692898154535072 72:52:312049055023946856 72:53:117754360386395040 72:54:41432089765583440 72:55:13559593014190944 72:56:4116305022165108 72:57:1155454041309504 72:58:298824321028320 72:59:70907466006720 72:60:15363284301456 72:61:3022285436352 72:62:536211932256 72:63:85113005120 72:64:11969016345 72:65:1473109704 72:66:156238908 72:67:13991544 72:68:1028790 72:69:59640 72:70:2556 72:71:72 72:72:1 # binomial(73, k) for 0 <= k <= 73 73:0:1 73:1:73 73:2:2628 73:3:62196 73:4:1088430 73:5:15020334 73:6:170230452 73:7:1629348612 73:8:13442126049 73:9:97082021465 73:10:621324937376 73:11:3558497368608 73:12:18385569737808 73:13:86270750308176 73:14:369731787035040 73:15:1454278362337824 73:16:5271759063474612 73:17:17675898036356052 73:18:54991682779774384 73:19:159186450151978480 73:20:429803415410341896 73:21:1084741953178481928 73:22:2563935525694593648 73:23:5685248339583664176 73:24:11844267374132633700 73:25:23214764053299962052 73:26:42858025944553776096 73:27:74604711829408425056 73:28:122564883719742412592 73:29:190186888530634778160 73:30:278940769844931007968 73:31:386917842042968817504 73:32:507829667681396572974 73:33:630939890149613923998 73:34:742282223705428145880 73:35:827114477843191362552 73:36:873065282167813104916 73:37:873065282167813104916 73:38:827114477843191362552 73:39:742282223705428145880 73:40:630939890149613923998 73:41:507829667681396572974 73:42:386917842042968817504 73:43:278940769844931007968 73:44:190186888530634778160 73:45:122564883719742412592 73:46:74604711829408425056 73:47:42858025944553776096 73:48:23214764053299962052 73:49:11844267374132633700 73:50:5685248339583664176 73:51:2563935525694593648 73:52:1084741953178481928 73:53:429803415410341896 73:54:159186450151978480 73:55:54991682779774384 73:56:17675898036356052 73:57:5271759063474612 73:58:1454278362337824 73:59:369731787035040 73:60:86270750308176 73:61:18385569737808 73:62:3558497368608 73:63:621324937376 73:64:97082021465 73:65:13442126049 73:66:1629348612 73:67:170230452 73:68:15020334 73:69:1088430 73:70:62196 73:71:2628 73:72:73 73:73:1 # binomial(74, k) for 0 <= k <= 74 74:0:1 74:1:74 74:2:2701 74:3:64824 74:4:1150626 74:5:16108764 74:6:185250786 74:7:1799579064 74:8:15071474661 74:9:110524147514 74:10:718406958841 74:11:4179822305984 74:12:21944067106416 74:13:104656320045984 74:14:456002537343216 74:15:1824010149372864 74:16:6726037425812436 74:17:22947657099830664 74:18:72667580816130436 74:19:214178132931752864 74:20:588989865562320376 74:21:1514545368588823824 74:22:3648677478873075576 74:23:8249183865278257824 74:24:17529515713716297876 74:25:35059031427432595752 74:26:66072789997853738148 74:27:117462737773962201152 74:28:197169595549150837648 74:29:312751772250377190752 74:30:469127658375565786128 74:31:665858611887899825472 74:32:894747509724365390478 74:33:1138769557831010496972 74:34:1373222113855042069878 74:35:1569396701548619508432 74:36:1700179760011004467468 74:37:1746130564335626209832 74:38:1700179760011004467468 74:39:1569396701548619508432 74:40:1373222113855042069878 74:41:1138769557831010496972 74:42:894747509724365390478 74:43:665858611887899825472 74:44:469127658375565786128 74:45:312751772250377190752 74:46:197169595549150837648 74:47:117462737773962201152 74:48:66072789997853738148 74:49:35059031427432595752 74:50:17529515713716297876 74:51:8249183865278257824 74:52:3648677478873075576 74:53:1514545368588823824 74:54:588989865562320376 74:55:214178132931752864 74:56:72667580816130436 74:57:22947657099830664 74:58:6726037425812436 74:59:1824010149372864 74:60:456002537343216 74:61:104656320045984 74:62:21944067106416 74:63:4179822305984 74:64:718406958841 74:65:110524147514 74:66:15071474661 74:67:1799579064 74:68:185250786 74:69:16108764 74:70:1150626 74:71:64824 74:72:2701 74:73:74 74:74:1 # binomial(75, k) for 0 <= k <= 75 75:0:1 75:1:75 75:2:2775 75:3:67525 75:4:1215450 75:5:17259390 75:6:201359550 75:7:1984829850 75:8:16871053725 75:9:125595622175 75:10:828931106355 75:11:4898229264825 75:12:26123889412400 75:13:126600387152400 75:14:560658857389200 75:15:2280012686716080 75:16:8550047575185300 75:17:29673694525643100 75:18:95615237915961100 75:19:286845713747883300 75:20:803167998494073240 75:21:2103535234151144200 75:22:5163222847461899400 75:23:11897861344151333400 75:24:25778699578994555700 75:25:52588547141148893628 75:26:101131821425286333900 75:27:183535527771815939300 75:28:314632333323113038800 75:29:509921367799528028400 75:30:781879430625942976880 75:31:1134986270263465611600 75:32:1560606121612265215950 75:33:2033517067555375887450 75:34:2511991671686052566850 75:35:2942618815403661578310 75:36:3269576461559623975900 75:37:3446310324346630677300 75:38:3446310324346630677300 75:39:3269576461559623975900 75:40:2942618815403661578310 75:41:2511991671686052566850 75:42:2033517067555375887450 75:43:1560606121612265215950 75:44:1134986270263465611600 75:45:781879430625942976880 75:46:509921367799528028400 75:47:314632333323113038800 75:48:183535527771815939300 75:49:101131821425286333900 75:50:52588547141148893628 75:51:25778699578994555700 75:52:11897861344151333400 75:53:5163222847461899400 75:54:2103535234151144200 75:55:803167998494073240 75:56:286845713747883300 75:57:95615237915961100 75:58:29673694525643100 75:59:8550047575185300 75:60:2280012686716080 75:61:560658857389200 75:62:126600387152400 75:63:26123889412400 75:64:4898229264825 75:65:828931106355 75:66:125595622175 75:67:16871053725 75:68:1984829850 75:69:201359550 75:70:17259390 75:71:1215450 75:72:67525 75:73:2775 75:74:75 75:75:1 # binomial(76, k) for 0 <= k <= 76 76:0:1 76:1:76 76:2:2850 76:3:70300 76:4:1282975 76:5:18474840 76:6:218618940 76:7:2186189400 76:8:18855883575 76:9:142466675900 76:10:954526728530 76:11:5727160371180 76:12:31022118677225 76:13:152724276564800 76:14:687259244541600 76:15:2840671544105280 76:16:10830060261901380 76:17:38223742100828400 76:18:125288932441604200 76:19:382460951663844400 76:20:1090013712241956540 76:21:2906703232645217440 76:22:7266758081613043600 76:23:17061084191613232800 76:24:37676560923145889100 76:25:78367246720143449328 76:26:153720368566435227528 76:27:284667349197102273200 76:28:498167861094928978100 76:29:824553701122641067200 76:30:1291800798425471005280 76:31:1916865700889408588480 76:32:2695592391875730827550 76:33:3594123189167641103400 76:34:4545508739241428454300 76:35:5454610487089714145160 76:36:6212195276963285554210 76:37:6715886785906254653200 76:38:6892620648693261354600 76:39:6715886785906254653200 76:40:6212195276963285554210 76:41:5454610487089714145160 76:42:4545508739241428454300 76:43:3594123189167641103400 76:44:2695592391875730827550 76:45:1916865700889408588480 76:46:1291800798425471005280 76:47:824553701122641067200 76:48:498167861094928978100 76:49:284667349197102273200 76:50:153720368566435227528 76:51:78367246720143449328 76:52:37676560923145889100 76:53:17061084191613232800 76:54:7266758081613043600 76:55:2906703232645217440 76:56:1090013712241956540 76:57:382460951663844400 76:58:125288932441604200 76:59:38223742100828400 76:60:10830060261901380 76:61:2840671544105280 76:62:687259244541600 76:63:152724276564800 76:64:31022118677225 76:65:5727160371180 76:66:954526728530 76:67:142466675900 76:68:18855883575 76:69:2186189400 76:70:218618940 76:71:18474840 76:72:1282975 76:73:70300 76:74:2850 76:75:76 76:76:1 # binomial(77, k) for 0 <= k <= 77 77:0:1 77:1:77 77:2:2926 77:3:73150 77:4:1353275 77:5:19757815 77:6:237093780 77:7:2404808340 77:8:21042072975 77:9:161322559475 77:10:1096993404430 77:11:6681687099710 77:12:36749279048405 77:13:183746395242025 77:14:839983521106400 77:15:3527930788646880 77:16:13670731806006660 77:17:49053802362729780 77:18:163512674542432600 77:19:507749884105448600 77:20:1472474663905800940 77:21:3996716944887173980 77:22:10173461314258261040 77:23:24327842273226276400 77:24:54737645114759121900 77:25:116043807643289338428 77:26:232087615286578676856 77:27:438387717763537500728 77:28:782835210292031251300 77:29:1322721562217570045300 77:30:2116354499548112072480 77:31:3208666499314879593760 77:32:4612458092765139416030 77:33:6289715581043371930950 77:34:8139631928409069557700 77:35:10000119226331142599460 77:36:11666805764052999699370 77:37:12928082062869540207410 77:38:13608507434599516007800 77:39:13608507434599516007800 77:40:12928082062869540207410 77:41:11666805764052999699370 77:42:10000119226331142599460 77:43:8139631928409069557700 77:44:6289715581043371930950 77:45:4612458092765139416030 77:46:3208666499314879593760 77:47:2116354499548112072480 77:48:1322721562217570045300 77:49:782835210292031251300 77:50:438387717763537500728 77:51:232087615286578676856 77:52:116043807643289338428 77:53:54737645114759121900 77:54:24327842273226276400 77:55:10173461314258261040 77:56:3996716944887173980 77:57:1472474663905800940 77:58:507749884105448600 77:59:163512674542432600 77:60:49053802362729780 77:61:13670731806006660 77:62:3527930788646880 77:63:839983521106400 77:64:183746395242025 77:65:36749279048405 77:66:6681687099710 77:67:1096993404430 77:68:161322559475 77:69:21042072975 77:70:2404808340 77:71:237093780 77:72:19757815 77:73:1353275 77:74:73150 77:75:2926 77:76:77 77:77:1 # binomial(78, k) for 0 <= k <= 78 78:0:1 78:1:78 78:2:3003 78:3:76076 78:4:1426425 78:5:21111090 78:6:256851595 78:7:2641902120 78:8:23446881315 78:9:182364632450 78:10:1258315963905 78:11:7778680504140 78:12:43430966148115 78:13:220495674290430 78:14:1023729916348425 78:15:4367914309753280 78:16:17198662594653540 78:17:62724534168736440 78:18:212566476905162380 78:19:671262558647881200 78:20:1980224548011249540 78:21:5469191608792974920 78:22:14170178259145435020 78:23:34501303587484537440 78:24:79065487387985398300 78:25:170781452758048460328 78:26:348131422929868015284 78:27:670475333050116177584 78:28:1221222928055568752028 78:29:2105556772509601296600 78:30:3439076061765682117780 78:31:5325020998862991666240 78:32:7821124592080019009790 78:33:10902173673808511346980 78:34:14429347509452441488650 78:35:18139751154740212157160 78:36:21666924990384142298830 78:37:24594887826922539906780 78:38:26536589497469056215210 78:39:27217014869199032015600 78:40:26536589497469056215210 78:41:24594887826922539906780 78:42:21666924990384142298830 78:43:18139751154740212157160 78:44:14429347509452441488650 78:45:10902173673808511346980 78:46:7821124592080019009790 78:47:5325020998862991666240 78:48:3439076061765682117780 78:49:2105556772509601296600 78:50:1221222928055568752028 78:51:670475333050116177584 78:52:348131422929868015284 78:53:170781452758048460328 78:54:79065487387985398300 78:55:34501303587484537440 78:56:14170178259145435020 78:57:5469191608792974920 78:58:1980224548011249540 78:59:671262558647881200 78:60:212566476905162380 78:61:62724534168736440 78:62:17198662594653540 78:63:4367914309753280 78:64:1023729916348425 78:65:220495674290430 78:66:43430966148115 78:67:7778680504140 78:68:1258315963905 78:69:182364632450 78:70:23446881315 78:71:2641902120 78:72:256851595 78:73:21111090 78:74:1426425 78:75:76076 78:76:3003 78:77:78 78:78:1 # binomial(79, k) for 0 <= k <= 79 79:0:1 79:1:79 79:2:3081 79:3:79079 79:4:1502501 79:5:22537515 79:6:277962685 79:7:2898753715 79:8:26088783435 79:9:205811513765 79:10:1440680596355 79:11:9036996468045 79:12:51209646652255 79:13:263926640438545 79:14:1244225590638855 79:15:5391644226101705 79:16:21566576904406820 79:17:79923196763389980 79:18:275291011073898820 79:19:883829035553043580 79:20:2651487106659130740 79:21:7449416156804224460 79:22:19639369867938409940 79:23:48671481846629972460 79:24:113566790975469935740 79:25:249846940146033858628 79:26:518912875687916475612 79:27:1018606755979984192868 79:28:1891698261105684929612 79:29:3326779700565170048628 79:30:5544632834275283414380 79:31:8764097060628673784020 79:32:13146145590943010676030 79:33:18723298265888530356770 79:34:25331521183260952835630 79:35:32569098664192653645810 79:36:39806676145124354455990 79:37:46261812817306682205610 79:38:51131477324391596121990 79:39:53753604366668088230810 79:40:53753604366668088230810 79:41:51131477324391596121990 79:42:46261812817306682205610 79:43:39806676145124354455990 79:44:32569098664192653645810 79:45:25331521183260952835630 79:46:18723298265888530356770 79:47:13146145590943010676030 79:48:8764097060628673784020 79:49:5544632834275283414380 79:50:3326779700565170048628 79:51:1891698261105684929612 79:52:1018606755979984192868 79:53:518912875687916475612 79:54:249846940146033858628 79:55:113566790975469935740 79:56:48671481846629972460 79:57:19639369867938409940 79:58:7449416156804224460 79:59:2651487106659130740 79:60:883829035553043580 79:61:275291011073898820 79:62:79923196763389980 79:63:21566576904406820 79:64:5391644226101705 79:65:1244225590638855 79:66:263926640438545 79:67:51209646652255 79:68:9036996468045 79:69:1440680596355 79:70:205811513765 79:71:26088783435 79:72:2898753715 79:73:277962685 79:74:22537515 79:75:1502501 79:76:79079 79:77:3081 79:78:79 79:79:1 # binomial(80, k) for 0 <= k <= 80 80:0:1 80:1:80 80:2:3160 80:3:82160 80:4:1581580 80:5:24040016 80:6:300500200 80:7:3176716400 80:8:28987537150 80:9:231900297200 80:10:1646492110120 80:11:10477677064400 80:12:60246643120300 80:13:315136287090800 80:14:1508152231077400 80:15:6635869816740560 80:16:26958221130508525 80:17:101489773667796800 80:18:355214207837288800 80:19:1159120046626942400 80:20:3535316142212174320 80:21:10100903263463355200 80:22:27088786024742634400 80:23:68310851714568382400 80:24:162238272822099908200 80:25:363413731121503794368 80:26:768759815833950334240 80:27:1537519631667900668480 80:28:2910305017085669122480 80:29:5218477961670854978240 80:30:8871412534840453463008 80:31:14308729894903957198400 80:32:21910242651571684460050 80:33:31869443856831541032800 80:34:44054819449149483192400 80:35:57900619847453606481440 80:36:72375774809317008101800 80:37:86068488962431036661600 80:38:97393290141698278327600 80:39:104885081691059684352800 80:40:107507208733336176461620 80:41:104885081691059684352800 80:42:97393290141698278327600 80:43:86068488962431036661600 80:44:72375774809317008101800 80:45:57900619847453606481440 80:46:44054819449149483192400 80:47:31869443856831541032800 80:48:21910242651571684460050 80:49:14308729894903957198400 80:50:8871412534840453463008 80:51:5218477961670854978240 80:52:2910305017085669122480 80:53:1537519631667900668480 80:54:768759815833950334240 80:55:363413731121503794368 80:56:162238272822099908200 80:57:68310851714568382400 80:58:27088786024742634400 80:59:10100903263463355200 80:60:3535316142212174320 80:61:1159120046626942400 80:62:355214207837288800 80:63:101489773667796800 80:64:26958221130508525 80:65:6635869816740560 80:66:1508152231077400 80:67:315136287090800 80:68:60246643120300 80:69:10477677064400 80:70:1646492110120 80:71:231900297200 80:72:28987537150 80:73:3176716400 80:74:300500200 80:75:24040016 80:76:1581580 80:77:82160 80:78:3160 80:79:80 80:80:1 # binomial(81, k) for 0 <= k <= 81 81:0:1 81:1:81 81:2:3240 81:3:85320 81:4:1663740 81:5:25621596 81:6:324540216 81:7:3477216600 81:8:32164253550 81:9:260887834350 81:10:1878392407320 81:11:12124169174520 81:12:70724320184700 81:13:375382930211100 81:14:1823288518168200 81:15:8144022047817960 81:16:33594090947249085 81:17:128447994798305325 81:18:456703981505085600 81:19:1514334254464231200 81:20:4694436188839116720 81:21:13636219405675529520 81:22:37189689288205989600 81:23:95399637739311016800 81:24:230549124536668290600 81:25:525652003943603702568 81:26:1132173546955454128608 81:27:2306279447501851002720 81:28:4447824648753569790960 81:29:8128782978756524100720 81:30:14089890496511308441248 81:31:23180142429744410661408 81:32:36218972546475641658450 81:33:53779686508403225492850 81:34:75924263305981024225200 81:35:101955439296603089673840 81:36:130276394656770614583240 81:37:158444263771748044763400 81:38:183461779104129314989200 81:39:202278371832757962680400 81:40:212392290424395860814420 81:41:212392290424395860814420 81:42:202278371832757962680400 81:43:183461779104129314989200 81:44:158444263771748044763400 81:45:130276394656770614583240 81:46:101955439296603089673840 81:47:75924263305981024225200 81:48:53779686508403225492850 81:49:36218972546475641658450 81:50:23180142429744410661408 81:51:14089890496511308441248 81:52:8128782978756524100720 81:53:4447824648753569790960 81:54:2306279447501851002720 81:55:1132173546955454128608 81:56:525652003943603702568 81:57:230549124536668290600 81:58:95399637739311016800 81:59:37189689288205989600 81:60:13636219405675529520 81:61:4694436188839116720 81:62:1514334254464231200 81:63:456703981505085600 81:64:128447994798305325 81:65:33594090947249085 81:66:8144022047817960 81:67:1823288518168200 81:68:375382930211100 81:69:70724320184700 81:70:12124169174520 81:71:1878392407320 81:72:260887834350 81:73:32164253550 81:74:3477216600 81:75:324540216 81:76:25621596 81:77:1663740 81:78:85320 81:79:3240 81:80:81 81:81:1 # binomial(82, k) for 0 <= k <= 82 82:0:1 82:1:82 82:2:3321 82:3:88560 82:4:1749060 82:5:27285336 82:6:350161812 82:7:3801756816 82:8:35641470150 82:9:293052087900 82:10:2139280241670 82:11:14002561581840 82:12:82848489359220 82:13:446107250395800 82:14:2198671448379300 82:15:9967310565986160 82:16:41738112995067045 82:17:162042085745554410 82:18:585151976303390925 82:19:1971038235969316800 82:20:6208770443303347920 82:21:18330655594514646240 82:22:50825908693881519120 82:23:132589327027517006400 82:24:325948762275979307400 82:25:756201128480271993168 82:26:1657825550899057831176 82:27:3438452994457305131328 82:28:6754104096255420793680 82:29:12576607627510093891680 82:30:22218673475267832541968 82:31:37270032926255719102656 82:32:59399114976220052319858 82:33:89998659054878867151300 82:34:129703949814384249718050 82:35:177879702602584113899040 82:36:232231833953373704257080 82:37:288720658428518659346640 82:38:341906042875877359752600 82:39:385740150936887277669600 82:40:414670662257153823494820 82:41:424784580848791721628840 82:42:414670662257153823494820 82:43:385740150936887277669600 82:44:341906042875877359752600 82:45:288720658428518659346640 82:46:232231833953373704257080 82:47:177879702602584113899040 82:48:129703949814384249718050 82:49:89998659054878867151300 82:50:59399114976220052319858 82:51:37270032926255719102656 82:52:22218673475267832541968 82:53:12576607627510093891680 82:54:6754104096255420793680 82:55:3438452994457305131328 82:56:1657825550899057831176 82:57:756201128480271993168 82:58:325948762275979307400 82:59:132589327027517006400 82:60:50825908693881519120 82:61:18330655594514646240 82:62:6208770443303347920 82:63:1971038235969316800 82:64:585151976303390925 82:65:162042085745554410 82:66:41738112995067045 82:67:9967310565986160 82:68:2198671448379300 82:69:446107250395800 82:70:82848489359220 82:71:14002561581840 82:72:2139280241670 82:73:293052087900 82:74:35641470150 82:75:3801756816 82:76:350161812 82:77:27285336 82:78:1749060 82:79:88560 82:80:3321 82:81:82 82:82:1 # binomial(83, k) for 0 <= k <= 83 83:0:1 83:1:83 83:2:3403 83:3:91881 83:4:1837620 83:5:29034396 83:6:377447148 83:7:4151918628 83:8:39443226966 83:9:328693558050 83:10:2432332329570 83:11:16141841823510 83:12:96851050941060 83:13:528955739755020 83:14:2644778698775100 83:15:12165982014365460 83:16:51705423561053205 83:17:203780198740621455 83:18:747194062048945335 83:19:2556190212272707725 83:20:8179808679272664720 83:21:24539426037817994160 83:22:69156564288396165360 83:23:183415235721398525520 83:24:458538089303496313800 83:25:1082149890756251300568 83:26:2414026679379329824344 83:27:5096278545356362962504 83:28:10192557090712725925008 83:29:19330711723765514685360 83:30:34795281102777926433648 83:31:59488706401523551644624 83:32:96669147902475771422514 83:33:149397774031098919471158 83:34:219702608869263116869350 83:35:307583652416968363617090 83:36:410111536555957818156120 83:37:520952492381892363603720 83:38:630626701304396019099240 83:39:727646193812764637422200 83:40:800410813194041101164420 83:41:839455243105945545123660 83:42:839455243105945545123660 83:43:800410813194041101164420 83:44:727646193812764637422200 83:45:630626701304396019099240 83:46:520952492381892363603720 83:47:410111536555957818156120 83:48:307583652416968363617090 83:49:219702608869263116869350 83:50:149397774031098919471158 83:51:96669147902475771422514 83:52:59488706401523551644624 83:53:34795281102777926433648 83:54:19330711723765514685360 83:55:10192557090712725925008 83:56:5096278545356362962504 83:57:2414026679379329824344 83:58:1082149890756251300568 83:59:458538089303496313800 83:60:183415235721398525520 83:61:69156564288396165360 83:62:24539426037817994160 83:63:8179808679272664720 83:64:2556190212272707725 83:65:747194062048945335 83:66:203780198740621455 83:67:51705423561053205 83:68:12165982014365460 83:69:2644778698775100 83:70:528955739755020 83:71:96851050941060 83:72:16141841823510 83:73:2432332329570 83:74:328693558050 83:75:39443226966 83:76:4151918628 83:77:377447148 83:78:29034396 83:79:1837620 83:80:91881 83:81:3403 83:82:83 83:83:1 # binomial(84, k) for 0 <= k <= 84 84:0:1 84:1:84 84:2:3486 84:3:95284 84:4:1929501 84:5:30872016 84:6:406481544 84:7:4529365776 84:8:43595145594 84:9:368136785016 84:10:2761025887620 84:11:18574174153080 84:12:112992892764570 84:13:625806790696080 84:14:3173734438530120 84:15:14810760713140560 84:16:63871405575418665 84:17:255485622301674660 84:18:950974260789566790 84:19:3303384274321653060 84:20:10735998891545372445 84:21:32719234717090658880 84:22:93695990326214159520 84:23:252571800009794690880 84:24:641953325024894839320 84:25:1540687980059747614368 84:26:3496176570135581124912 84:27:7510305224735692786848 84:28:15288835636069088887512 84:29:29523268814478240610368 84:30:54125992826543441119008 84:31:94283987504301478078272 84:32:156157854303999323067138 84:33:246066921933574690893672 84:34:369100382900362036340508 84:35:527286261286231480486440 84:36:717695188972926181773210 84:37:931064028937850181759840 84:38:1151579193686288382702960 84:39:1358272895117160656521440 84:40:1528057007006805738586620 84:41:1639866056299986646288080 84:42:1678910486211891090247320 84:43:1639866056299986646288080 84:44:1528057007006805738586620 84:45:1358272895117160656521440 84:46:1151579193686288382702960 84:47:931064028937850181759840 84:48:717695188972926181773210 84:49:527286261286231480486440 84:50:369100382900362036340508 84:51:246066921933574690893672 84:52:156157854303999323067138 84:53:94283987504301478078272 84:54:54125992826543441119008 84:55:29523268814478240610368 84:56:15288835636069088887512 84:57:7510305224735692786848 84:58:3496176570135581124912 84:59:1540687980059747614368 84:60:641953325024894839320 84:61:252571800009794690880 84:62:93695990326214159520 84:63:32719234717090658880 84:64:10735998891545372445 84:65:3303384274321653060 84:66:950974260789566790 84:67:255485622301674660 84:68:63871405575418665 84:69:14810760713140560 84:70:3173734438530120 84:71:625806790696080 84:72:112992892764570 84:73:18574174153080 84:74:2761025887620 84:75:368136785016 84:76:43595145594 84:77:4529365776 84:78:406481544 84:79:30872016 84:80:1929501 84:81:95284 84:82:3486 84:83:84 84:84:1 # binomial(85, k) for 0 <= k <= 85 85:0:1 85:1:85 85:2:3570 85:3:98770 85:4:2024785 85:5:32801517 85:6:437353560 85:7:4935847320 85:8:48124511370 85:9:411731930610 85:10:3129162672636 85:11:21335200040700 85:12:131567066917650 85:13:738799683460650 85:14:3799541229226200 85:15:17984495151670680 85:16:78682166288559225 85:17:319357027877093325 85:18:1206459883091241450 85:19:4254358535111219850 85:20:14039383165867025505 85:21:43455233608636031325 85:22:126415225043304818400 85:23:346267790336008850400 85:24:894525125034689530200 85:25:2182641305084642453688 85:26:5036864550195328739280 85:27:11006481794871273911760 85:28:22799140860804781674360 85:29:44812104450547329497880 85:30:83649261641021681729376 85:31:148409980330844919197280 85:32:250441841808300801145410 85:33:402224776237574013960810 85:34:615167304833936727234180 85:35:896386644186593516826948 85:36:1244981450259157662259650 85:37:1648759217910776363533050 85:38:2082643222624138564462800 85:39:2509852088803449039224400 85:40:2886329902123966395108060 85:41:3167923063306792384874700 85:42:3318776542511877736535400 85:43:3318776542511877736535400 85:44:3167923063306792384874700 85:45:2886329902123966395108060 85:46:2509852088803449039224400 85:47:2082643222624138564462800 85:48:1648759217910776363533050 85:49:1244981450259157662259650 85:50:896386644186593516826948 85:51:615167304833936727234180 85:52:402224776237574013960810 85:53:250441841808300801145410 85:54:148409980330844919197280 85:55:83649261641021681729376 85:56:44812104450547329497880 85:57:22799140860804781674360 85:58:11006481794871273911760 85:59:5036864550195328739280 85:60:2182641305084642453688 85:61:894525125034689530200 85:62:346267790336008850400 85:63:126415225043304818400 85:64:43455233608636031325 85:65:14039383165867025505 85:66:4254358535111219850 85:67:1206459883091241450 85:68:319357027877093325 85:69:78682166288559225 85:70:17984495151670680 85:71:3799541229226200 85:72:738799683460650 85:73:131567066917650 85:74:21335200040700 85:75:3129162672636 85:76:411731930610 85:77:48124511370 85:78:4935847320 85:79:437353560 85:80:32801517 85:81:2024785 85:82:98770 85:83:3570 85:84:85 85:85:1 # binomial(86, k) for 0 <= k <= 86 86:0:1 86:1:86 86:2:3655 86:3:102340 86:4:2123555 86:5:34826302 86:6:470155077 86:7:5373200880 86:8:53060358690 86:9:459856441980 86:10:3540894603246 86:11:24464362713336 86:12:152902266958350 86:13:870366750378300 86:14:4538340912686850 86:15:21784036380896880 86:16:96666661440229905 86:17:398039194165652550 86:18:1525816910968334775 86:19:5460818418202461300 86:20:18293741700978245355 86:21:57494616774503056830 86:22:169870458651940849725 86:23:472683015379313668800 86:24:1240792915370698380600 86:25:3077166430119331983888 86:26:7219505855279971192968 86:27:16043346345066602651040 86:28:33805622655676055586120 86:29:67611245311352111172240 86:30:128461366091569011227256 86:31:232059241971866600926656 86:32:398851822139145720342690 86:33:652666618045874815106220 86:34:1017392081071510741194990 86:35:1511553949020530244061128 86:36:2141368094445751179086598 86:37:2893740668169934025792700 86:38:3731402440534914927995850 86:39:4592495311427587603687200 86:40:5396181990927415434332460 86:41:6054252965430758779982760 86:42:6486699605818670121410100 86:43:6637553085023755473070800 86:44:6486699605818670121410100 86:45:6054252965430758779982760 86:46:5396181990927415434332460 86:47:4592495311427587603687200 86:48:3731402440534914927995850 86:49:2893740668169934025792700 86:50:2141368094445751179086598 86:51:1511553949020530244061128 86:52:1017392081071510741194990 86:53:652666618045874815106220 86:54:398851822139145720342690 86:55:232059241971866600926656 86:56:128461366091569011227256 86:57:67611245311352111172240 86:58:33805622655676055586120 86:59:16043346345066602651040 86:60:7219505855279971192968 86:61:3077166430119331983888 86:62:1240792915370698380600 86:63:472683015379313668800 86:64:169870458651940849725 86:65:57494616774503056830 86:66:18293741700978245355 86:67:5460818418202461300 86:68:1525816910968334775 86:69:398039194165652550 86:70:96666661440229905 86:71:21784036380896880 86:72:4538340912686850 86:73:870366750378300 86:74:152902266958350 86:75:24464362713336 86:76:3540894603246 86:77:459856441980 86:78:53060358690 86:79:5373200880 86:80:470155077 86:81:34826302 86:82:2123555 86:83:102340 86:84:3655 86:85:86 86:86:1 # binomial(87, k) for 0 <= k <= 87 87:0:1 87:1:87 87:2:3741 87:3:105995 87:4:2225895 87:5:36949857 87:6:504981379 87:7:5843355957 87:8:58433559570 87:9:512916800670 87:10:4000751045226 87:11:28005257316582 87:12:177366629671686 87:13:1023269017336650 87:14:5408707663065150 87:15:26322377293583730 87:16:118450697821126785 87:17:494705855605882455 87:18:1923856105133987325 87:19:6986635329170796075 87:20:23754560119180706655 87:21:75788358475481302185 87:22:227365075426443906555 87:23:642553474031254518525 87:24:1713475930750012049400 87:25:4317959345490030364488 87:26:10296672285399303176856 87:27:23262852200346573844008 87:28:49848969000742658237160 87:29:101416867967028166758360 87:30:196072611402921122399496 87:31:360520608063435612153912 87:32:630911064111012321269346 87:33:1051518440185020535448910 87:34:1670058699117385556301210 87:35:2528946030092040985256118 87:36:3652922043466281423147726 87:37:5035108762615685204879298 87:38:6625143108704848953788550 87:39:8323897751962502531683050 87:40:9988677302355003038019660 87:41:11450434956358174214315220 87:42:12540952571249428901392860 87:43:13124252690842425594480900 87:44:13124252690842425594480900 87:45:12540952571249428901392860 87:46:11450434956358174214315220 87:47:9988677302355003038019660 87:48:8323897751962502531683050 87:49:6625143108704848953788550 87:50:5035108762615685204879298 87:51:3652922043466281423147726 87:52:2528946030092040985256118 87:53:1670058699117385556301210 87:54:1051518440185020535448910 87:55:630911064111012321269346 87:56:360520608063435612153912 87:57:196072611402921122399496 87:58:101416867967028166758360 87:59:49848969000742658237160 87:60:23262852200346573844008 87:61:10296672285399303176856 87:62:4317959345490030364488 87:63:1713475930750012049400 87:64:642553474031254518525 87:65:227365075426443906555 87:66:75788358475481302185 87:67:23754560119180706655 87:68:6986635329170796075 87:69:1923856105133987325 87:70:494705855605882455 87:71:118450697821126785 87:72:26322377293583730 87:73:5408707663065150 87:74:1023269017336650 87:75:177366629671686 87:76:28005257316582 87:77:4000751045226 87:78:512916800670 87:79:58433559570 87:80:5843355957 87:81:504981379 87:82:36949857 87:83:2225895 87:84:105995 87:85:3741 87:86:87 87:87:1 # binomial(88, k) for 0 <= k <= 88 88:0:1 88:1:88 88:2:3828 88:3:109736 88:4:2331890 88:5:39175752 88:6:541931236 88:7:6348337336 88:8:64276915527 88:9:571350360240 88:10:4513667845896 88:11:32006008361808 88:12:205371886988268 88:13:1200635647008336 88:14:6431976680401800 88:15:31731084956648880 88:16:144773075114710515 88:17:613156553427009240 88:18:2418561960739869780 88:19:8910491434304783400 88:20:30741195448351502730 88:21:99542918594662008840 88:22:303153433901925208740 88:23:869918549457698425080 88:24:2356029404781266567925 88:25:6031435276240042413888 88:26:14614631630889333541344 88:27:33559524485745877020864 88:28:73111821201089232081168 88:29:151265836967770824995520 88:30:297489479369949289157856 88:31:556593219466356734553408 88:32:991431672174447933423258 88:33:1682429504296032856718256 88:34:2721577139302406091750120 88:35:4199004729209426541557328 88:36:6181868073558322408403844 88:37:8688030806081966628027024 88:38:11660251871320534158667848 88:39:14949040860667351485471600 88:40:18312575054317505569702710 88:41:21439112258713177252334880 88:42:23991387527607603115708080 88:43:25665205262091854495873760 88:44:26248505381684851188961800 88:45:25665205262091854495873760 88:46:23991387527607603115708080 88:47:21439112258713177252334880 88:48:18312575054317505569702710 88:49:14949040860667351485471600 88:50:11660251871320534158667848 88:51:8688030806081966628027024 88:52:6181868073558322408403844 88:53:4199004729209426541557328 88:54:2721577139302406091750120 88:55:1682429504296032856718256 88:56:991431672174447933423258 88:57:556593219466356734553408 88:58:297489479369949289157856 88:59:151265836967770824995520 88:60:73111821201089232081168 88:61:33559524485745877020864 88:62:14614631630889333541344 88:63:6031435276240042413888 88:64:2356029404781266567925 88:65:869918549457698425080 88:66:303153433901925208740 88:67:99542918594662008840 88:68:30741195448351502730 88:69:8910491434304783400 88:70:2418561960739869780 88:71:613156553427009240 88:72:144773075114710515 88:73:31731084956648880 88:74:6431976680401800 88:75:1200635647008336 88:76:205371886988268 88:77:32006008361808 88:78:4513667845896 88:79:571350360240 88:80:64276915527 88:81:6348337336 88:82:541931236 88:83:39175752 88:84:2331890 88:85:109736 88:86:3828 88:87:88 88:88:1 # binomial(89, k) for 0 <= k <= 89 89:0:1 89:1:89 89:2:3916 89:3:113564 89:4:2441626 89:5:41507642 89:6:581106988 89:7:6890268572 89:8:70625252863 89:9:635627275767 89:10:5085018206136 89:11:36519676207704 89:12:237377895350076 89:13:1406007533996604 89:14:7632612327410136 89:15:38163061637050680 89:16:176504160071359395 89:17:757929628541719755 89:18:3031718514166879020 89:19:11329053395044653180 89:20:39651686882656286130 89:21:130284114043013511570 89:22:402696352496587217580 89:23:1173071983359623633820 89:24:3225947954238964993005 89:25:8387464681021308981813 89:26:20646066907129375955232 89:27:48174156116635210562208 89:28:106671345686835109102032 89:29:224377658168860057076688 89:30:448755316337720114153376 89:31:854082698836306023711264 89:32:1548024891640804667976666 89:33:2673861176470480790141514 89:34:4404006643598438948468376 89:35:6920581868511832633307448 89:36:10380872802767748949961172 89:37:14869898879640289036430868 89:38:20348282677402500786694872 89:39:26609292731987885644139448 89:40:33261615914984857055174310 89:41:39751687313030682822037590 89:42:45430499786320780368042960 89:43:49656592789699457611581840 89:44:51913710643776705684835560 89:45:51913710643776705684835560 89:46:49656592789699457611581840 89:47:45430499786320780368042960 89:48:39751687313030682822037590 89:49:33261615914984857055174310 89:50:26609292731987885644139448 89:51:20348282677402500786694872 89:52:14869898879640289036430868 89:53:10380872802767748949961172 89:54:6920581868511832633307448 89:55:4404006643598438948468376 89:56:2673861176470480790141514 89:57:1548024891640804667976666 89:58:854082698836306023711264 89:59:448755316337720114153376 89:60:224377658168860057076688 89:61:106671345686835109102032 89:62:48174156116635210562208 89:63:20646066907129375955232 89:64:8387464681021308981813 89:65:3225947954238964993005 89:66:1173071983359623633820 89:67:402696352496587217580 89:68:130284114043013511570 89:69:39651686882656286130 89:70:11329053395044653180 89:71:3031718514166879020 89:72:757929628541719755 89:73:176504160071359395 89:74:38163061637050680 89:75:7632612327410136 89:76:1406007533996604 89:77:237377895350076 89:78:36519676207704 89:79:5085018206136 89:80:635627275767 89:81:70625252863 89:82:6890268572 89:83:581106988 89:84:41507642 89:85:2441626 89:86:113564 89:87:3916 89:88:89 89:89:1 # binomial(90, k) for 0 <= k <= 90 90:0:1 90:1:90 90:2:4005 90:3:117480 90:4:2555190 90:5:43949268 90:6:622614630 90:7:7471375560 90:8:77515521435 90:9:706252528630 90:10:5720645481903 90:11:41604694413840 90:12:273897571557780 90:13:1643385429346680 90:14:9038619861406740 90:15:45795673964460816 90:16:214667221708410075 90:17:934433788613079150 90:18:3789648142708598775 90:19:14360771909211532200 90:20:50980740277700939310 90:21:169935800925669797700 90:22:532980466539600729150 90:23:1575768335856210851400 90:24:4399019937598588626825 90:25:11613412635260273974818 90:26:29033531588150684937045 90:27:68820223023764586517440 90:28:154845501803470319664240 90:29:331049003855695166178720 90:30:673132974506580171230064 90:31:1302838015174026137864640 90:32:2402107590477110691687930 90:33:4221886068111285458118180 90:34:7077867820068919738609890 90:35:11324588512110271581775824 90:36:17301454671279581583268620 90:37:25250771682408037986392040 90:38:35218181557042789823125740 90:39:46957575409390386430834320 90:40:59870908646972742699313758 90:41:73013303228015539877211900 90:42:85182187099351463190080550 90:43:95087092576020237979624800 90:44:101570303433476163296417400 90:45:103827421287553411369671120 90:46:101570303433476163296417400 90:47:95087092576020237979624800 90:48:85182187099351463190080550 90:49:73013303228015539877211900 90:50:59870908646972742699313758 90:51:46957575409390386430834320 90:52:35218181557042789823125740 90:53:25250771682408037986392040 90:54:17301454671279581583268620 90:55:11324588512110271581775824 90:56:7077867820068919738609890 90:57:4221886068111285458118180 90:58:2402107590477110691687930 90:59:1302838015174026137864640 90:60:673132974506580171230064 90:61:331049003855695166178720 90:62:154845501803470319664240 90:63:68820223023764586517440 90:64:29033531588150684937045 90:65:11613412635260273974818 90:66:4399019937598588626825 90:67:1575768335856210851400 90:68:532980466539600729150 90:69:169935800925669797700 90:70:50980740277700939310 90:71:14360771909211532200 90:72:3789648142708598775 90:73:934433788613079150 90:74:214667221708410075 90:75:45795673964460816 90:76:9038619861406740 90:77:1643385429346680 90:78:273897571557780 90:79:41604694413840 90:80:5720645481903 90:81:706252528630 90:82:77515521435 90:83:7471375560 90:84:622614630 90:85:43949268 90:86:2555190 90:87:117480 90:88:4005 90:89:90 90:90:1 # binomial(91, k) for 0 <= k <= 91 91:0:1 91:1:91 91:2:4095 91:3:121485 91:4:2672670 91:5:46504458 91:6:666563898 91:7:8093990190 91:8:84986896995 91:9:783768050065 91:10:6426898010533 91:11:47325339895743 91:12:315502265971620 91:13:1917283000904460 91:14:10682005290753420 91:15:54834293825867556 91:16:260462895672870891 91:17:1149101010321489225 91:18:4724081931321677925 91:19:18150420051920130975 91:20:65341512186912471510 91:21:220916541203370737010 91:22:702916267465270526850 91:23:2108748802395811580550 91:24:5974788273454799478225 91:25:16012432572858862601643 91:26:40646944223410958911863 91:27:97853754611915271454485 91:28:223665724827234906181680 91:29:485894505659165485842960 91:30:1004181978362275337408784 91:31:1975970989680606309094704 91:32:3704945605651136829552570 91:33:6623993658588396149806110 91:34:11299753888180205196728070 91:35:18402456332179191320385714 91:36:28626043183389853165044444 91:37:42552226353687619569660660 91:38:60468953239450827809517780 91:39:82175756966433176253960060 91:40:106828484056363129130148078 91:41:132884211874988282576525658 91:42:158195490327367003067292450 91:43:180269279675371701169705350 91:44:196657396009496401276042200 91:45:205397724721029574666088520 91:46:205397724721029574666088520 91:47:196657396009496401276042200 91:48:180269279675371701169705350 91:49:158195490327367003067292450 91:50:132884211874988282576525658 91:51:106828484056363129130148078 91:52:82175756966433176253960060 91:53:60468953239450827809517780 91:54:42552226353687619569660660 91:55:28626043183389853165044444 91:56:18402456332179191320385714 91:57:11299753888180205196728070 91:58:6623993658588396149806110 91:59:3704945605651136829552570 91:60:1975970989680606309094704 91:61:1004181978362275337408784 91:62:485894505659165485842960 91:63:223665724827234906181680 91:64:97853754611915271454485 91:65:40646944223410958911863 91:66:16012432572858862601643 91:67:5974788273454799478225 91:68:2108748802395811580550 91:69:702916267465270526850 91:70:220916541203370737010 91:71:65341512186912471510 91:72:18150420051920130975 91:73:4724081931321677925 91:74:1149101010321489225 91:75:260462895672870891 91:76:54834293825867556 91:77:10682005290753420 91:78:1917283000904460 91:79:315502265971620 91:80:47325339895743 91:81:6426898010533 91:82:783768050065 91:83:84986896995 91:84:8093990190 91:85:666563898 91:86:46504458 91:87:2672670 91:88:121485 91:89:4095 91:90:91 91:91:1 # binomial(92, k) for 0 <= k <= 92 92:0:1 92:1:92 92:2:4186 92:3:125580 92:4:2794155 92:5:49177128 92:6:713068356 92:7:8760554088 92:8:93080887185 92:9:868754947060 92:10:7210666060598 92:11:53752237906276 92:12:362827605867363 92:13:2232785266876080 92:14:12599288291657880 92:15:65516299116620976 92:16:315297189498738447 92:17:1409563905994360116 92:18:5873182941643167150 92:19:22874501983241808900 92:20:83491932238832602485 92:21:286258053390283208520 92:22:923832808668641263860 92:23:2811665069861082107400 92:24:8083537075850611058775 92:25:21987220846313662079868 92:26:56659376796269821513506 92:27:138500698835326230366348 92:28:321519479439150177636165 92:29:709560230486400392024640 92:30:1490076484021440823251744 92:31:2980152968042881646503488 92:32:5680916595331743138647274 92:33:10328939264239532979358680 92:34:17923747546768601346534180 92:35:29702210220359396517113784 92:36:47028499515569044485430158 92:37:71178269537077472734705104 92:38:103021179593138447379178440 92:39:142644710205884004063477840 92:40:189004241022796305384108138 92:41:239712695931351411706673736 92:42:291079702202355285643818108 92:43:338464770002738704236997800 92:44:376926675684868102445747550 92:45:402055120730525975942130720 92:46:410795449442059149332177040 92:47:402055120730525975942130720 92:48:376926675684868102445747550 92:49:338464770002738704236997800 92:50:291079702202355285643818108 92:51:239712695931351411706673736 92:52:189004241022796305384108138 92:53:142644710205884004063477840 92:54:103021179593138447379178440 92:55:71178269537077472734705104 92:56:47028499515569044485430158 92:57:29702210220359396517113784 92:58:17923747546768601346534180 92:59:10328939264239532979358680 92:60:5680916595331743138647274 92:61:2980152968042881646503488 92:62:1490076484021440823251744 92:63:709560230486400392024640 92:64:321519479439150177636165 92:65:138500698835326230366348 92:66:56659376796269821513506 92:67:21987220846313662079868 92:68:8083537075850611058775 92:69:2811665069861082107400 92:70:923832808668641263860 92:71:286258053390283208520 92:72:83491932238832602485 92:73:22874501983241808900 92:74:5873182941643167150 92:75:1409563905994360116 92:76:315297189498738447 92:77:65516299116620976 92:78:12599288291657880 92:79:2232785266876080 92:80:362827605867363 92:81:53752237906276 92:82:7210666060598 92:83:868754947060 92:84:93080887185 92:85:8760554088 92:86:713068356 92:87:49177128 92:88:2794155 92:89:125580 92:90:4186 92:91:92 92:92:1 # binomial(93, k) for 0 <= k <= 93 93:0:1 93:1:93 93:2:4278 93:3:129766 93:4:2919735 93:5:51971283 93:6:762245484 93:7:9473622444 93:8:101841441273 93:9:961835834245 93:10:8079421007658 93:11:60962903966874 93:12:416579843773639 93:13:2595612872743443 93:14:14832073558533960 93:15:78115587408278856 93:16:380813488615359423 93:17:1724861095493098563 93:18:7282746847637527266 93:19:28747684924884976050 93:20:106366434222074411385 93:21:369749985629115811005 93:22:1210090862058924472380 93:23:3735497878529723371260 93:24:10895202145711693166175 93:25:30070757922164273138643 93:26:78646597642583483593374 93:27:195160075631596051879854 93:28:460020178274476408002513 93:29:1031079709925550569660805 93:30:2199636714507841215276384 93:31:4470229452064322469755232 93:32:8661069563374624785150762 93:33:16009855859571276118005954 93:34:28252686811008134325892860 93:35:47625957767127997863647964 93:36:76730709735928441002543942 93:37:118206769052646517220135262 93:38:174199449130215920113883544 93:39:245665889799022451442656280 93:40:331648951228680309447585978 93:41:428716936954147717090781874 93:42:530792398133706697350491844 93:43:629544472205093989880815908 93:44:715391445687606806682745350 93:45:778981796415394078387878270 93:46:812850570172585125274307760 93:47:812850570172585125274307760 93:48:778981796415394078387878270 93:49:715391445687606806682745350 93:50:629544472205093989880815908 93:51:530792398133706697350491844 93:52:428716936954147717090781874 93:53:331648951228680309447585978 93:54:245665889799022451442656280 93:55:174199449130215920113883544 93:56:118206769052646517220135262 93:57:76730709735928441002543942 93:58:47625957767127997863647964 93:59:28252686811008134325892860 93:60:16009855859571276118005954 93:61:8661069563374624785150762 93:62:4470229452064322469755232 93:63:2199636714507841215276384 93:64:1031079709925550569660805 93:65:460020178274476408002513 93:66:195160075631596051879854 93:67:78646597642583483593374 93:68:30070757922164273138643 93:69:10895202145711693166175 93:70:3735497878529723371260 93:71:1210090862058924472380 93:72:369749985629115811005 93:73:106366434222074411385 93:74:28747684924884976050 93:75:7282746847637527266 93:76:1724861095493098563 93:77:380813488615359423 93:78:78115587408278856 93:79:14832073558533960 93:80:2595612872743443 93:81:416579843773639 93:82:60962903966874 93:83:8079421007658 93:84:961835834245 93:85:101841441273 93:86:9473622444 93:87:762245484 93:88:51971283 93:89:2919735 93:90:129766 93:91:4278 93:92:93 93:93:1 # binomial(94, k) for 0 <= k <= 94 94:0:1 94:1:94 94:2:4371 94:3:134044 94:4:3049501 94:5:54891018 94:6:814216767 94:7:10235867928 94:8:111315063717 94:9:1063677275518 94:10:9041256841903 94:11:69042324974532 94:12:477542747740513 94:13:3012192716517082 94:14:17427686431277403 94:15:92947660966812816 94:16:458929076023638279 94:17:2105674584108457986 94:18:9007607943130625829 94:19:36030431772522503316 94:20:135114119146959387435 94:21:476116419851190222390 94:22:1579840847688040283385 94:23:4945588740588647843640 94:24:14630700024241416537435 94:25:40965960067875966304818 94:26:108717355564747756732017 94:27:273806673274179535473228 94:28:655180253906072459882367 94:29:1491099888200026977663318 94:30:3230716424433391784937189 94:31:6669866166572163685031616 94:32:13131299015438947254905994 94:33:24670925422945900903156716 94:34:44262542670579410443898814 94:35:75878644578136132189540824 94:36:124356667503056438866191906 94:37:194937478788574958222679204 94:38:292406218182862437334018806 94:39:419865338929238371556539824 94:40:577314841027702760890242258 94:41:760365888182828026538367852 94:42:959509335087854414441273718 94:43:1160336870338800687231307752 94:44:1344935917892700796563561258 94:45:1494373242103000885070623620 94:46:1591832366587979203662186030 94:47:1625701140345170250548615520 94:48:1591832366587979203662186030 94:49:1494373242103000885070623620 94:50:1344935917892700796563561258 94:51:1160336870338800687231307752 94:52:959509335087854414441273718 94:53:760365888182828026538367852 94:54:577314841027702760890242258 94:55:419865338929238371556539824 94:56:292406218182862437334018806 94:57:194937478788574958222679204 94:58:124356667503056438866191906 94:59:75878644578136132189540824 94:60:44262542670579410443898814 94:61:24670925422945900903156716 94:62:13131299015438947254905994 94:63:6669866166572163685031616 94:64:3230716424433391784937189 94:65:1491099888200026977663318 94:66:655180253906072459882367 94:67:273806673274179535473228 94:68:108717355564747756732017 94:69:40965960067875966304818 94:70:14630700024241416537435 94:71:4945588740588647843640 94:72:1579840847688040283385 94:73:476116419851190222390 94:74:135114119146959387435 94:75:36030431772522503316 94:76:9007607943130625829 94:77:2105674584108457986 94:78:458929076023638279 94:79:92947660966812816 94:80:17427686431277403 94:81:3012192716517082 94:82:477542747740513 94:83:69042324974532 94:84:9041256841903 94:85:1063677275518 94:86:111315063717 94:87:10235867928 94:88:814216767 94:89:54891018 94:90:3049501 94:91:134044 94:92:4371 94:93:94 94:94:1 # binomial(95, k) for 0 <= k <= 95 95:0:1 95:1:95 95:2:4465 95:3:138415 95:4:3183545 95:5:57940519 95:6:869107785 95:7:11050084695 95:8:121550931645 95:9:1174992339235 95:10:10104934117421 95:11:78083581816435 95:12:546585072715045 95:13:3489735464257595 95:14:20439879147794485 95:15:110375347398090219 95:16:551876736990451095 95:17:2564603660132096265 95:18:11113282527239083815 95:19:45038039715653129145 95:20:171144550919481890751 95:21:611230538998149609825 95:22:2055957267539230505775 95:23:6525429588276688127025 95:24:19576288764830064381075 95:25:55596660092117382842253 95:26:149683315632623723036835 95:27:382524028838927292205245 95:28:928986927180251995355595 95:29:2146280142106099437545685 95:30:4721816312633418762600507 95:31:9900582591005555469968805 95:32:19801165182011110939937610 95:33:37802224438384848158062710 95:34:68933468093525311347055530 95:35:120141187248715542633439638 95:36:200235312081192571055732730 95:37:319294146291631397088871110 95:38:487343696971437395556698010 95:39:712271557112100808890558630 95:40:997180179956941132446782082 95:41:1337680729210530787428610110 95:42:1719875223270682440979641570 95:43:2119846205426655101672581470 95:44:2505272788231501483794869010 95:45:2839309159995701681634184878 95:46:3086205608690980088732809650 95:47:3217533506933149454210801550 95:48:3217533506933149454210801550 95:49:3086205608690980088732809650 95:50:2839309159995701681634184878 95:51:2505272788231501483794869010 95:52:2119846205426655101672581470 95:53:1719875223270682440979641570 95:54:1337680729210530787428610110 95:55:997180179956941132446782082 95:56:712271557112100808890558630 95:57:487343696971437395556698010 95:58:319294146291631397088871110 95:59:200235312081192571055732730 95:60:120141187248715542633439638 95:61:68933468093525311347055530 95:62:37802224438384848158062710 95:63:19801165182011110939937610 95:64:9900582591005555469968805 95:65:4721816312633418762600507 95:66:2146280142106099437545685 95:67:928986927180251995355595 95:68:382524028838927292205245 95:69:149683315632623723036835 95:70:55596660092117382842253 95:71:19576288764830064381075 95:72:6525429588276688127025 95:73:2055957267539230505775 95:74:611230538998149609825 95:75:171144550919481890751 95:76:45038039715653129145 95:77:11113282527239083815 95:78:2564603660132096265 95:79:551876736990451095 95:80:110375347398090219 95:81:20439879147794485 95:82:3489735464257595 95:83:546585072715045 95:84:78083581816435 95:85:10104934117421 95:86:1174992339235 95:87:121550931645 95:88:11050084695 95:89:869107785 95:90:57940519 95:91:3183545 95:92:138415 95:93:4465 95:94:95 95:95:1 # binomial(96, k) for 0 <= k <= 96 96:0:1 96:1:96 96:2:4560 96:3:142880 96:4:3321960 96:5:61124064 96:6:927048304 96:7:11919192480 96:8:132601016340 96:9:1296543270880 96:10:11279926456656 96:11:88188515933856 96:12:624668654531480 96:13:4036320536972640 96:14:23929614612052080 96:15:130815226545884704 96:16:662252084388541314 96:17:3116480397122547360 96:18:13677886187371180080 96:19:56151322242892212960 96:20:216182590635135019896 96:21:782375089917631500576 96:22:2667187806537380115600 96:23:8581386855815918632800 96:24:26101718353106752508100 96:25:75172948856947447223328 96:26:205279975724741105879088 96:27:532207344471551015242080 96:28:1311510956019179287560840 96:29:3075267069286351432901280 96:30:6868096454739518200146192 96:31:14622398903638974232569312 96:32:29701747773016666409906415 96:33:57603389620395959098000320 96:34:106735692531910159505118240 96:35:189074655342240853980495168 96:36:320376499329908113689172368 96:37:519529458372823968144603840 96:38:806637843263068792645569120 96:39:1199615254083538204447256640 96:40:1709451737069041941337340712 96:41:2334860909167471919875392192 96:42:3057555952481213228408251680 96:43:3839721428697337542652223040 96:44:4625118993658156585467450480 96:45:5344581948227203165429053888 96:46:5925514768686681770366994528 96:47:6303739115624129542943611200 96:48:6435067013866298908421603100 96:49:6303739115624129542943611200 96:50:5925514768686681770366994528 96:51:5344581948227203165429053888 96:52:4625118993658156585467450480 96:53:3839721428697337542652223040 96:54:3057555952481213228408251680 96:55:2334860909167471919875392192 96:56:1709451737069041941337340712 96:57:1199615254083538204447256640 96:58:806637843263068792645569120 96:59:519529458372823968144603840 96:60:320376499329908113689172368 96:61:189074655342240853980495168 96:62:106735692531910159505118240 96:63:57603389620395959098000320 96:64:29701747773016666409906415 96:65:14622398903638974232569312 96:66:6868096454739518200146192 96:67:3075267069286351432901280 96:68:1311510956019179287560840 96:69:532207344471551015242080 96:70:205279975724741105879088 96:71:75172948856947447223328 96:72:26101718353106752508100 96:73:8581386855815918632800 96:74:2667187806537380115600 96:75:782375089917631500576 96:76:216182590635135019896 96:77:56151322242892212960 96:78:13677886187371180080 96:79:3116480397122547360 96:80:662252084388541314 96:81:130815226545884704 96:82:23929614612052080 96:83:4036320536972640 96:84:624668654531480 96:85:88188515933856 96:86:11279926456656 96:87:1296543270880 96:88:132601016340 96:89:11919192480 96:90:927048304 96:91:61124064 96:92:3321960 96:93:142880 96:94:4560 96:95:96 96:96:1 # binomial(97, k) for 0 <= k <= 97 97:0:1 97:1:97 97:2:4656 97:3:147440 97:4:3464840 97:5:64446024 97:6:988172368 97:7:12846240784 97:8:144520208820 97:9:1429144287220 97:10:12576469727536 97:11:99468442390512 97:12:712857170465336 97:13:4660989191504120 97:14:27965935149024720 97:15:154744841157936784 97:16:793067310934426018 97:17:3778732481511088674 97:18:16794366584493727440 97:19:69829208430263393040 97:20:272333912878027232856 97:21:998557680552766520472 97:22:3449562896455011616176 97:23:11248574662353298748400 97:24:34683105208922671140900 97:25:101274667210054199731428 97:26:280452924581688553102416 97:27:737487320196292121121168 97:28:1843718300490730302802920 97:29:4386778025305530720462120 97:30:9943363524025869633047472 97:31:21490495358378492432715504 97:32:44324146676655640642475727 97:33:87305137393412625507906735 97:34:164339082152306118603118560 97:35:295810347874151013485613408 97:36:509451154672148967669667536 97:37:839905957702732081833776208 97:38:1326167301635892760790172960 97:39:2006253097346606997092825760 97:40:2909066991152580145784597352 97:41:4044312646236513861212732904 97:42:5392416861648685148283643872 97:43:6897277381178550771060474720 97:44:8464840422355494128119673520 97:45:9969700941885359750896504368 97:46:11270096716913884935796048416 97:47:12229253884310811313310605728 97:48:12738806129490428451365214300 97:49:12738806129490428451365214300 97:50:12229253884310811313310605728 97:51:11270096716913884935796048416 97:52:9969700941885359750896504368 97:53:8464840422355494128119673520 97:54:6897277381178550771060474720 97:55:5392416861648685148283643872 97:56:4044312646236513861212732904 97:57:2909066991152580145784597352 97:58:2006253097346606997092825760 97:59:1326167301635892760790172960 97:60:839905957702732081833776208 97:61:509451154672148967669667536 97:62:295810347874151013485613408 97:63:164339082152306118603118560 97:64:87305137393412625507906735 97:65:44324146676655640642475727 97:66:21490495358378492432715504 97:67:9943363524025869633047472 97:68:4386778025305530720462120 97:69:1843718300490730302802920 97:70:737487320196292121121168 97:71:280452924581688553102416 97:72:101274667210054199731428 97:73:34683105208922671140900 97:74:11248574662353298748400 97:75:3449562896455011616176 97:76:998557680552766520472 97:77:272333912878027232856 97:78:69829208430263393040 97:79:16794366584493727440 97:80:3778732481511088674 97:81:793067310934426018 97:82:154744841157936784 97:83:27965935149024720 97:84:4660989191504120 97:85:712857170465336 97:86:99468442390512 97:87:12576469727536 97:88:1429144287220 97:89:144520208820 97:90:12846240784 97:91:988172368 97:92:64446024 97:93:3464840 97:94:147440 97:95:4656 97:96:97 97:97:1 # binomial(98, k) for 0 <= k <= 98 98:0:1 98:1:98 98:2:4753 98:3:152096 98:4:3612280 98:5:67910864 98:6:1052618392 98:7:13834413152 98:8:157366449604 98:9:1573664496040 98:10:14005614014756 98:11:112044912118048 98:12:812325612855848 98:13:5373846361969456 98:14:32626924340528840 98:15:182710776306961504 98:16:947812152092362802 98:17:4571799792445514692 98:18:20573099066004816114 98:19:86623575014757120480 98:20:342163121308290625896 98:21:1270891593430793753328 98:22:4448120577007778136648 98:23:14698137558808310364576 98:24:45931679871275969889300 98:25:135957772418976870872328 98:26:381727591791742752833844 98:27:1017940244777980674223584 98:28:2581205620687022423924088 98:29:6230496325796261023265040 98:30:14330141549331400353509592 98:31:31433858882404362065762976 98:32:65814642035034133075191231 98:33:131629284070068266150382462 98:34:251644219545718744111025295 98:35:460149430026457132088731968 98:36:805261502546299981155280944 98:37:1349357112374881049503443744 98:38:2166073259338624842623949168 98:39:3332420398982499757882998720 98:40:4915320088499187142877423112 98:41:6953379637389094006997330256 98:42:9436729507885199009496376776 98:43:12289694242827235919344118592 98:44:15362117803534044899180148240 98:45:18434541364240853879016177888 98:46:21239797658799244686692552784 98:47:23499350601224696249106654144 98:48:24968060013801239764675820028 98:49:25477612258980856902730428600 98:50:24968060013801239764675820028 98:51:23499350601224696249106654144 98:52:21239797658799244686692552784 98:53:18434541364240853879016177888 98:54:15362117803534044899180148240 98:55:12289694242827235919344118592 98:56:9436729507885199009496376776 98:57:6953379637389094006997330256 98:58:4915320088499187142877423112 98:59:3332420398982499757882998720 98:60:2166073259338624842623949168 98:61:1349357112374881049503443744 98:62:805261502546299981155280944 98:63:460149430026457132088731968 98:64:251644219545718744111025295 98:65:131629284070068266150382462 98:66:65814642035034133075191231 98:67:31433858882404362065762976 98:68:14330141549331400353509592 98:69:6230496325796261023265040 98:70:2581205620687022423924088 98:71:1017940244777980674223584 98:72:381727591791742752833844 98:73:135957772418976870872328 98:74:45931679871275969889300 98:75:14698137558808310364576 98:76:4448120577007778136648 98:77:1270891593430793753328 98:78:342163121308290625896 98:79:86623575014757120480 98:80:20573099066004816114 98:81:4571799792445514692 98:82:947812152092362802 98:83:182710776306961504 98:84:32626924340528840 98:85:5373846361969456 98:86:812325612855848 98:87:112044912118048 98:88:14005614014756 98:89:1573664496040 98:90:157366449604 98:91:13834413152 98:92:1052618392 98:93:67910864 98:94:3612280 98:95:152096 98:96:4753 98:97:98 98:98:1 # binomial(99, k) for 0 <= k <= 99 99:0:1 99:1:99 99:2:4851 99:3:156849 99:4:3764376 99:5:71523144 99:6:1120529256 99:7:14887031544 99:8:171200862756 99:9:1731030945644 99:10:15579278510796 99:11:126050526132804 99:12:924370524973896 99:13:6186171974825304 99:14:38000770702498296 99:15:215337700647490344 99:16:1130522928399324306 99:17:5519611944537877494 99:18:25144898858450330806 99:19:107196674080761936594 99:20:428786696323047746376 99:21:1613054714739084379224 99:22:5719012170438571889976 99:23:19146258135816088501224 99:24:60629817430084280253876 99:25:181889452290252840761628 99:26:517685364210719623706172 99:27:1399667836569723427057428 99:28:3599145865465003098147672 99:29:8811701946483283447189128 99:30:20560637875127661376774632 99:31:45764000431735762419272568 99:32:97248500917438495140954207 99:33:197443926105102399225573693 99:34:383273503615787010261407757 99:35:711793649572175876199757263 99:36:1265410932572757113244012912 99:37:2154618614921181030658724688 99:38:3515430371713505892127392912 99:39:5498493658321124600506947888 99:40:8247740487481686900760421832 99:41:11868699725888281149874753368 99:42:16390109145274293016493707032 99:43:21726423750712434928840495368 99:44:27651812046361280818524266832 99:45:33796659167774898778196326128 99:46:39674339023040098565708730672 99:47:44739148260023940935799206928 99:48:48467410615025936013782474172 99:49:50445672272782096667406248628 99:50:50445672272782096667406248628 99:51:48467410615025936013782474172 99:52:44739148260023940935799206928 99:53:39674339023040098565708730672 99:54:33796659167774898778196326128 99:55:27651812046361280818524266832 99:56:21726423750712434928840495368 99:57:16390109145274293016493707032 99:58:11868699725888281149874753368 99:59:8247740487481686900760421832 99:60:5498493658321124600506947888 99:61:3515430371713505892127392912 99:62:2154618614921181030658724688 99:63:1265410932572757113244012912 99:64:711793649572175876199757263 99:65:383273503615787010261407757 99:66:197443926105102399225573693 99:67:97248500917438495140954207 99:68:45764000431735762419272568 99:69:20560637875127661376774632 99:70:8811701946483283447189128 99:71:3599145865465003098147672 99:72:1399667836569723427057428 99:73:517685364210719623706172 99:74:181889452290252840761628 99:75:60629817430084280253876 99:76:19146258135816088501224 99:77:5719012170438571889976 99:78:1613054714739084379224 99:79:428786696323047746376 99:80:107196674080761936594 99:81:25144898858450330806 99:82:5519611944537877494 99:83:1130522928399324306 99:84:215337700647490344 99:85:38000770702498296 99:86:6186171974825304 99:87:924370524973896 99:88:126050526132804 99:89:15579278510796 99:90:1731030945644 99:91:171200862756 99:92:14887031544 99:93:1120529256 99:94:71523144 99:95:3764376 99:96:156849 99:97:4851 99:98:99 99:99:1 # binomial(100, k) for 0 <= k <= 100 100:0:1 100:1:100 100:2:4950 100:3:161700 100:4:3921225 100:5:75287520 100:6:1192052400 100:7:16007560800 100:8:186087894300 100:9:1902231808400 100:10:17310309456440 100:11:141629804643600 100:12:1050421051106700 100:13:7110542499799200 100:14:44186942677323600 100:15:253338471349988640 100:16:1345860629046814650 100:17:6650134872937201800 100:18:30664510802988208300 100:19:132341572939212267400 100:20:535983370403809682970 100:21:2041841411062132125600 100:22:7332066885177656269200 100:23:24865270306254660391200 100:24:79776075565900368755100 100:25:242519269720337121015504 100:26:699574816500972464467800 100:27:1917353200780443050763600 100:28:4998813702034726525205100 100:29:12410847811948286545336800 100:30:29372339821610944823963760 100:31:66324638306863423796047200 100:32:143012501349174257560226775 100:33:294692427022540894366527900 100:34:580717429720889409486981450 100:35:1095067153187962886461165020 100:36:1977204582144932989443770175 100:37:3420029547493938143902737600 100:38:5670048986634686922786117600 100:39:9013924030034630492634340800 100:40:13746234145802811501267369720 100:41:20116440213369968050635175200 100:42:28258808871162574166368460400 100:43:38116532895986727945334202400 100:44:49378235797073715747364762200 100:45:61448471214136179596720592960 100:46:73470998190814997343905056800 100:47:84413487283064039501507937600 100:48:93206558875049876949581681100 100:49:98913082887808032681188722800 100:50:100891344545564193334812497256 100:51:98913082887808032681188722800 100:52:93206558875049876949581681100 100:53:84413487283064039501507937600 100:54:73470998190814997343905056800 100:55:61448471214136179596720592960 100:56:49378235797073715747364762200 100:57:38116532895986727945334202400 100:58:28258808871162574166368460400 100:59:20116440213369968050635175200 100:60:13746234145802811501267369720 100:61:9013924030034630492634340800 100:62:5670048986634686922786117600 100:63:3420029547493938143902737600 100:64:1977204582144932989443770175 100:65:1095067153187962886461165020 100:66:580717429720889409486981450 100:67:294692427022540894366527900 100:68:143012501349174257560226775 100:69:66324638306863423796047200 100:70:29372339821610944823963760 100:71:12410847811948286545336800 100:72:4998813702034726525205100 100:73:1917353200780443050763600 100:74:699574816500972464467800 100:75:242519269720337121015504 100:76:79776075565900368755100 100:77:24865270306254660391200 100:78:7332066885177656269200 100:79:2041841411062132125600 100:80:535983370403809682970 100:81:132341572939212267400 100:82:30664510802988208300 100:83:6650134872937201800 100:84:1345860629046814650 100:85:253338471349988640 100:86:44186942677323600 100:87:7110542499799200 100:88:1050421051106700 100:89:141629804643600 100:90:17310309456440 100:91:1902231808400 100:92:186087894300 100:93:16007560800 100:94:1192052400 100:95:75287520 100:96:3921225 100:97:161700 100:98:4950 100:99:100 100:100:1 # binomial(101, k) for 0 <= k <= 101 101:0:1 101:1:101 101:2:5050 101:3:166650 101:4:4082925 101:5:79208745 101:6:1267339920 101:7:17199613200 101:8:202095455100 101:9:2088319702700 101:10:19212541264840 101:11:158940114100040 101:12:1192050855750300 101:13:8160963550905900 101:14:51297485177122800 101:15:297525414027312240 101:16:1599199100396803290 101:17:7995995501984016450 101:18:37314645675925410100 101:19:163006083742200475700 101:20:668324943343021950370 101:21:2577824781465941808570 101:22:9373908296239788394800 101:23:32197337191432316660400 101:24:104641345872155029146300 101:25:322295345286237489770604 101:26:942094086221309585483304 101:27:2616928017281415515231400 101:28:6916166902815169575968700 101:29:17409661513983013070541900 101:30:41783187633559231369300560 101:31:95696978128474368620010960 101:32:209337139656037681356273975 101:33:437704928371715151926754675 101:34:875409856743430303853509350 101:35:1675784582908852295948146470 101:36:3072271735332895875904935195 101:37:5397234129638871133346507775 101:38:9090078534128625066688855200 101:39:14683973016669317415420458400 101:40:22760158175837441993901710520 101:41:33862674359172779551902544920 101:42:48375249084532542217003635600 101:43:66375341767149302111702662800 101:44:87494768693060443692698964600 101:45:110826707011209895344085355160 101:46:134919469404951176940625649760 101:47:157884485473879036845412994400 101:48:177620046158113916451089618700 101:49:192119641762857909630770403900 101:50:199804427433372226016001220056 101:51:199804427433372226016001220056 101:52:192119641762857909630770403900 101:53:177620046158113916451089618700 101:54:157884485473879036845412994400 101:55:134919469404951176940625649760 101:56:110826707011209895344085355160 101:57:87494768693060443692698964600 101:58:66375341767149302111702662800 101:59:48375249084532542217003635600 101:60:33862674359172779551902544920 101:61:22760158175837441993901710520 101:62:14683973016669317415420458400 101:63:9090078534128625066688855200 101:64:5397234129638871133346507775 101:65:3072271735332895875904935195 101:66:1675784582908852295948146470 101:67:875409856743430303853509350 101:68:437704928371715151926754675 101:69:209337139656037681356273975 101:70:95696978128474368620010960 101:71:41783187633559231369300560 101:72:17409661513983013070541900 101:73:6916166902815169575968700 101:74:2616928017281415515231400 101:75:942094086221309585483304 101:76:322295345286237489770604 101:77:104641345872155029146300 101:78:32197337191432316660400 101:79:9373908296239788394800 101:80:2577824781465941808570 101:81:668324943343021950370 101:82:163006083742200475700 101:83:37314645675925410100 101:84:7995995501984016450 101:85:1599199100396803290 101:86:297525414027312240 101:87:51297485177122800 101:88:8160963550905900 101:89:1192050855750300 101:90:158940114100040 101:91:19212541264840 101:92:2088319702700 101:93:202095455100 101:94:17199613200 101:95:1267339920 101:96:79208745 101:97:4082925 101:98:166650 101:99:5050 101:100:101 101:101:1 # binomial(102, k) for 0 <= k <= 102 102:0:1 102:1:102 102:2:5151 102:3:171700 102:4:4249575 102:5:83291670 102:6:1346548665 102:7:18466953120 102:8:219295068300 102:9:2290415157800 102:10:21300860967540 102:11:178152655364880 102:12:1350990969850340 102:13:9353014406656200 102:14:59458448728028700 102:15:348822899204435040 102:16:1896724514424115530 102:17:9595194602380819740 102:18:45310641177909426550 102:19:200320729418125885800 102:20:831331027085222426070 102:21:3246149724808963758940 102:22:11951733077705730203370 102:23:41571245487672105055200 102:24:136838683063587345806700 102:25:426936691158392518916904 102:26:1264389431507547075253908 102:27:3559022103502725100714704 102:28:9533094920096585091200100 102:29:24325828416798182646510600 102:30:59192849147542244439842460 102:31:137480165762033599989311520 102:32:305034117784512049976284935 102:33:647042068027752833283028650 102:34:1313114785115145455780264025 102:35:2551194439652282599801655820 102:36:4748056318241748171853081665 102:37:8469505864971767009251442970 102:38:14487312663767496200035362975 102:39:23774051550797942482109313600 102:40:37444131192506759409322168920 102:41:56622832535010221545804255440 102:42:82237923443705321768906180520 102:43:114750590851681844328706298400 102:44:153870110460209745804401627400 102:45:198321475704270339036784319760 102:46:245746176416161072284711004920 102:47:292803954878830213786038644160 102:48:335504531631992953296502613100 102:49:369739687920971826081860022600 102:50:391924069196230135646771623956 102:51:399608854866744452032002440112 102:52:391924069196230135646771623956 102:53:369739687920971826081860022600 102:54:335504531631992953296502613100 102:55:292803954878830213786038644160 102:56:245746176416161072284711004920 102:57:198321475704270339036784319760 102:58:153870110460209745804401627400 102:59:114750590851681844328706298400 102:60:82237923443705321768906180520 102:61:56622832535010221545804255440 102:62:37444131192506759409322168920 102:63:23774051550797942482109313600 102:64:14487312663767496200035362975 102:65:8469505864971767009251442970 102:66:4748056318241748171853081665 102:67:2551194439652282599801655820 102:68:1313114785115145455780264025 102:69:647042068027752833283028650 102:70:305034117784512049976284935 102:71:137480165762033599989311520 102:72:59192849147542244439842460 102:73:24325828416798182646510600 102:74:9533094920096585091200100 102:75:3559022103502725100714704 102:76:1264389431507547075253908 102:77:426936691158392518916904 102:78:136838683063587345806700 102:79:41571245487672105055200 102:80:11951733077705730203370 102:81:3246149724808963758940 102:82:831331027085222426070 102:83:200320729418125885800 102:84:45310641177909426550 102:85:9595194602380819740 102:86:1896724514424115530 102:87:348822899204435040 102:88:59458448728028700 102:89:9353014406656200 102:90:1350990969850340 102:91:178152655364880 102:92:21300860967540 102:93:2290415157800 102:94:219295068300 102:95:18466953120 102:96:1346548665 102:97:83291670 102:98:4249575 102:99:171700 102:100:5151 102:101:102 102:102:1 # binomial(103, k) for 0 <= k <= 103 103:0:1 103:1:103 103:2:5253 103:3:176851 103:4:4421275 103:5:87541245 103:6:1429840335 103:7:19813501785 103:8:237762021420 103:9:2509710226100 103:10:23591276125340 103:11:199453516332420 103:12:1529143625215220 103:13:10704005376506540 103:14:68811463134684900 103:15:408281347932463740 103:16:2245547413628550570 103:17:11491919116804935270 103:18:54905835780290246290 103:19:245631370596035312350 103:20:1031651756503348311870 103:21:4077480751894186185010 103:22:15197882802514693962310 103:23:53522978565377835258570 103:24:178409928551259450861900 103:25:563775374221979864723604 103:26:1691326122665939594170812 103:27:4823411535010272175968612 103:28:13092117023599310191914804 103:29:33858923336894767737710700 103:30:83518677564340427086353060 103:31:196673014909575844429153980 103:32:442514283546545649965596455 103:33:952076185812264883259313585 103:34:1960156853142898289063292675 103:35:3864309224767428055581919845 103:36:7299250757894030771654737485 103:37:13217562183213515181104524635 103:38:22956818528739263209286805945 103:39:38261364214565438682144676575 103:40:61218182743304701891431482520 103:41:94066963727516980955126424360 103:42:138860755978715543314710435960 103:43:196988514295387166097612478920 103:44:268620701311891590133107925800 103:45:352191586164480084841185947160 103:46:444067652120431411321495324680 103:47:538550131294991286070749649080 103:48:628308486510823167082541257260 103:49:705244219552964779378362635700 103:50:761663757117201961728631646556 103:51:791532924062974587678774064068 103:52:791532924062974587678774064068 103:53:761663757117201961728631646556 103:54:705244219552964779378362635700 103:55:628308486510823167082541257260 103:56:538550131294991286070749649080 103:57:444067652120431411321495324680 103:58:352191586164480084841185947160 103:59:268620701311891590133107925800 103:60:196988514295387166097612478920 103:61:138860755978715543314710435960 103:62:94066963727516980955126424360 103:63:61218182743304701891431482520 103:64:38261364214565438682144676575 103:65:22956818528739263209286805945 103:66:13217562183213515181104524635 103:67:7299250757894030771654737485 103:68:3864309224767428055581919845 103:69:1960156853142898289063292675 103:70:952076185812264883259313585 103:71:442514283546545649965596455 103:72:196673014909575844429153980 103:73:83518677564340427086353060 103:74:33858923336894767737710700 103:75:13092117023599310191914804 103:76:4823411535010272175968612 103:77:1691326122665939594170812 103:78:563775374221979864723604 103:79:178409928551259450861900 103:80:53522978565377835258570 103:81:15197882802514693962310 103:82:4077480751894186185010 103:83:1031651756503348311870 103:84:245631370596035312350 103:85:54905835780290246290 103:86:11491919116804935270 103:87:2245547413628550570 103:88:408281347932463740 103:89:68811463134684900 103:90:10704005376506540 103:91:1529143625215220 103:92:199453516332420 103:93:23591276125340 103:94:2509710226100 103:95:237762021420 103:96:19813501785 103:97:1429840335 103:98:87541245 103:99:4421275 103:100:176851 103:101:5253 103:102:103 103:103:1 # binomial(104, k) for 0 <= k <= 104 104:0:1 104:1:104 104:2:5356 104:3:182104 104:4:4598126 104:5:91962520 104:6:1517381580 104:7:21243342120 104:8:257575523205 104:9:2747472247520 104:10:26100986351440 104:11:223044792457760 104:12:1728597141547640 104:13:12233149001721760 104:14:79515468511191440 104:15:477092811067148640 104:16:2653828761561014310 104:17:13737466530433485840 104:18:66397754897095181560 104:19:300537206376325558640 104:20:1277283127099383624220 104:21:5109132508397534496880 104:22:19275363554408880147320 104:23:68720861367892529220880 104:24:231932907116637286120470 104:25:742185302773239315585504 104:26:2255101496887919458894416 104:27:6514737657676211770139424 104:28:17915528558609582367883416 104:29:46951040360494077929625504 104:30:117377600901235194824063760 104:31:280191692473916271515507040 104:32:639187298456121494394750435 104:33:1394590469358810533224910040 104:34:2912233038955163172322606260 104:35:5824466077910326344645212520 104:36:11163559982661458827236657330 104:37:20516812941107545952759262120 104:38:36174380711952778390391330580 104:39:61218182743304701891431482520 104:40:99479546957870140573576159095 104:41:155285146470821682846557906880 104:42:232927719706232524269836860320 104:43:335849270274102709412322914880 104:44:465609215607278756230720404720 104:45:620812287476371674974293872960 104:46:796259238284911496162681271840 104:47:982617783415422697392244973760 104:48:1166858617805814453153290906340 104:49:1333552706063787946460903892960 104:50:1466907976670166741106994282256 104:51:1553196681180176549407405710624 104:52:1583065848125949175357548128136 104:53:1553196681180176549407405710624 104:54:1466907976670166741106994282256 104:55:1333552706063787946460903892960 104:56:1166858617805814453153290906340 104:57:982617783415422697392244973760 104:58:796259238284911496162681271840 104:59:620812287476371674974293872960 104:60:465609215607278756230720404720 104:61:335849270274102709412322914880 104:62:232927719706232524269836860320 104:63:155285146470821682846557906880 104:64:99479546957870140573576159095 104:65:61218182743304701891431482520 104:66:36174380711952778390391330580 104:67:20516812941107545952759262120 104:68:11163559982661458827236657330 104:69:5824466077910326344645212520 104:70:2912233038955163172322606260 104:71:1394590469358810533224910040 104:72:639187298456121494394750435 104:73:280191692473916271515507040 104:74:117377600901235194824063760 104:75:46951040360494077929625504 104:76:17915528558609582367883416 104:77:6514737657676211770139424 104:78:2255101496887919458894416 104:79:742185302773239315585504 104:80:231932907116637286120470 104:81:68720861367892529220880 104:82:19275363554408880147320 104:83:5109132508397534496880 104:84:1277283127099383624220 104:85:300537206376325558640 104:86:66397754897095181560 104:87:13737466530433485840 104:88:2653828761561014310 104:89:477092811067148640 104:90:79515468511191440 104:91:12233149001721760 104:92:1728597141547640 104:93:223044792457760 104:94:26100986351440 104:95:2747472247520 104:96:257575523205 104:97:21243342120 104:98:1517381580 104:99:91962520 104:100:4598126 104:101:182104 104:102:5356 104:103:104 104:104:1 # binomial(105, k) for 0 <= k <= 105 105:0:1 105:1:105 105:2:5460 105:3:187460 105:4:4780230 105:5:96560646 105:6:1609344100 105:7:22760723700 105:8:278818865325 105:9:3005047770725 105:10:28848458598960 105:11:249145778809200 105:12:1951641934005400 105:13:13961746143269400 105:14:91748617512913200 105:15:556608279578340080 105:16:3130921572628162950 105:17:16391295291994500150 105:18:80135221427528667400 105:19:366934961273420740200 105:20:1577820333475709182860 105:21:6386415635496918121100 105:22:24384496062806414644200 105:23:87996224922301409368200 105:24:300653768484529815341350 105:25:974118209889876601705974 105:26:2997286799661158774479920 105:27:8769839154564131229033840 105:28:24430266216285794138022840 105:29:64866568919103660297508920 105:30:164328641261729272753689264 105:31:397569293375151466339570800 105:32:919378990930037765910257475 105:33:2033777767814932027619660475 105:34:4306823508313973705547516300 105:35:8736699116865489516967818780 105:36:16988026060571785171881869850 105:37:31680372923769004779995919450 105:38:56691193653060324343150592700 105:39:97392563455257480281822813100 105:40:160697729701174842465007641615 105:41:254764693428691823420134065975 105:42:388212866177054207116394767200 105:43:568776989980335233682159775200 105:44:801458485881381465643043319600 105:45:1086421503083650431205014277680 105:46:1417071525761283171136975144800 105:47:1778877021700334193554926245600 105:48:2149476401221237150545535880100 105:49:2500411323869602399614194799300 105:50:2800460682733954687567898175216 105:51:3020104657850343290514399992880 105:52:3136262529306125724764953838760 105:53:3136262529306125724764953838760 105:54:3020104657850343290514399992880 105:55:2800460682733954687567898175216 105:56:2500411323869602399614194799300 105:57:2149476401221237150545535880100 105:58:1778877021700334193554926245600 105:59:1417071525761283171136975144800 105:60:1086421503083650431205014277680 105:61:801458485881381465643043319600 105:62:568776989980335233682159775200 105:63:388212866177054207116394767200 105:64:254764693428691823420134065975 105:65:160697729701174842465007641615 105:66:97392563455257480281822813100 105:67:56691193653060324343150592700 105:68:31680372923769004779995919450 105:69:16988026060571785171881869850 105:70:8736699116865489516967818780 105:71:4306823508313973705547516300 105:72:2033777767814932027619660475 105:73:919378990930037765910257475 105:74:397569293375151466339570800 105:75:164328641261729272753689264 105:76:64866568919103660297508920 105:77:24430266216285794138022840 105:78:8769839154564131229033840 105:79:2997286799661158774479920 105:80:974118209889876601705974 105:81:300653768484529815341350 105:82:87996224922301409368200 105:83:24384496062806414644200 105:84:6386415635496918121100 105:85:1577820333475709182860 105:86:366934961273420740200 105:87:80135221427528667400 105:88:16391295291994500150 105:89:3130921572628162950 105:90:556608279578340080 105:91:91748617512913200 105:92:13961746143269400 105:93:1951641934005400 105:94:249145778809200 105:95:28848458598960 105:96:3005047770725 105:97:278818865325 105:98:22760723700 105:99:1609344100 105:100:96560646 105:101:4780230 105:102:187460 105:103:5460 105:104:105 105:105:1 # binomial(106, k) for 0 <= k <= 106 106:0:1 106:1:106 106:2:5565 106:3:192920 106:4:4967690 106:5:101340876 106:6:1705904746 106:7:24370067800 106:8:301579589025 106:9:3283866636050 106:10:31853506369685 106:11:277994237408160 106:12:2200787712814600 106:13:15913388077274800 106:14:105710363656182600 106:15:648356897091253280 106:16:3687529852206503030 106:17:19522216864622663100 106:18:96526516719523167550 106:19:447070182700949407600 106:20:1944755294749129923060 106:21:7964235968972627303960 106:22:30770911698303332765300 106:23:112380720985107824012400 106:24:388649993406831224709550 106:25:1274771978374406417047324 106:26:3971405009551035376185894 106:27:11767125954225290003513760 106:28:33200105370849925367056680 106:29:89296835135389454435531760 106:30:229195210180832933051198184 106:31:561897934636880739093260064 106:32:1316948284305189232249828275 106:33:2953156758744969793529917950 106:34:6340601276128905733167176775 106:35:13043522625179463222515335080 106:36:25724725177437274688849688630 106:37:48668398984340789951877789300 106:38:88371566576829329123146512150 106:39:154083757108317804624973405800 106:40:258090293156432322746830454715 106:41:415462423129866665885141707590 106:42:642977559605746030536528833175 106:43:956989856157389440798554542400 106:44:1370235475861716699325203094800 106:45:1887879988965031896848057597280 106:46:2503493028844933602341989422480 106:47:3195948547461617364691901390400 106:48:3928353422921571344100462125700 106:49:4649887725090839550159730679400 106:50:5300872006603557087182092974516 106:51:5820565340584297978082298168096 106:52:6156367187156469015279353831640 106:53:6272525058612251449529907677520 106:54:6156367187156469015279353831640 106:55:5820565340584297978082298168096 106:56:5300872006603557087182092974516 106:57:4649887725090839550159730679400 106:58:3928353422921571344100462125700 106:59:3195948547461617364691901390400 106:60:2503493028844933602341989422480 106:61:1887879988965031896848057597280 106:62:1370235475861716699325203094800 106:63:956989856157389440798554542400 106:64:642977559605746030536528833175 106:65:415462423129866665885141707590 106:66:258090293156432322746830454715 106:67:154083757108317804624973405800 106:68:88371566576829329123146512150 106:69:48668398984340789951877789300 106:70:25724725177437274688849688630 106:71:13043522625179463222515335080 106:72:6340601276128905733167176775 106:73:2953156758744969793529917950 106:74:1316948284305189232249828275 106:75:561897934636880739093260064 106:76:229195210180832933051198184 106:77:89296835135389454435531760 106:78:33200105370849925367056680 106:79:11767125954225290003513760 106:80:3971405009551035376185894 106:81:1274771978374406417047324 106:82:388649993406831224709550 106:83:112380720985107824012400 106:84:30770911698303332765300 106:85:7964235968972627303960 106:86:1944755294749129923060 106:87:447070182700949407600 106:88:96526516719523167550 106:89:19522216864622663100 106:90:3687529852206503030 106:91:648356897091253280 106:92:105710363656182600 106:93:15913388077274800 106:94:2200787712814600 106:95:277994237408160 106:96:31853506369685 106:97:3283866636050 106:98:301579589025 106:99:24370067800 106:100:1705904746 106:101:101340876 106:102:4967690 106:103:192920 106:104:5565 106:105:106 106:106:1 # binomial(107, k) for 0 <= k <= 107 107:0:1 107:1:107 107:2:5671 107:3:198485 107:4:5160610 107:5:106308566 107:6:1807245622 107:7:26075972546 107:8:325949656825 107:9:3585446225075 107:10:35137373005735 107:11:309847743777845 107:12:2478781950222760 107:13:18114175790089400 107:14:121623751733457400 107:15:754067260747435880 107:16:4335886749297756310 107:17:23209746716829166130 107:18:116048733584145830650 107:19:543596699420472575150 107:20:2391825477450079330660 107:21:9908991263721757227020 107:22:38735147667275960069260 107:23:143151632683411156777700 107:24:501030714391939048721950 107:25:1663421971781237641756874 107:26:5246176987925441793233218 107:27:15738530963776325379699654 107:28:44967231325075215370570440 107:29:122496940506239379802588440 107:30:318492045316222387486729944 107:31:791093144817713672144458248 107:32:1878846218942069971343088339 107:33:4270105043050159025779746225 107:34:9293758034873875526697094725 107:35:19384123901308368955682511855 107:36:38768247802616737911365023710 107:37:74393124161778064640727477930 107:38:137039965561170119075024301450 107:39:242455323685147133748119917950 107:40:412174050264750127371803860515 107:41:673552716286298988631972162305 107:42:1058439982735612696421670540765 107:43:1599967415763135471335083375575 107:44:2327225332019106140123757637200 107:45:3258115464826748596173260692080 107:46:4391373017809965499190047019760 107:47:5699441576306550967033890812880 107:48:7124301970383188708792363516100 107:49:8578241148012410894260192805100 107:50:9950759731694396637341823653916 107:51:11121437347187855065264391142612 107:52:11976932527740766993361651999736 107:53:12428892245768720464809261509160 107:54:12428892245768720464809261509160 107:55:11976932527740766993361651999736 107:56:11121437347187855065264391142612 107:57:9950759731694396637341823653916 107:58:8578241148012410894260192805100 107:59:7124301970383188708792363516100 107:60:5699441576306550967033890812880 107:61:4391373017809965499190047019760 107:62:3258115464826748596173260692080 107:63:2327225332019106140123757637200 107:64:1599967415763135471335083375575 107:65:1058439982735612696421670540765 107:66:673552716286298988631972162305 107:67:412174050264750127371803860515 107:68:242455323685147133748119917950 107:69:137039965561170119075024301450 107:70:74393124161778064640727477930 107:71:38768247802616737911365023710 107:72:19384123901308368955682511855 107:73:9293758034873875526697094725 107:74:4270105043050159025779746225 107:75:1878846218942069971343088339 107:76:791093144817713672144458248 107:77:318492045316222387486729944 107:78:122496940506239379802588440 107:79:44967231325075215370570440 107:80:15738530963776325379699654 107:81:5246176987925441793233218 107:82:1663421971781237641756874 107:83:501030714391939048721950 107:84:143151632683411156777700 107:85:38735147667275960069260 107:86:9908991263721757227020 107:87:2391825477450079330660 107:88:543596699420472575150 107:89:116048733584145830650 107:90:23209746716829166130 107:91:4335886749297756310 107:92:754067260747435880 107:93:121623751733457400 107:94:18114175790089400 107:95:2478781950222760 107:96:309847743777845 107:97:35137373005735 107:98:3585446225075 107:99:325949656825 107:100:26075972546 107:101:1807245622 107:102:106308566 107:103:5160610 107:104:198485 107:105:5671 107:106:107 107:107:1 # binomial(108, k) for 0 <= k <= 108 108:0:1 108:1:108 108:2:5778 108:3:204156 108:4:5359095 108:5:111469176 108:6:1913554188 108:7:27883218168 108:8:352025629371 108:9:3911395881900 108:10:38722819230810 108:11:344985116783580 108:12:2788629694000605 108:13:20592957740312160 108:14:139737927523546800 108:15:875691012480893280 108:16:5089954010045192190 108:17:27545633466126922440 108:18:139258480300974996780 108:19:659645433004618405800 108:20:2935422176870551905810 108:21:12300816741171836557680 108:22:48644138930997717296280 108:23:181886780350687116846960 108:24:644182347075350205499650 108:25:2164452686173176690478824 108:26:6909598959706679434990092 108:27:20984707951701767172932872 108:28:60705762288851540750270094 108:29:167464171831314595173158880 108:30:440988985822461767289318384 108:31:1109585190133936059631188192 108:32:2669939363759783643487546587 108:33:6148951261992228997122834564 108:34:13563863077924034552476840950 108:35:28677881936182244482379606580 108:36:58152371703925106867047535565 108:37:113161371964394802552092501640 108:38:211433089722948183715751779380 108:39:379495289246317252823144219400 108:40:654629373949897261119923778465 108:41:1085726766551049116003776022820 108:42:1731992699021911685053642703070 108:43:2658407398498748167756753916340 108:44:3927192747782241611458841012775 108:45:5585340796845854736297018329280 108:46:7649488482636714095363307711840 108:47:10090814594116516466223937832640 108:48:12823743546689739675826254328980 108:49:15702543118395599603052556321200 108:50:18529000879706807531602016459016 108:51:21072197078882251702606214796528 108:52:23098369874928622058626043142348 108:53:24405824773509487458170913508896 108:54:24857784491537440929618523018320 108:55:24405824773509487458170913508896 108:56:23098369874928622058626043142348 108:57:21072197078882251702606214796528 108:58:18529000879706807531602016459016 108:59:15702543118395599603052556321200 108:60:12823743546689739675826254328980 108:61:10090814594116516466223937832640 108:62:7649488482636714095363307711840 108:63:5585340796845854736297018329280 108:64:3927192747782241611458841012775 108:65:2658407398498748167756753916340 108:66:1731992699021911685053642703070 108:67:1085726766551049116003776022820 108:68:654629373949897261119923778465 108:69:379495289246317252823144219400 108:70:211433089722948183715751779380 108:71:113161371964394802552092501640 108:72:58152371703925106867047535565 108:73:28677881936182244482379606580 108:74:13563863077924034552476840950 108:75:6148951261992228997122834564 108:76:2669939363759783643487546587 108:77:1109585190133936059631188192 108:78:440988985822461767289318384 108:79:167464171831314595173158880 108:80:60705762288851540750270094 108:81:20984707951701767172932872 108:82:6909598959706679434990092 108:83:2164452686173176690478824 108:84:644182347075350205499650 108:85:181886780350687116846960 108:86:48644138930997717296280 108:87:12300816741171836557680 108:88:2935422176870551905810 108:89:659645433004618405800 108:90:139258480300974996780 108:91:27545633466126922440 108:92:5089954010045192190 108:93:875691012480893280 108:94:139737927523546800 108:95:20592957740312160 108:96:2788629694000605 108:97:344985116783580 108:98:38722819230810 108:99:3911395881900 108:100:352025629371 108:101:27883218168 108:102:1913554188 108:103:111469176 108:104:5359095 108:105:204156 108:106:5778 108:107:108 108:108:1 # binomial(109, k) for 0 <= k <= 109 109:0:1 109:1:109 109:2:5886 109:3:209934 109:4:5563251 109:5:116828271 109:6:2025023364 109:7:29796772356 109:8:379908847539 109:9:4263421511271 109:10:42634215112710 109:11:383707936014390 109:12:3133614810784185 109:13:23381587434312765 109:14:160330885263858960 109:15:1015428940004440080 109:16:5965645022526085470 109:17:32635587476172114630 109:18:166804113767101919220 109:19:798903913305593402580 109:20:3595067609875170311610 109:21:15236238918042388463490 109:22:60944955672169553853960 109:23:230530919281684834143240 109:24:826069127426037322346610 109:25:2808635033248526895978474 109:26:9074051645879856125468916 109:27:27894306911408446607922964 109:28:81690470240553307923202966 109:29:228169934120166135923428974 109:30:608453157653776362462477264 109:31:1550574175956397826920506576 109:32:3779524553893719703118734779 109:33:8818890625752012640610381151 109:34:19712814339916263549599675514 109:35:42241745014106279034856447530 109:36:86830253640107351349427142145 109:37:171313743668319909419140037205 109:38:324594461687342986267844281020 109:39:590928378969265436538895998780 109:40:1034124663196214513943067997865 109:41:1740356140500946377123699801285 109:42:2817719465572960801057418725890 109:43:4390400097520659852810396619410 109:44:6585600146280989779215594929115 109:45:9512533544628096347755859342055 109:46:13234829279482568831660326041120 109:47:17740303076753230561587245544480 109:48:22914558140806256142050192161620 109:49:28526286665085339278878810650180 109:50:34231543998102407134654572780216 109:51:39601197958589059234208231255544 109:52:44170566953810873761232257938876 109:53:47504194648438109516796956651244 109:54:49263609265046928387789436527216 109:55:49263609265046928387789436527216 109:56:47504194648438109516796956651244 109:57:44170566953810873761232257938876 109:58:39601197958589059234208231255544 109:59:34231543998102407134654572780216 109:60:28526286665085339278878810650180 109:61:22914558140806256142050192161620 109:62:17740303076753230561587245544480 109:63:13234829279482568831660326041120 109:64:9512533544628096347755859342055 109:65:6585600146280989779215594929115 109:66:4390400097520659852810396619410 109:67:2817719465572960801057418725890 109:68:1740356140500946377123699801285 109:69:1034124663196214513943067997865 109:70:590928378969265436538895998780 109:71:324594461687342986267844281020 109:72:171313743668319909419140037205 109:73:86830253640107351349427142145 109:74:42241745014106279034856447530 109:75:19712814339916263549599675514 109:76:8818890625752012640610381151 109:77:3779524553893719703118734779 109:78:1550574175956397826920506576 109:79:608453157653776362462477264 109:80:228169934120166135923428974 109:81:81690470240553307923202966 109:82:27894306911408446607922964 109:83:9074051645879856125468916 109:84:2808635033248526895978474 109:85:826069127426037322346610 109:86:230530919281684834143240 109:87:60944955672169553853960 109:88:15236238918042388463490 109:89:3595067609875170311610 109:90:798903913305593402580 109:91:166804113767101919220 109:92:32635587476172114630 109:93:5965645022526085470 109:94:1015428940004440080 109:95:160330885263858960 109:96:23381587434312765 109:97:3133614810784185 109:98:383707936014390 109:99:42634215112710 109:100:4263421511271 109:101:379908847539 109:102:29796772356 109:103:2025023364 109:104:116828271 109:105:5563251 109:106:209934 109:107:5886 109:108:109 109:109:1 # binomial(110, k) for 0 <= k <= 110 110:0:1 110:1:110 110:2:5995 110:3:215820 110:4:5773185 110:5:122391522 110:6:2141851635 110:7:31821795720 110:8:409705619895 110:9:4643330358810 110:10:46897636623981 110:11:426342151127100 110:12:3517322746798575 110:13:26515202245096950 110:14:183712472698171725 110:15:1175759825268299040 110:16:6981073962530525550 110:17:38601232498698200100 110:18:199439701243274033850 110:19:965708027072695321800 110:20:4393971523180763714190 110:21:18831306527917558775100 110:22:76181194590211942317450 110:23:291475874953854387997200 110:24:1056600046707722156489850 110:25:3634704160674564218325084 110:26:11882686679128383021447390 110:27:36968358557288302733391880 110:28:109584777151961754531125930 110:29:309860404360719443846631940 110:30:836623091773942498385906238 110:31:2159027333610174189382983840 110:32:5330098729850117530039241355 110:33:12598415179645732343729115930 110:34:28531704965668276190210056665 110:35:61954559354022542584456123044 110:36:129071998654213630384283589675 110:37:258143997308427260768567179350 110:38:495908205355662895686984318225 110:39:915522840656608422806740279800 110:40:1625053042165479950481963996645 110:41:2774480803697160891066767799150 110:42:4558075606073907178181118527175 110:43:7208119563093620653867815345300 110:44:10976000243801649632025991548525 110:45:16098133690909086126971454271170 110:46:22747362824110665179416185383175 110:47:30975132356235799393247571585600 110:48:40654861217559486703637437706100 110:49:51440844805891595420929002811800 110:50:62757830663187746413533383430396 110:51:73832741956691466368862804035760 110:52:83771764912399932995440489194420 110:53:91674761602248983278029214590120 110:54:96767803913485037904586393178460 110:55:98527218530093856775578873054432 110:56:96767803913485037904586393178460 110:57:91674761602248983278029214590120 110:58:83771764912399932995440489194420 110:59:73832741956691466368862804035760 110:60:62757830663187746413533383430396 110:61:51440844805891595420929002811800 110:62:40654861217559486703637437706100 110:63:30975132356235799393247571585600 110:64:22747362824110665179416185383175 110:65:16098133690909086126971454271170 110:66:10976000243801649632025991548525 110:67:7208119563093620653867815345300 110:68:4558075606073907178181118527175 110:69:2774480803697160891066767799150 110:70:1625053042165479950481963996645 110:71:915522840656608422806740279800 110:72:495908205355662895686984318225 110:73:258143997308427260768567179350 110:74:129071998654213630384283589675 110:75:61954559354022542584456123044 110:76:28531704965668276190210056665 110:77:12598415179645732343729115930 110:78:5330098729850117530039241355 110:79:2159027333610174189382983840 110:80:836623091773942498385906238 110:81:309860404360719443846631940 110:82:109584777151961754531125930 110:83:36968358557288302733391880 110:84:11882686679128383021447390 110:85:3634704160674564218325084 110:86:1056600046707722156489850 110:87:291475874953854387997200 110:88:76181194590211942317450 110:89:18831306527917558775100 110:90:4393971523180763714190 110:91:965708027072695321800 110:92:199439701243274033850 110:93:38601232498698200100 110:94:6981073962530525550 110:95:1175759825268299040 110:96:183712472698171725 110:97:26515202245096950 110:98:3517322746798575 110:99:426342151127100 110:100:46897636623981 110:101:4643330358810 110:102:409705619895 110:103:31821795720 110:104:2141851635 110:105:122391522 110:106:5773185 110:107:215820 110:108:5995 110:109:110 110:110:1 # binomial(111, k) for 0 <= k <= 111 111:0:1 111:1:111 111:2:6105 111:3:221815 111:4:5989005 111:5:128164707 111:6:2264243157 111:7:33963647355 111:8:441527415615 111:9:5053035978705 111:10:51540966982791 111:11:473239787751081 111:12:3943664897925675 111:13:30032524991895525 111:14:210227674943268675 111:15:1359472297966470765 111:16:8156833787798824590 111:17:45582306461228725650 111:18:238040933741972233950 111:19:1165147728315969355650 111:20:5359679550253459035990 111:21:23225278051098322489290 111:22:95012501118129501092550 111:23:367657069544066330314650 111:24:1348075921661576544487050 111:25:4691304207382286374814934 111:26:15517390839802947239772474 111:27:48851045236416685754839270 111:28:146553135709250057264517810 111:29:419445181512681198377757870 111:30:1146483496134661942232538178 111:31:2995650425384116687768890078 111:32:7489126063460291719422225195 111:33:17928513909495849873768357285 111:34:41130120145314008533939172595 111:35:90486264319690818774666179709 111:36:191026558008236172968739712719 111:37:387215995962640891152850769025 111:38:754052202664090156455551497575 111:39:1411431046012271318493724598025 111:40:2540575882822088373288704276445 111:41:4399533845862640841548731795795 111:42:7332556409771068069247886326325 111:43:11766195169167527832048933872475 111:44:18184119806895270285893806893825 111:45:27074133934710735758997445819695 111:46:38845496515019751306387639654345 111:47:53722495180346464572663756968775 111:48:71629993573795286096885009291700 111:49:92095706023451082124566440517900 111:50:114198675469079341834462386242196 111:51:136590572619879212782396187466156 111:52:157604506869091399364303293230180 111:53:175446526514648916273469703784540 111:54:188442565515734021182615607768580 111:55:195295022443578894680165266232892 111:56:195295022443578894680165266232892 111:57:188442565515734021182615607768580 111:58:175446526514648916273469703784540 111:59:157604506869091399364303293230180 111:60:136590572619879212782396187466156 111:61:114198675469079341834462386242196 111:62:92095706023451082124566440517900 111:63:71629993573795286096885009291700 111:64:53722495180346464572663756968775 111:65:38845496515019751306387639654345 111:66:27074133934710735758997445819695 111:67:18184119806895270285893806893825 111:68:11766195169167527832048933872475 111:69:7332556409771068069247886326325 111:70:4399533845862640841548731795795 111:71:2540575882822088373288704276445 111:72:1411431046012271318493724598025 111:73:754052202664090156455551497575 111:74:387215995962640891152850769025 111:75:191026558008236172968739712719 111:76:90486264319690818774666179709 111:77:41130120145314008533939172595 111:78:17928513909495849873768357285 111:79:7489126063460291719422225195 111:80:2995650425384116687768890078 111:81:1146483496134661942232538178 111:82:419445181512681198377757870 111:83:146553135709250057264517810 111:84:48851045236416685754839270 111:85:15517390839802947239772474 111:86:4691304207382286374814934 111:87:1348075921661576544487050 111:88:367657069544066330314650 111:89:95012501118129501092550 111:90:23225278051098322489290 111:91:5359679550253459035990 111:92:1165147728315969355650 111:93:238040933741972233950 111:94:45582306461228725650 111:95:8156833787798824590 111:96:1359472297966470765 111:97:210227674943268675 111:98:30032524991895525 111:99:3943664897925675 111:100:473239787751081 111:101:51540966982791 111:102:5053035978705 111:103:441527415615 111:104:33963647355 111:105:2264243157 111:106:128164707 111:107:5989005 111:108:221815 111:109:6105 111:110:111 111:111:1 # binomial(112, k) for 0 <= k <= 112 112:0:1 112:1:112 112:2:6216 112:3:227920 112:4:6210820 112:5:134153712 112:6:2392407864 112:7:36227890512 112:8:475491062970 112:9:5494563394320 112:10:56594002961496 112:11:524780754733872 112:12:4416904685676756 112:13:33976189889821200 112:14:240260199935164200 112:15:1569699972909739440 112:16:9516306085765295355 112:17:53739140249027550240 112:18:283623240203200959600 112:19:1403188662057941589600 112:20:6524827278569428391640 112:21:28584957601351781525280 112:22:118237779169227823581840 112:23:462669570662195831407200 112:24:1715732991205642874801700 112:25:6039380129043862919301984 112:26:20208695047185233614587408 112:27:64368436076219632994611744 112:28:195404180945666743019357080 112:29:565998317221931255642275680 112:30:1565928677647343140610296048 112:31:4142133921518778630001428256 112:32:10484776488844408407191115273 112:33:25417639972956141593190582480 112:34:59058634054809858407707529880 112:35:131616384465004827308605352304 112:36:281512822327926991743405892428 112:37:578242553970877064121590481744 112:38:1141268198626731047608402266600 112:39:2165483248676361474949276095600 112:40:3952006928834359691782428874470 112:41:6940109728684729214837436072240 112:42:11732090255633708910796618122120 112:43:19098751578938595901296820198800 112:44:29950314976062798117942740766300 112:45:45258253741606006044891252713520 112:46:65919630449730487065385085474040 112:47:92567991695366215879051396623120 112:48:125352488754141750669548766260475 112:49:163725699597246368221451449809600 112:50:206294381492530423959028826760096 112:51:250789248088958554616858573708352 112:52:294195079488970612146699480696336 112:53:333051033383740315637772997014720 112:54:363889092030382937456085311553120 112:55:383737587959312915862780874001472 112:56:390590044887157789360330532465784 112:57:383737587959312915862780874001472 112:58:363889092030382937456085311553120 112:59:333051033383740315637772997014720 112:60:294195079488970612146699480696336 112:61:250789248088958554616858573708352 112:62:206294381492530423959028826760096 112:63:163725699597246368221451449809600 112:64:125352488754141750669548766260475 112:65:92567991695366215879051396623120 112:66:65919630449730487065385085474040 112:67:45258253741606006044891252713520 112:68:29950314976062798117942740766300 112:69:19098751578938595901296820198800 112:70:11732090255633708910796618122120 112:71:6940109728684729214837436072240 112:72:3952006928834359691782428874470 112:73:2165483248676361474949276095600 112:74:1141268198626731047608402266600 112:75:578242553970877064121590481744 112:76:281512822327926991743405892428 112:77:131616384465004827308605352304 112:78:59058634054809858407707529880 112:79:25417639972956141593190582480 112:80:10484776488844408407191115273 112:81:4142133921518778630001428256 112:82:1565928677647343140610296048 112:83:565998317221931255642275680 112:84:195404180945666743019357080 112:85:64368436076219632994611744 112:86:20208695047185233614587408 112:87:6039380129043862919301984 112:88:1715732991205642874801700 112:89:462669570662195831407200 112:90:118237779169227823581840 112:91:28584957601351781525280 112:92:6524827278569428391640 112:93:1403188662057941589600 112:94:283623240203200959600 112:95:53739140249027550240 112:96:9516306085765295355 112:97:1569699972909739440 112:98:240260199935164200 112:99:33976189889821200 112:100:4416904685676756 112:101:524780754733872 112:102:56594002961496 112:103:5494563394320 112:104:475491062970 112:105:36227890512 112:106:2392407864 112:107:134153712 112:108:6210820 112:109:227920 112:110:6216 112:111:112 112:112:1 # binomial(113, k) for 0 <= k <= 113 113:0:1 113:1:113 113:2:6328 113:3:234136 113:4:6438740 113:5:140364532 113:6:2526561576 113:7:38620298376 113:8:511718953482 113:9:5970054457290 113:10:62088566355816 113:11:581374757695368 113:12:4941685440410628 113:13:38393094575497956 113:14:274236389824985400 113:15:1809960172844903640 113:16:11086006058675034795 113:17:63255446334792845595 113:18:337362380452228509840 113:19:1686811902261142549200 113:20:7928015940627369981240 113:21:35109784879921209916920 113:22:146822736770579605107120 113:23:580907349831423654989040 113:24:2178402561867838706208900 113:25:7755113120249505794103684 113:26:26248075176229096533889392 113:27:84577131123404866609199152 113:28:259772617021886376013968824 113:29:761402498167597998661632760 113:30:2131926994869274396252571728 113:31:5708062599166121770611724304 113:32:14626910410363187037192543529 113:33:35902416461800550000381697753 113:34:84476274027766000000898112360 113:35:190675018519814685716312882184 113:36:413129206792931819052011244732 113:37:859755376298804055864996374172 113:38:1719510752597608111729992748344 113:39:3306751447303092522557678362200 113:40:6117490177510721166731704970070 113:41:10892116657519088906619864946710 113:42:18672199984318438125634054194360 113:43:30830841834572304812093438320920 113:44:49049066555001394019239560965100 113:45:75208568717668804162833993479820 113:46:111177884191336493110276338187560 113:47:158487622145096702944436482097160 113:48:217920480449507966548600162883595 113:49:289078188351388118891000216070075 113:50:370020081089776792180480276569696 113:51:457083629581488978575887400468448 113:52:544984327577929166763558054404688 113:53:627246112872710927784472477711056 113:54:696940125414123253093858308567840 113:55:747626679989695853318866185554592 113:56:774327632846470705223111406467256 113:57:774327632846470705223111406467256 113:58:747626679989695853318866185554592 113:59:696940125414123253093858308567840 113:60:627246112872710927784472477711056 113:61:544984327577929166763558054404688 113:62:457083629581488978575887400468448 113:63:370020081089776792180480276569696 113:64:289078188351388118891000216070075 113:65:217920480449507966548600162883595 113:66:158487622145096702944436482097160 113:67:111177884191336493110276338187560 113:68:75208568717668804162833993479820 113:69:49049066555001394019239560965100 113:70:30830841834572304812093438320920 113:71:18672199984318438125634054194360 113:72:10892116657519088906619864946710 113:73:6117490177510721166731704970070 113:74:3306751447303092522557678362200 113:75:1719510752597608111729992748344 113:76:859755376298804055864996374172 113:77:413129206792931819052011244732 113:78:190675018519814685716312882184 113:79:84476274027766000000898112360 113:80:35902416461800550000381697753 113:81:14626910410363187037192543529 113:82:5708062599166121770611724304 113:83:2131926994869274396252571728 113:84:761402498167597998661632760 113:85:259772617021886376013968824 113:86:84577131123404866609199152 113:87:26248075176229096533889392 113:88:7755113120249505794103684 113:89:2178402561867838706208900 113:90:580907349831423654989040 113:91:146822736770579605107120 113:92:35109784879921209916920 113:93:7928015940627369981240 113:94:1686811902261142549200 113:95:337362380452228509840 113:96:63255446334792845595 113:97:11086006058675034795 113:98:1809960172844903640 113:99:274236389824985400 113:100:38393094575497956 113:101:4941685440410628 113:102:581374757695368 113:103:62088566355816 113:104:5970054457290 113:105:511718953482 113:106:38620298376 113:107:2526561576 113:108:140364532 113:109:6438740 113:110:234136 113:111:6328 113:112:113 113:113:1 # binomial(114, k) for 0 <= k <= 114 114:0:1 114:1:114 114:2:6441 114:3:240464 114:4:6672876 114:5:146803272 114:6:2666926108 114:7:41146859952 114:8:550339251858 114:9:6481773410772 114:10:68058620813106 114:11:643463324051184 114:12:5523060198105996 114:13:43334780015908584 114:14:312629484400483356 114:15:2084196562669889040 114:16:12895966231519938435 114:17:74341452393467880390 114:18:400617826787021355435 114:19:2024174282713371059040 114:20:9614827842888512530440 114:21:43037800820548579898160 114:22:181932521650500815024040 114:23:727730086602003260096160 114:24:2759309911699262361197940 114:25:9933515682117344500312584 114:26:34003188296478602327993076 114:27:110825206299633963143088544 114:28:344349748145291242623167976 114:29:1021175115189484374675601584 114:30:2893329493036872394914204488 114:31:7839989594035396166864296032 114:32:20334973009529308807804267833 114:33:50529326872163737037574241282 114:34:120378690489566550001279810113 114:35:275151292547580685717210994544 114:36:603804225312746504768324126916 114:37:1272884583091735874917007618904 114:38:2579266128896412167594989122516 114:39:5026262199900700634287671110544 114:40:9424241624813813689289383332270 114:41:17009606835029810073351569916780 114:42:29564316641837527032253919141070 114:43:49503041818890742937727492515280 114:44:79879908389573698831332999286020 114:45:124257635272670198182073554444920 114:46:186386452909005297273110331667380 114:47:269665506336433196054712820284720 114:48:376408102594604669493036644980755 114:49:506998668800896085439600378953670 114:50:659098269441164911071480492639771 114:51:827103710671265770756367677038144 114:52:1002067957159418145339445454873136 114:53:1172230440450640094548030532115744 114:54:1324186238286834180878330786278896 114:55:1444566805403819106412724494122432 114:56:1521954312836166558541977592021848 114:57:1548655265692941410446222812934512 114:58:1521954312836166558541977592021848 114:59:1444566805403819106412724494122432 114:60:1324186238286834180878330786278896 114:61:1172230440450640094548030532115744 114:62:1002067957159418145339445454873136 114:63:827103710671265770756367677038144 114:64:659098269441164911071480492639771 114:65:506998668800896085439600378953670 114:66:376408102594604669493036644980755 114:67:269665506336433196054712820284720 114:68:186386452909005297273110331667380 114:69:124257635272670198182073554444920 114:70:79879908389573698831332999286020 114:71:49503041818890742937727492515280 114:72:29564316641837527032253919141070 114:73:17009606835029810073351569916780 114:74:9424241624813813689289383332270 114:75:5026262199900700634287671110544 114:76:2579266128896412167594989122516 114:77:1272884583091735874917007618904 114:78:603804225312746504768324126916 114:79:275151292547580685717210994544 114:80:120378690489566550001279810113 114:81:50529326872163737037574241282 114:82:20334973009529308807804267833 114:83:7839989594035396166864296032 114:84:2893329493036872394914204488 114:85:1021175115189484374675601584 114:86:344349748145291242623167976 114:87:110825206299633963143088544 114:88:34003188296478602327993076 114:89:9933515682117344500312584 114:90:2759309911699262361197940 114:91:727730086602003260096160 114:92:181932521650500815024040 114:93:43037800820548579898160 114:94:9614827842888512530440 114:95:2024174282713371059040 114:96:400617826787021355435 114:97:74341452393467880390 114:98:12895966231519938435 114:99:2084196562669889040 114:100:312629484400483356 114:101:43334780015908584 114:102:5523060198105996 114:103:643463324051184 114:104:68058620813106 114:105:6481773410772 114:106:550339251858 114:107:41146859952 114:108:2666926108 114:109:146803272 114:110:6672876 114:111:240464 114:112:6441 114:113:114 114:114:1 # binomial(115, k) for 0 <= k <= 115 115:0:1 115:1:115 115:2:6555 115:3:246905 115:4:6913340 115:5:153476148 115:6:2813729380 115:7:43813786060 115:8:591486111810 115:9:7032112662630 115:10:74540394223878 115:11:711521944864290 115:12:6166523522157180 115:13:48857840214014580 115:14:355964264416391940 115:15:2396826047070372396 115:16:14980162794189827475 115:17:87237418624987818825 115:18:474959279180489235825 115:19:2424792109500392414475 115:20:11639002125601883589480 115:21:52652628663437092428600 115:22:224970322471049394922200 115:23:909662608252504075120200 115:24:3487039998301265621294100 115:25:12692825593816606861510524 115:26:43936703978595946828305660 115:27:144828394596112565471081620 115:28:455174954444925205766256520 115:29:1365524863334775617298769560 115:30:3914504608226356769589806072 115:31:10733319087072268561778500520 115:32:28174962603564704974668563865 115:33:70864299881693045845378509115 115:34:170908017361730287038854051395 115:35:395529983037147235718490804657 115:36:878955517860327190485535121460 115:37:1876688808404482379685331745820 115:38:3852150711988148042511996741420 115:39:7605528328797112801882660233060 115:40:14450503824714514323577054442814 115:41:26433848459843623762640953249050 115:42:46573923476867337105605489057850 115:43:79067358460728269969981411656350 115:44:129382950208464441769060491801300 115:45:204137543662243897013406553730940 115:46:310644088181675495455183886112300 115:47:456051959245438493327823151952100 115:48:646073608931037865547749465265475 115:49:883406771395500754932637023934425 115:50:1166096938242060996511080871593441 115:51:1486201980112430681827848169677915 115:52:1829171667830683916095813131911280 115:53:2174298397610058239887475986988880 115:54:2496416678737474275426361318394640 115:55:2768753043690653287291055280401328 115:56:2966521118239985664954702086144280 115:57:3070609578529107968988200404956360 115:58:3070609578529107968988200404956360 115:59:2966521118239985664954702086144280 115:60:2768753043690653287291055280401328 115:61:2496416678737474275426361318394640 115:62:2174298397610058239887475986988880 115:63:1829171667830683916095813131911280 115:64:1486201980112430681827848169677915 115:65:1166096938242060996511080871593441 115:66:883406771395500754932637023934425 115:67:646073608931037865547749465265475 115:68:456051959245438493327823151952100 115:69:310644088181675495455183886112300 115:70:204137543662243897013406553730940 115:71:129382950208464441769060491801300 115:72:79067358460728269969981411656350 115:73:46573923476867337105605489057850 115:74:26433848459843623762640953249050 115:75:14450503824714514323577054442814 115:76:7605528328797112801882660233060 115:77:3852150711988148042511996741420 115:78:1876688808404482379685331745820 115:79:878955517860327190485535121460 115:80:395529983037147235718490804657 115:81:170908017361730287038854051395 115:82:70864299881693045845378509115 115:83:28174962603564704974668563865 115:84:10733319087072268561778500520 115:85:3914504608226356769589806072 115:86:1365524863334775617298769560 115:87:455174954444925205766256520 115:88:144828394596112565471081620 115:89:43936703978595946828305660 115:90:12692825593816606861510524 115:91:3487039998301265621294100 115:92:909662608252504075120200 115:93:224970322471049394922200 115:94:52652628663437092428600 115:95:11639002125601883589480 115:96:2424792109500392414475 115:97:474959279180489235825 115:98:87237418624987818825 115:99:14980162794189827475 115:100:2396826047070372396 115:101:355964264416391940 115:102:48857840214014580 115:103:6166523522157180 115:104:711521944864290 115:105:74540394223878 115:106:7032112662630 115:107:591486111810 115:108:43813786060 115:109:2813729380 115:110:153476148 115:111:6913340 115:112:246905 115:113:6555 115:114:115 115:115:1 # binomial(116, k) for 0 <= k <= 116 116:0:1 116:1:116 116:2:6670 116:3:253460 116:4:7160245 116:5:160389488 116:6:2967205528 116:7:46627515440 116:8:635299897870 116:9:7623598774440 116:10:81572506886508 116:11:786062339088168 116:12:6878045467021470 116:13:55024363736171760 116:14:404822104630406520 116:15:2752790311486764336 116:16:17376988841260199871 116:17:102217581419177646300 116:18:562196697805477054650 116:19:2899751388680881650300 116:20:14063794235102276003955 116:21:64291630789038976018080 116:22:277622951134486487350800 116:23:1134632930723553470042400 116:24:4396702606553769696414300 116:25:16179865592117872482804624 116:26:56629529572412553689816184 116:27:188765098574708512299387280 116:28:600003349041037771237338140 116:29:1820699817779700823065026080 116:30:5280029471561132386888575632 116:31:14647823695298625331368306592 116:32:38908281690636973536447064385 116:33:99039262485257750820047072980 116:34:241772317243423332884232560510 116:35:566438000398877522757344856052 116:36:1274485500897474426204025926117 116:37:2755644326264809570170866867280 116:38:5728839520392630422197328487240 116:39:11457679040785260844394656974480 116:40:22056032153511627125459714675874 116:41:40884352284558138086218007691864 116:42:73007771936710960868246442306900 116:43:125641281937595607075586900714200 116:44:208450308669192711739041903457650 116:45:333520493870708338782467045532240 116:46:514781631843919392468590439843240 116:47:766696047427113988783007038064400 116:48:1102125568176476358875572617217575 116:49:1529480380326538620480386489199900 116:50:2049503709637561751443717895527866 116:51:2652298918354491678338929041271356 116:52:3315373647943114597923661301589195 116:53:4003470065440742155983289118900160 116:54:4670715076347532515313837305383520 116:55:5265169722428127562717416598795968 116:56:5735274161930638952245757366545608 116:57:6037130696769093633942902491100640 116:58:6141219157058215937976400809912720 116:59:6037130696769093633942902491100640 116:60:5735274161930638952245757366545608 116:61:5265169722428127562717416598795968 116:62:4670715076347532515313837305383520 116:63:4003470065440742155983289118900160 116:64:3315373647943114597923661301589195 116:65:2652298918354491678338929041271356 116:66:2049503709637561751443717895527866 116:67:1529480380326538620480386489199900 116:68:1102125568176476358875572617217575 116:69:766696047427113988783007038064400 116:70:514781631843919392468590439843240 116:71:333520493870708338782467045532240 116:72:208450308669192711739041903457650 116:73:125641281937595607075586900714200 116:74:73007771936710960868246442306900 116:75:40884352284558138086218007691864 116:76:22056032153511627125459714675874 116:77:11457679040785260844394656974480 116:78:5728839520392630422197328487240 116:79:2755644326264809570170866867280 116:80:1274485500897474426204025926117 116:81:566438000398877522757344856052 116:82:241772317243423332884232560510 116:83:99039262485257750820047072980 116:84:38908281690636973536447064385 116:85:14647823695298625331368306592 116:86:5280029471561132386888575632 116:87:1820699817779700823065026080 116:88:600003349041037771237338140 116:89:188765098574708512299387280 116:90:56629529572412553689816184 116:91:16179865592117872482804624 116:92:4396702606553769696414300 116:93:1134632930723553470042400 116:94:277622951134486487350800 116:95:64291630789038976018080 116:96:14063794235102276003955 116:97:2899751388680881650300 116:98:562196697805477054650 116:99:102217581419177646300 116:100:17376988841260199871 116:101:2752790311486764336 116:102:404822104630406520 116:103:55024363736171760 116:104:6878045467021470 116:105:786062339088168 116:106:81572506886508 116:107:7623598774440 116:108:635299897870 116:109:46627515440 116:110:2967205528 116:111:160389488 116:112:7160245 116:113:253460 116:114:6670 116:115:116 116:116:1 # binomial(117, k) for 0 <= k <= 117 117:0:1 117:1:117 117:2:6786 117:3:260130 117:4:7413705 117:5:167549733 117:6:3127595016 117:7:49594720968 117:8:681927413310 117:9:8258898672310 117:10:89196105660948 117:11:867634845974676 117:12:7664107806109638 117:13:61902409203193230 117:14:459846468366578280 117:15:3157612416117170856 117:16:20129779152746964207 117:17:119594570260437846171 117:18:664414279224654700950 117:19:3461948086486358704950 117:20:16963545623783157654255 117:21:78355425024141252022035 117:22:341914581923525463368880 117:23:1412255881858039957393200 117:24:5531335537277323166456700 117:25:20576568198671642179218924 117:26:72809395164530426172620808 117:27:245394628147121065989203464 117:28:788768447615746283536725420 117:29:2420703166820738594302364220 117:30:7100729289340833209953601712 117:31:19927853166859757718256882224 117:32:53556105385935598867815370977 117:33:137947544175894724356494137365 117:34:340811579728681083704279633490 117:35:808210317642300855641577416562 117:36:1840923501296351948961370782169 117:37:4030129827162283996374892793397 117:38:8484483846657439992368195354520 117:39:17186518561177891266591985461720 117:40:33513711194296887969854371650354 117:41:62940384438069765211677722367738 117:42:113892124221269098954464449998764 117:43:198649053874306567943833343021100 117:44:334091590606788318814628804171850 117:45:541970802539901050521508948989890 117:46:848302125714627731251057485375480 117:47:1281477679271033381251597477907640 117:48:1868821615603590347658579655281975 117:49:2631605948503014979355959106417475 117:50:3578984089964100371924104384727766 117:51:4701802627992053429782646936799222 117:52:5967672566297606276262590342860551 117:53:7318843713383856753906950420489355 117:54:8674185141788274671297126424283680 117:55:9935884798775660078031253904179488 117:56:11000443884358766514963173965341576 117:57:11772404858699732586188659857646248 117:58:12178349853827309571919303301013360 117:59:12178349853827309571919303301013360 117:60:11772404858699732586188659857646248 117:61:11000443884358766514963173965341576 117:62:9935884798775660078031253904179488 117:63:8674185141788274671297126424283680 117:64:7318843713383856753906950420489355 117:65:5967672566297606276262590342860551 117:66:4701802627992053429782646936799222 117:67:3578984089964100371924104384727766 117:68:2631605948503014979355959106417475 117:69:1868821615603590347658579655281975 117:70:1281477679271033381251597477907640 117:71:848302125714627731251057485375480 117:72:541970802539901050521508948989890 117:73:334091590606788318814628804171850 117:74:198649053874306567943833343021100 117:75:113892124221269098954464449998764 117:76:62940384438069765211677722367738 117:77:33513711194296887969854371650354 117:78:17186518561177891266591985461720 117:79:8484483846657439992368195354520 117:80:4030129827162283996374892793397 117:81:1840923501296351948961370782169 117:82:808210317642300855641577416562 117:83:340811579728681083704279633490 117:84:137947544175894724356494137365 117:85:53556105385935598867815370977 117:86:19927853166859757718256882224 117:87:7100729289340833209953601712 117:88:2420703166820738594302364220 117:89:788768447615746283536725420 117:90:245394628147121065989203464 117:91:72809395164530426172620808 117:92:20576568198671642179218924 117:93:5531335537277323166456700 117:94:1412255881858039957393200 117:95:341914581923525463368880 117:96:78355425024141252022035 117:97:16963545623783157654255 117:98:3461948086486358704950 117:99:664414279224654700950 117:100:119594570260437846171 117:101:20129779152746964207 117:102:3157612416117170856 117:103:459846468366578280 117:104:61902409203193230 117:105:7664107806109638 117:106:867634845974676 117:107:89196105660948 117:108:8258898672310 117:109:681927413310 117:110:49594720968 117:111:3127595016 117:112:167549733 117:113:7413705 117:114:260130 117:115:6786 117:116:117 117:117:1 # binomial(118, k) for 0 <= k <= 118 118:0:1 118:1:118 118:2:6903 118:3:266916 118:4:7673835 118:5:174963438 118:6:3295144749 118:7:52722315984 118:8:731522134278 118:9:8940826085620 118:10:97455004333258 118:11:956830951635624 118:12:8531742652084314 118:13:69566517009302868 118:14:521748877569771510 118:15:3617458884483749136 118:16:23287391568864135063 118:17:139724349413184810378 118:18:784008849485092547121 118:19:4126362365711013405900 118:20:20425493710269516359205 118:21:95318970647924409676290 118:22:420270006947666715390915 118:23:1754170463781565420762080 118:24:6943591419135363123849900 118:25:26107903735948965345675624 118:26:93385963363202068351839732 118:27:318204023311651492161824272 118:28:1034163075762867349525928884 118:29:3209471614436484877839089640 118:30:9521432456161571804255965932 118:31:27028582456200590928210483936 118:32:73483958552795356586072253201 118:33:191503649561830323224309508342 118:34:478759123904575808060773770855 118:35:1149021897370981939345857050052 118:36:2649133818938652804602948198731 118:37:5871053328458635945336263575566 118:38:12514613673819723988743088147917 118:39:25671002407835331258960180816240 118:40:50700229755474779236446357112074 118:41:96454095632366653181532094018092 118:42:176832508659338864166142172366502 118:43:312541178095575666898297793019864 118:44:532740644481094886758462147192950 118:45:876062393146689369336137753161740 118:46:1390272928254528781772566434365370 118:47:2129779804985661112502654963283120 118:48:3150299294874623728910177133189615 118:49:4500427564106605327014538761699450 118:50:6210590038467115351280063491145241 118:51:8280786717956153801706751321526988 118:52:10669475194289659706045237279659773 118:53:13286516279681463030169540763349906 118:54:15993028855172131425204076844773035 118:55:18610069940563934749328380328463168 118:56:20936328683134426592994427869521064 118:57:22772848743058499101151833822987824 118:58:23950754712527042158107963158659608 118:59:24356699707654619143838606602026720 118:60:23950754712527042158107963158659608 118:61:22772848743058499101151833822987824 118:62:20936328683134426592994427869521064 118:63:18610069940563934749328380328463168 118:64:15993028855172131425204076844773035 118:65:13286516279681463030169540763349906 118:66:10669475194289659706045237279659773 118:67:8280786717956153801706751321526988 118:68:6210590038467115351280063491145241 118:69:4500427564106605327014538761699450 118:70:3150299294874623728910177133189615 118:71:2129779804985661112502654963283120 118:72:1390272928254528781772566434365370 118:73:876062393146689369336137753161740 118:74:532740644481094886758462147192950 118:75:312541178095575666898297793019864 118:76:176832508659338864166142172366502 118:77:96454095632366653181532094018092 118:78:50700229755474779236446357112074 118:79:25671002407835331258960180816240 118:80:12514613673819723988743088147917 118:81:5871053328458635945336263575566 118:82:2649133818938652804602948198731 118:83:1149021897370981939345857050052 118:84:478759123904575808060773770855 118:85:191503649561830323224309508342 118:86:73483958552795356586072253201 118:87:27028582456200590928210483936 118:88:9521432456161571804255965932 118:89:3209471614436484877839089640 118:90:1034163075762867349525928884 118:91:318204023311651492161824272 118:92:93385963363202068351839732 118:93:26107903735948965345675624 118:94:6943591419135363123849900 118:95:1754170463781565420762080 118:96:420270006947666715390915 118:97:95318970647924409676290 118:98:20425493710269516359205 118:99:4126362365711013405900 118:100:784008849485092547121 118:101:139724349413184810378 118:102:23287391568864135063 118:103:3617458884483749136 118:104:521748877569771510 118:105:69566517009302868 118:106:8531742652084314 118:107:956830951635624 118:108:97455004333258 118:109:8940826085620 118:110:731522134278 118:111:52722315984 118:112:3295144749 118:113:174963438 118:114:7673835 118:115:266916 118:116:6903 118:117:118 118:118:1 # binomial(119, k) for 0 <= k <= 119 119:0:1 119:1:119 119:2:7021 119:3:273819 119:4:7940751 119:5:182637273 119:6:3470108187 119:7:56017460733 119:8:784244450262 119:9:9672348219898 119:10:106395830418878 119:11:1054285955968882 119:12:9488573603719938 119:13:78098259661387182 119:14:591315394579074378 119:15:4139207762053520646 119:16:26904850453347884199 119:17:163011740982048945441 119:18:923733198898277357499 119:19:4910371215196105953021 119:20:24551856075980529765105 119:21:115744464358193926035495 119:22:515588977595591125067205 119:23:2174440470729232136152995 119:24:8697761882916928544611980 119:25:33051495155084328469525524 119:26:119493867099151033697515356 119:27:411589986674853560513664004 119:28:1352367099074518841687753156 119:29:4243634690199352227365018524 119:30:12730904070598056682095055572 119:31:36550014912362162732466449868 119:32:100512541008995947514282737137 119:33:264987608114625679810381761543 119:34:670262773466406131285083279197 119:35:1627781021275557747406630820907 119:36:3798155716309634743948805248783 119:37:8520187147397288749939211774297 119:38:18385667002278359934079351723483 119:39:38185616081655055247703268964157 119:40:76371232163310110495406537928314 119:41:147154325387841432417978451130166 119:42:273286604291705517347674266384594 119:43:489373686754914531064439965386366 119:44:845281822576670553656759940212814 119:45:1408803037627784256094599900354690 119:46:2266335321401218151108704187527110 119:47:3520052733240189894275221397648490 119:48:5280079099860284841412832096472735 119:49:7650726858981229055924715894889065 119:50:10711017602573720678294602252844691 119:51:14491376756423269152986814812672229 119:52:18950261912245813507751988601186761 119:53:23955991473971122736214778043009679 119:54:29279545134853594455373617608122941 119:55:34603098795736066174532457173236203 119:56:39546398623698361342322808197984232 119:57:43709177426192925694146261692508888 119:58:46723603455585541259259796981647432 119:59:48307454420181661301946569760686328 119:60:48307454420181661301946569760686328 119:61:46723603455585541259259796981647432 119:62:43709177426192925694146261692508888 119:63:39546398623698361342322808197984232 119:64:34603098795736066174532457173236203 119:65:29279545134853594455373617608122941 119:66:23955991473971122736214778043009679 119:67:18950261912245813507751988601186761 119:68:14491376756423269152986814812672229 119:69:10711017602573720678294602252844691 119:70:7650726858981229055924715894889065 119:71:5280079099860284841412832096472735 119:72:3520052733240189894275221397648490 119:73:2266335321401218151108704187527110 119:74:1408803037627784256094599900354690 119:75:845281822576670553656759940212814 119:76:489373686754914531064439965386366 119:77:273286604291705517347674266384594 119:78:147154325387841432417978451130166 119:79:76371232163310110495406537928314 119:80:38185616081655055247703268964157 119:81:18385667002278359934079351723483 119:82:8520187147397288749939211774297 119:83:3798155716309634743948805248783 119:84:1627781021275557747406630820907 119:85:670262773466406131285083279197 119:86:264987608114625679810381761543 119:87:100512541008995947514282737137 119:88:36550014912362162732466449868 119:89:12730904070598056682095055572 119:90:4243634690199352227365018524 119:91:1352367099074518841687753156 119:92:411589986674853560513664004 119:93:119493867099151033697515356 119:94:33051495155084328469525524 119:95:8697761882916928544611980 119:96:2174440470729232136152995 119:97:515588977595591125067205 119:98:115744464358193926035495 119:99:24551856075980529765105 119:100:4910371215196105953021 119:101:923733198898277357499 119:102:163011740982048945441 119:103:26904850453347884199 119:104:4139207762053520646 119:105:591315394579074378 119:106:78098259661387182 119:107:9488573603719938 119:108:1054285955968882 119:109:106395830418878 119:110:9672348219898 119:111:784244450262 119:112:56017460733 119:113:3470108187 119:114:182637273 119:115:7940751 119:116:273819 119:117:7021 119:118:119 119:119:1 # binomial(120, k) for 0 <= k <= 120 120:0:1 120:1:120 120:2:7140 120:3:280840 120:4:8214570 120:5:190578024 120:6:3652745460 120:7:59487568920 120:8:840261910995 120:9:10456592670160 120:10:116068178638776 120:11:1160681786387760 120:12:10542859559688820 120:13:87586833265107120 120:14:669413654240461560 120:15:4730523156632595024 120:16:31044058215401404845 120:17:189916591435396829640 120:18:1086744939880326302940 120:19:5834104414094383310520 120:20:29462227291176635718126 120:21:140296320434174455800600 120:22:631333441953785051102700 120:23:2690029448324823261220200 120:24:10872202353646160680764975 120:25:41749257038001257014137504 120:26:152545362254235362167040880 120:27:531083853774004594211179360 120:28:1763957085749372402201417160 120:29:5596001789273871069052771680 120:30:16974538760797408909460074096 120:31:49280918982960219414561505440 120:32:137062555921358110246749187005 120:33:365500149123621627324664498680 120:34:935250381581031811095465040740 120:35:2298043794741963878691714100104 120:36:5425936737585192491355436069690 120:37:12318342863706923493888017023080 120:38:26905854149675648684018563497780 120:39:56571283083933415181782620687640 120:40:114556848244965165743109806892471 120:41:223525557551151542913384989058480 120:42:420440929679546949765652717514760 120:43:762660291046620048412114231770960 120:44:1334655509331585084721199905599180 120:45:2254084860204454809751359840567504 120:46:3675138359029002407203304087881800 120:47:5786388054641408045383925585175600 120:48:8800131833100474735688053494121225 120:49:12930805958841513897337547991361800 120:50:18361744461554949734219318147733756 120:51:25202394358996989831281417065516920 120:52:33441638668669082660738803413858990 120:53:42906253386216936243966766644196440 120:54:53235536608824717191588395651132620 120:55:63882643930589660629906074781359144 120:56:74149497419434427516855265371220435 120:57:83255576049891287036469069890493120 120:58:90432780881778466953406058674156320 120:59:95031057875767202561206366742333760 120:60:96614908840363322603893139521372656 120:61:95031057875767202561206366742333760 120:62:90432780881778466953406058674156320 120:63:83255576049891287036469069890493120 120:64:74149497419434427516855265371220435 120:65:63882643930589660629906074781359144 120:66:53235536608824717191588395651132620 120:67:42906253386216936243966766644196440 120:68:33441638668669082660738803413858990 120:69:25202394358996989831281417065516920 120:70:18361744461554949734219318147733756 120:71:12930805958841513897337547991361800 120:72:8800131833100474735688053494121225 120:73:5786388054641408045383925585175600 120:74:3675138359029002407203304087881800 120:75:2254084860204454809751359840567504 120:76:1334655509331585084721199905599180 120:77:762660291046620048412114231770960 120:78:420440929679546949765652717514760 120:79:223525557551151542913384989058480 120:80:114556848244965165743109806892471 120:81:56571283083933415181782620687640 120:82:26905854149675648684018563497780 120:83:12318342863706923493888017023080 120:84:5425936737585192491355436069690 120:85:2298043794741963878691714100104 120:86:935250381581031811095465040740 120:87:365500149123621627324664498680 120:88:137062555921358110246749187005 120:89:49280918982960219414561505440 120:90:16974538760797408909460074096 120:91:5596001789273871069052771680 120:92:1763957085749372402201417160 120:93:531083853774004594211179360 120:94:152545362254235362167040880 120:95:41749257038001257014137504 120:96:10872202353646160680764975 120:97:2690029448324823261220200 120:98:631333441953785051102700 120:99:140296320434174455800600 120:100:29462227291176635718126 120:101:5834104414094383310520 120:102:1086744939880326302940 120:103:189916591435396829640 120:104:31044058215401404845 120:105:4730523156632595024 120:106:669413654240461560 120:107:87586833265107120 120:108:10542859559688820 120:109:1160681786387760 120:110:116068178638776 120:111:10456592670160 120:112:840261910995 120:113:59487568920 120:114:3652745460 120:115:190578024 120:116:8214570 120:117:280840 120:118:7140 120:119:120 120:120:1 # binomial(121, k) for 0 <= k <= 121 121:0:1 121:1:121 121:2:7260 121:3:287980 121:4:8495410 121:5:198792594 121:6:3843323484 121:7:63140314380 121:8:899749479915 121:9:11296854581155 121:10:126524771308936 121:11:1276749965026536 121:12:11703541346076580 121:13:98129692824795940 121:14:757000487505568680 121:15:5399936810873056584 121:16:35774581372033999869 121:17:220960649650798234485 121:18:1276661531315723132580 121:19:6920849353974709613460 121:20:35296331705271019028646 121:21:169758547725351091518726 121:22:771629762387959506903300 121:23:3321362890278608312322900 121:24:13562231801970983941985175 121:25:52621459391647417694902479 121:26:194294619292236619181178384 121:27:683629216028239956378220240 121:28:2295040939523376996412596520 121:29:7359958875023243471254188840 121:30:22570540550071279978512845776 121:31:66255457743757628324021579536 121:32:186343474904318329661310692445 121:33:502562705044979737571413685685 121:34:1300750530704653438420129539420 121:35:3233294176322995689787179140844 121:36:7723980532327156370047150169794 121:37:17744279601292115985243453092770 121:38:39224197013382572177906580520860 121:39:83477137233609063865801184185420 121:40:171128131328898580924892427580111 121:41:338082405796116708656494795950951 121:42:643966487230698492679037706573240 121:43:1183101220726166998177766949285720 121:44:2097315800378205133133314137370140 121:45:3588740369536039894472559746166684 121:46:5929223219233457216954663928449304 121:47:9461526413670410452587229673057400 121:48:14586519887741882781071979079296825 121:49:21730937791941988633025601485483025 121:50:31292550420396463631556866139095556 121:51:43564138820551939565500735213250676 121:52:58644033027666072492020220479375910 121:53:76347892054886018904705570058055430 121:54:96141789995041653435555162295329060 121:55:117118180539414377821494470432491764 121:56:138032141350024088146761340152579579 121:57:157405073469325714553324335261713555 121:58:173688356931669753989875128564649440 121:59:185463838757545669514612425416490080 121:60:191645966716130525165099506263706416 121:61:191645966716130525165099506263706416 121:62:185463838757545669514612425416490080 121:63:173688356931669753989875128564649440 121:64:157405073469325714553324335261713555 121:65:138032141350024088146761340152579579 121:66:117118180539414377821494470432491764 121:67:96141789995041653435555162295329060 121:68:76347892054886018904705570058055430 121:69:58644033027666072492020220479375910 121:70:43564138820551939565500735213250676 121:71:31292550420396463631556866139095556 121:72:21730937791941988633025601485483025 121:73:14586519887741882781071979079296825 121:74:9461526413670410452587229673057400 121:75:5929223219233457216954663928449304 121:76:3588740369536039894472559746166684 121:77:2097315800378205133133314137370140 121:78:1183101220726166998177766949285720 121:79:643966487230698492679037706573240 121:80:338082405796116708656494795950951 121:81:171128131328898580924892427580111 121:82:83477137233609063865801184185420 121:83:39224197013382572177906580520860 121:84:17744279601292115985243453092770 121:85:7723980532327156370047150169794 121:86:3233294176322995689787179140844 121:87:1300750530704653438420129539420 121:88:502562705044979737571413685685 121:89:186343474904318329661310692445 121:90:66255457743757628324021579536 121:91:22570540550071279978512845776 121:92:7359958875023243471254188840 121:93:2295040939523376996412596520 121:94:683629216028239956378220240 121:95:194294619292236619181178384 121:96:52621459391647417694902479 121:97:13562231801970983941985175 121:98:3321362890278608312322900 121:99:771629762387959506903300 121:100:169758547725351091518726 121:101:35296331705271019028646 121:102:6920849353974709613460 121:103:1276661531315723132580 121:104:220960649650798234485 121:105:35774581372033999869 121:106:5399936810873056584 121:107:757000487505568680 121:108:98129692824795940 121:109:11703541346076580 121:110:1276749965026536 121:111:126524771308936 121:112:11296854581155 121:113:899749479915 121:114:63140314380 121:115:3843323484 121:116:198792594 121:117:8495410 121:118:287980 121:119:7260 121:120:121 121:121:1 # binomial(122, k) for 0 <= k <= 122 122:0:1 122:1:122 122:2:7381 122:3:295240 122:4:8783390 122:5:207288004 122:6:4042116078 122:7:66983637864 122:8:962889794295 122:9:12196604061070 122:10:137821625890091 122:11:1403274736335472 122:12:12980291311103116 122:13:109833234170872520 122:14:855130180330364620 122:15:6156937298378625264 122:16:41174518182907056453 122:17:256735231022832234354 122:18:1497622180966521367065 122:19:8197510885290432746040 122:20:42217181059245728642106 122:21:205054879430622110547372 122:22:941388310113310598422026 122:23:4092992652666567819226200 122:24:16883594692249592254308075 122:25:66183691193618401636887654 122:26:246916078683884036876080863 122:27:877923835320476575559398624 122:28:2978670155551616952790816760 122:29:9654999814546620467666785360 122:30:29930499425094523449767034616 122:31:88825998293828908302534425312 122:32:252598932648075957985332271981 122:33:688906179949298067232724378130 122:34:1803313235749633175991543225105 122:35:4534044707027649128207308680264 122:36:10957274708650152059834329310638 122:37:25468260133619272355290603262564 122:38:56968476614674688163150033613630 122:39:122701334246991636043707764706280 122:40:254605268562507644790693611765531 122:41:509210537125015289581387223531062 122:42:982048893026815201335532502524191 122:43:1827067707956865490856804655858960 122:44:3280417021104372131311081086655860 122:45:5686056169914245027605873883536824 122:46:9517963588769497111427223674615988 122:47:15390749632903867669541893601506704 122:48:24048046301412293233659208752354225 122:49:36317457679683871414097580564779850 122:50:53023488212338452264582467624578581 122:51:74856689240948403197057601352346232 122:52:102208171848218012057520955692626586 122:53:134991925082552091396725790537431340 122:54:172489682049927672340260732353384490 122:55:213259970534456031257049632727820824 122:56:255150321889438465968255810585071343 122:57:295437214819349802700085675414293134 122:58:331093430400995468543199463826362995 122:59:359152195689215423504487553981139520 122:60:377109805473676194679711931680196496 122:61:383291933432261050330199012527412832 122:62:377109805473676194679711931680196496 122:63:359152195689215423504487553981139520 122:64:331093430400995468543199463826362995 122:65:295437214819349802700085675414293134 122:66:255150321889438465968255810585071343 122:67:213259970534456031257049632727820824 122:68:172489682049927672340260732353384490 122:69:134991925082552091396725790537431340 122:70:102208171848218012057520955692626586 122:71:74856689240948403197057601352346232 122:72:53023488212338452264582467624578581 122:73:36317457679683871414097580564779850 122:74:24048046301412293233659208752354225 122:75:15390749632903867669541893601506704 122:76:9517963588769497111427223674615988 122:77:5686056169914245027605873883536824 122:78:3280417021104372131311081086655860 122:79:1827067707956865490856804655858960 122:80:982048893026815201335532502524191 122:81:509210537125015289581387223531062 122:82:254605268562507644790693611765531 122:83:122701334246991636043707764706280 122:84:56968476614674688163150033613630 122:85:25468260133619272355290603262564 122:86:10957274708650152059834329310638 122:87:4534044707027649128207308680264 122:88:1803313235749633175991543225105 122:89:688906179949298067232724378130 122:90:252598932648075957985332271981 122:91:88825998293828908302534425312 122:92:29930499425094523449767034616 122:93:9654999814546620467666785360 122:94:2978670155551616952790816760 122:95:877923835320476575559398624 122:96:246916078683884036876080863 122:97:66183691193618401636887654 122:98:16883594692249592254308075 122:99:4092992652666567819226200 122:100:941388310113310598422026 122:101:205054879430622110547372 122:102:42217181059245728642106 122:103:8197510885290432746040 122:104:1497622180966521367065 122:105:256735231022832234354 122:106:41174518182907056453 122:107:6156937298378625264 122:108:855130180330364620 122:109:109833234170872520 122:110:12980291311103116 122:111:1403274736335472 122:112:137821625890091 122:113:12196604061070 122:114:962889794295 122:115:66983637864 122:116:4042116078 122:117:207288004 122:118:8783390 122:119:295240 122:120:7381 122:121:122 122:122:1 # binomial(123, k) for 0 <= k <= 123 123:0:1 123:1:123 123:2:7503 123:3:302621 123:4:9078630 123:5:216071394 123:6:4249404082 123:7:71025753942 123:8:1029873432159 123:9:13159493855365 123:10:150018229951161 123:11:1541096362225563 123:12:14383566047438588 123:13:122813525481975636 123:14:964963414501237140 123:15:7012067478708989884 123:16:47331455481285681717 123:17:297909749205739290807 123:18:1754357411989353601419 123:19:9695133066256954113105 123:20:50414691944536161388146 123:21:247272060489867839189478 123:22:1146443189543932708969398 123:23:5034380962779878417648226 123:24:20976587344916160073534275 123:25:83067285885867993891195729 123:26:313099769877502438512968517 123:27:1124839914004360612435479487 123:28:3856593990872093528350215384 123:29:12633669970098237420457602120 123:30:39585499239641143917433819976 123:31:118756497718923431752301459928 123:32:341424930941904866287866697293 123:33:941505112597374025218056650111 123:34:2492219415698931243224267603235 123:35:6337357942777282304198851905369 123:36:15491319415677801188041637990902 123:37:36425534842269424415124932573202 123:38:82436736748293960518440636876194 123:39:179669810861666324206857798319910 123:40:377306602809499280834401376471811 123:41:763815805687522934372080835296593 123:42:1491259430151830490916919726055253 123:43:2809116600983680692192337158383151 123:44:5107484729061237622167885742514820 123:45:8966473191018617158916954970192684 123:46:15204019758683742139033097558152812 123:47:24908713221673364780969117276122692 123:48:39438795934316160903201102353860929 123:49:60365503981096164647756789317134075 123:50:89340945892022323678680048189358431 123:51:127880177453286855461640068976924813 123:52:177064861089166415254578557044972818 123:53:237200096930770103454246746230057926 123:54:307481607132479763736986522890815830 123:55:385749652584383703597310365081205314 123:56:468410292423894497225305443312892167 123:57:550587536708788268668341485999364477 123:58:626530645220345271243285139240656129 123:59:690245626090210892047687017807502515 123:60:736262001162891618184199485661336016 123:61:760401738905937245009910944207609328 123:62:760401738905937245009910944207609328 123:63:736262001162891618184199485661336016 123:64:690245626090210892047687017807502515 123:65:626530645220345271243285139240656129 123:66:550587536708788268668341485999364477 123:67:468410292423894497225305443312892167 123:68:385749652584383703597310365081205314 123:69:307481607132479763736986522890815830 123:70:237200096930770103454246746230057926 123:71:177064861089166415254578557044972818 123:72:127880177453286855461640068976924813 123:73:89340945892022323678680048189358431 123:74:60365503981096164647756789317134075 123:75:39438795934316160903201102353860929 123:76:24908713221673364780969117276122692 123:77:15204019758683742139033097558152812 123:78:8966473191018617158916954970192684 123:79:5107484729061237622167885742514820 123:80:2809116600983680692192337158383151 123:81:1491259430151830490916919726055253 123:82:763815805687522934372080835296593 123:83:377306602809499280834401376471811 123:84:179669810861666324206857798319910 123:85:82436736748293960518440636876194 123:86:36425534842269424415124932573202 123:87:15491319415677801188041637990902 123:88:6337357942777282304198851905369 123:89:2492219415698931243224267603235 123:90:941505112597374025218056650111 123:91:341424930941904866287866697293 123:92:118756497718923431752301459928 123:93:39585499239641143917433819976 123:94:12633669970098237420457602120 123:95:3856593990872093528350215384 123:96:1124839914004360612435479487 123:97:313099769877502438512968517 123:98:83067285885867993891195729 123:99:20976587344916160073534275 123:100:5034380962779878417648226 123:101:1146443189543932708969398 123:102:247272060489867839189478 123:103:50414691944536161388146 123:104:9695133066256954113105 123:105:1754357411989353601419 123:106:297909749205739290807 123:107:47331455481285681717 123:108:7012067478708989884 123:109:964963414501237140 123:110:122813525481975636 123:111:14383566047438588 123:112:1541096362225563 123:113:150018229951161 123:114:13159493855365 123:115:1029873432159 123:116:71025753942 123:117:4249404082 123:118:216071394 123:119:9078630 123:120:302621 123:121:7503 123:122:123 123:123:1 # binomial(124, k) for 0 <= k <= 124 124:0:1 124:1:124 124:2:7626 124:3:310124 124:4:9381251 124:5:225150024 124:6:4465475476 124:7:75275158024 124:8:1100899186101 124:9:14189367287524 124:10:163177723806526 124:11:1691114592176724 124:12:15924662409664151 124:13:137197091529414224 124:14:1087776939983212776 124:15:7977030893210227024 124:16:54343522959994671601 124:17:345241204687024972524 124:18:2052267161195092892226 124:19:11449490478246307714524 124:20:60109825010793115501251 124:21:297686752434404000577624 124:22:1393715250033800548158876 124:23:6180824152323811126617624 124:24:26010968307696038491182501 124:25:104043873230784153964730004 124:26:396167055763370432404164246 124:27:1437939683881863050948448004 124:28:4981433904876454140785694871 124:29:16490263960970330948807817504 124:30:52219169209739381337891422096 124:31:158341996958564575669735279904 124:32:460181428660828298040168157221 124:33:1282930043539278891505923347404 124:34:3433724528296305268442324253346 124:35:8829577358476213547423119508604 124:36:21828677358455083492240489896271 124:37:51916854257947225603166570564104 124:38:118862271590563384933565569449396 124:39:262106547609960284725298435196104 124:40:556976413671165605041259174791721 124:41:1141122408497022215206482211768404 124:42:2255075235839353425289000561351846 124:43:4300376031135511183109256884438404 124:44:7916601330044918314360222900897971 124:45:14073957920079854781084840712707504 124:46:24170492949702359297950052528345496 124:47:40112732980357106920002214834275504 124:48:64347509155989525684170219629983621 124:49:99804299915412325550957891670995004 124:50:149706449873118488326436837506492506 124:51:217221123345309179140320117166283244 124:52:304945038542453270716218626021897631 124:53:414264958019936518708825303275030744 124:54:544681704063249867191233269120873756 124:55:693231259716863467334296887972021144 124:56:854159945008278200822615808394097481 124:57:1018997829132682765893646929312256644 124:58:1177118181929133539911626625240020606 124:59:1316776271310556163290972157048158644 124:60:1426507627253102510231886503468838531 124:61:1496663740068828863194110429868945344 124:62:1520803477811874490019821888415218656 124:63:1496663740068828863194110429868945344 124:64:1426507627253102510231886503468838531 124:65:1316776271310556163290972157048158644 124:66:1177118181929133539911626625240020606 124:67:1018997829132682765893646929312256644 124:68:854159945008278200822615808394097481 124:69:693231259716863467334296887972021144 124:70:544681704063249867191233269120873756 124:71:414264958019936518708825303275030744 124:72:304945038542453270716218626021897631 124:73:217221123345309179140320117166283244 124:74:149706449873118488326436837506492506 124:75:99804299915412325550957891670995004 124:76:64347509155989525684170219629983621 124:77:40112732980357106920002214834275504 124:78:24170492949702359297950052528345496 124:79:14073957920079854781084840712707504 124:80:7916601330044918314360222900897971 124:81:4300376031135511183109256884438404 124:82:2255075235839353425289000561351846 124:83:1141122408497022215206482211768404 124:84:556976413671165605041259174791721 124:85:262106547609960284725298435196104 124:86:118862271590563384933565569449396 124:87:51916854257947225603166570564104 124:88:21828677358455083492240489896271 124:89:8829577358476213547423119508604 124:90:3433724528296305268442324253346 124:91:1282930043539278891505923347404 124:92:460181428660828298040168157221 124:93:158341996958564575669735279904 124:94:52219169209739381337891422096 124:95:16490263960970330948807817504 124:96:4981433904876454140785694871 124:97:1437939683881863050948448004 124:98:396167055763370432404164246 124:99:104043873230784153964730004 124:100:26010968307696038491182501 124:101:6180824152323811126617624 124:102:1393715250033800548158876 124:103:297686752434404000577624 124:104:60109825010793115501251 124:105:11449490478246307714524 124:106:2052267161195092892226 124:107:345241204687024972524 124:108:54343522959994671601 124:109:7977030893210227024 124:110:1087776939983212776 124:111:137197091529414224 124:112:15924662409664151 124:113:1691114592176724 124:114:163177723806526 124:115:14189367287524 124:116:1100899186101 124:117:75275158024 124:118:4465475476 124:119:225150024 124:120:9381251 124:121:310124 124:122:7626 124:123:124 124:124:1 # binomial(125, k) for 0 <= k <= 125 125:0:1 125:1:125 125:2:7750 125:3:317750 125:4:9691375 125:5:234531275 125:6:4690625500 125:7:79740633500 125:8:1176174344125 125:9:15290266473625 125:10:177367091094050 125:11:1854292315983250 125:12:17615777001840875 125:13:153121753939078375 125:14:1224974031512627000 125:15:9064807833193439800 125:16:62320553853204898625 125:17:399584727647019644125 125:18:2397508365882117864750 125:19:13501757639441400606750 125:20:71559315489039423215775 125:21:357796577445197116078875 125:22:1691402002468204548736500 125:23:7574539402357611674776500 125:24:32191792460019849617800125 125:25:130054841538480192455912505 125:26:500210928994154586368894250 125:27:1834106739645233483352612250 125:28:6419373588758317191734142875 125:29:21471697865846785089593512375 125:30:68709433170709712286699239600 125:31:210561166168303957007626702000 125:32:618523425619392873709903437125 125:33:1743111472200107189546091504625 125:34:4716654571835584159948247600750 125:35:12263301886772518815865443761950 125:36:30658254716931297039663609404875 125:37:73745531616402309095407060460375 125:38:170779125848510610536732140013500 125:39:380968819200523669658864004645500 125:40:819082961281125889766557609987825 125:41:1698098822168187820247741386560125 125:42:3396197644336375640495482773120250 125:43:6555451266974864608398257445790250 125:44:12216977361180429497469479785336375 125:45:21990559250124773095445063613605475 125:46:38244450869782214079034893241053000 125:47:64283225930059466217952267362621000 125:48:104460242136346632604172434464259125 125:49:164151809071401851235128111300978625 125:50:249510749788530813877394729177487510 125:51:366927573218427667466756954672775750 125:52:522166161887762449856538743188180875 125:53:719209996562389789425043929296928375 125:54:958946662083186385900058572395904500 125:55:1237912963780113334525530157092894900 125:56:1547391204725141668156912696366118625 125:57:1873157774140960966716262737706354125 125:58:2196116011061816305805273554552277250 125:59:2493894453239689703202598782288179250 125:60:2743283898563658673522858660516997175 125:61:2923171367321931373425996933337783875 125:62:3017467217880703353213932318284164000 125:63:3017467217880703353213932318284164000 125:64:2923171367321931373425996933337783875 125:65:2743283898563658673522858660516997175 125:66:2493894453239689703202598782288179250 125:67:2196116011061816305805273554552277250 125:68:1873157774140960966716262737706354125 125:69:1547391204725141668156912696366118625 125:70:1237912963780113334525530157092894900 125:71:958946662083186385900058572395904500 125:72:719209996562389789425043929296928375 125:73:522166161887762449856538743188180875 125:74:366927573218427667466756954672775750 125:75:249510749788530813877394729177487510 125:76:164151809071401851235128111300978625 125:77:104460242136346632604172434464259125 125:78:64283225930059466217952267362621000 125:79:38244450869782214079034893241053000 125:80:21990559250124773095445063613605475 125:81:12216977361180429497469479785336375 125:82:6555451266974864608398257445790250 125:83:3396197644336375640495482773120250 125:84:1698098822168187820247741386560125 125:85:819082961281125889766557609987825 125:86:380968819200523669658864004645500 125:87:170779125848510610536732140013500 125:88:73745531616402309095407060460375 125:89:30658254716931297039663609404875 125:90:12263301886772518815865443761950 125:91:4716654571835584159948247600750 125:92:1743111472200107189546091504625 125:93:618523425619392873709903437125 125:94:210561166168303957007626702000 125:95:68709433170709712286699239600 125:96:21471697865846785089593512375 125:97:6419373588758317191734142875 125:98:1834106739645233483352612250 125:99:500210928994154586368894250 125:100:130054841538480192455912505 125:101:32191792460019849617800125 125:102:7574539402357611674776500 125:103:1691402002468204548736500 125:104:357796577445197116078875 125:105:71559315489039423215775 125:106:13501757639441400606750 125:107:2397508365882117864750 125:108:399584727647019644125 125:109:62320553853204898625 125:110:9064807833193439800 125:111:1224974031512627000 125:112:153121753939078375 125:113:17615777001840875 125:114:1854292315983250 125:115:177367091094050 125:116:15290266473625 125:117:1176174344125 125:118:79740633500 125:119:4690625500 125:120:234531275 125:121:9691375 125:122:317750 125:123:7750 125:124:125 125:125:1 # binomial(126, k) for 0 <= k <= 126 126:0:1 126:1:126 126:2:7875 126:3:325500 126:4:10009125 126:5:244222650 126:6:4925156775 126:7:84431259000 126:8:1255914977625 126:9:16466440817750 126:10:192657357567675 126:11:2031659407077300 126:12:19470069317824125 126:13:170737530940919250 126:14:1378095785451705375 126:15:10289781864706066800 126:16:71385361686398338425 126:17:461905281500224542750 126:18:2797093093529137508875 126:19:15899266005323518471500 126:20:85061073128480823822525 126:21:429355892934236539294650 126:22:2049198579913401664815375 126:23:9265941404825816223513000 126:24:39766331862377461292576625 126:25:162246633998500042073712630 126:26:630265770532634778824806755 126:27:2334317668639388069721506500 126:28:8253480328403550675086755125 126:29:27891071454605102281327655250 126:30:90181131036556497376292751975 126:31:279270599339013669294325941600 126:32:829084591787696830717530139125 126:33:2361634897819500063255994941750 126:34:6459766044035691349494339105375 126:35:16979956458608102975813691362700 126:36:42921556603703815855529053166825 126:37:104403786333333606135070669865250 126:38:244524657464912919632139200473875 126:39:551747945049034280195596144659000 126:40:1200051780481649559425421614633325 126:41:2517181783449313710014298996547950 126:42:5094296466504563460743224159680375 126:43:9951648911311240248893740218910500 126:44:18772428628155294105867737231126625 126:45:34207536611305202592914543398941850 126:46:60235010119906987174479956854658475 126:47:102527676799841680296987160603674000 126:48:168743468066406098822124701826880125 126:49:268612051207748483839300545765237750 126:50:413662558859932665112522840478466135 126:51:616438323006958481344151683850263260 126:52:889093735106190117323295697860956625 126:53:1241376158450152239281582672485109250 126:54:1678156658645576175325102501692832875 126:55:2196859625863299720425588729488799400 126:56:2785304168505255002682442853459013525 126:57:3420548978866102634873175434072472750 126:58:4069273785202777272521536292258631375 126:59:4690010464301506009007872336840456500 126:60:5237178351803348376725457442805176425 126:61:5666455265885590046948855593854781050 126:62:5940638585202634726639929251621947875 126:63:6034934435761406706427864636568328000 126:64:5940638585202634726639929251621947875 126:65:5666455265885590046948855593854781050 126:66:5237178351803348376725457442805176425 126:67:4690010464301506009007872336840456500 126:68:4069273785202777272521536292258631375 126:69:3420548978866102634873175434072472750 126:70:2785304168505255002682442853459013525 126:71:2196859625863299720425588729488799400 126:72:1678156658645576175325102501692832875 126:73:1241376158450152239281582672485109250 126:74:889093735106190117323295697860956625 126:75:616438323006958481344151683850263260 126:76:413662558859932665112522840478466135 126:77:268612051207748483839300545765237750 126:78:168743468066406098822124701826880125 126:79:102527676799841680296987160603674000 126:80:60235010119906987174479956854658475 126:81:34207536611305202592914543398941850 126:82:18772428628155294105867737231126625 126:83:9951648911311240248893740218910500 126:84:5094296466504563460743224159680375 126:85:2517181783449313710014298996547950 126:86:1200051780481649559425421614633325 126:87:551747945049034280195596144659000 126:88:244524657464912919632139200473875 126:89:104403786333333606135070669865250 126:90:42921556603703815855529053166825 126:91:16979956458608102975813691362700 126:92:6459766044035691349494339105375 126:93:2361634897819500063255994941750 126:94:829084591787696830717530139125 126:95:279270599339013669294325941600 126:96:90181131036556497376292751975 126:97:27891071454605102281327655250 126:98:8253480328403550675086755125 126:99:2334317668639388069721506500 126:100:630265770532634778824806755 126:101:162246633998500042073712630 126:102:39766331862377461292576625 126:103:9265941404825816223513000 126:104:2049198579913401664815375 126:105:429355892934236539294650 126:106:85061073128480823822525 126:107:15899266005323518471500 126:108:2797093093529137508875 126:109:461905281500224542750 126:110:71385361686398338425 126:111:10289781864706066800 126:112:1378095785451705375 126:113:170737530940919250 126:114:19470069317824125 126:115:2031659407077300 126:116:192657357567675 126:117:16466440817750 126:118:1255914977625 126:119:84431259000 126:120:4925156775 126:121:244222650 126:122:10009125 126:123:325500 126:124:7875 126:125:126 126:126:1 # binomial(127, k) for 0 <= k <= 127 127:0:1 127:1:127 127:2:8001 127:3:333375 127:4:10334625 127:5:254231775 127:6:5169379425 127:7:89356415775 127:8:1340346236625 127:9:17722355795375 127:10:209123798385425 127:11:2224316764644975 127:12:21501728724901425 127:13:190207600258743375 127:14:1548833316392624625 127:15:11667877650157772175 127:16:81675143551104405225 127:17:533290643186622881175 127:18:3258998375029362051625 127:19:18696359098852655980375 127:20:100960339133804342294025 127:21:514416966062717363117175 127:22:2478554472847638204110025 127:23:11315139984739217888328375 127:24:49032273267203277516089625 127:25:202012965860877503366289255 127:26:792512404531134820898519385 127:27:2964583439172022848546313255 127:28:10587797997042938744808261625 127:29:36144551783008652956414410375 127:30:118072202491161599657620407225 127:31:369451730375570166670618693575 127:32:1108355191126710500011856080725 127:33:3190719489607196893973525080875 127:34:8821400941855191412750334047125 127:35:23439722502643794325308030468075 127:36:59901513062311918831342744529525 127:37:147325342937037421990599723032075 127:38:348928443798246525767209870339125 127:39:796272602513947199827735345132875 127:40:1751799725530683839621017759292325 127:41:3717233563930963269439720611181275 127:42:7611478249953877170757523156228325 127:43:15045945377815803709636964378590875 127:44:28724077539466534354761477450037125 127:45:52979965239460496698782280630068475 127:46:94442546731212189767394500253600325 127:47:162762686919748667471467117458332475 127:48:271271144866247779119111862430554125 127:49:437355519274154582661425247592117875 127:50:682274610067681148951823386243703885 127:51:1030100881866891146456674524328729395 127:52:1505532058113148598667447381711219885 127:53:2130469893556342356604878370346065875 127:54:2919532817095728414606685174177942125 127:55:3875016284508875895750691231181632275 127:56:4982163794368554723108031582947812925 127:57:6205853147371357637555618287531486275 127:58:7489822764068879907394711726331104125 127:59:8759284249504283281529408629099087875 127:60:9927188816104854385733329779645632925 127:61:10903633617688938423674313036659957475 127:62:11607093851088224773588784845476728925 127:63:11975573020964041433067793888190275875 127:64:11975573020964041433067793888190275875 127:65:11607093851088224773588784845476728925 127:66:10903633617688938423674313036659957475 127:67:9927188816104854385733329779645632925 127:68:8759284249504283281529408629099087875 127:69:7489822764068879907394711726331104125 127:70:6205853147371357637555618287531486275 127:71:4982163794368554723108031582947812925 127:72:3875016284508875895750691231181632275 127:73:2919532817095728414606685174177942125 127:74:2130469893556342356604878370346065875 127:75:1505532058113148598667447381711219885 127:76:1030100881866891146456674524328729395 127:77:682274610067681148951823386243703885 127:78:437355519274154582661425247592117875 127:79:271271144866247779119111862430554125 127:80:162762686919748667471467117458332475 127:81:94442546731212189767394500253600325 127:82:52979965239460496698782280630068475 127:83:28724077539466534354761477450037125 127:84:15045945377815803709636964378590875 127:85:7611478249953877170757523156228325 127:86:3717233563930963269439720611181275 127:87:1751799725530683839621017759292325 127:88:796272602513947199827735345132875 127:89:348928443798246525767209870339125 127:90:147325342937037421990599723032075 127:91:59901513062311918831342744529525 127:92:23439722502643794325308030468075 127:93:8821400941855191412750334047125 127:94:3190719489607196893973525080875 127:95:1108355191126710500011856080725 127:96:369451730375570166670618693575 127:97:118072202491161599657620407225 127:98:36144551783008652956414410375 127:99:10587797997042938744808261625 127:100:2964583439172022848546313255 127:101:792512404531134820898519385 127:102:202012965860877503366289255 127:103:49032273267203277516089625 127:104:11315139984739217888328375 127:105:2478554472847638204110025 127:106:514416966062717363117175 127:107:100960339133804342294025 127:108:18696359098852655980375 127:109:3258998375029362051625 127:110:533290643186622881175 127:111:81675143551104405225 127:112:11667877650157772175 127:113:1548833316392624625 127:114:190207600258743375 127:115:21501728724901425 127:116:2224316764644975 127:117:209123798385425 127:118:17722355795375 127:119:1340346236625 127:120:89356415775 127:121:5169379425 127:122:254231775 127:123:10334625 127:124:333375 127:125:8001 127:126:127 127:127:1 # binomial(128, k) for 0 <= k <= 128 128:0:1 128:1:128 128:2:8128 128:3:341376 128:4:10668000 128:5:264566400 128:6:5423611200 128:7:94525795200 128:8:1429702652400 128:9:19062702032000 128:10:226846154180800 128:11:2433440563030400 128:12:23726045489546400 128:13:211709328983644800 128:14:1739040916651368000 128:15:13216710966550396800 128:16:93343021201262177400 128:17:614965786737727286400 128:18:3792289018215984932800 128:19:21955357473882018032000 128:20:119656698232656998274400 128:21:615377305196521705411200 128:22:2992971438910355567227200 128:23:13793694457586856092438400 128:24:60347413251942495404418000 128:25:251045239128080780882378880 128:26:994525370392012324264808640 128:27:3757095843703157669444832640 128:28:13552381436214961593354574880 128:29:46732349780051591701222672000 128:30:154216754274170252614034817600 128:31:487523932866731766328239100800 128:32:1477806921502280666682474774300 128:33:4299074680733907393985381161600 128:34:12012120431462388306723859128000 128:35:32261123444498985738058364515200 128:36:83341235564955713156650774997600 128:37:207226855999349340821942467561600 128:38:496253786735283947757809593371200 128:39:1145201046312193725594945215472000 128:40:2548072328044631039448753104425200 128:41:5469033289461647109060738370473600 128:42:11328711813884840440197243767409600 128:43:22657423627769680880394487534819200 128:44:43770022917282338064398441828628000 128:45:81704042778927031053543758080105600 128:46:147422511970672686466176780883668800 128:47:257205233650960857238861617711932800 128:48:434033831785996446590578979888886600 128:49:708626664140402361780537110022672000 128:50:1119630129341835731613248633835821760 128:51:1712375491934572295408497910572433280 128:52:2535632939980039745124121906039949280 128:53:3636001951669490955272325752057285760 128:54:5050002710652070771211563544524008000 128:55:6794549101604604310357376405359574400 128:56:8857180078877430618858722814129445200 128:57:11188016941739912360663649870479299200 128:58:13695675911440237544950330013862590400 128:59:16249107013573163188924120355430192000 128:60:18686473065609137667262738408744720800 128:61:20830822433793792809407642816305590400 128:62:22510727468777163197263097882136686400 128:63:23582666872052266206656578733667004800 128:64:23951146041928082866135587776380551750 128:65:23582666872052266206656578733667004800 128:66:22510727468777163197263097882136686400 128:67:20830822433793792809407642816305590400 128:68:18686473065609137667262738408744720800 128:69:16249107013573163188924120355430192000 128:70:13695675911440237544950330013862590400 128:71:11188016941739912360663649870479299200 128:72:8857180078877430618858722814129445200 128:73:6794549101604604310357376405359574400 128:74:5050002710652070771211563544524008000 128:75:3636001951669490955272325752057285760 128:76:2535632939980039745124121906039949280 128:77:1712375491934572295408497910572433280 128:78:1119630129341835731613248633835821760 128:79:708626664140402361780537110022672000 128:80:434033831785996446590578979888886600 128:81:257205233650960857238861617711932800 128:82:147422511970672686466176780883668800 128:83:81704042778927031053543758080105600 128:84:43770022917282338064398441828628000 128:85:22657423627769680880394487534819200 128:86:11328711813884840440197243767409600 128:87:5469033289461647109060738370473600 128:88:2548072328044631039448753104425200 128:89:1145201046312193725594945215472000 128:90:496253786735283947757809593371200 128:91:207226855999349340821942467561600 128:92:83341235564955713156650774997600 128:93:32261123444498985738058364515200 128:94:12012120431462388306723859128000 128:95:4299074680733907393985381161600 128:96:1477806921502280666682474774300 128:97:487523932866731766328239100800 128:98:154216754274170252614034817600 128:99:46732349780051591701222672000 128:100:13552381436214961593354574880 128:101:3757095843703157669444832640 128:102:994525370392012324264808640 128:103:251045239128080780882378880 128:104:60347413251942495404418000 128:105:13793694457586856092438400 128:106:2992971438910355567227200 128:107:615377305196521705411200 128:108:119656698232656998274400 128:109:21955357473882018032000 128:110:3792289018215984932800 128:111:614965786737727286400 128:112:93343021201262177400 128:113:13216710966550396800 128:114:1739040916651368000 128:115:211709328983644800 128:116:23726045489546400 128:117:2433440563030400 128:118:226846154180800 128:119:19062702032000 128:120:1429702652400 128:121:94525795200 128:122:5423611200 128:123:264566400 128:124:10668000 128:125:341376 128:126:8128 128:127:128 128:128:1 # binomial(129, k) for 0 <= k <= 129 129:0:1 129:1:129 129:2:8256 129:3:349504 129:4:11009376 129:5:275234400 129:6:5688177600 129:7:99949406400 129:8:1524228447600 129:9:20492404684400 129:10:245908856212800 129:11:2660286717211200 129:12:26159486052576800 129:13:235435374473191200 129:14:1950750245635012800 129:15:14955751883201764800 129:16:106559732167812574200 129:17:708308807938989463800 129:18:4407254804953712219200 129:19:25747646492098002964800 129:20:141612055706539016306400 129:21:735034003429178703685600 129:22:3608348744106877272638400 129:23:16786665896497211659665600 129:24:74141107709529351496856400 129:25:311392652380023276286796880 129:26:1245570609520093105147187520 129:27:4751621214095169993709641280 129:28:17309477279918119262799407520 129:29:60284731216266553294577246880 129:30:200949104054221844315257489600 129:31:641740687140902018942273918400 129:32:1965330854369012433010713875100 129:33:5776881602236188060667855935900 129:34:16311195112196295700709240289600 129:35:44273243875961374044782223643200 129:36:115602359009454698894709139512800 129:37:290568091564305053978593242559200 129:38:703480642734633288579752060932800 129:39:1641454833047477673352754808843200 129:40:3693273374356824765043698319897200 129:41:8017105617506278148509491474898800 129:42:16797745103346487549257982137883200 129:43:33986135441654521320591731302228800 129:44:66427446545052018944792929363447200 129:45:125474065696209369117942199908733600 129:46:229126554749599717519720538963774400 129:47:404627745621633543705038398595601600 129:48:691239065436957303829440597600819400 129:49:1142660495926398808371116089911558600 129:50:1828256793482238093393785743858493760 129:51:2832005621276408027021746544408255040 129:52:4248008431914612040532619816612382560 129:53:6171634891649530700396447658097235040 129:54:8686004662321561726483889296581293760 129:55:11844551812256675081568939949883582400 129:56:15651729180482034929216099219489019600 129:57:20045197020617342979522372684608744400 129:58:24883692853180149905613979884341889600 129:59:29944782925013400733874450369292782400 129:60:34935580079182300856186858764174912800 129:61:39517295499402930476670381225050311200 129:62:43341549902570956006670740698442276800 129:63:46093394340829429403919676615803691200 129:64:47533812913980349072792166510047556550 129:65:47533812913980349072792166510047556550 129:66:46093394340829429403919676615803691200 129:67:43341549902570956006670740698442276800 129:68:39517295499402930476670381225050311200 129:69:34935580079182300856186858764174912800 129:70:29944782925013400733874450369292782400 129:71:24883692853180149905613979884341889600 129:72:20045197020617342979522372684608744400 129:73:15651729180482034929216099219489019600 129:74:11844551812256675081568939949883582400 129:75:8686004662321561726483889296581293760 129:76:6171634891649530700396447658097235040 129:77:4248008431914612040532619816612382560 129:78:2832005621276408027021746544408255040 129:79:1828256793482238093393785743858493760 129:80:1142660495926398808371116089911558600 129:81:691239065436957303829440597600819400 129:82:404627745621633543705038398595601600 129:83:229126554749599717519720538963774400 129:84:125474065696209369117942199908733600 129:85:66427446545052018944792929363447200 129:86:33986135441654521320591731302228800 129:87:16797745103346487549257982137883200 129:88:8017105617506278148509491474898800 129:89:3693273374356824765043698319897200 129:90:1641454833047477673352754808843200 129:91:703480642734633288579752060932800 129:92:290568091564305053978593242559200 129:93:115602359009454698894709139512800 129:94:44273243875961374044782223643200 129:95:16311195112196295700709240289600 129:96:5776881602236188060667855935900 129:97:1965330854369012433010713875100 129:98:641740687140902018942273918400 129:99:200949104054221844315257489600 129:100:60284731216266553294577246880 129:101:17309477279918119262799407520 129:102:4751621214095169993709641280 129:103:1245570609520093105147187520 129:104:311392652380023276286796880 129:105:74141107709529351496856400 129:106:16786665896497211659665600 129:107:3608348744106877272638400 129:108:735034003429178703685600 129:109:141612055706539016306400 129:110:25747646492098002964800 129:111:4407254804953712219200 129:112:708308807938989463800 129:113:106559732167812574200 129:114:14955751883201764800 129:115:1950750245635012800 129:116:235435374473191200 129:117:26159486052576800 129:118:2660286717211200 129:119:245908856212800 129:120:20492404684400 129:121:1524228447600 129:122:99949406400 129:123:5688177600 129:124:275234400 129:125:11009376 129:126:349504 129:127:8256 129:128:129 129:129:1 # binomial(130, k) for 0 <= k <= 130 130:0:1 130:1:130 130:2:8385 130:3:357760 130:4:11358880 130:5:286243776 130:6:5963412000 130:7:105637584000 130:8:1624177854000 130:9:22016633132000 130:10:266401260897200 130:11:2906195573424000 130:12:28819772769788000 130:13:261594860525768000 130:14:2186185620108204000 130:15:16906502128836777600 130:16:121515484051014339000 130:17:814868540106802038000 130:18:5115563612892701683000 130:19:30154901297051715184000 130:20:167359702198637019271200 130:21:876646059135717719992000 130:22:4343382747536055976324000 130:23:20395014640604088932304000 130:24:90927773606026563156522000 130:25:385533760089552627783653280 130:26:1556963261900116381433984400 130:27:5997191823615263098856828800 130:28:22061098494013289256509048800 130:29:77594208496184672557376654400 130:30:261233835270488397609834736480 130:31:842689791195123863257531408000 130:32:2607071541509914451952987793500 130:33:7742212456605200493678569811000 130:34:22088076714432483761377096225500 130:35:60584438988157669745491463932800 130:36:159875602885416072939491363156000 130:37:406170450573759752873302382072000 130:38:994048734298938342558345303492000 130:39:2344935475782110961932506869776000 130:40:5334728207404302438396453128740400 130:41:11710378991863102913553189794796000 130:42:24814850720852765697767473612782000 130:43:50783880545001008869849713440112000 130:44:100413581986706540265384660665676000 130:45:191901512241261388062735129272180800 130:46:354600620445809086637662738872508000 130:47:633754300371233261224758937559376000 130:48:1095866811058590847534478996196421000 130:49:1833899561363356112200556687512378000 130:50:2970917289408636901764901833770052360 130:51:4660262414758646120415532288266748800 130:52:7080014053191020067554366361020637600 130:53:10419643323564142740929067474709617600 130:54:14857639553971092426880336954678528800 130:55:20530556474578236808052829246464876160 130:56:27496280992738710010785039169372602000 130:57:35696926201099377908738471904097764000 130:58:44928889873797492885136352568950634000 130:59:54828475778193550639488430253634672000 130:60:64880363004195701590061309133467695200 130:61:74452875578585231332857239989225224000 130:62:82858845401973886483341121923492588000 130:63:89434944243400385410590417314245968000 130:64:93627207254809778476711843125851247750 130:65:95067625827960698145584333020095113100 130:66:93627207254809778476711843125851247750 130:67:89434944243400385410590417314245968000 130:68:82858845401973886483341121923492588000 130:69:74452875578585231332857239989225224000 130:70:64880363004195701590061309133467695200 130:71:54828475778193550639488430253634672000 130:72:44928889873797492885136352568950634000 130:73:35696926201099377908738471904097764000 130:74:27496280992738710010785039169372602000 130:75:20530556474578236808052829246464876160 130:76:14857639553971092426880336954678528800 130:77:10419643323564142740929067474709617600 130:78:7080014053191020067554366361020637600 130:79:4660262414758646120415532288266748800 130:80:2970917289408636901764901833770052360 130:81:1833899561363356112200556687512378000 130:82:1095866811058590847534478996196421000 130:83:633754300371233261224758937559376000 130:84:354600620445809086637662738872508000 130:85:191901512241261388062735129272180800 130:86:100413581986706540265384660665676000 130:87:50783880545001008869849713440112000 130:88:24814850720852765697767473612782000 130:89:11710378991863102913553189794796000 130:90:5334728207404302438396453128740400 130:91:2344935475782110961932506869776000 130:92:994048734298938342558345303492000 130:93:406170450573759752873302382072000 130:94:159875602885416072939491363156000 130:95:60584438988157669745491463932800 130:96:22088076714432483761377096225500 130:97:7742212456605200493678569811000 130:98:2607071541509914451952987793500 130:99:842689791195123863257531408000 130:100:261233835270488397609834736480 130:101:77594208496184672557376654400 130:102:22061098494013289256509048800 130:103:5997191823615263098856828800 130:104:1556963261900116381433984400 130:105:385533760089552627783653280 130:106:90927773606026563156522000 130:107:20395014640604088932304000 130:108:4343382747536055976324000 130:109:876646059135717719992000 130:110:167359702198637019271200 130:111:30154901297051715184000 130:112:5115563612892701683000 130:113:814868540106802038000 130:114:121515484051014339000 130:115:16906502128836777600 130:116:2186185620108204000 130:117:261594860525768000 130:118:28819772769788000 130:119:2906195573424000 130:120:266401260897200 130:121:22016633132000 130:122:1624177854000 130:123:105637584000 130:124:5963412000 130:125:286243776 130:126:11358880 130:127:357760 130:128:8385 130:129:130 130:130:1 # binomial(131, k) for 0 <= k <= 131 131:0:1 131:1:131 131:2:8515 131:3:366145 131:4:11716640 131:5:297602656 131:6:6249655776 131:7:111600996000 131:8:1729815438000 131:9:23640810986000 131:10:288417894029200 131:11:3172596834321200 131:12:31725968343212000 131:13:290414633295556000 131:14:2447780480633972000 131:15:19092687748944981600 131:16:138421986179851116600 131:17:936384024157816377000 131:18:5930432152999503721000 131:19:35270464909944416867000 131:20:197514603495688734455200 131:21:1044005761334354739263200 131:22:5220028806671773696316000 131:23:24738397388140144908628000 131:24:111322788246630652088826000 131:25:476461533695579190940175280 131:26:1942497021989669009217637680 131:27:7554155085515379480290813200 131:28:28058290317628552355365877600 131:29:99655306990197961813885703200 131:30:338828043766673070167211390880 131:31:1103923626465612260867366144480 131:32:3449761332705038315210519201500 131:33:10349283998115114945631557604500 131:34:29830289171037684255055666036500 131:35:82672515702590153506868560158300 131:36:220460041873573742684982827088800 131:37:566046053459175825812793745228000 131:38:1400219184872698095431647685564000 131:39:3338984210081049304490852173268000 131:40:7679663683186413400328959998516400 131:41:17045107199267405351949642923536400 131:42:36525229712715868611320663407578000 131:43:75598731265853774567617187052894000 131:44:151197462531707549135234374105788000 131:45:292315094227967928328119789937856800 131:46:546502132687070474700397868144688800 131:47:988354920817042347862421676431884000 131:48:1729621111429824108759237933755797000 131:49:2929766372421946959735035683708799000 131:50:4804816850771993013965458521282430360 131:51:7631179704167283022180434122036801160 131:52:11740276467949666187969898649287386400 131:53:17499657376755162808483433835730255200 131:54:25277282877535235167809404429388146400 131:55:35388196028549329234933166201143404960 131:56:48026837467316946818837868415837478160 131:57:63193207193838087919523511073470366000 131:58:80625816074896870793874824473048398000 131:59:99757365651991043524624782822585306000 131:60:119708838782389252229549739387102367200 131:61:139333238582780932922918549122692919200 131:62:157311720980559117816198361912717812000 131:63:172293789645374271893931539237738556000 131:64:183062151498210163887302260440097215750 131:65:188694833082770476622296176145946360850 131:66:188694833082770476622296176145946360850 131:67:183062151498210163887302260440097215750 131:68:172293789645374271893931539237738556000 131:69:157311720980559117816198361912717812000 131:70:139333238582780932922918549122692919200 131:71:119708838782389252229549739387102367200 131:72:99757365651991043524624782822585306000 131:73:80625816074896870793874824473048398000 131:74:63193207193838087919523511073470366000 131:75:48026837467316946818837868415837478160 131:76:35388196028549329234933166201143404960 131:77:25277282877535235167809404429388146400 131:78:17499657376755162808483433835730255200 131:79:11740276467949666187969898649287386400 131:80:7631179704167283022180434122036801160 131:81:4804816850771993013965458521282430360 131:82:2929766372421946959735035683708799000 131:83:1729621111429824108759237933755797000 131:84:988354920817042347862421676431884000 131:85:546502132687070474700397868144688800 131:86:292315094227967928328119789937856800 131:87:151197462531707549135234374105788000 131:88:75598731265853774567617187052894000 131:89:36525229712715868611320663407578000 131:90:17045107199267405351949642923536400 131:91:7679663683186413400328959998516400 131:92:3338984210081049304490852173268000 131:93:1400219184872698095431647685564000 131:94:566046053459175825812793745228000 131:95:220460041873573742684982827088800 131:96:82672515702590153506868560158300 131:97:29830289171037684255055666036500 131:98:10349283998115114945631557604500 131:99:3449761332705038315210519201500 131:100:1103923626465612260867366144480 131:101:338828043766673070167211390880 131:102:99655306990197961813885703200 131:103:28058290317628552355365877600 131:104:7554155085515379480290813200 131:105:1942497021989669009217637680 131:106:476461533695579190940175280 131:107:111322788246630652088826000 131:108:24738397388140144908628000 131:109:5220028806671773696316000 131:110:1044005761334354739263200 131:111:197514603495688734455200 131:112:35270464909944416867000 131:113:5930432152999503721000 131:114:936384024157816377000 131:115:138421986179851116600 131:116:19092687748944981600 131:117:2447780480633972000 131:118:290414633295556000 131:119:31725968343212000 131:120:3172596834321200 131:121:288417894029200 131:122:23640810986000 131:123:1729815438000 131:124:111600996000 131:125:6249655776 131:126:297602656 131:127:11716640 131:128:366145 131:129:8515 131:130:131 131:131:1 # binomial(132, k) for 0 <= k <= 132 132:0:1 132:1:132 132:2:8646 132:3:374660 132:4:12082785 132:5:309319296 132:6:6547258432 132:7:117850651776 132:8:1841416434000 132:9:25370626424000 132:10:312058705015200 132:11:3461014728350400 132:12:34898565177533200 132:13:322140601638768000 132:14:2738195113929528000 132:15:21540468229578953600 132:16:157514673928796098200 132:17:1074806010337667493600 132:18:6866816177157320098000 132:19:41200897062943920588000 132:20:232785068405633151322200 132:21:1241520364830043473718400 132:22:6264034568006128435579200 132:23:29958426194811918604944000 132:24:136061185634770796997454000 132:25:587784321942209843029001280 132:26:2418958555685248200157812960 132:27:9496652107505048489508450880 132:28:35612445403143931835656690800 132:29:127713597307826514169251580800 132:30:438483350756871031981097094080 132:31:1442751670232285331034577535360 132:32:4553684959170650576077885345980 132:33:13799045330820153260842076806000 132:34:40179573169152799200687223641000 132:35:112502804873627837761924226194800 132:36:303132557576163896191851387247100 132:37:786506095332749568497776572316800 132:38:1966265238331873921244441430792000 132:39:4739203394953747399922499858832000 132:40:11018647893267462704819812171784400 132:41:24724770882453818752278602922052800 132:42:53570336911983273963270306331114400 132:43:112123960978569643178937850460472000 132:44:226796193797561323702851561158682000 132:45:443512556759675477463354164043644800 132:46:838817226915038403028517658082545600 132:47:1534857053504112822562819544576572800 132:48:2717976032246866456621659610187681000 132:49:4659387483851771068494273617464596000 132:50:7734583223193939973700494204991229360 132:51:12435996554939276036145892643319231520 132:52:19371456172116949210150332771324187560 132:53:29239933844704828996453332485017641600 132:54:42776940254290397976292838265118401600 132:55:60665478906084564402742570630531551360 132:56:83415033495866276053771034616980883120 132:57:111220044661155034738361379489307844160 132:58:143819023268734958713398335546518764000 132:59:180383181726887914318499607295633704000 132:60:219466204434380295754174522209687673200 132:61:259042077365170185152468288509795286400 132:62:296644959563340050739116911035410731200 132:63:329605510625933389710129901150456368000 132:64:355355941143584435781233799677835771750 132:65:371756984580980640509598436586043576600 132:66:377389666165540953244592352291892721700 132:67:371756984580980640509598436586043576600 132:68:355355941143584435781233799677835771750 132:69:329605510625933389710129901150456368000 132:70:296644959563340050739116911035410731200 132:71:259042077365170185152468288509795286400 132:72:219466204434380295754174522209687673200 132:73:180383181726887914318499607295633704000 132:74:143819023268734958713398335546518764000 132:75:111220044661155034738361379489307844160 132:76:83415033495866276053771034616980883120 132:77:60665478906084564402742570630531551360 132:78:42776940254290397976292838265118401600 132:79:29239933844704828996453332485017641600 132:80:19371456172116949210150332771324187560 132:81:12435996554939276036145892643319231520 132:82:7734583223193939973700494204991229360 132:83:4659387483851771068494273617464596000 132:84:2717976032246866456621659610187681000 132:85:1534857053504112822562819544576572800 132:86:838817226915038403028517658082545600 132:87:443512556759675477463354164043644800 132:88:226796193797561323702851561158682000 132:89:112123960978569643178937850460472000 132:90:53570336911983273963270306331114400 132:91:24724770882453818752278602922052800 132:92:11018647893267462704819812171784400 132:93:4739203394953747399922499858832000 132:94:1966265238331873921244441430792000 132:95:786506095332749568497776572316800 132:96:303132557576163896191851387247100 132:97:112502804873627837761924226194800 132:98:40179573169152799200687223641000 132:99:13799045330820153260842076806000 132:100:4553684959170650576077885345980 132:101:1442751670232285331034577535360 132:102:438483350756871031981097094080 132:103:127713597307826514169251580800 132:104:35612445403143931835656690800 132:105:9496652107505048489508450880 132:106:2418958555685248200157812960 132:107:587784321942209843029001280 132:108:136061185634770796997454000 132:109:29958426194811918604944000 132:110:6264034568006128435579200 132:111:1241520364830043473718400 132:112:232785068405633151322200 132:113:41200897062943920588000 132:114:6866816177157320098000 132:115:1074806010337667493600 132:116:157514673928796098200 132:117:21540468229578953600 132:118:2738195113929528000 132:119:322140601638768000 132:120:34898565177533200 132:121:3461014728350400 132:122:312058705015200 132:123:25370626424000 132:124:1841416434000 132:125:117850651776 132:126:6547258432 132:127:309319296 132:128:12082785 132:129:374660 132:130:8646 132:131:132 132:132:1 # binomial(133, k) for 0 <= k <= 133 133:0:1 133:1:133 133:2:8778 133:3:383306 133:4:12457445 133:5:321402081 133:6:6856577728 133:7:124397910208 133:8:1959267085776 133:9:27212042858000 133:10:337429331439200 133:11:3773073433365600 133:12:38359579905883600 133:13:357039166816301200 133:14:3060335715568296000 133:15:24278663343508481600 133:16:179055142158375051800 133:17:1232320684266463591800 133:18:7941622187494987591600 133:19:48067713240101240686000 133:20:273985965468577071910200 133:21:1474305433235676625040600 133:22:7505554932836171909297600 133:23:36222460762818047040523200 133:24:166019611829582715602398000 133:25:723845507576980640026455280 133:26:3006742877627458043186814240 133:27:11915610663190296689666263840 133:28:45109097510648980325165141680 133:29:163326042710970446004908271600 133:30:566196948064697546150348674880 133:31:1881235020989156363015674629440 133:32:5996436629402935907112462881340 133:33:18352730289990803836919962151980 133:34:53978618499972952461529300447000 133:35:152682378042780636962611449835800 133:36:415635362449791733953775613441900 133:37:1089638652908913464689627959563900 133:38:2752771333664623489742218003108800 133:39:6705468633285621321166941289624000 133:40:15757851288221210104742312030616400 133:41:35743418775721281457098415093837200 133:42:78295107794437092715548909253167200 133:43:165694297890552917142208156791586400 133:44:338920154776130966881789411619154000 133:45:670308750557236801166205725202326800 133:46:1282329783674713880491871822126190400 133:47:2373674280419151225591337202659118400 133:48:4252833085750979279184479154764253800 133:49:7377363516098637525115933227652277000 133:50:12393970707045711042194767822455825360 133:51:20170579778133216009846386848310460880 133:52:31807452727056225246296225414643419080 133:53:48611390016821778206603665256341829160 133:54:72016874098995226972746170750136043200 133:55:103442419160374962379035408895649952960 133:56:144080512401950840456513605247512434480 133:57:194635078157021310792132414106288727280 133:58:255039067929889993451759715035826608160 133:59:324202204995622873031897942842152468000 133:60:399849386161268210072674129505321377200 133:61:478508281799550480906642810719482959600 133:62:555687036928510235891585199545206017600 133:63:626250470189273440449246812185867099200 133:64:684961451769517825491363700828292139750 133:65:727112925724565076290832236263879348350 133:66:749146650746521593754190788877936298300 133:67:749146650746521593754190788877936298300 133:68:727112925724565076290832236263879348350 133:69:684961451769517825491363700828292139750 133:70:626250470189273440449246812185867099200 133:71:555687036928510235891585199545206017600 133:72:478508281799550480906642810719482959600 133:73:399849386161268210072674129505321377200 133:74:324202204995622873031897942842152468000 133:75:255039067929889993451759715035826608160 133:76:194635078157021310792132414106288727280 133:77:144080512401950840456513605247512434480 133:78:103442419160374962379035408895649952960 133:79:72016874098995226972746170750136043200 133:80:48611390016821778206603665256341829160 133:81:31807452727056225246296225414643419080 133:82:20170579778133216009846386848310460880 133:83:12393970707045711042194767822455825360 133:84:7377363516098637525115933227652277000 133:85:4252833085750979279184479154764253800 133:86:2373674280419151225591337202659118400 133:87:1282329783674713880491871822126190400 133:88:670308750557236801166205725202326800 133:89:338920154776130966881789411619154000 133:90:165694297890552917142208156791586400 133:91:78295107794437092715548909253167200 133:92:35743418775721281457098415093837200 133:93:15757851288221210104742312030616400 133:94:6705468633285621321166941289624000 133:95:2752771333664623489742218003108800 133:96:1089638652908913464689627959563900 133:97:415635362449791733953775613441900 133:98:152682378042780636962611449835800 133:99:53978618499972952461529300447000 133:100:18352730289990803836919962151980 133:101:5996436629402935907112462881340 133:102:1881235020989156363015674629440 133:103:566196948064697546150348674880 133:104:163326042710970446004908271600 133:105:45109097510648980325165141680 133:106:11915610663190296689666263840 133:107:3006742877627458043186814240 133:108:723845507576980640026455280 133:109:166019611829582715602398000 133:110:36222460762818047040523200 133:111:7505554932836171909297600 133:112:1474305433235676625040600 133:113:273985965468577071910200 133:114:48067713240101240686000 133:115:7941622187494987591600 133:116:1232320684266463591800 133:117:179055142158375051800 133:118:24278663343508481600 133:119:3060335715568296000 133:120:357039166816301200 133:121:38359579905883600 133:122:3773073433365600 133:123:337429331439200 133:124:27212042858000 133:125:1959267085776 133:126:124397910208 133:127:6856577728 133:128:321402081 133:129:12457445 133:130:383306 133:131:8778 133:132:133 133:133:1 # binomial(134, k) for 0 <= k <= 134 134:0:1 134:1:134 134:2:8911 134:3:392084 134:4:12840751 134:5:333859526 134:6:7177979809 134:7:131254487936 134:8:2083664995984 134:9:29171309943776 134:10:364641374297200 134:11:4110502764804800 134:12:42132653339249200 134:13:395398746722184800 134:14:3417374882384597200 134:15:27338999059076777600 134:16:203333805501883533400 134:17:1411375826424838643600 134:18:9173942871761451183400 134:19:56009335427596228277600 134:20:322053678708678312596200 134:21:1748291398704253696950800 134:22:8979860366071848534338200 134:23:43728015695654218949820800 134:24:202242072592400762642921200 134:25:889865119406563355628853280 134:26:3730588385204438683213269520 134:27:14922353540817754732853078080 134:28:57024708173839277014831405520 134:29:208435140221619426330073413280 134:30:729522990775667992155256946480 134:31:2447431969053853909166023304320 134:32:7877671650392092270128137510780 134:33:24349166919393739744032425033320 134:34:72331348789963756298449262598980 134:35:206660996542753589424140750282800 134:36:568317740492572370916387063277700 134:37:1505274015358705198643403573005800 134:38:3842409986573536954431845962672700 134:39:9458239966950244810909159292732800 134:40:22463319921506831425909253320240400 134:41:51501270063942491561840727124453600 134:42:114038526570158374172647324347004400 134:43:243989405684990009857757066044753600 134:44:504614452666683884023997568410740400 134:45:1009228905333367768047995136821480800 134:46:1952638534231950681658077547328517200 134:47:3656004064093865106083209024785308800 134:48:6626507366170130504775816357423372200 134:49:11630196601849616804300412382416530800 134:50:19771334223144348567310701050108102360 134:51:32564550485178927052041154670766286240 134:52:51978032505189441256142612262953879960 134:53:80418842743878003452899890670985248240 134:54:120628264115817005179349836006477872360 134:55:175459293259370189351781579645785996160 134:56:247522931562325802835549014143162387440 134:57:338715590558972151248646019353801161760 134:58:449674146086911304243892129142115335440 134:59:579241272925512866483657657877979076160 134:60:724051591156891083104572072347473845200 134:61:878357667960818690979316940224804336800 134:62:1034195318728060716798228010264688977200 134:63:1181937507117783676340832011731073116800 134:64:1311211921958791265940610513014159238950 134:65:1412074377494082901782195937092171488100 134:66:1476259576471086670045023025141815646650 134:67:1498293301493043187508381577755872596600 134:68:1476259576471086670045023025141815646650 134:69:1412074377494082901782195937092171488100 134:70:1311211921958791265940610513014159238950 134:71:1181937507117783676340832011731073116800 134:72:1034195318728060716798228010264688977200 134:73:878357667960818690979316940224804336800 134:74:724051591156891083104572072347473845200 134:75:579241272925512866483657657877979076160 134:76:449674146086911304243892129142115335440 134:77:338715590558972151248646019353801161760 134:78:247522931562325802835549014143162387440 134:79:175459293259370189351781579645785996160 134:80:120628264115817005179349836006477872360 134:81:80418842743878003452899890670985248240 134:82:51978032505189441256142612262953879960 134:83:32564550485178927052041154670766286240 134:84:19771334223144348567310701050108102360 134:85:11630196601849616804300412382416530800 134:86:6626507366170130504775816357423372200 134:87:3656004064093865106083209024785308800 134:88:1952638534231950681658077547328517200 134:89:1009228905333367768047995136821480800 134:90:504614452666683884023997568410740400 134:91:243989405684990009857757066044753600 134:92:114038526570158374172647324347004400 134:93:51501270063942491561840727124453600 134:94:22463319921506831425909253320240400 134:95:9458239966950244810909159292732800 134:96:3842409986573536954431845962672700 134:97:1505274015358705198643403573005800 134:98:568317740492572370916387063277700 134:99:206660996542753589424140750282800 134:100:72331348789963756298449262598980 134:101:24349166919393739744032425033320 134:102:7877671650392092270128137510780 134:103:2447431969053853909166023304320 134:104:729522990775667992155256946480 134:105:208435140221619426330073413280 134:106:57024708173839277014831405520 134:107:14922353540817754732853078080 134:108:3730588385204438683213269520 134:109:889865119406563355628853280 134:110:202242072592400762642921200 134:111:43728015695654218949820800 134:112:8979860366071848534338200 134:113:1748291398704253696950800 134:114:322053678708678312596200 134:115:56009335427596228277600 134:116:9173942871761451183400 134:117:1411375826424838643600 134:118:203333805501883533400 134:119:27338999059076777600 134:120:3417374882384597200 134:121:395398746722184800 134:122:42132653339249200 134:123:4110502764804800 134:124:364641374297200 134:125:29171309943776 134:126:2083664995984 134:127:131254487936 134:128:7177979809 134:129:333859526 134:130:12840751 134:131:392084 134:132:8911 134:133:134 134:134:1 # binomial(135, k) for 0 <= k <= 135 135:0:1 135:1:135 135:2:9045 135:3:400995 135:4:13232835 135:5:346700277 135:6:7511839335 135:7:138432467745 135:8:2214919483920 135:9:31254974939760 135:10:393812684240976 135:11:4475144139102000 135:12:46243156104054000 135:13:437531400061434000 135:14:3812773629106782000 135:15:30756373941461374800 135:16:230672804560960311000 135:17:1614709631926722177000 135:18:10585318698186289827000 135:19:65183278299357679461000 135:20:378063014136274540873800 135:21:2070345077412932009547000 135:22:10728151764776102231289000 135:23:52707876061726067484159000 135:24:245970088288054981592742000 135:25:1092107191998964118271774480 135:26:4620453504611002038842122800 135:27:18652941926022193416066347600 135:28:71947061714657031747684483600 135:29:265459848395458703344904818800 135:30:937958130997287418485330359760 135:31:3176954959829521901321280250800 135:32:10325103619445946179294160815100 135:33:32226838569785832014160562544100 135:34:96680515709357496042481687632300 135:35:278992345332717345722590012881780 135:36:774978737035325960340527813560500 135:37:2073591755851277569559790636283500 135:38:5347684001932242153075249535678500 135:39:13300649953523781765341005255405500 135:40:31921559888457076236818412612973200 135:41:73964589985449322987749980444694000 135:42:165539796634100865734488051471458000 135:43:358027932255148384030404390391758000 135:44:748603858351673893881754634455494000 135:45:1513843358000051652071992705232221200 135:46:2961867439565318449706072684149998000 135:47:5608642598325815787741286572113826000 135:48:10282511430263995610859025382208681000 135:49:18256703968019747309076228739839903000 135:50:31401530824993965371611113432524633160 135:51:52335884708323275619351855720874388600 135:52:84542582990368368308183766933720166200 135:53:132396875249067444709042502933939128200 135:54:201047106859695008632249726677463120600 135:55:296087557375187194531131415652263868520 135:56:422982224821695992187330593788948383600 135:57:586238522121297954084195033496963549200 135:58:788389736645883455492538148495916497200 135:59:1028915419012424170727549787020094411600 135:60:1303292864082403949588229730225452921360 135:61:1602409259117709774083889012572278182000 135:62:1912552986688879407777544950489493314000 135:63:2216132825845844393139060021995762094000 135:64:2493149429076574942281442524745232355750 135:65:2723286299452874167722806450106330727050 135:66:2888333953965169571827218962233987134750 135:67:2974552877964129857553404602897688243250 135:68:2974552877964129857553404602897688243250 135:69:2888333953965169571827218962233987134750 135:70:2723286299452874167722806450106330727050 135:71:2493149429076574942281442524745232355750 135:72:2216132825845844393139060021995762094000 135:73:1912552986688879407777544950489493314000 135:74:1602409259117709774083889012572278182000 135:75:1303292864082403949588229730225452921360 135:76:1028915419012424170727549787020094411600 135:77:788389736645883455492538148495916497200 135:78:586238522121297954084195033496963549200 135:79:422982224821695992187330593788948383600 135:80:296087557375187194531131415652263868520 135:81:201047106859695008632249726677463120600 135:82:132396875249067444709042502933939128200 135:83:84542582990368368308183766933720166200 135:84:52335884708323275619351855720874388600 135:85:31401530824993965371611113432524633160 135:86:18256703968019747309076228739839903000 135:87:10282511430263995610859025382208681000 135:88:5608642598325815787741286572113826000 135:89:2961867439565318449706072684149998000 135:90:1513843358000051652071992705232221200 135:91:748603858351673893881754634455494000 135:92:358027932255148384030404390391758000 135:93:165539796634100865734488051471458000 135:94:73964589985449322987749980444694000 135:95:31921559888457076236818412612973200 135:96:13300649953523781765341005255405500 135:97:5347684001932242153075249535678500 135:98:2073591755851277569559790636283500 135:99:774978737035325960340527813560500 135:100:278992345332717345722590012881780 135:101:96680515709357496042481687632300 135:102:32226838569785832014160562544100 135:103:10325103619445946179294160815100 135:104:3176954959829521901321280250800 135:105:937958130997287418485330359760 135:106:265459848395458703344904818800 135:107:71947061714657031747684483600 135:108:18652941926022193416066347600 135:109:4620453504611002038842122800 135:110:1092107191998964118271774480 135:111:245970088288054981592742000 135:112:52707876061726067484159000 135:113:10728151764776102231289000 135:114:2070345077412932009547000 135:115:378063014136274540873800 135:116:65183278299357679461000 135:117:10585318698186289827000 135:118:1614709631926722177000 135:119:230672804560960311000 135:120:30756373941461374800 135:121:3812773629106782000 135:122:437531400061434000 135:123:46243156104054000 135:124:4475144139102000 135:125:393812684240976 135:126:31254974939760 135:127:2214919483920 135:128:138432467745 135:129:7511839335 135:130:346700277 135:131:13232835 135:132:400995 135:133:9045 135:134:135 135:135:1 # binomial(136, k) for 0 <= k <= 136 136:0:1 136:1:136 136:2:9180 136:3:410040 136:4:13633830 136:5:359933112 136:6:7858539612 136:7:145944307080 136:8:2353351951665 136:9:33469894423680 136:10:425067659180736 136:11:4868956823342976 136:12:50718300243156000 136:13:483774556165488000 136:14:4250305029168216000 136:15:34569147570568156800 136:16:261429178502421685800 136:17:1845382436487682488000 136:18:12200028330113012004000 136:19:75768596997543969288000 136:20:443246292435632220334800 136:21:2448408091549206550420800 136:22:12798496842189034240836000 136:23:63436027826502169715448000 136:24:298677964349781049076901000 136:25:1338077280287019099864516480 136:26:5712560696609966157113897280 136:27:23273395430633195454908470400 136:28:90600003640679225163750831200 136:29:337406910110115735092589302400 136:30:1203417979392746121830235178560 136:31:4114913090826809319806610610560 136:32:13502058579275468080615441065900 136:33:42551942189231778193454723359200 136:34:128907354279143328056642250176400 136:35:375672861042074841765071700514080 136:36:1053971082368043306063117826442280 136:37:2848570492886603529900318449844000 136:38:7421275757783519722635040171962000 136:39:18648333955456023918416254791084000 136:40:45222209841980858002159417868378700 136:41:105886149873906399224568393057667200 136:42:239504386619550188722238031916152000 136:43:523567728889249249764892441863216000 136:44:1106631790606822277912159024847252000 136:45:2262447216351725545953747339687715200 136:46:4475710797565370101778065389382219200 136:47:8570510037891134237447359256263824000 136:48:15891154028589811398600311954322507000 136:49:28539215398283742919935254122048584000 136:50:49658234793013712680687342172364536160 136:51:83737415533317240990962969153399021760 136:52:136878467698691643927535622654594554800 136:53:216939458239435813017226269867659294400 136:54:333443982108762453341292229611402248800 136:55:497134664234882203163381142329726989120 136:56:719069782196883186718462009441212252120 136:57:1009220746942993946271525627285911932800 136:58:1374628258767181409576733181992880046400 136:59:1817305155658307626220087935516010908800 136:60:2332208283094828120315779517245547332960 136:61:2905702123200113723672118742797731103360 136:62:3514962245806589181861433963061771496000 136:63:4128685812534723800916604972485255408000 136:64:4709282254922419335420502546740994449750 136:65:5216435728529449110004248974851563082800 136:66:5611620253418043739550025412340317861800 136:67:5862886831929299429380623565131675378000 136:68:5949105755928259715106809205795376486500 136:69:5862886831929299429380623565131675378000 136:70:5611620253418043739550025412340317861800 136:71:5216435728529449110004248974851563082800 136:72:4709282254922419335420502546740994449750 136:73:4128685812534723800916604972485255408000 136:74:3514962245806589181861433963061771496000 136:75:2905702123200113723672118742797731103360 136:76:2332208283094828120315779517245547332960 136:77:1817305155658307626220087935516010908800 136:78:1374628258767181409576733181992880046400 136:79:1009220746942993946271525627285911932800 136:80:719069782196883186718462009441212252120 136:81:497134664234882203163381142329726989120 136:82:333443982108762453341292229611402248800 136:83:216939458239435813017226269867659294400 136:84:136878467698691643927535622654594554800 136:85:83737415533317240990962969153399021760 136:86:49658234793013712680687342172364536160 136:87:28539215398283742919935254122048584000 136:88:15891154028589811398600311954322507000 136:89:8570510037891134237447359256263824000 136:90:4475710797565370101778065389382219200 136:91:2262447216351725545953747339687715200 136:92:1106631790606822277912159024847252000 136:93:523567728889249249764892441863216000 136:94:239504386619550188722238031916152000 136:95:105886149873906399224568393057667200 136:96:45222209841980858002159417868378700 136:97:18648333955456023918416254791084000 136:98:7421275757783519722635040171962000 136:99:2848570492886603529900318449844000 136:100:1053971082368043306063117826442280 136:101:375672861042074841765071700514080 136:102:128907354279143328056642250176400 136:103:42551942189231778193454723359200 136:104:13502058579275468080615441065900 136:105:4114913090826809319806610610560 136:106:1203417979392746121830235178560 136:107:337406910110115735092589302400 136:108:90600003640679225163750831200 136:109:23273395430633195454908470400 136:110:5712560696609966157113897280 136:111:1338077280287019099864516480 136:112:298677964349781049076901000 136:113:63436027826502169715448000 136:114:12798496842189034240836000 136:115:2448408091549206550420800 136:116:443246292435632220334800 136:117:75768596997543969288000 136:118:12200028330113012004000 136:119:1845382436487682488000 136:120:261429178502421685800 136:121:34569147570568156800 136:122:4250305029168216000 136:123:483774556165488000 136:124:50718300243156000 136:125:4868956823342976 136:126:425067659180736 136:127:33469894423680 136:128:2353351951665 136:129:145944307080 136:130:7858539612 136:131:359933112 136:132:13633830 136:133:410040 136:134:9180 136:135:136 136:136:1 # binomial(137, k) for 0 <= k <= 137 137:0:1 137:1:137 137:2:9316 137:3:419220 137:4:14043870 137:5:373566942 137:6:8218472724 137:7:153802846692 137:8:2499296258745 137:9:35823246375345 137:10:458537553604416 137:11:5294024482523712 137:12:55587257066498976 137:13:534492856408644000 137:14:4734079585333704000 137:15:38819452599736372800 137:16:295998326072989842600 137:17:2106811614990104173800 137:18:14045410766600694492000 137:19:87968625327656981292000 137:20:519014889433176189622800 137:21:2891654383984838770755600 137:22:15246904933738240791256800 137:23:76234524668691203956284000 137:24:362113992176283218792349000 137:25:1636755244636800148941417480 137:26:7050637976896985256978413760 137:27:28985956127243161612022367680 137:28:113873399071312420618659301600 137:29:428006913750794960256340133600 137:30:1540824889502861856922824480960 137:31:5318331070219555441636845789120 137:32:17616971670102277400422051676460 137:33:56054000768507246274070164425100 137:34:171459296468375106250096973535600 137:35:504580215321218169821713950690480 137:36:1429643943410118147828189526956360 137:37:3902541575254646835963436276286280 137:38:10269846250670123252535358621806000 137:39:26069609713239543641051294963046000 137:40:63870543797436881920575672659462700 137:41:151108359715887257226727810926045900 137:42:345390536493456587946806424973819200 137:43:763072115508799438487130473779368000 137:44:1630199519496071527677051466710468000 137:45:3369079006958547823865906364534967200 137:46:6738158013917095647731812729069934400 137:47:13046220835456504339225424645646043200 137:48:24461664066480945636047671210586331000 137:49:44430369426873554318535566076371091000 137:50:78197450191297455600622596294413120160 137:51:133395650326330953671650311325763557920 137:52:220615883232008884918498591807993576560 137:53:353817925938127456944761892522253849200 137:54:550383440348198266358518499479061543200 137:55:830578646343644656504673371941129237920 137:56:1216204446431765389881843151770939241240 137:57:1728290529139877132989987636727124184920 137:58:2383849005710175355848258809278791979200 137:59:3191933414425489035796821117508890955200 137:60:4149513438753135746535867452761558241760 137:61:5237910406294941843987898260043278436320 137:62:6420664369006702905533552705859502599360 137:63:7643648058341312982778038935547026904000 137:64:8837968067457143136337107519226249857750 137:65:9925717983451868445424751521592557532550 137:66:10828055981947492849554274387191880944600 137:67:11474507085347343168930648977471993239800 137:68:11811992587857559144487432770927051864500 137:69:11811992587857559144487432770927051864500 137:70:11474507085347343168930648977471993239800 137:71:10828055981947492849554274387191880944600 137:72:9925717983451868445424751521592557532550 137:73:8837968067457143136337107519226249857750 137:74:7643648058341312982778038935547026904000 137:75:6420664369006702905533552705859502599360 137:76:5237910406294941843987898260043278436320 137:77:4149513438753135746535867452761558241760 137:78:3191933414425489035796821117508890955200 137:79:2383849005710175355848258809278791979200 137:80:1728290529139877132989987636727124184920 137:81:1216204446431765389881843151770939241240 137:82:830578646343644656504673371941129237920 137:83:550383440348198266358518499479061543200 137:84:353817925938127456944761892522253849200 137:85:220615883232008884918498591807993576560 137:86:133395650326330953671650311325763557920 137:87:78197450191297455600622596294413120160 137:88:44430369426873554318535566076371091000 137:89:24461664066480945636047671210586331000 137:90:13046220835456504339225424645646043200 137:91:6738158013917095647731812729069934400 137:92:3369079006958547823865906364534967200 137:93:1630199519496071527677051466710468000 137:94:763072115508799438487130473779368000 137:95:345390536493456587946806424973819200 137:96:151108359715887257226727810926045900 137:97:63870543797436881920575672659462700 137:98:26069609713239543641051294963046000 137:99:10269846250670123252535358621806000 137:100:3902541575254646835963436276286280 137:101:1429643943410118147828189526956360 137:102:504580215321218169821713950690480 137:103:171459296468375106250096973535600 137:104:56054000768507246274070164425100 137:105:17616971670102277400422051676460 137:106:5318331070219555441636845789120 137:107:1540824889502861856922824480960 137:108:428006913750794960256340133600 137:109:113873399071312420618659301600 137:110:28985956127243161612022367680 137:111:7050637976896985256978413760 137:112:1636755244636800148941417480 137:113:362113992176283218792349000 137:114:76234524668691203956284000 137:115:15246904933738240791256800 137:116:2891654383984838770755600 137:117:519014889433176189622800 137:118:87968625327656981292000 137:119:14045410766600694492000 137:120:2106811614990104173800 137:121:295998326072989842600 137:122:38819452599736372800 137:123:4734079585333704000 137:124:534492856408644000 137:125:55587257066498976 137:126:5294024482523712 137:127:458537553604416 137:128:35823246375345 137:129:2499296258745 137:130:153802846692 137:131:8218472724 137:132:373566942 137:133:14043870 137:134:419220 137:135:9316 137:136:137 137:137:1 # binomial(138, k) for 0 <= k <= 138 138:0:1 138:1:138 138:2:9453 138:3:428536 138:4:14463090 138:5:387610812 138:6:8592039666 138:7:162021319416 138:8:2653099105437 138:9:38322542634090 138:10:494360799979761 138:11:5752562036128128 138:12:60881281549022688 138:13:590080113475142976 138:14:5268572441742348000 138:15:43553532185070076800 138:16:334817778672726215400 138:17:2402809941063094016400 138:18:16152222381590798665800 138:19:102014036094257675784000 138:20:606983514760833170914800 138:21:3410669273418014960378400 138:22:18138559317723079562012400 138:23:91481429602429444747540800 138:24:438348516844974422748633000 138:25:1998869236813083367733766480 138:26:8687393221533785405919831240 138:27:36036594104140146869000781440 138:28:142859355198555582230681669280 138:29:541880312822107380874999435200 138:30:1968831803253656817179164614560 138:31:6859155959722417298559670270080 138:32:22935302740321832842058897465580 138:33:73670972438609523674492216101560 138:34:227513297236882352524167137960700 138:35:676039511789593276071810924226080 138:36:1934224158731336317649903477646840 138:37:5332185518664764983791625803242640 138:38:14172387825924770088498794898092280 138:39:36339455963909666893586653584852000 138:40:89940153510676425561626967622508700 138:41:214978903513324139147303483585508600 138:42:496498896209343845173534235899865100 138:43:1108462652002256026433936898753187200 138:44:2393271635004870966164181940489836000 138:45:4999278526454619351542957831245435200 138:46:10107237020875643471597719093604901600 138:47:19784378849373599986957237374715977600 138:48:37507884901937449975273095856232374200 138:49:68892033493354499954583237286957422000 138:50:122627819618171009919158162370784211160 138:51:211593100517628409272272907620176678080 138:52:354011533558339838590148903133757134480 138:53:574433809170136341863260484330247425760 138:54:904201366286325723303280392001315392400 138:55:1380962086691842922863191871420190781120 138:56:2046783092775410046386516523712068479160 138:57:2944494975571642522871830788498063426160 138:58:4112139534850052488838246446005916164120 138:59:5575782420135664391645079926787682934400 138:60:7341446853178624782332688570270449196960 138:61:9387423845048077590523765712804836678080 138:62:11658574775301644749521450965902781035680 138:63:14064312427348015888311591641406529503360 138:64:16481616125798456119115146454773276761750 138:65:18763686050909011581761859040818807390300 138:66:20753773965399361294979025908784438477150 138:67:22302563067294836018484923364663874184400 138:68:23286499673204902313418081748399045104300 138:69:23623985175715118288974865541854103729000 138:70:23286499673204902313418081748399045104300 138:71:22302563067294836018484923364663874184400 138:72:20753773965399361294979025908784438477150 138:73:18763686050909011581761859040818807390300 138:74:16481616125798456119115146454773276761750 138:75:14064312427348015888311591641406529503360 138:76:11658574775301644749521450965902781035680 138:77:9387423845048077590523765712804836678080 138:78:7341446853178624782332688570270449196960 138:79:5575782420135664391645079926787682934400 138:80:4112139534850052488838246446005916164120 138:81:2944494975571642522871830788498063426160 138:82:2046783092775410046386516523712068479160 138:83:1380962086691842922863191871420190781120 138:84:904201366286325723303280392001315392400 138:85:574433809170136341863260484330247425760 138:86:354011533558339838590148903133757134480 138:87:211593100517628409272272907620176678080 138:88:122627819618171009919158162370784211160 138:89:68892033493354499954583237286957422000 138:90:37507884901937449975273095856232374200 138:91:19784378849373599986957237374715977600 138:92:10107237020875643471597719093604901600 138:93:4999278526454619351542957831245435200 138:94:2393271635004870966164181940489836000 138:95:1108462652002256026433936898753187200 138:96:496498896209343845173534235899865100 138:97:214978903513324139147303483585508600 138:98:89940153510676425561626967622508700 138:99:36339455963909666893586653584852000 138:100:14172387825924770088498794898092280 138:101:5332185518664764983791625803242640 138:102:1934224158731336317649903477646840 138:103:676039511789593276071810924226080 138:104:227513297236882352524167137960700 138:105:73670972438609523674492216101560 138:106:22935302740321832842058897465580 138:107:6859155959722417298559670270080 138:108:1968831803253656817179164614560 138:109:541880312822107380874999435200 138:110:142859355198555582230681669280 138:111:36036594104140146869000781440 138:112:8687393221533785405919831240 138:113:1998869236813083367733766480 138:114:438348516844974422748633000 138:115:91481429602429444747540800 138:116:18138559317723079562012400 138:117:3410669273418014960378400 138:118:606983514760833170914800 138:119:102014036094257675784000 138:120:16152222381590798665800 138:121:2402809941063094016400 138:122:334817778672726215400 138:123:43553532185070076800 138:124:5268572441742348000 138:125:590080113475142976 138:126:60881281549022688 138:127:5752562036128128 138:128:494360799979761 138:129:38322542634090 138:130:2653099105437 138:131:162021319416 138:132:8592039666 138:133:387610812 138:134:14463090 138:135:428536 138:136:9453 138:137:138 138:138:1 # binomial(139, k) for 0 <= k <= 139 139:0:1 139:1:139 139:2:9591 139:3:437989 139:4:14891626 139:5:402073902 139:6:8979650478 139:7:170613359082 139:8:2815120424853 139:9:40975641739527 139:10:532683342613851 139:11:6246922836107889 139:12:66633843585150816 139:13:650961395024165664 139:14:5858652555217490976 139:15:48822104626812424800 139:16:378371310857796292200 139:17:2737627719735820231800 139:18:18555032322653892682200 139:19:118166258475848474449800 139:20:708997550855090846698800 139:21:4017652788178848131293200 139:22:21549228591141094522390800 139:23:109619988920152524309553200 139:24:529829946447403867496173800 139:25:2437217753658057790482399480 139:26:10686262458346868773653597720 139:27:44723987325673932274920612680 139:28:178895949302695729099682450720 139:29:684739668020662963105681104480 139:30:2510712116075764198054164049760 139:31:8827987762976074115738834884640 139:32:29794458700044250140618567735660 139:33:96606275178931356516551113567140 139:34:301184269675491876198659354062260 139:35:903552809026475628595978062186780 139:36:2610263670520929593721714401872920 139:37:7266409677396101301441529280889480 139:38:19504573344589535072290420701334920 139:39:50511843789834436982085448482944280 139:40:126279609474586092455213621207360700 139:41:304919057024000564708930451208017300 139:42:711477799722667984320837719485373700 139:43:1604961548211599871607471134653052300 139:44:3501734287007126992598118839243023200 139:45:7392550161459490317707139771735271200 139:46:15106515547330262823140676924850336800 139:47:29891615870249243458554956468320879200 139:48:57292263751311049962230333230948351800 139:49:106399918395291949929856333143189796200 139:50:191519853111525509873741399657741633160 139:51:334220920135799419191431069990960889240 139:52:565604634075968247862421810753933812560 139:53:928445342728476180453409387464004560240 139:54:1478635175456462065166540876331562818160 139:55:2285163452978168646166472263421506173520 139:56:3427745179467252969249708395132259260280 139:57:4991278068347052569258347312210131905320 139:58:7056634510421695011710077234503979590280 139:59:9687921954985716880483326372793599098520 139:60:12917229273314289173977768497058132131360 139:61:16728870698226702372856454283075285875040 139:62:21045998620349722340045216678707617713760 139:63:25722887202649660637833042607309310539040 139:64:30545928553146472007426738096179806265110 139:65:35245302176707467700877005495592084152050 139:66:39517460016308372876740884949603245867450 139:67:43056337032694197313463949273448312661550 139:68:45589062740499738331903005113062919288700 139:69:46910484848920020602392947290253148833300 139:70:46910484848920020602392947290253148833300 139:71:45589062740499738331903005113062919288700 139:72:43056337032694197313463949273448312661550 139:73:39517460016308372876740884949603245867450 139:74:35245302176707467700877005495592084152050 139:75:30545928553146472007426738096179806265110 139:76:25722887202649660637833042607309310539040 139:77:21045998620349722340045216678707617713760 139:78:16728870698226702372856454283075285875040 139:79:12917229273314289173977768497058132131360 139:80:9687921954985716880483326372793599098520 139:81:7056634510421695011710077234503979590280 139:82:4991278068347052569258347312210131905320 139:83:3427745179467252969249708395132259260280 139:84:2285163452978168646166472263421506173520 139:85:1478635175456462065166540876331562818160 139:86:928445342728476180453409387464004560240 139:87:565604634075968247862421810753933812560 139:88:334220920135799419191431069990960889240 139:89:191519853111525509873741399657741633160 139:90:106399918395291949929856333143189796200 139:91:57292263751311049962230333230948351800 139:92:29891615870249243458554956468320879200 139:93:15106515547330262823140676924850336800 139:94:7392550161459490317707139771735271200 139:95:3501734287007126992598118839243023200 139:96:1604961548211599871607471134653052300 139:97:711477799722667984320837719485373700 139:98:304919057024000564708930451208017300 139:99:126279609474586092455213621207360700 139:100:50511843789834436982085448482944280 139:101:19504573344589535072290420701334920 139:102:7266409677396101301441529280889480 139:103:2610263670520929593721714401872920 139:104:903552809026475628595978062186780 139:105:301184269675491876198659354062260 139:106:96606275178931356516551113567140 139:107:29794458700044250140618567735660 139:108:8827987762976074115738834884640 139:109:2510712116075764198054164049760 139:110:684739668020662963105681104480 139:111:178895949302695729099682450720 139:112:44723987325673932274920612680 139:113:10686262458346868773653597720 139:114:2437217753658057790482399480 139:115:529829946447403867496173800 139:116:109619988920152524309553200 139:117:21549228591141094522390800 139:118:4017652788178848131293200 139:119:708997550855090846698800 139:120:118166258475848474449800 139:121:18555032322653892682200 139:122:2737627719735820231800 139:123:378371310857796292200 139:124:48822104626812424800 139:125:5858652555217490976 139:126:650961395024165664 139:127:66633843585150816 139:128:6246922836107889 139:129:532683342613851 139:130:40975641739527 139:131:2815120424853 139:132:170613359082 139:133:8979650478 139:134:402073902 139:135:14891626 139:136:437989 139:137:9591 139:138:139 139:139:1 # binomial(140, k) for 0 <= k <= 140 140:0:1 140:1:140 140:2:9730 140:3:447580 140:4:15329615 140:5:416965528 140:6:9381724380 140:7:179593009560 140:8:2985733783935 140:9:43790762164380 140:10:573658984353378 140:11:6779606178721740 140:12:72880766421258705 140:13:717595238609316480 140:14:6509613950241656640 140:15:54680757182029915776 140:16:427193415484608717000 140:17:3115999030593616524000 140:18:21292660042389712914000 140:19:136721290798502367132000 140:20:827163809330939321148600 140:21:4726650339033938977992000 140:22:25566881379319942653684000 140:23:131169217511293618831944000 140:24:639449935367556391805727000 140:25:2967047700105461657978573280 140:26:13123480212004926564135997200 140:27:55410249784020801048574210400 140:28:223619936628369661374603063400 140:29:863635617323358692205363555200 140:30:3195451784096427161159845154240 140:31:11338699879051838313792998934400 140:32:38622446463020324256357402620300 140:33:126400733878975606657169681302800 140:34:397790544854423232715210467629400 140:35:1204737078701967504794637416249040 140:36:3513816479547405222317692464059700 140:37:9876673347917030895163243682762400 140:38:26770983021985636373731949982224400 140:39:70016417134423972054375869184279200 140:40:176791453264420529437299069690304980 140:41:431198666498586657164144072415378000 140:42:1016396856746668549029768170693391000 140:43:2316439347934267855928308854138426000 140:44:5106695835218726864205589973896075500 140:45:10894284448466617310305258610978294400 140:46:22499065708789753140847816696585608000 140:47:44998131417579506281695633393171216000 140:48:87183879621560293420785289699269231000 140:49:163692182146602999892086666374138148000 140:50:297919771506817459803597732800931429360 140:51:525740773247324929065172469648702522400 140:52:899825554211767667053852880744894701800 140:53:1494049976804444428315831198217938372800 140:54:2407080518184938245619950263795567378400 140:55:3763798628434630711333013139753068991680 140:56:5712908632445421615416180658553765433800 140:57:8419023247814305538508055707342391165600 140:58:12047912578768747580968424546714111495600 140:59:16744556465407411892193403607297578688800 140:60:22605151228300006054461094869851731229880 140:61:29646099971540991546834222780133418006400 140:62:37774869318576424712901670961782903588800 140:63:46768885822999382977878259286016928252800 140:64:56268815755796132645259780703489116804150 140:65:65791230729853939708303743591771890417160 140:66:74762762193015840577617890445195330019500 140:67:82573797049002570190204834223051558529000 140:68:88645399773193935645366954386511231950250 140:69:92499547589419758934295952403316068122000 140:70:93820969697840041204785894580506297666600 140:71:92499547589419758934295952403316068122000 140:72:88645399773193935645366954386511231950250 140:73:82573797049002570190204834223051558529000 140:74:74762762193015840577617890445195330019500 140:75:65791230729853939708303743591771890417160 140:76:56268815755796132645259780703489116804150 140:77:46768885822999382977878259286016928252800 140:78:37774869318576424712901670961782903588800 140:79:29646099971540991546834222780133418006400 140:80:22605151228300006054461094869851731229880 140:81:16744556465407411892193403607297578688800 140:82:12047912578768747580968424546714111495600 140:83:8419023247814305538508055707342391165600 140:84:5712908632445421615416180658553765433800 140:85:3763798628434630711333013139753068991680 140:86:2407080518184938245619950263795567378400 140:87:1494049976804444428315831198217938372800 140:88:899825554211767667053852880744894701800 140:89:525740773247324929065172469648702522400 140:90:297919771506817459803597732800931429360 140:91:163692182146602999892086666374138148000 140:92:87183879621560293420785289699269231000 140:93:44998131417579506281695633393171216000 140:94:22499065708789753140847816696585608000 140:95:10894284448466617310305258610978294400 140:96:5106695835218726864205589973896075500 140:97:2316439347934267855928308854138426000 140:98:1016396856746668549029768170693391000 140:99:431198666498586657164144072415378000 140:100:176791453264420529437299069690304980 140:101:70016417134423972054375869184279200 140:102:26770983021985636373731949982224400 140:103:9876673347917030895163243682762400 140:104:3513816479547405222317692464059700 140:105:1204737078701967504794637416249040 140:106:397790544854423232715210467629400 140:107:126400733878975606657169681302800 140:108:38622446463020324256357402620300 140:109:11338699879051838313792998934400 140:110:3195451784096427161159845154240 140:111:863635617323358692205363555200 140:112:223619936628369661374603063400 140:113:55410249784020801048574210400 140:114:13123480212004926564135997200 140:115:2967047700105461657978573280 140:116:639449935367556391805727000 140:117:131169217511293618831944000 140:118:25566881379319942653684000 140:119:4726650339033938977992000 140:120:827163809330939321148600 140:121:136721290798502367132000 140:122:21292660042389712914000 140:123:3115999030593616524000 140:124:427193415484608717000 140:125:54680757182029915776 140:126:6509613950241656640 140:127:717595238609316480 140:128:72880766421258705 140:129:6779606178721740 140:130:573658984353378 140:131:43790762164380 140:132:2985733783935 140:133:179593009560 140:134:9381724380 140:135:416965528 140:136:15329615 140:137:447580 140:138:9730 140:139:140 140:140:1 # binomial(141, k) for 0 <= k <= 141 141:0:1 141:1:141 141:2:9870 141:3:457310 141:4:15777195 141:5:432295143 141:6:9798689908 141:7:188974733940 141:8:3165326793495 141:9:46776495948315 141:10:617449746517758 141:11:7353265163075118 141:12:79660372599980445 141:13:790476005030575185 141:14:7227209188850973120 141:15:61190371132271572416 141:16:481874172666638632776 141:17:3543192446078225241000 141:18:24408659072983329438000 141:19:158013950840892080046000 141:20:963885100129441688280600 141:21:5553814148364878299140600 141:22:30293531718353881631676000 141:23:156736098890613561485628000 141:24:770619152878850010637671000 141:25:3606497635473018049784300280 141:26:16090527912110388222114570480 141:27:68533729996025727612710207600 141:28:279030186412390462423177273800 141:29:1087255553951728353579966618600 141:30:4059087401419785853365208709440 141:31:14534151663148265474952844088640 141:32:49961146342072162570150401554700 141:33:165023180341995930913527083923100 141:34:524191278733398839372380148932200 141:35:1602527623556390737509847883878440 141:36:4718553558249372727112329880308740 141:37:13390489827464436117480936146822100 141:38:36647656369902667268895193664986800 141:39:96787400156409608428107819166503600 141:40:246807870398844501491674938874584180 141:41:607990119763007186601443142105682980 141:42:1447595523245255206193912243108769000 141:43:3332836204680936404958077024831817000 141:44:7423135183152994720133898828034501500 141:45:16000980283685344174510848584874369900 141:46:33393350157256370451153075307563902400 141:47:67497197126369259422543450089756824000 141:48:132182011039139799702480923092440447000 141:49:250876061768163293312871956073407379000 141:50:461611953653420459695684399175069577360 141:51:823660544754142388868770202449633951760 141:52:1425566327459092596119025350393597224200 141:53:2393875531016212095369684078962833074600 141:54:3901130494989382673935781462013505751200 141:55:6170879146619568956952963403548636370080 141:56:9476707260880052326749193798306834425480 141:57:14131931880259727153924236365896156599400 141:58:20466935826583053119476480254056502661200 141:59:28792469044176159473161828154011690184400 141:60:39349707693707417946654498477149309918680 141:61:52251251199840997601295317649985149236280 141:62:67420969290117416259735893741916321595200 141:63:84543755141575807690779930247799831841600 141:64:103037701578795515623138039989506045056950 141:65:122060046485650072353563524295261007221310 141:66:140553992922869780285921634036967220436660 141:67:157336559242018410767822724668246888548500 141:68:171219196822196505835571788609562790479250 141:69:181144947362613694579662906789827300072250 141:70:186320517287259800139081846983822365788600 141:71:186320517287259800139081846983822365788600 141:72:181144947362613694579662906789827300072250 141:73:171219196822196505835571788609562790479250 141:74:157336559242018410767822724668246888548500 141:75:140553992922869780285921634036967220436660 141:76:122060046485650072353563524295261007221310 141:77:103037701578795515623138039989506045056950 141:78:84543755141575807690779930247799831841600 141:79:67420969290117416259735893741916321595200 141:80:52251251199840997601295317649985149236280 141:81:39349707693707417946654498477149309918680 141:82:28792469044176159473161828154011690184400 141:83:20466935826583053119476480254056502661200 141:84:14131931880259727153924236365896156599400 141:85:9476707260880052326749193798306834425480 141:86:6170879146619568956952963403548636370080 141:87:3901130494989382673935781462013505751200 141:88:2393875531016212095369684078962833074600 141:89:1425566327459092596119025350393597224200 141:90:823660544754142388868770202449633951760 141:91:461611953653420459695684399175069577360 141:92:250876061768163293312871956073407379000 141:93:132182011039139799702480923092440447000 141:94:67497197126369259422543450089756824000 141:95:33393350157256370451153075307563902400 141:96:16000980283685344174510848584874369900 141:97:7423135183152994720133898828034501500 141:98:3332836204680936404958077024831817000 141:99:1447595523245255206193912243108769000 141:100:607990119763007186601443142105682980 141:101:246807870398844501491674938874584180 141:102:96787400156409608428107819166503600 141:103:36647656369902667268895193664986800 141:104:13390489827464436117480936146822100 141:105:4718553558249372727112329880308740 141:106:1602527623556390737509847883878440 141:107:524191278733398839372380148932200 141:108:165023180341995930913527083923100 141:109:49961146342072162570150401554700 141:110:14534151663148265474952844088640 141:111:4059087401419785853365208709440 141:112:1087255553951728353579966618600 141:113:279030186412390462423177273800 141:114:68533729996025727612710207600 141:115:16090527912110388222114570480 141:116:3606497635473018049784300280 141:117:770619152878850010637671000 141:118:156736098890613561485628000 141:119:30293531718353881631676000 141:120:5553814148364878299140600 141:121:963885100129441688280600 141:122:158013950840892080046000 141:123:24408659072983329438000 141:124:3543192446078225241000 141:125:481874172666638632776 141:126:61190371132271572416 141:127:7227209188850973120 141:128:790476005030575185 141:129:79660372599980445 141:130:7353265163075118 141:131:617449746517758 141:132:46776495948315 141:133:3165326793495 141:134:188974733940 141:135:9798689908 141:136:432295143 141:137:15777195 141:138:457310 141:139:9870 141:140:141 141:141:1 # binomial(142, k) for 0 <= k <= 142 142:0:1 142:1:142 142:2:10011 142:3:467180 142:4:16234505 142:5:448072338 142:6:10230985051 142:7:198773423848 142:8:3354301527435 142:9:49941822741810 142:10:664226242466073 142:11:7970714909592876 142:12:87013637763055563 142:13:870136377630555630 142:14:8017685193881548305 142:15:68417580321122545536 142:16:543064543798910205192 142:17:4025066618744863873776 142:18:27951851519061554679000 142:19:182422609913875409484000 142:20:1121899050970333768326600 142:21:6517699248494319987421200 142:22:35847345866718759930816600 142:23:187029630608967443117304000 142:24:927355251769463572123299000 142:25:4377116788351868060421971280 142:26:19697025547583406271898870760 142:27:84624257908136115834824778080 142:28:347563916408416190035887481400 142:29:1366285740364118816003143892400 142:30:5146342955371514206945175328040 142:31:18593239064568051328318052798080 142:32:64495298005220428045103245643340 142:33:214984326684068093483677485477800 142:34:689214459075394770285907232855300 142:35:2126718902289789576882228032810640 142:36:6321081181805763464622177764187180 142:37:18109043385713808844593266027130840 142:38:50038146197367103386376129811808900 142:39:133435056526312275697003012831490400 142:40:343595270555254109919782758041087780 142:41:854797990161851688093118080980267160 142:42:2055585643008262392795355385214451980 142:43:4780431727926191611151989267940586000 142:44:10755971387833931125091975852866318500 142:45:23424115466838338894644747412908871400 142:46:49394330440941714625663923892438272300 142:47:100890547283625629873696525397320726400 142:48:199679208165509059125024373182197271000 142:49:383058072807303093015352879165847826000 142:50:712488015421583753008556355248476956360 142:51:1285272498407562848564454601624703529120 142:52:2249226872213234984987795552843231175960 142:53:3819441858475304691488709429356430298800 142:54:6295006026005594769305465540976338825800 142:55:10072009641608951630888744865562142121280 142:56:15647586407499621283702157201855470795560 142:57:23608639141139779480673430164202991024880 142:58:34598867706842780273400716619952659260600 142:59:49259404870759212592638308408068192845600 142:60:68142176737883577419816326631161000103080 142:61:91600958893548415547949816127134459154960 142:62:119672220489958413861031211391901470831480 142:63:151964724431693223950515823989716153436800 142:64:187581456720371323313917970237305876898550 142:65:225097748064445587976701564284767052278260 142:66:262614039408519852639485158332228227657970 142:67:297890552164888191053744358705214108985160 142:68:328555756064214916603394513277809679027750 142:69:352364144184810200415234695399390090551500 142:70:367465464649873494718744753773649665860850 142:71:372641034574519600278163693967644731577200 142:72:367465464649873494718744753773649665860850 142:73:352364144184810200415234695399390090551500 142:74:328555756064214916603394513277809679027750 142:75:297890552164888191053744358705214108985160 142:76:262614039408519852639485158332228227657970 142:77:225097748064445587976701564284767052278260 142:78:187581456720371323313917970237305876898550 142:79:151964724431693223950515823989716153436800 142:80:119672220489958413861031211391901470831480 142:81:91600958893548415547949816127134459154960 142:82:68142176737883577419816326631161000103080 142:83:49259404870759212592638308408068192845600 142:84:34598867706842780273400716619952659260600 142:85:23608639141139779480673430164202991024880 142:86:15647586407499621283702157201855470795560 142:87:10072009641608951630888744865562142121280 142:88:6295006026005594769305465540976338825800 142:89:3819441858475304691488709429356430298800 142:90:2249226872213234984987795552843231175960 142:91:1285272498407562848564454601624703529120 142:92:712488015421583753008556355248476956360 142:93:383058072807303093015352879165847826000 142:94:199679208165509059125024373182197271000 142:95:100890547283625629873696525397320726400 142:96:49394330440941714625663923892438272300 142:97:23424115466838338894644747412908871400 142:98:10755971387833931125091975852866318500 142:99:4780431727926191611151989267940586000 142:100:2055585643008262392795355385214451980 142:101:854797990161851688093118080980267160 142:102:343595270555254109919782758041087780 142:103:133435056526312275697003012831490400 142:104:50038146197367103386376129811808900 142:105:18109043385713808844593266027130840 142:106:6321081181805763464622177764187180 142:107:2126718902289789576882228032810640 142:108:689214459075394770285907232855300 142:109:214984326684068093483677485477800 142:110:64495298005220428045103245643340 142:111:18593239064568051328318052798080 142:112:5146342955371514206945175328040 142:113:1366285740364118816003143892400 142:114:347563916408416190035887481400 142:115:84624257908136115834824778080 142:116:19697025547583406271898870760 142:117:4377116788351868060421971280 142:118:927355251769463572123299000 142:119:187029630608967443117304000 142:120:35847345866718759930816600 142:121:6517699248494319987421200 142:122:1121899050970333768326600 142:123:182422609913875409484000 142:124:27951851519061554679000 142:125:4025066618744863873776 142:126:543064543798910205192 142:127:68417580321122545536 142:128:8017685193881548305 142:129:870136377630555630 142:130:87013637763055563 142:131:7970714909592876 142:132:664226242466073 142:133:49941822741810 142:134:3354301527435 142:135:198773423848 142:136:10230985051 142:137:448072338 142:138:16234505 142:139:467180 142:140:10011 142:141:142 142:142:1 # binomial(143, k) for 0 <= k <= 143 143:0:1 143:1:143 143:2:10153 143:3:477191 143:4:16701685 143:5:464306843 143:6:10679057389 143:7:209004408899 143:8:3553074951283 143:9:53296124269245 143:10:714168065207883 143:11:8634941152058949 143:12:94984352672648439 143:13:957150015393611193 143:14:8887821571512103935 143:15:76435265515004093841 143:16:611482124120032750728 143:17:4568131162543774078968 143:18:31976918137806418552776 143:19:210374461432936964163000 143:20:1304321660884209177810600 143:21:7639598299464653755747800 143:22:42365045115213079918237800 143:23:222876976475686203048120600 143:24:1114384882378431015240603000 143:25:5304472040121331632545270280 143:26:24074142335935274332320842040 143:27:104321283455719522106723648840 143:28:432188174316552305870712259480 143:29:1713849656772535006039031373800 143:30:6512628695735633022948319220440 143:31:23739582019939565535263228126120 143:32:83088537069788479373421298441420 143:33:279479624689288521528780731121140 143:34:904198785759462863769584718333100 143:35:2815933361365184347168135265665940 143:36:8447800084095553041504405796997820 143:37:24430124567519572309215443791318020 143:38:68147189583080912230969395838939740 143:39:183473202723679379083379142643299300 143:40:477030327081566385616785770872578180 143:41:1198393260717105798012900839021354940 143:42:2910383633170114080888473466194719140 143:43:6836017370934454003947344653155037980 143:44:15536403115760122736243965120806904500 143:45:34180086854672270019736723265775189900 143:46:72818445907780053520308671305347143700 143:47:150284877724567344499360449289758998700 143:48:300569755449134688998720898579517997400 143:49:582737280972812152140377252348045097000 143:50:1095546088228886846023909234414324782360 143:51:1997760513829146601573010956873180485480 143:52:3534499370620797833552250154467934705080 143:53:6068668730688539676476504982199661474760 143:54:10114447884480899460794174970332769124600 143:55:16367015667614546400194210406538480947080 143:56:25719596049108572914590902067417612916840 143:57:39256225548639400764375587366058461820440 143:58:58207506847982559754074146784155650285480 143:59:83858272577601992866039025028020852106200 143:60:117401581608642790012454635039229192948680 143:61:159743135631431992967766142758295459258040 143:62:211273179383506829408981027519035929986440 143:63:271636944921651637811547035381617624268280 143:64:339546181152064547264433794227022030335350 143:65:412679204784816911290619534522072929176810 143:66:487711787472965440616186722616995279936230 143:67:560504591573408043693229517037442336643130 143:68:626446308229103107657138871983023788012910 143:69:680919900249025117018629208677199769579250 143:70:719829608834683695133979449173039756412350 143:71:740106499224393094996908447741294397438050 143:72:740106499224393094996908447741294397438050 143:73:719829608834683695133979449173039756412350 143:74:680919900249025117018629208677199769579250 143:75:626446308229103107657138871983023788012910 143:76:560504591573408043693229517037442336643130 143:77:487711787472965440616186722616995279936230 143:78:412679204784816911290619534522072929176810 143:79:339546181152064547264433794227022030335350 143:80:271636944921651637811547035381617624268280 143:81:211273179383506829408981027519035929986440 143:82:159743135631431992967766142758295459258040 143:83:117401581608642790012454635039229192948680 143:84:83858272577601992866039025028020852106200 143:85:58207506847982559754074146784155650285480 143:86:39256225548639400764375587366058461820440 143:87:25719596049108572914590902067417612916840 143:88:16367015667614546400194210406538480947080 143:89:10114447884480899460794174970332769124600 143:90:6068668730688539676476504982199661474760 143:91:3534499370620797833552250154467934705080 143:92:1997760513829146601573010956873180485480 143:93:1095546088228886846023909234414324782360 143:94:582737280972812152140377252348045097000 143:95:300569755449134688998720898579517997400 143:96:150284877724567344499360449289758998700 143:97:72818445907780053520308671305347143700 143:98:34180086854672270019736723265775189900 143:99:15536403115760122736243965120806904500 143:100:6836017370934454003947344653155037980 143:101:2910383633170114080888473466194719140 143:102:1198393260717105798012900839021354940 143:103:477030327081566385616785770872578180 143:104:183473202723679379083379142643299300 143:105:68147189583080912230969395838939740 143:106:24430124567519572309215443791318020 143:107:8447800084095553041504405796997820 143:108:2815933361365184347168135265665940 143:109:904198785759462863769584718333100 143:110:279479624689288521528780731121140 143:111:83088537069788479373421298441420 143:112:23739582019939565535263228126120 143:113:6512628695735633022948319220440 143:114:1713849656772535006039031373800 143:115:432188174316552305870712259480 143:116:104321283455719522106723648840 143:117:24074142335935274332320842040 143:118:5304472040121331632545270280 143:119:1114384882378431015240603000 143:120:222876976475686203048120600 143:121:42365045115213079918237800 143:122:7639598299464653755747800 143:123:1304321660884209177810600 143:124:210374461432936964163000 143:125:31976918137806418552776 143:126:4568131162543774078968 143:127:611482124120032750728 143:128:76435265515004093841 143:129:8887821571512103935 143:130:957150015393611193 143:131:94984352672648439 143:132:8634941152058949 143:133:714168065207883 143:134:53296124269245 143:135:3553074951283 143:136:209004408899 143:137:10679057389 143:138:464306843 143:139:16701685 143:140:477191 143:141:10153 143:142:143 143:143:1 # binomial(144, k) for 0 <= k <= 144 144:0:1 144:1:144 144:2:10296 144:3:487344 144:4:17178876 144:5:481008528 144:6:11143364232 144:7:219683466288 144:8:3762079360182 144:9:56849199220528 144:10:767464189477128 144:11:9349109217266832 144:12:103619293824707388 144:13:1052134368066259632 144:14:9844971586905715128 144:15:85323087086516197776 144:16:687917389635036844569 144:17:5179613286663806829696 144:18:36545049300350192631744 144:19:242351379570743382715776 144:20:1514696122317146141973600 144:21:8943919960348862933558400 144:22:50004643414677733673985600 144:23:265242021590899282966358400 144:24:1337261858854117218288723600 144:25:6418856922499762647785873280 144:26:29378614376056605964866112320 144:27:128395425791654796439044490880 144:28:536509457772271827977435908320 144:29:2146037831089087311909743633280 144:30:8226478352508168028987350594240 144:31:30252210715675198558211547346560 144:32:106828119089728044908684526567540 144:33:362568161759077000902202029562560 144:34:1183678410448751385298365449454240 144:35:3720132147124647210937719983999040 144:36:11263733445460737388672541062663760 144:37:32877924651615125350719849588315840 144:38:92577314150600484540184839630257760 144:39:251620392306760291314348538482239040 144:40:660503529805245764700164913515877480 144:41:1675423587798672183629686609893933120 144:42:4108776893887219878901374305216074080 144:43:9746401004104568084835818119349757120 144:44:22372420486694576740191309773961942480 144:45:49716489970432392755980688386582094400 144:46:106998532762452323540045394571122333600 144:47:223103323632347398019669120595106142400 144:48:450854633173702033498081347869276996100 144:49:883307036421946841139098150927563094400 144:50:1678283369201698998164286486762369879360 144:51:3093306602058033447596920191287505267840 144:52:5532259884449944435125261111341115190560 144:53:9603168101309337510028755136667596179840 144:54:16183116615169439137270679952532430599360 144:55:26481463552095445860988385376871250071680 144:56:42086611716723119314785112473956093863920 144:57:64975821597747973678966489433476074737280 144:58:97463732396621960518449734150214112105920 144:59:142065779425584552620113171812176502391680 144:60:201259854186244782878493660067250045054880 144:61:277144717240074782980220777797524652206720 144:62:371016315014938822376747170277331389244480 144:63:482910124305158467220528062900653554254720 144:64:611183126073716185075980829608639654603630 144:65:752225385936881458555053328749094959512160 144:66:900390992257782351906806257139068209113040 144:67:1048216379046373484309416239654437616579360 144:68:1186950899802511151350368389020466124656040 144:69:1307366208478128224675768080660223557592160 144:70:1400749509083708812152608657850239525991600 144:71:1459936108059076790130887896914334153850400 144:72:1480212998448786189993816895482588794876100 144:73:1459936108059076790130887896914334153850400 144:74:1400749509083708812152608657850239525991600 144:75:1307366208478128224675768080660223557592160 144:76:1186950899802511151350368389020466124656040 144:77:1048216379046373484309416239654437616579360 144:78:900390992257782351906806257139068209113040 144:79:752225385936881458555053328749094959512160 144:80:611183126073716185075980829608639654603630 144:81:482910124305158467220528062900653554254720 144:82:371016315014938822376747170277331389244480 144:83:277144717240074782980220777797524652206720 144:84:201259854186244782878493660067250045054880 144:85:142065779425584552620113171812176502391680 144:86:97463732396621960518449734150214112105920 144:87:64975821597747973678966489433476074737280 144:88:42086611716723119314785112473956093863920 144:89:26481463552095445860988385376871250071680 144:90:16183116615169439137270679952532430599360 144:91:9603168101309337510028755136667596179840 144:92:5532259884449944435125261111341115190560 144:93:3093306602058033447596920191287505267840 144:94:1678283369201698998164286486762369879360 144:95:883307036421946841139098150927563094400 144:96:450854633173702033498081347869276996100 144:97:223103323632347398019669120595106142400 144:98:106998532762452323540045394571122333600 144:99:49716489970432392755980688386582094400 144:100:22372420486694576740191309773961942480 144:101:9746401004104568084835818119349757120 144:102:4108776893887219878901374305216074080 144:103:1675423587798672183629686609893933120 144:104:660503529805245764700164913515877480 144:105:251620392306760291314348538482239040 144:106:92577314150600484540184839630257760 144:107:32877924651615125350719849588315840 144:108:11263733445460737388672541062663760 144:109:3720132147124647210937719983999040 144:110:1183678410448751385298365449454240 144:111:362568161759077000902202029562560 144:112:106828119089728044908684526567540 144:113:30252210715675198558211547346560 144:114:8226478352508168028987350594240 144:115:2146037831089087311909743633280 144:116:536509457772271827977435908320 144:117:128395425791654796439044490880 144:118:29378614376056605964866112320 144:119:6418856922499762647785873280 144:120:1337261858854117218288723600 144:121:265242021590899282966358400 144:122:50004643414677733673985600 144:123:8943919960348862933558400 144:124:1514696122317146141973600 144:125:242351379570743382715776 144:126:36545049300350192631744 144:127:5179613286663806829696 144:128:687917389635036844569 144:129:85323087086516197776 144:130:9844971586905715128 144:131:1052134368066259632 144:132:103619293824707388 144:133:9349109217266832 144:134:767464189477128 144:135:56849199220528 144:136:3762079360182 144:137:219683466288 144:138:11143364232 144:139:481008528 144:140:17178876 144:141:487344 144:142:10296 144:143:144 144:144:1 # binomial(145, k) for 0 <= k <= 145 145:0:1 145:1:145 145:2:10440 145:3:497640 145:4:17666220 145:5:498187404 145:6:11624372760 145:7:230826830520 145:8:3981762826470 145:9:60611278580710 145:10:824313388697656 145:11:10116573406743960 145:12:112968403041974220 145:13:1155753661890967020 145:14:10897105954971974760 145:15:95168058673421912904 145:16:773240476721553042345 145:17:5867530676298843674265 145:18:41724662587013999461440 145:19:278896428871093575347520 145:20:1757047501887889524689376 145:21:10458616082666009075532000 145:22:58948563375026596607544000 145:23:315246665005577016640344000 145:24:1602503880445016501255082000 145:25:7756118781353879866074596880 145:26:35797471298556368612651985600 145:27:157774040167711402403910603200 145:28:664904883563926624416480399200 145:29:2682547288861359139887179541600 145:30:10372516183597255340897094227520 145:31:38478689068183366587198897940800 145:32:137080329805403243466896073914100 145:33:469396280848805045810886556130100 145:34:1546246572207828386200567479016800 145:35:4903810557573398596236085433453280 145:36:14983865592585384599610261046662800 145:37:44141658097075862739392390650979600 145:38:125455238802215609890904689218573600 145:39:344197706457360775854533378112496800 145:40:912123922112006056014513451998116520 145:41:2335927117603917948329851523409810600 145:42:5784200481685892062531060915110007200 145:43:13855177897991787963737192424565831200 145:44:32118821490799144825027127893311699600 145:45:72088910457126969496171998160544036880 145:46:156715022732884716296026082957704428000 145:47:330101856394799721559714515166228476000 145:48:673957956806049431517750468464383138500 145:49:1334161669595648874637179498796840090500 145:50:2561590405623645839303384637689932973760 145:51:4771589971259732445761206678049875147200 145:52:8625566486507977882722181302628620458400 145:53:15135427985759281945154016248008711370400 145:54:25786284716478776647299435089200026779200 145:55:42664580167264884998259065329403680671040 145:56:68568075268818565175773497850827343935600 145:57:107062433314471092993751601907432168601200 145:58:162439553994369934197416223583690186843200 145:59:239529511822206513138562905962390614497600 145:60:343325633611829335498606831879426547446560 145:61:478404571426319565858714437864774697261600 145:62:648161032255013605356967948074856041451200 145:63:853926439320097289597275233177984943499200 145:64:1094093250378874652296508892509293208858350 145:65:1363408512010597643631034158357734614115790 145:66:1652616378194663810461859585888163168625200 145:67:1948607371304155836216222496793505825692400 145:68:2235167278848884635659784628674903741235400 145:69:2494317108280639376026136469680689682248200 145:70:2708115717561837036828376738510463083583760 145:71:2860685617142785602283496554764573679842000 145:72:2940149106507862980124704792396922948726500 145:73:2940149106507862980124704792396922948726500 145:74:2860685617142785602283496554764573679842000 145:75:2708115717561837036828376738510463083583760 145:76:2494317108280639376026136469680689682248200 145:77:2235167278848884635659784628674903741235400 145:78:1948607371304155836216222496793505825692400 145:79:1652616378194663810461859585888163168625200 145:80:1363408512010597643631034158357734614115790 145:81:1094093250378874652296508892509293208858350 145:82:853926439320097289597275233177984943499200 145:83:648161032255013605356967948074856041451200 145:84:478404571426319565858714437864774697261600 145:85:343325633611829335498606831879426547446560 145:86:239529511822206513138562905962390614497600 145:87:162439553994369934197416223583690186843200 145:88:107062433314471092993751601907432168601200 145:89:68568075268818565175773497850827343935600 145:90:42664580167264884998259065329403680671040 145:91:25786284716478776647299435089200026779200 145:92:15135427985759281945154016248008711370400 145:93:8625566486507977882722181302628620458400 145:94:4771589971259732445761206678049875147200 145:95:2561590405623645839303384637689932973760 145:96:1334161669595648874637179498796840090500 145:97:673957956806049431517750468464383138500 145:98:330101856394799721559714515166228476000 145:99:156715022732884716296026082957704428000 145:100:72088910457126969496171998160544036880 145:101:32118821490799144825027127893311699600 145:102:13855177897991787963737192424565831200 145:103:5784200481685892062531060915110007200 145:104:2335927117603917948329851523409810600 145:105:912123922112006056014513451998116520 145:106:344197706457360775854533378112496800 145:107:125455238802215609890904689218573600 145:108:44141658097075862739392390650979600 145:109:14983865592585384599610261046662800 145:110:4903810557573398596236085433453280 145:111:1546246572207828386200567479016800 145:112:469396280848805045810886556130100 145:113:137080329805403243466896073914100 145:114:38478689068183366587198897940800 145:115:10372516183597255340897094227520 145:116:2682547288861359139887179541600 145:117:664904883563926624416480399200 145:118:157774040167711402403910603200 145:119:35797471298556368612651985600 145:120:7756118781353879866074596880 145:121:1602503880445016501255082000 145:122:315246665005577016640344000 145:123:58948563375026596607544000 145:124:10458616082666009075532000 145:125:1757047501887889524689376 145:126:278896428871093575347520 145:127:41724662587013999461440 145:128:5867530676298843674265 145:129:773240476721553042345 145:130:95168058673421912904 145:131:10897105954971974760 145:132:1155753661890967020 145:133:112968403041974220 145:134:10116573406743960 145:135:824313388697656 145:136:60611278580710 145:137:3981762826470 145:138:230826830520 145:139:11624372760 145:140:498187404 145:141:17666220 145:142:497640 145:143:10440 145:144:145 145:145:1 # binomial(146, k) for 0 <= k <= 146 146:0:1 146:1:146 146:2:10585 146:3:508080 146:4:18163860 146:5:515853624 146:6:12122560164 146:7:242451203280 146:8:4212589656990 146:9:64593041407180 146:10:884924667278366 146:11:10940886795441616 146:12:123084976448718180 146:13:1268722064932941240 146:14:12052859616862941780 146:15:106065164628393887664 146:16:868408535394974955249 146:17:6640771153020396716610 146:18:47592193263312843135705 146:19:320621091458107574808960 146:20:2035943930758983100036896 146:21:12215663584553898600221376 146:22:69407179457692605683076000 146:23:374195228380603613247888000 146:24:1917750545450593517895426000 146:25:9358622661798896367329678880 146:26:43553590079910248478726582480 146:27:193571511466267771016562588800 146:28:822678923731638026820391002400 146:29:3347452172425285764303659940800 146:30:13055063472458614480784273769120 146:31:48851205251780621928095992168320 146:32:175559018873586610054094971854900 146:33:606476610654208289277782630044200 146:34:2015642853056633432011454035146900 146:35:6450057129781226982436652912470080 146:36:19887676150158783195846346480116080 146:37:59125523689661247339002651697642400 146:38:169596896899291472630297079869553200 146:39:469652945259576385745438067331070400 146:40:1256321628569366831869046830110613320 146:41:3248051039715924004344364975407927120 146:42:8120127599289810010860912438519817800 146:43:19639378379677680026268253339675838400 146:44:45973999388790932788764320317877530800 146:45:104207731947926114321199126053855736480 146:46:228803933190011685792198081118248464880 146:47:486816879127684437855740598123932904000 146:48:1004059813200849153077464983630611614500 146:49:2008119626401698306154929967261223229000 146:50:3895752075219294713940564136486773064260 146:51:7333180376883378285064591315739808120960 146:52:13397156457767710328483387980678495605600 146:53:23760994472267259827876197550637331828800 146:54:40921712702238058592453451337208738149600 146:55:68450864883743661645558500418603707450240 146:56:111232655436083450174032563180231024606640 146:57:175630508583289658169525099758259512536800 146:58:269501987308841027191167825491122355444400 146:59:401969065816576447335979129546080801340800 146:60:582855145434035848637169737841817161944160 146:61:821730205038148901357321269744201244708160 146:62:1126565603681333171215682385939630738712800 146:63:1502087471575110894954243181252840984950400 146:64:1948019689698971941893784125687278152357550 146:65:2457501762389472295927543050867027822974140 146:66:3016024890205261454092893744245897782740990 146:67:3601223749498819646678082082681668994317600 146:68:4183774650153040471876007125468409566927800 146:69:4729484387129524011685921098355593423483600 146:70:5202432825842476412854513208191152765831960 146:71:5568801334704622639111873293275036763425760 146:72:5800834723650648582408201347161496628568500 146:73:5880298213015725960249409584793845897453000 146:74:5800834723650648582408201347161496628568500 146:75:5568801334704622639111873293275036763425760 146:76:5202432825842476412854513208191152765831960 146:77:4729484387129524011685921098355593423483600 146:78:4183774650153040471876007125468409566927800 146:79:3601223749498819646678082082681668994317600 146:80:3016024890205261454092893744245897782740990 146:81:2457501762389472295927543050867027822974140 146:82:1948019689698971941893784125687278152357550 146:83:1502087471575110894954243181252840984950400 146:84:1126565603681333171215682385939630738712800 146:85:821730205038148901357321269744201244708160 146:86:582855145434035848637169737841817161944160 146:87:401969065816576447335979129546080801340800 146:88:269501987308841027191167825491122355444400 146:89:175630508583289658169525099758259512536800 146:90:111232655436083450174032563180231024606640 146:91:68450864883743661645558500418603707450240 146:92:40921712702238058592453451337208738149600 146:93:23760994472267259827876197550637331828800 146:94:13397156457767710328483387980678495605600 146:95:7333180376883378285064591315739808120960 146:96:3895752075219294713940564136486773064260 146:97:2008119626401698306154929967261223229000 146:98:1004059813200849153077464983630611614500 146:99:486816879127684437855740598123932904000 146:100:228803933190011685792198081118248464880 146:101:104207731947926114321199126053855736480 146:102:45973999388790932788764320317877530800 146:103:19639378379677680026268253339675838400 146:104:8120127599289810010860912438519817800 146:105:3248051039715924004344364975407927120 146:106:1256321628569366831869046830110613320 146:107:469652945259576385745438067331070400 146:108:169596896899291472630297079869553200 146:109:59125523689661247339002651697642400 146:110:19887676150158783195846346480116080 146:111:6450057129781226982436652912470080 146:112:2015642853056633432011454035146900 146:113:606476610654208289277782630044200 146:114:175559018873586610054094971854900 146:115:48851205251780621928095992168320 146:116:13055063472458614480784273769120 146:117:3347452172425285764303659940800 146:118:822678923731638026820391002400 146:119:193571511466267771016562588800 146:120:43553590079910248478726582480 146:121:9358622661798896367329678880 146:122:1917750545450593517895426000 146:123:374195228380603613247888000 146:124:69407179457692605683076000 146:125:12215663584553898600221376 146:126:2035943930758983100036896 146:127:320621091458107574808960 146:128:47592193263312843135705 146:129:6640771153020396716610 146:130:868408535394974955249 146:131:106065164628393887664 146:132:12052859616862941780 146:133:1268722064932941240 146:134:123084976448718180 146:135:10940886795441616 146:136:884924667278366 146:137:64593041407180 146:138:4212589656990 146:139:242451203280 146:140:12122560164 146:141:515853624 146:142:18163860 146:143:508080 146:144:10585 146:145:146 146:146:1 # binomial(147, k) for 0 <= k <= 147 147:0:1 147:1:147 147:2:10731 147:3:518665 147:4:18671940 147:5:534017484 147:6:12638413788 147:7:254573763444 147:8:4455040860270 147:9:68805631064170 147:10:949517708685546 147:11:11825811462719982 147:12:134025863244159796 147:13:1391807041381659420 147:14:13321581681795883020 147:15:118118024245256829444 147:16:974473700023368842913 147:17:7509179688415371671859 147:18:54232964416333239852315 147:19:368213284721420417944665 147:20:2356565022217090674845856 147:21:14251607515312881700258272 147:22:81622843042246504283297376 147:23:443602407838296218930964000 147:24:2291945773831197131143314000 147:25:11276373207249489885225104880 147:26:52912212741709144846056261360 147:27:237125101546178019495289171280 147:28:1016250435197905797836953591200 147:29:4170131096156923791124050943200 147:30:16402515644883900245087933709920 147:31:61906268724239236408880265937440 147:32:224410224125367231982190964023220 147:33:782035629527794899331877601899100 147:34:2622119463710841721289236665191100 147:35:8465699982837860414448106947616980 147:36:26337733279940010178282999392586160 147:37:79013199839820030534848998177758480 147:38:228722420588952719969299731567195600 147:39:639249842158867858375735147200623600 147:40:1725974573828943217614484897441683720 147:41:4504372668285290836213411805518540440 147:42:11368178639005734015205277413927744920 147:43:27759505978967490037129165778195656200 147:44:65613377768468612815032573657553369200 147:45:150181731336717047109963446371733267280 147:46:333011665137937800113397207172104201360 147:47:715620812317696123647938679242181368880 147:48:1490876692328533590933205581754544518500 147:49:3012179439602547459232394950891834843500 147:50:5903871701620993020095494103747996293260 147:51:11228932452102672999005155452226581185220 147:52:20730336834651088613547979296418303726560 147:53:37158150930034970156359585531315827434400 147:54:64682707174505318420329648887846069978400 147:55:109372577585981720238011951755812445599840 147:56:179683520319827111819591063598834732056880 147:57:286863164019373108343557662938490537143440 147:58:445132495892130685360692925249381867981200 147:59:671471053125417474527146955037203156785200 147:60:984824211250612295973148867387897963284960 147:61:1404585350472184749994491007586018406652320 147:62:1948295808719482072573003655683831983420960 147:63:2628653075256444066169925567192471723663200 147:64:3450107161274082836848027306940119137307950 147:65:4405521452088444237821327176554305975331690 147:66:5473526652594733750020436795112925605715130 147:67:6617248639704081100770975826927566777058590 147:68:7784998399651860118554089208150078561245400 147:69:8913259037282564483561928223824002990411400 147:70:9931917212972000424540434306546746189315560 147:71:10771234160547099051966386501466189529257720 147:72:11369636058355271221520074640436533391994260 147:73:11681132936666374542657610931955342526021500 147:74:11681132936666374542657610931955342526021500 147:75:11369636058355271221520074640436533391994260 147:76:10771234160547099051966386501466189529257720 147:77:9931917212972000424540434306546746189315560 147:78:8913259037282564483561928223824002990411400 147:79:7784998399651860118554089208150078561245400 147:80:6617248639704081100770975826927566777058590 147:81:5473526652594733750020436795112925605715130 147:82:4405521452088444237821327176554305975331690 147:83:3450107161274082836848027306940119137307950 147:84:2628653075256444066169925567192471723663200 147:85:1948295808719482072573003655683831983420960 147:86:1404585350472184749994491007586018406652320 147:87:984824211250612295973148867387897963284960 147:88:671471053125417474527146955037203156785200 147:89:445132495892130685360692925249381867981200 147:90:286863164019373108343557662938490537143440 147:91:179683520319827111819591063598834732056880 147:92:109372577585981720238011951755812445599840 147:93:64682707174505318420329648887846069978400 147:94:37158150930034970156359585531315827434400 147:95:20730336834651088613547979296418303726560 147:96:11228932452102672999005155452226581185220 147:97:5903871701620993020095494103747996293260 147:98:3012179439602547459232394950891834843500 147:99:1490876692328533590933205581754544518500 147:100:715620812317696123647938679242181368880 147:101:333011665137937800113397207172104201360 147:102:150181731336717047109963446371733267280 147:103:65613377768468612815032573657553369200 147:104:27759505978967490037129165778195656200 147:105:11368178639005734015205277413927744920 147:106:4504372668285290836213411805518540440 147:107:1725974573828943217614484897441683720 147:108:639249842158867858375735147200623600 147:109:228722420588952719969299731567195600 147:110:79013199839820030534848998177758480 147:111:26337733279940010178282999392586160 147:112:8465699982837860414448106947616980 147:113:2622119463710841721289236665191100 147:114:782035629527794899331877601899100 147:115:224410224125367231982190964023220 147:116:61906268724239236408880265937440 147:117:16402515644883900245087933709920 147:118:4170131096156923791124050943200 147:119:1016250435197905797836953591200 147:120:237125101546178019495289171280 147:121:52912212741709144846056261360 147:122:11276373207249489885225104880 147:123:2291945773831197131143314000 147:124:443602407838296218930964000 147:125:81622843042246504283297376 147:126:14251607515312881700258272 147:127:2356565022217090674845856 147:128:368213284721420417944665 147:129:54232964416333239852315 147:130:7509179688415371671859 147:131:974473700023368842913 147:132:118118024245256829444 147:133:13321581681795883020 147:134:1391807041381659420 147:135:134025863244159796 147:136:11825811462719982 147:137:949517708685546 147:138:68805631064170 147:139:4455040860270 147:140:254573763444 147:141:12638413788 147:142:534017484 147:143:18671940 147:144:518665 147:145:10731 147:146:147 147:147:1 # binomial(148, k) for 0 <= k <= 148 148:0:1 148:1:148 148:2:10878 148:3:529396 148:4:19190605 148:5:552689424 148:6:13172431272 148:7:267212177232 148:8:4709614623714 148:9:73260671924440 148:10:1018323339749716 148:11:12775329171405528 148:12:145851674706879778 148:13:1525832904625819216 148:14:14713388723177542440 148:15:131439605927052712464 148:16:1092591724268625672357 148:17:8483653388438740514772 148:18:61742144104748611524174 148:19:422446249137753657796980 148:20:2724778306938511092790521 148:21:16608172537529972375104128 148:22:95874450557559385983555648 148:23:525225250880542723214261376 148:24:2735548181669493350074278000 148:25:13568318981080687016368418880 148:26:64188585948958634731281366240 148:27:290037314287887164341345432640 148:28:1253375536744083817332242762480 148:29:5186381531354829588961004534400 148:30:20572646741040824036211984653120 148:31:78308784369123136653968199647360 148:32:286316492849606468391071229960660 148:33:1006445853653162131314068565922320 148:34:3404155093238636620621114267090200 148:35:11087819446548702135737343612808080 148:36:34803433262777870592731106340203140 148:37:105350933119760040713131997570344640 148:38:307735620428772750504148729744954080 148:39:867972262747820578345034878767819200 148:40:2365224415987811075990220044642307320 148:41:6230347242114234053827896702960224160 148:42:15872551307291024851418689219446285360 148:43:39127684617973224052334443192123401120 148:44:93372883747436102852161739435749025400 148:45:215795109105185659924996020029286636480 148:46:483193396474654847223360653543837468640 148:47:1048632477455633923761335886414285570240 148:48:2206497504646229714581144260996725887380 148:49:4503056131931081050165600532646379362000 148:50:8916051141223540479327889054639831136760 148:51:17132804153723666019100649555974577478480 148:52:31959269286753761612553134748644884911780 148:53:57888487764686058769907564827734131160960 148:54:101840858104540288576689234419161897412800 148:55:174055284760487038658341600643658515578240 148:56:289056097905808832057603015354647177656720 148:57:466546684339200220163148726537325269200320 148:58:731995659911503793704250588187872405124640 148:59:1116603549017548159887839880286585024766400 148:60:1656295264376029770500295822425101120070160 148:61:2389409561722797045967639874973916369937280 148:62:3352881159191666822567494663269850390073280 148:63:4576948883975926138742929222876303707084160 148:64:6078760236530526903017952874132590860971150 148:65:7855628613362527074669354483494425112639640 148:66:9879048104683177987841763971667231581046820 148:67:12090775292298814850791412622040492382773720 148:68:14402247039355941219325065035077645338303990 148:69:16698257436934424602116017431974081551656800 148:70:18845176250254564908102362530370749179726960 148:71:20703151373519099476506820808012935718573280 148:72:22140870218902370273486461141902722921251980 148:73:23050768995021645764177685572391875918015760 148:74:23362265873332749085315221863910685052043000 148:75:23050768995021645764177685572391875918015760 148:76:22140870218902370273486461141902722921251980 148:77:20703151373519099476506820808012935718573280 148:78:18845176250254564908102362530370749179726960 148:79:16698257436934424602116017431974081551656800 148:80:14402247039355941219325065035077645338303990 148:81:12090775292298814850791412622040492382773720 148:82:9879048104683177987841763971667231581046820 148:83:7855628613362527074669354483494425112639640 148:84:6078760236530526903017952874132590860971150 148:85:4576948883975926138742929222876303707084160 148:86:3352881159191666822567494663269850390073280 148:87:2389409561722797045967639874973916369937280 148:88:1656295264376029770500295822425101120070160 148:89:1116603549017548159887839880286585024766400 148:90:731995659911503793704250588187872405124640 148:91:466546684339200220163148726537325269200320 148:92:289056097905808832057603015354647177656720 148:93:174055284760487038658341600643658515578240 148:94:101840858104540288576689234419161897412800 148:95:57888487764686058769907564827734131160960 148:96:31959269286753761612553134748644884911780 148:97:17132804153723666019100649555974577478480 148:98:8916051141223540479327889054639831136760 148:99:4503056131931081050165600532646379362000 148:100:2206497504646229714581144260996725887380 148:101:1048632477455633923761335886414285570240 148:102:483193396474654847223360653543837468640 148:103:215795109105185659924996020029286636480 148:104:93372883747436102852161739435749025400 148:105:39127684617973224052334443192123401120 148:106:15872551307291024851418689219446285360 148:107:6230347242114234053827896702960224160 148:108:2365224415987811075990220044642307320 148:109:867972262747820578345034878767819200 148:110:307735620428772750504148729744954080 148:111:105350933119760040713131997570344640 148:112:34803433262777870592731106340203140 148:113:11087819446548702135737343612808080 148:114:3404155093238636620621114267090200 148:115:1006445853653162131314068565922320 148:116:286316492849606468391071229960660 148:117:78308784369123136653968199647360 148:118:20572646741040824036211984653120 148:119:5186381531354829588961004534400 148:120:1253375536744083817332242762480 148:121:290037314287887164341345432640 148:122:64188585948958634731281366240 148:123:13568318981080687016368418880 148:124:2735548181669493350074278000 148:125:525225250880542723214261376 148:126:95874450557559385983555648 148:127:16608172537529972375104128 148:128:2724778306938511092790521 148:129:422446249137753657796980 148:130:61742144104748611524174 148:131:8483653388438740514772 148:132:1092591724268625672357 148:133:131439605927052712464 148:134:14713388723177542440 148:135:1525832904625819216 148:136:145851674706879778 148:137:12775329171405528 148:138:1018323339749716 148:139:73260671924440 148:140:4709614623714 148:141:267212177232 148:142:13172431272 148:143:552689424 148:144:19190605 148:145:529396 148:146:10878 148:147:148 148:148:1 # binomial(149, k) for 0 <= k <= 149 149:0:1 149:1:149 149:2:11026 149:3:540274 149:4:19720001 149:5:571880029 149:6:13725120696 149:7:280384608504 149:8:4976826800946 149:9:77970286548154 149:10:1091584011674156 149:11:13793652511155244 149:12:158627003878285306 149:13:1671684579332698994 149:14:16239221627803361656 149:15:146152994650230254904 149:16:1224031330195678384821 149:17:9576245112707366187129 149:18:70225797493187352038946 149:19:484188393242502269321154 149:20:3147224556076264750587501 149:21:19332950844468483467894649 149:22:112482623095089358358659776 149:23:621099701438102109197817024 149:24:3260773432550036073288539376 149:25:16303867162750180366442696880 149:26:77756904930039321747649785120 149:27:354225900236845799072626798880 149:28:1543412851031970981673588195120 149:29:6439757068098913406293247296880 149:30:25759028272395653625172989187520 149:31:98881431110163960690180184300480 149:32:364625277218729605045039429608020 149:33:1292762346502768599705139795882980 149:34:4410600946891798751935182833012520 149:35:14491974539787338756358457879898280 149:36:45891252709326572728468449953011220 149:37:140154366382537911305863103910547780 149:38:413086553548532791217280727315298720 149:39:1175707883176593328849183608512773280 149:40:3233196678735631654335254923410126520 149:41:8595571658102045129818116747602531480 149:42:22102898549405258905246585922406509520 149:43:55000235925264248903753132411569686480 149:44:132500568365409326904496182627872426520 149:45:309167992852621762777157759465035661880 149:46:698988505579840507148356673573124105120 149:47:1531825873930288770984696539958123038880 149:48:3255129982101863638342480147411011457620 149:49:6709553636577310764746744793643105249380 149:50:13419107273154621529493489587286210498760 149:51:26048855294947206498428538610614408615240 149:52:49092073440477427631653784304619462390260 149:53:89847757051439820382460699576379016072740 149:54:159729345869226347346596799246896028573760 149:55:275896142865027327235030835062820412991040 149:56:463111382666295870715944615998305693234960 149:57:755602782245009052220751741891972446857040 149:58:1198542344250704013867399314725197674324960 149:59:1848599208929051953592090468474457429891040 149:60:2772898813393577930388135702711686144836560 149:61:4045704826098826816467935697399017490007440 149:62:5742290720914463868535134538243766760010560 149:63:7929830043167592961310423886146154097157440 149:64:10655709120506453041760882097008894568055310 149:65:13934388849893053977687307357627015973610790 149:66:17734676718045705062511118455161656693686460 149:67:21969823396981992838633176593707723963820540 149:68:26493022331654756070116477657118137721077710 149:69:31100504476290365821441082467051726889960790 149:70:35543433687188989510218379962344830731383760 149:71:39548327623773664384609183338383684898300240 149:72:42844021592421469749993281949915658639825260 149:73:45191639213924016037664146714294598839267740 149:74:46413034868354394849492907436302560970058760 149:75:46413034868354394849492907436302560970058760 149:76:45191639213924016037664146714294598839267740 149:77:42844021592421469749993281949915658639825260 149:78:39548327623773664384609183338383684898300240 149:79:35543433687188989510218379962344830731383760 149:80:31100504476290365821441082467051726889960790 149:81:26493022331654756070116477657118137721077710 149:82:21969823396981992838633176593707723963820540 149:83:17734676718045705062511118455161656693686460 149:84:13934388849893053977687307357627015973610790 149:85:10655709120506453041760882097008894568055310 149:86:7929830043167592961310423886146154097157440 149:87:5742290720914463868535134538243766760010560 149:88:4045704826098826816467935697399017490007440 149:89:2772898813393577930388135702711686144836560 149:90:1848599208929051953592090468474457429891040 149:91:1198542344250704013867399314725197674324960 149:92:755602782245009052220751741891972446857040 149:93:463111382666295870715944615998305693234960 149:94:275896142865027327235030835062820412991040 149:95:159729345869226347346596799246896028573760 149:96:89847757051439820382460699576379016072740 149:97:49092073440477427631653784304619462390260 149:98:26048855294947206498428538610614408615240 149:99:13419107273154621529493489587286210498760 149:100:6709553636577310764746744793643105249380 149:101:3255129982101863638342480147411011457620 149:102:1531825873930288770984696539958123038880 149:103:698988505579840507148356673573124105120 149:104:309167992852621762777157759465035661880 149:105:132500568365409326904496182627872426520 149:106:55000235925264248903753132411569686480 149:107:22102898549405258905246585922406509520 149:108:8595571658102045129818116747602531480 149:109:3233196678735631654335254923410126520 149:110:1175707883176593328849183608512773280 149:111:413086553548532791217280727315298720 149:112:140154366382537911305863103910547780 149:113:45891252709326572728468449953011220 149:114:14491974539787338756358457879898280 149:115:4410600946891798751935182833012520 149:116:1292762346502768599705139795882980 149:117:364625277218729605045039429608020 149:118:98881431110163960690180184300480 149:119:25759028272395653625172989187520 149:120:6439757068098913406293247296880 149:121:1543412851031970981673588195120 149:122:354225900236845799072626798880 149:123:77756904930039321747649785120 149:124:16303867162750180366442696880 149:125:3260773432550036073288539376 149:126:621099701438102109197817024 149:127:112482623095089358358659776 149:128:19332950844468483467894649 149:129:3147224556076264750587501 149:130:484188393242502269321154 149:131:70225797493187352038946 149:132:9576245112707366187129 149:133:1224031330195678384821 149:134:146152994650230254904 149:135:16239221627803361656 149:136:1671684579332698994 149:137:158627003878285306 149:138:13793652511155244 149:139:1091584011674156 149:140:77970286548154 149:141:4976826800946 149:142:280384608504 149:143:13725120696 149:144:571880029 149:145:19720001 149:146:540274 149:147:11026 149:148:149 149:149:1 # binomial(150, k) for 0 <= k <= 150 150:0:1 150:1:150 150:2:11175 150:3:551300 150:4:20260275 150:5:591600030 150:6:14297000725 150:7:294109729200 150:8:5257211409450 150:9:82947113349100 150:10:1169554298222310 150:11:14885236522829400 150:12:172420656389440550 150:13:1830311583210984300 150:14:17910906207136060650 150:15:162392216278033616560 150:16:1370184324845908639725 150:17:10800276442903044571950 150:18:79802042605894718226075 150:19:554414190735689621360100 150:20:3631412949318767019908655 150:21:22480175400544748218482150 150:22:131815573939557841826554425 150:23:733582324533191467556476800 150:24:3881873133988138182486356400 150:25:19564640595300216439731236256 150:26:94060772092789502114092482000 150:27:431982805166885120820276584000 150:28:1897638751268816780746214994000 150:29:7983169919130884387966835492000 150:30:32198785340494567031466236484400 150:31:124640459382559614315353173488000 150:32:463506708328893565735219613908500 150:33:1657387623721498204750179225491000 150:34:5703363293394567351640322628895500 150:35:18902575486679137508293640712910800 150:36:60383227249113911484826907832909500 150:37:186045619091864484034331553863559000 150:38:553240919931070702523143831225846500 150:39:1588794436725126120066464335828072000 150:40:4408904561912224983184438531922899800 150:41:11828768336837676784153371671012658000 150:42:30698470207507304035064702670009041000 150:43:77103134474669507808999718333976196000 150:44:187500804290673575808249315039442113000 150:45:441668561218031089681653942092908088400 150:46:1008156498432462269925514433038159767000 150:47:2230814379510129278133053213531247144000 150:48:4786955856032152409327176687369134496500 150:49:9964683618679174403089224941054116707000 150:50:20128660909731932294240234380929315748140 150:51:39467962568101828027922028197900619114000 150:52:75140928735424634130082322915233871005500 150:53:138939830491917248014114483880998478463000 150:54:249577102920666167729057498823275044646500 150:55:435625488734253674581627634309716441564800 150:56:739007525531323197950975451061126106226000 150:57:1218714164911304922936696357890278140092000 150:58:1954145126495713066088151056617170121182000 150:59:3047141553179755967459489783199655104216000 150:60:4621498022322629883980226171186143574727600 150:61:6818603639492404746856071400110703634844000 150:62:9787995547013290685003070235642784250018000 150:63:13672120764082056829845558424389920857168000 150:64:18585539163674046003071305983155048665212750 150:65:24590097970399507019448189454635910541666100 150:66:31669065567938759040198425812788672667297250 150:67:39704500115027697901144295048869380657507000 150:68:48462845728636748908749654250825861684898250 150:69:57593526807945121891557560124169864611038500 150:70:66643938163479355331659462429396557621344550 150:71:75091761310962653894827563300728515629684000 150:72:82392349216195134134602465288299343538125500 150:73:88035660806345485787657428664210257479093000 150:74:91604674082278410887157054150597159809326500 150:75:92826069736708789698985814872605121940117520 150:76:91604674082278410887157054150597159809326500 150:77:88035660806345485787657428664210257479093000 150:78:82392349216195134134602465288299343538125500 150:79:75091761310962653894827563300728515629684000 150:80:66643938163479355331659462429396557621344550 150:81:57593526807945121891557560124169864611038500 150:82:48462845728636748908749654250825861684898250 150:83:39704500115027697901144295048869380657507000 150:84:31669065567938759040198425812788672667297250 150:85:24590097970399507019448189454635910541666100 150:86:18585539163674046003071305983155048665212750 150:87:13672120764082056829845558424389920857168000 150:88:9787995547013290685003070235642784250018000 150:89:6818603639492404746856071400110703634844000 150:90:4621498022322629883980226171186143574727600 150:91:3047141553179755967459489783199655104216000 150:92:1954145126495713066088151056617170121182000 150:93:1218714164911304922936696357890278140092000 150:94:739007525531323197950975451061126106226000 150:95:435625488734253674581627634309716441564800 150:96:249577102920666167729057498823275044646500 150:97:138939830491917248014114483880998478463000 150:98:75140928735424634130082322915233871005500 150:99:39467962568101828027922028197900619114000 150:100:20128660909731932294240234380929315748140 150:101:9964683618679174403089224941054116707000 150:102:4786955856032152409327176687369134496500 150:103:2230814379510129278133053213531247144000 150:104:1008156498432462269925514433038159767000 150:105:441668561218031089681653942092908088400 150:106:187500804290673575808249315039442113000 150:107:77103134474669507808999718333976196000 150:108:30698470207507304035064702670009041000 150:109:11828768336837676784153371671012658000 150:110:4408904561912224983184438531922899800 150:111:1588794436725126120066464335828072000 150:112:553240919931070702523143831225846500 150:113:186045619091864484034331553863559000 150:114:60383227249113911484826907832909500 150:115:18902575486679137508293640712910800 150:116:5703363293394567351640322628895500 150:117:1657387623721498204750179225491000 150:118:463506708328893565735219613908500 150:119:124640459382559614315353173488000 150:120:32198785340494567031466236484400 150:121:7983169919130884387966835492000 150:122:1897638751268816780746214994000 150:123:431982805166885120820276584000 150:124:94060772092789502114092482000 150:125:19564640595300216439731236256 150:126:3881873133988138182486356400 150:127:733582324533191467556476800 150:128:131815573939557841826554425 150:129:22480175400544748218482150 150:130:3631412949318767019908655 150:131:554414190735689621360100 150:132:79802042605894718226075 150:133:10800276442903044571950 150:134:1370184324845908639725 150:135:162392216278033616560 150:136:17910906207136060650 150:137:1830311583210984300 150:138:172420656389440550 150:139:14885236522829400 150:140:1169554298222310 150:141:82947113349100 150:142:5257211409450 150:143:294109729200 150:144:14297000725 150:145:591600030 150:146:20260275 150:147:551300 150:148:11175 150:149:150 150:150:1 # binomial(151, k) for 0 <= k <= 151 151:0:1 151:1:151 151:2:11325 151:3:562475 151:4:20811575 151:5:611860305 151:6:14888600755 151:7:308406729925 151:8:5551321138650 151:9:88204324758550 151:10:1252501411571410 151:11:16054790821051710 151:12:187305892912269950 151:13:2002732239600424850 151:14:19741217790347044950 151:15:180303122485169677210 151:16:1532576541123942256285 151:17:12170460767748953211675 151:18:90602319048797762798025 151:19:634216233341584339586175 151:20:4185827140054456641268755 151:21:26111588349863515238390805 151:22:154295749340102590045036575 151:23:865397898472749309383031225 151:24:4615455458521329650042833200 151:25:23446513729288354622217592656 151:26:113625412688089718553823718256 151:27:526043577259674622934369066000 151:28:2329621556435701901566491578000 151:29:9880808670399701168713050486000 151:30:40181955259625451419433071976400 151:31:156839244723054181346819409972400 151:32:588147167711453180050572787396500 151:33:2120894332050391770485398839399500 151:34:7360750917116065556390501854386500 151:35:24605938780073704859933963341806300 151:36:79285802735793048993120548545820300 151:37:246428846340978395519158461696468500 151:38:739286539022935186557475385089405500 151:39:2142035356656196822589608167053918500 151:40:5997698998637351103250902867750971800 151:41:16237672898749901767337810202935557800 151:42:42527238544344980819218074341021699000 151:43:107801604682176811844064421003985237000 151:44:264603938765343083617249033373418309000 151:45:629169365508704665489903257132350201400 151:46:1449825059650493359607168375131067855400 151:47:3238970877942591548058567646569406911000 151:48:7017770235542281687460229900900381640500 151:49:14751639474711326812416401628423251203500 151:50:30093344528411106697329459321983432455140 151:51:59596623477833760322162262578829934862140 151:52:114608891303526462158004351113134490119500 151:53:214080759227341882144196806796232349468500 151:54:388516933412583415743171982704273523109500 151:55:685202591654919842310685133132991486211300 151:56:1174633014265576872532603085370842547790800 151:57:1957721690442628120887671808951404246318000 151:58:3172859291407017989024847414507448261274000 151:59:5001286679675469033547640839816825225398000 151:60:7668639575502385851439715954385798678943600 151:61:11440101661815034630836297571296847209571600 151:62:16606599186505695431859141635753487884862000 151:63:23460116311095347514848628660032705107186000 151:64:32257659927756102832916864407544969522380750 151:65:43175637134073553022519495437790959206878850 151:66:56259163538338266059646615267424583208963350 151:67:71373565682966456941342720861658053324804250 151:68:88167345843664446809893949299695242342405250 151:69:106056372536581870800307214374995726295936750 151:70:124237464971424477223217022553566422232383050 151:71:141735699474442009226487025730125073251028550 151:72:157484110527157788029430028589027859167809500 151:73:170428010022540619922259893952509601017218500 151:74:179640334888623896674814482814807417288419500 151:75:184430743818987200586142869023202281749444020 151:76:184430743818987200586142869023202281749444020 151:77:179640334888623896674814482814807417288419500 151:78:170428010022540619922259893952509601017218500 151:79:157484110527157788029430028589027859167809500 151:80:141735699474442009226487025730125073251028550 151:81:124237464971424477223217022553566422232383050 151:82:106056372536581870800307214374995726295936750 151:83:88167345843664446809893949299695242342405250 151:84:71373565682966456941342720861658053324804250 151:85:56259163538338266059646615267424583208963350 151:86:43175637134073553022519495437790959206878850 151:87:32257659927756102832916864407544969522380750 151:88:23460116311095347514848628660032705107186000 151:89:16606599186505695431859141635753487884862000 151:90:11440101661815034630836297571296847209571600 151:91:7668639575502385851439715954385798678943600 151:92:5001286679675469033547640839816825225398000 151:93:3172859291407017989024847414507448261274000 151:94:1957721690442628120887671808951404246318000 151:95:1174633014265576872532603085370842547790800 151:96:685202591654919842310685133132991486211300 151:97:388516933412583415743171982704273523109500 151:98:214080759227341882144196806796232349468500 151:99:114608891303526462158004351113134490119500 151:100:59596623477833760322162262578829934862140 151:101:30093344528411106697329459321983432455140 151:102:14751639474711326812416401628423251203500 151:103:7017770235542281687460229900900381640500 151:104:3238970877942591548058567646569406911000 151:105:1449825059650493359607168375131067855400 151:106:629169365508704665489903257132350201400 151:107:264603938765343083617249033373418309000 151:108:107801604682176811844064421003985237000 151:109:42527238544344980819218074341021699000 151:110:16237672898749901767337810202935557800 151:111:5997698998637351103250902867750971800 151:112:2142035356656196822589608167053918500 151:113:739286539022935186557475385089405500 151:114:246428846340978395519158461696468500 151:115:79285802735793048993120548545820300 151:116:24605938780073704859933963341806300 151:117:7360750917116065556390501854386500 151:118:2120894332050391770485398839399500 151:119:588147167711453180050572787396500 151:120:156839244723054181346819409972400 151:121:40181955259625451419433071976400 151:122:9880808670399701168713050486000 151:123:2329621556435701901566491578000 151:124:526043577259674622934369066000 151:125:113625412688089718553823718256 151:126:23446513729288354622217592656 151:127:4615455458521329650042833200 151:128:865397898472749309383031225 151:129:154295749340102590045036575 151:130:26111588349863515238390805 151:131:4185827140054456641268755 151:132:634216233341584339586175 151:133:90602319048797762798025 151:134:12170460767748953211675 151:135:1532576541123942256285 151:136:180303122485169677210 151:137:19741217790347044950 151:138:2002732239600424850 151:139:187305892912269950 151:140:16054790821051710 151:141:1252501411571410 151:142:88204324758550 151:143:5551321138650 151:144:308406729925 151:145:14888600755 151:146:611860305 151:147:20811575 151:148:562475 151:149:11325 151:150:151 151:151:1 # binomial(152, k) for 0 <= k <= 152 152:0:1 152:1:152 152:2:11476 152:3:573800 152:4:21374050 152:5:632671880 152:6:15500461060 152:7:323295330680 152:8:5859727868575 152:9:93755645897200 152:10:1340705736329960 152:11:17307292232623120 152:12:203360683733321660 152:13:2190038132512694800 152:14:21743950029947469800 152:15:200044340275516722160 152:16:1712879663609111933495 152:17:13703037308872895467960 152:18:102772779816546716009700 152:19:724818552390382102384200 152:20:4820043373396040980854930 152:21:30297415489917971879659560 152:22:180407337689966105283427380 152:23:1019693647812851899428067800 152:24:5480853356994078959425864425 152:25:28061969187809684272260425856 152:26:137071926417378073176041310912 152:27:639668989947764341488192784256 152:28:2855665133695376524500860644000 152:29:12210430226835403070279542064000 152:30:50062763930025152588146122462400 152:31:197021199982679632766252481948800 152:32:744986412434507361397392197368900 152:33:2709041499761844950535971626796000 152:34:9481645249166457326875900693786000 152:35:31966689697189770416324465196192800 152:36:103891741515866753853054511887626600 152:37:325714649076771444512279010242288800 152:38:985715385363913582076633846785874000 152:39:2881321895679132009147083552143324000 152:40:8139734355293547925840511034804890300 152:41:22235371897387252870588713070686529600 152:42:58764911443094882586555884543957256800 152:43:150328843226521792663282495345006936000 152:44:372405543447519895461313454377403546000 152:45:893773304274047749107152290505768510400 152:46:2078994425159198025097071632263418056800 152:47:4688795937593084907665736021700474766400 152:48:10256741113484873235518797547469788551500 152:49:21769409710253608499876631529323632844000 152:50:44844984003122433509745860950406683658640 152:51:89689968006244867019491721900813367317280 152:52:174205514781360222480166613691964424981640 152:53:328689650530868344302201157909366839588000 152:54:602597692639925297887368789500505872578000 152:55:1073719525067503258053857115837265009320800 152:56:1859835605920496714843288218503834034002100 152:57:3132354704708204993420274894322246794108800 152:58:5130580981849646109912519223458852507592000 152:59:8174145971082487022572488254324273486672000 152:60:12669926255177854884987356794202623904341600 152:61:19108741237317420482276013525682645888515200 152:62:28046700848320730062695439207050335094433600 152:63:40066715497601042946707770295786192992048000 152:64:55717776238851450347765493067577674629566750 152:65:75433297061829655855436359845335928729259600 152:66:99434800672411819082166110705215542415842200 152:67:127632729221304723000989336129082636533767600 152:68:159540911526630903751236670161353295667209500 152:69:194223718380246317610201163674690968638342000 152:70:230293837508006348023524236928562148528319800 152:71:265973164445866486449704048283691495483411600 152:72:299219810001599797255917054319152932418838050 152:73:327912120549698407951689922541537460185028000 152:74:350068344911164516597074376767317018305638000 152:75:364071078707611097260957351838009699037863520 152:76:368861487637974401172285738046404563498888040 152:77:364071078707611097260957351838009699037863520 152:78:350068344911164516597074376767317018305638000 152:79:327912120549698407951689922541537460185028000 152:80:299219810001599797255917054319152932418838050 152:81:265973164445866486449704048283691495483411600 152:82:230293837508006348023524236928562148528319800 152:83:194223718380246317610201163674690968638342000 152:84:159540911526630903751236670161353295667209500 152:85:127632729221304723000989336129082636533767600 152:86:99434800672411819082166110705215542415842200 152:87:75433297061829655855436359845335928729259600 152:88:55717776238851450347765493067577674629566750 152:89:40066715497601042946707770295786192992048000 152:90:28046700848320730062695439207050335094433600 152:91:19108741237317420482276013525682645888515200 152:92:12669926255177854884987356794202623904341600 152:93:8174145971082487022572488254324273486672000 152:94:5130580981849646109912519223458852507592000 152:95:3132354704708204993420274894322246794108800 152:96:1859835605920496714843288218503834034002100 152:97:1073719525067503258053857115837265009320800 152:98:602597692639925297887368789500505872578000 152:99:328689650530868344302201157909366839588000 152:100:174205514781360222480166613691964424981640 152:101:89689968006244867019491721900813367317280 152:102:44844984003122433509745860950406683658640 152:103:21769409710253608499876631529323632844000 152:104:10256741113484873235518797547469788551500 152:105:4688795937593084907665736021700474766400 152:106:2078994425159198025097071632263418056800 152:107:893773304274047749107152290505768510400 152:108:372405543447519895461313454377403546000 152:109:150328843226521792663282495345006936000 152:110:58764911443094882586555884543957256800 152:111:22235371897387252870588713070686529600 152:112:8139734355293547925840511034804890300 152:113:2881321895679132009147083552143324000 152:114:985715385363913582076633846785874000 152:115:325714649076771444512279010242288800 152:116:103891741515866753853054511887626600 152:117:31966689697189770416324465196192800 152:118:9481645249166457326875900693786000 152:119:2709041499761844950535971626796000 152:120:744986412434507361397392197368900 152:121:197021199982679632766252481948800 152:122:50062763930025152588146122462400 152:123:12210430226835403070279542064000 152:124:2855665133695376524500860644000 152:125:639668989947764341488192784256 152:126:137071926417378073176041310912 152:127:28061969187809684272260425856 152:128:5480853356994078959425864425 152:129:1019693647812851899428067800 152:130:180407337689966105283427380 152:131:30297415489917971879659560 152:132:4820043373396040980854930 152:133:724818552390382102384200 152:134:102772779816546716009700 152:135:13703037308872895467960 152:136:1712879663609111933495 152:137:200044340275516722160 152:138:21743950029947469800 152:139:2190038132512694800 152:140:203360683733321660 152:141:17307292232623120 152:142:1340705736329960 152:143:93755645897200 152:144:5859727868575 152:145:323295330680 152:146:15500461060 152:147:632671880 152:148:21374050 152:149:573800 152:150:11476 152:151:152 152:152:1 # binomial(153, k) for 0 <= k <= 153 153:0:1 153:1:153 153:2:11628 153:3:585276 153:4:21947850 153:5:654045930 153:6:16133132940 153:7:338795791740 153:8:6183023199255 153:9:99615373765775 153:10:1434461382227160 153:11:18647997968953080 153:12:220667975965944780 153:13:2393398816246016460 153:14:23933988162460164600 153:15:221788290305464191960 153:16:1912924003884628655655 153:17:15415916972482007401455 153:18:116475817125419611477660 153:19:827591332206928818393900 153:20:5544861925786423083239130 153:21:35117458863314012860514490 153:22:210704753179884077163086940 153:23:1200100985502818004711495180 153:24:6500547004806930858853932225 153:25:33542822544803763231686290281 153:26:165133895605187757448301736768 153:27:776740916365142414664234095168 153:28:3495334123643140865989053428256 153:29:15066095360530779594780402708000 153:30:62273194156860555658425664526400 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153:71:496267001953872834473228285212253644011731400 153:72:565192974447466283705621102602844427902249650 153:73:627131930551298205207606976860690392603866050 153:74:677980465460862924548764299308854478490666000 153:75:714139423618775613858031728605326717343501520 153:76:732932566345585498433243089884414262536751560 153:77:732932566345585498433243089884414262536751560 153:78:714139423618775613858031728605326717343501520 153:79:677980465460862924548764299308854478490666000 153:80:627131930551298205207606976860690392603866050 153:81:565192974447466283705621102602844427902249650 153:82:496267001953872834473228285212253644011731400 153:83:424517555888252665633725400603253117166661800 153:84:353764629906877221361437833836044264305551500 153:85:287173640747935626752226006290435932200977100 153:86:227067529893716542083155446834298178949609800 153:87:174868097734241474937602470550551471145101800 153:88:131151073300681106203201852912913603358826350 153:89:95784491736452493294473263363363867621614750 153:90:68113416345921773009403209502836528086481600 153:91:47155442085638150544971452732732980982948800 153:92:31778667492495275367263370319885269792856800 153:93:20844072226260341907559845048526897391013600 153:94:13304726952932133132485007477783125994264000 153:95:8262935686557851103332794117781099301700800 153:96:4992190310628701708263563112826080828110900 153:97:2933555130987999972897145334341099043322900 153:98:1676317217707428555941225905337770881898800 153:99:931287343170793642189569947409872712166000 153:100:502895165312228566782367771601331264569640 153:101:263895482787605089499658335592777792298920 153:102:134534952009367300529237582851220050975920 153:103:66614393713376042009622492479730316502640 153:104:32026150823738481735395429076793421395500 153:105:14945537051077958143184533569170263317900 153:106:6767790362752282932762807653963892823200 153:107:2972767729433245774204223922769186567200 153:108:1266178847721567644568465744883172056400 153:109:522734386674041688124595949722410482000 153:110:209093754669616675249838379888964192800 153:111:81000283340482135457144597614643786400 153:112:30375106252680800796429224105491419900 153:113:11021056250972679934987594586948214300 153:114:3867037281043045591223717398929198000 153:115:1311430034440685026588912857028162800 153:116:429606390592638198365333522129915400 153:117:135858431213056524269378977083819400 153:118:41448334946356227743200365889978800 153:119:12190686748928302277411872320582000 153:120:3454027912196352311933363824164900 153:121:942007612417186994163644679317700 153:122:247083963912704785354398604411200 153:123:62273194156860555658425664526400 153:124:15066095360530779594780402708000 153:125:3495334123643140865989053428256 153:126:776740916365142414664234095168 153:127:165133895605187757448301736768 153:128:33542822544803763231686290281 153:129:6500547004806930858853932225 153:130:1200100985502818004711495180 153:131:210704753179884077163086940 153:132:35117458863314012860514490 153:133:5544861925786423083239130 153:134:827591332206928818393900 153:135:116475817125419611477660 153:136:15415916972482007401455 153:137:1912924003884628655655 153:138:221788290305464191960 153:139:23933988162460164600 153:140:2393398816246016460 153:141:220667975965944780 153:142:18647997968953080 153:143:1434461382227160 153:144:99615373765775 153:145:6183023199255 153:146:338795791740 153:147:16133132940 153:148:654045930 153:149:21947850 153:150:585276 153:151:11628 153:152:153 153:153:1 # binomial(154, k) for 0 <= k <= 154 154:0:1 154:1:154 154:2:11781 154:3:596904 154:4:22533126 154:5:675993780 154:6:16787178870 154:7:354928924680 154:8:6521818990995 154:9:105798396965030 154:10:1534076755992935 154:11:20082459351180240 154:12:239315973934897860 154:13:2614066792211961240 154:14:26327386978706181060 154:15:245722278467924356560 154:16:2134712294190092847615 154:17:17328840976366636057110 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154:43:290094038010098810706982977503607979200 154:44:731828141343658363374434329611374674800 154:45:1788913234395609332693061694605582538400 154:46:4238946577154813418772689667652358623600 154:47:9740558092185528706967031576733079390400 154:48:21713327413830241075947341223134156141100 154:49:46971687874816439878579962645963684713400 154:50:98640544537114523745017921556523737898140 154:51:201149345722743342538860075330950367478560 154:52:398430434796972390028895918443997843274840 154:53:766790648099833656282026107194109056868560 154:54:1434182508483022208971937719011203976735640 154:55:2607604560878222198130795852747643594064800 154:56:4609872348695428528838371239678869925221700 154:57:7925745441616701681160708447167179871433800 154:58:13255125997186552811596357230607180129811700 154:59:21567662639489984235817801595564225295964800 154:60:34148799179192475040044852526310023385277600 154:61:52622739718755617274823215368412167183870400 154:62:78934109578133425912234823052618250775805600 154:63:115268858431559923554374662235569509069430400 154:64:163897908082374266303876472866200395708096350 154:65:226935565037133599497675116276277470980441100 154:66:306019171034922581140804323463465074503928150 154:67:401935627627958017020757917384849650094711600 154:68:514241170641652168835381453124734111150586900 154:69:640938270654812848113663840126480196506528600 154:70:778282185795129886995163234439297381472213300 154:71:920784557842125500106953685815506761178393200 154:72:1061459976401339118178849387815098071913981050 154:73:1192324904998764488913228079463534820506115700 154:74:1305112396012161129756371276169544871094532050 154:75:1392119889079638538406796027914181195834167520 154:76:1447071989964361112291274818489740979880253080 154:77:1465865132691170996866486179768828525073503120 154:78:1447071989964361112291274818489740979880253080 154:79:1392119889079638538406796027914181195834167520 154:80:1305112396012161129756371276169544871094532050 154:81:1192324904998764488913228079463534820506115700 154:82:1061459976401339118178849387815098071913981050 154:83:920784557842125500106953685815506761178393200 154:84:778282185795129886995163234439297381472213300 154:85:640938270654812848113663840126480196506528600 154:86:514241170641652168835381453124734111150586900 154:87:401935627627958017020757917384849650094711600 154:88:306019171034922581140804323463465074503928150 154:89:226935565037133599497675116276277470980441100 154:90:163897908082374266303876472866200395708096350 154:91:115268858431559923554374662235569509069430400 154:92:78934109578133425912234823052618250775805600 154:93:52622739718755617274823215368412167183870400 154:94:34148799179192475040044852526310023385277600 154:95:21567662639489984235817801595564225295964800 154:96:13255125997186552811596357230607180129811700 154:97:7925745441616701681160708447167179871433800 154:98:4609872348695428528838371239678869925221700 154:99:2607604560878222198130795852747643594064800 154:100:1434182508483022208971937719011203976735640 154:101:766790648099833656282026107194109056868560 154:102:398430434796972390028895918443997843274840 154:103:201149345722743342538860075330950367478560 154:104:98640544537114523745017921556523737898140 154:105:46971687874816439878579962645963684713400 154:106:21713327413830241075947341223134156141100 154:107:9740558092185528706967031576733079390400 154:108:4238946577154813418772689667652358623600 154:109:1788913234395609332693061694605582538400 154:110:731828141343658363374434329611374674800 154:111:290094038010098810706982977503607979200 154:112:111375389593162936253573821720135206300 154:113:41396162503653480731416818692439634200 154:114:14888093532015725526211311985877412300 154:115:5178467315483730617812630255957360800 154:116:1741036425033323224954246379158078200 154:117:565464821805694722634712499213734800 154:118:177306766159412752012579342973798200 154:119:53639021695284530020612238210560800 154:120:15644714661124654589345236144746900 154:121:4396035524613539306097008503482600 154:122:1189091576329891779518043283728900 154:123:309357158069565341012824268937600 154:124:77339289517391335253206067234400 154:125:18561429484173920460769456136256 154:126:4272075040008283280653287523424 154:127:941874811970330172112535831936 154:128:198676718149991520679988027049 154:129:40043369549610694090540222506 154:130:7700647990309748863565427405 154:131:1410805738682702081874582120 154:132:245822212043198090023601430 154:133:40662320789100435943753620 154:134:6372453257993351901633030 154:135:944067149332348429871560 154:136:131891734097901618879115 154:137:17328840976366636057110 154:138:2134712294190092847615 154:139:245722278467924356560 154:140:26327386978706181060 154:141:2614066792211961240 154:142:239315973934897860 154:143:20082459351180240 154:144:1534076755992935 154:145:105798396965030 154:146:6521818990995 154:147:354928924680 154:148:16787178870 154:149:675993780 154:150:22533126 154:151:596904 154:152:11781 154:153:154 154:154:1 # binomial(155, k) for 0 <= k <= 155 155:0:1 155:1:155 155:2:11935 155:3:608685 155:4:23130030 155:5:698526906 155:6:17463172650 155:7:371716103550 155:8:6876747915675 155:9:112320215956025 155:10:1639875152957965 155:11:21616536107173175 155:12:259398433286078100 155:13:2853382766146859100 155:14:28941453770918142300 155:15:272049665446630537620 155:16:2380434572658017204175 155:17:19463553270556728904725 155:18:149220575074268254936225 155:19:1075958883430250048750675 155:20:7316520407325700331504590 155:21:47034774047093787845386650 155:22:286484532832298525967355050 155:23:1656627950725900171898183550 155:24:9111453728992450945440009525 155:25:47744017539920442954105649911 155:26:238720087699602214770528249555 155:27:1140551530120321692792523858985 155:28:5213949851978613452765823355360 155:29:22833504524182203741422743659680 155:30:95900719001565255713975523370656 155:31:386696447586956676266030336172000 155:32:1498448734399457120530867552666500 155:33:5585127100943431085615051787211500 155:34:20040750185738193895442244648229500 155:35:69283736356409184609957474355307700 155:36:230945787854697282033191581184359000 155:37:742771587965107474647291842187533000 155:38:2306501246839017947588958878371813000 155:39:6919503740517053842766876635115439000 155:40:20066560847499456144023942241834773100 155:41:56284256035669206257628130678317046500 155:42:152771552096816416984990640412574840500 155:43:401469427603261746960556799223743185500 155:44:1021922179353757174081417307114982654000 155:45:2520741375739267696067496024216957213200 155:46:6027859811550422751465751362257941162000 155:47:13979504669340342125739721244385438014000 155:48:31453885506015769782914372799867235531500 155:49:68685015288646680954527303869097840854500 155:50:145612232411930963623597884202487422611540 155:51:299789890259857866283877996887474105376700 155:52:599579780519715732567755993774948210753400 155:53:1165221082896806046310922025638106900143400 155:54:2200973156582855865253963826205313033604200 155:55:4041787069361244407102733571758847570800440 155:56:7217476909573650726969167092426513519286500 155:57:12535617790312130209999079686846049796655500 155:58:21180871438803254492757065677774360001245500 155:59:34822788636676537047414158826171405425776500 155:60:55716461818682459275862654121874248681242400 155:61:86771538897948092314868067894722190569148000 155:62:131556849296889043187058038421030417959676000 155:63:194202968009693349466609485288187759845236000 155:64:279166766513934189858251135101769904777526750 155:65:390833473119507865801551589142477866688537450 155:66:532954736072056180638479439739742545484369250 155:67:707954798662880598161562240848314724598639750 155:68:916176798269610185856139370509583761245298500 155:69:1155179441296465016949045293251214307657115500 155:70:1419220456449942735108827074565777577978741900 155:71:1699066743637255387102116920254804142650606500 155:72:1982244534243464618285803073630604833092374250 155:73:2253784881400103607092077467278632892420096750 155:74:2497437301010925618669599355633079691600647750 155:75:2697232285091799668163167304083726066928699570 155:76:2839191879043999650698070846403922175714420600 155:77:2912937122655532109157760998258569504953756200 155:78:2912937122655532109157760998258569504953756200 155:79:2839191879043999650698070846403922175714420600 155:80:2697232285091799668163167304083726066928699570 155:81:2497437301010925618669599355633079691600647750 155:82:2253784881400103607092077467278632892420096750 155:83:1982244534243464618285803073630604833092374250 155:84:1699066743637255387102116920254804142650606500 155:85:1419220456449942735108827074565777577978741900 155:86:1155179441296465016949045293251214307657115500 155:87:916176798269610185856139370509583761245298500 155:88:707954798662880598161562240848314724598639750 155:89:532954736072056180638479439739742545484369250 155:90:390833473119507865801551589142477866688537450 155:91:279166766513934189858251135101769904777526750 155:92:194202968009693349466609485288187759845236000 155:93:131556849296889043187058038421030417959676000 155:94:86771538897948092314868067894722190569148000 155:95:55716461818682459275862654121874248681242400 155:96:34822788636676537047414158826171405425776500 155:97:21180871438803254492757065677774360001245500 155:98:12535617790312130209999079686846049796655500 155:99:7217476909573650726969167092426513519286500 155:100:4041787069361244407102733571758847570800440 155:101:2200973156582855865253963826205313033604200 155:102:1165221082896806046310922025638106900143400 155:103:599579780519715732567755993774948210753400 155:104:299789890259857866283877996887474105376700 155:105:145612232411930963623597884202487422611540 155:106:68685015288646680954527303869097840854500 155:107:31453885506015769782914372799867235531500 155:108:13979504669340342125739721244385438014000 155:109:6027859811550422751465751362257941162000 155:110:2520741375739267696067496024216957213200 155:111:1021922179353757174081417307114982654000 155:112:401469427603261746960556799223743185500 155:113:152771552096816416984990640412574840500 155:114:56284256035669206257628130678317046500 155:115:20066560847499456144023942241834773100 155:116:6919503740517053842766876635115439000 155:117:2306501246839017947588958878371813000 155:118:742771587965107474647291842187533000 155:119:230945787854697282033191581184359000 155:120:69283736356409184609957474355307700 155:121:20040750185738193895442244648229500 155:122:5585127100943431085615051787211500 155:123:1498448734399457120530867552666500 155:124:386696447586956676266030336172000 155:125:95900719001565255713975523370656 155:126:22833504524182203741422743659680 155:127:5213949851978613452765823355360 155:128:1140551530120321692792523858985 155:129:238720087699602214770528249555 155:130:47744017539920442954105649911 155:131:9111453728992450945440009525 155:132:1656627950725900171898183550 155:133:286484532832298525967355050 155:134:47034774047093787845386650 155:135:7316520407325700331504590 155:136:1075958883430250048750675 155:137:149220575074268254936225 155:138:19463553270556728904725 155:139:2380434572658017204175 155:140:272049665446630537620 155:141:28941453770918142300 155:142:2853382766146859100 155:143:259398433286078100 155:144:21616536107173175 155:145:1639875152957965 155:146:112320215956025 155:147:6876747915675 155:148:371716103550 155:149:17463172650 155:150:698526906 155:151:23130030 155:152:608685 155:153:11935 155:154:155 155:155:1 # binomial(156, k) for 0 <= k <= 156 156:0:1 156:1:156 156:2:12090 156:3:620620 156:4:23738715 156:5:721656936 156:6:18161699556 156:7:389179276200 156:8:7248464019225 156:9:119196963871700 156:10:1752195368913990 156:11:23256411260131140 156:12:281014969393251275 156:13:3112781199432937200 156:14:31794836537065001400 156:15:300991119217548679920 156:16:2652484238104647741795 156:17:21843987843214746108900 156:18:168684128344824983840950 156:19:1225179458504518303686900 156:20:8392479290755950380255265 156:21:54351294454419488176891240 156:22:333519306879392313812741700 156:23:1943112483558198697865538600 156:24:10768081679718351117338193075 156:25:56855471268912893899545659436 156:26:286464105239522657724633899466 156:27:1379271617819923907563052108540 156:28:6354501382098935145558347214345 156:29:28047454376160817194188567015040 156:30:118734223525747459455398267030336 156:31:482597166588521931980005859542656 156:32:1885145181986413796796897888838500 156:33:7083575835342888206145919339878000 156:34:25625877286681624981057296435441000 156:35:89324486542147378505399719003537200 156:36:300229524211106466643149055539666700 156:37:973717375819804756680483423371892000 156:38:3049272834804125422236250720559346000 156:39:9226004987356071790355835513487252000 156:40:26986064588016509986790818876950212100 156:41:76350816883168662401652072920151819600 156:42:209055808132485623242618771090891887000 156:43:554240979700078163945547439636318026000 156:44:1423391606957018921041974106338725839500 156:45:3542663555093024870148913331331939867200 156:46:8548601187289690447533247386474898375200 156:47:20007364480890764877205472606643379176000 156:48:45433390175356111908654094044252673545500 156:49:100138900794662450737441676668965076386000 156:50:214297247700577644578125188071585263466040 156:51:445402122671788829907475881089961527988240 156:52:899369670779573598851633990662422316130100 156:53:1764800863416521778878678019413055110896800 156:54:3366194239479661911564885851843419933747600 156:55:6242760225944100272356697397964160604404640 156:56:11259263978934895134071900664185361090086940 156:57:19753094699885780936968246779272563315942000 156:58:33716489229115384702756145364620409797901000 156:59:56003660075479791540171224503945765427022000 156:60:90539250455358996323276812948045654107018900 156:61:142488000716630551590730722016596439250390400 156:62:218328388194837135501926106315752608528824000 156:63:325759817306582392653667523709218177804912000 156:64:473369734523627539324860620389957664622762750 156:65:670000239633442055659802724244247771466064200 156:66:923788209191564046440031028882220412172906700 156:67:1240909534734936778800041680588057270083009000 156:68:1624131596932490784017701611357898485843938250 156:69:2071356239566075202805184663760798068902414000 156:70:2574399897746407752057872367816991885635857400 156:71:3118287200087198122210943994820581720629348400 156:72:3681311277880720005387919993885408975742980750 156:73:4236029415643568225377880540909237725512471000 156:74:4751222182411029225761676822911712584020744500 156:75:5194669586102725286832766659716805758529347320 156:76:5536424164135799318861238150487648242643120170 156:77:5752129001699531759855831844662491680668176800 156:78:5825874245311064218315521996517139009907512400 156:79:5752129001699531759855831844662491680668176800 156:80:5536424164135799318861238150487648242643120170 156:81:5194669586102725286832766659716805758529347320 156:82:4751222182411029225761676822911712584020744500 156:83:4236029415643568225377880540909237725512471000 156:84:3681311277880720005387919993885408975742980750 156:85:3118287200087198122210943994820581720629348400 156:86:2574399897746407752057872367816991885635857400 156:87:2071356239566075202805184663760798068902414000 156:88:1624131596932490784017701611357898485843938250 156:89:1240909534734936778800041680588057270083009000 156:90:923788209191564046440031028882220412172906700 156:91:670000239633442055659802724244247771466064200 156:92:473369734523627539324860620389957664622762750 156:93:325759817306582392653667523709218177804912000 156:94:218328388194837135501926106315752608528824000 156:95:142488000716630551590730722016596439250390400 156:96:90539250455358996323276812948045654107018900 156:97:56003660075479791540171224503945765427022000 156:98:33716489229115384702756145364620409797901000 156:99:19753094699885780936968246779272563315942000 156:100:11259263978934895134071900664185361090086940 156:101:6242760225944100272356697397964160604404640 156:102:3366194239479661911564885851843419933747600 156:103:1764800863416521778878678019413055110896800 156:104:899369670779573598851633990662422316130100 156:105:445402122671788829907475881089961527988240 156:106:214297247700577644578125188071585263466040 156:107:100138900794662450737441676668965076386000 156:108:45433390175356111908654094044252673545500 156:109:20007364480890764877205472606643379176000 156:110:8548601187289690447533247386474898375200 156:111:3542663555093024870148913331331939867200 156:112:1423391606957018921041974106338725839500 156:113:554240979700078163945547439636318026000 156:114:209055808132485623242618771090891887000 156:115:76350816883168662401652072920151819600 156:116:26986064588016509986790818876950212100 156:117:9226004987356071790355835513487252000 156:118:3049272834804125422236250720559346000 156:119:973717375819804756680483423371892000 156:120:300229524211106466643149055539666700 156:121:89324486542147378505399719003537200 156:122:25625877286681624981057296435441000 156:123:7083575835342888206145919339878000 156:124:1885145181986413796796897888838500 156:125:482597166588521931980005859542656 156:126:118734223525747459455398267030336 156:127:28047454376160817194188567015040 156:128:6354501382098935145558347214345 156:129:1379271617819923907563052108540 156:130:286464105239522657724633899466 156:131:56855471268912893899545659436 156:132:10768081679718351117338193075 156:133:1943112483558198697865538600 156:134:333519306879392313812741700 156:135:54351294454419488176891240 156:136:8392479290755950380255265 156:137:1225179458504518303686900 156:138:168684128344824983840950 156:139:21843987843214746108900 156:140:2652484238104647741795 156:141:300991119217548679920 156:142:31794836537065001400 156:143:3112781199432937200 156:144:281014969393251275 156:145:23256411260131140 156:146:1752195368913990 156:147:119196963871700 156:148:7248464019225 156:149:389179276200 156:150:18161699556 156:151:721656936 156:152:23738715 156:153:620620 156:154:12090 156:155:156 156:156:1 # binomial(157, k) for 0 <= k <= 157 157:0:1 157:1:157 157:2:12246 157:3:632710 157:4:24359335 157:5:745395651 157:6:18883356492 157:7:407340975756 157:8:7637643295425 157:9:126445427890925 157:10:1871392332785690 157:11:25008606629045130 157:12:304271380653382415 157:13:3393796168826188475 157:14:34907617736497938600 157:15:332785955754613681320 157:16:2953475357322196421715 157:17:24496472081319393850695 157:18:190528116188039729949850 157:19:1393863586849343287527850 157:20:9617658749260468683942165 157:21:62743773745175438557146505 157:22:387870601333811801989632940 157:23:2276631790437591011678280300 157:24:12711194163276549815203731675 157:25:67623552948631245016883852511 157:26:343319576508435551624179558902 157:27:1665735723059446565287686008006 157:28:7733772999918859053121399322885 157:29:34401955758259752339746914229385 157:30:146781677901908276649586834045376 157:31:601331390114269391435404126572992 157:32:2367742348574935728776903748381156 157:33:8968721017329302002942817228716500 157:34:32709453122024513187203215775319000 157:35:114950363828829003486457015438978200 157:36:389554010753253845148548774543203900 157:37:1273946900030911223323632478911558700 157:38:4022990210623930178916734143931238000 157:39:12275277822160197212592086234046598000 157:40:36212069575372581777146654390437464100 157:41:103336881471185172388442891797102031700 157:42:285406625015654285644270844011043706600 157:43:763296787832563787188166210727209913000 157:44:1977632586657097084987521545975043865500 157:45:4966055162050043791190887437670665706700 157:46:12091264742382715317682160717806838242400 157:47:28555965668180455324738719993118277551200 157:48:65440754656246876785859566650896052721500 157:49:145572290970018562646095770713217749931500 157:50:314436148495240095315566864740550339852040 157:51:659699370372366474485601069161546791454280 157:52:1344771793451362428759109871752383844118340 157:53:2664170534196095377730312010075477427026900 157:54:5130995102896183690443563871256475044644400 157:55:9608954465423762183921583249807580538152240 157:56:17502024204878995406428598062149521694491580 157:57:31012358678820676071040147443457924406028940 157:58:53469583929001165639724392143892973113843000 157:59:89720149304595176242927369868566175224923000 157:60:146542910530838787863448037451991419534040900 157:61:233027251171989547914007534964642093357409300 157:62:360816388911467687092656828332349047779214400 157:63:544088205501419528155593630024970786333736000 157:64:799129551830209931978528144099175842427674750 157:65:1143369974157069594984663344634205436088826950 157:66:1593788448825006102099833753126468183638970900 157:67:2164697743926500825240072709470277682255915700 157:68:2865041131667427562817743291945955755926947250 157:69:3695487836498565986822886275118696554746352250 157:70:4645756137312482954863057031577789954538271400 157:71:5692687097833605874268816362637573606265205800 157:72:6799598477967918127598863988705990696372329150 157:73:7917340693524288230765800534794646701255451750 157:74:8987251598054597451139557363820950309533215500 157:75:9945891768513754512594443482628518342550091820 157:76:10731093750238524605694004810204454001172467490 157:77:11288553165835331078717069995150139923311296970 157:78:11578003247010595978171353841179630690575689200 157:79:11578003247010595978171353841179630690575689200 157:80:11288553165835331078717069995150139923311296970 157:81:10731093750238524605694004810204454001172467490 157:82:9945891768513754512594443482628518342550091820 157:83:8987251598054597451139557363820950309533215500 157:84:7917340693524288230765800534794646701255451750 157:85:6799598477967918127598863988705990696372329150 157:86:5692687097833605874268816362637573606265205800 157:87:4645756137312482954863057031577789954538271400 157:88:3695487836498565986822886275118696554746352250 157:89:2865041131667427562817743291945955755926947250 157:90:2164697743926500825240072709470277682255915700 157:91:1593788448825006102099833753126468183638970900 157:92:1143369974157069594984663344634205436088826950 157:93:799129551830209931978528144099175842427674750 157:94:544088205501419528155593630024970786333736000 157:95:360816388911467687092656828332349047779214400 157:96:233027251171989547914007534964642093357409300 157:97:146542910530838787863448037451991419534040900 157:98:89720149304595176242927369868566175224923000 157:99:53469583929001165639724392143892973113843000 157:100:31012358678820676071040147443457924406028940 157:101:17502024204878995406428598062149521694491580 157:102:9608954465423762183921583249807580538152240 157:103:5130995102896183690443563871256475044644400 157:104:2664170534196095377730312010075477427026900 157:105:1344771793451362428759109871752383844118340 157:106:659699370372366474485601069161546791454280 157:107:314436148495240095315566864740550339852040 157:108:145572290970018562646095770713217749931500 157:109:65440754656246876785859566650896052721500 157:110:28555965668180455324738719993118277551200 157:111:12091264742382715317682160717806838242400 157:112:4966055162050043791190887437670665706700 157:113:1977632586657097084987521545975043865500 157:114:763296787832563787188166210727209913000 157:115:285406625015654285644270844011043706600 157:116:103336881471185172388442891797102031700 157:117:36212069575372581777146654390437464100 157:118:12275277822160197212592086234046598000 157:119:4022990210623930178916734143931238000 157:120:1273946900030911223323632478911558700 157:121:389554010753253845148548774543203900 157:122:114950363828829003486457015438978200 157:123:32709453122024513187203215775319000 157:124:8968721017329302002942817228716500 157:125:2367742348574935728776903748381156 157:126:601331390114269391435404126572992 157:127:146781677901908276649586834045376 157:128:34401955758259752339746914229385 157:129:7733772999918859053121399322885 157:130:1665735723059446565287686008006 157:131:343319576508435551624179558902 157:132:67623552948631245016883852511 157:133:12711194163276549815203731675 157:134:2276631790437591011678280300 157:135:387870601333811801989632940 157:136:62743773745175438557146505 157:137:9617658749260468683942165 157:138:1393863586849343287527850 157:139:190528116188039729949850 157:140:24496472081319393850695 157:141:2953475357322196421715 157:142:332785955754613681320 157:143:34907617736497938600 157:144:3393796168826188475 157:145:304271380653382415 157:146:25008606629045130 157:147:1871392332785690 157:148:126445427890925 157:149:7637643295425 157:150:407340975756 157:151:18883356492 157:152:745395651 157:153:24359335 157:154:632710 157:155:12246 157:156:157 157:157:1 # binomial(158, k) for 0 <= k <= 158 158:0:1 158:1:158 158:2:12403 158:3:644956 158:4:24992045 158:5:769754986 158:6:19628752143 158:7:426224332248 158:8:8044984271181 158:9:134083071186350 158:10:1997837760676615 158:11:26879998961830820 158:12:329279987282427545 158:13:3698067549479570890 158:14:38301413905324127075 158:15:367693573491111619920 158:16:3286261313076810103035 158:17:27449947438641590272410 158:18:215024588269359123800545 158:19:1584391703037383017477700 158:20:11011522336109811971470015 158:21:72361432494435907241088670 158:22:450614375078987240546779445 158:23:2664502391771402813667913240 158:24:14987825953714140826882011975 158:25:80334747111907794832087584186 158:26:410943129457066796641063411413 158:27:2009055299567882116911865566908 158:28:9399508722978305618409085330891 158:29:42135728758178611392868313552270 158:30:181183633660168028989333748274761 158:31:748113068016177668084990960618368 158:32:2969073738689205120212307874954148 158:33:11336463365904237731719720977097656 158:34:41678174139353815190146033004035500 158:35:147659816950853516673660231214297200 158:36:504504374582082848635005789982182100 158:37:1663500910784165068472181253454762600 158:38:5296937110654841402240366622842796700 158:39:16298268032784127391508820377977836000 158:40:48487347397532778989738740624484062100 158:41:139548951046557754165589546187539495800 158:42:388743506486839458032713735808145738300 158:43:1048703412848218072832437054738253619600 158:44:2740929374489660872175687756702253778500 158:45:6943687748707140876178408983645709572200 158:46:17057319904432759108873048155477503949100 158:47:40647230410563170642420880710925115793600 158:48:93996720324427332110598286644014330272700 158:49:211013045626265439431955337364113802653000 158:50:460008439465258657961662635453768089783540 158:51:974135518867606569801167933902097131306320 158:52:2004471163823728903244710940913930635572620 158:53:4008942327647457806489421881827861271145240 158:54:7795165637092279068173875881331952471671300 158:55:14739949568319945874365147121064055582796640 158:56:27110978670302757590350181311957102232643820 158:57:48514382883699671477468745505607446100520520 158:58:84481942607821841710764539587350897519871940 158:59:143189733233596341882651762012459148338766000 158:60:236263059835433964106375407320557594758963900 158:61:379570161702828335777455572416633512891450200 158:62:593843640083457235006664363296991141136623700 158:63:904904594412887215248250458357319834112950400 158:64:1343217757331629460134121774124146628761410750 158:65:1942499525987279526963191488733381278516501700 158:66:2737158422982075697084497097760673619727797850 158:67:3758486192751506927339906462596745865894886600 158:68:5029738875593928388057816001416233438182862950 158:69:6560528968165993549640629567064652310673299500 158:70:8341243973811048941685943306696486509284623650 158:71:10338443235146088829131873394215363560803477200 158:72:12492285575801524001867680351343564302637534950 158:73:14716939171492206358364664523500637397627780900 158:74:16904592291578885681905357898615597010788667250 158:75:18933143366568351963734000846449468652083307320 158:76:20676985518752279118288448292832972343722559310 158:77:22019646916073855684411074805354593924483764460 158:78:22866556412845927056888423836329770613886986170 158:79:23156006494021191956342707682359261381151378400 158:80:22866556412845927056888423836329770613886986170 158:81:22019646916073855684411074805354593924483764460 158:82:20676985518752279118288448292832972343722559310 158:83:18933143366568351963734000846449468652083307320 158:84:16904592291578885681905357898615597010788667250 158:85:14716939171492206358364664523500637397627780900 158:86:12492285575801524001867680351343564302637534950 158:87:10338443235146088829131873394215363560803477200 158:88:8341243973811048941685943306696486509284623650 158:89:6560528968165993549640629567064652310673299500 158:90:5029738875593928388057816001416233438182862950 158:91:3758486192751506927339906462596745865894886600 158:92:2737158422982075697084497097760673619727797850 158:93:1942499525987279526963191488733381278516501700 158:94:1343217757331629460134121774124146628761410750 158:95:904904594412887215248250458357319834112950400 158:96:593843640083457235006664363296991141136623700 158:97:379570161702828335777455572416633512891450200 158:98:236263059835433964106375407320557594758963900 158:99:143189733233596341882651762012459148338766000 158:100:84481942607821841710764539587350897519871940 158:101:48514382883699671477468745505607446100520520 158:102:27110978670302757590350181311957102232643820 158:103:14739949568319945874365147121064055582796640 158:104:7795165637092279068173875881331952471671300 158:105:4008942327647457806489421881827861271145240 158:106:2004471163823728903244710940913930635572620 158:107:974135518867606569801167933902097131306320 158:108:460008439465258657961662635453768089783540 158:109:211013045626265439431955337364113802653000 158:110:93996720324427332110598286644014330272700 158:111:40647230410563170642420880710925115793600 158:112:17057319904432759108873048155477503949100 158:113:6943687748707140876178408983645709572200 158:114:2740929374489660872175687756702253778500 158:115:1048703412848218072832437054738253619600 158:116:388743506486839458032713735808145738300 158:117:139548951046557754165589546187539495800 158:118:48487347397532778989738740624484062100 158:119:16298268032784127391508820377977836000 158:120:5296937110654841402240366622842796700 158:121:1663500910784165068472181253454762600 158:122:504504374582082848635005789982182100 158:123:147659816950853516673660231214297200 158:124:41678174139353815190146033004035500 158:125:11336463365904237731719720977097656 158:126:2969073738689205120212307874954148 158:127:748113068016177668084990960618368 158:128:181183633660168028989333748274761 158:129:42135728758178611392868313552270 158:130:9399508722978305618409085330891 158:131:2009055299567882116911865566908 158:132:410943129457066796641063411413 158:133:80334747111907794832087584186 158:134:14987825953714140826882011975 158:135:2664502391771402813667913240 158:136:450614375078987240546779445 158:137:72361432494435907241088670 158:138:11011522336109811971470015 158:139:1584391703037383017477700 158:140:215024588269359123800545 158:141:27449947438641590272410 158:142:3286261313076810103035 158:143:367693573491111619920 158:144:38301413905324127075 158:145:3698067549479570890 158:146:329279987282427545 158:147:26879998961830820 158:148:1997837760676615 158:149:134083071186350 158:150:8044984271181 158:151:426224332248 158:152:19628752143 158:153:769754986 158:154:24992045 158:155:644956 158:156:12403 158:157:158 158:158:1 # binomial(159, k) for 0 <= k <= 159 159:0:1 159:1:159 159:2:12561 159:3:657359 159:4:25637001 159:5:794747031 159:6:20398507129 159:7:445853084391 159:8:8471208603429 159:9:142128055457531 159:10:2131920831862965 159:11:28877836722507435 159:12:356159986244258365 159:13:4027347536761998435 159:14:41999481454803697965 159:15:405994987396435746995 159:16:3653954886567921722955 159:17:30736208751718400375445 159:18:242474535708000714072955 159:19:1799416291306742141278245 159:20:12595914039147194988947715 159:21:83372954830545719212558685 159:22:522975807573423147787868115 159:23:3115116766850390054214692685 159:24:17652328345485543640549925215 159:25:95322573065621935658969596161 159:26:491277876568974591473150995599 159:27:2419998429024948913552928978321 159:28:11408564022546187735320950897799 159:29:51535237481156917011277398883161 159:30:223319362418346640382202061827031 159:31:929296701676345697074324708893129 159:32:3717186806705382788297298835572516 159:33:14305537104593442851932028852051804 159:34:53014637505258052921865753981133156 159:35:189337991090207331863806264218332700 159:36:652164191532936365308666021196479300 159:37:2168005285366247917107187043436944700 159:38:6960438021439006470712547876297559300 159:39:21595205143438968793749187000820632700 159:40:64785615430316906381247561002461898100 159:41:188036298444090533155328286812023557900 159:42:528292457533397212198303281995685234100 159:43:1437446919335057530865150790546399357900 159:44:3789632787337878945008124811440507398100 159:45:9684617123196801748354096740347963350700 159:46:24001007653139899985051457139123213521300 159:47:57704550314995929751293928866402619742700 159:48:134643950734990502753019167354939446066300 159:49:305009765950692771542553624008128132925700 159:50:671021485091524097393617972817881892436540 159:51:1434143958332865227762830569355865221089860 159:52:2978606682691335473045878874816027766878940 159:53:6013413491471186709734132822741791906717860 159:54:11804107964739736874663297763159813742816540 159:55:22535115205412224942539023002396008054467940 159:56:41850928238622703464715328433021157815440460 159:57:75625361554002429067818926817564548333164340 159:58:132996325491521513188233285092958343620392460 159:59:227671675841418183593416301599810045858637940 159:60:379452793069030305989027169333016743097729900 159:61:615833221538262299883830979737191107650414100 159:62:973413801786285570784119935713624654028073900 159:63:1498748234496344450254914821654310975249574100 159:64:2248122351744516675382372232481466462874361150 159:65:3285717283318908987097313262857527907277912450 159:66:4679657948969355224047688586494054898244299550 159:67:6495644615733582624424403560357419485622684450 159:68:8788225068345435315397722464012979304077749550 159:69:11590267843759921937698445568480885748856162450 159:70:14901772941977042491326572873761138819957923150 159:71:18679687208957137770817816700911850070088100850 159:72:22830728810947612830999553745558927863441012150 159:73:27209224747293730360232344874844201700265315850 159:74:31621531463071092040270022422116234408416448150 159:75:35837735658147237645639358745065065662871974570 159:76:39610128885320631082022449139282440995805866630 159:77:42696632434826134802699523098187566268206323770 159:78:44886203328919782741299498641684364538370750630 159:79:46022562906867119013231131518689031995038364570 159:80:46022562906867119013231131518689031995038364570 159:81:44886203328919782741299498641684364538370750630 159:82:42696632434826134802699523098187566268206323770 159:83:39610128885320631082022449139282440995805866630 159:84:35837735658147237645639358745065065662871974570 159:85:31621531463071092040270022422116234408416448150 159:86:27209224747293730360232344874844201700265315850 159:87:22830728810947612830999553745558927863441012150 159:88:18679687208957137770817816700911850070088100850 159:89:14901772941977042491326572873761138819957923150 159:90:11590267843759921937698445568480885748856162450 159:91:8788225068345435315397722464012979304077749550 159:92:6495644615733582624424403560357419485622684450 159:93:4679657948969355224047688586494054898244299550 159:94:3285717283318908987097313262857527907277912450 159:95:2248122351744516675382372232481466462874361150 159:96:1498748234496344450254914821654310975249574100 159:97:973413801786285570784119935713624654028073900 159:98:615833221538262299883830979737191107650414100 159:99:379452793069030305989027169333016743097729900 159:100:227671675841418183593416301599810045858637940 159:101:132996325491521513188233285092958343620392460 159:102:75625361554002429067818926817564548333164340 159:103:41850928238622703464715328433021157815440460 159:104:22535115205412224942539023002396008054467940 159:105:11804107964739736874663297763159813742816540 159:106:6013413491471186709734132822741791906717860 159:107:2978606682691335473045878874816027766878940 159:108:1434143958332865227762830569355865221089860 159:109:671021485091524097393617972817881892436540 159:110:305009765950692771542553624008128132925700 159:111:134643950734990502753019167354939446066300 159:112:57704550314995929751293928866402619742700 159:113:24001007653139899985051457139123213521300 159:114:9684617123196801748354096740347963350700 159:115:3789632787337878945008124811440507398100 159:116:1437446919335057530865150790546399357900 159:117:528292457533397212198303281995685234100 159:118:188036298444090533155328286812023557900 159:119:64785615430316906381247561002461898100 159:120:21595205143438968793749187000820632700 159:121:6960438021439006470712547876297559300 159:122:2168005285366247917107187043436944700 159:123:652164191532936365308666021196479300 159:124:189337991090207331863806264218332700 159:125:53014637505258052921865753981133156 159:126:14305537104593442851932028852051804 159:127:3717186806705382788297298835572516 159:128:929296701676345697074324708893129 159:129:223319362418346640382202061827031 159:130:51535237481156917011277398883161 159:131:11408564022546187735320950897799 159:132:2419998429024948913552928978321 159:133:491277876568974591473150995599 159:134:95322573065621935658969596161 159:135:17652328345485543640549925215 159:136:3115116766850390054214692685 159:137:522975807573423147787868115 159:138:83372954830545719212558685 159:139:12595914039147194988947715 159:140:1799416291306742141278245 159:141:242474535708000714072955 159:142:30736208751718400375445 159:143:3653954886567921722955 159:144:405994987396435746995 159:145:41999481454803697965 159:146:4027347536761998435 159:147:356159986244258365 159:148:28877836722507435 159:149:2131920831862965 159:150:142128055457531 159:151:8471208603429 159:152:445853084391 159:153:20398507129 159:154:794747031 159:155:25637001 159:156:657359 159:157:12561 159:158:159 159:159:1 # binomial(160, k) for 0 <= k <= 160 160:0:1 160:1:160 160:2:12720 160:3:669920 160:4:26294360 160:5:820384032 160:6:21193254160 160:7:466251591520 160:8:8917061687820 160:9:150599264060960 160:10:2274048887320496 160:11:31009757554370400 160:12:385037822966765800 160:13:4383507523006256800 160:14:46026828991565696400 160:15:447994468851239444960 160:16:4059949873964357469950 160:17:34390163638286322098400 160:18:273210744459719114448400 160:19:2041890827014742855351200 160:20:14395330330453937130225960 160:21:95968868869692914201506400 160:22:606348762403968867000426800 160:23:3638092574423813202002560800 160:24:20767445112335933694764617900 160:25:112974901411107479299519521376 160:26:586600449634596527132120591760 160:27:2911276305593923505026079973920 160:28:13828562451571136648873879876120 160:29:62943801503703104746598349780960 160:30:274854599899503557393479460710192 160:31:1152616064094692337456526770720160 160:32:4646483508381728485371623544465645 160:33:18022723911298825640229327687624320 160:34:67320174609851495773797782833184960 160:35:242352628595465384785672018199465856 160:36:841502182623143697172472285414812000 160:37:2820169476899184282415853064633424000 160:38:9128443306805254387819734919734504000 160:39:28555643164877975264461734877118192000 160:40:86380820573755875174996748003282530800 160:41:252821913874407439536575847814485456000 160:42:716328755977487745353631568807708792000 160:43:1965739376868454743063454072542084592000 160:44:5227079706672936475873275601986906756000 160:45:13474249910534680693362221551788470748800 160:46:33685624776336701733405553879471176872000 160:47:81705557968135829736345386005525833264000 160:48:192348501049986432504313096221342065809000 160:49:439653716685683274295572791363067578992000 160:50:976031251042216868936171596826010025362240 160:51:2105165443424389325156448542173747113526400 160:52:4412750641024200700808709444171892987968800 160:53:8992020174162522182780011697557819673596800 160:54:17817521456210923584397430585901605649534400 160:55:34339223170151961817202320765555821797284480 160:56:64386043444034928407254351435417165869908400 160:57:117476289792625132532534255250585706148604800 160:58:208621687045523942256052211910522891953556800 160:59:360668001332939696781649586692768389479030400 160:60:607124468910448489582443470932826788956367840 160:61:995286014607292605872858149070207850748144000 160:62:1589247023324547870667950915450815761678488000 160:63:2472162036282630021039034757367935629277648000 160:64:3746870586240861125637287054135777438123935250 160:65:5533839635063425662479685495338994370152273600 160:66:7965375232288264211145001849351582805522212000 160:67:11175302564702937848472092146851474383866984000 160:68:15283869684079017939822126024370398789700434000 160:69:20378492912105357253096168032493865052933912000 160:70:26492040785736964429025018442242024568814085600 160:71:33581460150934180262144389574672988890046024000 160:72:41510416019904750601817370446470777933529113000 160:73:50039953558241343191231898620403129563706328000 160:74:58830756210364822400502367296960436108681764000 160:75:67459267121218329685909381167181300071288422720 160:76:75447864543467868727661807884347506658677841200 160:77:82306761320146765884721972237470007264012190400 160:78:87582835763745917543999021739871930806577074400 160:79:90908766235786901754530630160373396533409115200 160:80:92045125813734238026462263037378063990076729140 160:81:90908766235786901754530630160373396533409115200 160:82:87582835763745917543999021739871930806577074400 160:83:82306761320146765884721972237470007264012190400 160:84:75447864543467868727661807884347506658677841200 160:85:67459267121218329685909381167181300071288422720 160:86:58830756210364822400502367296960436108681764000 160:87:50039953558241343191231898620403129563706328000 160:88:41510416019904750601817370446470777933529113000 160:89:33581460150934180262144389574672988890046024000 160:90:26492040785736964429025018442242024568814085600 160:91:20378492912105357253096168032493865052933912000 160:92:15283869684079017939822126024370398789700434000 160:93:11175302564702937848472092146851474383866984000 160:94:7965375232288264211145001849351582805522212000 160:95:5533839635063425662479685495338994370152273600 160:96:3746870586240861125637287054135777438123935250 160:97:2472162036282630021039034757367935629277648000 160:98:1589247023324547870667950915450815761678488000 160:99:995286014607292605872858149070207850748144000 160:100:607124468910448489582443470932826788956367840 160:101:360668001332939696781649586692768389479030400 160:102:208621687045523942256052211910522891953556800 160:103:117476289792625132532534255250585706148604800 160:104:64386043444034928407254351435417165869908400 160:105:34339223170151961817202320765555821797284480 160:106:17817521456210923584397430585901605649534400 160:107:8992020174162522182780011697557819673596800 160:108:4412750641024200700808709444171892987968800 160:109:2105165443424389325156448542173747113526400 160:110:976031251042216868936171596826010025362240 160:111:439653716685683274295572791363067578992000 160:112:192348501049986432504313096221342065809000 160:113:81705557968135829736345386005525833264000 160:114:33685624776336701733405553879471176872000 160:115:13474249910534680693362221551788470748800 160:116:5227079706672936475873275601986906756000 160:117:1965739376868454743063454072542084592000 160:118:716328755977487745353631568807708792000 160:119:252821913874407439536575847814485456000 160:120:86380820573755875174996748003282530800 160:121:28555643164877975264461734877118192000 160:122:9128443306805254387819734919734504000 160:123:2820169476899184282415853064633424000 160:124:841502182623143697172472285414812000 160:125:242352628595465384785672018199465856 160:126:67320174609851495773797782833184960 160:127:18022723911298825640229327687624320 160:128:4646483508381728485371623544465645 160:129:1152616064094692337456526770720160 160:130:274854599899503557393479460710192 160:131:62943801503703104746598349780960 160:132:13828562451571136648873879876120 160:133:2911276305593923505026079973920 160:134:586600449634596527132120591760 160:135:112974901411107479299519521376 160:136:20767445112335933694764617900 160:137:3638092574423813202002560800 160:138:606348762403968867000426800 160:139:95968868869692914201506400 160:140:14395330330453937130225960 160:141:2041890827014742855351200 160:142:273210744459719114448400 160:143:34390163638286322098400 160:144:4059949873964357469950 160:145:447994468851239444960 160:146:46026828991565696400 160:147:4383507523006256800 160:148:385037822966765800 160:149:31009757554370400 160:150:2274048887320496 160:151:150599264060960 160:152:8917061687820 160:153:466251591520 160:154:21193254160 160:155:820384032 160:156:26294360 160:157:669920 160:158:12720 160:159:160 160:160:1 # binomial(161, k) for 0 <= k <= 161 161:0:1 161:1:161 161:2:12880 161:3:682640 161:4:26964280 161:5:846678392 161:6:22013638192 161:7:487444845680 161:8:9383313279340 161:9:159516325748780 161:10:2424648151381456 161:11:33283806441690896 161:12:416047580521136200 161:13:4768545345973022600 161:14:50410336514571953200 161:15:494021297842805141360 161:16:4507944342815596914910 161:17:38450113512250679568350 161:18:307600908098005436546800 161:19:2315101571474461969799600 161:20:16437221157468679985577160 161:21:110364199200146851331732360 161:22:702317631273661781201933200 161:23:4244441336827782069002987600 161:24:24405537686759746896767178700 161:25:133742346523443412994284139276 161:26:699575351045704006431640113136 161:27:3497876755228520032158200565680 161:28:16739838757165060153899959850040 161:29:76772363955274241395472229657080 161:30:337798401403206662140077810491152 161:31:1427470663994195894850006231430352 161:32:5799099572476420822828150315185805 161:33:22669207419680554125600951232089965 161:34:85342898521150321414027110520809280 161:35:309672803205316880559469801032650816 161:36:1083854811218609081958144303614277856 161:37:3661671659522327979588325350048236000 161:38:11948612783704438670235587984367928000 161:39:37684086471683229652281469796852696000 161:40:114936463738633850439458482880400722800 161:41:339202734448163314711572595817767986800 161:42:969150669851895184890207416622194248000 161:43:2682068132845942488417085641349793384000 161:44:7192819083541391218936729674528991348000 161:45:18701329617207617169235497153775377504800 161:46:47159874686871382426767775431259647620800 161:47:115391182744472531469750939884997010136000 161:48:274054059018122262240658482226867899073000 161:49:632002217735669706799885887584409644801000 161:50:1415684967727900143231744388189077604354240 161:51:3081196694466606194092620138999757138888640 161:52:6517916084448590025965157986345640101495200 161:53:13404770815186722883588721141729712661565600 161:54:26809541630373445767177442283459425323131200 161:55:52156744626362885401599751351457427446818880 161:56:98725266614186890224456672200972987667192880 161:57:181862333236660060939788606686002872018513200 161:58:326097976838149074788586467161108598102161600 161:59:569289688378463639037701798603291281432587200 161:60:967792470243388186364093057625595178435398240 161:61:1602410483517741095455301620003034639704511840 161:62:2584533037931840476540809064521023612426632000 161:63:4061409059607177891706985672818751390956136000 161:64:6219032622523491146676321811503713067401583250 161:65:9280710221304286788116972549474771808276208850 161:66:13499214867351689873624687344690577175674485600 161:67:19140677796991202059617093996203057189389196000 161:68:26459172248781955788294218171221873173567418000 161:69:35662362596184375192918294056864263842634346000 161:70:46870533697842321682121186474735889621747997600 161:71:60073500936671144691169408016915013458860109600 161:72:75091876170838930863961760021143766823575137000 161:73:91550369578146093793049269066873907497235441000 161:74:108870709768606165591734265917363565672388092000 161:75:126290023331583152086411748464141736179970186720 161:76:142907131664686198413571189051528806729966263920 161:77:157754625863614634612383780121817513922690031600 161:78:169889597083892683428720993977341938070589264800 161:79:178491601999532819298529651900245327339986189600 161:80:182953892049521139780992893197751460523485844340 161:81:182953892049521139780992893197751460523485844340 161:82:178491601999532819298529651900245327339986189600 161:83:169889597083892683428720993977341938070589264800 161:84:157754625863614634612383780121817513922690031600 161:85:142907131664686198413571189051528806729966263920 161:86:126290023331583152086411748464141736179970186720 161:87:108870709768606165591734265917363565672388092000 161:88:91550369578146093793049269066873907497235441000 161:89:75091876170838930863961760021143766823575137000 161:90:60073500936671144691169408016915013458860109600 161:91:46870533697842321682121186474735889621747997600 161:92:35662362596184375192918294056864263842634346000 161:93:26459172248781955788294218171221873173567418000 161:94:19140677796991202059617093996203057189389196000 161:95:13499214867351689873624687344690577175674485600 161:96:9280710221304286788116972549474771808276208850 161:97:6219032622523491146676321811503713067401583250 161:98:4061409059607177891706985672818751390956136000 161:99:2584533037931840476540809064521023612426632000 161:100:1602410483517741095455301620003034639704511840 161:101:967792470243388186364093057625595178435398240 161:102:569289688378463639037701798603291281432587200 161:103:326097976838149074788586467161108598102161600 161:104:181862333236660060939788606686002872018513200 161:105:98725266614186890224456672200972987667192880 161:106:52156744626362885401599751351457427446818880 161:107:26809541630373445767177442283459425323131200 161:108:13404770815186722883588721141729712661565600 161:109:6517916084448590025965157986345640101495200 161:110:3081196694466606194092620138999757138888640 161:111:1415684967727900143231744388189077604354240 161:112:632002217735669706799885887584409644801000 161:113:274054059018122262240658482226867899073000 161:114:115391182744472531469750939884997010136000 161:115:47159874686871382426767775431259647620800 161:116:18701329617207617169235497153775377504800 161:117:7192819083541391218936729674528991348000 161:118:2682068132845942488417085641349793384000 161:119:969150669851895184890207416622194248000 161:120:339202734448163314711572595817767986800 161:121:114936463738633850439458482880400722800 161:122:37684086471683229652281469796852696000 161:123:11948612783704438670235587984367928000 161:124:3661671659522327979588325350048236000 161:125:1083854811218609081958144303614277856 161:126:309672803205316880559469801032650816 161:127:85342898521150321414027110520809280 161:128:22669207419680554125600951232089965 161:129:5799099572476420822828150315185805 161:130:1427470663994195894850006231430352 161:131:337798401403206662140077810491152 161:132:76772363955274241395472229657080 161:133:16739838757165060153899959850040 161:134:3497876755228520032158200565680 161:135:699575351045704006431640113136 161:136:133742346523443412994284139276 161:137:24405537686759746896767178700 161:138:4244441336827782069002987600 161:139:702317631273661781201933200 161:140:110364199200146851331732360 161:141:16437221157468679985577160 161:142:2315101571474461969799600 161:143:307600908098005436546800 161:144:38450113512250679568350 161:145:4507944342815596914910 161:146:494021297842805141360 161:147:50410336514571953200 161:148:4768545345973022600 161:149:416047580521136200 161:150:33283806441690896 161:151:2424648151381456 161:152:159516325748780 161:153:9383313279340 161:154:487444845680 161:155:22013638192 161:156:846678392 161:157:26964280 161:158:682640 161:159:12880 161:160:161 161:161:1 # binomial(162, k) for 0 <= k <= 162 162:0:1 162:1:162 162:2:13041 162:3:695520 162:4:27646920 162:5:873642672 162:6:22860316584 162:7:509458483872 162:8:9870758125020 162:9:168899639028120 162:10:2584164477130236 162:11:35708454593072352 162:12:449331386962827096 162:13:5184592926494158800 162:14:55178881860544975800 162:15:544431634357377094560 162:16:5001965640658402056270 162:17:42958057855066276483260 162:18:346051021610256116115150 162:19:2622702479572467406346400 162:20:18752322728943141955376760 162:21:126801420357615531317309520 162:22:812681830473808632533665560 162:23:4946758968101443850204920800 162:24:28649979023587528965770166300 162:25:158147884210203159891051317976 162:26:833317697569147419425924252412 162:27:4197452106274224038589840678816 162:28:20237715512393580186058160415720 162:29:93512202712439301549372189507120 162:30:414570765358480903535550040148232 162:31:1765269065397402556990084041921504 162:32:7226570236470616717678156546616157 162:33:28468306992156974948429101547275770 162:34:108012105940830875539628061752899245 162:35:395015701726467201973496911553460096 162:36:1393527614423925962517614104646928672 162:37:4745526470740937061546469653662513856 162:38:15610284443226766649823913334416164000 162:39:49632699255387668322517057781220624000 162:40:152620550210317080091739952677253418800 162:41:454139198186797165151031078698168709600 162:42:1308353404300058499601780012439962234800 162:43:3651218802697837673307293057971987632000 162:44:9874887216387333707353815315878784732000 162:45:25894148700749008388172226828304368852800 162:46:65861204304078999596003272585035025125600 162:47:162551057431343913896518715316256657756800 162:48:389445241762594793710409422111864909209000 162:49:906056276753791969040544369811277543874000 162:50:2047687185463569850031630275773487249155240 162:51:4496881662194506337324364527188834743242880 162:52:9599112778915196220057778125345397240383840 162:53:19922686899635312909553879128075352763060800 162:54:40214312445560168650766163425189137984696800 162:55:78966286256736331168777193634916852769950080 162:56:150882011240549775626056423552430415114011760 162:57:280587599850846951164245278886975859685706080 162:58:507960310074809135728375073847111470120674800 162:59:895387665216612713826288265764399879534748800 162:60:1537082158621851825401794856228886459867985440 162:61:2570202953761129281819394677628629818139910080 162:62:4186943521449581571996110684524058252131143840 162:63:6645942097539018368247794737339775003382768000 162:64:10280441682130669038383307484322464458357719250 162:65:15499742843827777934793294360978484875677792100 162:66:22779925088655976661741659894165348983950694450 162:67:32639892664342891933241781340893634365063681600 162:68:45599850045773157847911312167424930362956614000 162:69:62121534844966330981212512228086137016201764000 162:70:82532896294026696875039480531600153464382343600 162:71:106944034634513466373290594491650903080608107200 162:72:135165377107510075555131168038058780282435246600 162:73:166642245748985024657011029088017674320810578000 162:74:200421079346752259384783534984237473169623533000 162:75:235160733100189317678146014381505301852358278720 162:76:269197154996269350499982937515670542909936450640 162:77:300661757528300833025954969173346320652656295520 162:78:327644222947507318041104774099159451993279296400 162:79:348381199083425502727250645877587265410575454400 162:80:361445494049053959079522545097996787863472033940 162:81:365907784099042279561985786395502921046971688680 162:82:361445494049053959079522545097996787863472033940 162:83:348381199083425502727250645877587265410575454400 162:84:327644222947507318041104774099159451993279296400 162:85:300661757528300833025954969173346320652656295520 162:86:269197154996269350499982937515670542909936450640 162:87:235160733100189317678146014381505301852358278720 162:88:200421079346752259384783534984237473169623533000 162:89:166642245748985024657011029088017674320810578000 162:90:135165377107510075555131168038058780282435246600 162:91:106944034634513466373290594491650903080608107200 162:92:82532896294026696875039480531600153464382343600 162:93:62121534844966330981212512228086137016201764000 162:94:45599850045773157847911312167424930362956614000 162:95:32639892664342891933241781340893634365063681600 162:96:22779925088655976661741659894165348983950694450 162:97:15499742843827777934793294360978484875677792100 162:98:10280441682130669038383307484322464458357719250 162:99:6645942097539018368247794737339775003382768000 162:100:4186943521449581571996110684524058252131143840 162:101:2570202953761129281819394677628629818139910080 162:102:1537082158621851825401794856228886459867985440 162:103:895387665216612713826288265764399879534748800 162:104:507960310074809135728375073847111470120674800 162:105:280587599850846951164245278886975859685706080 162:106:150882011240549775626056423552430415114011760 162:107:78966286256736331168777193634916852769950080 162:108:40214312445560168650766163425189137984696800 162:109:19922686899635312909553879128075352763060800 162:110:9599112778915196220057778125345397240383840 162:111:4496881662194506337324364527188834743242880 162:112:2047687185463569850031630275773487249155240 162:113:906056276753791969040544369811277543874000 162:114:389445241762594793710409422111864909209000 162:115:162551057431343913896518715316256657756800 162:116:65861204304078999596003272585035025125600 162:117:25894148700749008388172226828304368852800 162:118:9874887216387333707353815315878784732000 162:119:3651218802697837673307293057971987632000 162:120:1308353404300058499601780012439962234800 162:121:454139198186797165151031078698168709600 162:122:152620550210317080091739952677253418800 162:123:49632699255387668322517057781220624000 162:124:15610284443226766649823913334416164000 162:125:4745526470740937061546469653662513856 162:126:1393527614423925962517614104646928672 162:127:395015701726467201973496911553460096 162:128:108012105940830875539628061752899245 162:129:28468306992156974948429101547275770 162:130:7226570236470616717678156546616157 162:131:1765269065397402556990084041921504 162:132:414570765358480903535550040148232 162:133:93512202712439301549372189507120 162:134:20237715512393580186058160415720 162:135:4197452106274224038589840678816 162:136:833317697569147419425924252412 162:137:158147884210203159891051317976 162:138:28649979023587528965770166300 162:139:4946758968101443850204920800 162:140:812681830473808632533665560 162:141:126801420357615531317309520 162:142:18752322728943141955376760 162:143:2622702479572467406346400 162:144:346051021610256116115150 162:145:42958057855066276483260 162:146:5001965640658402056270 162:147:544431634357377094560 162:148:55178881860544975800 162:149:5184592926494158800 162:150:449331386962827096 162:151:35708454593072352 162:152:2584164477130236 162:153:168899639028120 162:154:9870758125020 162:155:509458483872 162:156:22860316584 162:157:873642672 162:158:27646920 162:159:695520 162:160:13041 162:161:162 162:162:1 # binomial(163, k) for 0 <= k <= 163 163:0:1 163:1:163 163:2:13203 163:3:708561 163:4:28342440 163:5:901289592 163:6:23733959256 163:7:532318800456 163:8:10380216608892 163:9:178770397153140 163:10:2753064116158356 163:11:38292619070202588 163:12:485039841555899448 163:13:5633924313456985896 163:14:60363474787039134600 163:15:599610516217922070360 163:16:5546397275015779150830 163:17:47960023495724678539530 163:18:389009079465322392598410 163:19:2968753501182723522461550 163:20:21375025208515609361723160 163:21:145553743086558673272686280 163:22:939483250831424163850975080 163:23:5759440798575252482738586360 163:24:33596737991688972815975087100 163:25:186797863233790688856821484276 163:26:991465581779350579316975570388 163:27:5030769803843371458015764931228 163:28:24435167618667804224648001094536 163:29:113749918224832881735430349922840 163:30:508082968070920205084922229655352 163:31:2179839830755883460525634082069736 163:32:8991839301868019274668240588537661 163:33:35694877228627591666107258093891927 163:34:136480412932987850488057163300175015 163:35:503027807667298077513124973306359341 163:36:1788543316150393164491111016200388768 163:37:6139054085164863024064083758309442528 163:38:20355810913967703711370382988078677856 163:39:65242983698614434972340971115636788000 163:40:202253249465704748414257010458474042800 163:41:606759748397114245242771031375422128400 163:42:1762492602486855664752811091138130944400 163:43:4959572206997896172909073070411949866800 163:44:13526106019085171380661108373850772364000 163:45:35769035917136342095526042144183153584800 163:46:91755353004828007984175499413339393978400 163:47:228412261735422913492521987901291682882400 163:48:551996299193938707606928137428121566965800 163:49:1295501518516386762750953791923142453083000 163:50:2953743462217361819072174645584764793029240 163:51:6544568847658076187355994802962321992398120 163:52:14095994441109702557382142652534231983626720 163:53:29521799678550509129611657253420750003444640 163:54:60136999345195481560320042553264490747757600 163:55:119180598702296499819543357060105990754646880 163:56:229848297497286106794833617187347267883961840 163:57:431469611091396726790301702439406274799717840 163:58:788547909925656086892620352734087329806380880 163:59:1403347975291421849554663339611511349655423600 163:60:2432469823838464539228083121993286339402734240 163:61:4107285112382981107221189533857516278007895520 163:62:6757146475210710853815505362152688070271053920 163:63:10832885618988599940243905421863833255513911840 163:64:16926383779669687406631102221662239461740487250 163:65:25780184525958446973176601845300949334035511350 163:66:38279667932483754596534954255143833859628486550 163:67:55419817752998868594983441235058983349014376050 163:68:78239742710116049781153093508318564728020295600 163:69:107721384890739488829123824395511067379158378000 163:70:144654431138993027856251992759686290480584107600 163:71:189476930928540163248330075023251056544990450800 163:72:242109411742023541928421762529709683363043353800 163:73:301807622856495100212142197126076454603245824600 163:74:367063325095737284041794564072255147490434111000 163:75:435581812446941577062929549365742775021981811720 163:76:504357888096458668178128951897175844762294729360 163:77:569858912524570183525937906689016863562592746160 163:78:628305980475808151067059743272505772645935591920 163:79:676025422030932820768355419976746717403854750800 163:80:709826693132479461806773190975584053274047488340 163:81:727353278148096238641508331493499708910443722620 163:82:727353278148096238641508331493499708910443722620 163:83:709826693132479461806773190975584053274047488340 163:84:676025422030932820768355419976746717403854750800 163:85:628305980475808151067059743272505772645935591920 163:86:569858912524570183525937906689016863562592746160 163:87:504357888096458668178128951897175844762294729360 163:88:435581812446941577062929549365742775021981811720 163:89:367063325095737284041794564072255147490434111000 163:90:301807622856495100212142197126076454603245824600 163:91:242109411742023541928421762529709683363043353800 163:92:189476930928540163248330075023251056544990450800 163:93:144654431138993027856251992759686290480584107600 163:94:107721384890739488829123824395511067379158378000 163:95:78239742710116049781153093508318564728020295600 163:96:55419817752998868594983441235058983349014376050 163:97:38279667932483754596534954255143833859628486550 163:98:25780184525958446973176601845300949334035511350 163:99:16926383779669687406631102221662239461740487250 163:100:10832885618988599940243905421863833255513911840 163:101:6757146475210710853815505362152688070271053920 163:102:4107285112382981107221189533857516278007895520 163:103:2432469823838464539228083121993286339402734240 163:104:1403347975291421849554663339611511349655423600 163:105:788547909925656086892620352734087329806380880 163:106:431469611091396726790301702439406274799717840 163:107:229848297497286106794833617187347267883961840 163:108:119180598702296499819543357060105990754646880 163:109:60136999345195481560320042553264490747757600 163:110:29521799678550509129611657253420750003444640 163:111:14095994441109702557382142652534231983626720 163:112:6544568847658076187355994802962321992398120 163:113:2953743462217361819072174645584764793029240 163:114:1295501518516386762750953791923142453083000 163:115:551996299193938707606928137428121566965800 163:116:228412261735422913492521987901291682882400 163:117:91755353004828007984175499413339393978400 163:118:35769035917136342095526042144183153584800 163:119:13526106019085171380661108373850772364000 163:120:4959572206997896172909073070411949866800 163:121:1762492602486855664752811091138130944400 163:122:606759748397114245242771031375422128400 163:123:202253249465704748414257010458474042800 163:124:65242983698614434972340971115636788000 163:125:20355810913967703711370382988078677856 163:126:6139054085164863024064083758309442528 163:127:1788543316150393164491111016200388768 163:128:503027807667298077513124973306359341 163:129:136480412932987850488057163300175015 163:130:35694877228627591666107258093891927 163:131:8991839301868019274668240588537661 163:132:2179839830755883460525634082069736 163:133:508082968070920205084922229655352 163:134:113749918224832881735430349922840 163:135:24435167618667804224648001094536 163:136:5030769803843371458015764931228 163:137:991465581779350579316975570388 163:138:186797863233790688856821484276 163:139:33596737991688972815975087100 163:140:5759440798575252482738586360 163:141:939483250831424163850975080 163:142:145553743086558673272686280 163:143:21375025208515609361723160 163:144:2968753501182723522461550 163:145:389009079465322392598410 163:146:47960023495724678539530 163:147:5546397275015779150830 163:148:599610516217922070360 163:149:60363474787039134600 163:150:5633924313456985896 163:151:485039841555899448 163:152:38292619070202588 163:153:2753064116158356 163:154:178770397153140 163:155:10380216608892 163:156:532318800456 163:157:23733959256 163:158:901289592 163:159:28342440 163:160:708561 163:161:13203 163:162:163 163:163:1 # binomial(164, k) for 0 <= k <= 164 164:0:1 164:1:164 164:2:13366 164:3:721764 164:4:29051001 164:5:929632032 164:6:24635248848 164:7:556052759712 164:8:10912535409348 164:9:189150613762032 164:10:2931834513311496 164:11:41045683186360944 164:12:523332460626102036 164:13:6118964155012885344 164:14:65997399100496120496 164:15:659973991004961204960 164:16:6146007791233701221190 164:17:53506420770740457690360 164:18:436969102961047071137940 164:19:3357762580648045915059960 164:20:24343778709698332884184710 164:21:166928768295074282634409440 164:22:1085036993917982837123661360 164:23:6698924049406676646589561440 164:24:39356178790264225298713673460 164:25:220394601225479661672796571376 164:26:1178263445013141268173797054664 164:27:6022235385622722037332740501616 164:28:29465937422511175682663766025764 164:29:138185085843500685960078351017376 164:30:621832886295753086820352579578192 164:31:2687922798826803665610556311725088 164:32:11171679132623902735193874670607397 164:33:44686716530495610940775498682429588 164:34:172175290161615442154164421394066942 164:35:639508220600285928001182136606534356 164:36:2291571123817691242004235989506748109 164:37:7927597401315256188555194774509831296 164:38:26494864999132566735434466746388120384 164:39:85598794612582138683711354103715465856 164:40:267496233164319183386597981574110830800 164:41:809012997862818993657028041833896171200 164:42:2369252350883969909995582122513553072800 164:43:6722064809484751837661884161550080811200 164:44:18485678226083067553570181444262722230800 164:45:49295141936221513476187150518033925948800 164:46:127524388921964350079701541557522547563200 164:47:320167614740250921476697487314631076860800 164:48:780408560929361621099450125329413249848200 164:49:1847497817710325470357881929351264020048800 164:50:4249244980733748581823128437507907246112240 164:51:9498312309875438006428169448547086785427360 164:52:20640563288767778744738137455496553976024840 164:53:43617794119660211686993799905954981987071360 164:54:89658799023745990689931699806685240751202240 164:55:179317598047491981379863399613370481502404480 164:56:349028896199582606614376974247453258638608720 164:57:661317908588682833585135319626753542683679680 164:58:1220017521017052813682922055173493604606098720 164:59:2191895885217077936447283692345598679461804480 164:60:3835817799129886388782746461604797689058157840 164:61:6539754936221445646449272655850802617410629760 164:62:10864431587593691961036694896010204348278949440 164:63:17590032094199310794059410784016521325784965760 164:64:27759269398658287346875007643526072717254399090 164:65:42706568305628134379807704066963188795775998600 164:66:64059852458442201569711556100444783193663997900 164:67:93699485685482623191518395490202817208642862600 164:68:133659560463114918376136534743377548077034671650 164:69:185961127600855538610276917903829632107178673600 164:70:252375816029732516685375817155197357859742485600 164:71:334131362067533191104582067782937347025574558400 164:72:431586342670563705176751837552960739908033804600 164:73:543917034598518642140563959655786137966289178400 164:74:668870947952232384253936761198331602093679935600 164:75:802645137542678861104724113437997922512415922720 164:76:939939700543400245241058501262918619784276541080 164:77:1074216800621028851704066858586192708324887475520 164:78:1198164893000378334592997649961522636208528338080 164:79:1304331402506740971835415163249252490049790342720 164:80:1385852115163412282575128610952330770677902239140 164:81:1437179971280575700448281522469083762184491210960 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164:138:1178263445013141268173797054664 164:139:220394601225479661672796571376 164:140:39356178790264225298713673460 164:141:6698924049406676646589561440 164:142:1085036993917982837123661360 164:143:166928768295074282634409440 164:144:24343778709698332884184710 164:145:3357762580648045915059960 164:146:436969102961047071137940 164:147:53506420770740457690360 164:148:6146007791233701221190 164:149:659973991004961204960 164:150:65997399100496120496 164:151:6118964155012885344 164:152:523332460626102036 164:153:41045683186360944 164:154:2931834513311496 164:155:189150613762032 164:156:10912535409348 164:157:556052759712 164:158:24635248848 164:159:929632032 164:160:29051001 164:161:721764 164:162:13366 164:163:164 164:164:1 # binomial(165, k) for 0 <= k <= 165 165:0:1 165:1:165 165:2:13530 165:3:735130 165:4:29772765 165:5:958683033 165:6:25564880880 165:7:580688008560 165:8:11468588169060 165:9:200063149171380 165:10:3120985127073528 165:11:43977517699672440 165:12:564378143812462980 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166:87:4774877989128526492725477321758490470791734494400 166:88:4286538194785836283242189868396826672642579830200 166:89:3756741339250508203290907974550027870405856480400 166:90:3214100923580990351704443489337246066902788322120 166:91:2684304068045662271753161595490447264666064972320 166:92:2188291359819833373711816518062864617934292097000 166:93:1741221082007179243598649702544644964807931346000 166:94:1352224882835362604071291790274032791818925407000 166:95:1024844121727853763085610619997161694852238203200 166:96:757957631694558512282066187706234170151134504450 166:97:546979734212567998554068382880787545469890879500 166:98:385118384292522366328884881824227965687984394750 166:99:264525758907995160710749211758055572391746857000 166:100:177232258468356757676201971877897233502470394190 166:101:115815139197144019867617130138031855556069762540 166:102:73803765174650600896030524107569319717103280050 166:103:45858650205608140362582073231887732639753494400 166:104:27779759259166469642717986669316607272158366800 166:105:16403286419698296360462049271405996674988749920 166:106:9439627090581095075360235901469488652587865520 166:107:5293248835839866397398263122319339431357681600 166:108:2891682234394001087467569668674453948612066800 166:109:1538693299035340028193752667735030541463301600 166:110:797322891318312560064035473280879462394619920 166:111:402252990214644174446720599132695944991880320 166:112:197534950551834192808657437074091758701369800 166:113:94397233007071207182898244265495176724548400 166:114:43886432889252403339417604790098634792991800 166:115:19844300089053260640432308252914165297700640 166:116:8724649177083761143638342421539848536058040 166:117:3728482554309299634033479667324721596606000 166:118:1548268179331827814132546641516197951133000 166:119:624511534520401135112287720947710097936000 166:120:244600351020490444585646024037853121691600 166:121:92988563197872400420989397568109451221600 166:122:34299060195936541138889531889876436926000 166:123:12269582509115510651310076448411083128000 166:124:4254774579773927080696236187755456246000 166:125:1429604258804039499113935359085833298656 166:126:465188687388616027489455156527929882896 166:127:146516122012162528343135482371001537920 166:128:44641630925580770354549092284914531085 166:129:13150247869550924600564848890129861870 166:130:3742762855179878540160764684113883763 166:131:1028545517454012423250286478077097828 166:132:272720402355230566770909293429533515 166:133:69717997594570220076773804335369470 166:134:17169357616573263153235339873635765 166:135:4069773657261810525211339821898848 166:136:927668995405265634423173047638708 166:137:203139196074145759362738623570520 166:138:42688671638769761025503044083660 166:139:8599156876874484235353131182320 166:140:1658408826254364816818103870876 166:141:305805882855414788916813479736 166:142:53839063882995561429016457700 166:143:9035926805537716603471293600 166:144:1443238309217829735276664950 166:145:218974088295118994317838820 166:146:31496272973955471785442570 166:147:4285207207340880515026200 166:148:550127952293761687739850 166:149:66458410344212821337700 166:150:7531953172344119751606 166:151:798087753360966331296 166:152:78758659871147993220 166:153:7206674759451450360 166:154:608355661512135420 166:155:47098502826745968 166:156:3321048276244908 166:157:211531737340440 166:158:12049276177620 166:159:606252889440 166:160:26523563913 166:161:988455798 166:162:30507895 166:163:748660 166:164:13695 166:165:166 166:166:1 # binomial(167, k) for 0 <= k <= 167 167:0:1 167:1:167 167:2:13861 167:3:762355 167:4:31256555 167:5:1018963693 167:6:27512019711 167:7:632776453353 167:8:12655529067060 167:9:223581013518060 167:10:3532580013585348 167:11:50419551102990876 167:12:655454164338881388 167:13:7815030420963585780 167:14:85965334630599443580 167:15:876846413232114324516 167:16:8330040925705086082902 167:17:73990363516556941089306 167:18:616586362637974509077550 167:19:4835335159634642202766050 167:20:35781480181296352300468770 167:21:250470361269074466103281390 167:22:1662212397512948729594503770 167:23:10479165114755546338747958550 167:24:62874990688533278032487751300 167:25:359644946738410350345829937436 167:26:1964214709109779605734917350612 167:27:10257565703128849052171235053196 167:28:51287828515644245260856175265980 167:29:245827867712915520388241667654180 167:30:1130808191479411393785911671209228 167:31:4997442652667076159634512869537556 167:32:21239131273835073678446679695534613 167:33:86887355211143483230009144209005235 167:34:342438399949800786847683097764902985 167:35:1301265919809242990021195771506631343 167:36:4771308372633890963411051162190981591 167:37:16893010724730803140725613574243745633 167:38:57791878795131694955113941175044392955 167:39:191157752937743298697684574655916069005 167:40:611704809400778555832590638898931420816 167:41:1894792946192655526603390515613763181552 167:42:5684378838577966579810171546841289544656 167:43:16524357088889437732006312636166539374000 167:44:46568642705052051790199608338287520054000 167:45:127287623393808941559878929457985888147600 167:46:337588914218362845006635421605962572913200 167:47:869111885540891579697933744985563219627600 167:48:2172779713852228949244834362463908049069000 167:49:5276750733641127448166026308840919547739000 167:50:12453131731393060777671822088864570132664040 167:51:28568949266137021784070650674454013833758680 167:52:63730732978305663979849913043012800090692440 167:53:138283665896323610522315849055593811517540200 167:54:291932183558905399991555681339586935425918200 167:55:599787940766478367255378036206787703693250120 167:56:1199575881532956734510756072413575407386500240 167:57:2336016190353652588257788141015910003857921520 167:58:4430375533429341115661322336409484490075368400 167:59:8184931070233867484865832790993793379969748400 167:60:14732875926420961472758499023788828083945547120 167:61:25842913510279391435822285172875485327576615440 167:62:44183045678864766003180035940722603947147116720 167:63:73638409464774610005300059901204339911911861200 167:64:119662415380258741258612597339457052356856774450 167:65:189618904371794620763647654245601175273173042590 167:66:293047397665500777543819102015929089058540156730 167:67:441758017376351918386951183635952805894217251190 167:68:649644143200517527039634093582283538079731251750 167:69:932098118505090364882953264705015511157875274250 167:70:1304937365907126510836134570587021715621025383950 167:71:1782801753422412275367676807703395865003372707650 167:72:2377069004563216367156902410271194486671163610200 167:73:3093445964842541847669941492818677756626856753000 167:74:3929512441827012617310466220607509582742223443000 167:75:4872595427865495645464978113553311882600357069320 167:76:5898404991626652623457605084827693331568853294440 167:77:6970842262831498554995351463887273937308644802520 167:78:8043279534036344486533097842946854543048436310600 167:79:9061416183914362775967667190155317143434314324600 167:80:9967557802305799053564433909170848857777745757060 167:81:10705895417291413798272910495035356180576097294620 167:82:11228134218134897398188662226500495506457858138260 167:83:11498691669174292516217304689789664072878529418700 167:84:11498691669174292516217304689789664072878529418700 167:85:11228134218134897398188662226500495506457858138260 167:86:10705895417291413798272910495035356180576097294620 167:87:9967557802305799053564433909170848857777745757060 167:88:9061416183914362775967667190155317143434314324600 167:89:8043279534036344486533097842946854543048436310600 167:90:6970842262831498554995351463887273937308644802520 167:91:5898404991626652623457605084827693331568853294440 167:92:4872595427865495645464978113553311882600357069320 167:93:3929512441827012617310466220607509582742223443000 167:94:3093445964842541847669941492818677756626856753000 167:95:2377069004563216367156902410271194486671163610200 167:96:1782801753422412275367676807703395865003372707650 167:97:1304937365907126510836134570587021715621025383950 167:98:932098118505090364882953264705015511157875274250 167:99:649644143200517527039634093582283538079731251750 167:100:441758017376351918386951183635952805894217251190 167:101:293047397665500777543819102015929089058540156730 167:102:189618904371794620763647654245601175273173042590 167:103:119662415380258741258612597339457052356856774450 167:104:73638409464774610005300059901204339911911861200 167:105:44183045678864766003180035940722603947147116720 167:106:25842913510279391435822285172875485327576615440 167:107:14732875926420961472758499023788828083945547120 167:108:8184931070233867484865832790993793379969748400 167:109:4430375533429341115661322336409484490075368400 167:110:2336016190353652588257788141015910003857921520 167:111:1199575881532956734510756072413575407386500240 167:112:599787940766478367255378036206787703693250120 167:113:291932183558905399991555681339586935425918200 167:114:138283665896323610522315849055593811517540200 167:115:63730732978305663979849913043012800090692440 167:116:28568949266137021784070650674454013833758680 167:117:12453131731393060777671822088864570132664040 167:118:5276750733641127448166026308840919547739000 167:119:2172779713852228949244834362463908049069000 167:120:869111885540891579697933744985563219627600 167:121:337588914218362845006635421605962572913200 167:122:127287623393808941559878929457985888147600 167:123:46568642705052051790199608338287520054000 167:124:16524357088889437732006312636166539374000 167:125:5684378838577966579810171546841289544656 167:126:1894792946192655526603390515613763181552 167:127:611704809400778555832590638898931420816 167:128:191157752937743298697684574655916069005 167:129:57791878795131694955113941175044392955 167:130:16893010724730803140725613574243745633 167:131:4771308372633890963411051162190981591 167:132:1301265919809242990021195771506631343 167:133:342438399949800786847683097764902985 167:134:86887355211143483230009144209005235 167:135:21239131273835073678446679695534613 167:136:4997442652667076159634512869537556 167:137:1130808191479411393785911671209228 167:138:245827867712915520388241667654180 167:139:51287828515644245260856175265980 167:140:10257565703128849052171235053196 167:141:1964214709109779605734917350612 167:142:359644946738410350345829937436 167:143:62874990688533278032487751300 167:144:10479165114755546338747958550 167:145:1662212397512948729594503770 167:146:250470361269074466103281390 167:147:35781480181296352300468770 167:148:4835335159634642202766050 167:149:616586362637974509077550 167:150:73990363516556941089306 167:151:8330040925705086082902 167:152:876846413232114324516 167:153:85965334630599443580 167:154:7815030420963585780 167:155:655454164338881388 167:156:50419551102990876 167:157:3532580013585348 167:158:223581013518060 167:159:12655529067060 167:160:632776453353 167:161:27512019711 167:162:1018963693 167:163:31256555 167:164:762355 167:165:13861 167:166:167 167:167:1 # binomial(168, k) for 0 <= k <= 168 168:0:1 168:1:168 168:2:14028 168:3:776216 168:4:32018910 168:5:1050220248 168:6:28530983404 168:7:660288473064 168:8:13288305520413 168:9:236236542585120 168:10:3756161027103408 168:11:53952131116576224 168:12:705873715441872264 168:13:8470484585302467168 168:14:93780365051563029360 168:15:962811747862713768096 168:16:9206887338937200407418 168:17:82320404442262027172208 168:18:690576726154531450166856 168:19:5451921522272616711843600 168:20:40616815340930994503234820 168:21:286251841450370818403750160 168:22:1912682758782023195697785160 168:23:12141377512268495068342462320 168:24:73354155803288824371235709850 168:25:422519937426943628378317688736 168:26:2323859655848189956080747288048 168:27:12221780412238628657906152403808 168:28:61545394218773094313027410319176 168:29:297115696228559765649097842920160 168:30:1376636059192326914174153338863408 168:31:6128250844146487553420424540746784 168:32:26236573926502149838081192565072169 168:33:108126486484978556908455823904539848 168:34:429325755160944270077692241973908220 168:35:1643704319759043776868878869271534328 168:36:6072574292443133953432246933697612934 168:37:21664319097364694104136664736434727224 168:38:74684889519862498095839554749288138588 168:39:248949631732874993652798515830960461960 168:40:802862562338521854530275213554847489821 168:41:2506497755593434082435981154512694602368 168:42:7579171784770622106413562062455052726208 168:43:22208735927467404311816484183007828918656 168:44:63092999793941489522205920974454059428000 168:45:173856266098860993350078537796273408201600 168:46:464876537612171786566514351063948461060800 168:47:1206700799759254424704569166591525792540800 168:48:3041891599393120528942768107449471268696600 168:49:7449530447493356397410860671304827596808000 168:50:17729882465034188225837848397705489680403040 168:51:41022080997530082561742472763318583966422720 168:52:92299682244442685763920563717466813924451120 168:53:202014398874629274502165762098606611608232640 168:54:430215849455229010513871530395180746943458400 168:55:891720124325383767246933717546374639119168320 168:56:1799363822299435101766134108620363111079750360 168:57:3535592071886609322768544213429485411244421760 168:58:6766391723782993703919110477425394493933289920 168:59:12615306603663208600527155127403277870045116800 168:60:22917806996654828957624331814782621463915295520 168:61:40575789436700352908580784196664313411522162560 168:62:70025959189144157439002321113598089274723732160 168:63:117821455143639376008480095841926943859058977920 168:64:193300824845033351263912657240661392268768635650 168:65:309281319752053362022260251585058227630029817040 168:66:482666302037295398307466756261530264331713199320 168:67:734805415041852695930770285651881894952757407920 168:68:1091402160576869445426585277218236343973948502940 168:69:1581742261705607891922587358287299049237606526000 168:70:2237035484412216875719087835292037226778900658200 168:71:3087739119329538786203811378290417580624398091600 168:72:4159870757985628642524579217974590351674536317850 168:73:5470514969405758214826843903089872243298020363200 168:74:7022958406669554464980407713426187339369080196000 168:75:8802107869692508262775444334160821465342580512320 168:76:10771000419492148268922583198381005214169210363760 168:77:12869247254458151178452956548714967268877498096960 168:78:15014121796867843041528449306834128480357081113120 168:79:17104695717950707262500765033102171686482750635200 168:80:19028973986220161829532101099326166001212060081660 168:81:20673453219597212851837344404206205038353843051680 168:82:21934029635426311196461572721535851687033955432880 168:83:22726825887309189914405966916290159579336387556960 168:84:22997383338348585032434609379579328145757058837400 168:85:22726825887309189914405966916290159579336387556960 168:86:21934029635426311196461572721535851687033955432880 168:87:20673453219597212851837344404206205038353843051680 168:88:19028973986220161829532101099326166001212060081660 168:89:17104695717950707262500765033102171686482750635200 168:90:15014121796867843041528449306834128480357081113120 168:91:12869247254458151178452956548714967268877498096960 168:92:10771000419492148268922583198381005214169210363760 168:93:8802107869692508262775444334160821465342580512320 168:94:7022958406669554464980407713426187339369080196000 168:95:5470514969405758214826843903089872243298020363200 168:96:4159870757985628642524579217974590351674536317850 168:97:3087739119329538786203811378290417580624398091600 168:98:2237035484412216875719087835292037226778900658200 168:99:1581742261705607891922587358287299049237606526000 168:100:1091402160576869445426585277218236343973948502940 168:101:734805415041852695930770285651881894952757407920 168:102:482666302037295398307466756261530264331713199320 168:103:309281319752053362022260251585058227630029817040 168:104:193300824845033351263912657240661392268768635650 168:105:117821455143639376008480095841926943859058977920 168:106:70025959189144157439002321113598089274723732160 168:107:40575789436700352908580784196664313411522162560 168:108:22917806996654828957624331814782621463915295520 168:109:12615306603663208600527155127403277870045116800 168:110:6766391723782993703919110477425394493933289920 168:111:3535592071886609322768544213429485411244421760 168:112:1799363822299435101766134108620363111079750360 168:113:891720124325383767246933717546374639119168320 168:114:430215849455229010513871530395180746943458400 168:115:202014398874629274502165762098606611608232640 168:116:92299682244442685763920563717466813924451120 168:117:41022080997530082561742472763318583966422720 168:118:17729882465034188225837848397705489680403040 168:119:7449530447493356397410860671304827596808000 168:120:3041891599393120528942768107449471268696600 168:121:1206700799759254424704569166591525792540800 168:122:464876537612171786566514351063948461060800 168:123:173856266098860993350078537796273408201600 168:124:63092999793941489522205920974454059428000 168:125:22208735927467404311816484183007828918656 168:126:7579171784770622106413562062455052726208 168:127:2506497755593434082435981154512694602368 168:128:802862562338521854530275213554847489821 168:129:248949631732874993652798515830960461960 168:130:74684889519862498095839554749288138588 168:131:21664319097364694104136664736434727224 168:132:6072574292443133953432246933697612934 168:133:1643704319759043776868878869271534328 168:134:429325755160944270077692241973908220 168:135:108126486484978556908455823904539848 168:136:26236573926502149838081192565072169 168:137:6128250844146487553420424540746784 168:138:1376636059192326914174153338863408 168:139:297115696228559765649097842920160 168:140:61545394218773094313027410319176 168:141:12221780412238628657906152403808 168:142:2323859655848189956080747288048 168:143:422519937426943628378317688736 168:144:73354155803288824371235709850 168:145:12141377512268495068342462320 168:146:1912682758782023195697785160 168:147:286251841450370818403750160 168:148:40616815340930994503234820 168:149:5451921522272616711843600 168:150:690576726154531450166856 168:151:82320404442262027172208 168:152:9206887338937200407418 168:153:962811747862713768096 168:154:93780365051563029360 168:155:8470484585302467168 168:156:705873715441872264 168:157:53952131116576224 168:158:3756161027103408 168:159:236236542585120 168:160:13288305520413 168:161:660288473064 168:162:28530983404 168:163:1050220248 168:164:32018910 168:165:776216 168:166:14028 168:167:168 168:168:1 # binomial(169, k) for 0 <= k <= 169 169:0:1 169:1:169 169:2:14196 169:3:790244 169:4:32795126 169:5:1082239158 169:6:29581203652 169:7:688819456468 169:8:13948593993477 169:9:249524848105533 169:10:3992397569688528 169:11:57708292143679632 169:12:759825846558448488 169:13:9176358300744339432 169:14:102250849636865496528 169:15:1056592112914276797456 169:16:10169699086799914175514 169:17:91527291781199227579626 169:18:772897130596793477339064 169:19:6142498248427148162010456 169:20:46068736863203611215078420 169:21:326868656791301812906984980 169:22:2198934600232394014101535320 169:23:14054060271050518264040247480 169:24:85495533315557319439578172170 169:25:495874093230232452749553398586 169:26:2746379593275133584459064976784 169:27:14545640068086818613986899691856 169:28:73767174631011722970933562722984 169:29:358661090447332859962125253239336 169:30:1673751755420886679823251181783568 169:31:7504886903338814467594577879610192 169:32:32364824770648637391501617105818953 169:33:134363060411480706746537016469612017 169:34:537452241645922826986148065878448068 169:35:2073030074919988046946571111245442548 169:36:7716278612202177730301125802969147262 169:37:27736893389807828057568911670132340158 169:38:96349208617227192199976219485722865812 169:39:323634521252737491748638070580248600548 169:40:1051812194071396848183073729385807951781 169:41:3309360317931955936966256368067542092189 169:42:10085669540364056188849543216967747328576 169:43:29787907712238026418230046245462881644864 169:44:85301735721408893834022405157461888346656 169:45:236949265892802482872284458770727467629600 169:46:638732803711032779916592888860221869262400 169:47:1671577337371426211271083517655474253601600 169:48:4248592399152374953647337274040997061237400 169:49:10491422046886476926353628778754298865504600 169:50:25179412912527544623248709069010317277211040 169:51:58751963462564270787580321161024073646825760 169:52:133321763241972768325663036480785397890873840 169:53:294314081119071960266086325816073425532683760 169:54:632230248329858285016037292493787358551691040 169:55:1321935973780612777760805247941555386062626720 169:56:2691083946624818869013067826166737750198918680 169:57:5334955894186044424534678322049848522324172120 169:58:10301983795669603026687654690854879905177711680 169:59:19381698327446202304446265604828672363978406720 169:60:35533113600318037558151486942185899333960412320 169:61:63493596433355181866205116011446934875437458080 169:62:110601748625844510347583105310262402686245894720 169:63:187847414332783533447482416955525033133782710080 169:64:311122279988672727272392753082588336127827613570 169:65:502582144597086713286172908825719619898798452690 169:66:791947621789348760329727007846588491961743016360 169:67:1217471717079148094238237041913412159284470607240 169:68:1826207575618722141357355562870118238926705910860 169:69:2673144422282477337349172635505535393211555028940 169:70:3818777746117824767641675193579336276016507184200 169:71:5324774603741755661922899213582454807403298749800 169:72:7247609877315167428728390596265007932298934409450 169:73:9630385727391386857351423121064462594972556681050 169:74:12493473376075312679807251616516059582667100559200 169:75:15825066276362062727755852047587008804711660708320 169:76:19573108289184656531698027532541826679511790876080 169:77:23640247673950299447375539747095972483046708460720 169:78:27883369051325994219981405855549095749234579210080 169:79:32118817514818550304029214339936300166839831748320 169:80:36133669704170869092032866132428337687694810716860 169:81:39702427205817374681369445503532371039565903133340 169:82:42607482855023524048298917125742056725387798484560 169:83:44660855522735501110867539637826011266370342989840 169:84:45724209225657774946840576295869487725093446394360 169:85:45724209225657774946840576295869487725093446394360 169:86:44660855522735501110867539637826011266370342989840 169:87:42607482855023524048298917125742056725387798484560 169:88:39702427205817374681369445503532371039565903133340 169:89:36133669704170869092032866132428337687694810716860 169:90:32118817514818550304029214339936300166839831748320 169:91:27883369051325994219981405855549095749234579210080 169:92:23640247673950299447375539747095972483046708460720 169:93:19573108289184656531698027532541826679511790876080 169:94:15825066276362062727755852047587008804711660708320 169:95:12493473376075312679807251616516059582667100559200 169:96:9630385727391386857351423121064462594972556681050 169:97:7247609877315167428728390596265007932298934409450 169:98:5324774603741755661922899213582454807403298749800 169:99:3818777746117824767641675193579336276016507184200 169:100:2673144422282477337349172635505535393211555028940 169:101:1826207575618722141357355562870118238926705910860 169:102:1217471717079148094238237041913412159284470607240 169:103:791947621789348760329727007846588491961743016360 169:104:502582144597086713286172908825719619898798452690 169:105:311122279988672727272392753082588336127827613570 169:106:187847414332783533447482416955525033133782710080 169:107:110601748625844510347583105310262402686245894720 169:108:63493596433355181866205116011446934875437458080 169:109:35533113600318037558151486942185899333960412320 169:110:19381698327446202304446265604828672363978406720 169:111:10301983795669603026687654690854879905177711680 169:112:5334955894186044424534678322049848522324172120 169:113:2691083946624818869013067826166737750198918680 169:114:1321935973780612777760805247941555386062626720 169:115:632230248329858285016037292493787358551691040 169:116:294314081119071960266086325816073425532683760 169:117:133321763241972768325663036480785397890873840 169:118:58751963462564270787580321161024073646825760 169:119:25179412912527544623248709069010317277211040 169:120:10491422046886476926353628778754298865504600 169:121:4248592399152374953647337274040997061237400 169:122:1671577337371426211271083517655474253601600 169:123:638732803711032779916592888860221869262400 169:124:236949265892802482872284458770727467629600 169:125:85301735721408893834022405157461888346656 169:126:29787907712238026418230046245462881644864 169:127:10085669540364056188849543216967747328576 169:128:3309360317931955936966256368067542092189 169:129:1051812194071396848183073729385807951781 169:130:323634521252737491748638070580248600548 169:131:96349208617227192199976219485722865812 169:132:27736893389807828057568911670132340158 169:133:7716278612202177730301125802969147262 169:134:2073030074919988046946571111245442548 169:135:537452241645922826986148065878448068 169:136:134363060411480706746537016469612017 169:137:32364824770648637391501617105818953 169:138:7504886903338814467594577879610192 169:139:1673751755420886679823251181783568 169:140:358661090447332859962125253239336 169:141:73767174631011722970933562722984 169:142:14545640068086818613986899691856 169:143:2746379593275133584459064976784 169:144:495874093230232452749553398586 169:145:85495533315557319439578172170 169:146:14054060271050518264040247480 169:147:2198934600232394014101535320 169:148:326868656791301812906984980 169:149:46068736863203611215078420 169:150:6142498248427148162010456 169:151:772897130596793477339064 169:152:91527291781199227579626 169:153:10169699086799914175514 169:154:1056592112914276797456 169:155:102250849636865496528 169:156:9176358300744339432 169:157:759825846558448488 169:158:57708292143679632 169:159:3992397569688528 169:160:249524848105533 169:161:13948593993477 169:162:688819456468 169:163:29581203652 169:164:1082239158 169:165:32795126 169:166:790244 169:167:14196 169:168:169 169:169:1 # binomial(170, k) for 0 <= k <= 170 170:0:1 170:1:170 170:2:14365 170:3:804440 170:4:33585370 170:5:1115034284 170:6:30663442810 170:7:718400660120 170:8:14637413449945 170:9:263473442099010 170:10:4241922417794061 170:11:61700689713368160 170:12:817534138702128120 170:13:9936184147302787920 170:14:111427207937609835960 170:15:1158842962551142293984 170:16:11226291199714190972970 170:17:101696990867999141755140 170:18:864424422377992704918690 170:19:6915395379023941639349520 170:20:52211235111630759377088876 170:21:372937393654505424122063400 170:22:2525803257023695827008520300 170:23:16252994871282912278141782800 170:24:99549593586607837703618419650 170:25:581369626545789772189131570756 170:26:3242253686505366037208618375370 170:27:17292019661361952198445964668640 170:28:88312814699098541584920462414840 170:29:432428265078344582933058815962320 170:30:2032412845868219539785376435022904 170:31:9178638658759701147417829061393760 170:32:39869711673987451859096194985429145 170:33:166727885182129344138038633575430970 170:34:671815302057403533732685082348060085 170:35:2610482316565910873932719177123890616 170:36:9789308687122165777247696914214589810 170:37:35453172002010005787870037473101487420 170:38:124086102007035020257545131155855205970 170:39:419983729869964683948614290065971466360 170:40:1375446715324134339931711799966056552329 170:41:4361172512003352785149330097453350043970 170:42:13395029858296012125815799585035289420765 170:43:39873577252602082607079589462430628973440 170:44:115089643433646920252252451402924769991520 170:45:322251001614211376706306863928189355976256 170:46:875682069603835262788877347630949336892000 170:47:2310310141082458991187676406515696122864000 170:48:5920169736523801164918420791696471314839000 170:49:14740014446038851880000966052795295926742000 170:50:35670834959414021549602337847764616142715640 170:51:83931376375091815410829030230034390924036800 170:52:192073726704537039113243357641809471537699600 170:53:427635844361044728591749362296858823423557600 170:54:926544329448930245282123618309860784084374800 170:55:1954166222110471062776842540435342744614317760 170:56:4013019920405431646773873074108293136261545400 170:57:8026039840810863293547746148216586272523090800 170:58:15636939689855647451222333012904728427501883800 170:59:29683682123115805331133920295683552269156118400 170:60:54914811927764239862597752547014571697938819040 170:61:99026710033673219424356602953632834209397870400 170:62:174095345059199692213788221321709337561683352800 170:63:298449162958628043795065522265787435820028604800 170:64:498969694321456260719875170038113369261610323650 170:65:813704424585759440558565661908307956026626066260 170:66:1294529766386435473615899916672308111860541469050 170:67:2009419338868496854567964049760000651246213623600 170:68:3043679292697870235595592604783530398211176518100 170:69:4499351997901199478706528198375653632138260939800 170:70:6491922168400302104990847829084871669228062213140 170:71:9143552349859580429564574407161791083419805934000 170:72:12572384481056923090651289809847462739702233159250 170:73:16877995604706554286079813717329470527271491090500 170:74:22123859103466699537158674737580522177639657240250 170:75:28318539652437375407563103664103068387378761267520 170:76:35398174565546719259453879580128835484223451584400 170:77:43213355963134955979073567279637799162558499336800 170:78:51523616725276293667356945602645068232281287670800 170:79:60002186566144544524010620195485395916074410958400 170:80:68252487218989419396062080472364637854534642465180 170:81:75836096909988243773402311635960708727260713850200 170:82:82309910060840898729668362629274427764953701617900 170:83:87268338377759025159166456763568067991758141474400 170:84:90385064748393276057708115933695498991463789384200 170:85:91448418451315549893681152591738975450186892788720 170:86:90385064748393276057708115933695498991463789384200 170:87:87268338377759025159166456763568067991758141474400 170:88:82309910060840898729668362629274427764953701617900 170:89:75836096909988243773402311635960708727260713850200 170:90:68252487218989419396062080472364637854534642465180 170:91:60002186566144544524010620195485395916074410958400 170:92:51523616725276293667356945602645068232281287670800 170:93:43213355963134955979073567279637799162558499336800 170:94:35398174565546719259453879580128835484223451584400 170:95:28318539652437375407563103664103068387378761267520 170:96:22123859103466699537158674737580522177639657240250 170:97:16877995604706554286079813717329470527271491090500 170:98:12572384481056923090651289809847462739702233159250 170:99:9143552349859580429564574407161791083419805934000 170:100:6491922168400302104990847829084871669228062213140 170:101:4499351997901199478706528198375653632138260939800 170:102:3043679292697870235595592604783530398211176518100 170:103:2009419338868496854567964049760000651246213623600 170:104:1294529766386435473615899916672308111860541469050 170:105:813704424585759440558565661908307956026626066260 170:106:498969694321456260719875170038113369261610323650 170:107:298449162958628043795065522265787435820028604800 170:108:174095345059199692213788221321709337561683352800 170:109:99026710033673219424356602953632834209397870400 170:110:54914811927764239862597752547014571697938819040 170:111:29683682123115805331133920295683552269156118400 170:112:15636939689855647451222333012904728427501883800 170:113:8026039840810863293547746148216586272523090800 170:114:4013019920405431646773873074108293136261545400 170:115:1954166222110471062776842540435342744614317760 170:116:926544329448930245282123618309860784084374800 170:117:427635844361044728591749362296858823423557600 170:118:192073726704537039113243357641809471537699600 170:119:83931376375091815410829030230034390924036800 170:120:35670834959414021549602337847764616142715640 170:121:14740014446038851880000966052795295926742000 170:122:5920169736523801164918420791696471314839000 170:123:2310310141082458991187676406515696122864000 170:124:875682069603835262788877347630949336892000 170:125:322251001614211376706306863928189355976256 170:126:115089643433646920252252451402924769991520 170:127:39873577252602082607079589462430628973440 170:128:13395029858296012125815799585035289420765 170:129:4361172512003352785149330097453350043970 170:130:1375446715324134339931711799966056552329 170:131:419983729869964683948614290065971466360 170:132:124086102007035020257545131155855205970 170:133:35453172002010005787870037473101487420 170:134:9789308687122165777247696914214589810 170:135:2610482316565910873932719177123890616 170:136:671815302057403533732685082348060085 170:137:166727885182129344138038633575430970 170:138:39869711673987451859096194985429145 170:139:9178638658759701147417829061393760 170:140:2032412845868219539785376435022904 170:141:432428265078344582933058815962320 170:142:88312814699098541584920462414840 170:143:17292019661361952198445964668640 170:144:3242253686505366037208618375370 170:145:581369626545789772189131570756 170:146:99549593586607837703618419650 170:147:16252994871282912278141782800 170:148:2525803257023695827008520300 170:149:372937393654505424122063400 170:150:52211235111630759377088876 170:151:6915395379023941639349520 170:152:864424422377992704918690 170:153:101696990867999141755140 170:154:11226291199714190972970 170:155:1158842962551142293984 170:156:111427207937609835960 170:157:9936184147302787920 170:158:817534138702128120 170:159:61700689713368160 170:160:4241922417794061 170:161:263473442099010 170:162:14637413449945 170:163:718400660120 170:164:30663442810 170:165:1115034284 170:166:33585370 170:167:804440 170:168:14365 170:169:170 170:170:1 # binomial(171, k) for 0 <= k <= 171 171:0:1 171:1:171 171:2:14535 171:3:818805 171:4:34389810 171:5:1148619654 171:6:31778477094 171:7:749064102930 171:8:15355814110065 171:9:278110855548955 171:10:4505395859893071 171:11:65942612131162221 171:12:879234828415496280 171:13:10753718286004916040 171:14:121363392084912623880 171:15:1270270170488752129944 171:16:12385134162265333266954 171:17:112923282067713332728110 171:18:966121413245991846673830 171:19:7779819801401934344268210 171:20:59126630490654701016438396 171:21:425148628766136183499152276 171:22:2898740650678201251130583700 171:23:18778798128306608105150303100 171:24:115802588457890749981760202450 171:25:680919220132397609892749990406 171:26:3823623313051155809397749946126 171:27:20534273347867318235654583044010 171:28:105604834360460493783366427083480 171:29:520741079777443124517979278377160 171:30:2464841110946564122718435250985224 171:31:11211051504627920687203205496416664 171:32:49048350332747153006514024046822905 171:33:206597596856116795997134828560860115 171:34:838543187239532877870723715923491055 171:35:3282297618623314407665404259471950701 171:36:12399791003688076651180416091338480426 171:37:45242480689132171565117734387316077230 171:38:159539274009045026045415168628956693390 171:39:544069831876999704206159421221826672330 171:40:1795430445194099023880326090032028018689 171:41:5736619227327487125081041897419406596299 171:42:17756202370299364910965129682488639464735 171:43:53268607110898094732895389047465918394205 171:44:154963220686249002859332040865355398964960 171:45:437340645047858296958559315331114125967776 171:46:1197933071218046639495184211559138692868256 171:47:3185992210686294253976553754146645459756000 171:48:8230479877606260156106097198212167437703000 171:49:20660184182562653044919386844491767241581000 171:50:50410849405452873429603303900559912069457640 171:51:119602211334505836960431368077799007066752440 171:52:276005103079628854524072387871843862461736400 171:53:619709571065581767704992719938668294961257200 171:54:1354180173809974973873872980606719607507932400 171:55:2880710551559401308058966158745203528698692560 171:56:5967186142515902709550715614543635880875863160 171:57:12039059761216294940321619222324879408784636200 171:58:23662979530666510744770079161121314700024974600 171:59:45320621812971452782356253308588280696658002200 171:60:84598494050880045193731672842698123967094937440 171:61:153941521961437459286954355500647405907336689440 171:62:273122055092872911638144824275342171771081223200 171:63:472544508017827736008853743587496773381711957600 171:64:797418857280084304514940692303900805081638928450 171:65:1312674118907215701278440831946421325288236389910 171:66:2108234190972194914174465578580616067887167535310 171:67:3303949105254932328183863966432308763106755092650 171:68:5053098631566367090163556654543531049457390141700 171:69:7543031290599069714302120803159184030349437457900 171:70:10991274166301501583697376027460525301366323152940 171:71:15635474518259882534555422236246662752647868147140 171:72:21715936830916503520215864217009253823122039093250 171:73:29450380085763477376731103527176933266973724249750 171:74:39001854708173253823238488454909992704911148330750 171:75:50442398755904074944721778401683590565018418507770 171:76:63716714217984094667016983244231903871602212851920 171:77:78611530528681675238527446859766634646781950921200 171:78:94736972688411249646430512882282867394839787007600 171:79:111525803291420838191367565798130464148355698629200 171:80:128254673785133963920072700667850033770609053423580 171:81:144088584128977663169464392108325346581795356315380 171:82:158146006970829142503070674265235136492214415468100 171:83:169578248438599923888834819392842495756711843092300 171:84:177653403126152301216874572697263566983221930858600 171:85:181833483199708825951389268525434474441650682172920 171:86:181833483199708825951389268525434474441650682172920 171:87:177653403126152301216874572697263566983221930858600 171:88:169578248438599923888834819392842495756711843092300 171:89:158146006970829142503070674265235136492214415468100 171:90:144088584128977663169464392108325346581795356315380 171:91:128254673785133963920072700667850033770609053423580 171:92:111525803291420838191367565798130464148355698629200 171:93:94736972688411249646430512882282867394839787007600 171:94:78611530528681675238527446859766634646781950921200 171:95:63716714217984094667016983244231903871602212851920 171:96:50442398755904074944721778401683590565018418507770 171:97:39001854708173253823238488454909992704911148330750 171:98:29450380085763477376731103527176933266973724249750 171:99:21715936830916503520215864217009253823122039093250 171:100:15635474518259882534555422236246662752647868147140 171:101:10991274166301501583697376027460525301366323152940 171:102:7543031290599069714302120803159184030349437457900 171:103:5053098631566367090163556654543531049457390141700 171:104:3303949105254932328183863966432308763106755092650 171:105:2108234190972194914174465578580616067887167535310 171:106:1312674118907215701278440831946421325288236389910 171:107:797418857280084304514940692303900805081638928450 171:108:472544508017827736008853743587496773381711957600 171:109:273122055092872911638144824275342171771081223200 171:110:153941521961437459286954355500647405907336689440 171:111:84598494050880045193731672842698123967094937440 171:112:45320621812971452782356253308588280696658002200 171:113:23662979530666510744770079161121314700024974600 171:114:12039059761216294940321619222324879408784636200 171:115:5967186142515902709550715614543635880875863160 171:116:2880710551559401308058966158745203528698692560 171:117:1354180173809974973873872980606719607507932400 171:118:619709571065581767704992719938668294961257200 171:119:276005103079628854524072387871843862461736400 171:120:119602211334505836960431368077799007066752440 171:121:50410849405452873429603303900559912069457640 171:122:20660184182562653044919386844491767241581000 171:123:8230479877606260156106097198212167437703000 171:124:3185992210686294253976553754146645459756000 171:125:1197933071218046639495184211559138692868256 171:126:437340645047858296958559315331114125967776 171:127:154963220686249002859332040865355398964960 171:128:53268607110898094732895389047465918394205 171:129:17756202370299364910965129682488639464735 171:130:5736619227327487125081041897419406596299 171:131:1795430445194099023880326090032028018689 171:132:544069831876999704206159421221826672330 171:133:159539274009045026045415168628956693390 171:134:45242480689132171565117734387316077230 171:135:12399791003688076651180416091338480426 171:136:3282297618623314407665404259471950701 171:137:838543187239532877870723715923491055 171:138:206597596856116795997134828560860115 171:139:49048350332747153006514024046822905 171:140:11211051504627920687203205496416664 171:141:2464841110946564122718435250985224 171:142:520741079777443124517979278377160 171:143:105604834360460493783366427083480 171:144:20534273347867318235654583044010 171:145:3823623313051155809397749946126 171:146:680919220132397609892749990406 171:147:115802588457890749981760202450 171:148:18778798128306608105150303100 171:149:2898740650678201251130583700 171:150:425148628766136183499152276 171:151:59126630490654701016438396 171:152:7779819801401934344268210 171:153:966121413245991846673830 171:154:112923282067713332728110 171:155:12385134162265333266954 171:156:1270270170488752129944 171:157:121363392084912623880 171:158:10753718286004916040 171:159:879234828415496280 171:160:65942612131162221 171:161:4505395859893071 171:162:278110855548955 171:163:15355814110065 171:164:749064102930 171:165:31778477094 171:166:1148619654 171:167:34389810 171:168:818805 171:169:14535 171:170:171 171:171:1 # binomial(172, k) for 0 <= k <= 172 172:0:1 172:1:172 172:2:14706 172:3:833340 172:4:35208615 172:5:1183009464 172:6:32927096748 172:7:780842580024 172:8:16104878212995 172:9:293466669659020 172:10:4783506715442026 172:11:70448007991055292 172:12:945177440546658501 172:13:11632953114420412320 172:14:132117110370917539920 172:15:1391633562573664753824 172:16:13655404332754085396898 172:17:125308416229978665995064 172:18:1079044695313705179401940 172:19:8745941214647926190942040 172:20:66906450292056635360706606 172:21:484275259256790884515590672 172:22:3323889279444337434629735976 172:23:21677538778984809356280886800 172:24:134581386586197358086910505550 172:25:796721808590288359874510192856 172:26:4504542533183553419290499936532 172:27:24357896660918474045052332990136 172:28:126139107708327812019021010127490 172:29:626345914137903618301345705460640 172:30:2985582190724007247236414529362384 172:31:13675892615574484809921640747401888 172:32:60259401837375073693717229543239569 172:33:255645947188863949003648852607683020 172:34:1045140784095649673867858544484351170 172:35:4120840805862847285536127975395441756 172:36:15682088622311391058845820350810431127 172:37:57642271692820248216298150478654557656 172:38:204781754698177197610532903016272770620 172:39:703609105886044730251574589850783365720 172:40:2339500277071098728086485511253854691019 172:41:7532049672521586148961367987451434614988 172:42:23492821597626852036046171579908046061034 172:43:71024809481197459643860518729954557858940 172:44:208231827797147097592227429912821317359165 172:45:592303865734107299817891356196469524932736 172:46:1635273716265904936453743526890252818836032 172:47:4383925281904340893471737965705784152624256 172:48:11416472088292554410082650952358812897459000 172:49:28890664060168913201025484042703934679284000 172:50:71071033588015526474522690745051679311038640 172:51:170013060739958710390034671978358919136210080 172:52:395607314414134691484503755949642869528488840 172:53:895714674145210622229065107810512157422993600 172:54:1973889744875556741578865700545387902469189600 172:55:4234890725369376281932839139351923136206624960 172:56:8847896694075304017609681773288839409574555720 172:57:18006245903732197649872334836868515289660499360 172:58:35702039291882805685091698383446194108809610800 172:59:68983601343637963527126332469709595396682976800 172:60:129919115863851497976087926151286404663752939640 172:61:238540016012317504480686028343345529874431626880 172:62:427063577054310370925099179775989577678417912640 172:63:745666563110700647646998567862838945152793180800 172:64:1269963365297912040523794435891397578463350886050 172:65:2110092976187300005793381524250322130369875318360 172:66:3420908309879410615452906410527037393175403925220 172:67:5412183296227127242358329545012924830993922627960 172:68:8357047736821299418347420620975839812564145234350 172:69:12596129922165436804465677457702715079806827599600 172:70:18534305456900571297999496830619709331715760610840 172:71:26626748684561384118252798263707188054014191300080 172:72:37351411349176386054771286453255916575769907240390 172:73:51166316916679980896946967744186187090095763343000 172:74:68452234793936731199969591982086925971884872580500 172:75:89444253464077328767960266856593583269929566838520 172:76:114159112973888169611738761645915494436620631359690 172:77:142328244746665769905544430103998538518384163773120 172:78:173348503217092924884957959742049502041621737928800 172:79:206262775979832087837798078680413331543195485636800 172:80:239780477076554802111440266465980497918964752052780 172:81:272343257914111627089537092776175380352404409738960 172:82:302234591099806805672535066373560483074009771783480 172:83:327724255409429066391905493658077632248926258560400 172:84:347231651564752225105709392090106062739933773950900 172:85:359486886325861127168263841222698041424872613031520 172:86:363666966399417651902778537050868948883301364345840 172:87:359486886325861127168263841222698041424872613031520 172:88:347231651564752225105709392090106062739933773950900 172:89:327724255409429066391905493658077632248926258560400 172:90:302234591099806805672535066373560483074009771783480 172:91:272343257914111627089537092776175380352404409738960 172:92:239780477076554802111440266465980497918964752052780 172:93:206262775979832087837798078680413331543195485636800 172:94:173348503217092924884957959742049502041621737928800 172:95:142328244746665769905544430103998538518384163773120 172:96:114159112973888169611738761645915494436620631359690 172:97:89444253464077328767960266856593583269929566838520 172:98:68452234793936731199969591982086925971884872580500 172:99:51166316916679980896946967744186187090095763343000 172:100:37351411349176386054771286453255916575769907240390 172:101:26626748684561384118252798263707188054014191300080 172:102:18534305456900571297999496830619709331715760610840 172:103:12596129922165436804465677457702715079806827599600 172:104:8357047736821299418347420620975839812564145234350 172:105:5412183296227127242358329545012924830993922627960 172:106:3420908309879410615452906410527037393175403925220 172:107:2110092976187300005793381524250322130369875318360 172:108:1269963365297912040523794435891397578463350886050 172:109:745666563110700647646998567862838945152793180800 172:110:427063577054310370925099179775989577678417912640 172:111:238540016012317504480686028343345529874431626880 172:112:129919115863851497976087926151286404663752939640 172:113:68983601343637963527126332469709595396682976800 172:114:35702039291882805685091698383446194108809610800 172:115:18006245903732197649872334836868515289660499360 172:116:8847896694075304017609681773288839409574555720 172:117:4234890725369376281932839139351923136206624960 172:118:1973889744875556741578865700545387902469189600 172:119:895714674145210622229065107810512157422993600 172:120:395607314414134691484503755949642869528488840 172:121:170013060739958710390034671978358919136210080 172:122:71071033588015526474522690745051679311038640 172:123:28890664060168913201025484042703934679284000 172:124:11416472088292554410082650952358812897459000 172:125:4383925281904340893471737965705784152624256 172:126:1635273716265904936453743526890252818836032 172:127:592303865734107299817891356196469524932736 172:128:208231827797147097592227429912821317359165 172:129:71024809481197459643860518729954557858940 172:130:23492821597626852036046171579908046061034 172:131:7532049672521586148961367987451434614988 172:132:2339500277071098728086485511253854691019 172:133:703609105886044730251574589850783365720 172:134:204781754698177197610532903016272770620 172:135:57642271692820248216298150478654557656 172:136:15682088622311391058845820350810431127 172:137:4120840805862847285536127975395441756 172:138:1045140784095649673867858544484351170 172:139:255645947188863949003648852607683020 172:140:60259401837375073693717229543239569 172:141:13675892615574484809921640747401888 172:142:2985582190724007247236414529362384 172:143:626345914137903618301345705460640 172:144:126139107708327812019021010127490 172:145:24357896660918474045052332990136 172:146:4504542533183553419290499936532 172:147:796721808590288359874510192856 172:148:134581386586197358086910505550 172:149:21677538778984809356280886800 172:150:3323889279444337434629735976 172:151:484275259256790884515590672 172:152:66906450292056635360706606 172:153:8745941214647926190942040 172:154:1079044695313705179401940 172:155:125308416229978665995064 172:156:13655404332754085396898 172:157:1391633562573664753824 172:158:132117110370917539920 172:159:11632953114420412320 172:160:945177440546658501 172:161:70448007991055292 172:162:4783506715442026 172:163:293466669659020 172:164:16104878212995 172:165:780842580024 172:166:32927096748 172:167:1183009464 172:168:35208615 172:169:833340 172:170:14706 172:171:172 172:172:1 # binomial(173, k) for 0 <= k <= 173 173:0:1 173:1:173 173:2:14878 173:3:848046 173:4:36041955 173:5:1218218079 173:6:34110106212 173:7:813769676772 173:8:16885720793019 173:9:309571547872015 173:10:5076973385101046 173:11:75231514706497318 173:12:1015625448537713793 173:13:12578130554967070821 173:14:143750063485337952240 173:15:1523750672944582293744 173:16:15047037895327750150722 173:17:138963820562732751391962 173:18:1204353111543683845397004 173:19:9824985909961631370343980 173:20:75652391506704561551648646 173:21:551181709548847519876297278 173:22:3808164538701128319145326648 173:23:25001428058429146790910622776 173:24:156258925365182167443191392350 173:25:931303195176485717961420698406 173:26:5301264341773841779165010129388 173:27:28862439194102027464342832926668 173:28:150497004369246286064073343117626 173:29:752485021846231430320366715588130 173:30:3611928104861910865537760234823024 173:31:16661474806298492057158055276764272 173:32:73935294452949558503638870290641457 173:33:315905349026239022697366082150922589 173:34:1300786731284513622871507397092034190 173:35:5165981589958496959403986519879792926 173:36:19802929428174238344381948326205872883 173:37:73324360315131639275143970829464988783 173:38:262424026390997445826831053494927328276 173:39:908390860584221927862107492867056136340 173:40:3043109382957143458338060101104638056739 173:41:9871549949592684877047853498705289306007 173:42:31024871270148438185007539567359480676022 173:43:94517631078824311679906690309862603919974 173:44:279256637278344557236087948642775875218105 173:45:800535693531254397410118786109290842291901 173:46:2227577582000012236271634883086722343768768 173:47:6019198998170245829925481492596036971460288 173:48:15800397370196895303554388918064597050083256 173:49:40307136148461467611108134995062747576743000 173:50:99961697648184439675548174787755613990322640 173:51:241084094327974236864557362723410598447248720 173:52:565620375154093401874538427928001788664698920 173:53:1291321988559345313713568863760155026951482440 173:54:2869604419020767363807930808355900059892183200 173:55:6208780470244933023511704839897311038675814560 173:56:13082787419444680299542520912640762545781180680 173:57:26854142597807501667482016610157354699235055080 173:58:53708285195615003334964033220314709398470110160 173:59:104685640635520769212218030853155789505492587600 173:60:198902717207489461503214258620996000060435916440 173:61:368459131876169002456773954494631934538184566520 173:62:665603593066627875405785208119335107552849539520 173:63:1172730140165011018572097747638828522831211093440 173:64:2015629928408612688170793003754236523616144066850 173:65:3380056341485212046317175960141719708833226204410 173:66:5531001286066710621246287934777359523545279243580 173:67:8833091606106537857811235955539962224169326553180 173:68:13769231033048426660705750165988764643558067862310 173:69:20953177658986736222813098078678554892370972833950 173:70:31130435379066008102465174288322424411522588210440 173:71:45161054141461955416252295094326897385729951910920 173:72:63978160033737770173024084716963104629784098540470 173:73:88517728265856366951718254197442103665865670583390 173:74:119618551710616712096916559726273113061980635923500 173:75:157896488258014059967929858838680509241814439419020 173:76:203603366437965498379699028502509077706550198198210 173:77:256487357720553939517283191749914032955004795132810 173:78:315676747963758694790502389846048040560005901701920 173:79:379611279196925012722756038422462833584817223565600 173:80:446043253056386889949238345146393829462160237689580 173:81:512123734990666429200977359242155878271369161791740 173:82:574577849013918432762072159149735863426414181522440 173:83:629958846509235872064440560031638115322936030343880 173:84:674955906974181291497614885748183694988860032511300 173:85:706718537890613352273973233312804104164806386982420 173:86:723153852725278779071042378273566990308173977377360 173:87:723153852725278779071042378273566990308173977377360 173:88:706718537890613352273973233312804104164806386982420 173:89:674955906974181291497614885748183694988860032511300 173:90:629958846509235872064440560031638115322936030343880 173:91:574577849013918432762072159149735863426414181522440 173:92:512123734990666429200977359242155878271369161791740 173:93:446043253056386889949238345146393829462160237689580 173:94:379611279196925012722756038422462833584817223565600 173:95:315676747963758694790502389846048040560005901701920 173:96:256487357720553939517283191749914032955004795132810 173:97:203603366437965498379699028502509077706550198198210 173:98:157896488258014059967929858838680509241814439419020 173:99:119618551710616712096916559726273113061980635923500 173:100:88517728265856366951718254197442103665865670583390 173:101:63978160033737770173024084716963104629784098540470 173:102:45161054141461955416252295094326897385729951910920 173:103:31130435379066008102465174288322424411522588210440 173:104:20953177658986736222813098078678554892370972833950 173:105:13769231033048426660705750165988764643558067862310 173:106:8833091606106537857811235955539962224169326553180 173:107:5531001286066710621246287934777359523545279243580 173:108:3380056341485212046317175960141719708833226204410 173:109:2015629928408612688170793003754236523616144066850 173:110:1172730140165011018572097747638828522831211093440 173:111:665603593066627875405785208119335107552849539520 173:112:368459131876169002456773954494631934538184566520 173:113:198902717207489461503214258620996000060435916440 173:114:104685640635520769212218030853155789505492587600 173:115:53708285195615003334964033220314709398470110160 173:116:26854142597807501667482016610157354699235055080 173:117:13082787419444680299542520912640762545781180680 173:118:6208780470244933023511704839897311038675814560 173:119:2869604419020767363807930808355900059892183200 173:120:1291321988559345313713568863760155026951482440 173:121:565620375154093401874538427928001788664698920 173:122:241084094327974236864557362723410598447248720 173:123:99961697648184439675548174787755613990322640 173:124:40307136148461467611108134995062747576743000 173:125:15800397370196895303554388918064597050083256 173:126:6019198998170245829925481492596036971460288 173:127:2227577582000012236271634883086722343768768 173:128:800535693531254397410118786109290842291901 173:129:279256637278344557236087948642775875218105 173:130:94517631078824311679906690309862603919974 173:131:31024871270148438185007539567359480676022 173:132:9871549949592684877047853498705289306007 173:133:3043109382957143458338060101104638056739 173:134:908390860584221927862107492867056136340 173:135:262424026390997445826831053494927328276 173:136:73324360315131639275143970829464988783 173:137:19802929428174238344381948326205872883 173:138:5165981589958496959403986519879792926 173:139:1300786731284513622871507397092034190 173:140:315905349026239022697366082150922589 173:141:73935294452949558503638870290641457 173:142:16661474806298492057158055276764272 173:143:3611928104861910865537760234823024 173:144:752485021846231430320366715588130 173:145:150497004369246286064073343117626 173:146:28862439194102027464342832926668 173:147:5301264341773841779165010129388 173:148:931303195176485717961420698406 173:149:156258925365182167443191392350 173:150:25001428058429146790910622776 173:151:3808164538701128319145326648 173:152:551181709548847519876297278 173:153:75652391506704561551648646 173:154:9824985909961631370343980 173:155:1204353111543683845397004 173:156:138963820562732751391962 173:157:15047037895327750150722 173:158:1523750672944582293744 173:159:143750063485337952240 173:160:12578130554967070821 173:161:1015625448537713793 173:162:75231514706497318 173:163:5076973385101046 173:164:309571547872015 173:165:16885720793019 173:166:813769676772 173:167:34110106212 173:168:1218218079 173:169:36041955 173:170:848046 173:171:14878 173:172:173 173:173:1 # binomial(174, k) for 0 <= k <= 174 174:0:1 174:1:174 174:2:15051 174:3:862924 174:4:36890001 174:5:1254260034 174:6:35328324291 174:7:847879782984 174:8:17699490469791 174:9:326457268665034 174:10:5386544932973061 174:11:80308488091598364 174:12:1090856963244211111 174:13:13593756003504784614 174:14:156328194040305023061 174:15:1667500736429920245984 174:16:16570788568272332444466 174:17:154010858458060501542684 174:18:1343316932106416596788966 174:19:11029339021505315215740984 174:20:85477377416666192921992626 174:21:626834101055552081427945924 174:22:4359346248249975839021623926 174:23:28809592597130275110055949424 174:24:181260353423611314234102015126 174:25:1087562120541667885404612090756 174:26:6232567536950327497126430827794 174:27:34163703535875869243507843056056 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174:49:56107533518658362914662523913127344626826256 174:50:140268833796645907286656309782818361567065640 174:51:341045791976158676540105537511166212437571360 174:52:806704469482067638739095790651412387111947640 174:53:1856942363713438715588107291688156815616181360 174:54:4160926407580112677521499672116055086843665640 174:55:9078384889265700387319635648253211098567997760 174:56:19291567889689613323054225752538073584456995240 174:57:39936930017252181967024537522798117245016235760 174:58:80562427793422505002446049830472064097705165240 174:59:158393925831135772547182064073470498903962697760 174:60:303588357843010230715432289474151789565928504040 174:61:567361849083658463959988213115627934598620482960 174:62:1034062724942796877862559162613967042091034106040 174:63:1838333733231638893977882955758163630384060632960 174:64:3188360068573623706742890751393065046447355160290 174:65:5395686269893824734487968963895956232449370271260 174:66:8911057627551922667563463894919079232378505447990 174:67:14364092892173248479057523890317321747714605796760 174:68:22602322639154964518516986121528726867727394415490 174:69:34722408692035162883518848244667319535929040696260 174:70:52083613038052744325278272367000979303893561044390 174:71:76291489520527963518717469382649321797252540121360 174:72:109139214175199725589276379811290002015514050451390 174:73:152495888299594137124742338914405208295649769123860 174:74:208136279976473079048634813923715216727846306506890 174:75:277515039968630772064846418564953622303795075342520 174:76:361499854695979558347628887341189586948364637617230 174:77:460090724158519437896982220252423110661554993331020 174:78:572164105684312634307785581595962073515010696834730 174:79:695288027160683707513258428268510874144823125267520 174:80:825654532253311902671994383568856663046977461255180 174:81:958166988047053319150215704388549707733529399481320 174:82:1086701584004584861963049518391891741697783343314180 174:83:1204536695523154304826512719181373978749350211866320 174:84:1304914753483417163562055445779821810311796062855180 174:85:1381674444864794643771588119060987799153666419493720 174:86:1429872390615892131345015611586371094472980364359780 174:87:1446307705450557558142084756547133980616347954754720 174:88:1429872390615892131345015611586371094472980364359780 174:89:1381674444864794643771588119060987799153666419493720 174:90:1304914753483417163562055445779821810311796062855180 174:91:1204536695523154304826512719181373978749350211866320 174:92:1086701584004584861963049518391891741697783343314180 174:93:958166988047053319150215704388549707733529399481320 174:94:825654532253311902671994383568856663046977461255180 174:95:695288027160683707513258428268510874144823125267520 174:96:572164105684312634307785581595962073515010696834730 174:97:460090724158519437896982220252423110661554993331020 174:98:361499854695979558347628887341189586948364637617230 174:99:277515039968630772064846418564953622303795075342520 174:100:208136279976473079048634813923715216727846306506890 174:101:152495888299594137124742338914405208295649769123860 174:102:109139214175199725589276379811290002015514050451390 174:103:76291489520527963518717469382649321797252540121360 174:104:52083613038052744325278272367000979303893561044390 174:105:34722408692035162883518848244667319535929040696260 174:106:22602322639154964518516986121528726867727394415490 174:107:14364092892173248479057523890317321747714605796760 174:108:8911057627551922667563463894919079232378505447990 174:109:5395686269893824734487968963895956232449370271260 174:110:3188360068573623706742890751393065046447355160290 174:111:1838333733231638893977882955758163630384060632960 174:112:1034062724942796877862559162613967042091034106040 174:113:567361849083658463959988213115627934598620482960 174:114:303588357843010230715432289474151789565928504040 174:115:158393925831135772547182064073470498903962697760 174:116:80562427793422505002446049830472064097705165240 174:117:39936930017252181967024537522798117245016235760 174:118:19291567889689613323054225752538073584456995240 174:119:9078384889265700387319635648253211098567997760 174:120:4160926407580112677521499672116055086843665640 174:121:1856942363713438715588107291688156815616181360 174:122:806704469482067638739095790651412387111947640 174:123:341045791976158676540105537511166212437571360 174:124:140268833796645907286656309782818361567065640 174:125:56107533518658362914662523913127344626826256 174:126:21819596368367141133479870410660634021543544 174:127:8246776580170258066197116375682759315229056 174:128:3028113275531266633681753669196013186060669 174:129:1079792330809598954646206734752066717510006 174:130:373774268357168868915994638952638479138079 174:131:125542502348972749864914229877222084595996 174:132:40896421219741123062055393066064769982029 174:133:12914659332549828335385913599809927362746 174:134:3951500243541365386200167593971694193079 174:135:1170814886975219373688938546361983464616 174:136:335748386706129085101975024324392317059 174:137:93127289743305877619525919155670861666 174:138:24968911018132735303785934846085665809 174:139:6466768321243010582275493916971827116 174:140:1616692080310752645568873479242956779 174:141:389840643479188581201004952441564046 174:142:90596769259248050560796925567405729 174:143:20273402911160402922695815511587296 174:144:4364413126708142295858126950411154 174:145:902982026215477716384440058705756 174:146:179359443563348313528416176044294 174:147:34163703535875869243507843056056 174:148:6232567536950327497126430827794 174:149:1087562120541667885404612090756 174:150:181260353423611314234102015126 174:151:28809592597130275110055949424 174:152:4359346248249975839021623926 174:153:626834101055552081427945924 174:154:85477377416666192921992626 174:155:11029339021505315215740984 174:156:1343316932106416596788966 174:157:154010858458060501542684 174:158:16570788568272332444466 174:159:1667500736429920245984 174:160:156328194040305023061 174:161:13593756003504784614 174:162:1090856963244211111 174:163:80308488091598364 174:164:5386544932973061 174:165:326457268665034 174:166:17699490469791 174:167:847879782984 174:168:35328324291 174:169:1254260034 174:170:36890001 174:171:862924 174:172:15051 174:173:174 174:174:1 # binomial(175, k) for 0 <= k <= 175 175:0:1 175:1:175 175:2:15225 175:3:877975 175:4:37752925 175:5:1291150035 175:6:36582584325 175:7:883208107275 175:8:18547370252775 175:9:344156759134825 175:10:5713002201638095 175:11:85695033024571425 175:12:1171165451335809475 175:13:14684612966748995725 175:14:169921950043809807675 175:15:1823828930470225269045 175:16:18238289304702252690450 175:17:170581647026332833987150 175:18:1497327790564477098331650 175:19:12372655953611731812529950 175:20:96506716438171508137733610 175:21:712311478472218274349938550 175:22:4986180349305527920449569850 175:23:33168938845380250949077573350 175:24:210069946020741589344157964550 175:25:1268822473965279199638714105882 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175:47:11274889855701524699878870044878772501289725 175:48:30066372948537399199676986786343393336772600 175:49:77927129887025504048142394323787978648369800 175:50:196376367315304270201318833695945706193891896 175:51:481314625772804583826761847293984574004637000 175:52:1147750261458226315279201328162578599549519000 175:53:2663646833195506354327203082339569202728129000 175:54:6017868771293551393109606963804211902459847000 175:55:13239311296845813064841135320369266185411663400 175:56:28369952778955313710373861400791284683024993000 175:57:59228497906941795290078763275336190829473231000 175:58:120499357810674686969470587353270181342721401000 175:59:238956353624558277549628113903942563001667863000 175:60:461982283674146003262614353547622288469891201800 175:61:870950206926668694675420502589779724164548987000 175:62:1601424574026455341822547375729594976689654589000 175:63:2872396458174435771840442118372130672475094739000 175:64:5026693801805262600720773707151228676831415793250 175:65:8584046338467448441230859715289021278896725431550 175:66:14306743897445747402051432858815035464827875719250 175:67:23275150519725171146620987785236400980093111244750 175:68:36966415531328212997574510011846048615442000212250 175:69:57324731331190127402035834366196046403656435111750 175:70:86806021730087907208797120611668298839822601740650 175:71:128375102558580707843995741749650301101146101165750 175:72:185430703695727689107993849193939323812766590572750 175:73:261635102474793862714018718725695210311163819575250 175:74:360632168276067216173377152838120425023496075630750 175:75:485651319945103851113481232488668839031641381849410 175:76:639014894664610330412475305906143209252159712959750 175:77:821590578854498996244611107593612697609919630948250 175:78:1032254829842832072204767801848385184176565690165750 175:79:1267452132844996341821044009864472947659833822102250 175:80:1520942559413995610185252811837367537191800586522700 175:81:1783821520300365221822210087957406370780506860736500 175:82:2044868572051638181113265222780441449431312742795500 175:83:2291238279527739166789562237573265720447133555180500 175:84:2509451449006571468388568164961195789061146274721500 175:85:2686589198348211807333643564840809609465462482348900 175:86:2811546835480686775116603730647358893626646783853500 175:87:2876180096066449689487100368133505075089328319114500 175:88:2876180096066449689487100368133505075089328319114500 175:89:2811546835480686775116603730647358893626646783853500 175:90:2686589198348211807333643564840809609465462482348900 175:91:2509451449006571468388568164961195789061146274721500 175:92:2291238279527739166789562237573265720447133555180500 175:93:2044868572051638181113265222780441449431312742795500 175:94:1783821520300365221822210087957406370780506860736500 175:95:1520942559413995610185252811837367537191800586522700 175:96:1267452132844996341821044009864472947659833822102250 175:97:1032254829842832072204767801848385184176565690165750 175:98:821590578854498996244611107593612697609919630948250 175:99:639014894664610330412475305906143209252159712959750 175:100:485651319945103851113481232488668839031641381849410 175:101:360632168276067216173377152838120425023496075630750 175:102:261635102474793862714018718725695210311163819575250 175:103:185430703695727689107993849193939323812766590572750 175:104:128375102558580707843995741749650301101146101165750 175:105:86806021730087907208797120611668298839822601740650 175:106:57324731331190127402035834366196046403656435111750 175:107:36966415531328212997574510011846048615442000212250 175:108:23275150519725171146620987785236400980093111244750 175:109:14306743897445747402051432858815035464827875719250 175:110:8584046338467448441230859715289021278896725431550 175:111:5026693801805262600720773707151228676831415793250 175:112:2872396458174435771840442118372130672475094739000 175:113:1601424574026455341822547375729594976689654589000 175:114:870950206926668694675420502589779724164548987000 175:115:461982283674146003262614353547622288469891201800 175:116:238956353624558277549628113903942563001667863000 175:117:120499357810674686969470587353270181342721401000 175:118:59228497906941795290078763275336190829473231000 175:119:28369952778955313710373861400791284683024993000 175:120:13239311296845813064841135320369266185411663400 175:121:6017868771293551393109606963804211902459847000 175:122:2663646833195506354327203082339569202728129000 175:123:1147750261458226315279201328162578599549519000 175:124:481314625772804583826761847293984574004637000 175:125:196376367315304270201318833695945706193891896 175:126:77927129887025504048142394323787978648369800 175:127:30066372948537399199676986786343393336772600 175:128:11274889855701524699878870044878772501289725 175:129:4107905606340865588327960403948079903570675 175:130:1453566599166767823562201373704705196648085 175:131:499316770706141618780908868829860563734075 175:132:166438923568713872926969622943286854578025 175:133:53811080552290951397441306665874697344775 175:134:16866159576091193721586081193781621555825 175:135:5122315130516584759889106140333677657695 175:136:1506563273681348458790913570686375781675 175:137:428875676449434962721500943480063178725 175:138:118096200761438612923311854001756527475 175:139:31435679339375745886061428763057492925 175:140:8083460401553763227844367396214783895 175:141:2006532723789941226769878431684520825 175:142:480437412738436631761801878008969775 175:143:110870172170408453483492741078993025 175:144:24637816037868545218553942461998450 175:145:5267395152923620012242567009116910 175:146:1082341469778826029912856234750050 175:147:213523147099224182771924019100350 175:148:40396271072826196740634273883850 175:149:7320129657491995382531042918550 175:150:1268822473965279199638714105882 175:151:210069946020741589344157964550 175:152:33168938845380250949077573350 175:153:4986180349305527920449569850 175:154:712311478472218274349938550 175:155:96506716438171508137733610 175:156:12372655953611731812529950 175:157:1497327790564477098331650 175:158:170581647026332833987150 175:159:18238289304702252690450 175:160:1823828930470225269045 175:161:169921950043809807675 175:162:14684612966748995725 175:163:1171165451335809475 175:164:85695033024571425 175:165:5713002201638095 175:166:344156759134825 175:167:18547370252775 175:168:883208107275 175:169:36582584325 175:170:1291150035 175:171:37752925 175:172:877975 175:173:15225 175:174:175 175:175:1 # binomial(176, k) for 0 <= k <= 176 176:0:1 176:1:176 176:2:15400 176:3:893200 176:4:38630900 176:5:1328902960 176:6:37873734360 176:7:919790691600 176:8:19430578360050 176:9:362704129387600 176:10:6057158960772920 176:11:91408035226209520 176:12:1256860484360380900 176:13:15855778418084805200 176:14:184606563010558803400 176:15:1993750880514035076720 176:16:20062118235172477959495 176:17:188819936331035086677600 176:18:1667909437590809932318800 176:19:13869983744176208910861600 176:20:108879372391783239950263560 176:21:808818194910389782487672160 176:22:5698491827777746194799508400 176:23:38155119194685778869527143200 176:24:243238884866121840293235537900 176:25:1478892419986020788982872070432 176:26:8588952131457274582169757024432 176:27:47716400730318192123165316802400 176:28:253919418172050379512558292984200 176:29:1295864616878050212684780253850400 176:30:6349736622702446042155423243866960 176:31:29905211190792165230796509471115360 176:32:135507988208276998702046683540991475 176:33:591307584908845085245294619087962800 176:34:2486970136528377858531680309693490600 176:35:10089993125343704454614245827899304720 176:36:39519139740929509113905796159272276820 176:37:149531880100814358809373282764814020400 176:38:546971877210873575644812797481819706200 176:39:1935438950130783421512414514166438960400 176:40:6628878404197933218680019711020053439370 176:41:21988474706607778481475187334115299213520 176:42:70677240128382145119027387859656318900600 176:43:220250004121004824324410929609161551922800 176:44:665755694274855491707878491773147418312100 176:45:1952883369872909442343110242534565760382160 176:46:5561472205507633411890161777652785100218760 176:47:15382795462042390288206830448826852404860400 176:48:41341262804238923899555856831222165838062325 176:49:107993502835562903247819381110131371985142400 176:50:274303497202329774249461228019733684842261696 176:51:677690993088108854028080680989930280198528896 176:52:1629064887231030899105963175456563173554156000 176:53:3811397094653732669606404410502147802277648000 176:54:8681515604489057747436810046143781105187976000 176:55:19257180068139364457950742284173478087871510400 176:56:41609264075801126775214996721160550868436656400 176:57:87598450685897109000452624676127475512498224000 176:58:179727855717616482259549350628606372172194632000 176:59:359455711435232964519098701257212744344389264000 176:60:700938637298704280812242467451564851471559064800 176:61:1332932490600814697938034856137402012634440188800 176:62:2472374780953124036497967878319374700854203576000 176:63:4473821032200891113662989494101725649164749328000 176:64:7899090259979698372561215825523359349306510532250 176:65:13610740140272711041951633422440249955728141224800 176:66:22890790235913195843282292574104056743724601150800 176:67:37581894417170918548672420644051436444920986964000 176:68:60241566051053384144195497797082449595535111457000 176:69:94291146862518340399610344378042095019098435324000 176:70:144130753061278034610832954977864345243479036852400 176:71:215181124288668615052792862361318599940968702906400 176:72:313805806254308396951989590943589624913912691738500 176:73:447065806170521551822012567919634534123930410148000 176:74:622267270750861078887395871563815635334659895206000 176:75:846283488221171067286858385326789264055137457480160 176:76:1124666214609714181525956538394812048283801094809160 176:77:1460605473519109326657086413499755906862079343908000 176:78:1853845408697331068449378909441997881786485321114000 176:79:2299706962687828414025811811712858131836399512268000 176:80:2788394692258991952006296821701840484851634408624950 176:81:3304764079714360832007462899794773907972307447259200 176:82:3828690092352003402935475310737847820211819603532000 176:83:4336106851579377347902827460353707169878446297976000 176:84:4800689728534310635178130402534461509508279829902000 176:85:5196040647354783275722211729802005398526608757070400 176:86:5498136033828898582450247295488168503092109266202400 176:87:5687726931547136464603704098780863968715975102968000 176:88:5752360192132899378974200736267010150178656638229000 176:89:5687726931547136464603704098780863968715975102968000 176:90:5498136033828898582450247295488168503092109266202400 176:91:5196040647354783275722211729802005398526608757070400 176:92:4800689728534310635178130402534461509508279829902000 176:93:4336106851579377347902827460353707169878446297976000 176:94:3828690092352003402935475310737847820211819603532000 176:95:3304764079714360832007462899794773907972307447259200 176:96:2788394692258991952006296821701840484851634408624950 176:97:2299706962687828414025811811712858131836399512268000 176:98:1853845408697331068449378909441997881786485321114000 176:99:1460605473519109326657086413499755906862079343908000 176:100:1124666214609714181525956538394812048283801094809160 176:101:846283488221171067286858385326789264055137457480160 176:102:622267270750861078887395871563815635334659895206000 176:103:447065806170521551822012567919634534123930410148000 176:104:313805806254308396951989590943589624913912691738500 176:105:215181124288668615052792862361318599940968702906400 176:106:144130753061278034610832954977864345243479036852400 176:107:94291146862518340399610344378042095019098435324000 176:108:60241566051053384144195497797082449595535111457000 176:109:37581894417170918548672420644051436444920986964000 176:110:22890790235913195843282292574104056743724601150800 176:111:13610740140272711041951633422440249955728141224800 176:112:7899090259979698372561215825523359349306510532250 176:113:4473821032200891113662989494101725649164749328000 176:114:2472374780953124036497967878319374700854203576000 176:115:1332932490600814697938034856137402012634440188800 176:116:700938637298704280812242467451564851471559064800 176:117:359455711435232964519098701257212744344389264000 176:118:179727855717616482259549350628606372172194632000 176:119:87598450685897109000452624676127475512498224000 176:120:41609264075801126775214996721160550868436656400 176:121:19257180068139364457950742284173478087871510400 176:122:8681515604489057747436810046143781105187976000 176:123:3811397094653732669606404410502147802277648000 176:124:1629064887231030899105963175456563173554156000 176:125:677690993088108854028080680989930280198528896 176:126:274303497202329774249461228019733684842261696 176:127:107993502835562903247819381110131371985142400 176:128:41341262804238923899555856831222165838062325 176:129:15382795462042390288206830448826852404860400 176:130:5561472205507633411890161777652785100218760 176:131:1952883369872909442343110242534565760382160 176:132:665755694274855491707878491773147418312100 176:133:220250004121004824324410929609161551922800 176:134:70677240128382145119027387859656318900600 176:135:21988474706607778481475187334115299213520 176:136:6628878404197933218680019711020053439370 176:137:1935438950130783421512414514166438960400 176:138:546971877210873575644812797481819706200 176:139:149531880100814358809373282764814020400 176:140:39519139740929509113905796159272276820 176:141:10089993125343704454614245827899304720 176:142:2486970136528377858531680309693490600 176:143:591307584908845085245294619087962800 176:144:135507988208276998702046683540991475 176:145:29905211190792165230796509471115360 176:146:6349736622702446042155423243866960 176:147:1295864616878050212684780253850400 176:148:253919418172050379512558292984200 176:149:47716400730318192123165316802400 176:150:8588952131457274582169757024432 176:151:1478892419986020788982872070432 176:152:243238884866121840293235537900 176:153:38155119194685778869527143200 176:154:5698491827777746194799508400 176:155:808818194910389782487672160 176:156:108879372391783239950263560 176:157:13869983744176208910861600 176:158:1667909437590809932318800 176:159:188819936331035086677600 176:160:20062118235172477959495 176:161:1993750880514035076720 176:162:184606563010558803400 176:163:15855778418084805200 176:164:1256860484360380900 176:165:91408035226209520 176:166:6057158960772920 176:167:362704129387600 176:168:19430578360050 176:169:919790691600 176:170:37873734360 176:171:1328902960 176:172:38630900 176:173:893200 176:174:15400 176:175:176 176:176:1 # binomial(177, k) for 0 <= k <= 177 177:0:1 177:1:177 177:2:15576 177:3:908600 177:4:39524100 177:5:1367533860 177:6:39202637320 177:7:957664425960 177:8:20350369051650 177:9:382134707747650 177:10:6419863090160520 177:11:97465194186982440 177:12:1348268519586590420 177:13:17112638902445186100 177:14:200462341428643608600 177:15:2178357443524593880120 177:16:22055869115686513036215 177:17:208882054566207564637095 177:18:1856729373921845018996400 177:19:15537893181767018843180400 177:20:122749356135959448861125160 177:21:917697567302173022437935720 177:22:6507310022688135977287180560 177:23:43853611022463525064326651600 177:24:281394004060807619162762681100 177:25:1722131304852142629276107608332 177:26:10067844551443295371152629094864 177:27:56305352861775466705335073826832 177:28:301635818902368571635723609786600 177:29:1549784035050100592197338546834600 177:30:7645601239580496254840203497717360 177:31:36254947813494611272951932714982320 177:32:165413199399069163932843193012106835 177:33:726815573117122083947341302628954275 177:34:3078277721437222943776974928781453400 177:35:12576963261872082313145926137592795320 177:36:49609132866273213568520041987171581540 177:37:189051019841743867923279078924086297220 177:38:696503757311687934454186080246633726600 177:39:2482410827341656997157227311648258666600 177:40:8564317354328716640192434225186492399770 177:41:28617353110805711700155207045135352652890 177:42:92665714834989923600502575193771618114120 177:43:290927244249386969443438317468817870823400 177:44:886005698395860316032289421382308970234900 177:45:2618639064147764934050988734307713178694260 177:46:7514355575380542854233272020187350860600920 177:47:20944267667550023700096992226479637505079160 177:48:56724058266281314187762687280049018242922725 177:49:149334765639801827147375237941353537823204725 177:50:382297000037892677497280609129865056827404096 177:51:951994490290438628277541909009663965040790592 177:52:2306755880319139753134043856446493453752684896 177:53:5440461981884763568712367585958710975831804000 177:54:12492912699142790417043214456645928907465624000 177:55:27938695672628422205387552330317259193059486400 177:56:60866444143940491233165739005334028956308166800 177:57:129207714761698235775667621397288026380934880400 177:58:267326306403513591260001975304733847684692856000 177:59:539183567152849446778648051885819116516583896000 177:60:1060394348733937245331341168708777595815948328800 177:61:2033871127899518978750277323588966864105999253600 177:62:3805307271553938734436002734456776713488643764800 177:63:6946195813154015150160957372421100350018952904000 177:64:12372911292180589486224205319625084998471259860250 177:65:21509830400252409414512849247963609305034651757050 177:66:36501530376185906885233925996544306699452742375600 177:67:60472684653084114391954713218155493188645588114800 177:68:97823460468224302692867918441133886040456098421000 177:69:154532712913571724543805842175124544614633546781000 177:70:238421899923796375010443299355906440262577472176400 177:71:359311877349946649663625817339182945184447739758800 177:72:528986930542977012004782453304908224854881394644900 177:73:760871612424829948774002158863224159037843101886500 177:74:1069333076921382630709408439483450169458590305354000 177:75:1468550758972032146174254256890604899389797352686160 177:76:1970949702830885248812814923721601312338938552289320 177:77:2585271688128823508183042951894567955145880438717160 177:78:3314450882216440395106465322941753788648564665022000 177:79:4153552371385159482475190721154856013622884833382000 177:80:5088101654946820366032108633414698616688033920892950 177:81:6093158771973352784013759721496614392823941855884150 177:82:7133454172066364234942938210532621728184127050791200 177:83:8164796943931380750838302771091554990090265901508000 177:84:9136796580113687983080957862888168679386726127878000 177:85:9996730375889093910900342132336466908034888586972400 177:86:10694176681183681858172459025290173901618718023272800 177:87:11185862965376035047053951394269032471808084369170400 177:88:11440087123680035843577904835047874118894631741197000 177:89:11440087123680035843577904835047874118894631741197000 177:90:11185862965376035047053951394269032471808084369170400 177:91:10694176681183681858172459025290173901618718023272800 177:92:9996730375889093910900342132336466908034888586972400 177:93:9136796580113687983080957862888168679386726127878000 177:94:8164796943931380750838302771091554990090265901508000 177:95:7133454172066364234942938210532621728184127050791200 177:96:6093158771973352784013759721496614392823941855884150 177:97:5088101654946820366032108633414698616688033920892950 177:98:4153552371385159482475190721154856013622884833382000 177:99:3314450882216440395106465322941753788648564665022000 177:100:2585271688128823508183042951894567955145880438717160 177:101:1970949702830885248812814923721601312338938552289320 177:102:1468550758972032146174254256890604899389797352686160 177:103:1069333076921382630709408439483450169458590305354000 177:104:760871612424829948774002158863224159037843101886500 177:105:528986930542977012004782453304908224854881394644900 177:106:359311877349946649663625817339182945184447739758800 177:107:238421899923796375010443299355906440262577472176400 177:108:154532712913571724543805842175124544614633546781000 177:109:97823460468224302692867918441133886040456098421000 177:110:60472684653084114391954713218155493188645588114800 177:111:36501530376185906885233925996544306699452742375600 177:112:21509830400252409414512849247963609305034651757050 177:113:12372911292180589486224205319625084998471259860250 177:114:6946195813154015150160957372421100350018952904000 177:115:3805307271553938734436002734456776713488643764800 177:116:2033871127899518978750277323588966864105999253600 177:117:1060394348733937245331341168708777595815948328800 177:118:539183567152849446778648051885819116516583896000 177:119:267326306403513591260001975304733847684692856000 177:120:129207714761698235775667621397288026380934880400 177:121:60866444143940491233165739005334028956308166800 177:122:27938695672628422205387552330317259193059486400 177:123:12492912699142790417043214456645928907465624000 177:124:5440461981884763568712367585958710975831804000 177:125:2306755880319139753134043856446493453752684896 177:126:951994490290438628277541909009663965040790592 177:127:382297000037892677497280609129865056827404096 177:128:149334765639801827147375237941353537823204725 177:129:56724058266281314187762687280049018242922725 177:130:20944267667550023700096992226479637505079160 177:131:7514355575380542854233272020187350860600920 177:132:2618639064147764934050988734307713178694260 177:133:886005698395860316032289421382308970234900 177:134:290927244249386969443438317468817870823400 177:135:92665714834989923600502575193771618114120 177:136:28617353110805711700155207045135352652890 177:137:8564317354328716640192434225186492399770 177:138:2482410827341656997157227311648258666600 177:139:696503757311687934454186080246633726600 177:140:189051019841743867923279078924086297220 177:141:49609132866273213568520041987171581540 177:142:12576963261872082313145926137592795320 177:143:3078277721437222943776974928781453400 177:144:726815573117122083947341302628954275 177:145:165413199399069163932843193012106835 177:146:36254947813494611272951932714982320 177:147:7645601239580496254840203497717360 177:148:1549784035050100592197338546834600 177:149:301635818902368571635723609786600 177:150:56305352861775466705335073826832 177:151:10067844551443295371152629094864 177:152:1722131304852142629276107608332 177:153:281394004060807619162762681100 177:154:43853611022463525064326651600 177:155:6507310022688135977287180560 177:156:917697567302173022437935720 177:157:122749356135959448861125160 177:158:15537893181767018843180400 177:159:1856729373921845018996400 177:160:208882054566207564637095 177:161:22055869115686513036215 177:162:2178357443524593880120 177:163:200462341428643608600 177:164:17112638902445186100 177:165:1348268519586590420 177:166:97465194186982440 177:167:6419863090160520 177:168:382134707747650 177:169:20350369051650 177:170:957664425960 177:171:39202637320 177:172:1367533860 177:173:39524100 177:174:908600 177:175:15576 177:176:177 177:177:1 # binomial(178, k) for 0 <= k <= 178 178:0:1 178:1:178 178:2:15753 178:3:924176 178:4:40432700 178:5:1407057960 178:6:40570171180 178:7:996867063280 178:8:21308033477610 178:9:402485076799300 178:10:6801997797908170 178:11:103885057277142960 178:12:1445733713773572860 178:13:18460907422031776520 178:14:217574980331088794700 178:15:2378819784953237488720 178:16:24234226559211106916335 178:17:230937923681894077673310 178:18:2065611428488052583633495 178:19:17394622555688863862176800 178:20:138287249317726467704305560 178:21:1040446923438132471299060880 178:22:7425007589990308999725116280 178:23:50360921045151661041613832160 178:24:325247615083271144227089332700 178:25:2003525308912950248438870289432 178:26:11789975856295438000428736703196 178:27:66373197413218762076487702921696 178:28:357941171764144038341058683613432 178:29:1851419853952469163833062156621200 178:30:9195385274630596847037542044551960 178:31:43900549053075107527792136212699680 178:32:201668147212563775205795125727089155 178:33:892228772516191247880184495641061110 178:34:3805093294554345027724316231410407675 178:35:15655240983309305256922901066374248720 178:36:62186096128145295881665968124764376860 178:37:238660152708017081491799120911257878760 178:38:885554777153431802377465159170720023820 178:39:3178914584653344931611413391894892393200 178:40:11046728181670373637349661536834751066370 178:41:37181670465134428340347641270321845052660 178:42:121283067945795635300657782238906970767010 178:43:383592959084376893043940892662589488937520 178:44:1176932942645247285475727738851126841058300 178:45:3504644762543625250083278155690022148929160 178:46:10132994639528307788284260754495064039295180 178:47:28458623242930566554330264246666988365680080 178:48:77668325933831337887859679506528655748001885 178:49:206058823906083141335137925221402556066127450 178:50:531631765677694504644655847071218594650608821 178:51:1334291490328331305774822518139529021868194688 178:52:3258750370609578381411585765456157418793475488 178:53:7747217862203903321846411442405204429584488896 178:54:17933374681027553985755582042604639883297428000 178:55:40431608371771212622430766786963188100525110400 178:56:88805139816568913438553291335651288149367653200 178:57:190074158905638727008833360402622055337243047200 178:58:396534021165211827035669596702021874065627736400 178:59:806509873556363038038650027190552964201276752000 178:60:1599577915886786692109989220594596712332532224800 178:61:3094265476633456224081618492297744459921947582400 178:62:5839178399453457713186280058045743577594643018400 178:63:10751503084707953884596960106877877063507596668800 178:64:19319107105334604636385162692046185348490212764250 178:65:33882741692432998900737054567588694303505911617300 178:66:58011360776438316299746775244507916004487394132650 178:67:96974215029270021277188639214699799888098330490400 178:68:158296145121308417084822631659289379229101686535800 178:69:252356173381796027236673760616258430655089645202000 178:70:392954612837368099554249141531030984877211018957400 178:71:597733777273743024674069116695089385447025211935200 178:72:888298807892923661668408270644091170039329134403700 178:73:1289858542967806960778784612168132383892724496531400 178:74:1830204689346212579483410598346674328496433407240500 178:75:2537883835893414776883662696374055068848387658040160 178:76:3439500461802917394987069180612206211728735904975480 178:77:4556221390959708756995857875616169267484818991006480 178:78:5899722570345263903289508274836321743794445103739160 178:79:7468003253601599877581656044096609802271449498404000 178:80:9241654026331979848507299354569554630310918754274950 178:81:11181260426920173150045868354911313009511975776777100 178:82:13226612944039717018956697932029236121008068906675350 178:83:15298251115997744985781240981624176718274392952299200 178:84:17301593524045068733919260633979723669476992029386000 178:85:19133526956002781893981299995224635587421614714850400 178:86:20690907057072775769072801157626640809653606610245200 178:87:21880039646559716905226410419559206373426802392443200 178:88:22625950089056070890631856229316906590702716110367400 178:89:22880174247360071687155809670095748237789263482394000 178:90:22625950089056070890631856229316906590702716110367400 178:91:21880039646559716905226410419559206373426802392443200 178:92:20690907057072775769072801157626640809653606610245200 178:93:19133526956002781893981299995224635587421614714850400 178:94:17301593524045068733919260633979723669476992029386000 178:95:15298251115997744985781240981624176718274392952299200 178:96:13226612944039717018956697932029236121008068906675350 178:97:11181260426920173150045868354911313009511975776777100 178:98:9241654026331979848507299354569554630310918754274950 178:99:7468003253601599877581656044096609802271449498404000 178:100:5899722570345263903289508274836321743794445103739160 178:101:4556221390959708756995857875616169267484818991006480 178:102:3439500461802917394987069180612206211728735904975480 178:103:2537883835893414776883662696374055068848387658040160 178:104:1830204689346212579483410598346674328496433407240500 178:105:1289858542967806960778784612168132383892724496531400 178:106:888298807892923661668408270644091170039329134403700 178:107:597733777273743024674069116695089385447025211935200 178:108:392954612837368099554249141531030984877211018957400 178:109:252356173381796027236673760616258430655089645202000 178:110:158296145121308417084822631659289379229101686535800 178:111:96974215029270021277188639214699799888098330490400 178:112:58011360776438316299746775244507916004487394132650 178:113:33882741692432998900737054567588694303505911617300 178:114:19319107105334604636385162692046185348490212764250 178:115:10751503084707953884596960106877877063507596668800 178:116:5839178399453457713186280058045743577594643018400 178:117:3094265476633456224081618492297744459921947582400 178:118:1599577915886786692109989220594596712332532224800 178:119:806509873556363038038650027190552964201276752000 178:120:396534021165211827035669596702021874065627736400 178:121:190074158905638727008833360402622055337243047200 178:122:88805139816568913438553291335651288149367653200 178:123:40431608371771212622430766786963188100525110400 178:124:17933374681027553985755582042604639883297428000 178:125:7747217862203903321846411442405204429584488896 178:126:3258750370609578381411585765456157418793475488 178:127:1334291490328331305774822518139529021868194688 178:128:531631765677694504644655847071218594650608821 178:129:206058823906083141335137925221402556066127450 178:130:77668325933831337887859679506528655748001885 178:131:28458623242930566554330264246666988365680080 178:132:10132994639528307788284260754495064039295180 178:133:3504644762543625250083278155690022148929160 178:134:1176932942645247285475727738851126841058300 178:135:383592959084376893043940892662589488937520 178:136:121283067945795635300657782238906970767010 178:137:37181670465134428340347641270321845052660 178:138:11046728181670373637349661536834751066370 178:139:3178914584653344931611413391894892393200 178:140:885554777153431802377465159170720023820 178:141:238660152708017081491799120911257878760 178:142:62186096128145295881665968124764376860 178:143:15655240983309305256922901066374248720 178:144:3805093294554345027724316231410407675 178:145:892228772516191247880184495641061110 178:146:201668147212563775205795125727089155 178:147:43900549053075107527792136212699680 178:148:9195385274630596847037542044551960 178:149:1851419853952469163833062156621200 178:150:357941171764144038341058683613432 178:151:66373197413218762076487702921696 178:152:11789975856295438000428736703196 178:153:2003525308912950248438870289432 178:154:325247615083271144227089332700 178:155:50360921045151661041613832160 178:156:7425007589990308999725116280 178:157:1040446923438132471299060880 178:158:138287249317726467704305560 178:159:17394622555688863862176800 178:160:2065611428488052583633495 178:161:230937923681894077673310 178:162:24234226559211106916335 178:163:2378819784953237488720 178:164:217574980331088794700 178:165:18460907422031776520 178:166:1445733713773572860 178:167:103885057277142960 178:168:6801997797908170 178:169:402485076799300 178:170:21308033477610 178:171:996867063280 178:172:40570171180 178:173:1407057960 178:174:40432700 178:175:924176 178:176:15753 178:177:178 178:178:1 # binomial(179, k) for 0 <= k <= 179 179:0:1 179:1:179 179:2:15931 179:3:939929 179:4:41356876 179:5:1447490660 179:6:41977229140 179:7:1037437234460 179:8:22304900540890 179:9:423793110276910 179:10:7204482874707470 179:11:110687055075051130 179:12:1549618771050715820 179:13:19906641135805349380 179:14:236035887753120571220 179:15:2596394765284326283420 179:16:26613046344164344405055 179:17:255172150241105184589645 179:18:2296549352169946661306805 179:19:19460233984176916445810295 179:20:155681871873415331566482360 179:21:1178734172755858939003366440 179:22:8465454513428441471024177160 179:23:57785928635141970041338948440 179:24:375608536128422805268703164860 179:25:2328772923996221392665959622132 179:26:13793501165208388248867606992628 179:27:78163173269514200076916439624892 179:28:424314369177362800417546386535128 179:29:2209361025716613202174120840234632 179:30:11046805128583066010870604201173160 179:31:53095934327705704374829678257251640 179:32:245568696265638882733587261939788835 179:33:1093896919728755023085979621368150265 179:34:4697322067070536275604500727051468785 179:35:19460334277863650284647217297784656395 179:36:77841337111454601138588869191138625580 179:37:300846248836162377373465089036022255620 179:38:1124214929861448883869264280081977902580 179:39:4064469361806776733988878551065612417020 179:40:14225642766323718568961074928729643459570 179:41:48228398646804801977697302807156596119030 179:42:158464738410930063641005423509228815819670 179:43:504876027030172528344598674901496459704530 179:44:1560525901729624178519668631513716329995820 179:45:4681577705188872535559005894541148989987460 179:46:13637639402071933038367538910185086188224340 179:47:38591617882458874342614525001162052404975260 179:48:106126949176761904442189943753195644113681965 179:49:283727149839914479222997604727931211814129335 179:50:737690589583777645979793772292621150716736271 179:51:1865923256006025810419478365210747616518803509 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179:69:410652318503104444321496392275547809884191331737800 179:70:645310786219164126790922902147289415532300664159400 179:71:990688390111111124228318258226120370324236230892600 179:72:1486032585166666686342477387339180555486354346338900 179:73:2178157350860730622447192882812223553932053630935100 179:74:3120063232314019540262195210514806712389157903771900 179:75:4368088525239627356367073294720729397344821065280660 179:76:5977384297696332171870731876986261280577123563015640 179:77:7995721852762626151982927056228375479213554895981960 179:78:10455943961304972660285366150452491011279264094745640 179:79:13367725823946863780871164318932931546065894602143160 179:80:16709657279933579726088955398666164432582368252678950 179:81:20422914453252152998553167709480867639822894531052050 179:82:24407873370959890169002566286940549130520044683452450 179:83:28524864060037462004737938913653412839282461858974550 179:84:32599844640042813719700501615603900387751384981685200 179:85:36435120480047850627900560629204359256898606744236400 179:86:39824434013075557663054101152851276397075221325095600 179:87:42570946703632492674299211577185847183080409002688400 179:88:44505989735615787795858266648876112964129518502810600 179:89:45506124336416142577787665899412654828491979592761400 179:90:45506124336416142577787665899412654828491979592761400 179:91:44505989735615787795858266648876112964129518502810600 179:92:42570946703632492674299211577185847183080409002688400 179:93:39824434013075557663054101152851276397075221325095600 179:94:36435120480047850627900560629204359256898606744236400 179:95:32599844640042813719700501615603900387751384981685200 179:96:28524864060037462004737938913653412839282461858974550 179:97:24407873370959890169002566286940549130520044683452450 179:98:20422914453252152998553167709480867639822894531052050 179:99:16709657279933579726088955398666164432582368252678950 179:100:13367725823946863780871164318932931546065894602143160 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179:135:1560525901729624178519668631513716329995820 179:136:504876027030172528344598674901496459704530 179:137:158464738410930063641005423509228815819670 179:138:48228398646804801977697302807156596119030 179:139:14225642766323718568961074928729643459570 179:140:4064469361806776733988878551065612417020 179:141:1124214929861448883869264280081977902580 179:142:300846248836162377373465089036022255620 179:143:77841337111454601138588869191138625580 179:144:19460334277863650284647217297784656395 179:145:4697322067070536275604500727051468785 179:146:1093896919728755023085979621368150265 179:147:245568696265638882733587261939788835 179:148:53095934327705704374829678257251640 179:149:11046805128583066010870604201173160 179:150:2209361025716613202174120840234632 179:151:424314369177362800417546386535128 179:152:78163173269514200076916439624892 179:153:13793501165208388248867606992628 179:154:2328772923996221392665959622132 179:155:375608536128422805268703164860 179:156:57785928635141970041338948440 179:157:8465454513428441471024177160 179:158:1178734172755858939003366440 179:159:155681871873415331566482360 179:160:19460233984176916445810295 179:161:2296549352169946661306805 179:162:255172150241105184589645 179:163:26613046344164344405055 179:164:2596394765284326283420 179:165:236035887753120571220 179:166:19906641135805349380 179:167:1549618771050715820 179:168:110687055075051130 179:169:7204482874707470 179:170:423793110276910 179:171:22304900540890 179:172:1037437234460 179:173:41977229140 179:174:1447490660 179:175:41356876 179:176:939929 179:177:15931 179:178:179 179:179:1 # binomial(180, k) for 0 <= k <= 180 180:0:1 180:1:180 180:2:16110 180:3:955860 180:4:42296805 180:5:1488847536 180:6:43424719800 180:7:1079414463600 180:8:23342337775350 180:9:446098010817800 180:10:7628275984984380 180:11:117891537949758600 180:12:1660305826125766950 180:13:21456259906856065200 180:14:255942528888925920600 180:15:2832430653037446854640 180:16:29209441109448670688475 180:17:281785196585269528994700 180:18:2551721502411051845896450 180:19:21756783336346863107117100 180:20:175142105857592248012292655 180:21:1334416044629274270569848800 180:22:9644188686184300410027543600 180:23:66251383148570411512363125600 180:24:433394464763564775310042113300 180:25:2704381460124644197934662786992 180:26:16122274089204609641533566614760 180:27:91956674434722588325784046617520 180:28:502477542446877000494462826160020 180:29:2633675394893976002591667226769760 180:30:13256166154299679213044725041407792 180:31:64142739456288770385700282458424800 180:32:298664630593344587108416940197040475 180:33:1339465615994393905819566883307939100 180:34:5791218986799291298690480348419619050 180:35:24157656344934186560251718024836125180 180:36:97301671389318251423236086488923281975 180:37:378687585947616978512053958227160881200 180:38:1425061178697611261242729369118000158200 180:39:5188684291668225617858142831147590319600 180:40:18290112128130495302949953479795255876590 180:41:62454041413128520546658377735886239578600 180:42:206693137057734865618702726316385411938700 180:43:663340765441102591985604098410725275524200 180:44:2065401928759796706864267306415212789700350 180:45:6242103606918496714078674526054865319983280 180:46:18319217107260805573926544804726235178211800 180:47:52229257284530807380982063911347138593199600 180:48:144718567059220778784804468754357696518657225 180:49:389854099016676383665187548481126855927811300 180:50:1021417739423692125202791377020552362530865606 180:51:2603613845589803456399272137503368767235539780 180:52:6458965116943935497605886648806434057180473685 180:53:15599010093751391390444405491457048289039634560 180:54:36686560776044939010859990692871206161259881280 180:55:84045575596030223915788342314577672296704455296 180:56:187601731241138892669170406952182304233715302000 180:57:408116046910547766508370709860887819736503464000 180:58:865487478793058194491889608842917272889481484000 180:59:1789652074792425419118822580997218767669775272000 180:60:3609131684164724595222958871677724514800713465200 180:61:7099931181963392646340246960677490848788288784000 180:62:13627287268607156853459506263235829209771070408000 180:63:25524125360248325535051138715267108678618830288000 180:64:46661291674203970118765362963847683053100049120250 180:65:83272458987810162058104340058558942063993933814600 180:66:145095951266638918737606047071731489959989430131500 180:67:246879678274579652777419244271304326200579030373000 180:68:410255935956286775938946685333196895009785741649250 180:69:665922678653682882683507663149536989001391348764000 180:70:1055963104722268571112419294422837225416491995897200 180:71:1635999176330275251019241160373409785856536895052000 180:72:2476720975277777810570795645565300925810590577231500 180:73:3664189936027397308789670270151404109418407977274000 180:74:5298220583174750162709388093327030266321211534707000 180:75:7488151757553646896629268505235536109733978969052560 180:76:10345472822935959528237805171706990677921944628296300 180:77:13973106150458958323853658933214636759790678458997600 180:78:18451665814067598812268293206680866490492818990727600 180:79:23823669785251836441156530469385422557345158696888800 180:80:30077383103880443506960119717599095978648262854822110 180:81:37132571733185732724642123108147032072405262783731000 180:82:44830787824212043167555733996421416770342939214504500 180:83:52932737430997352173740505200593961969802506542427000 180:84:61124708700080275724438440529257313227033846840659750 180:85:69034965120090664347601062244808259644649991725921600 180:86:76259554493123408290954661782055635653973828069332000 180:87:82395380716708050337353312730037123580155630327784000 180:88:87076936439248280470157478226061960147209927505499000 180:89:90012114072031930373645932548288767792621498095572000 180:90:91012248672832285155575331798825309656983959185522800 180:91:90012114072031930373645932548288767792621498095572000 180:92:87076936439248280470157478226061960147209927505499000 180:93:82395380716708050337353312730037123580155630327784000 180:94:76259554493123408290954661782055635653973828069332000 180:95:69034965120090664347601062244808259644649991725921600 180:96:61124708700080275724438440529257313227033846840659750 180:97:52932737430997352173740505200593961969802506542427000 180:98:44830787824212043167555733996421416770342939214504500 180:99:37132571733185732724642123108147032072405262783731000 180:100:30077383103880443506960119717599095978648262854822110 180:101:23823669785251836441156530469385422557345158696888800 180:102:18451665814067598812268293206680866490492818990727600 180:103:13973106150458958323853658933214636759790678458997600 180:104:10345472822935959528237805171706990677921944628296300 180:105:7488151757553646896629268505235536109733978969052560 180:106:5298220583174750162709388093327030266321211534707000 180:107:3664189936027397308789670270151404109418407977274000 180:108:2476720975277777810570795645565300925810590577231500 180:109:1635999176330275251019241160373409785856536895052000 180:110:1055963104722268571112419294422837225416491995897200 180:111:665922678653682882683507663149536989001391348764000 180:112:410255935956286775938946685333196895009785741649250 180:113:246879678274579652777419244271304326200579030373000 180:114:145095951266638918737606047071731489959989430131500 180:115:83272458987810162058104340058558942063993933814600 180:116:46661291674203970118765362963847683053100049120250 180:117:25524125360248325535051138715267108678618830288000 180:118:13627287268607156853459506263235829209771070408000 180:119:7099931181963392646340246960677490848788288784000 180:120:3609131684164724595222958871677724514800713465200 180:121:1789652074792425419118822580997218767669775272000 180:122:865487478793058194491889608842917272889481484000 180:123:408116046910547766508370709860887819736503464000 180:124:187601731241138892669170406952182304233715302000 180:125:84045575596030223915788342314577672296704455296 180:126:36686560776044939010859990692871206161259881280 180:127:15599010093751391390444405491457048289039634560 180:128:6458965116943935497605886648806434057180473685 180:129:2603613845589803456399272137503368767235539780 180:130:1021417739423692125202791377020552362530865606 180:131:389854099016676383665187548481126855927811300 180:132:144718567059220778784804468754357696518657225 180:133:52229257284530807380982063911347138593199600 180:134:18319217107260805573926544804726235178211800 180:135:6242103606918496714078674526054865319983280 180:136:2065401928759796706864267306415212789700350 180:137:663340765441102591985604098410725275524200 180:138:206693137057734865618702726316385411938700 180:139:62454041413128520546658377735886239578600 180:140:18290112128130495302949953479795255876590 180:141:5188684291668225617858142831147590319600 180:142:1425061178697611261242729369118000158200 180:143:378687585947616978512053958227160881200 180:144:97301671389318251423236086488923281975 180:145:24157656344934186560251718024836125180 180:146:5791218986799291298690480348419619050 180:147:1339465615994393905819566883307939100 180:148:298664630593344587108416940197040475 180:149:64142739456288770385700282458424800 180:150:13256166154299679213044725041407792 180:151:2633675394893976002591667226769760 180:152:502477542446877000494462826160020 180:153:91956674434722588325784046617520 180:154:16122274089204609641533566614760 180:155:2704381460124644197934662786992 180:156:433394464763564775310042113300 180:157:66251383148570411512363125600 180:158:9644188686184300410027543600 180:159:1334416044629274270569848800 180:160:175142105857592248012292655 180:161:21756783336346863107117100 180:162:2551721502411051845896450 180:163:281785196585269528994700 180:164:29209441109448670688475 180:165:2832430653037446854640 180:166:255942528888925920600 180:167:21456259906856065200 180:168:1660305826125766950 180:169:117891537949758600 180:170:7628275984984380 180:171:446098010817800 180:172:23342337775350 180:173:1079414463600 180:174:43424719800 180:175:1488847536 180:176:42296805 180:177:955860 180:178:16110 180:179:180 180:180:1 # binomial(181, k) for 0 <= k <= 181 181:0:1 181:1:181 181:2:16290 181:3:971970 181:4:43252665 181:5:1531144341 181:6:44913567336 181:7:1122839183400 181:8:24421752238950 181:9:469440348593150 181:10:8074373995802180 181:11:125519813934742980 181:12:1778197364075525550 181:13:23116565732981832150 181:14:277398788795781985800 181:15:3088373181926372775240 181:16:32041871762486117543115 181:17:310994637694718199683175 181:18:2833506698996321374891150 181:19:24308504838757914953013550 181:20:196898889193939111119409755 181:21:1509558150486866518582141455 181:22:10978604730813574680597392400 181:23:75895571834754711922390669200 181:24:499645847912135186822405238900 181:25:3137775924888208973244704900292 181:26:18826655549329253839468229401752 181:27:108078948523927197967317613232280 181:28:594434216881599588820246872777540 181:29:3136152937340853003086130052929780 181:30:15889841549193655215636392268177552 181:31:77398905610588449598745007499832592 181:32:362807370049633357494117222655465275 181:33:1638130246587738492927983823504979575 181:34:7130684602793685204510047231727558150 181:35:29948875331733477858942198373255744230 181:36:121459327734252437983487804513759407155 181:37:475989257336935229935290044716084163175 181:38:1803748764645228239754783327345161039400 181:39:6613745470365836879100872200265590477800 181:40:23478796419798720920808096310942846196190 181:41:80744153541259015849608331215681495455190 181:42:269147178470863386165361104052271651517300 181:43:870033902498837457604306824727110687462900 181:44:2728742694200899298849871404825938065224550 181:45:8307505535678293420942941832470078109683630 181:46:24561320714179302288005219330781100498195080 181:47:70548474391791612954908608716073373771411400 181:48:196947824343751586165786532665704835111856825 181:49:534572666075897162449992017235484552446468525 181:50:1411271838440368508867978925501679218458676906 181:51:3625031585013495581602063514523921129766405386 181:52:9062578962533738954005158786309802824416013465 181:53:22057975210695326888050292140263482346220108245 181:54:52285570869796330401304396184328254450299515840 181:55:120732136372075162926648333007448878457964336576 181:56:271647306837169116584958749266759976530419757296 181:57:595717778151686659177541116813070123970218766000 181:58:1273603525703605961000260318703805092625984948000 181:59:2655139553585483613610712189840136040559256756000 181:60:5398783758957150014341781452674943282470488737200 181:61:10709062866128117241563205832355215363589002249200 181:62:20727218450570549499799753223913320058559359192000 181:63:39151412628855482388510644978502937888389900696000 181:64:72185417034452295653816501679114791731718879408250 181:65:129933750662014132176869703022406625117093982934850 181:66:228368410254449080795710387130290432023983363946100 181:67:391975629541218571515025291343035816160568460504500 181:68:657135614230866428716365929604501221210364772022250 181:69:1076178614609969658622454348482733884011177090413250 181:70:1721885783375951453795926957572374214417883344661200 181:71:2691962281052543822131660454796247011273028890949200 181:72:4112720151608053061590036805938710711667127472283500 181:73:6140910911305175119360465915716705035228998554505500 181:74:8962410519202147471499058363478434375739619511981000 181:75:12786372340728397059338656598562566376055190503759560 181:76:17833624580489606424867073676942526787655923597348860 181:77:24318578973394917852091464104921627437712623087293900 181:78:32424771964526557136121952139895503250283497449725200 181:79:42275335599319435253424823676066289047837977687616400 181:80:53901052889132279948116650186984518535993421551710910 181:81:67209954837066176231602242825746128051053525638553110 181:82:81963359557397775892197857104568448842748201998235500 181:83:97763525255209395341296239197015378740145445756931500 181:84:114057446131077627898178945729851275196836353383086750 181:85:130159673820170940072039502774065572871683838566581350 181:86:145294519613214072638555724026863895298623819795253600 181:87:158654935209831458628307974512092759234129458397116000 181:88:169472317155956330807510790956099083727365557833283000 181:89:177089050511280210843803410774350727939831425601071000 181:90:181024362744864215529221264347114077449605457281094800 181:91:181024362744864215529221264347114077449605457281094800 181:92:177089050511280210843803410774350727939831425601071000 181:93:169472317155956330807510790956099083727365557833283000 181:94:158654935209831458628307974512092759234129458397116000 181:95:145294519613214072638555724026863895298623819795253600 181:96:130159673820170940072039502774065572871683838566581350 181:97:114057446131077627898178945729851275196836353383086750 181:98:97763525255209395341296239197015378740145445756931500 181:99:81963359557397775892197857104568448842748201998235500 181:100:67209954837066176231602242825746128051053525638553110 181:101:53901052889132279948116650186984518535993421551710910 181:102:42275335599319435253424823676066289047837977687616400 181:103:32424771964526557136121952139895503250283497449725200 181:104:24318578973394917852091464104921627437712623087293900 181:105:17833624580489606424867073676942526787655923597348860 181:106:12786372340728397059338656598562566376055190503759560 181:107:8962410519202147471499058363478434375739619511981000 181:108:6140910911305175119360465915716705035228998554505500 181:109:4112720151608053061590036805938710711667127472283500 181:110:2691962281052543822131660454796247011273028890949200 181:111:1721885783375951453795926957572374214417883344661200 181:112:1076178614609969658622454348482733884011177090413250 181:113:657135614230866428716365929604501221210364772022250 181:114:391975629541218571515025291343035816160568460504500 181:115:228368410254449080795710387130290432023983363946100 181:116:129933750662014132176869703022406625117093982934850 181:117:72185417034452295653816501679114791731718879408250 181:118:39151412628855482388510644978502937888389900696000 181:119:20727218450570549499799753223913320058559359192000 181:120:10709062866128117241563205832355215363589002249200 181:121:5398783758957150014341781452674943282470488737200 181:122:2655139553585483613610712189840136040559256756000 181:123:1273603525703605961000260318703805092625984948000 181:124:595717778151686659177541116813070123970218766000 181:125:271647306837169116584958749266759976530419757296 181:126:120732136372075162926648333007448878457964336576 181:127:52285570869796330401304396184328254450299515840 181:128:22057975210695326888050292140263482346220108245 181:129:9062578962533738954005158786309802824416013465 181:130:3625031585013495581602063514523921129766405386 181:131:1411271838440368508867978925501679218458676906 181:132:534572666075897162449992017235484552446468525 181:133:196947824343751586165786532665704835111856825 181:134:70548474391791612954908608716073373771411400 181:135:24561320714179302288005219330781100498195080 181:136:8307505535678293420942941832470078109683630 181:137:2728742694200899298849871404825938065224550 181:138:870033902498837457604306824727110687462900 181:139:269147178470863386165361104052271651517300 181:140:80744153541259015849608331215681495455190 181:141:23478796419798720920808096310942846196190 181:142:6613745470365836879100872200265590477800 181:143:1803748764645228239754783327345161039400 181:144:475989257336935229935290044716084163175 181:145:121459327734252437983487804513759407155 181:146:29948875331733477858942198373255744230 181:147:7130684602793685204510047231727558150 181:148:1638130246587738492927983823504979575 181:149:362807370049633357494117222655465275 181:150:77398905610588449598745007499832592 181:151:15889841549193655215636392268177552 181:152:3136152937340853003086130052929780 181:153:594434216881599588820246872777540 181:154:108078948523927197967317613232280 181:155:18826655549329253839468229401752 181:156:3137775924888208973244704900292 181:157:499645847912135186822405238900 181:158:75895571834754711922390669200 181:159:10978604730813574680597392400 181:160:1509558150486866518582141455 181:161:196898889193939111119409755 181:162:24308504838757914953013550 181:163:2833506698996321374891150 181:164:310994637694718199683175 181:165:32041871762486117543115 181:166:3088373181926372775240 181:167:277398788795781985800 181:168:23116565732981832150 181:169:1778197364075525550 181:170:125519813934742980 181:171:8074373995802180 181:172:469440348593150 181:173:24421752238950 181:174:1122839183400 181:175:44913567336 181:176:1531144341 181:177:43252665 181:178:971970 181:179:16290 181:180:181 181:181:1 # binomial(182, k) for 0 <= k <= 182 182:0:1 182:1:182 182:2:16471 182:3:988260 182:4:44224635 182:5:1574397006 182:6:46444711677 182:7:1167752750736 182:8:25544591422350 182:9:493862100832100 182:10:8543814344395330 182:11:133594187930545160 182:12:1903717178010268530 182:13:24894763097057357700 182:14:300515354528763817950 182:15:3365771970722154761040 182:16:35130244944412490318355 182:17:343036509457204317226290 182:18:3144501336691039574574325 182:19:27142011537754236327904700 182:20:221207394032697026072423305 182:21:1706457039680805629701551210 182:22:12488162881300441199179533855 182:23:86874176565568286602988061600 182:24:575541419746889898744795908100 182:25:3637421772800344160067110139192 182:26:21964431474217462812712934302044 182:27:126905604073256451806785842634032 182:28:702513165405526786787564486009820 182:29:3730587154222452591906376925707320 182:30:19025994486534508218722522321107332 182:31:93288747159782104814381399768010144 182:32:440206275660221807092862230155297867 182:33:2000937616637371850422101046160444850 182:34:8768814849381423697438031055232537725 182:35:37079559934527163063452245604983302380 182:36:151408203065985915842430002887015151385 182:37:597448585071187667918777849229843570330 182:38:2279738021982163469690073372061245202575 182:39:8417494235011065118855655527610751517200 182:40:30092541890164557799908968511208436673990 182:41:104222949961057736770416427526624341651380 182:42:349891332012122402014969435267953146972490 182:43:1139181080969700843769667928779382338980200 182:44:3598776596699736756454178229553048752687450 182:45:11036248229879192719792813237296016174908180 182:46:32868826249857595708948161163251178607878710 182:47:95109795105970915242913828046854474269606480 182:48:267496298735543199120695141381778208883268225 182:49:731520490419648748615778549901189387558325350 182:50:1945844504516265671317970942737163770905145431 182:51:5036303423453864090470042440025600348225082292 182:52:12687610547547234535607222300833723954182418851 182:53:31120554173229065842055450926573285170636121710 182:54:74343546080491657289354688324591736796519624085 182:55:173017707241871493327952729191777132908263852416 182:56:392379443209244279511607082274208854988384093872 182:57:867365084988855775762499866079830100500638523296 182:58:1869321303855292620177801435516875216596203714000 182:59:3928743079289089574610972508543941133185241704000 182:60:8053923312542633627952493642515079323029745493200 182:61:16107846625085267255904987285030158646059490986400 182:62:31436281316698666741362959056268535422148361441200 182:63:59878631079426031888310398202416257946949259888000 182:64:111336829663307778042327146657617729620108780104250 182:65:202119167696466427830686204701521416848812862343100 182:66:358302160916463212972580090152697057141077346880950 182:67:620344039795667652310735678473326248184551824450600 182:68:1049111243772085000231391220947537037370933232526750 182:69:1733314228840836087338820278087235105221541862435500 182:70:2798064397985921112418381306055108098429060435074450 182:71:4413848064428495275927587412368621225690912235610400 182:72:6804682432660596883721697260734957722940156363232700 182:73:10253631062913228180950502721655415746896126026789000 182:74:15103321430507322590859524279195139410968618066486500 182:75:21748782859930544530837714962041000751794810015740560 182:76:30619996921218003484205730275505093163711114101108420 182:77:42152203553884524276958537781864154225368546684642760 182:78:56743350937921474988213416244817130687996120537019100 182:79:74700107563845992389546775815961792298121475137341600 182:80:96176388488451715201541473863050807583831399239327310 182:81:121111007726198456179718893012730646587046947190264020 182:82:149173314394463952123800099930314576893801727636788610 182:83:179726884812607171233494096301583827582893647755167000 182:84:211820971386287023239475184926866653936981799140018250 182:85:244217119951248567970218448503916848068520191949668100 182:86:275454193433385012710595226800929468170307658361834950 182:87:303949454823045531266863698538956654532753278192369600 182:88:328127252365787789435818765468191842961495016230399000 182:89:346561367667236541651314201730449811667196983434354000 182:90:358113413256144426373024675121464805389436882882165800 182:91:362048725489728431058442528694228154899210914562189600 182:92:358113413256144426373024675121464805389436882882165800 182:93:346561367667236541651314201730449811667196983434354000 182:94:328127252365787789435818765468191842961495016230399000 182:95:303949454823045531266863698538956654532753278192369600 182:96:275454193433385012710595226800929468170307658361834950 182:97:244217119951248567970218448503916848068520191949668100 182:98:211820971386287023239475184926866653936981799140018250 182:99:179726884812607171233494096301583827582893647755167000 182:100:149173314394463952123800099930314576893801727636788610 182:101:121111007726198456179718893012730646587046947190264020 182:102:96176388488451715201541473863050807583831399239327310 182:103:74700107563845992389546775815961792298121475137341600 182:104:56743350937921474988213416244817130687996120537019100 182:105:42152203553884524276958537781864154225368546684642760 182:106:30619996921218003484205730275505093163711114101108420 182:107:21748782859930544530837714962041000751794810015740560 182:108:15103321430507322590859524279195139410968618066486500 182:109:10253631062913228180950502721655415746896126026789000 182:110:6804682432660596883721697260734957722940156363232700 182:111:4413848064428495275927587412368621225690912235610400 182:112:2798064397985921112418381306055108098429060435074450 182:113:1733314228840836087338820278087235105221541862435500 182:114:1049111243772085000231391220947537037370933232526750 182:115:620344039795667652310735678473326248184551824450600 182:116:358302160916463212972580090152697057141077346880950 182:117:202119167696466427830686204701521416848812862343100 182:118:111336829663307778042327146657617729620108780104250 182:119:59878631079426031888310398202416257946949259888000 182:120:31436281316698666741362959056268535422148361441200 182:121:16107846625085267255904987285030158646059490986400 182:122:8053923312542633627952493642515079323029745493200 182:123:3928743079289089574610972508543941133185241704000 182:124:1869321303855292620177801435516875216596203714000 182:125:867365084988855775762499866079830100500638523296 182:126:392379443209244279511607082274208854988384093872 182:127:173017707241871493327952729191777132908263852416 182:128:74343546080491657289354688324591736796519624085 182:129:31120554173229065842055450926573285170636121710 182:130:12687610547547234535607222300833723954182418851 182:131:5036303423453864090470042440025600348225082292 182:132:1945844504516265671317970942737163770905145431 182:133:731520490419648748615778549901189387558325350 182:134:267496298735543199120695141381778208883268225 182:135:95109795105970915242913828046854474269606480 182:136:32868826249857595708948161163251178607878710 182:137:11036248229879192719792813237296016174908180 182:138:3598776596699736756454178229553048752687450 182:139:1139181080969700843769667928779382338980200 182:140:349891332012122402014969435267953146972490 182:141:104222949961057736770416427526624341651380 182:142:30092541890164557799908968511208436673990 182:143:8417494235011065118855655527610751517200 182:144:2279738021982163469690073372061245202575 182:145:597448585071187667918777849229843570330 182:146:151408203065985915842430002887015151385 182:147:37079559934527163063452245604983302380 182:148:8768814849381423697438031055232537725 182:149:2000937616637371850422101046160444850 182:150:440206275660221807092862230155297867 182:151:93288747159782104814381399768010144 182:152:19025994486534508218722522321107332 182:153:3730587154222452591906376925707320 182:154:702513165405526786787564486009820 182:155:126905604073256451806785842634032 182:156:21964431474217462812712934302044 182:157:3637421772800344160067110139192 182:158:575541419746889898744795908100 182:159:86874176565568286602988061600 182:160:12488162881300441199179533855 182:161:1706457039680805629701551210 182:162:221207394032697026072423305 182:163:27142011537754236327904700 182:164:3144501336691039574574325 182:165:343036509457204317226290 182:166:35130244944412490318355 182:167:3365771970722154761040 182:168:300515354528763817950 182:169:24894763097057357700 182:170:1903717178010268530 182:171:133594187930545160 182:172:8543814344395330 182:173:493862100832100 182:174:25544591422350 182:175:1167752750736 182:176:46444711677 182:177:1574397006 182:178:44224635 182:179:988260 182:180:16471 182:181:182 182:182:1 # binomial(183, k) for 0 <= k <= 183 183:0:1 183:1:183 183:2:16653 183:3:1004731 183:4:45212895 183:5:1618621641 183:6:48019108683 183:7:1214197462413 183:8:26712344173086 183:9:519406692254450 183:10:9037676445227430 183:11:142138002274940490 183:12:2037311365940813690 183:13:26798480275067626230 183:14:325410117625821175650 183:15:3666287325250918578990 183:16:38496016915134645079395 183:17:378166754401616807544645 183:18:3487537846148243891800615 183:19:30286512874445275902479025 183:20:248349405570451262400328005 183:21:1927664433713502655773974515 183:22:14194619920981246828881085065 183:23:99362339446868727802167595455 183:24:662415596312458185347783969700 183:25:4212963192547234058811906047292 183:26:25601853247017806972780044441236 183:27:148870035547473914619498776936076 183:28:829418769478783238594350328643852 183:29:4433100319627979378693941411717140 183:30:22756581640756960810628899246814652 183:31:112314741646316613033103922089117476 183:32:533495022820003911907243629923308011 183:33:2441143892297593657514963276315742717 183:34:10769752466018795547860132101392982575 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183:54:105464100253720723131410139251165021967155745795 183:55:247361253322363150617307417516368869704783476501 183:56:565397150451115772839559811465985987896647946288 183:57:1259744528198100055274106948354038955489022617168 183:58:2736686388844148395940301301596705317096842237296 183:59:5798064383144382194788773944060816349781445418000 183:60:11982666391831723202563466151059020456214987197200 183:61:24161769937627900883857480927545237969089236479600 183:62:47544127941783933997267946341298694068207852427600 183:63:91314912396124698629673357258684793369097621329200 183:64:171215460742733809930637544860033987567058039992250 183:65:313455997359774205873013351359139146468921642447350 183:66:560421328612929640803266294854218473989890209224050 183:67:978646200712130865283315768626023305325629171331550 183:68:1669455283567752652542126899420863285555485056977350 183:69:2782425472612921087570211499034772142592475094962250 183:70:4531378626826757199757201584142343203650602297509950 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183:156:148870035547473914619498776936076 183:157:25601853247017806972780044441236 183:158:4212963192547234058811906047292 183:159:662415596312458185347783969700 183:160:99362339446868727802167595455 183:161:14194619920981246828881085065 183:162:1927664433713502655773974515 183:163:248349405570451262400328005 183:164:30286512874445275902479025 183:165:3487537846148243891800615 183:166:378166754401616807544645 183:167:38496016915134645079395 183:168:3666287325250918578990 183:169:325410117625821175650 183:170:26798480275067626230 183:171:2037311365940813690 183:172:142138002274940490 183:173:9037676445227430 183:174:519406692254450 183:175:26712344173086 183:176:1214197462413 183:177:48019108683 183:178:1618621641 183:179:45212895 183:180:1004731 183:181:16653 183:182:183 183:183:1 # binomial(184, k) for 0 <= k <= 184 184:0:1 184:1:184 184:2:16836 184:3:1021384 184:4:46217626 184:5:1663834536 184:6:49637730324 184:7:1262216571096 184:8:27926541635499 184:9:546119036427536 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184:73:28276843992662917224321484655493952418467350988864800 184:74:42415265988994375836482226983240928627701026483297200 184:75:62209056783858417893507266242086695320628172175502560 184:76:89220884071586415136740684478782234078269352199076040 184:77:125140980256251075776207713294915341304585584902600160 184:78:171667754966908527026336222084050532302444328007413040 184:79:230339012993573466642932146087460207899482262896022560 184:80:302319954554065174968848441739791522868070470051029610 184:81:388163892266947878972348616554794054052831220806260240 184:82:487571718335312579684779359818826677651727021256643960 184:83:599184521327733531660813189174943627957544050219008240 184:84:720448055405965317830263477460348885996570822287140860 184:85:847585947536429785682662914659233983525377437984871600 184:86:975709404722169171890507308735629818244329841401189400 184:87:1099074961641064124658272600644732438941888786865707600 184:88:1211480355445263864680141389347034620197309230976973150 184:89:1306765327221857651789815431205790152122940294087521600 184:90:1379363400956405299111471844050556271685325865981272800 184:91:1424836919669253825455806080667607577345281663760875200 184:92:1440324277491745714862934407631385920577295594888710800 184:93:1424836919669253825455806080667607577345281663760875200 184:94:1379363400956405299111471844050556271685325865981272800 184:95:1306765327221857651789815431205790152122940294087521600 184:96:1211480355445263864680141389347034620197309230976973150 184:97:1099074961641064124658272600644732438941888786865707600 184:98:975709404722169171890507308735629818244329841401189400 184:99:847585947536429785682662914659233983525377437984871600 184:100:720448055405965317830263477460348885996570822287140860 184:101:599184521327733531660813189174943627957544050219008240 184:102:487571718335312579684779359818826677651727021256643960 184:103:388163892266947878972348616554794054052831220806260240 184:104:302319954554065174968848441739791522868070470051029610 184:105:230339012993573466642932146087460207899482262896022560 184:106:171667754966908527026336222084050532302444328007413040 184:107:125140980256251075776207713294915341304585584902600160 184:108:89220884071586415136740684478782234078269352199076040 184:109:62209056783858417893507266242086695320628172175502560 184:110:42415265988994375836482226983240928627701026483297200 184:111:28276843992662917224321484655493952418467350988864800 184:112:18430442959503508547995253391527308272751041269527950 184:113:11743291089241173588103170302566072527770574968194800 184:114:7313804099439678287327413083177115346243077392472200 184:115:4451880756180673740112338398455635428147960151939600 184:116:2648101484279883517825442668046886590881114228308900 184:117:1539067529325060506086582063480241779315519380555600 184:118:873877325972703846676279646213357620458811851671400 184:119:484671458102508015803650896219173134035979682439600 184:120:262530373138858508560310902118718780936155661321450 184:121:138859040337908632626941303599983487437305473756800 184:122:71705897879411834881125427268843932037297088907200 184:123:36144436329459624086420947078604258425304223676800 184:124:17780730774976105397352240095119836805996432615200 184:125:8534750771988530590729075245657521666878287655296 184:126:3996430917042248451214408249950744272585864854464 184:127:1825141678649215828113666759820024943385670563456 184:128:812758403773478923456867228982354857601431422789 184:129:352825353576083873748717556767533891671939222296 184:130:149272264974497023509072812478572031091974286356 184:131:61532078691777399003739937968266333427226041704 184:132:24706061898971228387865278123622088421537728866 184:133:9659512922906044181721762875401117277593698504 184:134:3676381784091106367670223183921320754905064356 184:135:1361622882996706062100082660711600279594468280 184:136:490584715197342625315470958638738336030359895 184:137:171883695835565299380602963610652847660272080 184:138:58540099306315717904987965867396259710382520 184:139:19372982504248367076470837625181496019263280 184:140:6227030090651260846008483522379766577620340 184:141:1943186694955003384570023226841912974576560 184:142:588429773824402433355711258832410266949240 184:143:172825527976397917489090020076651966516560 184:144:49207268382168851507310352938491184910965 184:145:13574418864046579726154580120963085492680 184:146:3626043395190524721370059073407947494620 184:147:937344551137686662667090100608857175480 184:148:234336137784421665666772525152214293870 184:149:56618127249927382308750408761608822680 184:150:13210896358316389205375095377708725292 184:151:2974638915117597569422206906239050728 184:152:645809764466320524940347552012425487 184:153:135071323287073573843732821335932128 184:154:27189681960384940189322840658531792 184:155:5262519089106762617288291740360992 184:156:978288805026257153213849105579928 184:157:174471888794491721592278821377312 184:158:29814816439565041031591950488528 184:159:4875378788859692244159690016992 184:160:761777935759326913149951565155 184:161:113556959367849974631048680520 184:162:16122284354694749484655059580 184:163:2176013839283953918174302520 184:164:278635918444896538302807030 184:165:33774050720593519794279640 184:166:3865704600549860699345260 184:167:416662771316751452624040 184:168:42162304240385563658385 184:169:3991697442876739754640 184:170:352208597900888801880 184:171:28835791641008439920 184:172:2179449368215754180 184:173:151175678720167920 184:174:9557083137481880 184:175:546119036427536 184:176:27926541635499 184:177:1262216571096 184:178:49637730324 184:179:1663834536 184:180:46217626 184:181:1021384 184:182:16836 184:183:184 184:184:1 # binomial(185, k) for 0 <= k <= 185 185:0:1 185:1:185 185:2:17020 185:3:1038220 185:4:47239010 185:5:1710052162 185:6:51301564860 185:7:1311854301420 185:8:29188758206595 185:9:574045578063035 185:10:10103202173909416 185:11:160732761857649800 185:12:2330625046935922100 185:13:31015241009224194100 185:14:381044389541897241800 185:15:4343906040777628556520 185:16:46154001683262303413025 185:17:458825075557137016282425 185:18:4282367371866612151969300 185:19:37639755321143380493624900 185:20:312409969165490058097086670 185:21:2454649757728850456477109550 185:22:18298298193978703402829362100 185:23:129679243722544724115703740100 185:24:875334895127176887781000245675 185:25:5637156724619019157309641582147 185:26:34690195228424733275751640505520 185:27:204286705234056762623870771865840 185:28:1152760693820748874806127926957240 185:29:6240807894133019770502140845940920 185:30:32452201049491702806611132398892784 185:31:162261005247458514033055661994463920 185:32:780881087753394098784080373348357615 185:33:3620448679583918094362554458251476215 185:34:16185535273433986774797302283947776020 185:35:69829023608243771514125504139317547972 185:36:290954265034349047975522933913823116550 185:37:1171680688922108328333862625761071469350 185:38:4563387946328211384037149174016804670100 185:39:17200462259237104447524639194371032987300 185:40:62781687246215431233464933059454270403645 185:41:222032796358566768996400373015143151427525 185:42:761255301800800350844801278909062233465800 185:43:2531616468779405817925734485674323241525800 185:44:8170216785606264230578506749221679552196900 185:45:25600012594899627922479321147561262596883620 185:46:77913081810564084981458803492577755729645800 185:47:230423795141881017285590929478049107370654600 185:48:662468411032907924696073922249391183690631975 185:49:1852207598194048687415553619350338615624828175 185:50:5038004667087812429770305844632921034499532636 185:51:13335894706997150549391986059322438032498762860 185:52:34365574821877272569587040999023205699131427370 185:53:86238140590748627391605216091888421848763770570 185:54:210804343666274422512812750446838364519200328060 185:55:502097618550580897257790369246105922763913508652 185:56:1165583757349562797205584785749888749273370645085 185:57:2637900082422694751570533988802379800987101986245 185:58:5821572595691464279328075009770769215971535417920 185:59:12531181689030779041943483495608265939464152509760 185:60:26315481546964635988081315340777358472874720270496 185:61:53925167104435729483773187173724095231300656292000 185:62:107850334208871458967546374347448190462601312584000 185:63:210564938217320467508066730868827419474602562664000 185:64:401389413476767141187252205718702268373461135078250 185:65:747201831241366524363961798337891914972135343761050 185:66:1358548784075211862479930542432530754494791534111000 185:67:2412944855297764352762861709693599399774331232227000 185:68:4187169013604944023912024731527128370196633608864500 185:69:7099982240460557257937781066502522019029074380248500 185:70:11765684855620352027439751481632750774391037544411800 185:71:19057095188680851875430583385743187874013652360667000 185:72:30173734048744682136098423694093380800521616237722750 185:73:46707286952166425772316738047021260691218392258392750 185:74:70692109981657293060803711638734881046168377472162000 185:75:104624322772852793729989493225327623948329198658799760 185:76:151429940855444833030247950720868929398897524374578600 185:77:214361864327837490912948397773697575382854937101676200 185:78:296808735223159602802543935378965873607029912910013200 185:79:402006767960481993669268368171510740201926590903435600 185:80:532658967547638641611780587827251730767552732947052170 185:81:690483846821013053941197058294585576920901690857289850 185:82:875735610602260458657127976373620731704558242062904200 185:83:1086756239663046111345592548993770305609271071475652200 185:84:1319632576733698849491076666635292513954114872506149100 185:85:1568034002942395103512926392119582869521948260272012460 185:86:1823295352258598957573170223394863801769707279386061000 185:87:2074784366363233296548779909380362257186218628266897000 185:88:2310555317086327989338413989991767059139198017842680750 185:89:2518245682667121516469956820552824772320249525064494750 185:90:2686128728178262950901287275256346423808266160068794400 185:91:2804200320625659124567277924718163849030607529742148000 185:92:2865161197160999540318740488298993497922577258649586000 185:93:2865161197160999540318740488298993497922577258649586000 185:94:2804200320625659124567277924718163849030607529742148000 185:95:2686128728178262950901287275256346423808266160068794400 185:96:2518245682667121516469956820552824772320249525064494750 185:97:2310555317086327989338413989991767059139198017842680750 185:98:2074784366363233296548779909380362257186218628266897000 185:99:1823295352258598957573170223394863801769707279386061000 185:100:1568034002942395103512926392119582869521948260272012460 185:101:1319632576733698849491076666635292513954114872506149100 185:102:1086756239663046111345592548993770305609271071475652200 185:103:875735610602260458657127976373620731704558242062904200 185:104:690483846821013053941197058294585576920901690857289850 185:105:532658967547638641611780587827251730767552732947052170 185:106:402006767960481993669268368171510740201926590903435600 185:107:296808735223159602802543935378965873607029912910013200 185:108:214361864327837490912948397773697575382854937101676200 185:109:151429940855444833030247950720868929398897524374578600 185:110:104624322772852793729989493225327623948329198658799760 185:111:70692109981657293060803711638734881046168377472162000 185:112:46707286952166425772316738047021260691218392258392750 185:113:30173734048744682136098423694093380800521616237722750 185:114:19057095188680851875430583385743187874013652360667000 185:115:11765684855620352027439751481632750774391037544411800 185:116:7099982240460557257937781066502522019029074380248500 185:117:4187169013604944023912024731527128370196633608864500 185:118:2412944855297764352762861709693599399774331232227000 185:119:1358548784075211862479930542432530754494791534111000 185:120:747201831241366524363961798337891914972135343761050 185:121:401389413476767141187252205718702268373461135078250 185:122:210564938217320467508066730868827419474602562664000 185:123:107850334208871458967546374347448190462601312584000 185:124:53925167104435729483773187173724095231300656292000 185:125:26315481546964635988081315340777358472874720270496 185:126:12531181689030779041943483495608265939464152509760 185:127:5821572595691464279328075009770769215971535417920 185:128:2637900082422694751570533988802379800987101986245 185:129:1165583757349562797205584785749888749273370645085 185:130:502097618550580897257790369246105922763913508652 185:131:210804343666274422512812750446838364519200328060 185:132:86238140590748627391605216091888421848763770570 185:133:34365574821877272569587040999023205699131427370 185:134:13335894706997150549391986059322438032498762860 185:135:5038004667087812429770305844632921034499532636 185:136:1852207598194048687415553619350338615624828175 185:137:662468411032907924696073922249391183690631975 185:138:230423795141881017285590929478049107370654600 185:139:77913081810564084981458803492577755729645800 185:140:25600012594899627922479321147561262596883620 185:141:8170216785606264230578506749221679552196900 185:142:2531616468779405817925734485674323241525800 185:143:761255301800800350844801278909062233465800 185:144:222032796358566768996400373015143151427525 185:145:62781687246215431233464933059454270403645 185:146:17200462259237104447524639194371032987300 185:147:4563387946328211384037149174016804670100 185:148:1171680688922108328333862625761071469350 185:149:290954265034349047975522933913823116550 185:150:69829023608243771514125504139317547972 185:151:16185535273433986774797302283947776020 185:152:3620448679583918094362554458251476215 185:153:780881087753394098784080373348357615 185:154:162261005247458514033055661994463920 185:155:32452201049491702806611132398892784 185:156:6240807894133019770502140845940920 185:157:1152760693820748874806127926957240 185:158:204286705234056762623870771865840 185:159:34690195228424733275751640505520 185:160:5637156724619019157309641582147 185:161:875334895127176887781000245675 185:162:129679243722544724115703740100 185:163:18298298193978703402829362100 185:164:2454649757728850456477109550 185:165:312409969165490058097086670 185:166:37639755321143380493624900 185:167:4282367371866612151969300 185:168:458825075557137016282425 185:169:46154001683262303413025 185:170:4343906040777628556520 185:171:381044389541897241800 185:172:31015241009224194100 185:173:2330625046935922100 185:174:160732761857649800 185:175:10103202173909416 185:176:574045578063035 185:177:29188758206595 185:178:1311854301420 185:179:51301564860 185:180:1710052162 185:181:47239010 185:182:1038220 185:183:17020 185:184:185 185:185:1 # binomial(186, k) for 0 <= k <= 186 186:0:1 186:1:186 186:2:17205 186:3:1055240 186:4:48277230 186:5:1757291172 186:6:53011617022 186:7:1363155866280 186:8:30500612508015 186:9:603234336269630 186:10:10677247751972451 186:11:170835964031559216 186:12:2491357808793571900 186:13:33345866056160116200 186:14:412059630551121435900 186:15:4724950430319525798320 186:16:50497907724039931969545 186:17:504979077240399319695450 186:18:4741192447423749168251725 186:19:41922122693009992645594200 186:20:350049724486633438590711570 186:21:2767059726894340514574196220 186:22:20752947951707553859306471650 186:23:147977541916523427518533102200 186:24:1005014138849721611896703985775 186:25:6512491619746196045090641827822 186:26:40327351953043752433061282087667 186:27:238976900462481495899622412371360 186:28:1357047399054805637429998698823080 186:29:7393568587953768645308268772898160 186:30:38693008943624722577113273244833704 186:31:194713206296950216839666794393356704 186:32:943142093000852612817136035342821535 186:33:4401329767337312193146634831599833830 186:34:19805983953017904869159856742199252235 186:35:86014558881677758288922806423265323992 186:36:360783288642592819489648438053140664522 186:37:1462634953956457376309385559674894585900 186:38:5735068635250319712371011799777876139450 186:39:21763850205565315831561788368387837657400 186:40:79982149505452535680989572253825303390945 186:41:284814483604782200229865306074597421831170 186:42:983288098159367119841201651924205384893325 186:43:3292871770580206168770535764583385474991600 186:44:10701833254385670048504241234896002793722700 186:45:33770229380505892153057827896782942149080520 186:46:103513094405463712903938124640139018326529420 186:47:308336876952445102267049732970626863100300400 186:48:892892206174788941981664851727440291061286575 186:49:2514676009226956612111627541599729799315460150 186:50:6890212265281861117185859463983259650124360811 186:51:18373899374084962979162291903955359066998295496 186:52:47701469528874423118979027058345643731630190230 186:53:120603715412625899961192257090911627547895197940 186:54:297042484257023049904417966538726786367964098630 186:55:712901962216855319770603119692944287283113836712 186:56:1667681375900143694463375154995994672037284153737 186:57:3803483839772257548776118774552268550260472631330 186:58:8459472678114159030898608998573149016958637404165 186:59:18352754284722243321271558505379035155435687927680 186:60:38846663235995415030024798836385624412338872780256 186:61:80240648651400365471854502514501453704175376562496 186:62:161775501313307188451319561521172285693901968876000 186:63:318415272426191926475613105216275609937203875248000 186:64:611954351694087608695318936587529687848063697742250 186:65:1148591244718133665551214004056594183345596478839300 186:66:2105750615316578386843892340770422669466926877872050 186:67:3771493639372976215242792252126130154269122766338000 186:68:6600113868902708376674886441220727769970964841091500 186:69:11287151254065501281849805798029650389225707989113000 186:70:18865667096080909285377532548135272793420111924660300 186:71:30822780044301203902870334867375938648404689905078800 186:72:49230829237425534011529007079836568674535268598389750 186:73:76881021000911107908415161741114641491740008496115500 186:74:117399396933823718833120449685756141737386769730554750 186:75:175316432754510086790793204864062504994497576130961760 186:76:256054263628297626760237443946196553347226723033378360 186:77:365791805183282323943196348494566504781752461476254800 186:78:511170599550997093715492333152663448989884850011689400 186:79:698815503183641596471812303550476613808956503813448800 186:80:934665735508120635281048955998762470969479323850487770 186:81:1223142814368651695552977646121837307688454423804342020 186:82:1566219457423273512598325034668206308625459932920194050 186:83:1962491850265306570002720525367391037313829313538556400 186:84:2406388816396744960836669215629062819563385943981801300 186:85:2887666579676093953004003058754875383476063132778161560 186:86:3391329355200994061086096615514446671291655539658073460 186:87:3898079718621832254121950132775226058955925907652958000 186:88:4385339683449561285887193899372129316325416646109577750 186:89:4828800999753449505808370810544591831459447542907175500 186:90:5204374410845384467371244095809171196128515685133289150 186:91:5490329048803922075468565199974510272838873689810942400 186:92:5669361517786658664886018413017157346953184788391734000 186:93:5730322394321999080637480976597986995845154517299172000 186:94:5669361517786658664886018413017157346953184788391734000 186:95:5490329048803922075468565199974510272838873689810942400 186:96:5204374410845384467371244095809171196128515685133289150 186:97:4828800999753449505808370810544591831459447542907175500 186:98:4385339683449561285887193899372129316325416646109577750 186:99:3898079718621832254121950132775226058955925907652958000 186:100:3391329355200994061086096615514446671291655539658073460 186:101:2887666579676093953004003058754875383476063132778161560 186:102:2406388816396744960836669215629062819563385943981801300 186:103:1962491850265306570002720525367391037313829313538556400 186:104:1566219457423273512598325034668206308625459932920194050 186:105:1223142814368651695552977646121837307688454423804342020 186:106:934665735508120635281048955998762470969479323850487770 186:107:698815503183641596471812303550476613808956503813448800 186:108:511170599550997093715492333152663448989884850011689400 186:109:365791805183282323943196348494566504781752461476254800 186:110:256054263628297626760237443946196553347226723033378360 186:111:175316432754510086790793204864062504994497576130961760 186:112:117399396933823718833120449685756141737386769730554750 186:113:76881021000911107908415161741114641491740008496115500 186:114:49230829237425534011529007079836568674535268598389750 186:115:30822780044301203902870334867375938648404689905078800 186:116:18865667096080909285377532548135272793420111924660300 186:117:11287151254065501281849805798029650389225707989113000 186:118:6600113868902708376674886441220727769970964841091500 186:119:3771493639372976215242792252126130154269122766338000 186:120:2105750615316578386843892340770422669466926877872050 186:121:1148591244718133665551214004056594183345596478839300 186:122:611954351694087608695318936587529687848063697742250 186:123:318415272426191926475613105216275609937203875248000 186:124:161775501313307188451319561521172285693901968876000 186:125:80240648651400365471854502514501453704175376562496 186:126:38846663235995415030024798836385624412338872780256 186:127:18352754284722243321271558505379035155435687927680 186:128:8459472678114159030898608998573149016958637404165 186:129:3803483839772257548776118774552268550260472631330 186:130:1667681375900143694463375154995994672037284153737 186:131:712901962216855319770603119692944287283113836712 186:132:297042484257023049904417966538726786367964098630 186:133:120603715412625899961192257090911627547895197940 186:134:47701469528874423118979027058345643731630190230 186:135:18373899374084962979162291903955359066998295496 186:136:6890212265281861117185859463983259650124360811 186:137:2514676009226956612111627541599729799315460150 186:138:892892206174788941981664851727440291061286575 186:139:308336876952445102267049732970626863100300400 186:140:103513094405463712903938124640139018326529420 186:141:33770229380505892153057827896782942149080520 186:142:10701833254385670048504241234896002793722700 186:143:3292871770580206168770535764583385474991600 186:144:983288098159367119841201651924205384893325 186:145:284814483604782200229865306074597421831170 186:146:79982149505452535680989572253825303390945 186:147:21763850205565315831561788368387837657400 186:148:5735068635250319712371011799777876139450 186:149:1462634953956457376309385559674894585900 186:150:360783288642592819489648438053140664522 186:151:86014558881677758288922806423265323992 186:152:19805983953017904869159856742199252235 186:153:4401329767337312193146634831599833830 186:154:943142093000852612817136035342821535 186:155:194713206296950216839666794393356704 186:156:38693008943624722577113273244833704 186:157:7393568587953768645308268772898160 186:158:1357047399054805637429998698823080 186:159:238976900462481495899622412371360 186:160:40327351953043752433061282087667 186:161:6512491619746196045090641827822 186:162:1005014138849721611896703985775 186:163:147977541916523427518533102200 186:164:20752947951707553859306471650 186:165:2767059726894340514574196220 186:166:350049724486633438590711570 186:167:41922122693009992645594200 186:168:4741192447423749168251725 186:169:504979077240399319695450 186:170:50497907724039931969545 186:171:4724950430319525798320 186:172:412059630551121435900 186:173:33345866056160116200 186:174:2491357808793571900 186:175:170835964031559216 186:176:10677247751972451 186:177:603234336269630 186:178:30500612508015 186:179:1363155866280 186:180:53011617022 186:181:1757291172 186:182:48277230 186:183:1055240 186:184:17205 186:185:186 186:186:1 # binomial(187, k) for 0 <= k <= 187 187:0:1 187:1:187 187:2:17391 187:3:1072445 187:4:49332470 187:5:1805568402 187:6:54768908194 187:7:1416167483302 187:8:31863768374295 187:9:633734948777645 187:10:11280482088242081 187:11:181513211783531667 187:12:2662193772825131116 187:13:35837223864953688100 187:14:445405496607281552100 187:15:5137010060870647234220 187:16:55222858154359457767865 187:17:555476984964439251664995 187:18:5246171524664148487947175 187:19:46663315140433741813845925 187:20:391971847179643431236305770 187:21:3117109451380973953164907790 187:22:23520007678601894373880667870 187:23:168730489868230981377839573850 187:24:1152991680766245039415237087975 187:25:7517505758595917656987345813597 187:26:46839843572789948478151923915489 187:27:279304252415525248332683694459027 187:28:1596024299517287133329621111194440 187:29:8750615987008574282738267471721240 187:30:46086577531578491222421542017731864 187:31:233406215240574939416780067638190408 187:32:1137855299297802829656802829736178239 187:33:5344471860338164805963770866942655365 187:34:24207313720355217062306491573799086065 187:35:105820542834695663158082663165464576227 187:36:446797847524270577778571244476405988514 187:37:1823418242599050195799033997728035250422 187:38:7197703589206777088680397359452770725350 187:39:27498918840815635543932800168165713796850 187:40:101745999711017851512551360622213141048345 187:41:364796633110234735910854878328422725222115 187:42:1268102581764149320071066957998802806724495 187:43:4276159868739573288611737416507590859884925 187:44:13994705024965876217274776999479388268714300 187:45:44472062634891562201562069131678944942803220 187:46:137283323785969605056995952536921960475609940 187:47:411849971357908815170987857610765881426829820 187:48:1201229083127234044248714584698067154161586975 187:49:3407568215401745554093292393327170090376746725 187:50:9404888274508817729297487005582989449439820961 187:51:25264111639366824096348151367938618717122656307 187:52:66075368902959386098141318962301002798628485726 187:53:168305184941500323080171284149257271279525388170 187:54:417646199669648949865610223629638413915859296570 187:55:1009944446473878369675021086231671073651077935342 187:56:2380583338116999014233978274688938959320397990449 187:57:5471165215672401243239493929548263222297756785067 187:58:12262956517886416579674727773125417567219110035495 187:59:26812226962836402352170167503952184172394325331845 187:60:57199417520717658351296357341764659567774560707936 187:61:119087311887395780501879301350887078116514249342752 187:62:242016149964707553923174064035673739398077345438496 187:63:480190773739499114926932666737447895631105844124000 187:64:930369624120279535170932041803805297785267572990250 187:65:1760545596412221274246532940644123871193660176581550 187:66:3254341860034712052395106344827016852812523356711350 187:67:5877244254689554602086684592896552823736049644210050 187:68:10371607508275684591917678693346857924240087607429500 187:69:17887265122968209658524692239250378159196672830204500 187:70:30152818350146410567227338346164923182645819913773300 187:71:49688447140382113188247867415511211441824801829739100 187:72:80053609281726737914399341947212507322939958503468550 187:73:126111850238336641919944168820951210166275277094505250 187:74:194280417934734826741535611426870783229126778226670250 187:75:292715829688333805623913654549818646731884345861516510 187:76:431370696382807713551030648810259058341724299164340120 187:77:621846068811579950703433792440763058128979184509633160 187:78:876962404734279417658688681647229953771637311487944200 187:79:1209986102734638690187304636703140062798841353825138200 187:80:1633481238691762231752861259549239084778435827663936570 187:81:2157808549876772330834026602120599778657933747654829790 187:82:2789362271791925208151302680790043616313914356724536070 187:83:3528711307688580082601045560035597345939289246458750450 187:84:4368880666662051530839389740996453856877215257520357700 187:85:5294055396072838913840672274383938203039449076759962860 187:86:6278995934877088014090099674269322054767718672436235020 187:87:7289409073822826315208046748289672730247581447311031460 187:88:8283419402071393540009144032147355375281342553762535750 187:89:9214140683203010791695564709916721147784864189016753250 187:90:10033175410598833973179614906353763027587963228040464650 187:91:10694703459649306542839809295783681468967389374944231550 187:92:11159690566590580740354583612991667619792058478202676400 187:93:11399683912108657745523499389615144342798339305690906000 187:94:11399683912108657745523499389615144342798339305690906000 187:95:11159690566590580740354583612991667619792058478202676400 187:96:10694703459649306542839809295783681468967389374944231550 187:97:10033175410598833973179614906353763027587963228040464650 187:98:9214140683203010791695564709916721147784864189016753250 187:99:8283419402071393540009144032147355375281342553762535750 187:100:7289409073822826315208046748289672730247581447311031460 187:101:6278995934877088014090099674269322054767718672436235020 187:102:5294055396072838913840672274383938203039449076759962860 187:103:4368880666662051530839389740996453856877215257520357700 187:104:3528711307688580082601045560035597345939289246458750450 187:105:2789362271791925208151302680790043616313914356724536070 187:106:2157808549876772330834026602120599778657933747654829790 187:107:1633481238691762231752861259549239084778435827663936570 187:108:1209986102734638690187304636703140062798841353825138200 187:109:876962404734279417658688681647229953771637311487944200 187:110:621846068811579950703433792440763058128979184509633160 187:111:431370696382807713551030648810259058341724299164340120 187:112:292715829688333805623913654549818646731884345861516510 187:113:194280417934734826741535611426870783229126778226670250 187:114:126111850238336641919944168820951210166275277094505250 187:115:80053609281726737914399341947212507322939958503468550 187:116:49688447140382113188247867415511211441824801829739100 187:117:30152818350146410567227338346164923182645819913773300 187:118:17887265122968209658524692239250378159196672830204500 187:119:10371607508275684591917678693346857924240087607429500 187:120:5877244254689554602086684592896552823736049644210050 187:121:3254341860034712052395106344827016852812523356711350 187:122:1760545596412221274246532940644123871193660176581550 187:123:930369624120279535170932041803805297785267572990250 187:124:480190773739499114926932666737447895631105844124000 187:125:242016149964707553923174064035673739398077345438496 187:126:119087311887395780501879301350887078116514249342752 187:127:57199417520717658351296357341764659567774560707936 187:128:26812226962836402352170167503952184172394325331845 187:129:12262956517886416579674727773125417567219110035495 187:130:5471165215672401243239493929548263222297756785067 187:131:2380583338116999014233978274688938959320397990449 187:132:1009944446473878369675021086231671073651077935342 187:133:417646199669648949865610223629638413915859296570 187:134:168305184941500323080171284149257271279525388170 187:135:66075368902959386098141318962301002798628485726 187:136:25264111639366824096348151367938618717122656307 187:137:9404888274508817729297487005582989449439820961 187:138:3407568215401745554093292393327170090376746725 187:139:1201229083127234044248714584698067154161586975 187:140:411849971357908815170987857610765881426829820 187:141:137283323785969605056995952536921960475609940 187:142:44472062634891562201562069131678944942803220 187:143:13994705024965876217274776999479388268714300 187:144:4276159868739573288611737416507590859884925 187:145:1268102581764149320071066957998802806724495 187:146:364796633110234735910854878328422725222115 187:147:101745999711017851512551360622213141048345 187:148:27498918840815635543932800168165713796850 187:149:7197703589206777088680397359452770725350 187:150:1823418242599050195799033997728035250422 187:151:446797847524270577778571244476405988514 187:152:105820542834695663158082663165464576227 187:153:24207313720355217062306491573799086065 187:154:5344471860338164805963770866942655365 187:155:1137855299297802829656802829736178239 187:156:233406215240574939416780067638190408 187:157:46086577531578491222421542017731864 187:158:8750615987008574282738267471721240 187:159:1596024299517287133329621111194440 187:160:279304252415525248332683694459027 187:161:46839843572789948478151923915489 187:162:7517505758595917656987345813597 187:163:1152991680766245039415237087975 187:164:168730489868230981377839573850 187:165:23520007678601894373880667870 187:166:3117109451380973953164907790 187:167:391971847179643431236305770 187:168:46663315140433741813845925 187:169:5246171524664148487947175 187:170:555476984964439251664995 187:171:55222858154359457767865 187:172:5137010060870647234220 187:173:445405496607281552100 187:174:35837223864953688100 187:175:2662193772825131116 187:176:181513211783531667 187:177:11280482088242081 187:178:633734948777645 187:179:31863768374295 187:180:1416167483302 187:181:54768908194 187:182:1805568402 187:183:49332470 187:184:1072445 187:185:17391 187:186:187 187:187:1 # binomial(188, k) for 0 <= k <= 188 188:0:1 188:1:188 188:2:17578 188:3:1089836 188:4:50404915 188:5:1854900872 188:6:56574476596 188:7:1470936391496 188:8:33279935857597 188:9:665598717151940 188:10:11914217037019726 188:11:192793693871773748 188:12:2843706984608662783 188:13:38499417637778819216 188:14:481242720472235240200 188:15:5582415557477928786320 188:16:60359868215230105002085 188:17:610699843118798709432860 188:18:5801648509628587739612170 188:19:51909486665097890301793100 188:20:438635162320077173050151695 188:21:3509081298560617384401213560 188:22:26637117129982868327045575660 188:23:192250497546832875751720241720 188:24:1321722170634476020793076661825 188:25:8670497439362162696402582901572 188:26:54357349331385866135139269729086 188:27:326144095988315196810835618374516 188:28:1875328551932812381662304805653467 188:29:10346640286525861416067888582915680 188:30:54837193518587065505159809489453104 188:31:279492792772153430639201609655922272 188:32:1371261514538377769073582897374368647 188:33:6482327159635967635620573696678833604 188:34:29551785580693381868270262440741741430 188:35:130027856555050880220389154739263662292 188:36:552618390358966240936653907641870564741 188:37:2270216090123320773577605242204441238936 188:38:9021121831805827284479431357180805975772 188:39:34696622430022412632613197527618484522200 188:40:129244918551833487056484160790378854845195 188:41:466542632821252587423406238950635866270460 188:42:1632899214874384055981921836327225531946610 188:43:5544262450503722608682804374506393666609420 188:44:18270864893705449505886514415986979128599225 188:45:58466767659857438418836846131158333211517520 188:46:181755386420861167258558021668600905418413160 188:47:549133295143878420227983810147687841902439760 188:48:1613079054485142859419702442308833035588416795 188:49:4608797298528979598342006978025237244538333700 188:50:12812456489910563283390779398910159539816567686 188:51:34668999913875641825645638373521608166562477268 188:52:91339480542326210194489470330239621515751142033 188:53:234380553844459709178312603111558274078153873896 188:54:585951384611149272945781507778895685195384684740 188:55:1427590646143527319540631309861309487566937231912 188:56:3390527784590877383908999360920610032971475925791 188:57:7851748553789400257473472204237202181618154775516 188:58:17734121733558817822914221702673680789516866820562 188:59:39075183480722818931844895277077601739613435367340 188:60:84011644483554060703466524845716843740168886039781 188:61:176286729408113438853175658692651737684288810050688 188:62:361103461852103334425053365386560817514591594781248 188:63:722206923704206668850106730773121635029183189562496 188:64:1410560397859778650097864708541253193416373417114250 188:65:2690915220532500809417464982447929168978927749571800 188:66:5014887456446933326641639285471140724006183533292900 188:67:9131586114724266654481790937723569676548573000921400 188:68:16248851762965239194004363286243410747976137251639550 188:69:28258872631243894250442370932597236083436760437634000 188:70:48040083473114620225752030585415301341842492743977800 188:71:79841265490528523755475205761676134624470621743512400 188:72:129742056422108851102647209362723718764764760333207650 188:73:206165459520063379834343510768163717489215235597973800 188:74:320392268173071468661479780247821993395402055321175500 188:75:486996247623068632365449265976689429961011124088186760 188:76:724086526071141519174944303360077705073608645025856630 188:77:1053216765194387664254464441251022116470703483673973280 188:78:1498808473545859368362122474087993011900616495997577360 188:79:2086948507468918107845993318350370016570478665313082400 188:80:2843467341426400921940165896252379147577277181489074770 188:81:3791289788568534562586887861669838863436369575318766360 188:82:4947170821668697538985329282910643394971848104379365860 188:83:6318073579480505290752348240825640962253203603183286520 188:84:7897591974350631613440435301032051202816504503979108150 188:85:9662936062734890444680062015380392059916664334280320560 188:86:11573051330949926927930771948653260257807167749196197880 188:87:13568405008699914329298146422558994785015300119747266480 188:88:15572828475894219855217190780437028105528924001073567210 188:89:17497560085274404331704708742064076523066206742779289000 188:90:19247316093801844764875179616270484175372827417057217900 188:91:20727878870248140516019424202137444496555352602984696200 188:92:21854394026239887283194392908775349088759447853146907950 188:93:22559374478699238485878083002606811962590397783893582400 188:94:22799367824217315491046998779230288685596678611381812000 188:95:22559374478699238485878083002606811962590397783893582400 188:96:21854394026239887283194392908775349088759447853146907950 188:97:20727878870248140516019424202137444496555352602984696200 188:98:19247316093801844764875179616270484175372827417057217900 188:99:17497560085274404331704708742064076523066206742779289000 188:100:15572828475894219855217190780437028105528924001073567210 188:101:13568405008699914329298146422558994785015300119747266480 188:102:11573051330949926927930771948653260257807167749196197880 188:103:9662936062734890444680062015380392059916664334280320560 188:104:7897591974350631613440435301032051202816504503979108150 188:105:6318073579480505290752348240825640962253203603183286520 188:106:4947170821668697538985329282910643394971848104379365860 188:107:3791289788568534562586887861669838863436369575318766360 188:108:2843467341426400921940165896252379147577277181489074770 188:109:2086948507468918107845993318350370016570478665313082400 188:110:1498808473545859368362122474087993011900616495997577360 188:111:1053216765194387664254464441251022116470703483673973280 188:112:724086526071141519174944303360077705073608645025856630 188:113:486996247623068632365449265976689429961011124088186760 188:114:320392268173071468661479780247821993395402055321175500 188:115:206165459520063379834343510768163717489215235597973800 188:116:129742056422108851102647209362723718764764760333207650 188:117:79841265490528523755475205761676134624470621743512400 188:118:48040083473114620225752030585415301341842492743977800 188:119:28258872631243894250442370932597236083436760437634000 188:120:16248851762965239194004363286243410747976137251639550 188:121:9131586114724266654481790937723569676548573000921400 188:122:5014887456446933326641639285471140724006183533292900 188:123:2690915220532500809417464982447929168978927749571800 188:124:1410560397859778650097864708541253193416373417114250 188:125:722206923704206668850106730773121635029183189562496 188:126:361103461852103334425053365386560817514591594781248 188:127:176286729408113438853175658692651737684288810050688 188:128:84011644483554060703466524845716843740168886039781 188:129:39075183480722818931844895277077601739613435367340 188:130:17734121733558817822914221702673680789516866820562 188:131:7851748553789400257473472204237202181618154775516 188:132:3390527784590877383908999360920610032971475925791 188:133:1427590646143527319540631309861309487566937231912 188:134:585951384611149272945781507778895685195384684740 188:135:234380553844459709178312603111558274078153873896 188:136:91339480542326210194489470330239621515751142033 188:137:34668999913875641825645638373521608166562477268 188:138:12812456489910563283390779398910159539816567686 188:139:4608797298528979598342006978025237244538333700 188:140:1613079054485142859419702442308833035588416795 188:141:549133295143878420227983810147687841902439760 188:142:181755386420861167258558021668600905418413160 188:143:58466767659857438418836846131158333211517520 188:144:18270864893705449505886514415986979128599225 188:145:5544262450503722608682804374506393666609420 188:146:1632899214874384055981921836327225531946610 188:147:466542632821252587423406238950635866270460 188:148:129244918551833487056484160790378854845195 188:149:34696622430022412632613197527618484522200 188:150:9021121831805827284479431357180805975772 188:151:2270216090123320773577605242204441238936 188:152:552618390358966240936653907641870564741 188:153:130027856555050880220389154739263662292 188:154:29551785580693381868270262440741741430 188:155:6482327159635967635620573696678833604 188:156:1371261514538377769073582897374368647 188:157:279492792772153430639201609655922272 188:158:54837193518587065505159809489453104 188:159:10346640286525861416067888582915680 188:160:1875328551932812381662304805653467 188:161:326144095988315196810835618374516 188:162:54357349331385866135139269729086 188:163:8670497439362162696402582901572 188:164:1321722170634476020793076661825 188:165:192250497546832875751720241720 188:166:26637117129982868327045575660 188:167:3509081298560617384401213560 188:168:438635162320077173050151695 188:169:51909486665097890301793100 188:170:5801648509628587739612170 188:171:610699843118798709432860 188:172:60359868215230105002085 188:173:5582415557477928786320 188:174:481242720472235240200 188:175:38499417637778819216 188:176:2843706984608662783 188:177:192793693871773748 188:178:11914217037019726 188:179:665598717151940 188:180:33279935857597 188:181:1470936391496 188:182:56574476596 188:183:1854900872 188:184:50404915 188:185:1089836 188:186:17578 188:187:188 188:188:1 # binomial(189, k) for 0 <= k <= 189 189:0:1 189:1:189 189:2:17766 189:3:1107414 189:4:51494751 189:5:1905305787 189:6:58429377468 189:7:1527510868092 189:8:34750872249093 189:9:698878653009537 189:10:12579815754171666 189:11:204707910908793474 189:12:3036500678480436531 189:13:41343124622387481999 189:14:519742138110014059416 189:15:6063658277950164026520 189:16:65942283772708033788405 189:17:671059711334028814434945 189:18:6412348352747386449045030 189:19:57711135174726478041405270 189:20:490544648985175063351944795 189:21:3947716460880694557451365255 189:22:30146198428543485711446789220 189:23:218887614676815744078765817380 189:24:1513972668181308896544796903545 189:25:9992219609996638717195659563397 189:26:63027846770748028831541852630658 189:27:380501445319701062945974888103602 189:28:2201472647921127578473140424027983 189:29:12221968838458673797730193388569147 189:30:65183833805112926921227698072368784 189:31:334329986290740496144361419145375376 189:32:1650754307310531199712784507030290919 189:33:7853588674174345404694156594053202251 189:34:36034112740329349503890836137420575034 189:35:159579642135744262088659417180005403722 189:36:682646246914017121157043062381134227033 189:37:2822834480482287014514259149846311803677 189:38:11291337921929148058057036599385247214708 189:39:43717744261828239917092628884799290497972 189:40:163941540981855899689097358317997339367395 189:41:595787551373086074479890399741014721115655 189:42:2099441847695636643405328075277861398217070 189:43:7177161665378106664664726210833619198556030 189:44:23815127344209172114569318790493372795208645 189:45:76737632553562887924723360547145312340116745 189:46:240222154080718605677394867799759238629930680 189:47:730888681564739587486541831816288747320852920 189:48:2162212349629021279647686252456520877490856555 189:49:6221876353014122457761709420334070280126750495 189:50:17421253788439542881732786376935396784354901386 189:51:47481456403786205109036417772431767706379044954 189:52:126008480456201852020135108703761229682313619301 189:53:325720034386785919372802073441797895593905015929 189:54:820331938455608982124094110890453959273538558636 189:55:2013542030754676592486412817640205172762321916652 189:56:4818118430734404703449630670781919520538413157703 189:57:11242276338380277641382471565157812214589630701307 189:58:25585870287348218080387693906910882971135021596078 189:59:56809305214281636754759116979751282529130302187902 189:60:123086827964276879635311420122794445479782321407121 189:61:260298373891667499556642183538368581424457696090469 189:62:537390191260216773278229024079212555198880404831936 189:63:1083310385556310003275160096159682452543774784343744 189:64:2132767321563985318947971439314374828445556606676746 189:65:4101475618392279459515329690989182362395301166686050 189:66:7705802676979434136059104267919069892985111282864700 189:67:14146473571171199981123430223194710400554756534214300 189:68:25380437877689505848486154223966980424524710252560950 189:69:44507724394209133444446734218840646831412897689273550 189:70:76298956104358514476194401518012537425279253181611800 189:71:127881348963643143981227236347091435966313114487490200 189:72:209583321912637374858122415124399853389235382076720050 189:73:335907515942172230936990720130887436253979995931181450 189:74:526557727693134848495823291015985710884617290919149300 189:75:807388515796140101026929046224511423356413179409362260 189:76:1211082773694210151540393569336767135034619769114043390 189:77:1777303291265529183429408744611099821544312128699829910 189:78:2552025238740247032616586915339015128371319979671550640 189:79:3585756981014777476208115792438363028471095161310659760 189:80:4930415848895319029786159214602749164147755846802157170 189:81:6634757129994935484527053757922218011013646756807841130 189:82:8738460610237232101572217144580482258408217679698132220 189:83:11265244401149202829737677523736284357225051707562652380 189:84:14215665553831136904192783541857692165069708107162394670 189:85:17560528037085522058120497316412443262733168838259428710 189:86:21235987393684817372610833964033652317723832083476518440 189:87:25141456339649841257228918371212255042822467868943464360 189:88:29141233484594134184515337202996022890544224120820833690 189:89:33070388561168624186921899522501104628595130743852856210 189:90:36744876179076249096579888358334560698439034159836506900 189:91:39975194964049985280894603818407928671928180020041914100 189:92:42582272896488027799213817110912793585314800456131604150 189:93:44413768504939125769072475911382161051349845637040490350 189:94:45358742302916553976925081781837100648187076395275394400 189:95:45358742302916553976925081781837100648187076395275394400 189:96:44413768504939125769072475911382161051349845637040490350 189:97:42582272896488027799213817110912793585314800456131604150 189:98:39975194964049985280894603818407928671928180020041914100 189:99:36744876179076249096579888358334560698439034159836506900 189:100:33070388561168624186921899522501104628595130743852856210 189:101:29141233484594134184515337202996022890544224120820833690 189:102:25141456339649841257228918371212255042822467868943464360 189:103:21235987393684817372610833964033652317723832083476518440 189:104:17560528037085522058120497316412443262733168838259428710 189:105:14215665553831136904192783541857692165069708107162394670 189:106:11265244401149202829737677523736284357225051707562652380 189:107:8738460610237232101572217144580482258408217679698132220 189:108:6634757129994935484527053757922218011013646756807841130 189:109:4930415848895319029786159214602749164147755846802157170 189:110:3585756981014777476208115792438363028471095161310659760 189:111:2552025238740247032616586915339015128371319979671550640 189:112:1777303291265529183429408744611099821544312128699829910 189:113:1211082773694210151540393569336767135034619769114043390 189:114:807388515796140101026929046224511423356413179409362260 189:115:526557727693134848495823291015985710884617290919149300 189:116:335907515942172230936990720130887436253979995931181450 189:117:209583321912637374858122415124399853389235382076720050 189:118:127881348963643143981227236347091435966313114487490200 189:119:76298956104358514476194401518012537425279253181611800 189:120:44507724394209133444446734218840646831412897689273550 189:121:25380437877689505848486154223966980424524710252560950 189:122:14146473571171199981123430223194710400554756534214300 189:123:7705802676979434136059104267919069892985111282864700 189:124:4101475618392279459515329690989182362395301166686050 189:125:2132767321563985318947971439314374828445556606676746 189:126:1083310385556310003275160096159682452543774784343744 189:127:537390191260216773278229024079212555198880404831936 189:128:260298373891667499556642183538368581424457696090469 189:129:123086827964276879635311420122794445479782321407121 189:130:56809305214281636754759116979751282529130302187902 189:131:25585870287348218080387693906910882971135021596078 189:132:11242276338380277641382471565157812214589630701307 189:133:4818118430734404703449630670781919520538413157703 189:134:2013542030754676592486412817640205172762321916652 189:135:820331938455608982124094110890453959273538558636 189:136:325720034386785919372802073441797895593905015929 189:137:126008480456201852020135108703761229682313619301 189:138:47481456403786205109036417772431767706379044954 189:139:17421253788439542881732786376935396784354901386 189:140:6221876353014122457761709420334070280126750495 189:141:2162212349629021279647686252456520877490856555 189:142:730888681564739587486541831816288747320852920 189:143:240222154080718605677394867799759238629930680 189:144:76737632553562887924723360547145312340116745 189:145:23815127344209172114569318790493372795208645 189:146:7177161665378106664664726210833619198556030 189:147:2099441847695636643405328075277861398217070 189:148:595787551373086074479890399741014721115655 189:149:163941540981855899689097358317997339367395 189:150:43717744261828239917092628884799290497972 189:151:11291337921929148058057036599385247214708 189:152:2822834480482287014514259149846311803677 189:153:682646246914017121157043062381134227033 189:154:159579642135744262088659417180005403722 189:155:36034112740329349503890836137420575034 189:156:7853588674174345404694156594053202251 189:157:1650754307310531199712784507030290919 189:158:334329986290740496144361419145375376 189:159:65183833805112926921227698072368784 189:160:12221968838458673797730193388569147 189:161:2201472647921127578473140424027983 189:162:380501445319701062945974888103602 189:163:63027846770748028831541852630658 189:164:9992219609996638717195659563397 189:165:1513972668181308896544796903545 189:166:218887614676815744078765817380 189:167:30146198428543485711446789220 189:168:3947716460880694557451365255 189:169:490544648985175063351944795 189:170:57711135174726478041405270 189:171:6412348352747386449045030 189:172:671059711334028814434945 189:173:65942283772708033788405 189:174:6063658277950164026520 189:175:519742138110014059416 189:176:41343124622387481999 189:177:3036500678480436531 189:178:204707910908793474 189:179:12579815754171666 189:180:698878653009537 189:181:34750872249093 189:182:1527510868092 189:183:58429377468 189:184:1905305787 189:185:51494751 189:186:1107414 189:187:17766 189:188:189 189:189:1 # binomial(190, k) for 0 <= k <= 190 190:0:1 190:1:190 190:2:17955 190:3:1125180 190:4:52602165 190:5:1956800538 190:6:60334683255 190:7:1585940245560 190:8:36278383117185 190:9:733629525258630 190:10:13278694407181203 190:11:217287726662965140 190:12:3241208589389230005 190:13:44379625300867918530 190:14:561085262732401541415 190:15:6583400416060178085936 190:16:72005942050658197814925 190:17:737001995106736848223350 190:18:7083408064081415263479975 190:19:64123483527473864490450300 190:20:548255784159901541393350065 190:21:4438261109865869620803310050 190:22:34093914889424180268898154475 190:23:249033813105359229790212606600 190:24:1732860282858124640623562720925 190:25:11506192278177947613740456466942 190:26:73020066380744667548737512194055 190:27:443529292090449091777516740734260 190:28:2581974093240828641419115312131585 190:29:14423441486379801376203333812597130 190:30:77405802643571600718957891460937931 190:31:399513820095853423065589117217744160 190:32:1985084293601271695857145926175666295 190:33:9504342981484876604406941101083493170 190:34:43887701414503694908584992731473777285 190:35:195613754876073611592550253317425978756 190:36:842225889049761383245702479561139630755 190:37:3505480727396304135671302212227446030710 190:38:14114172402411435072571295749231559018385 190:39:55009082183757387975149665484184537712680 190:40:207659285243684139606189987202796629865367 190:41:759729092354941974168987758059012060483050 190:42:2695229399068722717885218475018876119332725 190:43:9276603513073743308070054286111480596773100 190:44:30992289009587278779234045001326991993764675 190:45:100552759897772060039292679337638685135325390 190:46:316959786634281493602118228346904550970047425 190:47:971110835645458193163936699616047985950783600 190:48:2893101031193760867134228084272809624811709475 190:49:8384088702643143737409395672790591157617607050 190:50:23643130141453665339494495797269467064481651881 190:51:64902710192225747990769204149367164490733946340 190:52:173489936859988057129171526476192997388692664255 190:53:451728514842987771392937182145559125276218635230 190:54:1146051972842394901496896184332251854867443574565 190:55:2833873969210285574610506928530659132035860475288 190:56:6831660461489081295936043488422124693300735074355 190:57:16060394769114682344832102235939731735128043859010 190:58:36828146625728495721770165472068695185724652297385 190:59:82395175501629854835146810886662165500265323783980 190:60:179896133178558516390070537102545728008912623595023 190:61:383385201855944379191953603661163026904240017497590 190:62:797688565151884272834871207617581136623338100922405 190:63:1620700576816526776553389120238895007742655189175680 190:64:3216077707120295322223131535474057280989331391020490 190:65:6234242939956264778463301130303557190840857773362796 190:66:11807278295371713595574433958908252255380412449550750 190:67:21852276248150634117182534491113780293539867817079000 190:68:39526911448860705829609584447161690825079466786775250 190:69:69888162271898639292932888442807627255937607941834500 190:70:120806680498567647920641135736853184256692150870885350 190:71:204180305068001658457421637865103973391592367669102000 190:72:337464670876280518839349651471491289355548496564210250 190:73:545490837854809605795113135255287289643215378007901500 190:74:862465243635307079432814011146873147138597286850330750 190:75:1333946243489274949522752337240497134241030470328511560 190:76:2018471289490350252567322615561278558391032948523405650 190:77:2988386064959739334969802313947866956578931897813873300 190:78:4329328530005776216045995659950114949915632108371380550 190:79:6137782219755024508824702707777378156842415140982210400 190:80:8516172829910096505994275007041112192618851008112816930 190:81:11565172978890254514313212972524967175161402603609998300 190:82:15373217740232167586099270902502700269421864436505973350 190:83:20003705011386434931309894668316766615633269387260784600 190:84:25480909954980339733930461065593976522294759814725047050 190:85:31776193590916658962313280858270135427802876945421823380 190:86:38796515430770339430731331280446095580457000921735947150 190:87:46377443733334658629839752335245907360546299952419982800 190:88:54282689824243975441744255574208277933366691989764298050 190:89:62211622045762758371437236725497127519139354864673689900 190:90:69815264740244873283501787880835665327034164903689363110 190:91:76720071143126234377474492176742489370367214179878421000 190:92:82557467860538013080108420929320722257242980476173518250 190:93:86996041401427153568286293022294954636664646093172094500 190:94:89772510807855679745997557693219261699536922032315884750 190:95:90717484605833107953850163563674201296374152790550788800 190:96:89772510807855679745997557693219261699536922032315884750 190:97:86996041401427153568286293022294954636664646093172094500 190:98:82557467860538013080108420929320722257242980476173518250 190:99:76720071143126234377474492176742489370367214179878421000 190:100:69815264740244873283501787880835665327034164903689363110 190:101:62211622045762758371437236725497127519139354864673689900 190:102:54282689824243975441744255574208277933366691989764298050 190:103:46377443733334658629839752335245907360546299952419982800 190:104:38796515430770339430731331280446095580457000921735947150 190:105:31776193590916658962313280858270135427802876945421823380 190:106:25480909954980339733930461065593976522294759814725047050 190:107:20003705011386434931309894668316766615633269387260784600 190:108:15373217740232167586099270902502700269421864436505973350 190:109:11565172978890254514313212972524967175161402603609998300 190:110:8516172829910096505994275007041112192618851008112816930 190:111:6137782219755024508824702707777378156842415140982210400 190:112:4329328530005776216045995659950114949915632108371380550 190:113:2988386064959739334969802313947866956578931897813873300 190:114:2018471289490350252567322615561278558391032948523405650 190:115:1333946243489274949522752337240497134241030470328511560 190:116:862465243635307079432814011146873147138597286850330750 190:117:545490837854809605795113135255287289643215378007901500 190:118:337464670876280518839349651471491289355548496564210250 190:119:204180305068001658457421637865103973391592367669102000 190:120:120806680498567647920641135736853184256692150870885350 190:121:69888162271898639292932888442807627255937607941834500 190:122:39526911448860705829609584447161690825079466786775250 190:123:21852276248150634117182534491113780293539867817079000 190:124:11807278295371713595574433958908252255380412449550750 190:125:6234242939956264778463301130303557190840857773362796 190:126:3216077707120295322223131535474057280989331391020490 190:127:1620700576816526776553389120238895007742655189175680 190:128:797688565151884272834871207617581136623338100922405 190:129:383385201855944379191953603661163026904240017497590 190:130:179896133178558516390070537102545728008912623595023 190:131:82395175501629854835146810886662165500265323783980 190:132:36828146625728495721770165472068695185724652297385 190:133:16060394769114682344832102235939731735128043859010 190:134:6831660461489081295936043488422124693300735074355 190:135:2833873969210285574610506928530659132035860475288 190:136:1146051972842394901496896184332251854867443574565 190:137:451728514842987771392937182145559125276218635230 190:138:173489936859988057129171526476192997388692664255 190:139:64902710192225747990769204149367164490733946340 190:140:23643130141453665339494495797269467064481651881 190:141:8384088702643143737409395672790591157617607050 190:142:2893101031193760867134228084272809624811709475 190:143:971110835645458193163936699616047985950783600 190:144:316959786634281493602118228346904550970047425 190:145:100552759897772060039292679337638685135325390 190:146:30992289009587278779234045001326991993764675 190:147:9276603513073743308070054286111480596773100 190:148:2695229399068722717885218475018876119332725 190:149:759729092354941974168987758059012060483050 190:150:207659285243684139606189987202796629865367 190:151:55009082183757387975149665484184537712680 190:152:14114172402411435072571295749231559018385 190:153:3505480727396304135671302212227446030710 190:154:842225889049761383245702479561139630755 190:155:195613754876073611592550253317425978756 190:156:43887701414503694908584992731473777285 190:157:9504342981484876604406941101083493170 190:158:1985084293601271695857145926175666295 190:159:399513820095853423065589117217744160 190:160:77405802643571600718957891460937931 190:161:14423441486379801376203333812597130 190:162:2581974093240828641419115312131585 190:163:443529292090449091777516740734260 190:164:73020066380744667548737512194055 190:165:11506192278177947613740456466942 190:166:1732860282858124640623562720925 190:167:249033813105359229790212606600 190:168:34093914889424180268898154475 190:169:4438261109865869620803310050 190:170:548255784159901541393350065 190:171:64123483527473864490450300 190:172:7083408064081415263479975 190:173:737001995106736848223350 190:174:72005942050658197814925 190:175:6583400416060178085936 190:176:561085262732401541415 190:177:44379625300867918530 190:178:3241208589389230005 190:179:217287726662965140 190:180:13278694407181203 190:181:733629525258630 190:182:36278383117185 190:183:1585940245560 190:184:60334683255 190:185:1956800538 190:186:52602165 190:187:1125180 190:188:17955 190:189:190 190:190:1 # binomial(191, k) for 0 <= k <= 191 191:0:1 191:1:191 191:2:18145 191:3:1143135 191:4:53727345 191:5:2009402703 191:6:62291483793 191:7:1646274928815 191:8:37864323362745 191:9:769907908375815 191:10:14012323932439833 191:11:230566421070146343 191:12:3458496316052195145 191:13:47620833890257148535 191:14:605464888033269459945 191:15:7144485678792579627351 191:16:78589342466718375900861 191:17:809007937157395046038275 191:18:7820410059188152111703325 191:19:71206891591555279753930275 191:20:612379267687375405883800365 191:21:4986516894025771162196660115 191:22:38532175999290049889701464525 191:23:283127727994783410059110761075 191:24:1981894095963483870413775327525 191:25:13239052561036072254364019187867 191:26:84526258658922615162477968660997 191:27:516549358471193759326254252928315 191:28:3025503385331277733196632052865845 191:29:17005415579620630017622449124728715 191:30:91829244129951402095161225273535061 191:31:476919622739425023784547008678682091 191:32:2384598113697125118922735043393410455 191:33:11489427275086148300264087027259159465 191:34:53392044395988571512991933832557270455 191:35:239501456290577306501135246048899756041 191:36:1037839643925834994838252732878565609511 191:37:4347706616446065518917004691788585661465 191:38:17619653129807739208242597961459005049095 191:39:69123254586168823047720961233416096731065 191:40:262668367427441527581339652686981167578047 191:41:967388377598626113775177745261808690348417 191:42:3454958491423664692054206233077888179815775 191:43:11971832912142466025955272761130356716105825 191:44:40268892522661022087304099287438472590537775 191:45:131545048907359338818526724338965677129090065 191:46:417512546532053553641410907684543236105372815 191:47:1288070622279739686766054927962952536920831025 191:48:3864211866839219060298164783888857610762493075 191:49:11277189733836904604543623757063400782429316525 191:50:32027218844096809076903891470060058222099258931 191:51:88545840333679413330263699946636631555215598221 191:52:238392647052213805119940730625560161879426610595 191:53:625218451702975828522108708621752122664911299485 191:54:1597780487685382672889833366477810980143662209795 191:55:3979925942052680476107403112862910986903304049853 191:56:9665534430699366870546550416952783825336595549643 191:57:22892055230603763640768145724361856428428778933365 191:58:52888541394843178066602267708008426920852696156395 191:59:119223322127358350556916976358730860685989976081365 191:60:262291308680188371225217347989207893509177947379003 191:61:563281335034502895582024140763708754913152641092613 191:62:1181073767007828652026824811278744163527578118419995 191:63:2418389141968411049388260327856476144365993290098085 191:64:4836778283936822098776520655712952288731986580196170 191:65:9450320647076560100686432665777614471830189164383286 191:66:18041521235327978374037735089211809446221270222913546 191:67:33659554543522347712756968450022032548920280266629750 191:68:61379187697011339946792118938275471118619334603854250 191:69:109415073720759345122542472889969318081017074728609750 191:70:190694842770466287213574024179660811512629758812719850 191:71:324986985566569306378062773601957157648284518539987350 191:72:541644975944282177296771289336595262747140864233312250 191:73:882955508731090124634462786726778578998763874572111750 191:74:1407956081490116685227927146402160436781812664858232250 191:75:2196411487124582028955566348387370281379627757178842310 191:76:3352417532979625202090074952801775692632063418851917210 191:77:5006857354450089587537124929509145514969964846337278950 191:78:7317714594965515551015797973897981906494564006185253850 191:79:10467110749760800724870698367727493106758047249353590950 191:80:14653955049665121014818977714818490349461266149095027330 191:81:20081345808800351020307487979566079367780253611722815230 191:82:26938390719122422100412483875027667444583267040115971650 191:83:35376922751618602517409165570819466885055133823766757950 191:84:45484614966366774665240355733910743137928029201985831650 191:85:57257103545896998696243741923864111950097636760146870430 191:86:70572709021686998393044612138716231008259877867157770530 191:87:85173959164104998060571083615692002941003300874155929950 191:88:100660133557578634071584007909454185293912991942184280850 191:89:116494311870006733813181492299705405452506046854437987950 191:90:132026886786007631654939024606332792846173519768363053010 191:91:146535335883371107660976280057578154697401379083567784110 191:92:159277539003664247457582913106063211627610194656051939250 191:93:169553509261965166648394713951615676893907626569345612750 191:94:176768552209282833314283850715514216336201568125487979250 191:95:180489995413688787699847721256893462995911074822866673550 191:96:180489995413688787699847721256893462995911074822866673550 191:97:176768552209282833314283850715514216336201568125487979250 191:98:169553509261965166648394713951615676893907626569345612750 191:99:159277539003664247457582913106063211627610194656051939250 191:100:146535335883371107660976280057578154697401379083567784110 191:101:132026886786007631654939024606332792846173519768363053010 191:102:116494311870006733813181492299705405452506046854437987950 191:103:100660133557578634071584007909454185293912991942184280850 191:104:85173959164104998060571083615692002941003300874155929950 191:105:70572709021686998393044612138716231008259877867157770530 191:106:57257103545896998696243741923864111950097636760146870430 191:107:45484614966366774665240355733910743137928029201985831650 191:108:35376922751618602517409165570819466885055133823766757950 191:109:26938390719122422100412483875027667444583267040115971650 191:110:20081345808800351020307487979566079367780253611722815230 191:111:14653955049665121014818977714818490349461266149095027330 191:112:10467110749760800724870698367727493106758047249353590950 191:113:7317714594965515551015797973897981906494564006185253850 191:114:5006857354450089587537124929509145514969964846337278950 191:115:3352417532979625202090074952801775692632063418851917210 191:116:2196411487124582028955566348387370281379627757178842310 191:117:1407956081490116685227927146402160436781812664858232250 191:118:882955508731090124634462786726778578998763874572111750 191:119:541644975944282177296771289336595262747140864233312250 191:120:324986985566569306378062773601957157648284518539987350 191:121:190694842770466287213574024179660811512629758812719850 191:122:109415073720759345122542472889969318081017074728609750 191:123:61379187697011339946792118938275471118619334603854250 191:124:33659554543522347712756968450022032548920280266629750 191:125:18041521235327978374037735089211809446221270222913546 191:126:9450320647076560100686432665777614471830189164383286 191:127:4836778283936822098776520655712952288731986580196170 191:128:2418389141968411049388260327856476144365993290098085 191:129:1181073767007828652026824811278744163527578118419995 191:130:563281335034502895582024140763708754913152641092613 191:131:262291308680188371225217347989207893509177947379003 191:132:119223322127358350556916976358730860685989976081365 191:133:52888541394843178066602267708008426920852696156395 191:134:22892055230603763640768145724361856428428778933365 191:135:9665534430699366870546550416952783825336595549643 191:136:3979925942052680476107403112862910986903304049853 191:137:1597780487685382672889833366477810980143662209795 191:138:625218451702975828522108708621752122664911299485 191:139:238392647052213805119940730625560161879426610595 191:140:88545840333679413330263699946636631555215598221 191:141:32027218844096809076903891470060058222099258931 191:142:11277189733836904604543623757063400782429316525 191:143:3864211866839219060298164783888857610762493075 191:144:1288070622279739686766054927962952536920831025 191:145:417512546532053553641410907684543236105372815 191:146:131545048907359338818526724338965677129090065 191:147:40268892522661022087304099287438472590537775 191:148:11971832912142466025955272761130356716105825 191:149:3454958491423664692054206233077888179815775 191:150:967388377598626113775177745261808690348417 191:151:262668367427441527581339652686981167578047 191:152:69123254586168823047720961233416096731065 191:153:17619653129807739208242597961459005049095 191:154:4347706616446065518917004691788585661465 191:155:1037839643925834994838252732878565609511 191:156:239501456290577306501135246048899756041 191:157:53392044395988571512991933832557270455 191:158:11489427275086148300264087027259159465 191:159:2384598113697125118922735043393410455 191:160:476919622739425023784547008678682091 191:161:91829244129951402095161225273535061 191:162:17005415579620630017622449124728715 191:163:3025503385331277733196632052865845 191:164:516549358471193759326254252928315 191:165:84526258658922615162477968660997 191:166:13239052561036072254364019187867 191:167:1981894095963483870413775327525 191:168:283127727994783410059110761075 191:169:38532175999290049889701464525 191:170:4986516894025771162196660115 191:171:612379267687375405883800365 191:172:71206891591555279753930275 191:173:7820410059188152111703325 191:174:809007937157395046038275 191:175:78589342466718375900861 191:176:7144485678792579627351 191:177:605464888033269459945 191:178:47620833890257148535 191:179:3458496316052195145 191:180:230566421070146343 191:181:14012323932439833 191:182:769907908375815 191:183:37864323362745 191:184:1646274928815 191:185:62291483793 191:186:2009402703 191:187:53727345 191:188:1143135 191:189:18145 191:190:191 191:191:1 # binomial(192, k) for 0 <= k <= 192 192:0:1 192:1:192 192:2:18336 192:3:1161280 192:4:54870480 192:5:2063130048 192:6:64300886496 192:7:1708566412608 192:8:39510598291560 192:9:807772231738560 192:10:14782231840815648 192:11:244578745002586176 192:12:3689062737122341488 192:13:51079330206309343680 192:14:653085721923526608480 192:15:7749950566825849087296 192:16:85733828145510955528212 192:17:887597279624113421939136 192:18:8629417996345547157741600 192:19:79027301650743431865633600 192:20:683586159278930685637730640 192:21:5598896161713146568080460480 192:22:43518692893315821051898124640 192:23:321659903994073459948812225600 192:24:2265021823958267280472886088600 192:25:15220946656999556124777794515392 192:26:97765311219958687416841987848864 192:27:601075617130116374488732221589312 192:28:3542052743802471492522886305794160 192:29:20030918964951907750819081177594560 192:30:108834659709572032112783674398263776 192:31:568748866869376425879708233952217152 192:32:2861517736436550142707282052072092546 192:33:13874025388783273419186822070652569920 192:34:64881471671074719813256020859816429920 192:35:292893500686565878014127179881457026496 192:36:1277341100216412301339387978927465365552 192:37:5385546260371900513755257424667151270976 192:38:21967359746253804727159602653247590710560 192:39:86742907715976562255963559194875101780160 192:40:331791622013610350629060613920397264309112 192:41:1230056745026067641356517397948789857926464 192:42:4422346869022290805829383978339696870164192 192:43:15426791403566130718009478994208244895921600 192:44:52240725434803488113259372048568829306643600 192:45:171813941430020360905830823626404149719627840 192:46:549057595439412892459937632023508913234462880 192:47:1705583168811793240407465835647495773026203840 192:48:5152282489118958747064219711851810147683324100 192:49:15141401600676123664841788540952258393191809600 192:50:43304408577933713681447515227123459004528575456 192:51:120573059177776222407167591416696689777314857152 192:52:326938487385893218450204430572196793434642208816 192:53:863611098755189633642049439247312284544337910080 192:54:2222998939388358501411942075099563102808573509280 192:55:5577706429738063148997236479340721967046966259648 192:56:13645460372752047346653953529815694812239899599496 192:57:32557589661303130511314696141314640253765374483008 192:58:75780596625446941707370413432370283349281475089760 192:59:172111863522201528623519244066739287606842672237760 192:60:381514630807546721782134324347938754195167923460368 192:61:825572643714691266807241488752916648422330588471616 192:62:1744355102042331547608848952042452918440730759512608 192:63:3599462908976239701415085139135220307893571408518080 192:64:7255167425905233148164780983569428433097979870294255 192:65:14287098931013382199462953321490566760562175744579456 192:66:27491841882404538474724167754989423918051459387296832 192:67:51701075778850326086794703539233841995141550489543296 192:68:95038742240533687659549087388297503667539614870484000 192:69:170794261417770685069334591828244789199636409332464000 192:70:300109916491225632336116497069630129593646833541329600 192:71:515681828337035593591636797781617969160914277352707200 192:72:866631961510851483674834062938552420395425382773299600 192:73:1424600484675372301931234076063373841745904738805424000 192:74:2290911590221206809862389933128939015780576539430344000 192:75:3604367568614698714183493494789530718161440422037074560 192:76:5548829020104207231045641301189145974011691176030759520 192:77:8359274887429714789627199882310921207602028265189196160 192:78:12324571949415605138552922903407127421464528852522532800 192:79:17784825344726316275886496341625475013252611255538844800 192:80:25121065799425921739689676082545983456219313398448618280 192:81:34735300858465472035126465694384569717241519760817842560 192:82:47019736527922773120719971854593746812363520651838786880 192:83:62315313470741024617821649445847134329638400863882729600 192:84:80861537717985377182649521304730210022983163025752589600 192:85:102741718512263773361484097657774855088025665962132702080 192:86:127829812567583997089288354062580342958357514627304640960 192:87:155746668185791996453615695754408233949263178741313700480 192:88:185834092721683632132155091525146188234916292816340210800 192:89:217154445427585367884765500209159590746419038796622268800 192:90:248521198656014365468120516906038198298679566622801040960 192:91:278562222669378739315915304663910947543574898851930837120 192:92:305812874887035355118559193163641366325011573739619723360 192:93:328831048265629414105977627057678888521517821225397552000 192:94:346322061471247999962678564667129893230109194694833592000 192:95:357258547622971621014131571972407679332112642948354652800 192:96:360979990827377575399695442513786925991822149645733347100 192:97:357258547622971621014131571972407679332112642948354652800 192:98:346322061471247999962678564667129893230109194694833592000 192:99:328831048265629414105977627057678888521517821225397552000 192:100:305812874887035355118559193163641366325011573739619723360 192:101:278562222669378739315915304663910947543574898851930837120 192:102:248521198656014365468120516906038198298679566622801040960 192:103:217154445427585367884765500209159590746419038796622268800 192:104:185834092721683632132155091525146188234916292816340210800 192:105:155746668185791996453615695754408233949263178741313700480 192:106:127829812567583997089288354062580342958357514627304640960 192:107:102741718512263773361484097657774855088025665962132702080 192:108:80861537717985377182649521304730210022983163025752589600 192:109:62315313470741024617821649445847134329638400863882729600 192:110:47019736527922773120719971854593746812363520651838786880 192:111:34735300858465472035126465694384569717241519760817842560 192:112:25121065799425921739689676082545983456219313398448618280 192:113:17784825344726316275886496341625475013252611255538844800 192:114:12324571949415605138552922903407127421464528852522532800 192:115:8359274887429714789627199882310921207602028265189196160 192:116:5548829020104207231045641301189145974011691176030759520 192:117:3604367568614698714183493494789530718161440422037074560 192:118:2290911590221206809862389933128939015780576539430344000 192:119:1424600484675372301931234076063373841745904738805424000 192:120:866631961510851483674834062938552420395425382773299600 192:121:515681828337035593591636797781617969160914277352707200 192:122:300109916491225632336116497069630129593646833541329600 192:123:170794261417770685069334591828244789199636409332464000 192:124:95038742240533687659549087388297503667539614870484000 192:125:51701075778850326086794703539233841995141550489543296 192:126:27491841882404538474724167754989423918051459387296832 192:127:14287098931013382199462953321490566760562175744579456 192:128:7255167425905233148164780983569428433097979870294255 192:129:3599462908976239701415085139135220307893571408518080 192:130:1744355102042331547608848952042452918440730759512608 192:131:825572643714691266807241488752916648422330588471616 192:132:381514630807546721782134324347938754195167923460368 192:133:172111863522201528623519244066739287606842672237760 192:134:75780596625446941707370413432370283349281475089760 192:135:32557589661303130511314696141314640253765374483008 192:136:13645460372752047346653953529815694812239899599496 192:137:5577706429738063148997236479340721967046966259648 192:138:2222998939388358501411942075099563102808573509280 192:139:863611098755189633642049439247312284544337910080 192:140:326938487385893218450204430572196793434642208816 192:141:120573059177776222407167591416696689777314857152 192:142:43304408577933713681447515227123459004528575456 192:143:15141401600676123664841788540952258393191809600 192:144:5152282489118958747064219711851810147683324100 192:145:1705583168811793240407465835647495773026203840 192:146:549057595439412892459937632023508913234462880 192:147:171813941430020360905830823626404149719627840 192:148:52240725434803488113259372048568829306643600 192:149:15426791403566130718009478994208244895921600 192:150:4422346869022290805829383978339696870164192 192:151:1230056745026067641356517397948789857926464 192:152:331791622013610350629060613920397264309112 192:153:86742907715976562255963559194875101780160 192:154:21967359746253804727159602653247590710560 192:155:5385546260371900513755257424667151270976 192:156:1277341100216412301339387978927465365552 192:157:292893500686565878014127179881457026496 192:158:64881471671074719813256020859816429920 192:159:13874025388783273419186822070652569920 192:160:2861517736436550142707282052072092546 192:161:568748866869376425879708233952217152 192:162:108834659709572032112783674398263776 192:163:20030918964951907750819081177594560 192:164:3542052743802471492522886305794160 192:165:601075617130116374488732221589312 192:166:97765311219958687416841987848864 192:167:15220946656999556124777794515392 192:168:2265021823958267280472886088600 192:169:321659903994073459948812225600 192:170:43518692893315821051898124640 192:171:5598896161713146568080460480 192:172:683586159278930685637730640 192:173:79027301650743431865633600 192:174:8629417996345547157741600 192:175:887597279624113421939136 192:176:85733828145510955528212 192:177:7749950566825849087296 192:178:653085721923526608480 192:179:51079330206309343680 192:180:3689062737122341488 192:181:244578745002586176 192:182:14782231840815648 192:183:807772231738560 192:184:39510598291560 192:185:1708566412608 192:186:64300886496 192:187:2063130048 192:188:54870480 192:189:1161280 192:190:18336 192:191:192 192:192:1 # binomial(193, k) for 0 <= k <= 193 193:0:1 193:1:193 193:2:18528 193:3:1179616 193:4:56031760 193:5:2118000528 193:6:66364016544 193:7:1772867299104 193:8:41219164704168 193:9:847282830030120 193:10:15590004072554208 193:11:259360976843401824 193:12:3933641482124927664 193:13:54768392943431685168 193:14:704165052129835952160 193:15:8403036288749375695776 193:16:93483778712336804615508 193:17:973331107769624377467348 193:18:9517015275969660579680736 193:19:87656719647088979023375200 193:20:762613460929674117503364240 193:21:6282482320992077253718191120 193:22:49117589055028967619978585120 193:23:365178596887389281000710350240 193:24:2586681727952340740421698314200 193:25:17485968480957823405250680603992 193:26:112986257876958243541619782364256 193:27:698840928350075061905574209438176 193:28:4143128360932587867011618527383472 193:29:23572971708754379243341967483388720 193:30:128865578674523939863602755575858336 193:31:677583526578948457992491908350480928 193:32:3430266603305926568586990286024309698 193:33:16735543125219823561894104122724662466 193:34:78755497059857993232442842930468999840 193:35:357774972357640597827383200741273456416 193:36:1570234600902978179353515158808922392048 193:37:6662887360588312815094645403594616636528 193:38:27352906006625705240914860077914741981536 193:39:108710267462230366983123161848122692490720 193:40:418534529729586912885024173115272366089272 193:41:1561848367039677991985578011869187122235576 193:42:5652403614048358447185901376288486728090656 193:43:19849138272588421523838862972547941766085792 193:44:67667516838369618831268851042777074202565200 193:45:224054666864823849019090195674972979026271440 193:46:720871536869433253365768455649913062954090720 193:47:2254640764251206132867403467671004686260666720 193:48:6857865657930751987471685547499305920709527940 193:49:20293684089795082411906008252804068540875133700 193:50:58445810178609837346289303768075717397720385056 193:51:163877467755709936088615106643820148781843432608 193:52:447511546563669440857372021988893483211957065968 193:53:1190549586141082852092253869819509077978980118896 193:54:3086610038143548135053991514346875387352911419360 193:55:7800705369126421650409178554440285069855539768928 193:56:19223166802490110495651190009156416779286865859144 193:57:46203050034055177857968649671130335066005274082504 193:58:108338186286750072218685109573684923603046849572768 193:59:247892460147648470330889657499109570956124147327520 193:60:553626494329748250405653568414678041802010595698128 193:61:1207087274522237988589375813100855402617498511931984 193:62:2569927745757022814416090440795369566863061347984224 193:63:5343818011018571249023934091177673226334302168030688 193:64:10854630334881472849579866122704648740991551278812335 193:65:21542266356918615347627734305059995193660155614873711 193:66:41778940813417920674187121076479990678613635131876288 193:67:79192917661254864561518871294223265913193009876840128 193:68:146739818019384013746343790927531345662681165360027296 193:69:265833003658304372728883679216542292867176024202948000 193:70:470904177908996317405451088897874918793283242873793600 193:71:815791744828261225927753294851248098754561110894036800 193:72:1382313789847887077266470860720170389556339660126006800 193:73:2291232446186223785606068139001926262141330121578723600 193:74:3715512074896579111793624009192312857526481278235768000 193:75:5895279158835905524045883427918469733942016961467418560 193:76:9153196588718905945229134795978676692173131598067834080 193:77:13908103907533922020672841183500067181613719441219955680 193:78:20683846836845319928180122785718048629066557117711728960 193:79:30109397294141921414439419245032602434717140108061377600 193:80:42905891144152238015576172424171458469471924653987463080 193:81:59856366657891393774816141776930553173460833159266460840 193:82:81755037386388245155846437548978316529605040412656629440 193:83:109335049998663797738541621300440881142001921515721516480 193:84:143176851188726401800471170750577344352621563889635319200 193:85:183603256230249150544133618962505065111008828987885291680 193:86:230571531079847770450772451720355198046383180589437343040 193:87:283576480753375993542904049816988576907620693368618341440 193:88:341580760907475628585770787279554422184179471557653911280 193:89:402988538149269000016920591734305778981335331612962479600 193:90:465675644083599733352886017115197789045098605419423309760 193:91:527083421325393104784035821569949145842254465474731878080 193:92:584375097556414094434474497827552313868586472591550560480 193:93:634643923152664769224536820221320254846529394965017275360 193:94:675153109736877414068656191724808781751627015920231144000 193:95:703580609094219620976810136639537572562221837643188244800 193:96:718238538450349196413827014486194605323934792594087999900 193:97:718238538450349196413827014486194605323934792594087999900 193:98:703580609094219620976810136639537572562221837643188244800 193:99:675153109736877414068656191724808781751627015920231144000 193:100:634643923152664769224536820221320254846529394965017275360 193:101:584375097556414094434474497827552313868586472591550560480 193:102:527083421325393104784035821569949145842254465474731878080 193:103:465675644083599733352886017115197789045098605419423309760 193:104:402988538149269000016920591734305778981335331612962479600 193:105:341580760907475628585770787279554422184179471557653911280 193:106:283576480753375993542904049816988576907620693368618341440 193:107:230571531079847770450772451720355198046383180589437343040 193:108:183603256230249150544133618962505065111008828987885291680 193:109:143176851188726401800471170750577344352621563889635319200 193:110:109335049998663797738541621300440881142001921515721516480 193:111:81755037386388245155846437548978316529605040412656629440 193:112:59856366657891393774816141776930553173460833159266460840 193:113:42905891144152238015576172424171458469471924653987463080 193:114:30109397294141921414439419245032602434717140108061377600 193:115:20683846836845319928180122785718048629066557117711728960 193:116:13908103907533922020672841183500067181613719441219955680 193:117:9153196588718905945229134795978676692173131598067834080 193:118:5895279158835905524045883427918469733942016961467418560 193:119:3715512074896579111793624009192312857526481278235768000 193:120:2291232446186223785606068139001926262141330121578723600 193:121:1382313789847887077266470860720170389556339660126006800 193:122:815791744828261225927753294851248098754561110894036800 193:123:470904177908996317405451088897874918793283242873793600 193:124:265833003658304372728883679216542292867176024202948000 193:125:146739818019384013746343790927531345662681165360027296 193:126:79192917661254864561518871294223265913193009876840128 193:127:41778940813417920674187121076479990678613635131876288 193:128:21542266356918615347627734305059995193660155614873711 193:129:10854630334881472849579866122704648740991551278812335 193:130:5343818011018571249023934091177673226334302168030688 193:131:2569927745757022814416090440795369566863061347984224 193:132:1207087274522237988589375813100855402617498511931984 193:133:553626494329748250405653568414678041802010595698128 193:134:247892460147648470330889657499109570956124147327520 193:135:108338186286750072218685109573684923603046849572768 193:136:46203050034055177857968649671130335066005274082504 193:137:19223166802490110495651190009156416779286865859144 193:138:7800705369126421650409178554440285069855539768928 193:139:3086610038143548135053991514346875387352911419360 193:140:1190549586141082852092253869819509077978980118896 193:141:447511546563669440857372021988893483211957065968 193:142:163877467755709936088615106643820148781843432608 193:143:58445810178609837346289303768075717397720385056 193:144:20293684089795082411906008252804068540875133700 193:145:6857865657930751987471685547499305920709527940 193:146:2254640764251206132867403467671004686260666720 193:147:720871536869433253365768455649913062954090720 193:148:224054666864823849019090195674972979026271440 193:149:67667516838369618831268851042777074202565200 193:150:19849138272588421523838862972547941766085792 193:151:5652403614048358447185901376288486728090656 193:152:1561848367039677991985578011869187122235576 193:153:418534529729586912885024173115272366089272 193:154:108710267462230366983123161848122692490720 193:155:27352906006625705240914860077914741981536 193:156:6662887360588312815094645403594616636528 193:157:1570234600902978179353515158808922392048 193:158:357774972357640597827383200741273456416 193:159:78755497059857993232442842930468999840 193:160:16735543125219823561894104122724662466 193:161:3430266603305926568586990286024309698 193:162:677583526578948457992491908350480928 193:163:128865578674523939863602755575858336 193:164:23572971708754379243341967483388720 193:165:4143128360932587867011618527383472 193:166:698840928350075061905574209438176 193:167:112986257876958243541619782364256 193:168:17485968480957823405250680603992 193:169:2586681727952340740421698314200 193:170:365178596887389281000710350240 193:171:49117589055028967619978585120 193:172:6282482320992077253718191120 193:173:762613460929674117503364240 193:174:87656719647088979023375200 193:175:9517015275969660579680736 193:176:973331107769624377467348 193:177:93483778712336804615508 193:178:8403036288749375695776 193:179:704165052129835952160 193:180:54768392943431685168 193:181:3933641482124927664 193:182:259360976843401824 193:183:15590004072554208 193:184:847282830030120 193:185:41219164704168 193:186:1772867299104 193:187:66364016544 193:188:2118000528 193:189:56031760 193:190:1179616 193:191:18528 193:192:193 193:193:1 # binomial(194, k) for 0 <= k <= 194 194:0:1 194:1:194 194:2:18721 194:3:1198144 194:4:57211376 194:5:2174032288 194:6:68482017072 194:7:1839231315648 194:8:42992032003272 194:9:888501994734288 194:10:16437286902584328 194:11:274950980915956032 194:12:4193002458968329488 194:13:58702034425556612832 194:14:758933445073267637328 194:15:9107201340879211647936 194:16:101886815001086180311284 194:17:1066814886481961182082856 194:18:10490346383739284957148084 194:19:97173734923058639603055936 194:20:850270180576763096526739440 194:21:7045095781921751371221555360 194:22:55400071376021044873696776240 194:23:414296185942418248620688935360 194:24:2951860324839730021422408664440 194:25:20072650208910164145672378918192 194:26:130472226357916066946870462968248 194:27:811827186227033305447193991802432 194:28:4841969289282662928917192736821648 194:29:27716100069686967110353586010772192 194:30:152438550383278319106944723059247056 194:31:806449105253472397856094663926339264 194:32:4107850129884875026579482194374790626 194:33:20165809728525750130481094408748972164 194:34:95491040185077816794336947053193662306 194:35:436530469417498591059826043671742456256 194:36:1928009573260618777180898359550195848464 194:37:8233121961491290994448160562403539028576 194:38:34015793367214018056009505481509358618064 194:39:136063173468856072224038021926037434472256 194:40:527244797191817279868147334963395058579992 194:41:1980382896769264904870602184984459488324848 194:42:7214251981088036439171479388157673850326232 194:43:25501541886636779971024764348836428494176448 194:44:87516655110958040355107714015325015968650992 194:45:291722183703193467850359046717750053228836640 194:46:944926203734257102384858651324886041980362160 194:47:2975512301120639386233171923320917749214757440 194:48:9112506422181958120339089015170310606970194660 194:49:27151549747725834399377693800303374461584661640 194:50:78739494268404919758195312020879785938595518756 194:51:222323277934319773434904410411895866179563817664 194:52:611389014319379376945987128632713631993800498576 194:53:1638061132704752292949625891808402561190937184864 194:54:4277159624284630987146245384166384465331891538256 194:55:10887315407269969785463170068787160457208451188288 194:56:27023872171616532146060368563596701849142405628072 194:57:65426216836545288353619839680286751845292139941648 194:58:154541236320805250076653759244815258669052123655272 194:59:356230646434398542549574767072794494559170996900288 194:60:801518954477396720736543225913787612758134743025648 194:61:1760713768851986238995029381515533444419509107630112 194:62:3777015020279260803005466253896224969480559859916208 194:63:7913745756775594063440024531973042793197363516014912 194:64:16198448345900044098603800213882321967325853446843023 194:65:32396896691800088197207600427764643934651706893686046 194:66:63321207170336536021814855381539985872273790746749999 194:67:120971858474672785235705992370703256591806645008716416 194:68:225932735680638878307862662221754611575874175236867424 194:69:412572821677688386475227470144073638529857189562975296 194:70:736737181567300690134334768114417211660459267076741600 194:71:1286695922737257543333204383749123017547844353767830400 194:72:2198105534676148303194224155571418488310900771020043600 194:73:3673546236034110862872538999722096651697669781704730400 194:74:6006744521082802897399692148194239119667811399814491600 194:75:9610791233732484635839507437110782591468498239703186560 194:76:15048475747554811469275018223897146426115148559535252640 194:77:23061300496252827965901975979478743873786851039287789760 194:78:34591950744379241948852963969218115810680276558931684640 194:79:50793244130987241342619542030750651063783697225773106560 194:80:73015288438294159430015591669204060904189064762048840680 194:81:102762257802043631790392314201102011642932757813253923920 194:82:141611404044279638930662579325908869703065873571923090280 194:83:191090087385052042894388058849419197671606961928378145920 194:84:252511901187390199539012792051018225494623485405356835680 194:85:326780107418975552344604789713082409463630392877520610880 194:86:414174787310096920994906070682860263157392009577322634720 194:87:514148011833223763993676501537343774954003873958055684480 194:88:625157241660851622128674837096542999091800164926272252720 194:89:744569299056744628602691379013860201165514803170616390880 194:90:868664182232868733369806608849503568026433937032385789360 194:91:992759065408992838136921838685146934887353070894155187840 194:92:1111458518881807199218510319397501459710840938066282438560 194:93:1219019020709078863659011318048872568715115867556567835840 194:94:1309797032889542183293193011946129036598156410885248419360 194:95:1378733718831097035045466328364346354313848853563419388800 194:96:1421819147544568817390637151125732177886156630237276244700 194:97:1436477076900698392827654028972389210647869585188175999800 194:98:1421819147544568817390637151125732177886156630237276244700 194:99:1378733718831097035045466328364346354313848853563419388800 194:100:1309797032889542183293193011946129036598156410885248419360 194:101:1219019020709078863659011318048872568715115867556567835840 194:102:1111458518881807199218510319397501459710840938066282438560 194:103:992759065408992838136921838685146934887353070894155187840 194:104:868664182232868733369806608849503568026433937032385789360 194:105:744569299056744628602691379013860201165514803170616390880 194:106:625157241660851622128674837096542999091800164926272252720 194:107:514148011833223763993676501537343774954003873958055684480 194:108:414174787310096920994906070682860263157392009577322634720 194:109:326780107418975552344604789713082409463630392877520610880 194:110:252511901187390199539012792051018225494623485405356835680 194:111:191090087385052042894388058849419197671606961928378145920 194:112:141611404044279638930662579325908869703065873571923090280 194:113:102762257802043631790392314201102011642932757813253923920 194:114:73015288438294159430015591669204060904189064762048840680 194:115:50793244130987241342619542030750651063783697225773106560 194:116:34591950744379241948852963969218115810680276558931684640 194:117:23061300496252827965901975979478743873786851039287789760 194:118:15048475747554811469275018223897146426115148559535252640 194:119:9610791233732484635839507437110782591468498239703186560 194:120:6006744521082802897399692148194239119667811399814491600 194:121:3673546236034110862872538999722096651697669781704730400 194:122:2198105534676148303194224155571418488310900771020043600 194:123:1286695922737257543333204383749123017547844353767830400 194:124:736737181567300690134334768114417211660459267076741600 194:125:412572821677688386475227470144073638529857189562975296 194:126:225932735680638878307862662221754611575874175236867424 194:127:120971858474672785235705992370703256591806645008716416 194:128:63321207170336536021814855381539985872273790746749999 194:129:32396896691800088197207600427764643934651706893686046 194:130:16198448345900044098603800213882321967325853446843023 194:131:7913745756775594063440024531973042793197363516014912 194:132:3777015020279260803005466253896224969480559859916208 194:133:1760713768851986238995029381515533444419509107630112 194:134:801518954477396720736543225913787612758134743025648 194:135:356230646434398542549574767072794494559170996900288 194:136:154541236320805250076653759244815258669052123655272 194:137:65426216836545288353619839680286751845292139941648 194:138:27023872171616532146060368563596701849142405628072 194:139:10887315407269969785463170068787160457208451188288 194:140:4277159624284630987146245384166384465331891538256 194:141:1638061132704752292949625891808402561190937184864 194:142:611389014319379376945987128632713631993800498576 194:143:222323277934319773434904410411895866179563817664 194:144:78739494268404919758195312020879785938595518756 194:145:27151549747725834399377693800303374461584661640 194:146:9112506422181958120339089015170310606970194660 194:147:2975512301120639386233171923320917749214757440 194:148:944926203734257102384858651324886041980362160 194:149:291722183703193467850359046717750053228836640 194:150:87516655110958040355107714015325015968650992 194:151:25501541886636779971024764348836428494176448 194:152:7214251981088036439171479388157673850326232 194:153:1980382896769264904870602184984459488324848 194:154:527244797191817279868147334963395058579992 194:155:136063173468856072224038021926037434472256 194:156:34015793367214018056009505481509358618064 194:157:8233121961491290994448160562403539028576 194:158:1928009573260618777180898359550195848464 194:159:436530469417498591059826043671742456256 194:160:95491040185077816794336947053193662306 194:161:20165809728525750130481094408748972164 194:162:4107850129884875026579482194374790626 194:163:806449105253472397856094663926339264 194:164:152438550383278319106944723059247056 194:165:27716100069686967110353586010772192 194:166:4841969289282662928917192736821648 194:167:811827186227033305447193991802432 194:168:130472226357916066946870462968248 194:169:20072650208910164145672378918192 194:170:2951860324839730021422408664440 194:171:414296185942418248620688935360 194:172:55400071376021044873696776240 194:173:7045095781921751371221555360 194:174:850270180576763096526739440 194:175:97173734923058639603055936 194:176:10490346383739284957148084 194:177:1066814886481961182082856 194:178:101886815001086180311284 194:179:9107201340879211647936 194:180:758933445073267637328 194:181:58702034425556612832 194:182:4193002458968329488 194:183:274950980915956032 194:184:16437286902584328 194:185:888501994734288 194:186:42992032003272 194:187:1839231315648 194:188:68482017072 194:189:2174032288 194:190:57211376 194:191:1198144 194:192:18721 194:193:194 194:194:1 # binomial(195, k) for 0 <= k <= 195 195:0:1 195:1:195 195:2:18915 195:3:1216865 195:4:58409520 195:5:2231243664 195:6:70656049360 195:7:1907713332720 195:8:44831263318920 195:9:931494026737560 195:10:17325788897318616 195:11:291388267818540360 195:12:4467953439884285520 195:13:62895036884524942320 195:14:817635479498824250160 195:15:9866134785952479285264 195:16:110994016341965391959220 195:17:1168701701483047362394140 195:18:11557161270221246139230940 195:19:107664081306797924560204020 195:20:947443915499821736129795376 195:21:7895365962498514467748294800 195:22:62445167157942796244918331600 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195:44:113018196997594820326132478364161444462827440 195:45:379238838814151508205466760733075069197487632 195:46:1236648387437450570235217698042636095209198800 195:47:3920438504854896488618030574645803791195119600 195:48:12088018723302597506572260938491228356184952100 195:49:36264056169907792519716782815473685068554856300 195:50:105891044016130754157573005821183160400180180396 195:51:301062772202724693193099722432775652118159336420 195:52:833712292253699150380891539044609498173364316240 195:53:2249450147024131669895613020441116193184737683440 195:54:5915220756989383280095871275974787026522828723120 195:55:15164475031554600772609415452953544922540342726544 195:56:37911187578886501931523538632383862306350856816360 195:57:92450089008161820499680208243883453694434545569720 195:58:219967453157350538430273598925102010514344263596920 195:59:510771882755203792626228526317609753228223120555560 195:60:1157749600911795263286117992986582107317305739925936 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195:92:2104217584290800037355432158082648394598194008960437626400 195:93:2330477539590886062877521637446374028425956805622850274400 195:94:2528816053598621046952204329995001605313272278441816255200 195:95:2688530751720639218338659340310475390912005264448667808160 195:96:2800552866375665852436103479490078532200005483800695633500 195:97:2858296224445267210218291180098121388534026215425452244500 195:98:2858296224445267210218291180098121388534026215425452244500 195:99:2800552866375665852436103479490078532200005483800695633500 195:100:2688530751720639218338659340310475390912005264448667808160 195:101:2528816053598621046952204329995001605313272278441816255200 195:102:2330477539590886062877521637446374028425956805622850274400 195:103:2104217584290800037355432158082648394598194008960437626400 195:104:1861423247641861571506728447534650502913787007926540977200 195:105:1613233481289613361972497987863363769191948740203002180240 195:106:1369726540717596250731366216110403200257314968096888643600 195:107:1139305253494075386122351338633886774045804038884327937200 195:108:928322799143320684988582572220204038111395883535378319200 195:109:740954894729072473339510860395942672621022402454843245600 195:110:579292008606365751883617581764100634958253878282877446560 195:111:443601988572442242433400850900437423166230447333734981600 195:112:332701491429331681825050638175328067374672835500301236200 195:113:244373661846323270721054893527010881345998631385177014200 195:114:175777546240337791220407905870306072547121822575302764600 195:115:123808532569281400772635133699954711967972761987821947240 195:116:85385194875366483291472505999968766874463973784704791200 195:117:57653251240632069914754939948696859684467127598219474400 195:118:38109776243807639435176994203375890299901999598823042400 195:119:24659266981287296105114525661007929017583646799238439200 195:120:15617535754815287533239199585305021711136309639517678160 195:121:9680290757116913760272231147916335771365481181519222000 195:122:5871651770710259166066763155293515140008570552724774000 195:123:3484801457413405846527428539320541505858745124787874000 195:124:2023433104304558233467539151863540229208303620844572000 195:125:1149310003244989076609562238258490850190316456639716896 195:126:638505557358327264783090132365828250105731364799842720 195:127:346904594155311663543568654592457868167680820245583840 195:128:184293065645009321257520847752243242464080435755466415 195:129:95718103862136624219022455809304629806925497640436045 195:130:48595345037700132295811400641646965901977560340529069 195:131:24112194102675638162043824745855364760523216962857935 195:132:11690760777054854866445490785869267762677923375931120 195:133:5537728789131247042000495635411758413900068967546320 195:134:2562232723329382959731572607429321057177643850655760 195:135:1157749600911795263286117992986582107317305739925936 195:136:510771882755203792626228526317609753228223120555560 195:137:219967453157350538430273598925102010514344263596920 195:138:92450089008161820499680208243883453694434545569720 195:139:37911187578886501931523538632383862306350856816360 195:140:15164475031554600772609415452953544922540342726544 195:141:5915220756989383280095871275974787026522828723120 195:142:2249450147024131669895613020441116193184737683440 195:143:833712292253699150380891539044609498173364316240 195:144:301062772202724693193099722432775652118159336420 195:145:105891044016130754157573005821183160400180180396 195:146:36264056169907792519716782815473685068554856300 195:147:12088018723302597506572260938491228356184952100 195:148:3920438504854896488618030574645803791195119600 195:149:1236648387437450570235217698042636095209198800 195:150:379238838814151508205466760733075069197487632 195:151:113018196997594820326132478364161444462827440 195:152:32715793867724816410196243736994102344502680 195:153:9194634877857301344042081573142133338651080 195:154:2507627693961082184738749519947854546904840 195:155:663307970660673352092185356889432493052248 195:156:170078966836070090280047527407546793090320 195:157:42248915328705309050457666043912897646640 195:158:10161131534751909771629058921953734877040 195:159:2364540042678117368240724403221938304720 195:160:532021509602576407854162990724936118562 195:161:115656849913603566924818041461942634470 195:162:24273659858410625157060576603123762790 195:163:4914299235138347424435576858301129890 195:164:958887655636750716963039386985586320 195:165:180154650452965286217298309070019248 195:166:32558069358969630039270778747593840 195:167:5653796475509696234364386728624080 195:168:942299412584949372394064454770680 195:169:150544876566826231092542841886440 195:170:23024510533749894167094787582632 195:171:3366156510782148270043097599800 195:172:469696257318439293494385711600 195:173:62445167157942796244918331600 195:174:7895365962498514467748294800 195:175:947443915499821736129795376 195:176:107664081306797924560204020 195:177:11557161270221246139230940 195:178:1168701701483047362394140 195:179:110994016341965391959220 195:180:9866134785952479285264 195:181:817635479498824250160 195:182:62895036884524942320 195:183:4467953439884285520 195:184:291388267818540360 195:185:17325788897318616 195:186:931494026737560 195:187:44831263318920 195:188:1907713332720 195:189:70656049360 195:190:2231243664 195:191:58409520 195:192:1216865 195:193:18915 195:194:195 195:195:1 # binomial(196, k) for 0 <= k <= 196 196:0:1 196:1:196 196:2:19110 196:3:1235780 196:4:59626385 196:5:2289653184 196:6:72887293024 196:7:1978369382080 196:8:46738976651640 196:9:976325290056480 196:10:18257282924056176 196:11:308714056715858976 196:12:4759341707702825880 196:13:67362990324409227840 196:14:880530516383349192480 196:15:10683770265451303535424 196:16:120860151127917871244484 196:17:1279695717825012754353360 196:18:12725862971704293501625080 196:19:119221242577019170699434960 196:20:1055107996806619660689999396 196:21:8842809877998336203878090176 196:22:70340533120441310712666626400 196:23:532141424476382089739304043200 196:24:3835852768100587563537483311400 196:25:26390667044532042437137885182432 196:26:173569387100576125259637629469072 196:27:1092844289151775603486607296657120 196:28:6596095888094645606758451183394760 196:29:38211865834479326273635165476217920 196:30:212712719811934916256569087817613088 196:31:1139042306089716003180337696055605568 196:32:5873186890775098141398616245286716210 196:33:29187959093548972581496153461424892680 196:34:139930509772014192081878618065066397260 196:35:647678359516179974778981032186878753032 196:36:2896561552280693776094887393946874423282 196:37:12525671577430027139869783325175673181760 196:38:52410046863457218822086724965866632523680 196:39:212327882164775399330505193451459690736960 196:40:833386937496743442372232884296979286142568 196:41:3170935664621755536830934876837287039957088 196:42:11702262571818383528780831093089987885555920 196:43:41910428745582117754238325310136235683153760 196:44:145733990865319636736328722101155546807330120 196:45:492257035811746328531599239097236513660315072 196:46:1615887226251602078440684458775711164406686432 196:47:5157086892292347058853248272688439886404318400 196:48:16008457228157493995190291513137032147380071700 196:49:48352074893210390026289043753964913424739808400 196:50:142155100186038546677289788636656845468735036696 196:51:406953816218855447350672728253958812518339516816 196:52:1134775064456423843573991261477385150291523652660 196:53:3083162439277830820276504559485725691358101999680 196:54:8164670904013514949991484296415903219707566406560 196:55:21079695788543984052705286728928331949063171449664 196:56:53075662610441102704132954085337407228891199542904 196:57:130361276587048322431203746876267316000785402386080 196:58:312417542165512358929953807168985464208778809166640 196:59:730739335912554331056502125242711763742567384152480 196:60:1668521483666999055912346519304191860545528860481496 196:61:3719982324241178223017690600415903164494949590581696 196:62:8099961512460630001732068242841079471077712818202080 196:63:17228489566186101908445986421281026176577992343477440 196:64:35802954879730493028489315531724632523201140338789055 196:65:72707539140375770457855225387502330662500777303387004 196:66:144313448899836756514833856450951595708903057980965114 196:67:280011169507145945476543303561547872271005933395902460 196:68:531197659800320984801089502344701110631761256001050255 196:69:985410151513638928326658786958286118273412185045426560 196:70:1787815560603316341392652370624319100296047821439559616 196:71:3172743107549547310077101390122031079398620077484288896 196:72:5508234561717964079994967691184081735067048745632446000 196:73:9356453228123665012594191694614056645867315677512648000 196:74:15551942527827172926338994303209850911374051734243996000 196:75:25297826511932201293511430733221357482501790821036900160 196:76:40276802736102583638353725246312950728719956438756117360 196:77:62769043225094935540291519864383819317485646398061481600 196:78:95763027484439709349931934152072749984369127197042516800 196:79:143038446115998553206227445948665626558931101382924265600 196:80:209193727444647884064107639699923478842436735772526738440 196:81:299586078809619191993043039570260784515094584563124711840 196:82:420151208086661061941462799397316953893120453960479778800 196:83:577075153275654952546105531702338948720671466885478250400 196:84:776303480001773924258451489075765490540903282834036217800 196:85:1022893997178807994317018432664538058124484325616612428160 196:86:1320246903335438225223128442160043307579276280737720692160 196:87:1669277693872393158328093432616146710732418285990221564800 196:88:2067628052637396071110933910854090812157199922419706256400 196:89:2509031794211671636853717554744289974303119006981216580800 196:90:2982960022007209612703864203973766969449263708299890823840 196:91:3474656728931474933479226435398014272105735748129543157440 196:92:3965640831932661608862160605617298897511981016886978603600 196:93:4434695123881686100232953795529022423024150814583287900800 196:94:4859293593189507109829725967441375633739229084064666529600 196:95:5217346805319260265290863670305476996225277542890484063360 196:96:5489083618096305070774762819800553923112010748249363441660 196:97:5658849090820933062654394659588199920734031699226147878000 196:98:5716592448890534420436582360196242777068052430850904489000 196:99:5658849090820933062654394659588199920734031699226147878000 196:100:5489083618096305070774762819800553923112010748249363441660 196:101:5217346805319260265290863670305476996225277542890484063360 196:102:4859293593189507109829725967441375633739229084064666529600 196:103:4434695123881686100232953795529022423024150814583287900800 196:104:3965640831932661608862160605617298897511981016886978603600 196:105:3474656728931474933479226435398014272105735748129543157440 196:106:2982960022007209612703864203973766969449263708299890823840 196:107:2509031794211671636853717554744289974303119006981216580800 196:108:2067628052637396071110933910854090812157199922419706256400 196:109:1669277693872393158328093432616146710732418285990221564800 196:110:1320246903335438225223128442160043307579276280737720692160 196:111:1022893997178807994317018432664538058124484325616612428160 196:112:776303480001773924258451489075765490540903282834036217800 196:113:577075153275654952546105531702338948720671466885478250400 196:114:420151208086661061941462799397316953893120453960479778800 196:115:299586078809619191993043039570260784515094584563124711840 196:116:209193727444647884064107639699923478842436735772526738440 196:117:143038446115998553206227445948665626558931101382924265600 196:118:95763027484439709349931934152072749984369127197042516800 196:119:62769043225094935540291519864383819317485646398061481600 196:120:40276802736102583638353725246312950728719956438756117360 196:121:25297826511932201293511430733221357482501790821036900160 196:122:15551942527827172926338994303209850911374051734243996000 196:123:9356453228123665012594191694614056645867315677512648000 196:124:5508234561717964079994967691184081735067048745632446000 196:125:3172743107549547310077101390122031079398620077484288896 196:126:1787815560603316341392652370624319100296047821439559616 196:127:985410151513638928326658786958286118273412185045426560 196:128:531197659800320984801089502344701110631761256001050255 196:129:280011169507145945476543303561547872271005933395902460 196:130:144313448899836756514833856450951595708903057980965114 196:131:72707539140375770457855225387502330662500777303387004 196:132:35802954879730493028489315531724632523201140338789055 196:133:17228489566186101908445986421281026176577992343477440 196:134:8099961512460630001732068242841079471077712818202080 196:135:3719982324241178223017690600415903164494949590581696 196:136:1668521483666999055912346519304191860545528860481496 196:137:730739335912554331056502125242711763742567384152480 196:138:312417542165512358929953807168985464208778809166640 196:139:130361276587048322431203746876267316000785402386080 196:140:53075662610441102704132954085337407228891199542904 196:141:21079695788543984052705286728928331949063171449664 196:142:8164670904013514949991484296415903219707566406560 196:143:3083162439277830820276504559485725691358101999680 196:144:1134775064456423843573991261477385150291523652660 196:145:406953816218855447350672728253958812518339516816 196:146:142155100186038546677289788636656845468735036696 196:147:48352074893210390026289043753964913424739808400 196:148:16008457228157493995190291513137032147380071700 196:149:5157086892292347058853248272688439886404318400 196:150:1615887226251602078440684458775711164406686432 196:151:492257035811746328531599239097236513660315072 196:152:145733990865319636736328722101155546807330120 196:153:41910428745582117754238325310136235683153760 196:154:11702262571818383528780831093089987885555920 196:155:3170935664621755536830934876837287039957088 196:156:833386937496743442372232884296979286142568 196:157:212327882164775399330505193451459690736960 196:158:52410046863457218822086724965866632523680 196:159:12525671577430027139869783325175673181760 196:160:2896561552280693776094887393946874423282 196:161:647678359516179974778981032186878753032 196:162:139930509772014192081878618065066397260 196:163:29187959093548972581496153461424892680 196:164:5873186890775098141398616245286716210 196:165:1139042306089716003180337696055605568 196:166:212712719811934916256569087817613088 196:167:38211865834479326273635165476217920 196:168:6596095888094645606758451183394760 196:169:1092844289151775603486607296657120 196:170:173569387100576125259637629469072 196:171:26390667044532042437137885182432 196:172:3835852768100587563537483311400 196:173:532141424476382089739304043200 196:174:70340533120441310712666626400 196:175:8842809877998336203878090176 196:176:1055107996806619660689999396 196:177:119221242577019170699434960 196:178:12725862971704293501625080 196:179:1279695717825012754353360 196:180:120860151127917871244484 196:181:10683770265451303535424 196:182:880530516383349192480 196:183:67362990324409227840 196:184:4759341707702825880 196:185:308714056715858976 196:186:18257282924056176 196:187:976325290056480 196:188:46738976651640 196:189:1978369382080 196:190:72887293024 196:191:2289653184 196:192:59626385 196:193:1235780 196:194:19110 196:195:196 196:196:1 # binomial(197, k) for 0 <= k <= 197 197:0:1 197:1:197 197:2:19306 197:3:1254890 197:4:60862165 197:5:2349279569 197:6:75176946208 197:7:2051256675104 197:8:48717346033720 197:9:1023064266708120 197:10:19233608214112656 197:11:326971339639915152 197:12:5068055764418684856 197:13:72122332032112053720 197:14:947893506707758420320 197:15:11564300781834652727904 197:16:131543921393369174779908 197:17:1400555868952930625597844 197:18:14005558689529306255978440 197:19:131947105548723464201060040 197:20:1174329239383638831389434356 197:21:9897917874804955864568089572 197:22:79183342998439646916544716576 197:23:602481957596823400451970669600 197:24:4367994192576969653276787354600 197:25:30226519812632630000675368493832 197:26:199960054145108167696775514651504 197:27:1266413676252351728746244926126192 197:28:7688940177246421210245058480051880 197:29:44807961722573971880393616659612680 197:30:250924585646414242530204253293831008 197:31:1351755025901650919436906783873218656 197:32:7012229196864814144578953941342321778 197:33:35061145984324070722894769706711608890 197:34:169118468865563164663374771526491289940 197:35:787608869288194166860859650251945150292 197:36:3544239911796873750873868426133753176314 197:37:15422233129710720915964670719122547605042 197:38:64935718440887245961956508291042305705440 197:39:264737929028232618152591918417326323260640 197:40:1045714819661518841702738077748438976879528 197:41:4004322602118498979203167761134266326099656 197:42:14873198236440139065611765969927274925513008 197:43:53612691317400501283019156403226223568709680 197:44:187644419610901754490567047411291782490483880 197:45:637991026677065965267927961198392060467645192 197:46:2108144262063348406972283697872947678067001504 197:47:6772974118543949137293932731464151050811004832 197:48:21165544120449841054043539785825472033784390100 197:49:64360532121367884021479335267101945572119880100 197:50:190507175079248936703578832390621758893474845096 197:51:549108916404893994027962516890615657987074553512 197:52:1541728880675279290924663989731343962809863169476 197:53:4217937503734254663850495820963110841649625652340 197:54:11247833343291345770267988855901628911065668406240 197:55:29244366692557499002696771025344235168770737856224 197:56:74155358398985086756838240814265739177954370992568 197:57:183436939197489425135336700961604723229676601928984 197:58:442778818752560681361157554045252780209564211552720 197:59:1043156878078066689986455932411697227951346193319120 197:60:2399260819579553386968848644546903624288096244633976 197:61:5388503807908177278930037119720095025040478451063192 197:62:11819943836701808224749758843256982635572662408783776 197:63:25328451078646731910178054664122105647655705161679520 197:64:53031444445916594936935301953005658699779132682266495 197:65:108510494020106263486344540919226963185701917642176059 197:66:217020988040212526972689081838453926371403835284352118 197:67:424324618406982701991377160012499467979908991376867574 197:68:811208829307466930277632805906248982902767189396952715 197:69:1516607811313959913127748289302987228905173441046476815 197:70:2773225712116955269719311157582605218569460006484986176 197:71:4960558668152863651469753760746350179694667898923848512 197:72:8680977669267511390072069081306112814465668823116734896 197:73:14864687789841629092589159385798138380934364423145094000 197:74:24908395755950837938933185997823907557241367411756644000 197:75:40849769039759374219850425036431208393875842555280896160 197:76:65574629248034784931865155979534308211221747259793017520 197:77:103045845961197519178645245110696770046205602836817598960 197:78:158532070709534644890223454016456569301854773595103998400 197:79:238801473600438262556159380100738376543300228579966782400 197:80:352232173560646437270335085648589105401367837155451004040 197:81:508779806254267076057150679270184263357531320335651450280 197:82:719737286896280253934505838967577738408215038523604490640 197:83:997226361362316014487568331099655902613791920845958029200 197:84:1353378633277428876804557020778104439261574749719514468200 197:85:1799197477180581918575469921740303548665387608450648645960 197:86:2343140900514246219540146874824581365703760606354333120320 197:87:2989524597207831383551221874776190018311694566727942256960 197:88:3736905746509789229439027343470237522889618208409927821200 197:89:4576659846849067707964651465598380786460318929400922837200 197:90:5491991816218881249557581758718056943752382715281107404640 197:91:6457616750938684546183090639371781241554999456429433981280 197:92:7440297560864136542341387041015313169617716765016521761040 197:93:8400335955814347709095114401146321320536131831470266504400 197:94:9293988717071193210062679762970398056763379898647954430400 197:95:10076640398508767375120589637746852629964506626955150592960 197:96:10706430423415565336065626490106030919337288291139847505020 197:97:11147932708917238133429157479388753843846042447475511319660 197:98:11375441539711467483090977019784442697802084130077052367000 197:99:11375441539711467483090977019784442697802084130077052367000 197:100:11147932708917238133429157479388753843846042447475511319660 197:101:10706430423415565336065626490106030919337288291139847505020 197:102:10076640398508767375120589637746852629964506626955150592960 197:103:9293988717071193210062679762970398056763379898647954430400 197:104:8400335955814347709095114401146321320536131831470266504400 197:105:7440297560864136542341387041015313169617716765016521761040 197:106:6457616750938684546183090639371781241554999456429433981280 197:107:5491991816218881249557581758718056943752382715281107404640 197:108:4576659846849067707964651465598380786460318929400922837200 197:109:3736905746509789229439027343470237522889618208409927821200 197:110:2989524597207831383551221874776190018311694566727942256960 197:111:2343140900514246219540146874824581365703760606354333120320 197:112:1799197477180581918575469921740303548665387608450648645960 197:113:1353378633277428876804557020778104439261574749719514468200 197:114:997226361362316014487568331099655902613791920845958029200 197:115:719737286896280253934505838967577738408215038523604490640 197:116:508779806254267076057150679270184263357531320335651450280 197:117:352232173560646437270335085648589105401367837155451004040 197:118:238801473600438262556159380100738376543300228579966782400 197:119:158532070709534644890223454016456569301854773595103998400 197:120:103045845961197519178645245110696770046205602836817598960 197:121:65574629248034784931865155979534308211221747259793017520 197:122:40849769039759374219850425036431208393875842555280896160 197:123:24908395755950837938933185997823907557241367411756644000 197:124:14864687789841629092589159385798138380934364423145094000 197:125:8680977669267511390072069081306112814465668823116734896 197:126:4960558668152863651469753760746350179694667898923848512 197:127:2773225712116955269719311157582605218569460006484986176 197:128:1516607811313959913127748289302987228905173441046476815 197:129:811208829307466930277632805906248982902767189396952715 197:130:424324618406982701991377160012499467979908991376867574 197:131:217020988040212526972689081838453926371403835284352118 197:132:108510494020106263486344540919226963185701917642176059 197:133:53031444445916594936935301953005658699779132682266495 197:134:25328451078646731910178054664122105647655705161679520 197:135:11819943836701808224749758843256982635572662408783776 197:136:5388503807908177278930037119720095025040478451063192 197:137:2399260819579553386968848644546903624288096244633976 197:138:1043156878078066689986455932411697227951346193319120 197:139:442778818752560681361157554045252780209564211552720 197:140:183436939197489425135336700961604723229676601928984 197:141:74155358398985086756838240814265739177954370992568 197:142:29244366692557499002696771025344235168770737856224 197:143:11247833343291345770267988855901628911065668406240 197:144:4217937503734254663850495820963110841649625652340 197:145:1541728880675279290924663989731343962809863169476 197:146:549108916404893994027962516890615657987074553512 197:147:190507175079248936703578832390621758893474845096 197:148:64360532121367884021479335267101945572119880100 197:149:21165544120449841054043539785825472033784390100 197:150:6772974118543949137293932731464151050811004832 197:151:2108144262063348406972283697872947678067001504 197:152:637991026677065965267927961198392060467645192 197:153:187644419610901754490567047411291782490483880 197:154:53612691317400501283019156403226223568709680 197:155:14873198236440139065611765969927274925513008 197:156:4004322602118498979203167761134266326099656 197:157:1045714819661518841702738077748438976879528 197:158:264737929028232618152591918417326323260640 197:159:64935718440887245961956508291042305705440 197:160:15422233129710720915964670719122547605042 197:161:3544239911796873750873868426133753176314 197:162:787608869288194166860859650251945150292 197:163:169118468865563164663374771526491289940 197:164:35061145984324070722894769706711608890 197:165:7012229196864814144578953941342321778 197:166:1351755025901650919436906783873218656 197:167:250924585646414242530204253293831008 197:168:44807961722573971880393616659612680 197:169:7688940177246421210245058480051880 197:170:1266413676252351728746244926126192 197:171:199960054145108167696775514651504 197:172:30226519812632630000675368493832 197:173:4367994192576969653276787354600 197:174:602481957596823400451970669600 197:175:79183342998439646916544716576 197:176:9897917874804955864568089572 197:177:1174329239383638831389434356 197:178:131947105548723464201060040 197:179:14005558689529306255978440 197:180:1400555868952930625597844 197:181:131543921393369174779908 197:182:11564300781834652727904 197:183:947893506707758420320 197:184:72122332032112053720 197:185:5068055764418684856 197:186:326971339639915152 197:187:19233608214112656 197:188:1023064266708120 197:189:48717346033720 197:190:2051256675104 197:191:75176946208 197:192:2349279569 197:193:60862165 197:194:1254890 197:195:19306 197:196:197 197:197:1 # binomial(198, k) for 0 <= k <= 198 198:0:1 198:1:198 198:2:19503 198:3:1274196 198:4:62117055 198:5:2410141734 198:6:77526225777 198:7:2126433621312 198:8:50768602708824 198:9:1071781612741840 198:10:20256672480820776 198:11:346204947854027808 198:12:5395027104058600008 198:13:77190387796530738576 198:14:1020015838739870474040 198:15:12512194288542411148224 198:16:143108222175203827507812 198:17:1532099790346299800377752 198:18:15406114558482236881576284 198:19:145952664238252770457038480 198:20:1306276344932362295590494396 198:21:11072247114188594695957523928 198:22:89081260873244602781112806148 198:23:681665300595263047368515386176 198:24:4970476150173793053728758024200 198:25:34594514005209599653952155848432 198:26:230186573957740797697450883145336 198:27:1466373730397459896443020440777696 198:28:8955353853498772938991303406178072 198:29:52496901899820393090638675139664560 198:30:295732547368988214410597869953443688 198:31:1602679611548065161967111037167049664 198:32:8363984222766465064015860725215540434 198:33:42073375181188884867473723648053930668 198:34:204179614849887235386269541233202898830 198:35:956727338153757331524234421778436440232 198:36:4331848781085067917734728076385698326606 198:37:18966473041507594666838539145256300781356 198:38:80357951570597966877921179010164853310482 198:39:329673647469119864114548426708368628966080 198:40:1310452748689751459855329996165765300140168 198:41:5050037421780017820905905838882705302979184 198:42:18877520838558638044814933731061541251612664 198:43:68485889553840640348630922373153498494222688 198:44:241257110928302255773586203814518006059193560 198:45:825635446287967719758495008609683842958129072 198:46:2746135288740414372240211659071339738534646696 198:47:8881118380607297544266216429337098728878006336 198:48:27938518238993790191337472517289623084595394932 198:49:85526076241817725075522875052927417605904270200 198:50:254867707200616820725058167657723704465594725196 198:51:739616091484142930731541349281237416880549398608 198:52:2090837797080173284952626506621959620796937722988 198:53:5759666384409533954775159810694454804459488821816 198:54:15465770847025600434118484676864739752715294058580 198:55:40492200035848844772964759881245864079836406262464 198:56:103399725091542585759535011839609974346725108848792 198:57:257592297596474511892174941775870462407630972921552 198:58:626215757950050106496494255006857503439240813481704 198:59:1485935696830627371347613486456950008160910404871840 198:60:3442417697657620076955304576958600852239442437953096 198:61:7787764627487730665898885764266998649328574695697168 198:62:17208447644609985503679795962977077660613140859846968 198:63:37148394915348540134927813507379088283228367570463296 198:64:78359895524563326847113356617127764347434837843946015 198:65:161541938466022858423279842872232621885481050324442554 198:66:325531482060318790459033622757680889557105752926528177 198:67:641345606447195228964066241850953394351312826661219692 198:68:1235533447714449632269009965918748450882676180773820289 198:69:2327816640621426843405381095209236211807940630443429530 198:70:4289833523430915182847059446885592447474633447531462991 198:71:7733784380269818921189064918328955398264127905408834688 198:72:13641536337420375041541822842052462994160336722040583408 198:73:23545665459109140482661228467104251195400033246261828896 198:74:39773083545792467031522345383622045938175731834901738000 198:75:65758164795710212158783611034255115951117209967037540160 198:76:106424398287794159151715581015965516605097589815073913680 198:77:168620475209232304110510401090231078257427350096610616480 198:78:261577916670732164068868699127153339348060376431921597360 198:79:397333544309972907446382834117194945845155002175070780800 198:80:591033647161084699826494465749327481944668065735417786440 198:81:861011979814913513327485764918773368758899157491102454320 198:82:1228517093150547329991656518237762001765746358859255940920 198:83:1716963648258596268422074170067233641022006959369562519840 198:84:2350604994639744891292125351877760341875366670565472497400 198:85:3152576110458010795380026942518407987926962358170163114160 198:86:4142338377694828138115616796564884914369148214804981766280 198:87:5332665497722077603091368749600771384015455173082275377280 198:88:6726430343717620612990249218246427541201312775137870078160 198:89:8313565593358856937403678809068618309349937137810850658400 198:90:10068651663067948957522233224316437730212701644682030241840 198:91:11949608567157565795740672398089838185307382171710541385920 198:92:13897914311802821088524477680387094411172716221445955742320 198:93:15840633516678484251436501442161634490153848596486788265440 198:94:17694324672885540919157794164116719377299511730118220934800 198:95:19370629115579960585183269400717250686727886525603105023360 198:96:20783070821924332711186216127852883549301794918094998097980 198:97:21854363132332803469494783969494784763183330738615358824680 198:98:22523374248628705616520134499173196541648126577552563686660 198:99:22750883079422934966181954039568885395604168260154104734000 198:100:22523374248628705616520134499173196541648126577552563686660 198:101:21854363132332803469494783969494784763183330738615358824680 198:102:20783070821924332711186216127852883549301794918094998097980 198:103:19370629115579960585183269400717250686727886525603105023360 198:104:17694324672885540919157794164116719377299511730118220934800 198:105:15840633516678484251436501442161634490153848596486788265440 198:106:13897914311802821088524477680387094411172716221445955742320 198:107:11949608567157565795740672398089838185307382171710541385920 198:108:10068651663067948957522233224316437730212701644682030241840 198:109:8313565593358856937403678809068618309349937137810850658400 198:110:6726430343717620612990249218246427541201312775137870078160 198:111:5332665497722077603091368749600771384015455173082275377280 198:112:4142338377694828138115616796564884914369148214804981766280 198:113:3152576110458010795380026942518407987926962358170163114160 198:114:2350604994639744891292125351877760341875366670565472497400 198:115:1716963648258596268422074170067233641022006959369562519840 198:116:1228517093150547329991656518237762001765746358859255940920 198:117:861011979814913513327485764918773368758899157491102454320 198:118:591033647161084699826494465749327481944668065735417786440 198:119:397333544309972907446382834117194945845155002175070780800 198:120:261577916670732164068868699127153339348060376431921597360 198:121:168620475209232304110510401090231078257427350096610616480 198:122:106424398287794159151715581015965516605097589815073913680 198:123:65758164795710212158783611034255115951117209967037540160 198:124:39773083545792467031522345383622045938175731834901738000 198:125:23545665459109140482661228467104251195400033246261828896 198:126:13641536337420375041541822842052462994160336722040583408 198:127:7733784380269818921189064918328955398264127905408834688 198:128:4289833523430915182847059446885592447474633447531462991 198:129:2327816640621426843405381095209236211807940630443429530 198:130:1235533447714449632269009965918748450882676180773820289 198:131:641345606447195228964066241850953394351312826661219692 198:132:325531482060318790459033622757680889557105752926528177 198:133:161541938466022858423279842872232621885481050324442554 198:134:78359895524563326847113356617127764347434837843946015 198:135:37148394915348540134927813507379088283228367570463296 198:136:17208447644609985503679795962977077660613140859846968 198:137:7787764627487730665898885764266998649328574695697168 198:138:3442417697657620076955304576958600852239442437953096 198:139:1485935696830627371347613486456950008160910404871840 198:140:626215757950050106496494255006857503439240813481704 198:141:257592297596474511892174941775870462407630972921552 198:142:103399725091542585759535011839609974346725108848792 198:143:40492200035848844772964759881245864079836406262464 198:144:15465770847025600434118484676864739752715294058580 198:145:5759666384409533954775159810694454804459488821816 198:146:2090837797080173284952626506621959620796937722988 198:147:739616091484142930731541349281237416880549398608 198:148:254867707200616820725058167657723704465594725196 198:149:85526076241817725075522875052927417605904270200 198:150:27938518238993790191337472517289623084595394932 198:151:8881118380607297544266216429337098728878006336 198:152:2746135288740414372240211659071339738534646696 198:153:825635446287967719758495008609683842958129072 198:154:241257110928302255773586203814518006059193560 198:155:68485889553840640348630922373153498494222688 198:156:18877520838558638044814933731061541251612664 198:157:5050037421780017820905905838882705302979184 198:158:1310452748689751459855329996165765300140168 198:159:329673647469119864114548426708368628966080 198:160:80357951570597966877921179010164853310482 198:161:18966473041507594666838539145256300781356 198:162:4331848781085067917734728076385698326606 198:163:956727338153757331524234421778436440232 198:164:204179614849887235386269541233202898830 198:165:42073375181188884867473723648053930668 198:166:8363984222766465064015860725215540434 198:167:1602679611548065161967111037167049664 198:168:295732547368988214410597869953443688 198:169:52496901899820393090638675139664560 198:170:8955353853498772938991303406178072 198:171:1466373730397459896443020440777696 198:172:230186573957740797697450883145336 198:173:34594514005209599653952155848432 198:174:4970476150173793053728758024200 198:175:681665300595263047368515386176 198:176:89081260873244602781112806148 198:177:11072247114188594695957523928 198:178:1306276344932362295590494396 198:179:145952664238252770457038480 198:180:15406114558482236881576284 198:181:1532099790346299800377752 198:182:143108222175203827507812 198:183:12512194288542411148224 198:184:1020015838739870474040 198:185:77190387796530738576 198:186:5395027104058600008 198:187:346204947854027808 198:188:20256672480820776 198:189:1071781612741840 198:190:50768602708824 198:191:2126433621312 198:192:77526225777 198:193:2410141734 198:194:62117055 198:195:1274196 198:196:19503 198:197:198 198:198:1 # binomial(199, k) for 0 <= k <= 199 199:0:1 199:1:199 199:2:19701 199:3:1293699 199:4:63391251 199:5:2472258789 199:6:79936367511 199:7:2203959847089 199:8:52895036330136 199:9:1122550215450664 199:10:21328454093562616 199:11:366461620334848584 199:12:5741232051912627816 199:13:82585414900589338584 199:14:1097206226536401212616 199:15:13532210127282281622264 199:16:155620416463746238656036 199:17:1675208012521503627885564 199:18:16938214348828536681954036 199:19:161358778796735007338614764 199:20:1452229009170615066047532876 199:21:12378523459120956991548018324 199:22:100153507987433197477070330076 199:23:770746561468507650149628192324 199:24:5652141450769056101097273410376 199:25:39564990155383392707680913872632 199:26:264781087962950397351403038993768 199:27:1696560304355200694140471323923032 199:28:10421727583896232835434323846955768 199:29:61452255753319166029629978545842632 199:30:348229449268808607501236545093108248 199:31:1898412158917053376377708907120493352 199:32:9966663834314530225982971762382590098 199:33:50437359403955349931489584373269471102 199:34:246252990031076120253743264881256829498 199:35:1160906953003644566910503963011639339062 199:36:5288576119238825249258962498164134766838 199:37:23298321822592662584573267221641999107962 199:38:99324424612105561544759718155421154091838 199:39:410031599039717830992469605718533482276562 199:40:1640126396158871323969878422874133929106248 199:41:6360490170469769280761235835048470603119352 199:42:23927558260338655865720839569944246554591848 199:43:87363410392399278393445856104215039745835352 199:44:309743000482142896122217126187671504553416248 199:45:1066892557216269975532081212424201849017322632 199:46:3571770735028382091998706667681023581492775768 199:47:11627253669347711916506428088408438467412653032 199:48:36819636619601087735603688946626721813473401268 199:49:113464594480811515266860347570217040690499665132 199:50:340393783442434545800581042710651122071498995396 199:51:994483798684759751456599516938961121346144123804 199:52:2830453888564316215684167855903197037677487121596 199:53:7850504181489707239727786317316414425256426544804 199:54:21225437231435134388893644487559194557174782880396 199:55:55957970882874445207083244558110603832551700321044 199:56:143891925127391430532499771720855838426561515111256 199:57:360992022688017097651709953615480436754356081770344 199:58:883808055546524618388669196782727965846871786403256 199:59:2112151454780677477844107741463807511600151218353544 199:60:4928353394488247448302918063415550860400352842824936 199:61:11230182325145350742854190341225599501568017133650264 199:62:24996212272097716169578681727244076309941715555544136 199:63:54356842559958525638607609470356165943841508430310264 199:64:115508290439911866982041170124506852630663205414409311 199:65:239901833990586185270393199489360386232915888168388569 199:66:487073420526341648882313465629913511442586803250970731 199:67:966877088507514019423099864608634283908418579587747869 199:68:1876879054161644861233076207769701845233989007435039981 199:69:3563350088335876475674391061127984662690616811217249819 199:70:6617650164052342026252440542094828659282574077974892521 199:71:12023617903700734104036124365214547845738761352940297679 199:72:21375320717690193962730887760381418392424464627449418096 199:73:37187201796529515524203051309156714189560369968302412304 199:74:63318749004901607514183573850726297133575765081163566896 199:75:105531248341502679190305956417877161889292941801939278160 199:76:172182563083504371310499192050220632556214799782111453840 199:77:275044873497026463262225982106196594862524939911684530160 199:78:430198391879964468179379100217384417605487726528532213840 199:79:658911460980705071515251533244348285193215378606992378160 199:80:988367191471057607272877299866522427789823067910488567240 199:81:1452045626975998213153980230668100850703567223226520240760 199:82:2089529072965460843319142283156535370524645516350358395240 199:83:2945480741409143598413730688304995642787753318228818460760 199:84:4067568642898341159714199521944993982897373629935035017240 199:85:5503181105097755686672152294396168329802329028735635611560 199:86:7294914488152838933495643739083292902296110572975144880440 199:87:9475003875416905741206985546165656298384603387887257143560 199:88:12059095841439698216081617967847198925216767948220145455440 199:89:15039995937076477550393928027315045850551249912948720736560 199:90:18382217256426805894925912033385056039562638782492880900240 199:91:22018260230225514753262905622406275915520083816392571627760 199:92:25847522878960386884265150078476932596480098393156497128240 199:93:29738547828481305339960979122548728901326564817932744007760 199:94:33534958189564025170594295606278353867453360326605009200240 199:95:37064953788465501504341063564833970064027398255721325958160 199:96:40153699937504293296369485528570134236029681443698103121340 199:97:42637433954257136180681000097347668312485125656710356922660 199:98:44377737380961509086014918468667981304831457316167922511340 199:99:45274257328051640582702088538742081937252294837706668420660 199:100:45274257328051640582702088538742081937252294837706668420660 199:101:44377737380961509086014918468667981304831457316167922511340 199:102:42637433954257136180681000097347668312485125656710356922660 199:103:40153699937504293296369485528570134236029681443698103121340 199:104:37064953788465501504341063564833970064027398255721325958160 199:105:33534958189564025170594295606278353867453360326605009200240 199:106:29738547828481305339960979122548728901326564817932744007760 199:107:25847522878960386884265150078476932596480098393156497128240 199:108:22018260230225514753262905622406275915520083816392571627760 199:109:18382217256426805894925912033385056039562638782492880900240 199:110:15039995937076477550393928027315045850551249912948720736560 199:111:12059095841439698216081617967847198925216767948220145455440 199:112:9475003875416905741206985546165656298384603387887257143560 199:113:7294914488152838933495643739083292902296110572975144880440 199:114:5503181105097755686672152294396168329802329028735635611560 199:115:4067568642898341159714199521944993982897373629935035017240 199:116:2945480741409143598413730688304995642787753318228818460760 199:117:2089529072965460843319142283156535370524645516350358395240 199:118:1452045626975998213153980230668100850703567223226520240760 199:119:988367191471057607272877299866522427789823067910488567240 199:120:658911460980705071515251533244348285193215378606992378160 199:121:430198391879964468179379100217384417605487726528532213840 199:122:275044873497026463262225982106196594862524939911684530160 199:123:172182563083504371310499192050220632556214799782111453840 199:124:105531248341502679190305956417877161889292941801939278160 199:125:63318749004901607514183573850726297133575765081163566896 199:126:37187201796529515524203051309156714189560369968302412304 199:127:21375320717690193962730887760381418392424464627449418096 199:128:12023617903700734104036124365214547845738761352940297679 199:129:6617650164052342026252440542094828659282574077974892521 199:130:3563350088335876475674391061127984662690616811217249819 199:131:1876879054161644861233076207769701845233989007435039981 199:132:966877088507514019423099864608634283908418579587747869 199:133:487073420526341648882313465629913511442586803250970731 199:134:239901833990586185270393199489360386232915888168388569 199:135:115508290439911866982041170124506852630663205414409311 199:136:54356842559958525638607609470356165943841508430310264 199:137:24996212272097716169578681727244076309941715555544136 199:138:11230182325145350742854190341225599501568017133650264 199:139:4928353394488247448302918063415550860400352842824936 199:140:2112151454780677477844107741463807511600151218353544 199:141:883808055546524618388669196782727965846871786403256 199:142:360992022688017097651709953615480436754356081770344 199:143:143891925127391430532499771720855838426561515111256 199:144:55957970882874445207083244558110603832551700321044 199:145:21225437231435134388893644487559194557174782880396 199:146:7850504181489707239727786317316414425256426544804 199:147:2830453888564316215684167855903197037677487121596 199:148:994483798684759751456599516938961121346144123804 199:149:340393783442434545800581042710651122071498995396 199:150:113464594480811515266860347570217040690499665132 199:151:36819636619601087735603688946626721813473401268 199:152:11627253669347711916506428088408438467412653032 199:153:3571770735028382091998706667681023581492775768 199:154:1066892557216269975532081212424201849017322632 199:155:309743000482142896122217126187671504553416248 199:156:87363410392399278393445856104215039745835352 199:157:23927558260338655865720839569944246554591848 199:158:6360490170469769280761235835048470603119352 199:159:1640126396158871323969878422874133929106248 199:160:410031599039717830992469605718533482276562 199:161:99324424612105561544759718155421154091838 199:162:23298321822592662584573267221641999107962 199:163:5288576119238825249258962498164134766838 199:164:1160906953003644566910503963011639339062 199:165:246252990031076120253743264881256829498 199:166:50437359403955349931489584373269471102 199:167:9966663834314530225982971762382590098 199:168:1898412158917053376377708907120493352 199:169:348229449268808607501236545093108248 199:170:61452255753319166029629978545842632 199:171:10421727583896232835434323846955768 199:172:1696560304355200694140471323923032 199:173:264781087962950397351403038993768 199:174:39564990155383392707680913872632 199:175:5652141450769056101097273410376 199:176:770746561468507650149628192324 199:177:100153507987433197477070330076 199:178:12378523459120956991548018324 199:179:1452229009170615066047532876 199:180:161358778796735007338614764 199:181:16938214348828536681954036 199:182:1675208012521503627885564 199:183:155620416463746238656036 199:184:13532210127282281622264 199:185:1097206226536401212616 199:186:82585414900589338584 199:187:5741232051912627816 199:188:366461620334848584 199:189:21328454093562616 199:190:1122550215450664 199:191:52895036330136 199:192:2203959847089 199:193:79936367511 199:194:2472258789 199:195:63391251 199:196:1293699 199:197:19701 199:198:199 199:199:1 # binomial(200, k) for 0 <= k <= 200 200:0:1 200:1:200 200:2:19900 200:3:1313400 200:4:64684950 200:5:2535650040 200:6:82408626300 200:7:2283896214600 200:8:55098996177225 200:9:1175445251780800 200:10:22451004309013280 200:11:387790074428411200 200:12:6107693672247476400 200:13:88326646952501966400 200:14:1179791641436990551200 200:15:14629416353818682834880 200:16:169152626591028520278300 200:17:1830828428985249866541600 200:18:18613422361350040309839600 200:19:178296993145563544020568800 200:20:1613587787967350073386147640 200:21:13830752468291572057595551200 200:22:112532031446554154468618348400 200:23:870900069455940847626698522400 200:24:6422888012237563751246901602700 200:25:45217131606152448808778187283008 200:26:304346078118333790059083952866400 200:27:1961341392318151091491874362916800 200:28:12118287888251433529574795170878800 200:29:71873983337215398865064302392798400 200:30:409681705022127773530866523638950880 200:31:2246641608185861983878945452213601600 200:32:11865075993231583602360680669503083450 200:33:60404023238269880157472556135652061200 200:34:296690349435031470185232849254526300600 200:35:1407159943034720687164247227892896168560 200:36:6449483072242469816169466461175774105900 200:37:28586897941831487833832229719806133874800 200:38:122622746434698224129332985377063153199800 200:39:509356023651823392537229323873954636368400 200:40:2050157995198589154962348028592667411382810 200:41:8000616566628640604731114257922604532225600 200:42:30288048430808425146482075404992717157711200 200:43:111290968652737934259166695674159286300427200 200:44:397106410874542174515662982291886544299251600 200:45:1376635557698412871654298338611873353570738880 200:46:4638663292244652067530787880105225430510098400 200:47:15199024404376094008505134756089462048905428800 200:48:48446890288948799652110117035035160280886054300 200:49:150284231100412603002464036516843762503973066400 200:50:453858377923246061067441390280868162761998660528 200:51:1334877582127194297257180559649612243417643119200 200:52:3824937687249075967140767372842158159023631245400 200:53:10680958070054023455411954173219611462933913666400 200:54:29075941412924841628621430804875608982431209425200 200:55:77183408114309579595976889045669798389726483201440 200:56:199849896010265875739583016278966442259113215432300 200:57:504883947815408528184209725336336275180917596881600 200:58:1244800078234541716040379150398208402601227868173600 200:59:2995959510327202096232776938246535477447023004756800 200:60:7040504849268924926147025804879358372000504061178480 200:61:16158535719633598191157108404641150361968369976475200 200:62:36226394597243066912432872068469675811509732689194400 200:63:79353054832056241808186291197600242253783223985854400 200:64:169865132999870392620648779594863018574504713844719575 200:65:355410124430498052252434369613867238863579093582797880 200:66:726975254516927834152706665119273897675502691419359300 200:67:1453950509033855668305413330238547795351005382838718600 200:68:2843756142669158880656176072378336129142407587022787850 200:69:5440229142497521336907467268897686507924605818652289800 200:70:10181000252388218501926831603222813321973190889192142340 200:71:18641268067753076130288564907309376505021335430915190200 200:72:33398938621390928066767012125595966238163225980389715775 200:73:58562522514219709486933939069538132581984834595751830400 200:74:100505950801431123038386625159883011323136135049465979200 200:75:168849997346404286704489530268603459022868706883102845056 200:76:277713811425007050500805148468097794445507741584050732000 200:77:447227436580530834572725174156417227418739739693795984000 200:78:705243265376990931441605082323581012468012666440216744000 200:79:1089109852860669539694630633461732702798703105135524592000 200:80:1647278652451762678788128833110870712983038446517480945400 200:81:2440412818447055820426857530534623278493390291137008808000 200:82:3541574699941459056473122513824636221228212739576878636000 200:83:5035009814374604441732872971461531013312398834579176856000 200:84:7013049384307484758127930210249989625685126948163853478000 200:85:9570749747996096846386351816341162312699702658670670628800 200:86:12798095593250594620167796033479461232098439601710780492000 200:87:16769918363569744674702629285248949200680713960862402024000 200:88:21534099716856603957288603514012855223601371336107402599000 200:89:27099091778516175766475545995162244775768017861168866192000 200:90:33422213193503283445319840060700101890113888695441601636800 200:91:40400477486652320648188817655791331955082722598885452528000 200:92:47865783109185901637528055700883208512000182209549068756000 200:93:55586070707441692224226129201025661497806663211089241136000 200:94:63273506018045330510555274728827082768779925144537753208000 200:95:70599911978029526674935359171112323931480758582326335158400 200:96:77218653725969794800710549093404104300057079699419429079500 200:97:82791133891761429477050485625917802548514807100408460044000 200:98:87015171335218645266695918566015649617316582972878279434000 200:99:89651994709013149668717007007410063242083752153874590932000 200:100:90548514656103281165404177077484163874504589675413336841320 200:101:89651994709013149668717007007410063242083752153874590932000 200:102:87015171335218645266695918566015649617316582972878279434000 200:103:82791133891761429477050485625917802548514807100408460044000 200:104:77218653725969794800710549093404104300057079699419429079500 200:105:70599911978029526674935359171112323931480758582326335158400 200:106:63273506018045330510555274728827082768779925144537753208000 200:107:55586070707441692224226129201025661497806663211089241136000 200:108:47865783109185901637528055700883208512000182209549068756000 200:109:40400477486652320648188817655791331955082722598885452528000 200:110:33422213193503283445319840060700101890113888695441601636800 200:111:27099091778516175766475545995162244775768017861168866192000 200:112:21534099716856603957288603514012855223601371336107402599000 200:113:16769918363569744674702629285248949200680713960862402024000 200:114:12798095593250594620167796033479461232098439601710780492000 200:115:9570749747996096846386351816341162312699702658670670628800 200:116:7013049384307484758127930210249989625685126948163853478000 200:117:5035009814374604441732872971461531013312398834579176856000 200:118:3541574699941459056473122513824636221228212739576878636000 200:119:2440412818447055820426857530534623278493390291137008808000 200:120:1647278652451762678788128833110870712983038446517480945400 200:121:1089109852860669539694630633461732702798703105135524592000 200:122:705243265376990931441605082323581012468012666440216744000 200:123:447227436580530834572725174156417227418739739693795984000 200:124:277713811425007050500805148468097794445507741584050732000 200:125:168849997346404286704489530268603459022868706883102845056 200:126:100505950801431123038386625159883011323136135049465979200 200:127:58562522514219709486933939069538132581984834595751830400 200:128:33398938621390928066767012125595966238163225980389715775 200:129:18641268067753076130288564907309376505021335430915190200 200:130:10181000252388218501926831603222813321973190889192142340 200:131:5440229142497521336907467268897686507924605818652289800 200:132:2843756142669158880656176072378336129142407587022787850 200:133:1453950509033855668305413330238547795351005382838718600 200:134:726975254516927834152706665119273897675502691419359300 200:135:355410124430498052252434369613867238863579093582797880 200:136:169865132999870392620648779594863018574504713844719575 200:137:79353054832056241808186291197600242253783223985854400 200:138:36226394597243066912432872068469675811509732689194400 200:139:16158535719633598191157108404641150361968369976475200 200:140:7040504849268924926147025804879358372000504061178480 200:141:2995959510327202096232776938246535477447023004756800 200:142:1244800078234541716040379150398208402601227868173600 200:143:504883947815408528184209725336336275180917596881600 200:144:199849896010265875739583016278966442259113215432300 200:145:77183408114309579595976889045669798389726483201440 200:146:29075941412924841628621430804875608982431209425200 200:147:10680958070054023455411954173219611462933913666400 200:148:3824937687249075967140767372842158159023631245400 200:149:1334877582127194297257180559649612243417643119200 200:150:453858377923246061067441390280868162761998660528 200:151:150284231100412603002464036516843762503973066400 200:152:48446890288948799652110117035035160280886054300 200:153:15199024404376094008505134756089462048905428800 200:154:4638663292244652067530787880105225430510098400 200:155:1376635557698412871654298338611873353570738880 200:156:397106410874542174515662982291886544299251600 200:157:111290968652737934259166695674159286300427200 200:158:30288048430808425146482075404992717157711200 200:159:8000616566628640604731114257922604532225600 200:160:2050157995198589154962348028592667411382810 200:161:509356023651823392537229323873954636368400 200:162:122622746434698224129332985377063153199800 200:163:28586897941831487833832229719806133874800 200:164:6449483072242469816169466461175774105900 200:165:1407159943034720687164247227892896168560 200:166:296690349435031470185232849254526300600 200:167:60404023238269880157472556135652061200 200:168:11865075993231583602360680669503083450 200:169:2246641608185861983878945452213601600 200:170:409681705022127773530866523638950880 200:171:71873983337215398865064302392798400 200:172:12118287888251433529574795170878800 200:173:1961341392318151091491874362916800 200:174:304346078118333790059083952866400 200:175:45217131606152448808778187283008 200:176:6422888012237563751246901602700 200:177:870900069455940847626698522400 200:178:112532031446554154468618348400 200:179:13830752468291572057595551200 200:180:1613587787967350073386147640 200:181:178296993145563544020568800 200:182:18613422361350040309839600 200:183:1830828428985249866541600 200:184:169152626591028520278300 200:185:14629416353818682834880 200:186:1179791641436990551200 200:187:88326646952501966400 200:188:6107693672247476400 200:189:387790074428411200 200:190:22451004309013280 200:191:1175445251780800 200:192:55098996177225 200:193:2283896214600 200:194:82408626300 200:195:2535650040 200:196:64684950 200:197:1313400 200:198:19900 200:199:200 200:200:1 # binomial(2^31-2, k) for 0 <= k <= 5 2147483648:0:1 2147483648:1:2147483648 2147483648:2:2305843008139952128 2147483648:3:1650586716741330691367632896 2147483648:4:886151994714063838812133581630996480 2147483648:5:380599382949285310124181851059140756844314624 # binomial(2^31-2, 2^31-2-k) for 0 <= k <= 5 2147483648:2147483648:1 2147483648:2147483647:2147483648 2147483648:2147483646:2305843008139952128 2147483648:2147483645:1650586716741330691367632896 2147483648:2147483644:886151994714063838812133581630996480 2147483648:2147483643:380599382949285310124181851059140756844314624 # binomial(2^31-1, k) for 0 <= k <= 5 2147483648:0:1 2147483648:1:2147483648 2147483648:2:2305843008139952128 2147483648:3:1650586716741330691367632896 2147483648:4:886151994714063838812133581630996480 2147483648:5:380599382949285310124181851059140756844314624 # binomial(2^31-1, 2^31-1-k) for 0 <= k <= 5 2147483648:2147483648:1 2147483648:2147483647:2147483648 2147483648:2147483646:2305843008139952128 2147483648:2147483645:1650586716741330691367632896 2147483648:2147483644:886151994714063838812133581630996480 2147483648:2147483643:380599382949285310124181851059140756844314624 # binomial(2^31, k) for 0 <= k <= 5 2147483648:0:1 2147483648:1:2147483648 2147483648:2:2305843008139952128 2147483648:3:1650586716741330691367632896 2147483648:4:886151994714063838812133581630996480 2147483648:5:380599382949285310124181851059140756844314624 # binomial(2^31, 2^31-k) for 0 <= k <= 5 2147483648:2147483648:1 2147483648:2147483647:2147483648 2147483648:2147483646:2305843008139952128 2147483648:2147483645:1650586716741330691367632896 2147483648:2147483644:886151994714063838812133581630996480 2147483648:2147483643:380599382949285310124181851059140756844314624 # binomial(2^31+1, k) for 0 <= k <= 5 2147483648:0:1 2147483648:1:2147483648 2147483648:2:2305843008139952128 2147483648:3:1650586716741330691367632896 2147483648:4:886151994714063838812133581630996480 2147483648:5:380599382949285310124181851059140756844314624 # binomial(2^31+1, 2^31+1-k) for 0 <= k <= 5 2147483648:2147483648:1 2147483648:2147483647:2147483648 2147483648:2147483646:2305843008139952128 2147483648:2147483645:1650586716741330691367632896 2147483648:2147483644:886151994714063838812133581630996480 2147483648:2147483643:380599382949285310124181851059140756844314624 # binomial(2^31+2, k) for 0 <= k <= 5 2147483648:0:1 2147483648:1:2147483648 2147483648:2:2305843008139952128 2147483648:3:1650586716741330691367632896 2147483648:4:886151994714063838812133581630996480 2147483648:5:380599382949285310124181851059140756844314624 # binomial(2^31+2, 2^31+2-k) for 0 <= k <= 5 2147483648:2147483648:1 2147483648:2147483647:2147483648 2147483648:2147483646:2305843008139952128 2147483648:2147483645:1650586716741330691367632896 2147483648:2147483644:886151994714063838812133581630996480 2147483648:2147483643:380599382949285310124181851059140756844314624 # binomial(2^32-2, k) for 0 <= k <= 5 4294967296:0:1 4294967296:1:4294967296 4294967296:2:9223372034707292160 4294967296:3:13204693743154017563500871680 4294967296:4:14178431935232062024195948610647490560 4294967296:5:12179180282733993764727382376328762979415752704 # binomial(2^32-2, 2^32-2-k) for 0 <= k <= 5 4294967296:4294967296:1 4294967296:4294967295:4294967296 4294967296:4294967294:9223372034707292160 4294967296:4294967293:13204693743154017563500871680 4294967296:4294967292:14178431935232062024195948610647490560 4294967296:4294967291:12179180282733993764727382376328762979415752704 # binomial(2^32-1, k) for 0 <= k <= 5 4294967296:0:1 4294967296:1:4294967296 4294967296:2:9223372034707292160 4294967296:3:13204693743154017563500871680 4294967296:4:14178431935232062024195948610647490560 4294967296:5:12179180282733993764727382376328762979415752704 # binomial(2^32-1, 2^32-1-k) for 0 <= k <= 5 4294967296:4294967296:1 4294967296:4294967295:4294967296 4294967296:4294967294:9223372034707292160 4294967296:4294967293:13204693743154017563500871680 4294967296:4294967292:14178431935232062024195948610647490560 4294967296:4294967291:12179180282733993764727382376328762979415752704 # binomial(2^32, k) for 0 <= k <= 5 4294967296:0:1 4294967296:1:4294967296 4294967296:2:9223372034707292160 4294967296:3:13204693743154017563500871680 4294967296:4:14178431935232062024195948610647490560 4294967296:5:12179180282733993764727382376328762979415752704 # binomial(2^32, 2^32-k) for 0 <= k <= 5 4294967296:4294967296:1 4294967296:4294967295:4294967296 4294967296:4294967294:9223372034707292160 4294967296:4294967293:13204693743154017563500871680 4294967296:4294967292:14178431935232062024195948610647490560 4294967296:4294967291:12179180282733993764727382376328762979415752704 # binomial(2^32+1, k) for 0 <= k <= 5 4294967296:0:1 4294967296:1:4294967296 4294967296:2:9223372034707292160 4294967296:3:13204693743154017563500871680 4294967296:4:14178431935232062024195948610647490560 4294967296:5:12179180282733993764727382376328762979415752704 # binomial(2^32+1, 2^32+1-k) for 0 <= k <= 5 4294967296:4294967296:1 4294967296:4294967295:4294967296 4294967296:4294967294:9223372034707292160 4294967296:4294967293:13204693743154017563500871680 4294967296:4294967292:14178431935232062024195948610647490560 4294967296:4294967291:12179180282733993764727382376328762979415752704 # binomial(2^32+2, k) for 0 <= k <= 5 4294967296:0:1 4294967296:1:4294967296 4294967296:2:9223372034707292160 4294967296:3:13204693743154017563500871680 4294967296:4:14178431935232062024195948610647490560 4294967296:5:12179180282733993764727382376328762979415752704 # binomial(2^32+2, 2^32+2-k) for 0 <= k <= 5 4294967296:4294967296:1 4294967296:4294967295:4294967296 4294967296:4294967294:9223372034707292160 4294967296:4294967293:13204693743154017563500871680 4294967296:4294967292:14178431935232062024195948610647490560 4294967296:4294967291:12179180282733993764727382376328762979415752704 # binomial(2^33-2, k) for 0 <= k <= 5 8589934592:0:1 8589934592:1:8589934592 8589934592:2:36893488143124135936 8589934592:3:105637549982125628646836142080 8589934592:4:226854911122169317314206760567077601280 8589934592:5:389733769501197622477930383275714876263029014528 # binomial(2^33-2, 2^33-2-k) for 0 <= k <= 5 8589934592:8589934592:1 8589934592:8589934591:8589934592 8589934592:8589934590:36893488143124135936 8589934592:8589934589:105637549982125628646836142080 8589934592:8589934588:226854911122169317314206760567077601280 8589934592:8589934587:389733769501197622477930383275714876263029014528 # binomial(2^33-1, k) for 0 <= k <= 5 8589934592:0:1 8589934592:1:8589934592 8589934592:2:36893488143124135936 8589934592:3:105637549982125628646836142080 8589934592:4:226854911122169317314206760567077601280 8589934592:5:389733769501197622477930383275714876263029014528 # binomial(2^33-1, 2^33-1-k) for 0 <= k <= 5 8589934592:8589934592:1 8589934592:8589934591:8589934592 8589934592:8589934590:36893488143124135936 8589934592:8589934589:105637549982125628646836142080 8589934592:8589934588:226854911122169317314206760567077601280 8589934592:8589934587:389733769501197622477930383275714876263029014528 # binomial(2^33, k) for 0 <= k <= 5 8589934592:0:1 8589934592:1:8589934592 8589934592:2:36893488143124135936 8589934592:3:105637549982125628646836142080 8589934592:4:226854911122169317314206760567077601280 8589934592:5:389733769501197622477930383275714876263029014528 # binomial(2^33, 2^33-k) for 0 <= k <= 5 8589934592:8589934592:1 8589934592:8589934591:8589934592 8589934592:8589934590:36893488143124135936 8589934592:8589934589:105637549982125628646836142080 8589934592:8589934588:226854911122169317314206760567077601280 8589934592:8589934587:389733769501197622477930383275714876263029014528 # binomial(2^33+1, k) for 0 <= k <= 5 8589934592:0:1 8589934592:1:8589934592 8589934592:2:36893488143124135936 8589934592:3:105637549982125628646836142080 8589934592:4:226854911122169317314206760567077601280 8589934592:5:389733769501197622477930383275714876263029014528 # binomial(2^33+1, 2^33+1-k) for 0 <= k <= 5 8589934592:8589934592:1 8589934592:8589934591:8589934592 8589934592:8589934590:36893488143124135936 8589934592:8589934589:105637549982125628646836142080 8589934592:8589934588:226854911122169317314206760567077601280 8589934592:8589934587:389733769501197622477930383275714876263029014528 # binomial(2^33+2, k) for 0 <= k <= 5 8589934592:0:1 8589934592:1:8589934592 8589934592:2:36893488143124135936 8589934592:3:105637549982125628646836142080 8589934592:4:226854911122169317314206760567077601280 8589934592:5:389733769501197622477930383275714876263029014528 # binomial(2^33+2, 2^33+2-k) for 0 <= k <= 5 8589934592:8589934592:1 8589934592:8589934591:8589934592 8589934592:8589934590:36893488143124135936 8589934592:8589934589:105637549982125628646836142080 8589934592:8589934588:226854911122169317314206760567077601280 8589934592:8589934587:389733769501197622477930383275714876263029014528 # binomial(2^63-2, k) for 0 <= k <= 5 9223372036854775808:0:1 9223372036854775808:1:9223372036854775808 9223372036854775808:2:42535295865117307928310139910543638528 9223372036854775808:3:130772952820555849204043650451709075738951703176314617856 9223372036854775808:4:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:5:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63-2, 2^63-2-k) for 0 <= k <= 5 9223372036854775808:9223372036854775808:1 9223372036854775808:9223372036854775807:9223372036854775808 9223372036854775808:9223372036854775806:42535295865117307928310139910543638528 9223372036854775808:9223372036854775805:130772952820555849204043650451709075738951703176314617856 9223372036854775808:9223372036854775804:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:9223372036854775803:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63-1, k) for 0 <= k <= 5 9223372036854775808:0:1 9223372036854775808:1:9223372036854775808 9223372036854775808:2:42535295865117307928310139910543638528 9223372036854775808:3:130772952820555849204043650451709075738951703176314617856 9223372036854775808:4:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:5:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63-1, 2^63-1-k) for 0 <= k <= 5 9223372036854775808:9223372036854775808:1 9223372036854775808:9223372036854775807:9223372036854775808 9223372036854775808:9223372036854775806:42535295865117307928310139910543638528 9223372036854775808:9223372036854775805:130772952820555849204043650451709075738951703176314617856 9223372036854775808:9223372036854775804:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:9223372036854775803:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63, k) for 0 <= k <= 5 9223372036854775808:0:1 9223372036854775808:1:9223372036854775808 9223372036854775808:2:42535295865117307928310139910543638528 9223372036854775808:3:130772952820555849204043650451709075738951703176314617856 9223372036854775808:4:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:5:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63, 2^63-k) for 0 <= k <= 5 9223372036854775808:9223372036854775808:1 9223372036854775808:9223372036854775807:9223372036854775808 9223372036854775808:9223372036854775806:42535295865117307928310139910543638528 9223372036854775808:9223372036854775805:130772952820555849204043650451709075738951703176314617856 9223372036854775808:9223372036854775804:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:9223372036854775803:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63+1, k) for 0 <= k <= 5 9223372036854775808:0:1 9223372036854775808:1:9223372036854775808 9223372036854775808:2:42535295865117307928310139910543638528 9223372036854775808:3:130772952820555849204043650451709075738951703176314617856 9223372036854775808:4:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:5:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63+1, 2^63+1-k) for 0 <= k <= 5 9223372036854775808:9223372036854775808:1 9223372036854775808:9223372036854775807:9223372036854775808 9223372036854775808:9223372036854775806:42535295865117307928310139910543638528 9223372036854775808:9223372036854775805:130772952820555849204043650451709075738951703176314617856 9223372036854775808:9223372036854775804:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:9223372036854775803:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63+2, k) for 0 <= k <= 5 9223372036854775808:0:1 9223372036854775808:1:9223372036854775808 9223372036854775808:2:42535295865117307928310139910543638528 9223372036854775808:3:130772952820555849204043650451709075738951703176314617856 9223372036854775808:4:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:5:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^63+2, 2^63+2-k) for 0 <= k <= 5 9223372036854775808:9223372036854775808:1 9223372036854775808:9223372036854775807:9223372036854775808 9223372036854775808:9223372036854775806:42535295865117307928310139910543638528 9223372036854775808:9223372036854775805:130772952820555849204043650451709075738951703176314617856 9223372036854775808:9223372036854775804:301541899055510925386056677562624319537012853467890258952428014806782443520 9223372036854775808:9223372036854775803:556246623937737000020619771203965678908874756546101541583994658070340197361341754906578518016 # binomial(2^64-2, k) for 0 <= k <= 5 18446744073709551616:0:1 18446744073709551616:1:18446744073709551616 18446744073709551616:2:170141183460469231722463931679029329920 18446744073709551616:3:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:4:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:5:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64-2, 2^64-2-k) for 0 <= k <= 5 18446744073709551616:18446744073709551616:1 18446744073709551616:18446744073709551615:18446744073709551616 18446744073709551616:18446744073709551614:170141183460469231722463931679029329920 18446744073709551616:18446744073709551613:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:18446744073709551612:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:18446744073709551611:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64-1, k) for 0 <= k <= 5 18446744073709551616:0:1 18446744073709551616:1:18446744073709551616 18446744073709551616:2:170141183460469231722463931679029329920 18446744073709551616:3:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:4:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:5:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64-1, 2^64-1-k) for 0 <= k <= 5 18446744073709551616:18446744073709551616:1 18446744073709551616:18446744073709551615:18446744073709551616 18446744073709551616:18446744073709551614:170141183460469231722463931679029329920 18446744073709551616:18446744073709551613:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:18446744073709551612:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:18446744073709551611:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64, k) for 0 <= k <= 5 18446744073709551616:0:1 18446744073709551616:1:18446744073709551616 18446744073709551616:2:170141183460469231722463931679029329920 18446744073709551616:3:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:4:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:5:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64, 2^64-k) for 0 <= k <= 5 18446744073709551616:18446744073709551616:1 18446744073709551616:18446744073709551615:18446744073709551616 18446744073709551616:18446744073709551614:170141183460469231722463931679029329920 18446744073709551616:18446744073709551613:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:18446744073709551612:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:18446744073709551611:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64+1, k) for 0 <= k <= 5 18446744073709551616:0:1 18446744073709551616:1:18446744073709551616 18446744073709551616:2:170141183460469231722463931679029329920 18446744073709551616:3:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:4:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:5:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64+1, 2^64+1-k) for 0 <= k <= 5 18446744073709551616:18446744073709551616:1 18446744073709551616:18446744073709551615:18446744073709551616 18446744073709551616:18446744073709551614:170141183460469231722463931679029329920 18446744073709551616:18446744073709551613:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:18446744073709551612:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:18446744073709551611:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64+2, k) for 0 <= k <= 5 18446744073709551616:0:1 18446744073709551616:1:18446744073709551616 18446744073709551616:2:170141183460469231722463931679029329920 18446744073709551616:3:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:4:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:5:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^64+2, 2^64+2-k) for 0 <= k <= 5 18446744073709551616:18446744073709551616:1 18446744073709551616:18446744073709551615:18446744073709551616 18446744073709551616:18446744073709551614:170141183460469231722463931679029329920 18446744073709551616:18446744073709551613:1046183622564446793802490387074141837624854185052691496960 18446744073709551616:18446744073709551612:4824670384888174807746182274848659303083264756771870360034578814934838149120 18446744073709551616:18446744073709551611:17799891966007584010309173448303251338222443608402562651096502271933629056474342849885438476288 # binomial(2^65-2, k) for 0 <= k <= 5 36893488147419103232:0:1 36893488147419103232:1:36893488147419103232 36893488147419103232:2:680564733841876926908302470789826871296 36893488147419103232:3:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:4:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:5:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65-2, 2^65-2-k) for 0 <= k <= 5 36893488147419103232:36893488147419103232:1 36893488147419103232:36893488147419103231:36893488147419103232 36893488147419103232:36893488147419103230:680564733841876926908302470789826871296 36893488147419103232:36893488147419103229:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:36893488147419103228:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:36893488147419103227:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65-1, k) for 0 <= k <= 5 36893488147419103232:0:1 36893488147419103232:1:36893488147419103232 36893488147419103232:2:680564733841876926908302470789826871296 36893488147419103232:3:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:4:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:5:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65-1, 2^65-1-k) for 0 <= k <= 5 36893488147419103232:36893488147419103232:1 36893488147419103232:36893488147419103231:36893488147419103232 36893488147419103232:36893488147419103230:680564733841876926908302470789826871296 36893488147419103232:36893488147419103229:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:36893488147419103228:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:36893488147419103227:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65, k) for 0 <= k <= 5 36893488147419103232:0:1 36893488147419103232:1:36893488147419103232 36893488147419103232:2:680564733841876926908302470789826871296 36893488147419103232:3:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:4:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:5:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65, 2^65-k) for 0 <= k <= 5 36893488147419103232:36893488147419103232:1 36893488147419103232:36893488147419103231:36893488147419103232 36893488147419103232:36893488147419103230:680564733841876926908302470789826871296 36893488147419103232:36893488147419103229:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:36893488147419103228:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:36893488147419103227:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65+1, k) for 0 <= k <= 5 36893488147419103232:0:1 36893488147419103232:1:36893488147419103232 36893488147419103232:2:680564733841876926908302470789826871296 36893488147419103232:3:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:4:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:5:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65+1, 2^65+1-k) for 0 <= k <= 5 36893488147419103232:36893488147419103232:1 36893488147419103232:36893488147419103231:36893488147419103232 36893488147419103232:36893488147419103230:680564733841876926908302470789826871296 36893488147419103232:36893488147419103229:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:36893488147419103228:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:36893488147419103227:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65+2, k) for 0 <= k <= 5 36893488147419103232:0:1 36893488147419103232:1:36893488147419103232 36893488147419103232:2:680564733841876926908302470789826871296 36893488147419103232:3:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:4:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:5:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 # binomial(2^65+2, 2^65+2-k) for 0 <= k <= 5 36893488147419103232:36893488147419103232:1 36893488147419103232:36893488147419103231:36893488147419103232 36893488147419103232:36893488147419103230:680564733841876926908302470789826871296 36893488147419103232:36893488147419103229:8369468980515574351100487830435011627888689207137649295360 36893488147419103232:36893488147419103228:77194726158210796936493119868351910375132261936700097043773975191268737679360 36893488147419103232:36893488147419103227:569596542912242688484283002662125636677273129999425783296567487241020832354034618384565000994816 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_nok.t0000644403072340010010000001032013024051250023355 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 82645; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_nok'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_nok(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_nok() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_nok(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_nok() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_pow.t0000644403072340010010000001061413024051250023401 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 1357; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_pow'); my @data; # Small numbers. for (my $x = 0; $x <= 24 ; ++ $x) { for (my $y = 0; $y <= 24 ; ++ $y) { my $z = $x ** $y; next if $z > 2147483647; push @data, [ $x, $y, $z ]; } } # Powers of 10. for (my $p = 0; $p <= 10 ; ++ $p) { for (my $q = 0; $q <= 6 ; ++ $q) { my $x = "1" . ("0" x $p); my $y = "1" . ("0" x $q); my $zn = $p * $y; next if $zn >= 1e4; my $z = "1" . ("0" x $zn); push @data, [ $x, $y, $z ]; } } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_pow(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_pow() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' first output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_pow(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_add() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_root.dat0000644403072340010010001102017113012340550024066 0ustar ospjadomain users # Each line contain x:y:z, for all small values of x and y. # # Number of test cases: 15010. 0:1:0 0:2:0 0:3:0 0:4:0 0:5:0 0:6:0 0:7:0 0:8:0 0:9:0 0:10:0 1:1:1 1:2:1 1:3:1 1:4:1 1:5:1 1:6:1 1:7:1 1:8:1 1:9:1 1:10:1 2:1:2 2:2:1 2:3:1 2:4:1 2:5:1 2:6:1 2:7:1 2:8:1 2:9:1 2:10:1 3:1:3 3:2:1 3:3:1 3:4:1 3:5:1 3:6:1 3:7:1 3:8:1 3:9:1 3:10:1 4:1:4 4:2:2 4:3:1 4:4:1 4:5:1 4:6:1 4:7:1 4:8:1 4:9:1 4:10:1 5:1:5 5:2:2 5:3:1 5:4:1 5:5:1 5:6:1 5:7:1 5:8:1 5:9:1 5:10:1 6:1:6 6:2:2 6:3:1 6:4:1 6:5:1 6:6:1 6:7:1 6:8:1 6:9:1 6:10:1 7:1:7 7:2:2 7:3:1 7:4:1 7:5:1 7:6:1 7:7:1 7:8:1 7:9:1 7:10:1 8:1:8 8:2:2 8:3:2 8:4:1 8:5:1 8:6:1 8:7:1 8:8:1 8:9:1 8:10:1 9:1:9 9:2:3 9:3:2 9:4:1 9:5:1 9:6:1 9:7:1 9:8:1 9:9:1 9:10:1 10:1:10 10:2:3 10:3:2 10:4:1 10:5:1 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1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001:102:10 # Each line contain x:y:z, where x is close to, or exactly equal to, z^y, and # y is a power of 2. # # Number of test cases: 14967. 1520:2:38 1521:2:39 1522:2:39 1599:2:39 1600:2:40 1601:2:40 1680:2:40 1681:2:41 1682:2:41 1763:2:41 1764:2:42 1765:2:42 1848:2:42 1849:2:43 1850:2:43 1935:2:43 1936:2:44 1937:2:44 2024:2:44 2025:2:45 2026:2:45 2115:2:45 2116:2:46 2117:2:46 2208:2:46 2209:2:47 2210:2:47 2303:2:47 2304:2:48 2305:2:48 2400:2:48 2401:2:49 2402:2:49 2499:2:49 2500:2:50 2501:2:50 2600:2:50 2601:2:51 2602:2:51 2703:2:51 2704:2:52 2705:2:52 2808:2:52 2809:2:53 2810:2:53 2915:2:53 2916:2:54 2917:2:54 3024:2:54 3025:2:55 3026:2:55 3135:2:55 3136:2:56 3137:2:56 3248:2:56 3249:2:57 3250:2:57 3363:2:57 3364:2:58 3365:2:58 3480:2:58 3481:2:59 3482:2:59 3599:2:59 3600:2:60 3601:2:60 3720:2:60 3721:2:61 3722:2:61 3843:2:61 3844:2:62 3845:2:62 3968:2:62 3969:2:63 3970:2:63 4095:2:63 4096:2:64 4097:2:64 4224:2:64 4225:2:65 4226:2:65 4355:2:65 4356:2:66 4357:2:66 4488:2:66 4489:2:67 4490:2:67 4623:2:67 4624:2:68 4625:2:68 4760:2:68 4761:2:69 4762:2:69 4899:2:69 4900:2:70 4901:2:70 5040:2:70 5041:2:71 5042:2:71 5183:2:71 5184:2:72 5185:2:72 5328:2:72 5329:2:73 5330:2:73 5475:2:73 5476:2:74 5477:2:74 5624:2:74 5625:2:75 5626:2:75 5775:2:75 5776:2:76 5777:2:76 5928:2:76 5929:2:77 5930:2:77 6083:2:77 6084:2:78 6085:2:78 6240:2:78 6241:2:79 6242:2:79 6399:2:79 6400:2:80 6401:2:80 6560:2:80 6561:2:81 6562:2:81 6723:2:81 6724:2:82 6725:2:82 6888:2:82 6889:2:83 6890:2:83 7055:2:83 7056:2:84 7057:2:84 7224:2:84 7225:2:85 7226:2:85 7395:2:85 7396:2:86 7397:2:86 7568:2:86 7569:2:87 7570:2:87 7743:2:87 7744:2:88 7745:2:88 7920:2:88 7921:2:89 7922:2:89 8099:2:89 8100:2:90 8101:2:90 8280:2:90 8281:2:91 8282:2:91 8463:2:91 8464:2:92 8465:2:92 8648:2:92 8649:2:93 8650:2:93 8835:2:93 8836:2:94 8837:2:94 9024:2:94 9025:2:95 9026:2:95 9215:2:95 9216:2:96 9217:2:96 9408:2:96 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35364163556449226879254006193095546476798382214081763:99:3 86549310357874886680734159305815988142408298321360136:99:3 47481529570184569808518539106401201129529770307620983:99:3 51515052977690105914026100608446660161094659090227986:99:3 10574001303758182972410605066481971744431927388580081:99:3 63435766232424628845013782053100823507276436385632617:100:3 76123284463328105985072953753039936173373724236563752:100:3 90113305548948576297914094790880646738013257037465377:100:3 58699858704067723292925483187742517008468090704659943:100:3 92467064301643661447075569946571958365458596365063881:100:3 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_root.t0000644403072340010010000001032613024051250023557 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 276117; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_root'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_root(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_root() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_root(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_root() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_sub.dat0000644403072340010010000006535713012340550023711 0ustar ospjadomain users133:38:95 633:51:582 3336:77:3259 49016:77:48939 785833:87:785746 8013144:51:8013093 84981879:17:84981862 518094066:73:518093993 2050839895:30:2050839865 29590479939:47:29590479892 881113766723:82:881113766641 2365621927567:94:2365621927473 57129686171320:42:57129686171278 714600987410026:97:714600987409929 9193587152443818:16:9193587152443802 34574756119616356:69:34574756119616287 129203528618918503:63:129203528618918440 4564395485854842846:89:4564395485854842757 43281574081450827789:52:43281574081450827737 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5407489659804451402540302:5407486861167440724261314:2798637010678278988 4083216859112673102149466:4083151706985507799310608:65152127165302838858 7219752816094268094417004:7219110157835469406203668:642658258798688213336 7046982686180116257763272:7043625276900062501518290:3357409280053756244982 2567747775486565143895290:2475791768058130306552480:91956007428434837342810 3553601079836557876973542:3250420820556278555501310:303180259280279321472232 11821254511570612874494542:2248566248782537066521058:9572688262788075807973484 Math-BigInt-1.999808/t/author-lib-arithmetic-binary-_sub.t0000644403072340010010000001552713024051250023375 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 7209; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_sub'); my @data; # Small numbers. for (my $x = 0; $x <= 24 ; ++ $x) { for (my $y = 0; $y <= $x ; ++ $y) { push @data, [ $x, $y, $x - $y ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context without swap flag. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_sub(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_sub() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context without swap flag. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_sub(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_sub() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # List context with swap flag. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_sub(\$x, \$y, 1);|; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_sub() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($x), "'$test' output arg is not the first input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); is($LIB->_str($x), $in0, "'$test' first input arg is unmodified"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); ok($LIB->_str($y) eq $out0 || $LIB->_str($y) eq $in1, "'$test' second input arg has the correct value"); }; } # Scalar context with swap flag. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_sub(\$x, \$y, 1);|; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_sub() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($x), "'$test' output arg is not the first input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); is($LIB->_str($x), $in0, "'$test' first input arg is unmodified"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); ok($LIB->_str($y) eq $out0 || $LIB->_str($y) eq $in1, "'$test' second input arg has the correct value"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-ternary-_lsft.dat0000644403072340010010000106033713012340550024262 0ustar ospjadomain users220:0:2:220 220:0:3:220 220:0:4:220 220:0:5:220 220:0:6:220 220:0:7:220 220:0:8:220 220:0:9:220 220:0:10:220 220:0:11:220 220:0:12:220 220:0:13:220 220:0:14:220 220:0:15:220 220:0:16:220 220:0:17:220 220:0:18:220 220:0:19:220 220:0:20:220 220:1:2:440 220:1:3:660 220:1:4:880 220:1:5:1100 220:1:6:1320 220:1:7:1540 220:1:8:1760 220:1:9:1980 220:1:10:2200 220:1:11:2420 220:1:12:2640 220:1:13:2860 220:1:14:3080 220:1:15:3300 220:1:16:3520 220:1:17:3740 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82321682164470047679:20:20:8632054019729134471505510400000000000000000000 Math-BigInt-1.999808/t/author-lib-arithmetic-ternary-_lsft.t0000644403072340010010000001040613024051250023743 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 32905; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_lsft'); my @data; # Small numbers. for (my $x = 0; $x <= 10 ; ++ $x) { for (my $n = 0; $n <= 10 ; ++ $n) { for (my $b = 2; $b <= 10 ; ++ $b) { my $y = $x * $b ** $n; last if $y > 2147483647; push @data, [ $x, $n, $b, $y ]; } } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $in2, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_lsft(\$x, \$y, $in2);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_lsft() in list context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $in2, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_lsft(\$x, \$y, $in2);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_lsft() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 7 : 6; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-ternary-_modpow.dat0000644403072340010010000134603713012340550024623 0ustar ospjadomain users# Small numbers. 0:0:1:0 0:0:2:1 0:0:3:1 0:0:4:1 0:0:5:1 0:0:6:1 0:0:7:1 0:0:8:1 0:0:9:1 0:0:10:1 0:0:11:1 0:0:12:1 0:0:13:1 0:0:14:1 0:0:15:1 0:0:16:1 0:0:17:1 0:0:18:1 0:0:19:1 0:0:20:1 0:1:1:0 0:1:2:0 0:1:3:0 0:1:4:0 0:1:5:0 0:1:6:0 0:1:7:0 0:1:8:0 0:1:9:0 0:1:10:0 0:1:11:0 0:1:12:0 0:1:13:0 0:1:14:0 0:1:15:0 0:1:16:0 0:1:17:0 0:1:18:0 0:1:19:0 0:1:20:0 0:2:1:0 0:2:2:0 0:2:3:0 0:2:4:0 0:2:5:0 0:2:6:0 0:2:7:0 0:2:8:0 0:2:9:0 0:2:10:0 0:2:11:0 0:2:12:0 0:2:13:0 0:2:14:0 0:2:15:0 0:2:16:0 0:2:17:0 0:2:18:0 0:2:19:0 0:2:20:0 0:3:1:0 0:3:2:0 0:3:3:0 0:3:4:0 0:3:5:0 0:3:6:0 0:3:7:0 0:3:8:0 0:3:9:0 0:3:10:0 0:3:11:0 0:3:12:0 0:3:13:0 0:3:14:0 0:3:15:0 0:3:16:0 0:3:17:0 0:3:18:0 0:3:19:0 0:3:20:0 0:4:1:0 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1:4:19:1 1:4:20:1 #1:5:0:1 1:5:1:0 1:5:2:1 1:5:3:1 1:5:4:1 1:5:5:1 1:5:6:1 1:5:7:1 1:5:8:1 1:5:9:1 1:5:10:1 1:5:11:1 1:5:12:1 1:5:13:1 1:5:14:1 1:5:15:1 1:5:16:1 1:5:17:1 1:5:18:1 1:5:19:1 1:5:20:1 #1:6:0:1 1:6:1:0 1:6:2:1 1:6:3:1 1:6:4:1 1:6:5:1 1:6:6:1 1:6:7:1 1:6:8:1 1:6:9:1 1:6:10:1 1:6:11:1 1:6:12:1 1:6:13:1 1:6:14:1 1:6:15:1 1:6:16:1 1:6:17:1 1:6:18:1 1:6:19:1 1:6:20:1 #1:7:0:1 1:7:1:0 1:7:2:1 1:7:3:1 1:7:4:1 1:7:5:1 1:7:6:1 1:7:7:1 1:7:8:1 1:7:9:1 1:7:10:1 1:7:11:1 1:7:12:1 1:7:13:1 1:7:14:1 1:7:15:1 1:7:16:1 1:7:17:1 1:7:18:1 1:7:19:1 1:7:20:1 #1:8:0:1 1:8:1:0 1:8:2:1 1:8:3:1 1:8:4:1 1:8:5:1 1:8:6:1 1:8:7:1 1:8:8:1 1:8:9:1 1:8:10:1 1:8:11:1 1:8:12:1 1:8:13:1 1:8:14:1 1:8:15:1 1:8:16:1 1:8:17:1 1:8:18:1 1:8:19:1 1:8:20:1 #1:9:0:1 1:9:1:0 1:9:2:1 1:9:3:1 1:9:4:1 1:9:5:1 1:9:6:1 1:9:7:1 1:9:8:1 1:9:9:1 1:9:10:1 1:9:11:1 1:9:12:1 1:9:13:1 1:9:14:1 1:9:15:1 1:9:16:1 1:9:17:1 1:9:18:1 1:9:19:1 1:9:20:1 #1:10:0:1 1:10:1:0 1:10:2:1 1:10:3:1 1:10:4:1 1:10:5:1 1:10:6:1 1:10:7:1 1:10:8:1 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19:20:14:11 19:20:15:1 19:20:16:1 19:20:17:16 19:20:18:1 19:20:19:0 19:20:20:1 #20:0:0:20 20:0:1:0 20:0:2:1 20:0:3:1 20:0:4:1 20:0:5:1 20:0:6:1 20:0:7:1 20:0:8:1 20:0:9:1 20:0:10:1 20:0:11:1 20:0:12:1 20:0:13:1 20:0:14:1 20:0:15:1 20:0:16:1 20:0:17:1 20:0:18:1 20:0:19:1 20:0:20:1 #20:1:0:20 20:1:1:0 20:1:2:0 20:1:3:2 20:1:4:0 20:1:5:0 20:1:6:2 20:1:7:6 20:1:8:4 20:1:9:2 20:1:10:0 20:1:11:9 20:1:12:8 20:1:13:7 20:1:14:6 20:1:15:5 20:1:16:4 20:1:17:3 20:1:18:2 20:1:19:1 20:1:20:0 #20:2:0:20 20:2:1:0 20:2:2:0 20:2:3:1 20:2:4:0 20:2:5:0 20:2:6:4 20:2:7:1 20:2:8:0 20:2:9:4 20:2:10:0 20:2:11:4 20:2:12:4 20:2:13:10 20:2:14:8 20:2:15:10 20:2:16:0 20:2:17:9 20:2:18:4 20:2:19:1 20:2:20:0 #20:3:0:20 20:3:1:0 20:3:2:0 20:3:3:2 20:3:4:0 20:3:5:0 20:3:6:2 20:3:7:6 20:3:8:0 20:3:9:8 20:3:10:0 20:3:11:3 20:3:12:8 20:3:13:5 20:3:14:6 20:3:15:5 20:3:16:0 20:3:17:10 20:3:18:8 20:3:19:1 20:3:20:0 #20:4:0:20 20:4:1:0 20:4:2:0 20:4:3:1 20:4:4:0 20:4:5:0 20:4:6:4 20:4:7:1 20:4:8:0 20:4:9:7 20:4:10:0 20:4:11:5 20:4:12:4 20:4:13:9 20:4:14:8 20:4:15:10 20:4:16:0 20:4:17:13 20:4:18:16 20:4:19:1 20:4:20:0 #20:5:0:20 20:5:1:0 20:5:2:0 20:5:3:2 20:5:4:0 20:5:5:0 20:5:6:2 20:5:7:6 20:5:8:0 20:5:9:5 20:5:10:0 20:5:11:1 20:5:12:8 20:5:13:11 20:5:14:6 20:5:15:5 20:5:16:0 20:5:17:5 20:5:18:14 20:5:19:1 20:5:20:0 #20:6:0:20 20:6:1:0 20:6:2:0 20:6:3:1 20:6:4:0 20:6:5:0 20:6:6:4 20:6:7:1 20:6:8:0 20:6:9:1 20:6:10:0 20:6:11:9 20:6:12:4 20:6:13:12 20:6:14:8 20:6:15:10 20:6:16:0 20:6:17:15 20:6:18:10 20:6:19:1 20:6:20:0 #20:7:0:20 20:7:1:0 20:7:2:0 20:7:3:2 20:7:4:0 20:7:5:0 20:7:6:2 20:7:7:6 20:7:8:0 20:7:9:2 20:7:10:0 20:7:11:4 20:7:12:8 20:7:13:6 20:7:14:6 20:7:15:5 20:7:16:0 20:7:17:11 20:7:18:2 20:7:19:1 20:7:20:0 #20:8:0:20 20:8:1:0 20:8:2:0 20:8:3:1 20:8:4:0 20:8:5:0 20:8:6:4 20:8:7:1 20:8:8:0 20:8:9:4 20:8:10:0 20:8:11:3 20:8:12:4 20:8:13:3 20:8:14:8 20:8:15:10 20:8:16:0 20:8:17:16 20:8:18:4 20:8:19:1 20:8:20:0 #20:9:0:20 20:9:1:0 20:9:2:0 20:9:3:2 20:9:4:0 20:9:5:0 20:9:6:2 20:9:7:6 20:9:8:0 20:9:9:8 20:9:10:0 20:9:11:5 20:9:12:8 20:9:13:8 20:9:14:6 20:9:15:5 20:9:16:0 20:9:17:14 20:9:18:8 20:9:19:1 20:9:20:0 #20:10:0:20 20:10:1:0 20:10:2:0 20:10:3:1 20:10:4:0 20:10:5:0 20:10:6:4 20:10:7:1 20:10:8:0 20:10:9:7 20:10:10:0 20:10:11:1 20:10:12:4 20:10:13:4 20:10:14:8 20:10:15:10 20:10:16:0 20:10:17:8 20:10:18:16 20:10:19:1 20:10:20:0 #20:11:0:20 20:11:1:0 20:11:2:0 20:11:3:2 20:11:4:0 20:11:5:0 20:11:6:2 20:11:7:6 20:11:8:0 20:11:9:5 20:11:10:0 20:11:11:9 20:11:12:8 20:11:13:2 20:11:14:6 20:11:15:5 20:11:16:0 20:11:17:7 20:11:18:14 20:11:19:1 20:11:20:0 #20:12:0:20 20:12:1:0 20:12:2:0 20:12:3:1 20:12:4:0 20:12:5:0 20:12:6:4 20:12:7:1 20:12:8:0 20:12:9:1 20:12:10:0 20:12:11:4 20:12:12:4 20:12:13:1 20:12:14:8 20:12:15:10 20:12:16:0 20:12:17:4 20:12:18:10 20:12:19:1 20:12:20:0 #20:13:0:20 20:13:1:0 20:13:2:0 20:13:3:2 20:13:4:0 20:13:5:0 20:13:6:2 20:13:7:6 20:13:8:0 20:13:9:2 20:13:10:0 20:13:11:3 20:13:12:8 20:13:13:7 20:13:14:6 20:13:15:5 20:13:16:0 20:13:17:12 20:13:18:2 20:13:19:1 20:13:20:0 #20:14:0:20 20:14:1:0 20:14:2:0 20:14:3:1 20:14:4:0 20:14:5:0 20:14:6:4 20:14:7:1 20:14:8:0 20:14:9:4 20:14:10:0 20:14:11:5 20:14:12:4 20:14:13:10 20:14:14:8 20:14:15:10 20:14:16:0 20:14:17:2 20:14:18:4 20:14:19:1 20:14:20:0 #20:15:0:20 20:15:1:0 20:15:2:0 20:15:3:2 20:15:4:0 20:15:5:0 20:15:6:2 20:15:7:6 20:15:8:0 20:15:9:8 20:15:10:0 20:15:11:1 20:15:12:8 20:15:13:5 20:15:14:6 20:15:15:5 20:15:16:0 20:15:17:6 20:15:18:8 20:15:19:1 20:15:20:0 #20:16:0:20 20:16:1:0 20:16:2:0 20:16:3:1 20:16:4:0 20:16:5:0 20:16:6:4 20:16:7:1 20:16:8:0 20:16:9:7 20:16:10:0 20:16:11:9 20:16:12:4 20:16:13:9 20:16:14:8 20:16:15:10 20:16:16:0 20:16:17:1 20:16:18:16 20:16:19:1 20:16:20:0 #20:17:0:20 20:17:1:0 20:17:2:0 20:17:3:2 20:17:4:0 20:17:5:0 20:17:6:2 20:17:7:6 20:17:8:0 20:17:9:5 20:17:10:0 20:17:11:4 20:17:12:8 20:17:13:11 20:17:14:6 20:17:15:5 20:17:16:0 20:17:17:3 20:17:18:14 20:17:19:1 20:17:20:0 #20:18:0:20 20:18:1:0 20:18:2:0 20:18:3:1 20:18:4:0 20:18:5:0 20:18:6:4 20:18:7:1 20:18:8:0 20:18:9:1 20:18:10:0 20:18:11:3 20:18:12:4 20:18:13:12 20:18:14:8 20:18:15:10 20:18:16:0 20:18:17:9 20:18:18:10 20:18:19:1 20:18:20:0 #20:19:0:20 20:19:1:0 20:19:2:0 20:19:3:2 20:19:4:0 20:19:5:0 20:19:6:2 20:19:7:6 20:19:8:0 20:19:9:2 20:19:10:0 20:19:11:5 20:19:12:8 20:19:13:6 20:19:14:6 20:19:15:5 20:19:16:0 20:19:17:10 20:19:18:2 20:19:19:1 20:19:20:0 #20:20:0:20 20:20:1:0 20:20:2:0 20:20:3:1 20:20:4:0 20:20:5:0 20:20:6:4 20:20:7:1 20:20:8:0 20:20:9:4 20:20:10:0 20:20:11:1 20:20:12:4 20:20:13:3 20:20:14:8 20:20:15:10 20:20:16:0 20:20:17:13 20:20:18:4 20:20:19:1 20:20:20:0 # Big random numbers. 541:932:670:551 498:741:2680:1408 493:294:29036:23885 677:381:502319:424929 124:644:7815376:4902592 426:674:47705196:2470560 155:403:271658034:152714351 427:777:7990472785:2194110682 541:674:84600919454:17880105491 253:135:112528687926:77780019859 276:467:6122946012602:3096828804900 699:780:88480707542432:8894145315281 138:333:349791384844673:207924571073190 831:100:5854671569773773:4440287816019162 200:836:79038250231977980:35876942782673280 811:741:262201765657826441:85984560493797893 753:895:7388064555903808170:1339377145516017987 286:480:54531236813928854129:43472388089876990938 491:9803:285:161 433:9659:9871:1465 684:5067:62231:23717 394:4166:519632:501024 308:6701:8044636:3396276 640:5574:76215172:12639896 808:5113:131053547:70094021 121:6507:9714479326:5503201901 331:2057:59233158691:21832383773 467:9658:275940562063:118346986660 640:8151:9607541157595:8654341820635 734:8303:35705723433562:10983103751332 848:8993:110609576255236:105032128915984 126:7721:7911054700394194:3065609710284666 293:7473:86189023701437480:39136164821952053 555:4499:334838206326379543:217033347465538026 278:8664:2778564673161967338:2120193459410838112 924:5030:44112241480900862925:5853445669636213851 783:75508:980:1 790:89067:8822:7726 717:62743:22972:4717 701:18606:559823:437055 772:94978:3268034:2906654 530:20956:59311351:1450546 345:81569:508697885:346063565 231:18408:7806728798:508476419 565:45522:25042780712:8220171345 812:53244:909369872313:488516394478 551:68433:1935753632100:1873501974251 894:53151:94742836908308:20236603928548 731:80470:807760250301739:706525077838934 767:81348:8485082936215942:4707824873846599 774:20201:85009547437512836:13098723952095424 626:24968:343839340372068071:233809051594134824 211:16238:9775086293701306245:1224272992724500636 311:41471:64058629844284800999:38568043487197139129 277:733219:338:251 283:813026:7716:1645 191:288862:53410:19091 236:996237:279188:167796 516:464599:6709608:3939840 382:805803:65474738:4357886 271:652960:609995674:466915967 489:111032:6479461981:1342731508 715:337403:85858682552:61933684155 224:233900:745567785838:597129478158 669:228678:1141386674103:336943853505 920:762949:28775289412198:16830263994260 586:428461:512653996846703:501202195027249 888:139025:2139987661831769:1156452254146473 567:341378:10568081898469204:7720172962148489 740:989293:193538031552851328:24393474289875584 100:271606:8724538733549024775:1428699418275160975 140:173021:59846738846570856659:43219946764093194084 653:9614244:464:161 680:1864916:7213:2186 114:9726128:81366:7278 896:8675941:494012:153176 357:5449387:5799628:2788601 724:5238068:35357925:6135301 994:4033780:887957976:137621872 517:2769973:9557521723:4244998651 281:3555901:90755622720:16603302521 105:3437874:754380655775:73057833400 730:2415908:3044449833105:2669580139030 287:5472053:11883757191483:4922772001217 449:5037773:273037505443735:44278239317889 733:9477665:7915870602107761:7387949851323917 109:9721684:71141784154170477:68561542302260668 563:5834073:103693130265475231:67323100545011505 411:3298330:5683448882990098162:5185124661333521931 127:8294662:23004302162139021508:4694297664746943125 874:20102901:649:181 971:15478949:5544:1907 860:27235775:68780:15320 839:84217637:664946:242159 904:79326096:3506461:2716127 144:69136272:79690052:13872860 117:93882782:340384276:215896569 910:39553137:2084943486:1900134796 726:40739946:13161645477:2570575770 399:89280294:381998874843:293309377182 265:30717048:7170593453793:4731708735370 356:75194979:85743937410153:81298827223067 102:82903853:632474475812580:152423018474472 864:80373596:8471790831846713:7114746809062741 953:81404302:59670219812529475:34918987140857809 424:53972813:773785741386205243:618032041370694417 562:75700680:7339122993873807100:2902317585126748076 289:57951507:30445461016021299051:10353055399247003230 913:816569729:625:123 716:677654571:7584:5696 128:886627167:76824:512 358:708776197:599937:477913 687:913202087:9266684:2944411 712:652743105:71531194:56444366 428:617635642:350293434:335458816 343:986629398:4990141032:3864821545 974:287254454:55495610693:34785576931 726:953544142:466450699360:415050029216 251:234480022:5505621483891:1263352976011 246:410380258:75603089710301:11802900653375 338:958913179:721536315372638:643758569378034 455:765230296:6499613307910203:21102003223717 388:756154159:46587353740800261:15196260301988599 508:240252491:443404347535246315:343870473061272587 985:955930099:5446929295683463407:3595799635029690943 458:264683008:72046116068526564402:11325826018497849982 566:4821175400:586:222 454:8468110056:4437:2872 487:3895397439:31089:6700 856:4811847765:381041:188177 991:4048747767:7705495:4753036 317:7754450053:27029860:20662777 329:3269671879:599955218:88961327 354:3276285524:2700459227:1542551681 747:3068267390:33591131025:18357224574 912:7482140686:410638275166:119137041732 919:2180728302:8764448277705:7045754421241 459:5883070584:23402365905881:12932158115033 527:4184532134:598093895000592:364336399657537 334:4278374376:2350297638367788:1188327483963592 468:4016253803:61083183897586343:41101540908612478 411:3225649770:354575772961695456:323162216307436473 899:5001209429:2738001529528063689:730329296722705379 482:7607104246:39402731724352549380:18640684735753395784 124:29619454271:806:496 160:25346208232:7070:6140 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99876013115789323001:84285928869856133933:63950820532341962147:42228132008199549953 Math-BigInt-1.999808/t/author-lib-arithmetic-ternary-_modpow.t0000644403072340010010000001167513024051250024311 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 58609; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_modpow'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $in2, $out0) = @{ $data[$i] }; my ($x, $y, $m, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$m = $LIB->_new("$in2"); | . qq|\@got = $LIB->_modpow(\$x, \$y, \$m);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_modpow() in list context: $test", sub { plan tests => $scalar_util_ok ? 12 : 10; cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; isnt(refaddr($got[0]), refaddr($m), "'$test' output arg is not the third input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); is(ref($m), $REF, "'$test' third input arg is still a $REF"); is($LIB->_str($m), $in2, "'$test' third input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $in2, $out0) = @{ $data[$i] }; my ($x, $y, $m, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$m = $LIB->_new("$in2"); | . qq|\$got = $LIB->_modpow(\$x, \$y, \$m);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_modpow() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 11 : 9; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; isnt(refaddr($got), refaddr($m), "'$test' output arg is not the third input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' first input arg has the correct value"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); is(ref($m), $REF, "'$test' third input arg is still a $REF"); is($LIB->_str($m), $in2, "'$test' third input arg is unmodified"); }; } 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11736061446441134093:18:9:78 11736061446441134093:18:10:11 11736061446441134093:18:11:2 11736061446441134093:18:12:0 11736061446441134093:18:13:0 11736061446441134093:19:2:22384760754472 11736061446441134093:19:3:10097608653 11736061446441134093:19:4:42695542 11736061446441134093:19:5:615307 11736061446441134093:19:6:19259 11736061446441134093:19:7:1029 11736061446441134093:19:8:81 11736061446441134093:19:9:8 11736061446441134093:19:10:1 11736061446441134093:19:11:0 11736061446441134093:19:12:0 11736061446441134093:20:2:11192380377236 11736061446441134093:20:3:3365869551 11736061446441134093:20:4:10673885 11736061446441134093:20:5:123061 11736061446441134093:20:6:3209 11736061446441134093:20:7:147 11736061446441134093:20:8:10 11736061446441134093:20:9:0 11736061446441134093:20:10:0 Math-BigInt-1.999808/t/author-lib-arithmetic-ternary-_rsft.t0000644403072340010010000001035013024051250023747 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 54713; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_rsft'); my @data; # Small numbers. for (my $x = 0; $x <= 100 ; ++ $x) { for (my $n = 0; $n <= 5 ; ++ $n) { for (my $b = 2; $b <= 16 ; ++ $b) { my $y = int($x / ($b ** $n)); push @data, [ $x, $n, $b, $y ]; } } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $in2, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_rsft(\$x, \$y, $in2);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_rsft() in list context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $in2, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_rsft(\$x, \$y, $in2);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_rsft() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 7 : 6; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_dec.dat0000644403072340010010000011556413024050570023524 0ustar ospjadomain users# numbers close to 2^10 1022:1021 1023:1022 1024:1023 1025:1024 1026:1025 # numbers close to 2^11 2046:2045 2047:2046 2048:2047 2049:2048 2050:2049 # numbers close to 2^12 4094:4093 4095:4094 4096:4095 4097:4096 4098:4097 # numbers close to 2^13 8190:8189 8191:8190 8192:8191 8193:8192 8194:8193 # numbers close to 2^14 16382:16381 16383:16382 16384:16383 16385:16384 16386:16385 # numbers close to 2^15 32766:32765 32767:32766 32768:32767 32769:32768 32770:32769 # numbers close to 2^16 65534:65533 65535:65534 65536:65535 65537:65536 65538:65537 # numbers close to 2^17 131070:131069 131071:131070 131072:131071 131073:131072 131074:131073 # numbers close to 2^18 262142:262141 262143:262142 262144:262143 262145:262144 262146:262145 # numbers close to 2^19 524286:524285 524287:524286 524288:524287 524289:524288 524290:524289 # numbers close to 2^20 1048574:1048573 1048575:1048574 1048576:1048575 1048577:1048576 1048578:1048577 # numbers close to 2^21 2097150:2097149 2097151:2097150 2097152:2097151 2097153:2097152 2097154:2097153 # numbers close to 2^22 4194302:4194301 4194303:4194302 4194304:4194303 4194305:4194304 4194306:4194305 # numbers close to 2^23 8388606:8388605 8388607:8388606 8388608:8388607 8388609:8388608 8388610:8388609 # numbers close to 2^24 16777214:16777213 16777215:16777214 16777216:16777215 16777217:16777216 16777218:16777217 # numbers close to 2^25 33554430:33554429 33554431:33554430 33554432:33554431 33554433:33554432 33554434:33554433 # numbers close to 2^26 67108862:67108861 67108863:67108862 67108864:67108863 67108865:67108864 67108866:67108865 # numbers close to 2^27 134217726:134217725 134217727:134217726 134217728:134217727 134217729:134217728 134217730:134217729 # numbers close to 2^28 268435454:268435453 268435455:268435454 268435456:268435455 268435457:268435456 268435458:268435457 # numbers close to 2^29 536870910:536870909 536870911:536870910 536870912:536870911 536870913:536870912 536870914:536870913 # numbers close to 2^30 1073741822:1073741821 1073741823:1073741822 1073741824:1073741823 1073741825:1073741824 1073741826:1073741825 # numbers close to 2^31 2147483646:2147483645 2147483647:2147483646 2147483648:2147483647 2147483649:2147483648 2147483650:2147483649 # numbers close to 2^32 4294967294:4294967293 4294967295:4294967294 4294967296:4294967295 4294967297:4294967296 4294967298:4294967297 # numbers close to 2^33 8589934590:8589934589 8589934591:8589934590 8589934592:8589934591 8589934593:8589934592 8589934594:8589934593 # numbers close to 2^34 17179869182:17179869181 17179869183:17179869182 17179869184:17179869183 17179869185:17179869184 17179869186:17179869185 # numbers close to 2^35 34359738366:34359738365 34359738367:34359738366 34359738368:34359738367 34359738369:34359738368 34359738370:34359738369 # numbers close to 2^36 68719476734:68719476733 68719476735:68719476734 68719476736:68719476735 68719476737:68719476736 68719476738:68719476737 # numbers close to 2^37 137438953470:137438953469 137438953471:137438953470 137438953472:137438953471 137438953473:137438953472 137438953474:137438953473 # numbers close to 2^38 274877906942:274877906941 274877906943:274877906942 274877906944:274877906943 274877906945:274877906944 274877906946:274877906945 # numbers close to 2^39 549755813886:549755813885 549755813887:549755813886 549755813888:549755813887 549755813889:549755813888 549755813890:549755813889 # numbers close to 2^40 1099511627774:1099511627773 1099511627775:1099511627774 1099511627776:1099511627775 1099511627777:1099511627776 1099511627778:1099511627777 # numbers close to 2^41 2199023255550:2199023255549 2199023255551:2199023255550 2199023255552:2199023255551 2199023255553:2199023255552 2199023255554:2199023255553 # numbers close to 2^42 4398046511102:4398046511101 4398046511103:4398046511102 4398046511104:4398046511103 4398046511105:4398046511104 4398046511106:4398046511105 # numbers close to 2^43 8796093022206:8796093022205 8796093022207:8796093022206 8796093022208:8796093022207 8796093022209:8796093022208 8796093022210:8796093022209 # numbers close to 2^44 17592186044414:17592186044413 17592186044415:17592186044414 17592186044416:17592186044415 17592186044417:17592186044416 17592186044418:17592186044417 # numbers close to 2^45 35184372088830:35184372088829 35184372088831:35184372088830 35184372088832:35184372088831 35184372088833:35184372088832 35184372088834:35184372088833 # numbers close to 2^46 70368744177662:70368744177661 70368744177663:70368744177662 70368744177664:70368744177663 70368744177665:70368744177664 70368744177666:70368744177665 # numbers close to 2^47 140737488355326:140737488355325 140737488355327:140737488355326 140737488355328:140737488355327 140737488355329:140737488355328 140737488355330:140737488355329 # numbers close to 2^48 281474976710654:281474976710653 281474976710655:281474976710654 281474976710656:281474976710655 281474976710657:281474976710656 281474976710658:281474976710657 # numbers close to 2^49 562949953421310:562949953421309 562949953421311:562949953421310 562949953421312:562949953421311 562949953421313:562949953421312 562949953421314:562949953421313 # numbers close to 2^50 1125899906842622:1125899906842621 1125899906842623:1125899906842622 1125899906842624:1125899906842623 1125899906842625:1125899906842624 1125899906842626:1125899906842625 # numbers close to 2^51 2251799813685246:2251799813685245 2251799813685247:2251799813685246 2251799813685248:2251799813685247 2251799813685249:2251799813685248 2251799813685250:2251799813685249 # numbers close to 2^52 4503599627370494:4503599627370493 4503599627370495:4503599627370494 4503599627370496:4503599627370495 4503599627370497:4503599627370496 4503599627370498:4503599627370497 # numbers close to 2^53 9007199254740990:9007199254740989 9007199254740991:9007199254740990 9007199254740992:9007199254740991 9007199254740993:9007199254740992 9007199254740994:9007199254740993 # numbers close to 2^54 18014398509481982:18014398509481981 18014398509481983:18014398509481982 18014398509481984:18014398509481983 18014398509481985:18014398509481984 18014398509481986:18014398509481985 # numbers close to 2^55 36028797018963966:36028797018963965 36028797018963967:36028797018963966 36028797018963968:36028797018963967 36028797018963969:36028797018963968 36028797018963970:36028797018963969 # numbers close to 2^56 72057594037927934:72057594037927933 72057594037927935:72057594037927934 72057594037927936:72057594037927935 72057594037927937:72057594037927936 72057594037927938:72057594037927937 # numbers close to 2^57 144115188075855870:144115188075855869 144115188075855871:144115188075855870 144115188075855872:144115188075855871 144115188075855873:144115188075855872 144115188075855874:144115188075855873 # numbers close to 2^58 288230376151711742:288230376151711741 288230376151711743:288230376151711742 288230376151711744:288230376151711743 288230376151711745:288230376151711744 288230376151711746:288230376151711745 # numbers close to 2^59 576460752303423486:576460752303423485 576460752303423487:576460752303423486 576460752303423488:576460752303423487 576460752303423489:576460752303423488 576460752303423490:576460752303423489 # numbers close to 2^60 1152921504606846974:1152921504606846973 1152921504606846975:1152921504606846974 1152921504606846976:1152921504606846975 1152921504606846977:1152921504606846976 1152921504606846978:1152921504606846977 # numbers close to 2^61 2305843009213693950:2305843009213693949 2305843009213693951:2305843009213693950 2305843009213693952:2305843009213693951 2305843009213693953:2305843009213693952 2305843009213693954:2305843009213693953 # numbers close to 2^62 4611686018427387902:4611686018427387901 4611686018427387903:4611686018427387902 4611686018427387904:4611686018427387903 4611686018427387905:4611686018427387904 4611686018427387906:4611686018427387905 # numbers close to 2^63 9223372036854775806:9223372036854775805 9223372036854775807:9223372036854775806 9223372036854775808:9223372036854775807 9223372036854775809:9223372036854775808 9223372036854775810:9223372036854775809 # numbers close to 2^64 18446744073709551614:18446744073709551613 18446744073709551615:18446744073709551614 18446744073709551616:18446744073709551615 18446744073709551617:18446744073709551616 18446744073709551618:18446744073709551617 # numbers close to 2^65 36893488147419103230:36893488147419103229 36893488147419103231:36893488147419103230 36893488147419103232:36893488147419103231 36893488147419103233:36893488147419103232 36893488147419103234:36893488147419103233 # numbers close to 2^66 73786976294838206462:73786976294838206461 73786976294838206463:73786976294838206462 73786976294838206464:73786976294838206463 73786976294838206465:73786976294838206464 73786976294838206466:73786976294838206465 # numbers close to 2^67 147573952589676412926:147573952589676412925 147573952589676412927:147573952589676412926 147573952589676412928:147573952589676412927 147573952589676412929:147573952589676412928 147573952589676412930:147573952589676412929 # numbers close to 2^68 295147905179352825854:295147905179352825853 295147905179352825855:295147905179352825854 295147905179352825856:295147905179352825855 295147905179352825857:295147905179352825856 295147905179352825858:295147905179352825857 # numbers close to 2^69 590295810358705651710:590295810358705651709 590295810358705651711:590295810358705651710 590295810358705651712:590295810358705651711 590295810358705651713:590295810358705651712 590295810358705651714:590295810358705651713 # numbers close to 2^70 1180591620717411303422:1180591620717411303421 1180591620717411303423:1180591620717411303422 1180591620717411303424:1180591620717411303423 1180591620717411303425:1180591620717411303424 1180591620717411303426:1180591620717411303425 # numbers close to 2^71 2361183241434822606846:2361183241434822606845 2361183241434822606847:2361183241434822606846 2361183241434822606848:2361183241434822606847 2361183241434822606849:2361183241434822606848 2361183241434822606850:2361183241434822606849 # numbers close to 2^72 4722366482869645213694:4722366482869645213693 4722366482869645213695:4722366482869645213694 4722366482869645213696:4722366482869645213695 4722366482869645213697:4722366482869645213696 4722366482869645213698:4722366482869645213697 # numbers close to 2^73 9444732965739290427390:9444732965739290427389 9444732965739290427391:9444732965739290427390 9444732965739290427392:9444732965739290427391 9444732965739290427393:9444732965739290427392 9444732965739290427394:9444732965739290427393 # numbers close to 2^74 18889465931478580854782:18889465931478580854781 18889465931478580854783:18889465931478580854782 18889465931478580854784:18889465931478580854783 18889465931478580854785:18889465931478580854784 18889465931478580854786:18889465931478580854785 # numbers close to 2^75 37778931862957161709566:37778931862957161709565 37778931862957161709567:37778931862957161709566 37778931862957161709568:37778931862957161709567 37778931862957161709569:37778931862957161709568 37778931862957161709570:37778931862957161709569 # numbers close to 2^76 75557863725914323419134:75557863725914323419133 75557863725914323419135:75557863725914323419134 75557863725914323419136:75557863725914323419135 75557863725914323419137:75557863725914323419136 75557863725914323419138:75557863725914323419137 # numbers close to 2^77 151115727451828646838270:151115727451828646838269 151115727451828646838271:151115727451828646838270 151115727451828646838272:151115727451828646838271 151115727451828646838273:151115727451828646838272 151115727451828646838274:151115727451828646838273 # numbers close to 2^78 302231454903657293676542:302231454903657293676541 302231454903657293676543:302231454903657293676542 302231454903657293676544:302231454903657293676543 302231454903657293676545:302231454903657293676544 302231454903657293676546:302231454903657293676545 # numbers close to 2^79 604462909807314587353086:604462909807314587353085 604462909807314587353087:604462909807314587353086 604462909807314587353088:604462909807314587353087 604462909807314587353089:604462909807314587353088 604462909807314587353090:604462909807314587353089 # numbers close to 2^80 1208925819614629174706174:1208925819614629174706173 1208925819614629174706175:1208925819614629174706174 1208925819614629174706176:1208925819614629174706175 1208925819614629174706177:1208925819614629174706176 1208925819614629174706178:1208925819614629174706177 # numbers close to 2^81 2417851639229258349412350:2417851639229258349412349 2417851639229258349412351:2417851639229258349412350 2417851639229258349412352:2417851639229258349412351 2417851639229258349412353:2417851639229258349412352 2417851639229258349412354:2417851639229258349412353 # numbers close to 2^82 4835703278458516698824702:4835703278458516698824701 4835703278458516698824703:4835703278458516698824702 4835703278458516698824704:4835703278458516698824703 4835703278458516698824705:4835703278458516698824704 4835703278458516698824706:4835703278458516698824705 # numbers close to 2^83 9671406556917033397649406:9671406556917033397649405 9671406556917033397649407:9671406556917033397649406 9671406556917033397649408:9671406556917033397649407 9671406556917033397649409:9671406556917033397649408 9671406556917033397649410:9671406556917033397649409 # numbers close to 2^84 19342813113834066795298814:19342813113834066795298813 19342813113834066795298815:19342813113834066795298814 19342813113834066795298816:19342813113834066795298815 19342813113834066795298817:19342813113834066795298816 19342813113834066795298818:19342813113834066795298817 # numbers close to 2^85 38685626227668133590597630:38685626227668133590597629 38685626227668133590597631:38685626227668133590597630 38685626227668133590597632:38685626227668133590597631 38685626227668133590597633:38685626227668133590597632 38685626227668133590597634:38685626227668133590597633 # numbers close to 2^86 77371252455336267181195262:77371252455336267181195261 77371252455336267181195263:77371252455336267181195262 77371252455336267181195264:77371252455336267181195263 77371252455336267181195265:77371252455336267181195264 77371252455336267181195266:77371252455336267181195265 # numbers close to 2^87 154742504910672534362390526:154742504910672534362390525 154742504910672534362390527:154742504910672534362390526 154742504910672534362390528:154742504910672534362390527 154742504910672534362390529:154742504910672534362390528 154742504910672534362390530:154742504910672534362390529 # numbers close to 2^88 309485009821345068724781054:309485009821345068724781053 309485009821345068724781055:309485009821345068724781054 309485009821345068724781056:309485009821345068724781055 309485009821345068724781057:309485009821345068724781056 309485009821345068724781058:309485009821345068724781057 # numbers close to 2^89 618970019642690137449562110:618970019642690137449562109 618970019642690137449562111:618970019642690137449562110 618970019642690137449562112:618970019642690137449562111 618970019642690137449562113:618970019642690137449562112 618970019642690137449562114:618970019642690137449562113 # numbers close to 2^90 1237940039285380274899124222:1237940039285380274899124221 1237940039285380274899124223:1237940039285380274899124222 1237940039285380274899124224:1237940039285380274899124223 1237940039285380274899124225:1237940039285380274899124224 1237940039285380274899124226:1237940039285380274899124225 # numbers close to 2^91 2475880078570760549798248446:2475880078570760549798248445 2475880078570760549798248447:2475880078570760549798248446 2475880078570760549798248448:2475880078570760549798248447 2475880078570760549798248449:2475880078570760549798248448 2475880078570760549798248450:2475880078570760549798248449 # numbers close to 2^92 4951760157141521099596496894:4951760157141521099596496893 4951760157141521099596496895:4951760157141521099596496894 4951760157141521099596496896:4951760157141521099596496895 4951760157141521099596496897:4951760157141521099596496896 4951760157141521099596496898:4951760157141521099596496897 # numbers close to 2^93 9903520314283042199192993790:9903520314283042199192993789 9903520314283042199192993791:9903520314283042199192993790 9903520314283042199192993792:9903520314283042199192993791 9903520314283042199192993793:9903520314283042199192993792 9903520314283042199192993794:9903520314283042199192993793 # numbers close to 2^94 19807040628566084398385987582:19807040628566084398385987581 19807040628566084398385987583:19807040628566084398385987582 19807040628566084398385987584:19807040628566084398385987583 19807040628566084398385987585:19807040628566084398385987584 19807040628566084398385987586:19807040628566084398385987585 # numbers close to 2^95 39614081257132168796771975166:39614081257132168796771975165 39614081257132168796771975167:39614081257132168796771975166 39614081257132168796771975168:39614081257132168796771975167 39614081257132168796771975169:39614081257132168796771975168 39614081257132168796771975170:39614081257132168796771975169 # numbers close to 2^96 79228162514264337593543950334:79228162514264337593543950333 79228162514264337593543950335:79228162514264337593543950334 79228162514264337593543950336:79228162514264337593543950335 79228162514264337593543950337:79228162514264337593543950336 79228162514264337593543950338:79228162514264337593543950337 # numbers close to 2^97 158456325028528675187087900670:158456325028528675187087900669 158456325028528675187087900671:158456325028528675187087900670 158456325028528675187087900672:158456325028528675187087900671 158456325028528675187087900673:158456325028528675187087900672 158456325028528675187087900674:158456325028528675187087900673 # numbers close to 2^98 316912650057057350374175801342:316912650057057350374175801341 316912650057057350374175801343:316912650057057350374175801342 316912650057057350374175801344:316912650057057350374175801343 316912650057057350374175801345:316912650057057350374175801344 316912650057057350374175801346:316912650057057350374175801345 # numbers close to 2^99 633825300114114700748351602686:633825300114114700748351602685 633825300114114700748351602687:633825300114114700748351602686 633825300114114700748351602688:633825300114114700748351602687 633825300114114700748351602689:633825300114114700748351602688 633825300114114700748351602690:633825300114114700748351602689 # numbers close to 2^100 1267650600228229401496703205374:1267650600228229401496703205373 1267650600228229401496703205375:1267650600228229401496703205374 1267650600228229401496703205376:1267650600228229401496703205375 1267650600228229401496703205377:1267650600228229401496703205376 1267650600228229401496703205378:1267650600228229401496703205377 # numbers close to 2^101 2535301200456458802993406410750:2535301200456458802993406410749 2535301200456458802993406410751:2535301200456458802993406410750 2535301200456458802993406410752:2535301200456458802993406410751 2535301200456458802993406410753:2535301200456458802993406410752 2535301200456458802993406410754:2535301200456458802993406410753 # numbers close to 2^102 5070602400912917605986812821502:5070602400912917605986812821501 5070602400912917605986812821503:5070602400912917605986812821502 5070602400912917605986812821504:5070602400912917605986812821503 5070602400912917605986812821505:5070602400912917605986812821504 5070602400912917605986812821506:5070602400912917605986812821505 # numbers close to 2^103 10141204801825835211973625643006:10141204801825835211973625643005 10141204801825835211973625643007:10141204801825835211973625643006 10141204801825835211973625643008:10141204801825835211973625643007 10141204801825835211973625643009:10141204801825835211973625643008 10141204801825835211973625643010:10141204801825835211973625643009 # numbers close to 2^104 20282409603651670423947251286014:20282409603651670423947251286013 20282409603651670423947251286015:20282409603651670423947251286014 20282409603651670423947251286016:20282409603651670423947251286015 20282409603651670423947251286017:20282409603651670423947251286016 20282409603651670423947251286018:20282409603651670423947251286017 # numbers close to 2^105 40564819207303340847894502572030:40564819207303340847894502572029 40564819207303340847894502572031:40564819207303340847894502572030 40564819207303340847894502572032:40564819207303340847894502572031 40564819207303340847894502572033:40564819207303340847894502572032 40564819207303340847894502572034:40564819207303340847894502572033 # numbers close to 2^106 81129638414606681695789005144062:81129638414606681695789005144061 81129638414606681695789005144063:81129638414606681695789005144062 81129638414606681695789005144064:81129638414606681695789005144063 81129638414606681695789005144065:81129638414606681695789005144064 81129638414606681695789005144066:81129638414606681695789005144065 # numbers close to 2^107 162259276829213363391578010288126:162259276829213363391578010288125 162259276829213363391578010288127:162259276829213363391578010288126 162259276829213363391578010288128:162259276829213363391578010288127 162259276829213363391578010288129:162259276829213363391578010288128 162259276829213363391578010288130:162259276829213363391578010288129 # numbers close to 2^108 324518553658426726783156020576254:324518553658426726783156020576253 324518553658426726783156020576255:324518553658426726783156020576254 324518553658426726783156020576256:324518553658426726783156020576255 324518553658426726783156020576257:324518553658426726783156020576256 324518553658426726783156020576258:324518553658426726783156020576257 # numbers close to 2^109 649037107316853453566312041152510:649037107316853453566312041152509 649037107316853453566312041152511:649037107316853453566312041152510 649037107316853453566312041152512:649037107316853453566312041152511 649037107316853453566312041152513:649037107316853453566312041152512 649037107316853453566312041152514:649037107316853453566312041152513 # numbers close to 2^110 1298074214633706907132624082305022:1298074214633706907132624082305021 1298074214633706907132624082305023:1298074214633706907132624082305022 1298074214633706907132624082305024:1298074214633706907132624082305023 1298074214633706907132624082305025:1298074214633706907132624082305024 1298074214633706907132624082305026:1298074214633706907132624082305025 # numbers close to 2^111 2596148429267413814265248164610046:2596148429267413814265248164610045 2596148429267413814265248164610047:2596148429267413814265248164610046 2596148429267413814265248164610048:2596148429267413814265248164610047 2596148429267413814265248164610049:2596148429267413814265248164610048 2596148429267413814265248164610050:2596148429267413814265248164610049 # numbers close to 2^112 5192296858534827628530496329220094:5192296858534827628530496329220093 5192296858534827628530496329220095:5192296858534827628530496329220094 5192296858534827628530496329220096:5192296858534827628530496329220095 5192296858534827628530496329220097:5192296858534827628530496329220096 5192296858534827628530496329220098:5192296858534827628530496329220097 # numbers close to 2^113 10384593717069655257060992658440190:10384593717069655257060992658440189 10384593717069655257060992658440191:10384593717069655257060992658440190 10384593717069655257060992658440192:10384593717069655257060992658440191 10384593717069655257060992658440193:10384593717069655257060992658440192 10384593717069655257060992658440194:10384593717069655257060992658440193 # numbers close to 2^114 20769187434139310514121985316880382:20769187434139310514121985316880381 20769187434139310514121985316880383:20769187434139310514121985316880382 20769187434139310514121985316880384:20769187434139310514121985316880383 20769187434139310514121985316880385:20769187434139310514121985316880384 20769187434139310514121985316880386:20769187434139310514121985316880385 # numbers close to 2^115 41538374868278621028243970633760766:41538374868278621028243970633760765 41538374868278621028243970633760767:41538374868278621028243970633760766 41538374868278621028243970633760768:41538374868278621028243970633760767 41538374868278621028243970633760769:41538374868278621028243970633760768 41538374868278621028243970633760770:41538374868278621028243970633760769 # numbers close to 2^116 83076749736557242056487941267521534:83076749736557242056487941267521533 83076749736557242056487941267521535:83076749736557242056487941267521534 83076749736557242056487941267521536:83076749736557242056487941267521535 83076749736557242056487941267521537:83076749736557242056487941267521536 83076749736557242056487941267521538:83076749736557242056487941267521537 # numbers close to 2^117 166153499473114484112975882535043070:166153499473114484112975882535043069 166153499473114484112975882535043071:166153499473114484112975882535043070 166153499473114484112975882535043072:166153499473114484112975882535043071 166153499473114484112975882535043073:166153499473114484112975882535043072 166153499473114484112975882535043074:166153499473114484112975882535043073 # numbers close to 2^118 332306998946228968225951765070086142:332306998946228968225951765070086141 332306998946228968225951765070086143:332306998946228968225951765070086142 332306998946228968225951765070086144:332306998946228968225951765070086143 332306998946228968225951765070086145:332306998946228968225951765070086144 332306998946228968225951765070086146:332306998946228968225951765070086145 # numbers close to 2^119 664613997892457936451903530140172286:664613997892457936451903530140172285 664613997892457936451903530140172287:664613997892457936451903530140172286 664613997892457936451903530140172288:664613997892457936451903530140172287 664613997892457936451903530140172289:664613997892457936451903530140172288 664613997892457936451903530140172290:664613997892457936451903530140172289 # numbers close to 2^120 1329227995784915872903807060280344574:1329227995784915872903807060280344573 1329227995784915872903807060280344575:1329227995784915872903807060280344574 1329227995784915872903807060280344576:1329227995784915872903807060280344575 1329227995784915872903807060280344577:1329227995784915872903807060280344576 1329227995784915872903807060280344578:1329227995784915872903807060280344577 # numbers close to 2^121 2658455991569831745807614120560689150:2658455991569831745807614120560689149 2658455991569831745807614120560689151:2658455991569831745807614120560689150 2658455991569831745807614120560689152:2658455991569831745807614120560689151 2658455991569831745807614120560689153:2658455991569831745807614120560689152 2658455991569831745807614120560689154:2658455991569831745807614120560689153 # numbers close to 2^122 5316911983139663491615228241121378302:5316911983139663491615228241121378301 5316911983139663491615228241121378303:5316911983139663491615228241121378302 5316911983139663491615228241121378304:5316911983139663491615228241121378303 5316911983139663491615228241121378305:5316911983139663491615228241121378304 5316911983139663491615228241121378306:5316911983139663491615228241121378305 # numbers close to 2^123 10633823966279326983230456482242756606:10633823966279326983230456482242756605 10633823966279326983230456482242756607:10633823966279326983230456482242756606 10633823966279326983230456482242756608:10633823966279326983230456482242756607 10633823966279326983230456482242756609:10633823966279326983230456482242756608 10633823966279326983230456482242756610:10633823966279326983230456482242756609 # numbers close to 2^124 21267647932558653966460912964485513214:21267647932558653966460912964485513213 21267647932558653966460912964485513215:21267647932558653966460912964485513214 21267647932558653966460912964485513216:21267647932558653966460912964485513215 21267647932558653966460912964485513217:21267647932558653966460912964485513216 21267647932558653966460912964485513218:21267647932558653966460912964485513217 # numbers close to 2^125 42535295865117307932921825928971026430:42535295865117307932921825928971026429 42535295865117307932921825928971026431:42535295865117307932921825928971026430 42535295865117307932921825928971026432:42535295865117307932921825928971026431 42535295865117307932921825928971026433:42535295865117307932921825928971026432 42535295865117307932921825928971026434:42535295865117307932921825928971026433 # numbers close to 2^126 85070591730234615865843651857942052862:85070591730234615865843651857942052861 85070591730234615865843651857942052863:85070591730234615865843651857942052862 85070591730234615865843651857942052864:85070591730234615865843651857942052863 85070591730234615865843651857942052865:85070591730234615865843651857942052864 85070591730234615865843651857942052866:85070591730234615865843651857942052865 # numbers close to 2^127 170141183460469231731687303715884105726:170141183460469231731687303715884105725 170141183460469231731687303715884105727:170141183460469231731687303715884105726 170141183460469231731687303715884105728:170141183460469231731687303715884105727 170141183460469231731687303715884105729:170141183460469231731687303715884105728 170141183460469231731687303715884105730:170141183460469231731687303715884105729 # numbers close to 2^128 340282366920938463463374607431768211454:340282366920938463463374607431768211453 340282366920938463463374607431768211455:340282366920938463463374607431768211454 340282366920938463463374607431768211456:340282366920938463463374607431768211455 340282366920938463463374607431768211457:340282366920938463463374607431768211456 340282366920938463463374607431768211458:340282366920938463463374607431768211457 # numbers close to 2^129 680564733841876926926749214863536422910:680564733841876926926749214863536422909 680564733841876926926749214863536422911:680564733841876926926749214863536422910 680564733841876926926749214863536422912:680564733841876926926749214863536422911 680564733841876926926749214863536422913:680564733841876926926749214863536422912 680564733841876926926749214863536422914:680564733841876926926749214863536422913 # numbers close to 2^130 1361129467683753853853498429727072845822:1361129467683753853853498429727072845821 1361129467683753853853498429727072845823:1361129467683753853853498429727072845822 1361129467683753853853498429727072845824:1361129467683753853853498429727072845823 1361129467683753853853498429727072845825:1361129467683753853853498429727072845824 1361129467683753853853498429727072845826:1361129467683753853853498429727072845825 # numbers close to 2^131 2722258935367507707706996859454145691646:2722258935367507707706996859454145691645 2722258935367507707706996859454145691647:2722258935367507707706996859454145691646 2722258935367507707706996859454145691648:2722258935367507707706996859454145691647 2722258935367507707706996859454145691649:2722258935367507707706996859454145691648 2722258935367507707706996859454145691650:2722258935367507707706996859454145691649 # numbers close to 2^132 5444517870735015415413993718908291383294:5444517870735015415413993718908291383293 5444517870735015415413993718908291383295:5444517870735015415413993718908291383294 5444517870735015415413993718908291383296:5444517870735015415413993718908291383295 5444517870735015415413993718908291383297:5444517870735015415413993718908291383296 5444517870735015415413993718908291383298:5444517870735015415413993718908291383297 # numbers close to 2^133 10889035741470030830827987437816582766590:10889035741470030830827987437816582766589 10889035741470030830827987437816582766591:10889035741470030830827987437816582766590 10889035741470030830827987437816582766592:10889035741470030830827987437816582766591 10889035741470030830827987437816582766593:10889035741470030830827987437816582766592 10889035741470030830827987437816582766594:10889035741470030830827987437816582766593 # numbers close to 2^134 21778071482940061661655974875633165533182:21778071482940061661655974875633165533181 21778071482940061661655974875633165533183:21778071482940061661655974875633165533182 21778071482940061661655974875633165533184:21778071482940061661655974875633165533183 21778071482940061661655974875633165533185:21778071482940061661655974875633165533184 21778071482940061661655974875633165533186:21778071482940061661655974875633165533185 # numbers close to 2^135 43556142965880123323311949751266331066366:43556142965880123323311949751266331066365 43556142965880123323311949751266331066367:43556142965880123323311949751266331066366 43556142965880123323311949751266331066368:43556142965880123323311949751266331066367 43556142965880123323311949751266331066369:43556142965880123323311949751266331066368 43556142965880123323311949751266331066370:43556142965880123323311949751266331066369 # numbers close to 2^136 87112285931760246646623899502532662132734:87112285931760246646623899502532662132733 87112285931760246646623899502532662132735:87112285931760246646623899502532662132734 87112285931760246646623899502532662132736:87112285931760246646623899502532662132735 87112285931760246646623899502532662132737:87112285931760246646623899502532662132736 87112285931760246646623899502532662132738:87112285931760246646623899502532662132737 # numbers close to 2^137 174224571863520493293247799005065324265470:174224571863520493293247799005065324265469 174224571863520493293247799005065324265471:174224571863520493293247799005065324265470 174224571863520493293247799005065324265472:174224571863520493293247799005065324265471 174224571863520493293247799005065324265473:174224571863520493293247799005065324265472 174224571863520493293247799005065324265474:174224571863520493293247799005065324265473 # numbers close to 2^138 348449143727040986586495598010130648530942:348449143727040986586495598010130648530941 348449143727040986586495598010130648530943:348449143727040986586495598010130648530942 348449143727040986586495598010130648530944:348449143727040986586495598010130648530943 348449143727040986586495598010130648530945:348449143727040986586495598010130648530944 348449143727040986586495598010130648530946:348449143727040986586495598010130648530945 # numbers close to 2^139 696898287454081973172991196020261297061886:696898287454081973172991196020261297061885 696898287454081973172991196020261297061887:696898287454081973172991196020261297061886 696898287454081973172991196020261297061888:696898287454081973172991196020261297061887 696898287454081973172991196020261297061889:696898287454081973172991196020261297061888 696898287454081973172991196020261297061890:696898287454081973172991196020261297061889 # numbers close to 2^140 1393796574908163946345982392040522594123774:1393796574908163946345982392040522594123773 1393796574908163946345982392040522594123775:1393796574908163946345982392040522594123774 1393796574908163946345982392040522594123776:1393796574908163946345982392040522594123775 1393796574908163946345982392040522594123777:1393796574908163946345982392040522594123776 1393796574908163946345982392040522594123778:1393796574908163946345982392040522594123777 # numbers close to 2^141 2787593149816327892691964784081045188247550:2787593149816327892691964784081045188247549 2787593149816327892691964784081045188247551:2787593149816327892691964784081045188247550 2787593149816327892691964784081045188247552:2787593149816327892691964784081045188247551 2787593149816327892691964784081045188247553:2787593149816327892691964784081045188247552 2787593149816327892691964784081045188247554:2787593149816327892691964784081045188247553 # numbers close to 2^142 5575186299632655785383929568162090376495102:5575186299632655785383929568162090376495101 5575186299632655785383929568162090376495103:5575186299632655785383929568162090376495102 5575186299632655785383929568162090376495104:5575186299632655785383929568162090376495103 5575186299632655785383929568162090376495105:5575186299632655785383929568162090376495104 5575186299632655785383929568162090376495106:5575186299632655785383929568162090376495105 # numbers close to 2^143 11150372599265311570767859136324180752990206:11150372599265311570767859136324180752990205 11150372599265311570767859136324180752990207:11150372599265311570767859136324180752990206 11150372599265311570767859136324180752990208:11150372599265311570767859136324180752990207 11150372599265311570767859136324180752990209:11150372599265311570767859136324180752990208 11150372599265311570767859136324180752990210:11150372599265311570767859136324180752990209 # numbers close to 2^144 22300745198530623141535718272648361505980414:22300745198530623141535718272648361505980413 22300745198530623141535718272648361505980415:22300745198530623141535718272648361505980414 22300745198530623141535718272648361505980416:22300745198530623141535718272648361505980415 22300745198530623141535718272648361505980417:22300745198530623141535718272648361505980416 22300745198530623141535718272648361505980418:22300745198530623141535718272648361505980417 # numbers close to 2^145 44601490397061246283071436545296723011960830:44601490397061246283071436545296723011960829 44601490397061246283071436545296723011960831:44601490397061246283071436545296723011960830 44601490397061246283071436545296723011960832:44601490397061246283071436545296723011960831 44601490397061246283071436545296723011960833:44601490397061246283071436545296723011960832 44601490397061246283071436545296723011960834:44601490397061246283071436545296723011960833 # numbers close to 2^146 89202980794122492566142873090593446023921662:89202980794122492566142873090593446023921661 89202980794122492566142873090593446023921663:89202980794122492566142873090593446023921662 89202980794122492566142873090593446023921664:89202980794122492566142873090593446023921663 89202980794122492566142873090593446023921665:89202980794122492566142873090593446023921664 89202980794122492566142873090593446023921666:89202980794122492566142873090593446023921665 # numbers close to 2^147 178405961588244985132285746181186892047843326:178405961588244985132285746181186892047843325 178405961588244985132285746181186892047843327:178405961588244985132285746181186892047843326 178405961588244985132285746181186892047843328:178405961588244985132285746181186892047843327 178405961588244985132285746181186892047843329:178405961588244985132285746181186892047843328 178405961588244985132285746181186892047843330:178405961588244985132285746181186892047843329 # numbers close to 2^148 356811923176489970264571492362373784095686654:356811923176489970264571492362373784095686653 356811923176489970264571492362373784095686655:356811923176489970264571492362373784095686654 356811923176489970264571492362373784095686656:356811923176489970264571492362373784095686655 356811923176489970264571492362373784095686657:356811923176489970264571492362373784095686656 356811923176489970264571492362373784095686658:356811923176489970264571492362373784095686657 # numbers close to 2^149 713623846352979940529142984724747568191373310:713623846352979940529142984724747568191373309 713623846352979940529142984724747568191373311:713623846352979940529142984724747568191373310 713623846352979940529142984724747568191373312:713623846352979940529142984724747568191373311 713623846352979940529142984724747568191373313:713623846352979940529142984724747568191373312 713623846352979940529142984724747568191373314:713623846352979940529142984724747568191373313 # numbers close to 2^150 1427247692705959881058285969449495136382746622:1427247692705959881058285969449495136382746621 1427247692705959881058285969449495136382746623:1427247692705959881058285969449495136382746622 1427247692705959881058285969449495136382746624:1427247692705959881058285969449495136382746623 1427247692705959881058285969449495136382746625:1427247692705959881058285969449495136382746624 1427247692705959881058285969449495136382746626:1427247692705959881058285969449495136382746625 Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_dec.t0000644403072340010010000000751313024051250023205 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5469; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_dec'); my @data; # Small numbers. for (my $x = 1; $x <= 512 ; ++ $x) { push @data, [ $x, $x - 1 ]; } # 11 - 1, 101 - 1, 1001 - 1, 10001 - 1, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "1" . ("0" x ($p - 1) . "1"); my $y = "1" . ("0" x $p); push @data, [ $x, $y ]; } # 10 - 1, 100 - 1, 1000 - 1, 10000 - 1, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "1" . ("0" x $p); my $y = ("9" x $p); push @data, [ $x, $y ]; } # 9 - 1, 99 - 1, 999 - 1, 9999 - 1, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "9" x $p; my $y = "9" x ($p - 1) . "8"; push @data, [ $x, $y ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_dec(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_dec() in list context: $test", sub { plan tests => 6, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_dec(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_dec() in scalar context: $test", sub { plan tests => 5, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_dfac.dat0000644403072340010010000002246313030261600023654 0ustar ospjadomain users0:1 1:1 2:2 3:3 4:8 5:15 6:48 7:105 8:384 9:945 10:3840 11:10395 12:46080 13:135135 14:645120 15:2027025 16:10321920 17:34459425 18:185794560 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Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 605; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_dfac'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_dfac(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_dfac() in list context: $test", sub { plan tests => 6, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_dfac(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_dfac() in scalar context: $test", sub { plan tests => 5, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_fac.dat0000644403072340010010000004342513012340550023513 0ustar ospjadomain users0:1 1:1 2:2 3:6 4:24 5:120 6:720 7:5040 8:40320 9:362880 10:3628800 11:39916800 12:479001600 13:6227020800 14:87178291200 15:1307674368000 16:20922789888000 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149:380892263763056972698595524350736933545970238573408427883655838887865527498969322620843829924502074302514052524979028027751108334657896696442372994639480443832950613971571859528835715269633083149369445271480789636247481797836800000000000000000000000000000000000 150:57133839564458545904789328652610540031895535786011264182548375833179829124845398393126574488675311145377107878746854204162666250198684504466355949195922066574942592095735778929325357290444962472405416790722118445437122269675520000000000000000000000000000000000000 Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_fac.t0000644403072340010010000000634213024051250023202 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 605; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_fac'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_fac(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_fac() in list context: $test", sub { plan tests => 6, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_fac(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_fac() in scalar context: $test", sub { plan tests => 5, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_inc.dat0000644403072340010010000011556413024050600023534 0ustar ospjadomain users# numbers close to 2^10 1022:1023 1023:1024 1024:1025 1025:1026 1026:1027 # numbers close to 2^11 2046:2047 2047:2048 2048:2049 2049:2050 2050:2051 # numbers close to 2^12 4094:4095 4095:4096 4096:4097 4097:4098 4098:4099 # numbers close to 2^13 8190:8191 8191:8192 8192:8193 8193:8194 8194:8195 # numbers close to 2^14 16382:16383 16383:16384 16384:16385 16385:16386 16386:16387 # numbers close to 2^15 32766:32767 32767:32768 32768:32769 32769:32770 32770:32771 # numbers close to 2^16 65534:65535 65535:65536 65536:65537 65537:65538 65538:65539 # numbers close to 2^17 131070:131071 131071:131072 131072:131073 131073:131074 131074:131075 # numbers close to 2^18 262142:262143 262143:262144 262144:262145 262145:262146 262146:262147 # numbers close to 2^19 524286:524287 524287:524288 524288:524289 524289:524290 524290:524291 # numbers close to 2^20 1048574:1048575 1048575:1048576 1048576:1048577 1048577:1048578 1048578:1048579 # numbers close to 2^21 2097150:2097151 2097151:2097152 2097152:2097153 2097153:2097154 2097154:2097155 # numbers close to 2^22 4194302:4194303 4194303:4194304 4194304:4194305 4194305:4194306 4194306:4194307 # numbers close to 2^23 8388606:8388607 8388607:8388608 8388608:8388609 8388609:8388610 8388610:8388611 # numbers close to 2^24 16777214:16777215 16777215:16777216 16777216:16777217 16777217:16777218 16777218:16777219 # numbers close to 2^25 33554430:33554431 33554431:33554432 33554432:33554433 33554433:33554434 33554434:33554435 # numbers close to 2^26 67108862:67108863 67108863:67108864 67108864:67108865 67108865:67108866 67108866:67108867 # numbers close to 2^27 134217726:134217727 134217727:134217728 134217728:134217729 134217729:134217730 134217730:134217731 # numbers close to 2^28 268435454:268435455 268435455:268435456 268435456:268435457 268435457:268435458 268435458:268435459 # numbers close to 2^29 536870910:536870911 536870911:536870912 536870912:536870913 536870913:536870914 536870914:536870915 # numbers close to 2^30 1073741822:1073741823 1073741823:1073741824 1073741824:1073741825 1073741825:1073741826 1073741826:1073741827 # numbers close to 2^31 2147483646:2147483647 2147483647:2147483648 2147483648:2147483649 2147483649:2147483650 2147483650:2147483651 # numbers close to 2^32 4294967294:4294967295 4294967295:4294967296 4294967296:4294967297 4294967297:4294967298 4294967298:4294967299 # numbers close to 2^33 8589934590:8589934591 8589934591:8589934592 8589934592:8589934593 8589934593:8589934594 8589934594:8589934595 # numbers close to 2^34 17179869182:17179869183 17179869183:17179869184 17179869184:17179869185 17179869185:17179869186 17179869186:17179869187 # numbers close to 2^35 34359738366:34359738367 34359738367:34359738368 34359738368:34359738369 34359738369:34359738370 34359738370:34359738371 # numbers close to 2^36 68719476734:68719476735 68719476735:68719476736 68719476736:68719476737 68719476737:68719476738 68719476738:68719476739 # numbers close to 2^37 137438953470:137438953471 137438953471:137438953472 137438953472:137438953473 137438953473:137438953474 137438953474:137438953475 # numbers close to 2^38 274877906942:274877906943 274877906943:274877906944 274877906944:274877906945 274877906945:274877906946 274877906946:274877906947 # numbers close to 2^39 549755813886:549755813887 549755813887:549755813888 549755813888:549755813889 549755813889:549755813890 549755813890:549755813891 # numbers close to 2^40 1099511627774:1099511627775 1099511627775:1099511627776 1099511627776:1099511627777 1099511627777:1099511627778 1099511627778:1099511627779 # numbers close to 2^41 2199023255550:2199023255551 2199023255551:2199023255552 2199023255552:2199023255553 2199023255553:2199023255554 2199023255554:2199023255555 # numbers close to 2^42 4398046511102:4398046511103 4398046511103:4398046511104 4398046511104:4398046511105 4398046511105:4398046511106 4398046511106:4398046511107 # numbers close to 2^43 8796093022206:8796093022207 8796093022207:8796093022208 8796093022208:8796093022209 8796093022209:8796093022210 8796093022210:8796093022211 # numbers close to 2^44 17592186044414:17592186044415 17592186044415:17592186044416 17592186044416:17592186044417 17592186044417:17592186044418 17592186044418:17592186044419 # numbers close to 2^45 35184372088830:35184372088831 35184372088831:35184372088832 35184372088832:35184372088833 35184372088833:35184372088834 35184372088834:35184372088835 # numbers close to 2^46 70368744177662:70368744177663 70368744177663:70368744177664 70368744177664:70368744177665 70368744177665:70368744177666 70368744177666:70368744177667 # numbers close to 2^47 140737488355326:140737488355327 140737488355327:140737488355328 140737488355328:140737488355329 140737488355329:140737488355330 140737488355330:140737488355331 # numbers close to 2^48 281474976710654:281474976710655 281474976710655:281474976710656 281474976710656:281474976710657 281474976710657:281474976710658 281474976710658:281474976710659 # numbers close to 2^49 562949953421310:562949953421311 562949953421311:562949953421312 562949953421312:562949953421313 562949953421313:562949953421314 562949953421314:562949953421315 # numbers close to 2^50 1125899906842622:1125899906842623 1125899906842623:1125899906842624 1125899906842624:1125899906842625 1125899906842625:1125899906842626 1125899906842626:1125899906842627 # numbers close to 2^51 2251799813685246:2251799813685247 2251799813685247:2251799813685248 2251799813685248:2251799813685249 2251799813685249:2251799813685250 2251799813685250:2251799813685251 # numbers close to 2^52 4503599627370494:4503599627370495 4503599627370495:4503599627370496 4503599627370496:4503599627370497 4503599627370497:4503599627370498 4503599627370498:4503599627370499 # numbers close to 2^53 9007199254740990:9007199254740991 9007199254740991:9007199254740992 9007199254740992:9007199254740993 9007199254740993:9007199254740994 9007199254740994:9007199254740995 # numbers close to 2^54 18014398509481982:18014398509481983 18014398509481983:18014398509481984 18014398509481984:18014398509481985 18014398509481985:18014398509481986 18014398509481986:18014398509481987 # numbers close to 2^55 36028797018963966:36028797018963967 36028797018963967:36028797018963968 36028797018963968:36028797018963969 36028797018963969:36028797018963970 36028797018963970:36028797018963971 # numbers close to 2^56 72057594037927934:72057594037927935 72057594037927935:72057594037927936 72057594037927936:72057594037927937 72057594037927937:72057594037927938 72057594037927938:72057594037927939 # numbers close to 2^57 144115188075855870:144115188075855871 144115188075855871:144115188075855872 144115188075855872:144115188075855873 144115188075855873:144115188075855874 144115188075855874:144115188075855875 # numbers close to 2^58 288230376151711742:288230376151711743 288230376151711743:288230376151711744 288230376151711744:288230376151711745 288230376151711745:288230376151711746 288230376151711746:288230376151711747 # numbers close to 2^59 576460752303423486:576460752303423487 576460752303423487:576460752303423488 576460752303423488:576460752303423489 576460752303423489:576460752303423490 576460752303423490:576460752303423491 # numbers close to 2^60 1152921504606846974:1152921504606846975 1152921504606846975:1152921504606846976 1152921504606846976:1152921504606846977 1152921504606846977:1152921504606846978 1152921504606846978:1152921504606846979 # numbers close to 2^61 2305843009213693950:2305843009213693951 2305843009213693951:2305843009213693952 2305843009213693952:2305843009213693953 2305843009213693953:2305843009213693954 2305843009213693954:2305843009213693955 # numbers close to 2^62 4611686018427387902:4611686018427387903 4611686018427387903:4611686018427387904 4611686018427387904:4611686018427387905 4611686018427387905:4611686018427387906 4611686018427387906:4611686018427387907 # numbers close to 2^63 9223372036854775806:9223372036854775807 9223372036854775807:9223372036854775808 9223372036854775808:9223372036854775809 9223372036854775809:9223372036854775810 9223372036854775810:9223372036854775811 # numbers close to 2^64 18446744073709551614:18446744073709551615 18446744073709551615:18446744073709551616 18446744073709551616:18446744073709551617 18446744073709551617:18446744073709551618 18446744073709551618:18446744073709551619 # numbers close to 2^65 36893488147419103230:36893488147419103231 36893488147419103231:36893488147419103232 36893488147419103232:36893488147419103233 36893488147419103233:36893488147419103234 36893488147419103234:36893488147419103235 # numbers close to 2^66 73786976294838206462:73786976294838206463 73786976294838206463:73786976294838206464 73786976294838206464:73786976294838206465 73786976294838206465:73786976294838206466 73786976294838206466:73786976294838206467 # numbers close to 2^67 147573952589676412926:147573952589676412927 147573952589676412927:147573952589676412928 147573952589676412928:147573952589676412929 147573952589676412929:147573952589676412930 147573952589676412930:147573952589676412931 # numbers close to 2^68 295147905179352825854:295147905179352825855 295147905179352825855:295147905179352825856 295147905179352825856:295147905179352825857 295147905179352825857:295147905179352825858 295147905179352825858:295147905179352825859 # numbers close to 2^69 590295810358705651710:590295810358705651711 590295810358705651711:590295810358705651712 590295810358705651712:590295810358705651713 590295810358705651713:590295810358705651714 590295810358705651714:590295810358705651715 # numbers close to 2^70 1180591620717411303422:1180591620717411303423 1180591620717411303423:1180591620717411303424 1180591620717411303424:1180591620717411303425 1180591620717411303425:1180591620717411303426 1180591620717411303426:1180591620717411303427 # numbers close to 2^71 2361183241434822606846:2361183241434822606847 2361183241434822606847:2361183241434822606848 2361183241434822606848:2361183241434822606849 2361183241434822606849:2361183241434822606850 2361183241434822606850:2361183241434822606851 # numbers close to 2^72 4722366482869645213694:4722366482869645213695 4722366482869645213695:4722366482869645213696 4722366482869645213696:4722366482869645213697 4722366482869645213697:4722366482869645213698 4722366482869645213698:4722366482869645213699 # numbers close to 2^73 9444732965739290427390:9444732965739290427391 9444732965739290427391:9444732965739290427392 9444732965739290427392:9444732965739290427393 9444732965739290427393:9444732965739290427394 9444732965739290427394:9444732965739290427395 # numbers close to 2^74 18889465931478580854782:18889465931478580854783 18889465931478580854783:18889465931478580854784 18889465931478580854784:18889465931478580854785 18889465931478580854785:18889465931478580854786 18889465931478580854786:18889465931478580854787 # numbers close to 2^75 37778931862957161709566:37778931862957161709567 37778931862957161709567:37778931862957161709568 37778931862957161709568:37778931862957161709569 37778931862957161709569:37778931862957161709570 37778931862957161709570:37778931862957161709571 # numbers close to 2^76 75557863725914323419134:75557863725914323419135 75557863725914323419135:75557863725914323419136 75557863725914323419136:75557863725914323419137 75557863725914323419137:75557863725914323419138 75557863725914323419138:75557863725914323419139 # numbers close to 2^77 151115727451828646838270:151115727451828646838271 151115727451828646838271:151115727451828646838272 151115727451828646838272:151115727451828646838273 151115727451828646838273:151115727451828646838274 151115727451828646838274:151115727451828646838275 # numbers close to 2^78 302231454903657293676542:302231454903657293676543 302231454903657293676543:302231454903657293676544 302231454903657293676544:302231454903657293676545 302231454903657293676545:302231454903657293676546 302231454903657293676546:302231454903657293676547 # numbers close to 2^79 604462909807314587353086:604462909807314587353087 604462909807314587353087:604462909807314587353088 604462909807314587353088:604462909807314587353089 604462909807314587353089:604462909807314587353090 604462909807314587353090:604462909807314587353091 # numbers close to 2^80 1208925819614629174706174:1208925819614629174706175 1208925819614629174706175:1208925819614629174706176 1208925819614629174706176:1208925819614629174706177 1208925819614629174706177:1208925819614629174706178 1208925819614629174706178:1208925819614629174706179 # numbers close to 2^81 2417851639229258349412350:2417851639229258349412351 2417851639229258349412351:2417851639229258349412352 2417851639229258349412352:2417851639229258349412353 2417851639229258349412353:2417851639229258349412354 2417851639229258349412354:2417851639229258349412355 # numbers close to 2^82 4835703278458516698824702:4835703278458516698824703 4835703278458516698824703:4835703278458516698824704 4835703278458516698824704:4835703278458516698824705 4835703278458516698824705:4835703278458516698824706 4835703278458516698824706:4835703278458516698824707 # numbers close to 2^83 9671406556917033397649406:9671406556917033397649407 9671406556917033397649407:9671406556917033397649408 9671406556917033397649408:9671406556917033397649409 9671406556917033397649409:9671406556917033397649410 9671406556917033397649410:9671406556917033397649411 # numbers close to 2^84 19342813113834066795298814:19342813113834066795298815 19342813113834066795298815:19342813113834066795298816 19342813113834066795298816:19342813113834066795298817 19342813113834066795298817:19342813113834066795298818 19342813113834066795298818:19342813113834066795298819 # numbers close to 2^85 38685626227668133590597630:38685626227668133590597631 38685626227668133590597631:38685626227668133590597632 38685626227668133590597632:38685626227668133590597633 38685626227668133590597633:38685626227668133590597634 38685626227668133590597634:38685626227668133590597635 # numbers close to 2^86 77371252455336267181195262:77371252455336267181195263 77371252455336267181195263:77371252455336267181195264 77371252455336267181195264:77371252455336267181195265 77371252455336267181195265:77371252455336267181195266 77371252455336267181195266:77371252455336267181195267 # numbers close to 2^87 154742504910672534362390526:154742504910672534362390527 154742504910672534362390527:154742504910672534362390528 154742504910672534362390528:154742504910672534362390529 154742504910672534362390529:154742504910672534362390530 154742504910672534362390530:154742504910672534362390531 # numbers close to 2^88 309485009821345068724781054:309485009821345068724781055 309485009821345068724781055:309485009821345068724781056 309485009821345068724781056:309485009821345068724781057 309485009821345068724781057:309485009821345068724781058 309485009821345068724781058:309485009821345068724781059 # numbers close to 2^89 618970019642690137449562110:618970019642690137449562111 618970019642690137449562111:618970019642690137449562112 618970019642690137449562112:618970019642690137449562113 618970019642690137449562113:618970019642690137449562114 618970019642690137449562114:618970019642690137449562115 # numbers close to 2^90 1237940039285380274899124222:1237940039285380274899124223 1237940039285380274899124223:1237940039285380274899124224 1237940039285380274899124224:1237940039285380274899124225 1237940039285380274899124225:1237940039285380274899124226 1237940039285380274899124226:1237940039285380274899124227 # numbers close to 2^91 2475880078570760549798248446:2475880078570760549798248447 2475880078570760549798248447:2475880078570760549798248448 2475880078570760549798248448:2475880078570760549798248449 2475880078570760549798248449:2475880078570760549798248450 2475880078570760549798248450:2475880078570760549798248451 # numbers close to 2^92 4951760157141521099596496894:4951760157141521099596496895 4951760157141521099596496895:4951760157141521099596496896 4951760157141521099596496896:4951760157141521099596496897 4951760157141521099596496897:4951760157141521099596496898 4951760157141521099596496898:4951760157141521099596496899 # numbers close to 2^93 9903520314283042199192993790:9903520314283042199192993791 9903520314283042199192993791:9903520314283042199192993792 9903520314283042199192993792:9903520314283042199192993793 9903520314283042199192993793:9903520314283042199192993794 9903520314283042199192993794:9903520314283042199192993795 # numbers close to 2^94 19807040628566084398385987582:19807040628566084398385987583 19807040628566084398385987583:19807040628566084398385987584 19807040628566084398385987584:19807040628566084398385987585 19807040628566084398385987585:19807040628566084398385987586 19807040628566084398385987586:19807040628566084398385987587 # numbers close to 2^95 39614081257132168796771975166:39614081257132168796771975167 39614081257132168796771975167:39614081257132168796771975168 39614081257132168796771975168:39614081257132168796771975169 39614081257132168796771975169:39614081257132168796771975170 39614081257132168796771975170:39614081257132168796771975171 # numbers close to 2^96 79228162514264337593543950334:79228162514264337593543950335 79228162514264337593543950335:79228162514264337593543950336 79228162514264337593543950336:79228162514264337593543950337 79228162514264337593543950337:79228162514264337593543950338 79228162514264337593543950338:79228162514264337593543950339 # numbers close to 2^97 158456325028528675187087900670:158456325028528675187087900671 158456325028528675187087900671:158456325028528675187087900672 158456325028528675187087900672:158456325028528675187087900673 158456325028528675187087900673:158456325028528675187087900674 158456325028528675187087900674:158456325028528675187087900675 # numbers close to 2^98 316912650057057350374175801342:316912650057057350374175801343 316912650057057350374175801343:316912650057057350374175801344 316912650057057350374175801344:316912650057057350374175801345 316912650057057350374175801345:316912650057057350374175801346 316912650057057350374175801346:316912650057057350374175801347 # numbers close to 2^99 633825300114114700748351602686:633825300114114700748351602687 633825300114114700748351602687:633825300114114700748351602688 633825300114114700748351602688:633825300114114700748351602689 633825300114114700748351602689:633825300114114700748351602690 633825300114114700748351602690:633825300114114700748351602691 # numbers close to 2^100 1267650600228229401496703205374:1267650600228229401496703205375 1267650600228229401496703205375:1267650600228229401496703205376 1267650600228229401496703205376:1267650600228229401496703205377 1267650600228229401496703205377:1267650600228229401496703205378 1267650600228229401496703205378:1267650600228229401496703205379 # numbers close to 2^101 2535301200456458802993406410750:2535301200456458802993406410751 2535301200456458802993406410751:2535301200456458802993406410752 2535301200456458802993406410752:2535301200456458802993406410753 2535301200456458802993406410753:2535301200456458802993406410754 2535301200456458802993406410754:2535301200456458802993406410755 # numbers close to 2^102 5070602400912917605986812821502:5070602400912917605986812821503 5070602400912917605986812821503:5070602400912917605986812821504 5070602400912917605986812821504:5070602400912917605986812821505 5070602400912917605986812821505:5070602400912917605986812821506 5070602400912917605986812821506:5070602400912917605986812821507 # numbers close to 2^103 10141204801825835211973625643006:10141204801825835211973625643007 10141204801825835211973625643007:10141204801825835211973625643008 10141204801825835211973625643008:10141204801825835211973625643009 10141204801825835211973625643009:10141204801825835211973625643010 10141204801825835211973625643010:10141204801825835211973625643011 # numbers close to 2^104 20282409603651670423947251286014:20282409603651670423947251286015 20282409603651670423947251286015:20282409603651670423947251286016 20282409603651670423947251286016:20282409603651670423947251286017 20282409603651670423947251286017:20282409603651670423947251286018 20282409603651670423947251286018:20282409603651670423947251286019 # numbers close to 2^105 40564819207303340847894502572030:40564819207303340847894502572031 40564819207303340847894502572031:40564819207303340847894502572032 40564819207303340847894502572032:40564819207303340847894502572033 40564819207303340847894502572033:40564819207303340847894502572034 40564819207303340847894502572034:40564819207303340847894502572035 # numbers close to 2^106 81129638414606681695789005144062:81129638414606681695789005144063 81129638414606681695789005144063:81129638414606681695789005144064 81129638414606681695789005144064:81129638414606681695789005144065 81129638414606681695789005144065:81129638414606681695789005144066 81129638414606681695789005144066:81129638414606681695789005144067 # numbers close to 2^107 162259276829213363391578010288126:162259276829213363391578010288127 162259276829213363391578010288127:162259276829213363391578010288128 162259276829213363391578010288128:162259276829213363391578010288129 162259276829213363391578010288129:162259276829213363391578010288130 162259276829213363391578010288130:162259276829213363391578010288131 # numbers close to 2^108 324518553658426726783156020576254:324518553658426726783156020576255 324518553658426726783156020576255:324518553658426726783156020576256 324518553658426726783156020576256:324518553658426726783156020576257 324518553658426726783156020576257:324518553658426726783156020576258 324518553658426726783156020576258:324518553658426726783156020576259 # numbers close to 2^109 649037107316853453566312041152510:649037107316853453566312041152511 649037107316853453566312041152511:649037107316853453566312041152512 649037107316853453566312041152512:649037107316853453566312041152513 649037107316853453566312041152513:649037107316853453566312041152514 649037107316853453566312041152514:649037107316853453566312041152515 # numbers close to 2^110 1298074214633706907132624082305022:1298074214633706907132624082305023 1298074214633706907132624082305023:1298074214633706907132624082305024 1298074214633706907132624082305024:1298074214633706907132624082305025 1298074214633706907132624082305025:1298074214633706907132624082305026 1298074214633706907132624082305026:1298074214633706907132624082305027 # numbers close to 2^111 2596148429267413814265248164610046:2596148429267413814265248164610047 2596148429267413814265248164610047:2596148429267413814265248164610048 2596148429267413814265248164610048:2596148429267413814265248164610049 2596148429267413814265248164610049:2596148429267413814265248164610050 2596148429267413814265248164610050:2596148429267413814265248164610051 # numbers close to 2^112 5192296858534827628530496329220094:5192296858534827628530496329220095 5192296858534827628530496329220095:5192296858534827628530496329220096 5192296858534827628530496329220096:5192296858534827628530496329220097 5192296858534827628530496329220097:5192296858534827628530496329220098 5192296858534827628530496329220098:5192296858534827628530496329220099 # numbers close to 2^113 10384593717069655257060992658440190:10384593717069655257060992658440191 10384593717069655257060992658440191:10384593717069655257060992658440192 10384593717069655257060992658440192:10384593717069655257060992658440193 10384593717069655257060992658440193:10384593717069655257060992658440194 10384593717069655257060992658440194:10384593717069655257060992658440195 # numbers close to 2^114 20769187434139310514121985316880382:20769187434139310514121985316880383 20769187434139310514121985316880383:20769187434139310514121985316880384 20769187434139310514121985316880384:20769187434139310514121985316880385 20769187434139310514121985316880385:20769187434139310514121985316880386 20769187434139310514121985316880386:20769187434139310514121985316880387 # numbers close to 2^115 41538374868278621028243970633760766:41538374868278621028243970633760767 41538374868278621028243970633760767:41538374868278621028243970633760768 41538374868278621028243970633760768:41538374868278621028243970633760769 41538374868278621028243970633760769:41538374868278621028243970633760770 41538374868278621028243970633760770:41538374868278621028243970633760771 # numbers close to 2^116 83076749736557242056487941267521534:83076749736557242056487941267521535 83076749736557242056487941267521535:83076749736557242056487941267521536 83076749736557242056487941267521536:83076749736557242056487941267521537 83076749736557242056487941267521537:83076749736557242056487941267521538 83076749736557242056487941267521538:83076749736557242056487941267521539 # numbers close to 2^117 166153499473114484112975882535043070:166153499473114484112975882535043071 166153499473114484112975882535043071:166153499473114484112975882535043072 166153499473114484112975882535043072:166153499473114484112975882535043073 166153499473114484112975882535043073:166153499473114484112975882535043074 166153499473114484112975882535043074:166153499473114484112975882535043075 # numbers close to 2^118 332306998946228968225951765070086142:332306998946228968225951765070086143 332306998946228968225951765070086143:332306998946228968225951765070086144 332306998946228968225951765070086144:332306998946228968225951765070086145 332306998946228968225951765070086145:332306998946228968225951765070086146 332306998946228968225951765070086146:332306998946228968225951765070086147 # numbers close to 2^119 664613997892457936451903530140172286:664613997892457936451903530140172287 664613997892457936451903530140172287:664613997892457936451903530140172288 664613997892457936451903530140172288:664613997892457936451903530140172289 664613997892457936451903530140172289:664613997892457936451903530140172290 664613997892457936451903530140172290:664613997892457936451903530140172291 # numbers close to 2^120 1329227995784915872903807060280344574:1329227995784915872903807060280344575 1329227995784915872903807060280344575:1329227995784915872903807060280344576 1329227995784915872903807060280344576:1329227995784915872903807060280344577 1329227995784915872903807060280344577:1329227995784915872903807060280344578 1329227995784915872903807060280344578:1329227995784915872903807060280344579 # numbers close to 2^121 2658455991569831745807614120560689150:2658455991569831745807614120560689151 2658455991569831745807614120560689151:2658455991569831745807614120560689152 2658455991569831745807614120560689152:2658455991569831745807614120560689153 2658455991569831745807614120560689153:2658455991569831745807614120560689154 2658455991569831745807614120560689154:2658455991569831745807614120560689155 # numbers close to 2^122 5316911983139663491615228241121378302:5316911983139663491615228241121378303 5316911983139663491615228241121378303:5316911983139663491615228241121378304 5316911983139663491615228241121378304:5316911983139663491615228241121378305 5316911983139663491615228241121378305:5316911983139663491615228241121378306 5316911983139663491615228241121378306:5316911983139663491615228241121378307 # numbers close to 2^123 10633823966279326983230456482242756606:10633823966279326983230456482242756607 10633823966279326983230456482242756607:10633823966279326983230456482242756608 10633823966279326983230456482242756608:10633823966279326983230456482242756609 10633823966279326983230456482242756609:10633823966279326983230456482242756610 10633823966279326983230456482242756610:10633823966279326983230456482242756611 # numbers close to 2^124 21267647932558653966460912964485513214:21267647932558653966460912964485513215 21267647932558653966460912964485513215:21267647932558653966460912964485513216 21267647932558653966460912964485513216:21267647932558653966460912964485513217 21267647932558653966460912964485513217:21267647932558653966460912964485513218 21267647932558653966460912964485513218:21267647932558653966460912964485513219 # numbers close to 2^125 42535295865117307932921825928971026430:42535295865117307932921825928971026431 42535295865117307932921825928971026431:42535295865117307932921825928971026432 42535295865117307932921825928971026432:42535295865117307932921825928971026433 42535295865117307932921825928971026433:42535295865117307932921825928971026434 42535295865117307932921825928971026434:42535295865117307932921825928971026435 # numbers close to 2^126 85070591730234615865843651857942052862:85070591730234615865843651857942052863 85070591730234615865843651857942052863:85070591730234615865843651857942052864 85070591730234615865843651857942052864:85070591730234615865843651857942052865 85070591730234615865843651857942052865:85070591730234615865843651857942052866 85070591730234615865843651857942052866:85070591730234615865843651857942052867 # numbers close to 2^127 170141183460469231731687303715884105726:170141183460469231731687303715884105727 170141183460469231731687303715884105727:170141183460469231731687303715884105728 170141183460469231731687303715884105728:170141183460469231731687303715884105729 170141183460469231731687303715884105729:170141183460469231731687303715884105730 170141183460469231731687303715884105730:170141183460469231731687303715884105731 # numbers close to 2^128 340282366920938463463374607431768211454:340282366920938463463374607431768211455 340282366920938463463374607431768211455:340282366920938463463374607431768211456 340282366920938463463374607431768211456:340282366920938463463374607431768211457 340282366920938463463374607431768211457:340282366920938463463374607431768211458 340282366920938463463374607431768211458:340282366920938463463374607431768211459 # numbers close to 2^129 680564733841876926926749214863536422910:680564733841876926926749214863536422911 680564733841876926926749214863536422911:680564733841876926926749214863536422912 680564733841876926926749214863536422912:680564733841876926926749214863536422913 680564733841876926926749214863536422913:680564733841876926926749214863536422914 680564733841876926926749214863536422914:680564733841876926926749214863536422915 # numbers close to 2^130 1361129467683753853853498429727072845822:1361129467683753853853498429727072845823 1361129467683753853853498429727072845823:1361129467683753853853498429727072845824 1361129467683753853853498429727072845824:1361129467683753853853498429727072845825 1361129467683753853853498429727072845825:1361129467683753853853498429727072845826 1361129467683753853853498429727072845826:1361129467683753853853498429727072845827 # numbers close to 2^131 2722258935367507707706996859454145691646:2722258935367507707706996859454145691647 2722258935367507707706996859454145691647:2722258935367507707706996859454145691648 2722258935367507707706996859454145691648:2722258935367507707706996859454145691649 2722258935367507707706996859454145691649:2722258935367507707706996859454145691650 2722258935367507707706996859454145691650:2722258935367507707706996859454145691651 # numbers close to 2^132 5444517870735015415413993718908291383294:5444517870735015415413993718908291383295 5444517870735015415413993718908291383295:5444517870735015415413993718908291383296 5444517870735015415413993718908291383296:5444517870735015415413993718908291383297 5444517870735015415413993718908291383297:5444517870735015415413993718908291383298 5444517870735015415413993718908291383298:5444517870735015415413993718908291383299 # numbers close to 2^133 10889035741470030830827987437816582766590:10889035741470030830827987437816582766591 10889035741470030830827987437816582766591:10889035741470030830827987437816582766592 10889035741470030830827987437816582766592:10889035741470030830827987437816582766593 10889035741470030830827987437816582766593:10889035741470030830827987437816582766594 10889035741470030830827987437816582766594:10889035741470030830827987437816582766595 # numbers close to 2^134 21778071482940061661655974875633165533182:21778071482940061661655974875633165533183 21778071482940061661655974875633165533183:21778071482940061661655974875633165533184 21778071482940061661655974875633165533184:21778071482940061661655974875633165533185 21778071482940061661655974875633165533185:21778071482940061661655974875633165533186 21778071482940061661655974875633165533186:21778071482940061661655974875633165533187 # numbers close to 2^135 43556142965880123323311949751266331066366:43556142965880123323311949751266331066367 43556142965880123323311949751266331066367:43556142965880123323311949751266331066368 43556142965880123323311949751266331066368:43556142965880123323311949751266331066369 43556142965880123323311949751266331066369:43556142965880123323311949751266331066370 43556142965880123323311949751266331066370:43556142965880123323311949751266331066371 # numbers close to 2^136 87112285931760246646623899502532662132734:87112285931760246646623899502532662132735 87112285931760246646623899502532662132735:87112285931760246646623899502532662132736 87112285931760246646623899502532662132736:87112285931760246646623899502532662132737 87112285931760246646623899502532662132737:87112285931760246646623899502532662132738 87112285931760246646623899502532662132738:87112285931760246646623899502532662132739 # numbers close to 2^137 174224571863520493293247799005065324265470:174224571863520493293247799005065324265471 174224571863520493293247799005065324265471:174224571863520493293247799005065324265472 174224571863520493293247799005065324265472:174224571863520493293247799005065324265473 174224571863520493293247799005065324265473:174224571863520493293247799005065324265474 174224571863520493293247799005065324265474:174224571863520493293247799005065324265475 # numbers close to 2^138 348449143727040986586495598010130648530942:348449143727040986586495598010130648530943 348449143727040986586495598010130648530943:348449143727040986586495598010130648530944 348449143727040986586495598010130648530944:348449143727040986586495598010130648530945 348449143727040986586495598010130648530945:348449143727040986586495598010130648530946 348449143727040986586495598010130648530946:348449143727040986586495598010130648530947 # numbers close to 2^139 696898287454081973172991196020261297061886:696898287454081973172991196020261297061887 696898287454081973172991196020261297061887:696898287454081973172991196020261297061888 696898287454081973172991196020261297061888:696898287454081973172991196020261297061889 696898287454081973172991196020261297061889:696898287454081973172991196020261297061890 696898287454081973172991196020261297061890:696898287454081973172991196020261297061891 # numbers close to 2^140 1393796574908163946345982392040522594123774:1393796574908163946345982392040522594123775 1393796574908163946345982392040522594123775:1393796574908163946345982392040522594123776 1393796574908163946345982392040522594123776:1393796574908163946345982392040522594123777 1393796574908163946345982392040522594123777:1393796574908163946345982392040522594123778 1393796574908163946345982392040522594123778:1393796574908163946345982392040522594123779 # numbers close to 2^141 2787593149816327892691964784081045188247550:2787593149816327892691964784081045188247551 2787593149816327892691964784081045188247551:2787593149816327892691964784081045188247552 2787593149816327892691964784081045188247552:2787593149816327892691964784081045188247553 2787593149816327892691964784081045188247553:2787593149816327892691964784081045188247554 2787593149816327892691964784081045188247554:2787593149816327892691964784081045188247555 # numbers close to 2^142 5575186299632655785383929568162090376495102:5575186299632655785383929568162090376495103 5575186299632655785383929568162090376495103:5575186299632655785383929568162090376495104 5575186299632655785383929568162090376495104:5575186299632655785383929568162090376495105 5575186299632655785383929568162090376495105:5575186299632655785383929568162090376495106 5575186299632655785383929568162090376495106:5575186299632655785383929568162090376495107 # numbers close to 2^143 11150372599265311570767859136324180752990206:11150372599265311570767859136324180752990207 11150372599265311570767859136324180752990207:11150372599265311570767859136324180752990208 11150372599265311570767859136324180752990208:11150372599265311570767859136324180752990209 11150372599265311570767859136324180752990209:11150372599265311570767859136324180752990210 11150372599265311570767859136324180752990210:11150372599265311570767859136324180752990211 # numbers close to 2^144 22300745198530623141535718272648361505980414:22300745198530623141535718272648361505980415 22300745198530623141535718272648361505980415:22300745198530623141535718272648361505980416 22300745198530623141535718272648361505980416:22300745198530623141535718272648361505980417 22300745198530623141535718272648361505980417:22300745198530623141535718272648361505980418 22300745198530623141535718272648361505980418:22300745198530623141535718272648361505980419 # numbers close to 2^145 44601490397061246283071436545296723011960830:44601490397061246283071436545296723011960831 44601490397061246283071436545296723011960831:44601490397061246283071436545296723011960832 44601490397061246283071436545296723011960832:44601490397061246283071436545296723011960833 44601490397061246283071436545296723011960833:44601490397061246283071436545296723011960834 44601490397061246283071436545296723011960834:44601490397061246283071436545296723011960835 # numbers close to 2^146 89202980794122492566142873090593446023921662:89202980794122492566142873090593446023921663 89202980794122492566142873090593446023921663:89202980794122492566142873090593446023921664 89202980794122492566142873090593446023921664:89202980794122492566142873090593446023921665 89202980794122492566142873090593446023921665:89202980794122492566142873090593446023921666 89202980794122492566142873090593446023921666:89202980794122492566142873090593446023921667 # numbers close to 2^147 178405961588244985132285746181186892047843326:178405961588244985132285746181186892047843327 178405961588244985132285746181186892047843327:178405961588244985132285746181186892047843328 178405961588244985132285746181186892047843328:178405961588244985132285746181186892047843329 178405961588244985132285746181186892047843329:178405961588244985132285746181186892047843330 178405961588244985132285746181186892047843330:178405961588244985132285746181186892047843331 # numbers close to 2^148 356811923176489970264571492362373784095686654:356811923176489970264571492362373784095686655 356811923176489970264571492362373784095686655:356811923176489970264571492362373784095686656 356811923176489970264571492362373784095686656:356811923176489970264571492362373784095686657 356811923176489970264571492362373784095686657:356811923176489970264571492362373784095686658 356811923176489970264571492362373784095686658:356811923176489970264571492362373784095686659 # numbers close to 2^149 713623846352979940529142984724747568191373310:713623846352979940529142984724747568191373311 713623846352979940529142984724747568191373311:713623846352979940529142984724747568191373312 713623846352979940529142984724747568191373312:713623846352979940529142984724747568191373313 713623846352979940529142984724747568191373313:713623846352979940529142984724747568191373314 713623846352979940529142984724747568191373314:713623846352979940529142984724747568191373315 # numbers close to 2^150 1427247692705959881058285969449495136382746622:1427247692705959881058285969449495136382746623 1427247692705959881058285969449495136382746623:1427247692705959881058285969449495136382746624 1427247692705959881058285969449495136382746624:1427247692705959881058285969449495136382746625 1427247692705959881058285969449495136382746625:1427247692705959881058285969449495136382746626 1427247692705959881058285969449495136382746626:1427247692705959881058285969449495136382746627 Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_inc.t0000644403072340010010000000754513024051250023230 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5473; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_inc'); my @data; # Small numbers. for (my $x = 0; $x <= 512 ; ++ $x) { push @data, [ $x, $x + 1 ]; } # 11 + 1, 101 + 1, 1001 + 1, 10001 + 1, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "1" . ("0" x ($p - 1) . "1"); my $y = "1" . ("0" x ($p - 1) . "2"); push @data, [ $x, $y ]; } # 10 + 1, 100 + 1, 1000 + 1, 10000 + 1, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "1" . ("0" x $p); my $y = "1" . ("0" x ($p - 1) . "1"); push @data, [ $x, $y ]; } # 9 + 1, 99 + 1, 999 + 1, 9999 + 1, ... for (my $p = 1; $p <= 50 ; ++ $p) { my $x = "9" x $p; my $y = "1" . ("0" x $p); push @data, [ $x, $y ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_inc(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_inc() in list context: $test", sub { plan tests => 6, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_inc(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_inc() in scalar context: $test", sub { plan tests => 5, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_sqrt.dat0000644403072340010010000023026013012340550023746 0ustar ospjadomain users7:2 5:2 1:1 5:2 5:2 6:2 5:2 3:1 6:2 6:2 13:3 72:8 36:6 57:7 43:6 10:3 44:6 14:3 55:7 34:5 203:14 575:23 304:17 626:25 241:15 275:16 536:23 575:23 133:11 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3770321060301037661677124763056634062551256551316063272360064320773726163207052525013740731063644066:61402940160069189163051308648575553177365592711427 Math-BigInt-1.999808/t/author-lib-arithmetic-unary-_sqrt.t0000644403072340010010000000762113024051250023443 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 14389; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_sqrt'); my @data; # Small numbers. for (my $x = 0; $x <= 2500 ; ++ $x) { push @data, [ $x, int sqrt $x ]; } # Powers of ten and nearby cases, e.g., # # 9999 ** (1/2) => 99 # 10000 ** (1/2) => 100 # 10001 ** (1/2) => 100 { my $max = 100; my $entry; for (my $e = 1 ; $e <= int($max / 2); ++ $e) { $entry = [ ("9" x ($e * 2)), "9" x $e ]; push @data, $entry if length("@$entry") < $max; $entry = [ "1" . ("0" x ($e * 2)), "1" . ("0" x $e) ]; push @data, $entry if length("@$entry") < $max; $entry = [ "1" . ("0" x ($e * 2 - 1)) . "1", "1" . ("0" x $e) ]; push @data, $entry if length("@$entry") < $max; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/; push @data, [ /^(\d+):(\d+)$/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_sqrt(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_sqrt() in list context: $test", sub { plan tests => 6, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_sqrt(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_sqrt() in scalar context: $test", sub { plan tests => 5, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); is(ref($x), $REF, "'$test' first input arg is still a $REF"); ok($LIB->_str($x) eq $out0 || $LIB->_str($x) eq $in0, "'$test' input arg has the correct value"); }; } Math-BigInt-1.999808/t/author-lib-bitwise-_and.dat0000644403072340010010000057140413012340550021710 0ustar ospjadomain users444:900:388 416:140:128 890:617:616 566:1144:48 308:5543:292 713:6613:193 594:13851:530 790:44486:262 716:33720:648 218:363375:74 804:440930:544 601:242176:512 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2056824815060073931140275:24320884551449455737:1154329018005466161 8724730784627171465408794:536512799610693014267:148762978213245784090 3722897056748306345719481:134379202843618474258:36921147465149345808 1782309787865569973172145:230609074528118610353:147576205782369604017 1195843465385684264759919:2306701411630115355017:1033722806933467049993 7147523397590999128219401:1413278087732286492843:221721252090918473737 3875390173107692764108536:1675793454880344039683:5786580507420557312 9291703987254308079375906:17655553300273732446318:16971582312755063324706 3580949287313319426952711:40420402712621296313202:205239168119020356098 7856991656416982554389507:83350401184663633691461:82647106677555763085313 6069364958537915393345103:921061764572410578555976:4884568131447201793096 5148745366159911912612440:481467413471119399989374:303412229206344022106200 7087245520577534008233521:206480243152023619629029:40293525784826772196897 1397400519586114828863973:3468519686659905796748368:30253823529311015043136 2343254365227623068781281:1070282352654792603710487:1058475490071503194587137 3373438295237690139856080:7161744932004629613143095:944665870494081577927696 Math-BigInt-1.999808/t/author-lib-bitwise-_and.t0000644403072340010010000001262113024051250021371 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 35945; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_and'); my @data; # Small numbers. for (my $x = 0; $x <= 64 ; ++ $x) { for (my $y = 0; $y <= 64 ; ++ $y) { push @data, [ $x, $y, $x & $y ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_and(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_and() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); if ($LIB->_str($x) eq $in0) { pass("'$test' first input value is unmodified"); } elsif ($LIB->_str($x) eq $out0) { pass("'$test' first input value is the output value"); } else { fail("'$test' first input value is neither unmodified nor the" . " output value"); diag(" got: '", $LIB->_str($x), "'"); if ($in0 eq $out0) { diag(" expected: '$in0' (first input and output value)"); } else { diag(" expected: '$in0' (first input value) or '$out0'", " (output value)"); } } is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_and(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_and() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); if ($LIB->_str($x) eq $in0) { pass("'$test' first input value is unmodified"); } elsif ($LIB->_str($x) eq $out0) { pass("'$test' first input value is the output value"); } else { fail("'$test' first input value is neither unmodified nor the" . " output value"); diag(" got: '", $LIB->_str($x), "'"); if ($in0 eq $out0) { diag(" expected: '$in0' (first input and output value)"); } else { diag(" expected: '$in0' (first input value) or '$out0'", " (output value)"); } } is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-bitwise-_or.dat0000644403072340010010000070613613012340550021570 0ustar ospjadomain users227:325:487 436:333:509 325:917:981 689:4553:5113 665:7474:8123 594:9379:9971 941:82085:82861 358:93609:93679 271:89450:89455 663:605406:605919 539:986448:986971 614:916493:917103 482:1902602:1903082 795:7971916:7972703 711:3213197:3213263 558:89649006:89649006 194:75293299:75293427 569:51237987:51238523 220:463858327:463858399 416:168017795:168017827 259:543472473:543472475 536:8664365174:8664365694 225:4367551515:4367551739 975:9354011770:9354012671 954:32569070976:32569071546 936:36009745555:36009746363 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6308580797918111301695060:1005863180279969984247751:7215775692974285273429975 Math-BigInt-1.999808/t/author-lib-bitwise-_or.t0000644403072340010010000001263713024051250021256 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 35945; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_or'); my @data; # Small numbers. for (my $x = 0; $x <= 64 ; ++ $x) { for (my $y = 0; $y <= 64 ; ++ $y) { push @data, [ $x, $y, $x | $y ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_or(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_or() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); if ($LIB->_str($x) eq $in0) { pass("'$test' first input value is unmodified"); } elsif ($LIB->_str($x) eq $out0) { pass("'$test' first input value is the output value"); } else { fail("'$test' first input value is neither unmodified nor the" . " output value"); diag(" got: '", $LIB->_str($x), "'"); if ($in0 eq $out0) { diag(" expected: '$in0' (first input and output value)"); } else { diag(" expected: '$in0' (first input value) or '$out0'", " (output value)"); } } is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_or(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_or() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); if ($LIB->_str($x) eq $in0) { pass("'$test' first input value is unmodified"); } elsif ($LIB->_str($x) eq $out0) { pass("'$test' first input value is the output value"); } else { fail("'$test' first input value is neither unmodified nor the" . " output value"); diag(" got: '", $LIB->_str($x), "'"); if ($in0 eq $out0) { diag(" expected: '$in0' (first input and output value)"); } else { diag(" expected: '$in0' (first input value) or '$out0'", " (output value)"); } } is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-bitwise-_xor.dat0000644403072340010010000070604313012340550021755 0ustar ospjadomain users225:956:861 536:589:85 288:997:709 933:4687:4586 793:6264:7009 498:3958:3716 204:87304:87492 978:60416:61394 146:15802:15656 886:962723:963541 781:417240:417493 728:577447:576895 382:4615683:4616061 224:6190429:6190525 164:3230398:3230234 361:61744220:61744437 776:85018356:85018108 817:63809096:63808889 353:966193761:966193920 719:998599474:998599165 548:801696624:801696084 710:4489757575:4489756993 584:5190381078:5190380638 856:5916359636:5916358796 898:18182229458:18182229584 980:83733933691:83733933487 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7899268309478540066548134:3234145585101621173420635:5007614486672208948489213 Math-BigInt-1.999808/t/author-lib-bitwise-_xor.t0000644403072340010010000001264413024051250021444 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 35945; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_xor'); my @data; # Small numbers. for (my $x = 0; $x <= 64 ; ++ $x) { for (my $y = 0; $y <= 64 ; ++ $y) { push @data, [ $x, $y, $x ^ $y ]; } } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_xor(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_xor() in list context: $test", sub { plan tests => $scalar_util_ok ? 9 : 8; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); if ($LIB->_str($x) eq $in0) { pass("'$test' first input value is unmodified"); } elsif ($LIB->_str($x) eq $out0) { pass("'$test' first input value is the output value"); } else { fail("'$test' first input value is neither unmodified nor the" . " output value"); diag(" got: '", $LIB->_str($x), "'"); if ($in0 eq $out0) { diag(" expected: '$in0' (first input and output value)"); } else { diag(" expected: '$in0' (first input value) or '$out0'", " (output value)"); } } is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_xor(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_xor() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 8 : 7; is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($y), "'$test' output arg is not the second input arg") if $scalar_util_ok; is(ref($x), $REF, "'$test' first input arg is still a $REF"); if ($LIB->_str($x) eq $in0) { pass("'$test' first input value is unmodified"); } elsif ($LIB->_str($x) eq $out0) { pass("'$test' first input value is the output value"); } else { fail("'$test' first input value is neither unmodified nor the" . " output value"); diag(" got: '", $LIB->_str($x), "'"); if ($in0 eq $out0) { diag(" expected: '$in0' (first input and output value)"); } else { diag(" expected: '$in0' (first input value) or '$out0'", " (output value)"); } } is(ref($y), $REF, "'$test' second input arg is still a $REF"); is($LIB->_str($y), $in1, "'$test' second input arg is unmodified"); }; } Math-BigInt-1.999808/t/author-lib-boolean-_is_even.t0000644403072340010010000000500213024051250022223 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 1597; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_is_even'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; for (my $x = 0 ; $x <= 100 ; ++ $x) { push @data, [ $x, $x % 2 == 0 ]; } for (my $n = 3 ; $n <= 300 ; ++ $n) { my $x = randstr($n, 10); # random big integer my $b = substr($x, -1, 1) % 2 == 0; push @data, [ $x, $b ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_is_even(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_even() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); ok($got[0] && $out0 || !$got[0] && !$out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_is_even(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_even() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); ok($got && $out0 || !$got && !$out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-boolean-_is_odd.t0000644403072340010010000000477513024051250022054 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 1597; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_is_odd'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; for (my $x = 0 ; $x <= 100 ; ++ $x) { push @data, [ $x, $x % 2 != 0 ]; } for (my $n = 3 ; $n <= 300 ; ++ $n) { my $x = randstr($n, 10); # random big integer my $b = substr($x, -1, 1) % 2 != 0; push @data, [ $x, $b ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_is_odd(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_odd() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); ok($got[0] && $out0 || !$got[0] && !$out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_is_odd(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_odd() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); ok($got && $out0 || !$got && !$out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-boolean-_is_one.t0000644403072340010010000000450413024051250022055 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 81; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_is_one'); # Generate test data. my @data; for (my $x = 0 ; $x <= 10 ; ++ $x) { push @data, [ $x, $x == 1 ]; } for (my $e = 2 ; $e <= 10 ; ++ $e) { my $x = "1" . ("0" x $e); push @data, [ $x, $x == 1 ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_is_one(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_one() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); ok($got[0] && $out0 || !$got[0] && !$out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_is_one(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_one() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); ok($got && $out0 || !$got && !$out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-boolean-_is_ten.t0000644403072340010010000000457013024051250022065 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 81; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_is_ten'); # Generate test data. my @data; for (my $x = 0 ; $x <= 10 ; ++ $x) { push @data, [ $x, $x == 10 ]; } for (my $e = 2 ; $e <= 10 ; ++ $e) { my $x = "1" . ("0" x $e); push @data, [ $x, $x == 10 ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_is_ten(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_ten() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); ok($got[0] && $out0 || !$got[0] && !$out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_is_ten(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_ten() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); ok($got && $out0 || !$got && !$out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-boolean-_is_two.t0000644403072340010010000000456613024051250022115 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 81; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_is_two'); # Generate test data. my @data; for (my $x = 0 ; $x <= 10 ; ++ $x) { push @data, [ $x, $x == 2 ]; } for (my $e = 2 ; $e <= 10 ; ++ $e) { my $x = "1" . ("0" x $e); push @data, [ $x, $x == 2 ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_is_two(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_two() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); ok($got[0] && $out0 || !$got[0] && !$out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_is_two(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_two() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); ok($got && $out0 || !$got && !$out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-boolean-_is_zero.t0000644403072340010010000000457313024051250022261 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 81; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_is_zero'); # Generate test data. my @data; for (my $x = 0 ; $x <= 10 ; ++ $x) { push @data, [ $x, $x == 0 ]; } for (my $e = 2 ; $e <= 10 ; ++ $e) { my $x = "1" . ("0" x $e); push @data, [ $x, $x == 0 ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_is_zero(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_zero() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); ok($got[0] && $out0 || !$got[0] && !$out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_is_zero(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_is_zero() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); ok($got && $out0 || !$got && !$out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-comparison-_acmp.t0000644403072340010010000000647113024051250022261 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5385; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; can_ok($LIB, '_acmp'); # Generate test data. my @data; # Small integers. for my $a (0 .. 10) { for my $b (0 .. 10) { push @data, [ $a, $b, $a <=> $b ]; } } # Integers close to a power of ten. for my $n (2 .. 26) { my $x = "9" x $n; # e.g., "9999" my $y = "1" . ("0" x $n); # e.g., "10000" my $z = "1" . ("0" x ($n - 1)) . "1"; # e.g., "10001" push @data, [ $x, $x, 0 ]; push @data, [ $x, $y, -1 ]; push @data, [ $x, $z, -1 ]; push @data, [ $y, $x, 1 ]; push @data, [ $y, $y, 0 ]; push @data, [ $y, $z, -1 ]; push @data, [ $z, $x, 1 ]; push @data, [ $z, $y, 1 ]; push @data, [ $z, $z, 0 ]; } # Random large integers. for (1 .. 1000) { my $na = 2 + int rand 35; # number of digits in $a my $nb = 2 + int rand 35; # number of digits in $a my $a = randstr($na, 10); # generate $a my $b = randstr($na, 10); # generate $b my $cmp = length($a) <=> length($b) || $a cmp $b; push @data, [ $a, $b, $cmp ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\@got = $LIB->_acmp(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_new() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' one output arg"); is(ref($got[0]), "", "'$test' output arg is a Perl scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $y, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$y = $LIB->_new("$in1"); | . qq|\$got = $LIB->_acmp(\$x, \$y);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_new() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a Perl scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-nullary-_one.t0000644403072340010010000000444313024051250024016 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_one'); my $out0 = '1'; # List context. { my @got; my $test = qq|\@got = $LIB->_one(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_one() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. { my $got; my $test = qq|\$got = $LIB->_one(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_one() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-nullary-_ten.t0000644403072340010010000000444413024051250024024 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_ten'); my $out0 = '10'; # List context. { my @got; my $test = qq|\@got = $LIB->_ten(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_ten() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. { my $got; my $test = qq|\$got = $LIB->_ten(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_ten() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-nullary-_two.t0000644403072340010010000000444313024051250024046 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_two'); my $out0 = '2'; # List context. { my @got; my $test = qq|\@got = $LIB->_two(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_two() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. { my $got; my $test = qq|\$got = $LIB->_two(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_two() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-nullary-_zero.t0000644403072340010010000000445013024051250024212 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_zero'); my $out0 = '0'; # List context. { my @got; my $test = qq|\@got = $LIB->_zero(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_zero() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. { my $got; my $test = qq|\$got = $LIB->_zero(); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_zero() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-unary-_copy.t0000644403072340010010000000653113024051250023657 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 1597; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### my $scalar_util_ok = eval { require Scalar::Util; }; Scalar::Util -> import('refaddr') if $scalar_util_ok; diag "Skipping some tests since Scalar::Util is not installed." unless $scalar_util_ok; can_ok($LIB, '_copy'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; for (my $x = 0 ; $x <= 100 ; ++ $x) { push @data, [ $x ]; } for (my $n = 3 ; $n <= 300 ; ++ $n) { my $x = randstr($n, 10); # random $n-digit integer push @data, [ $x ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0) = @{ $data[$i] }; my $out0 = $in0; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_copy(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_copy() in list context: $test", sub { plan tests => $scalar_util_ok ? 5 : 4, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); isnt(refaddr($got[0]), refaddr($x), "'$test' output arg is not the input arg") if $scalar_util_ok; }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0) = @{ $data[$i] }; my $out0 = $in0; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_copy(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_copy() in scalar context: $test", sub { plan tests => $scalar_util_ok ? 4 : 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); isnt(refaddr($got), refaddr($x), "'$test' output arg is not the input arg") if $scalar_util_ok; }; } Math-BigInt-1.999808/t/author-lib-constructor-unary-_from_bin.dat0000644403072340010010000011120213012340550024776 0ustar ospjadomain users0b110000001:385 0b110110010:434 0b110000001:385 0b101101000:360 0b100011011:283 0b110000111:391 0b101101100:364 0b111000010:450 0b101110010:370 0b101101111:367 0b1101100001:865 0b1110101011:939 0b1001101101:621 0b1100110101:821 0b1001010011:595 0b1001100111:615 0b1011101000:744 0b1101010010:850 0b1001100110:614 0b1111111100:1020 0b11101100110:1894 0b11111000111:1991 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0b1000101100001011000101000111110111100011001000110110101011110001110100100:5129791655388168709028 0b1100100110010011011111101111010100000001010101111000101011000110000110100:7436847520744746617908 0b1010100101011010100111110110001100010001100101000011100101110011111001110:6248059590737554237390 0b1110011110000010001000100010111001001000000010110110011010001010110001100:8541149978576018019724 Math-BigInt-1.999808/t/author-lib-constructor-unary-_from_bin.t0000644403072340010010000000561113024051250024476 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 3625; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_from_bin'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ sprintf("0b%b", $x), $x ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\@got = $LIB->_from_bin("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_bin() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$got = $LIB->_from_bin("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_bin() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-unary-_from_bytes.dat0000644403072340010010000020735713021270530025375 0ustar ospjadomain users\x00:0 \x01:1 \x02:2 \x07:7 \x13:19 \x17:23 \x1c:28 \x1d:29 \x1e:30 \x2b:43 \x30:48 \x3c:60 \x3e:62 \x40:64 \x4c:76 \x4f:79 \x53:83 \x54:84 \x61:97 \x65:101 \x69:105 \x72:114 \x78:120 \x7c:124 \x7d:125 \x7f:127 \x80:128 \x83:131 \x86:134 \x91:145 \x92:146 \x94:148 \x95:149 \xa2:162 \xa9:169 \xb0:176 \xb4:180 \xba:186 \xbd:189 \xc4:196 \xcf:207 \xd0:208 \xd3:211 \xd5:213 \xdd:221 \xde:222 \xef:239 \xfc:252 \xfe:254 \xff:255 \x01\x00:256 \x01\x01:257 \x01\xff:511 \x02\x00:512 \x02\x01:513 \x09\x5f:2399 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Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 4001; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_from_bytes'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\@got = $LIB->_from_bytes("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_bytes() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$got = $LIB->_from_bytes("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_bytes() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-unary-_from_hex.dat0000644403072340010010000003723313012340550025025 0ustar ospjadomain users0xc36:3126 0x695:1685 0x26f:623 0xe01:3585 0x255:597 0xc49:3145 0xf01:3841 0x5be:1470 0xaa2:2722 0x4e7:1255 0x5130:20784 0xbe8b:48779 0x60b4:24756 0x5bc1:23489 0xeae2:60130 0x6e5e:28254 0xee80:61056 0xa0ca:41162 0xbab7:47799 0xf3a8:62376 0xed5f2:972274 0x3c13a:246074 0x5a9a3:371107 0x4b8b5:309429 0xb4b84:740228 0xfb21d:1028637 0xf0ec4:986820 0x2b8db:178395 0xfc2d0:1032912 0x10f09:69385 0xd85243:14176835 0xdd0d9a:14486938 0x5f99d4:6265300 0x61c96b:6408555 0xf5b2cb:16102091 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Math-BigInt-1.999808/t/author-lib-constructor-unary-_from_hex.t0000644403072340010010000000561113024051250024512 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 2385; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_from_hex'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ sprintf("0x%x", $x), $x ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\@got = $LIB->_from_hex("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_hex() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$got = $LIB->_from_hex("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_hex() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-unary-_from_oct.dat0000644403072340010010000006417313012340550025031 0ustar ospjadomain users0515:333 0445:293 0736:478 0474:316 0772:506 0662:434 0764:500 0651:425 0447:295 0451:297 04313:2251 04454:2348 01124:596 06020:3088 02640:1440 07667:4023 02774:1532 04662:2482 02070:1080 06144:3172 044224:18580 017774:8188 073424:30484 066767:28151 015115:6733 021157:8815 060314:24780 064700:27072 054035:22557 046477:19775 0464171:157817 0747475:249661 0466403:158979 0772533:259419 0272447:95527 0315110:105032 0514042:170018 0535721:179153 0413747:137191 0277413:98059 07066734:1863132 02150733:578011 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0314247036520776204072024724164221032726324162652476:4556628504486465030629725405672903131888571710 Math-BigInt-1.999808/t/author-lib-constructor-unary-_from_oct.t0000644403072340010010000000561013024051250024512 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 2985; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_from_oct'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ sprintf("0%o", $x), $x ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\@got = $LIB->_from_oct("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_oct() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$got = $LIB->_from_oct("$in0");|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_from_oct() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-constructor-unary-_new.t0000644403072340010010000000550613024051250023477 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 2997; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_new'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; push @data, 0 .. 250; # small integers for (my $n = 3 ; $n <= 250 ; ++ $n) { push @data, "1" . ("0" x 3); # powers of 10 } for (my $n = 1 ; $n <= 250 ; ++ $n) { push @data, randstr($n, 10); # random big integer } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my $in0 = $data[$i]; my $out0 = $in0; my ($x, @got); my $test = qq|\@got = $LIB->_new("$in0"); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_new() in list context: $test", sub { plan tests => 4, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), $REF, "'$test' first output arg is a $REF"); is($LIB->_check($got[0]), 0, "'$test' output is valid"); is($LIB->_str($got[0]), $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my $in0 = $data[$i]; my $out0 = $in0; my ($x, $got); my $test = qq|\$got = $LIB->_new("$in0"); |; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_new() in scalar context: $test", sub { plan tests => 3, is(ref($got), $REF, "'$test' first output arg is a $REF"); is($LIB->_check($got), 0, "'$test' output is valid"); is($LIB->_str($got), $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-convert-number-_num.t0000644403072340010010000000657013024051250022734 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 3397; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, "_num"); use lib "t"; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; push @data, 0 .. 250; # small integers for (my $n = 3 ; $n <= 300 ; ++ $n) { push @data, "1" . ("0" x $n); # powers of 10 } for (my $n = 1 ; $n <= 300 ; ++ $n) { push @data, randstr($n, 10); # random big integers } # Tolerance for floating point number comparisons. my $tol = 2e-15; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my $str = $data[$i]; my ($x, @got); my $test = qq|\$x = $LIB->_new("$str"); | . qq|\@got = $LIB->_num(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_num() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a Perl scalar"); # If output does not use floating point notation, compare the # values exactly ... if ($got[0] =~ /^\d+\z/) { cmp_ok($got[0], "==", $str, "'$test' output value is exactly right"); } # ... otherwise compare them approximatly. else { my $rel_err = abs($got[0] - $str) / $str; cmp_ok($rel_err, "<", $tol, "'$test' output value is correct within" . " a relative error of $tol"); } }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my $str = $data[$i]; my ($x, $got); my $test = qq|\$x = $LIB->_new("$str"); | . qq|\$got = $LIB->_num(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_num() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a Perl scalar"); # If output does not use floating point notation, compare the # values exactly ... if ($got =~ /^\d+\z/) { cmp_ok($got, "==", $str, "'$test' output value is exactly right"); } # ... otherwise compare them approximatly. else { my $rel_err = abs($got - $str) / $str; cmp_ok($rel_err, "<", $tol, "'$test' output value is correct within" . 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7117075205464557801664:0b1100000011101000101000010011011110111110101001111001101101101000011000000 4833845377137258821730:0b1000001100000101100010100100101111011001000100110011100000111100001100010 5665981445059400430227:0b1001100110010011101001001110010001010000000010000000000111111001010010011 7209172766768821123614:0b1100001101100111101011110101100111000101010111011100101110011101000011110 5129791655388168709028:0b1000101100001011000101000111110111100011001000110110101011110001110100100 7436847520744746617908:0b1100100110010011011111101111010100000001010101111000101011000110000110100 6248059590737554237390:0b1010100101011010100111110110001100010001100101000011100101110011111001110 8541149978576018019724:0b1110011110000010001000100010111001001000000010110110011010001010110001100 Math-BigInt-1.999808/t/author-lib-convert-string-_as_bin.t0000644403072340010010000000503613026512523023411 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 3625; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_as_bin'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ $x, sprintf("0b%b", $x) ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_as_bin(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_as_bin() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_as_bin(\$x)|; diag("\n$test\n\n") 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############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_as_bytes'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; $out0 = eval qq|"$out0"|; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_as_bytes(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_as_bytes() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; $out0 = eval qq|"$out0"|; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_as_bytes(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_as_bytes() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-convert-string-_as_hex.dat0000644403072340010010000003723313012340550023730 0ustar ospjadomain users3126:0xc36 1685:0x695 623:0x26f 3585:0xe01 597:0x255 3145:0xc49 3841:0xf01 1470:0x5be 2722:0xaa2 1255:0x4e7 20784:0x5130 48779:0xbe8b 24756:0x60b4 23489:0x5bc1 60130:0xeae2 28254:0x6e5e 61056:0xee80 41162:0xa0ca 47799:0xbab7 62376:0xf3a8 972274:0xed5f2 246074:0x3c13a 371107:0x5a9a3 309429:0x4b8b5 740228:0xb4b84 1028637:0xfb21d 986820:0xf0ec4 178395:0x2b8db 1032912:0xfc2d0 69385:0x10f09 14176835:0xd85243 14486938:0xdd0d9a 6265300:0x5f99d4 6408555:0x61c96b 16102091:0xf5b2cb 7230921:0x6e55c9 12828906:0xc3c0ea 10074656:0x99ba20 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Math-BigInt-1.999808/t/author-lib-convert-string-_as_hex.t0000644403072340010010000000503613026512507023427 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 2385; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_as_hex'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ $x, sprintf("0x%x", $x) ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_as_hex(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_as_hex() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_as_hex(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_as_hex() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-convert-string-_as_oct.dat0000644403072340010010000006417313012340550023734 0ustar ospjadomain users333:0515 293:0445 478:0736 316:0474 506:0772 434:0662 500:0764 425:0651 295:0447 297:0451 2251:04313 2348:04454 596:01124 3088:06020 1440:02640 4023:07667 1532:02774 2482:04662 1080:02070 3172:06144 18580:044224 8188:017774 30484:073424 28151:066767 6733:015115 8815:021157 24780:060314 27072:064700 22557:054035 19775:046477 157817:0464171 249661:0747475 158979:0466403 259419:0772533 95527:0272447 105032:0315110 170018:0514042 179153:0535721 137191:0413747 98059:0277413 1863132:07066734 578011:02150733 331050:01206452 1986458:07447632 1503636:05570624 1890249:07153711 890356:03312764 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4556628504486465030629725405672903131888571710:0314247036520776204072024724164221032726324162652476 Math-BigInt-1.999808/t/author-lib-convert-string-_as_oct.t0000644403072340010010000000503513026512477023435 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 2985; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_as_oct'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ $x, sprintf("0%o", $x) ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_as_oct(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_oct() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_as_oct(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_oct() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-convert-string-_str.t0000644403072340010010000000477313024051250022766 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 11877; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_str'); use lib "t"; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; push @data, 0 .. 250; # small integers for (my $n = 3 ; $n <= 250 ; ++ $n) { push @data, "1" . ("0" x $n); # powers of 10 } for (my $n = 4 ; $n <= 250 ; ++ $n) { for (1 .. 10) { push @data, randstr($n, 10); # random $n-digit integer } } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0) = $data[$i]; my $out0 = $in0; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_str(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_str() in list context: $test", sub { plan tests => 3; cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0) = $data[$i]; my $out0 = $in0; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_str(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_str() in scalar context: 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7117075205464557801664:1100000011101000101000010011011110111110101001111001101101101000011000000 4833845377137258821730:1000001100000101100010100100101111011001000100110011100000111100001100010 5665981445059400430227:1001100110010011101001001110010001010000000010000000000111111001010010011 7209172766768821123614:1100001101100111101011110101100111000101010111011100101110011101000011110 5129791655388168709028:1000101100001011000101000111110111100011001000110110101011110001110100100 7436847520744746617908:1100100110010011011111101111010100000001010101111000101011000110000110100 6248059590737554237390:1010100101011010100111110110001100010001100101000011100101110011111001110 8541149978576018019724:1110011110000010001000100010111001001000000010110110011010001010110001100 Math-BigInt-1.999808/t/author-lib-convert-string-_to_bin.t0000644403072340010010000000503413026512734023432 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 3625; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_to_bin'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ $x, sprintf("%b", $x) ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_to_bin(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_bin() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_to_bin(\$x)|; diag("\n$test\n\n") 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1289002553246049725872987622570525161619110334766:\xe1\xc8\xdf\xa0\xd7\x30\xf4\xfe\x68\x0e\x31\xca\x4d\xef\xfb\x4e\xa5\x25\x91\x2e 1299699720357288158469698116372762213996730289480:\xe3\xa8\x8d\x15\x9c\xfd\xcc\x1b\x9b\x89\x06\x23\xbf\x22\x9e\xf1\x15\xc0\x8d\x48 1380508411373218081403828343115886164182876195339:\xf1\xd0\x23\x5d\x14\x65\x52\x4d\x79\xe5\x84\xc3\x0f\x1d\x40\x5a\xc3\x4e\x8a\x0b 1392801504342851537514365489400718531334955579302:\xf3\xf7\x61\x26\x6d\xf4\xa6\x53\x81\xe1\x39\xd1\x03\x68\xaf\x33\x9c\xe3\xb7\xa6 1421961811551523356914068742717017053094471918612:\xf9\x12\xf9\x0f\x68\xdb\xda\x4a\x95\x1c\xfd\x57\xae\x11\x7d\x14\x21\x25\xe4\x14 Math-BigInt-1.999808/t/author-lib-convert-string-_to_bytes.t0000644403072340010010000000477513031534733024022 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 4001; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_to_bytes'); my @data; # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; $out0 = eval qq|"$out0"|; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_to_bytes(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_bytes() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; $out0 = eval qq|"$out0"|; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_to_bytes(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_bytes() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-convert-string-_to_hex.dat0000644403072340010010000003576313026511431023760 0ustar ospjadomain users3126:c36 1685:695 623:26f 3585:e01 597:255 3145:c49 3841:f01 1470:5be 2722:aa2 1255:4e7 20784:5130 48779:be8b 24756:60b4 23489:5bc1 60130:eae2 28254:6e5e 61056:ee80 41162:a0ca 47799:bab7 62376:f3a8 972274:ed5f2 246074:3c13a 371107:5a9a3 309429:4b8b5 740228:b4b84 1028637:fb21d 986820:f0ec4 178395:2b8db 1032912:fc2d0 69385:10f09 14176835:d85243 14486938:dd0d9a 6265300:5f99d4 6408555:61c96b 16102091:f5b2cb 7230921:6e55c9 12828906:c3c0ea 10074656:99ba20 14222131:d90333 1589892:184284 253527184:f1c8490 52740107:324c00b 175139976:a706c88 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20067578297504078576702558367734434424958087:e65d4ff3732992f3bdd52a96f755564c2c87 3412382884554825484640759580553596711237210:272c178de869b6805accb19cd49ffe88765a 5205387933161353220201265273140599866832273:3bc142a143432614ea06abed7de842f0b591 Math-BigInt-1.999808/t/author-lib-convert-string-_to_hex.t0000644403072340010010000000503413026512610023437 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 2385; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_to_hex'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ $x, sprintf("%x", $x) ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_to_hex(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_hex() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_to_hex(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_hex() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-convert-string-_to_oct.dat0000644403072340010010000006322113026513003023744 0ustar ospjadomain users333:515 293:445 478:736 316:474 506:772 434:662 500:764 425:651 295:447 297:451 2251:4313 2348:4454 596:1124 3088:6020 1440:2640 4023:7667 1532:2774 2482:4662 1080:2070 3172:6144 18580:44224 8188:17774 30484:73424 28151:66767 6733:15115 8815:21157 24780:60314 27072:64700 22557:54035 19775:46477 157817:464171 249661:747475 158979:466403 259419:772533 95527:272447 105032:315110 170018:514042 179153:535721 137191:413747 98059:277413 1863132:7066734 578011:2150733 331050:1206452 1986458:7447632 1503636:5570624 1890249:7153711 890356:3312764 1666096:6266060 1528591:5651417 916069:3375145 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3655919425363778392509471921543889460220782917:243737626241530077036221202051775000435370553364505 2104054031105194403474721356234820404273278180:136262554214166525131413435376034410407117032166344 6295462823560579087001658801315334651887117021:432230571662563062541562610524407301332304717461335 4830948073396715443223444786269425031559102687:330501101543227227662231204330103475241341115340337 4556628504486465030629725405672903131888571710:314247036520776204072024724164221032726324162652476 Math-BigInt-1.999808/t/author-lib-convert-string-_to_oct.t0000644403072340010010000000503413026513255023446 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 2985; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_to_oct'); my @data; # Small numbers. for (my $x = 0; $x <= 255 ; ++ $x) { push @data, [ $x, sprintf("%o", $x) ]; } # Add data in data file. (my $datafile = $0) =~ s/\.t/.dat/; open DATAFILE, $datafile or die "$datafile: can't open file for reading: $!"; while () { s/\s+\z//; next if /^#/ || ! /\S/; push @data, [ split /:/ ]; } close DATAFILE or die "$datafile: can't close file after reading: $!"; # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_to_oct(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_oct() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_to_oct(\$x)|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_to_oct() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-misc-api_version.t0000644403072340010010000000364413024051250022300 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 5; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, 'api_version'); # List context. { my @got; my $test = qq|\@got = $LIB->api_version();|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "api_version() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output is a Perl scalar"); like($got[0], qr/^[1-9]\d*(\.\d+)?$/, "'$test' output is a decimal number'"); }; } # Scalar context. { my $got; my $test = qq|\$got = $LIB->api_version();|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "api_version() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output is a Perl scalar"); like($got, qr/^[1-9]\d*(\.\d+)?$/, "'$test' output is a decimal number'"); }; } Math-BigInt-1.999808/t/author-lib-misc-_check.t0000644403072340010010000000635713024051250021202 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 137; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_check'); # Generate test data. my @data; push @data, ([ "$LIB->_zero()", 1 ], # valid objects [ "$LIB->_one()", 1 ], [ "$LIB->_two()", 1 ], [ "$LIB->_ten()", 1 ]); for (my $n = 0 ; $n <= 24 ; ++ $n) { push @data, [ qq|$LIB->_new("1| . ("0" x $n) . qq|")|, 1 ]; } push @data, ([ "undef", 0 ], # invalid objects [ "''", 0 ], [ "1", 0 ], [ "[]", 0 ], [ "{}", 0 ]); # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $in0; | . qq|\@got = $LIB->_check(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_check() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); if ($out0) { # valid object ok(! $got[0], "'$test' output arg is false (object OK)") or diag(" got: $got[0]\n expected: (something false)"); } else { # invalid object ok($got[0], "'$test' output arg is true (object not OK)") or diag(" got: $got[0]\n expected: (something true)"); } }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $in0; | . qq|\$got = $LIB->_check(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_check() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); if ($out0) { # valid object ok(! $got, "'$test' output arg is false (object OK)") or diag(" got: $got\n expected: (something false)"); } else { # invalid object ok($got, "'$test' output arg is true (object not OK)") or diag(" got: $got\n expected: (something true)"); } }; } Math-BigInt-1.999808/t/author-lib-property-_alen.t0000644403072340010010000000553513024051250021772 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 4393; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_alen'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; # Small integers. for my $x (0 .. 99) { push @data, [ $x ]; } # Random large integers. for (3 .. 1000) { my $nx = 2 + int rand 35; # number of digits in $x my $x = randstr($nx, 10); # generate $a push @data, [ $x ]; } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_alen(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_alen() in list context: $test", sub { plan tests => 5, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a Perl scalar"); isnt($got[0], undef, "'$test' output arg is defined"); like($got[0], qr/^[+-]?(\d+(\.\d*)?|\.\d+)([Ee][+-]?\d+)?\z/, "'$test' output arg looks like a number"); is($got[0], int($got[0]), "'$test' output arg is an integer"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_alen(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_alen() in scalar context: $test", sub { plan tests => 4, is(ref($got), "", "'$test' output arg is a Perl scalar"); isnt($got, undef, "'$test' output arg is defined"); like($got, qr/^[+-]?(\d+(\.\d*)?|\.\d+)([Ee][+-]?\d+)?\z/, "'$test' output arg looks like a number"); is($got, int($got), "'$test' output arg is an integer"); }; } Math-BigInt-1.999808/t/author-lib-property-_digit.t0000644403072340010010000000551413024051250022150 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 41897; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_digit'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; sub add_test_cases { my $x = shift; my $n = length $x; # Digits from right to left (positive index 0 .. N-1). for (my $i = 0 ; $i < $n ; ++$i) { my $digit = substr $x, $n - 1 - $i, 1; push @data, [ $x, $i, $digit ]; } # Digits from left to right (negative index -1 .. -N). for (my $i = -1 ; $i >= -$n ; --$i) { my $digit = substr $x, -1 - $i, 1; push @data, [ $x, $i, $digit ]; } } for (my $x = 0 ; $x <= 100 ; ++ $x) { add_test_cases(sprintf "%u", $x); } for (my $n = 4 ; $n <= 100 ; ++ $n) { add_test_cases(randstr($n, 10)); } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_digit(\$x, $in1);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_digit() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $in1, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_digit(\$x, $in1);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_digit() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-property-_len.t0000644403072340010010000000467613024051250021636 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 4957; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_len'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; # Generate test data. my @data; for (my $x = 0 ; $x <= 250 ; ++ $x) { $x = sprintf "%u", $x; push @data, [ $x, length($x) ]; } for (my $n = 4 ; $n <= 250 ; ++ $n) { for (1 .. 4) { my $x = randstr($n, 10); push @data, [ $x, $n ]; } } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_len(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_len() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, '==', 1, "'$test' gives one output arg"); is(ref($got[0]), "", "'$test' output arg is a Perl scalar"); is($got[0], $out0, "'$test' output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_len(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_len() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "'$test' output arg is a Perl scalar"); is($got, $out0, "'$test' output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib-property-_zeros.t0000644403072340010010000000543213024310545022216 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 20993; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### can_ok($LIB, '_zeros'); use lib 't'; use Math::BigInt::Lib::TestUtil qw< randstr >; my @data; # Small numbers. for (my $x = 0; $x <= 9 ; ++ $x) { push @data, [ $x, 0 ]; } for (my $x = 10; $x <= 99 ; ++ $x) { push @data, [ $x, $x % 10 ? 0 : 1 ]; } # Random numbers. for (my $p = 0 ; $p <= 100 ; ++ $p) { for (my $q = 0 ; $q <= 50 ; ++ $q) { next if $p + $q < 2; # small numbers done above my $in0 = randstr($p, 10) # p digit number (base 10) . (1 + int rand 9) # ensure non-zero digit . ("0" x $q); # q zeros my $out0 = $q; push @data, [ $in0, $out0 ]; } } # List context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, @got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\@got = $LIB->_zeros(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_zeros() in list context: $test", sub { plan tests => 3, cmp_ok(scalar @got, "==", 1, "'$test' gives one output arg"); is(ref($got[0]), "", "output arg is a Perl scalar"); cmp_ok($got[0], "==", $out0, "output arg has the right value"); }; } # Scalar context. for (my $i = 0 ; $i <= $#data ; ++ $i) { my ($in0, $out0) = @{ $data[$i] }; my ($x, $got); my $test = qq|\$x = $LIB->_new("$in0"); | . qq|\$got = $LIB->_zeros(\$x);|; diag("\n$test\n\n") if $ENV{AUTHOR_DEBUGGING}; eval $test; is($@, "", "'$test' gives emtpy \$\@"); subtest "_zeros() in scalar context: $test", sub { plan tests => 2, is(ref($got), "", "output arg is a Perl scalar"); cmp_ok($got, "==", $out0, "output arg has the right value"); }; } Math-BigInt-1.999808/t/author-lib.ini0000644403072340010010000000005613011354232017343 0ustar ospjadomain userslib=Math::BigInt::Calc ref=Math::BigInt::Calc Math-BigInt-1.999808/t/author-lib.t0000644403072340010010000000237213012340550017031 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 1; ############################################################################### # Read and load configuration file and backend library. use Config::Tiny (); my $config_file = 't/author-lib.ini'; my $config = Config::Tiny -> read('t/author-lib.ini') or die Config::Tiny -> errstr(); # Read the library to test. our $LIB = $config->{_}->{lib}; die "No library defined in file '$config_file'" unless defined $LIB; die "Invalid library name '$LIB' in file '$config_file'" unless $LIB =~ /^[A-Za-z]\w*(::\w+)*\z/; # Read the reference type(s) the library uses. our $REF = $config->{_}->{ref}; die "No reference type defined in file '$config_file'" unless defined $REF; die "Invalid reference type '$REF' in file '$config_file'" unless $REF =~ /^[A-Za-z]\w*(::\w+)*\z/; # Load the library. eval "require $LIB"; die $@ if $@; ############################################################################### pass("Configuration loaded OK"); diag("\n\n$LIB version ", $LIB -> VERSION(), ", Perl $], $^X\n\n"); Math-BigInt-1.999808/t/author-numify-mbf.t0000644403072340010010000000360012734616177020354 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 9; use Math::BigFloat; use Math::Complex; my $inf = Math::Complex::Inf(); my $nan = $inf - $inf; ############################################################################### # Check numify() on finite values. { my $x = Math::BigFloat -> new("0.008"); my $y = Math::BigFloat -> new(2); $x -> bdiv(3, $y); cmp_ok($x, "==", "0.0027", qq|\$x = Math::BigFloat -> new("0.008");| . qq| \$y = Math::BigFloat -> new(2); \$x -> bdiv(3, \$y);|); cmp_ok(Math::BigFloat -> new("12345e67") -> numify(), "==", 1.2345e71, qq|Math::BigFloat -> new("12345e67") -> numify()|); } ############################################################################### # Verify that numify() underflows and overflows when given "extreme" values. # positive overflow cmp_ok(Math::BigFloat -> new("1e9999") -> numify(), "==", $inf, qq|Math::BigFloat -> new("1e9999") -> numify()|); # negative overflow cmp_ok(Math::BigFloat -> new("-1e9999") -> numify(), "==", -$inf, qq|Math::BigFloat -> new("-1e9999") -> numify()|); # positive underflow cmp_ok(Math::BigFloat -> new("1e-9999") -> numify(), "==", 0, qq|Math::BigFloat -> new("1e-9999") -> numify()|); # negative underflow cmp_ok(Math::BigFloat -> new("-1e-9999") -> numify(), "==", 0, qq|Math::BigFloat -> new("-1e-9999") -> numify()|); ############################################################################### # Check numify on non-finite objects. is(Math::BigFloat -> binf("+") -> numify(), $inf, "numify of +Inf"); is(Math::BigFloat -> binf("-") -> numify(), -$inf, "numify of -Inf"); is(Math::BigFloat -> bnan() -> numify(), $nan, "numify of NaN"); Math-BigInt-1.999808/t/author-numify-mbi.t0000644403072340010010000000523612741411606020352 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 14; use Math::BigInt; use Math::Complex; my $inf = Math::Complex::Inf(); my $nan = $inf - $inf; ############################################################################### # Check numify() on finite values. cmp_ok(Math::BigInt -> bzero() -> numify(), "==", 0, 'Math::BigInt -> bzero() -> numify()'); cmp_ok(Math::BigInt -> bone() -> numify(), "==", 1, 'Math::BigInt -> bone() -> numify()'); cmp_ok(Math::BigInt -> new("4711") -> numify(), "==", 4711, 'Math::BigInt -> new("4711") -> numify()'); cmp_ok(Math::BigInt -> new("-4711") -> numify(), "==", -4711, 'Math::BigInt -> new("-4711") -> numify()'); cmp_ok(Math::BigInt -> new("12345e67") -> numify(), "==", 12345e67, qq|Math::BigInt -> new("12345e67") -> numify()|); ############################################################################### # Verify that numify() overflows when given "extreme" values. # positive overflow is(Math::BigInt -> new("1e9999") -> numify(), $inf, qq|Math::BigInt -> new("1e9999") -> numify()|); # negative overflow is(Math::BigInt -> new("-1e9999") -> numify(), -$inf, qq|Math::BigInt -> new("-1e9999") -> numify()|); ############################################################################### # Check numify on non-finite objects. is(Math::BigInt -> binf("+") -> numify(), $inf, "numify of +Inf"); is(Math::BigInt -> binf("-") -> numify(), -$inf, "numify of -Inf"); is(Math::BigInt -> bnan() -> numify(), $nan, "numify of NaN"); ############################################################################### SKIP: { skip "insufficient 64 bit integer support", 4 unless ($Config::Config{ptrsize} == 8 && $] >= 5.008 && ($Config::Config{use64bitint} || $Config::Config{use64bitall})); # The following should not give "1.84467440737096e+19". { my $x = Math::BigInt -> new(2) -> bpow(64) -> bdec(); is($x -> bstr(), "18446744073709551615", "Math::BigInt 2**64-1 as string"); is($x -> numify(), "18446744073709551615", "Math::BigInt 2**64-1 as number"); } # The following should not give "-9.22337203685478e+18". { my $x = Math::BigInt -> new(2) -> bpow(63) -> bneg(); is($x -> bstr(), "-9223372036854775808", "Math::BigInt -2**63 as string"); is($x -> numify(), "-9223372036854775808", "Math::BigInt -2**63 as number"); } } Math-BigInt-1.999808/t/author-relop-mbi-mbf.t0000644403072340010010000002072312740677023020732 0ustar ospjadomain users#!perl BEGIN { unless ($ENV{AUTHOR_TESTING}) { require Test::More; Test::More::plan(skip_all => 'these tests are for testing by the author'); } } use strict; use warnings; use Test::More tests => 17642; use Math::Complex (); use Scalar::Util qw< refaddr >; my $inf = Math::Complex::Inf(); my $nan = $inf - $inf; my @table = ( [ '<=>', 'bcmp', ], [ '==', 'beq', ], [ '!=', 'bne', ], [ '<', 'blt', ], [ '<=', 'ble', ], [ '>', 'bgt', ], [ '>=', 'bge', ], ); my @values = (-$inf, -2, 0, 2, $inf, $nan); my @classes = ( 'Math::BigInt', 'Math::BigFloat', ); for my $class (@classes) { use_ok($class); for my $entry (@table) { my $operator = $entry -> [0]; my $method = $entry -> [1]; for my $xscalar (@values) { for my $yscalar (@values) { my $expected = eval qq|"$xscalar" $operator "$yscalar"|; note("#" x 70); note(""); note(qq|"$xscalar" $operator "$yscalar" = |, !defined $expected ? "undef" : !length $expected ? '""' : $expected); note(""); note("#" x 70); { my ($x, $y, $z); my ($xval, $xaddr); my ($yval, $yaddr); $x = $class -> new("$xscalar"); $y = $class -> new("$yscalar"); my $test = qq|\$x = $class -> new("$xscalar"); | . qq|\$y = $class -> new("$yscalar"); | . qq|\$xval = \$x -> copy(); | . qq|\$xaddr = refaddr(\$x); | . qq|\$yval = \$y -> copy(); | . qq|\$yaddr = refaddr(\$y); | . qq|\$z = \$x -> $method(\$y);|; note(""); note("\$x -> $method(\$y) where \$x is an object", " and \$y is an object"); note(""); note($test); note(""); eval $test; is($@, '', 'is $@ empty'); is($z, $expected, 'value of $z'); is(ref($z), '', '$z is not a reference'); is($x, $xval, 'value of $x is unchanged'); is(refaddr($x), $xaddr, 'address of $x is unchanged'); is($y, $yval, 'value of $y is unchanged'); is(refaddr($y), $yaddr, 'address of $y is unchanged'); } { my ($x, $y, $z); my ($xval, $xaddr); my ($yval, $yaddr); $x = $class -> new("$xscalar"); $y = $class -> new("$yscalar"); my $test = qq|\$x = $class -> new("$xscalar"); | . qq|\$y = $class -> new("$yscalar"); | . qq|\$xval = \$x -> copy(); | . qq|\$xaddr = refaddr(\$x); | . qq|\$yval = \$y -> copy(); | . qq|\$yaddr = refaddr(\$y); | . qq|\$z = \$x $operator \$y;|; note(""); note("\$x $operator \$y where \$x is an object and", " \$y is an object"); note(""); note($test); note(""); eval $test; is($@, '', 'is $@ empty'); is($z, $expected, 'value of $z'); is(ref($z), '', '$z is not a reference'); is($x, $xval, 'value of $x is unchanged'); is(refaddr($x), $xaddr, 'address of $x is unchanged'); is($y, $yval, 'value of $y is unchanged'); is(refaddr($y), $yaddr, 'address of $y is unchanged'); } { my ($x, $y, $z); my ($xval, $xaddr); my ($yval, $yaddr); $x = $class -> new("$xscalar"); $y = $yscalar; my $test = qq|\$x = $class -> new("$xscalar"); | . qq|\$y = "$yscalar"; | . qq|\$xval = \$x -> copy(); | . qq|\$xaddr = refaddr(\$x); | . qq|\$yval = "$yscalar"; | . qq|\$yaddr = refaddr(\$y); | . qq|\$z = \$x -> $method(\$y);|; note(""); note("\$x -> $method(\$y) where \$x is an object", " and \$y is a scalar"); note(""); note($test); note(""); eval $test; is($@, '', 'is $@ empty'); is($z, $expected, 'value of $z'); is(ref($z), '', '$z is not a reference'); is($x, $xval, 'value of $x is unchanged'); is(refaddr($x), $xaddr, 'address of $x is unchanged'); is($y, $yval, 'value of $y is unchanged'); is(refaddr($y), $yaddr, 'address of $y is unchanged'); } { my ($x, $y, $z); my ($xval, $xaddr); my ($yval, $yaddr); $x = $class -> new("$xscalar"); $y = $class -> new("$yscalar"); my $test = qq|\$x = $class -> new("$xscalar"); | . qq|\$y = "$yscalar"; | . qq|\$xval = \$x -> copy(); | . qq|\$xaddr = refaddr(\$x); | . qq|\$yval = "$yscalar"; | . qq|\$yaddr = refaddr(\$y); | . qq|\$z = \$x $operator \$y;|; note(""); note("\$x $operator \$y where \$x is an object", " and \$y is a scalar"); note(""); note($test); note(""); eval $test; is($@, '', 'is $@ empty'); is($z, $expected, 'value of $z'); is(ref($z), '', '$z is not a reference'); is($x, $xval, 'value of $x is unchanged'); is(refaddr($x), $xaddr, 'address of $x is unchanged'); is($y, $yval, 'value of $y is unchanged'); is(refaddr($y), $yaddr, 'address of $y is unchanged'); } { my ($x, $y, $z); my ($xval, $xaddr); my ($yval, $yaddr); $x = $class -> new("$xscalar"); $y = $class -> new("$yscalar"); my $test = qq|\$x = "$xscalar"; | . qq|\$y = $class -> new("$yscalar"); | . qq|\$xval = "$xscalar"; | . qq|\$xaddr = refaddr(\$x); | . qq|\$yval = \$y -> copy(); | . qq|\$yaddr = refaddr(\$y); | . qq|\$z = \$x $operator \$y;|; note(""); note("\$x $operator \$y where \$x is a scalar and", " \$y is an object:"); note(""); note($test); note(""); eval $test; is($@, '', 'is $@ empty'); is($z, $expected, 'value of $z'); is(ref($z), '', '$z is not a reference'); is($x, $xval, 'value of $x is unchanged'); is(refaddr($x), $xaddr, 'address of $x is unchanged'); is($y, $yval, 'value of $y is unchanged'); is(refaddr($y), $yaddr, 'address of $y is unchanged'); } } } } } Math-BigInt-1.999808/t/bare_mbf.t0000644403072340010010000000043113031667163016527 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 2436; use lib 't'; use Math::BigFloat lib => 'BareCalc'; our ($CLASS, $CALC); $CLASS = "Math::BigFloat"; $CALC = "Math::BigInt::BareCalc"; # backend require 't/bigfltpm.inc'; # all tests here for sharing Math-BigInt-1.999808/t/bare_mbi.t0000644403072340010010000000056513014573447016544 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 3913; # tests in require'd file use lib 't'; use Math::BigInt lib => 'BareCalc'; print "# ", Math::BigInt->config('lib'), "\n"; our ($CLASS, $CALC); $CLASS = "Math::BigInt"; $CALC = "Math::BigInt::BareCalc"; # backend require 't/bigintpm.inc'; # perform same tests as bigintpm.t Math-BigInt-1.999808/t/bare_mif.t0000644403072340010010000000105313014573461016535 0ustar ospjadomain users#!perl # test rounding, accuracy, precision and fallback, round_mode and mixing # of classes under Math::BigInt::BareCalc use strict; use warnings; use Test::More tests => 712 # tests in require'd file + 1; # tests in this file use lib 't'; use Math::BigInt lib => 'BareCalc'; use Math::BigFloat lib => 'BareCalc'; our ($mbi, $mbf); $mbi = 'Math::BigInt'; $mbf = 'Math::BigFloat'; is(Math::BigInt->config('lib'), 'Math::BigInt::BareCalc', "Math::BigInt->config('lib')"); require 't/mbimbf.inc'; Math-BigInt-1.999808/t/bdstr-mbf.t0000644403072340010010000001224612740677023016663 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 460; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); my $test = qq|\$x = Math::BigFloat -> new("$x_str");| . qq| \$str = \$x -> bdstr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0 # positive numbers 0.000000000001:0.000000000001 0.00000000001:0.00000000001 0.0000000001:0.0000000001 0.000000001:0.000000001 0.00000001:0.00000001 0.0000001:0.0000001 0.000001:0.000001 0.00001:0.00001 0.0001:0.0001 0.001:0.001 0.01:0.01 0.1:0.1 1:1 10:10 100:100 1000:1000 10000:10000 100000:100000 1000000:1000000 10000000:10000000 100000000:100000000 1000000000:1000000000 10000000000:10000000000 100000000000:100000000000 1000000000000:1000000000000 0.0000000000012:0.0000000000012 0.000000000012:0.000000000012 0.00000000012:0.00000000012 0.0000000012:0.0000000012 0.000000012:0.000000012 0.00000012:0.00000012 0.0000012:0.0000012 0.000012:0.000012 0.00012:0.00012 0.0012:0.0012 0.012:0.012 0.12:0.12 1.2:1.2 12:12 120:120 1200:1200 12000:12000 120000:120000 1200000:1200000 12000000:12000000 120000000:120000000 1200000000:1200000000 12000000000:12000000000 120000000000:120000000000 1200000000000:1200000000000 0.00000000000123:0.00000000000123 0.0000000000123:0.0000000000123 0.000000000123:0.000000000123 0.00000000123:0.00000000123 0.0000000123:0.0000000123 0.000000123:0.000000123 0.00000123:0.00000123 0.0000123:0.0000123 0.000123:0.000123 0.00123:0.00123 0.0123:0.0123 0.123:0.123 1.23:1.23 12.3:12.3 123:123 1230:1230 12300:12300 123000:123000 1230000:1230000 12300000:12300000 123000000:123000000 1230000000:1230000000 12300000000:12300000000 123000000000:123000000000 1230000000000:1230000000000 0.000000000001234:0.000000000001234 0.00000000001234:0.00000000001234 0.0000000001234:0.0000000001234 0.000000001234:0.000000001234 0.00000001234:0.00000001234 0.0000001234:0.0000001234 0.000001234:0.000001234 0.00001234:0.00001234 0.0001234:0.0001234 0.001234:0.001234 0.01234:0.01234 0.1234:0.1234 1.234:1.234 12.34:12.34 123.4:123.4 1234:1234 12340:12340 123400:123400 1234000:1234000 12340000:12340000 123400000:123400000 1234000000:1234000000 12340000000:12340000000 123400000000:123400000000 1234000000000:1234000000000 0.000003141592:0.000003141592 0.00003141592:0.00003141592 0.0003141592:0.0003141592 0.003141592:0.003141592 0.03141592:0.03141592 0.3141592:0.3141592 3.141592:3.141592 31.41592:31.41592 314.1592:314.1592 3141.592:3141.592 31415.92:31415.92 314159.2:314159.2 3141592:3141592 # negative numbers -0.000000000001:-0.000000000001 -0.00000000001:-0.00000000001 -0.0000000001:-0.0000000001 -0.000000001:-0.000000001 -0.00000001:-0.00000001 -0.0000001:-0.0000001 -0.000001:-0.000001 -0.00001:-0.00001 -0.0001:-0.0001 -0.001:-0.001 -0.01:-0.01 -0.1:-0.1 -1:-1 -10:-10 -100:-100 -1000:-1000 -10000:-10000 -100000:-100000 -1000000:-1000000 -10000000:-10000000 -100000000:-100000000 -1000000000:-1000000000 -10000000000:-10000000000 -100000000000:-100000000000 -1000000000000:-1000000000000 -0.0000000000012:-0.0000000000012 -0.000000000012:-0.000000000012 -0.00000000012:-0.00000000012 -0.0000000012:-0.0000000012 -0.000000012:-0.000000012 -0.00000012:-0.00000012 -0.0000012:-0.0000012 -0.000012:-0.000012 -0.00012:-0.00012 -0.0012:-0.0012 -0.012:-0.012 -0.12:-0.12 -1.2:-1.2 -12:-12 -120:-120 -1200:-1200 -12000:-12000 -120000:-120000 -1200000:-1200000 -12000000:-12000000 -120000000:-120000000 -1200000000:-1200000000 -12000000000:-12000000000 -120000000000:-120000000000 -1200000000000:-1200000000000 -0.00000000000123:-0.00000000000123 -0.0000000000123:-0.0000000000123 -0.000000000123:-0.000000000123 -0.00000000123:-0.00000000123 -0.0000000123:-0.0000000123 -0.000000123:-0.000000123 -0.00000123:-0.00000123 -0.0000123:-0.0000123 -0.000123:-0.000123 -0.00123:-0.00123 -0.0123:-0.0123 -0.123:-0.123 -1.23:-1.23 -12.3:-12.3 -123:-123 -1230:-1230 -12300:-12300 -123000:-123000 -1230000:-1230000 -12300000:-12300000 -123000000:-123000000 -1230000000:-1230000000 -12300000000:-12300000000 -123000000000:-123000000000 -1230000000000:-1230000000000 -0.000000000001234:-0.000000000001234 -0.00000000001234:-0.00000000001234 -0.0000000001234:-0.0000000001234 -0.000000001234:-0.000000001234 -0.00000001234:-0.00000001234 -0.0000001234:-0.0000001234 -0.000001234:-0.000001234 -0.00001234:-0.00001234 -0.0001234:-0.0001234 -0.001234:-0.001234 -0.01234:-0.01234 -0.1234:-0.1234 -1.234:-1.234 -12.34:-12.34 -123.4:-123.4 -1234:-1234 -12340:-12340 -123400:-123400 -1234000:-1234000 -12340000:-12340000 -123400000:-123400000 -1234000000:-1234000000 -12340000000:-12340000000 -123400000000:-123400000000 -1234000000000:-1234000000000 -0.000003141592:-0.000003141592 -0.00003141592:-0.00003141592 -0.0003141592:-0.0003141592 -0.003141592:-0.003141592 -0.03141592:-0.03141592 -0.3141592:-0.3141592 -3.141592:-3.141592 -31.41592:-31.41592 -314.1592:-314.1592 -3141.592:-3141.592 -31415.92:-31415.92 -314159.2:-314159.2 -3141592:-3141592 Math-BigInt-1.999808/t/bdstr-mbi.t0000644403072340010010000000472212740677023016666 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 220; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); my $test = qq|\$x = Math::BigInt -> new("$x_str");| . qq| \$str = \$x -> bdstr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0 # positive numbers 1:1 10:10 100:100 1000:1000 10000:10000 100000:100000 1000000:1000000 10000000:10000000 100000000:100000000 1000000000:1000000000 10000000000:10000000000 100000000000:100000000000 1000000000000:1000000000000 12:12 120:120 1200:1200 12000:12000 120000:120000 1200000:1200000 12000000:12000000 120000000:120000000 1200000000:1200000000 12000000000:12000000000 120000000000:120000000000 1200000000000:1200000000000 123:123 1230:1230 12300:12300 123000:123000 1230000:1230000 12300000:12300000 123000000:123000000 1230000000:1230000000 12300000000:12300000000 123000000000:123000000000 1230000000000:1230000000000 1234:1234 12340:12340 123400:123400 1234000:1234000 12340000:12340000 123400000:123400000 1234000000:1234000000 12340000000:12340000000 123400000000:123400000000 1234000000000:1234000000000 3:3 31:31 314:314 3141:3141 31415:31415 314159:314159 3141592:3141592 # negative numbers -1:-1 -10:-10 -100:-100 -1000:-1000 -10000:-10000 -100000:-100000 -1000000:-1000000 -10000000:-10000000 -100000000:-100000000 -1000000000:-1000000000 -10000000000:-10000000000 -100000000000:-100000000000 -1000000000000:-1000000000000 -12:-12 -120:-120 -1200:-1200 -12000:-12000 -120000:-120000 -1200000:-1200000 -12000000:-12000000 -120000000:-120000000 -1200000000:-1200000000 -12000000000:-12000000000 -120000000000:-120000000000 -1200000000000:-1200000000000 -123:-123 -1230:-1230 -12300:-12300 -123000:-123000 -1230000:-1230000 -12300000:-12300000 -123000000:-123000000 -1230000000:-1230000000 -12300000000:-12300000000 -123000000000:-123000000000 -1230000000000:-1230000000000 -1234:-1234 -12340:-12340 -123400:-123400 -1234000:-1234000 -12340000:-12340000 -123400000:-123400000 -1234000000:-1234000000 -12340000000:-12340000000 -123400000000:-123400000000 -1234000000000:-1234000000000 -3:-3 -31:-31 -314:-314 -3141:-3141 -31415:-31415 -314159:-314159 -3141592:-3141592 Math-BigInt-1.999808/t/bestr-mbf.t0000644403072340010010000001145112740677024016662 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 460; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); my $test = qq|\$x = Math::BigFloat -> new("$x_str");| . qq| \$str = \$x -> bestr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0e+0 # positive numbers 0.000000000001:1e-12 0.00000000001:10e-12 0.0000000001:100e-12 0.000000001:1e-9 0.00000001:10e-9 0.0000001:100e-9 0.000001:1e-6 0.00001:10e-6 0.0001:100e-6 0.001:1e-3 0.01:10e-3 0.1:100e-3 1:1e+0 10:10e+0 100:100e+0 1000:1e+3 10000:10e+3 100000:100e+3 1000000:1e+6 10000000:10e+6 100000000:100e+6 1000000000:1e+9 10000000000:10e+9 100000000000:100e+9 1000000000000:1e+12 0.0000000000012:1.2e-12 0.000000000012:12e-12 0.00000000012:120e-12 0.0000000012:1.2e-9 0.000000012:12e-9 0.00000012:120e-9 0.0000012:1.2e-6 0.000012:12e-6 0.00012:120e-6 0.0012:1.2e-3 0.012:12e-3 0.12:120e-3 1.2:1.2e+0 12:12e+0 120:120e+0 1200:1.2e+3 12000:12e+3 120000:120e+3 1200000:1.2e+6 12000000:12e+6 120000000:120e+6 1200000000:1.2e+9 12000000000:12e+9 120000000000:120e+9 1200000000000:1.2e+12 0.00000000000123:1.23e-12 0.0000000000123:12.3e-12 0.000000000123:123e-12 0.00000000123:1.23e-9 0.0000000123:12.3e-9 0.000000123:123e-9 0.00000123:1.23e-6 0.0000123:12.3e-6 0.000123:123e-6 0.00123:1.23e-3 0.0123:12.3e-3 0.123:123e-3 1.23:1.23e+0 12.3:12.3e+0 123:123e+0 1230:1.23e+3 12300:12.3e+3 123000:123e+3 1230000:1.23e+6 12300000:12.3e+6 123000000:123e+6 1230000000:1.23e+9 12300000000:12.3e+9 123000000000:123e+9 1230000000000:1.23e+12 0.000000000001234:1.234e-12 0.00000000001234:12.34e-12 0.0000000001234:123.4e-12 0.000000001234:1.234e-9 0.00000001234:12.34e-9 0.0000001234:123.4e-9 0.000001234:1.234e-6 0.00001234:12.34e-6 0.0001234:123.4e-6 0.001234:1.234e-3 0.01234:12.34e-3 0.1234:123.4e-3 1.234:1.234e+0 12.34:12.34e+0 123.4:123.4e+0 1234:1.234e+3 12340:12.34e+3 123400:123.4e+3 1234000:1.234e+6 12340000:12.34e+6 123400000:123.4e+6 1234000000:1.234e+9 12340000000:12.34e+9 123400000000:123.4e+9 1234000000000:1.234e+12 0.000003141592:3.141592e-6 0.00003141592:31.41592e-6 0.0003141592:314.1592e-6 0.003141592:3.141592e-3 0.03141592:31.41592e-3 0.3141592:314.1592e-3 3.141592:3.141592e+0 31.41592:31.41592e+0 314.1592:314.1592e+0 3141.592:3.141592e+3 31415.92:31.41592e+3 314159.2:314.1592e+3 3141592:3.141592e+6 # negative numbers -0.000000000001:-1e-12 -0.00000000001:-10e-12 -0.0000000001:-100e-12 -0.000000001:-1e-9 -0.00000001:-10e-9 -0.0000001:-100e-9 -0.000001:-1e-6 -0.00001:-10e-6 -0.0001:-100e-6 -0.001:-1e-3 -0.01:-10e-3 -0.1:-100e-3 -1:-1e+0 -10:-10e+0 -100:-100e+0 -1000:-1e+3 -10000:-10e+3 -100000:-100e+3 -1000000:-1e+6 -10000000:-10e+6 -100000000:-100e+6 -1000000000:-1e+9 -10000000000:-10e+9 -100000000000:-100e+9 -1000000000000:-1e+12 -0.0000000000012:-1.2e-12 -0.000000000012:-12e-12 -0.00000000012:-120e-12 -0.0000000012:-1.2e-9 -0.000000012:-12e-9 -0.00000012:-120e-9 -0.0000012:-1.2e-6 -0.000012:-12e-6 -0.00012:-120e-6 -0.0012:-1.2e-3 -0.012:-12e-3 -0.12:-120e-3 -1.2:-1.2e+0 -12:-12e+0 -120:-120e+0 -1200:-1.2e+3 -12000:-12e+3 -120000:-120e+3 -1200000:-1.2e+6 -12000000:-12e+6 -120000000:-120e+6 -1200000000:-1.2e+9 -12000000000:-12e+9 -120000000000:-120e+9 -1200000000000:-1.2e+12 -0.00000000000123:-1.23e-12 -0.0000000000123:-12.3e-12 -0.000000000123:-123e-12 -0.00000000123:-1.23e-9 -0.0000000123:-12.3e-9 -0.000000123:-123e-9 -0.00000123:-1.23e-6 -0.0000123:-12.3e-6 -0.000123:-123e-6 -0.00123:-1.23e-3 -0.0123:-12.3e-3 -0.123:-123e-3 -1.23:-1.23e+0 -12.3:-12.3e+0 -123:-123e+0 -1230:-1.23e+3 -12300:-12.3e+3 -123000:-123e+3 -1230000:-1.23e+6 -12300000:-12.3e+6 -123000000:-123e+6 -1230000000:-1.23e+9 -12300000000:-12.3e+9 -123000000000:-123e+9 -1230000000000:-1.23e+12 -0.000000000001234:-1.234e-12 -0.00000000001234:-12.34e-12 -0.0000000001234:-123.4e-12 -0.000000001234:-1.234e-9 -0.00000001234:-12.34e-9 -0.0000001234:-123.4e-9 -0.000001234:-1.234e-6 -0.00001234:-12.34e-6 -0.0001234:-123.4e-6 -0.001234:-1.234e-3 -0.01234:-12.34e-3 -0.1234:-123.4e-3 -1.234:-1.234e+0 -12.34:-12.34e+0 -123.4:-123.4e+0 -1234:-1.234e+3 -12340:-12.34e+3 -123400:-123.4e+3 -1234000:-1.234e+6 -12340000:-12.34e+6 -123400000:-123.4e+6 -1234000000:-1.234e+9 -12340000000:-12.34e+9 -123400000000:-123.4e+9 -1234000000000:-1.234e+12 -0.000003141592:-3.141592e-6 -0.00003141592:-31.41592e-6 -0.0003141592:-314.1592e-6 -0.003141592:-3.141592e-3 -0.03141592:-31.41592e-3 -0.3141592:-314.1592e-3 -3.141592:-3.141592e+0 -31.41592:-31.41592e+0 -314.1592:-314.1592e+0 -3141.592:-3.141592e+3 -31415.92:-31.41592e+3 -314159.2:-314.1592e+3 -3141592:-3.141592e+6 Math-BigInt-1.999808/t/bestr-mbi.t0000644403072340010010000000460512740677024016670 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 220; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); my $test = qq|\$x = Math::BigInt -> new("$x_str");| . qq| \$str = \$x -> bestr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0e+0 # positive numbers 1:1e+0 10:10e+0 100:100e+0 1000:1e+3 10000:10e+3 100000:100e+3 1000000:1e+6 10000000:10e+6 100000000:100e+6 1000000000:1e+9 10000000000:10e+9 100000000000:100e+9 1000000000000:1e+12 12:12e+0 120:120e+0 1200:1.2e+3 12000:12e+3 120000:120e+3 1200000:1.2e+6 12000000:12e+6 120000000:120e+6 1200000000:1.2e+9 12000000000:12e+9 120000000000:120e+9 1200000000000:1.2e+12 123:123e+0 1230:1.23e+3 12300:12.3e+3 123000:123e+3 1230000:1.23e+6 12300000:12.3e+6 123000000:123e+6 1230000000:1.23e+9 12300000000:12.3e+9 123000000000:123e+9 1230000000000:1.23e+12 1234:1.234e+3 12340:12.34e+3 123400:123.4e+3 1234000:1.234e+6 12340000:12.34e+6 123400000:123.4e+6 1234000000:1.234e+9 12340000000:12.34e+9 123400000000:123.4e+9 1234000000000:1.234e+12 3:3e+0 31:31e+0 314:314e+0 3141:3.141e+3 31415:31.415e+3 314159:314.159e+3 3141592:3.141592e+6 # negative numbers -1:-1e+0 -10:-10e+0 -100:-100e+0 -1000:-1e+3 -10000:-10e+3 -100000:-100e+3 -1000000:-1e+6 -10000000:-10e+6 -100000000:-100e+6 -1000000000:-1e+9 -10000000000:-10e+9 -100000000000:-100e+9 -1000000000000:-1e+12 -12:-12e+0 -120:-120e+0 -1200:-1.2e+3 -12000:-12e+3 -120000:-120e+3 -1200000:-1.2e+6 -12000000:-12e+6 -120000000:-120e+6 -1200000000:-1.2e+9 -12000000000:-12e+9 -120000000000:-120e+9 -1200000000000:-1.2e+12 -123:-123e+0 -1230:-1.23e+3 -12300:-12.3e+3 -123000:-123e+3 -1230000:-1.23e+6 -12300000:-12.3e+6 -123000000:-123e+6 -1230000000:-1.23e+9 -12300000000:-12.3e+9 -123000000000:-123e+9 -1230000000000:-1.23e+12 -1234:-1.234e+3 -12340:-12.34e+3 -123400:-123.4e+3 -1234000:-1.234e+6 -12340000:-12.34e+6 -123400000:-123.4e+6 -1234000000:-1.234e+9 -12340000000:-12.34e+9 -123400000000:-123.4e+9 -1234000000000:-1.234e+12 -3:-3e+0 -31:-31e+0 -314:-314e+0 -3141:-3.141e+3 -31415:-31.415e+3 -314159:-314.159e+3 -3141592:-3.141592e+6 Math-BigInt-1.999808/t/bigfltpm.inc0000644403072340010010000011707513031665735017124 0ustar ospjadomain users#include this file into another test for subclass testing... use strict; use warnings; our ($CLASS, $CALC); is($CLASS->config('lib'), $CALC, "$CLASS->config('lib')"); my ($x, $y, $z, @args, $try, $want, $got); my ($f, $setup); while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines if (s/^&//) { $f = $_; next; } if (/^\$/) { $setup = $_; $setup =~ s/\$/\$${CLASS}::/g; # round_mode, div_scale #print "\$setup== $setup\n"; next; } if (m|^(.*?):(/.+)$|) { $want = $2; @args = split(/:/, $1, 99); } else { @args = split(/:/, $_, 99); $want = pop(@args); } $try = qq|\$x = $CLASS->new("$args[0]");|; if ($f eq "bnorm") { $try .= qq| \$x;|; } elsif ($f =~ /^is_(zero|one|negative|positive|odd|even|nan|int)$/) { $try .= qq| \$x->$f();|; } elsif ($f eq "is_inf") { $try .= qq| \$x->is_inf("$args[1]");|; } elsif ($f eq "binf") { $try .= qq| \$x->binf("$args[1]");|; } elsif ($f eq "bone") { $try .= qq| \$x->bone("$args[1]");|; } elsif ($f eq "bstr") { $try .= qq| \$x->accuracy($args[1]); \$x->precision($args[2]);|; $try .= ' $x->bstr();'; # some unary ops } elsif ($f =~ /^b(nan|sstr|neg|floor|ceil|int|abs)$/) { $try .= qq| \$x->$f();|; # overloaded functions } elsif ($f =~ /^(log|exp|sin|cos|atan2|int|neg|abs|sqrt)$/) { $try .= qq| \$x = $f(\$x);|; } elsif ($f eq "parts") { # ->bstr() to see if an object is returned $try .= ' ($a, $b) = $x->parts(); $a = $a->bstr(); $b = $b->bstr();'; $try .= ' "$a $b";'; } elsif ($f eq "exponent") { # ->bstr() to see if an object is returned $try .= ' $x->exponent()->bstr();'; } elsif ($f eq "mantissa") { # ->bstr() to see if an object is returned $try .= ' $x->mantissa()->bstr();'; } elsif ($f =~ /^(numify|length|as_number|as_hex|as_bin)$/) { $try .= qq| \$x->$f();|; } elsif ($f eq "bpi") { $try .= qq| $CLASS->bpi(\$x);|; } elsif ($f eq "binc") { $try .= ' $x->binc();'; } elsif ($f eq "bdec") { $try .= ' $x->bdec();'; } elsif ($f eq "bround") { $try .= qq| $setup; \$x->bround($args[1]);|; } elsif ($f eq "bfround") { $try .= qq| $setup; \$x->bfround($args[1]);|; } elsif ($f eq "bsqrt") { $try .= qq| $setup; \$x->bsqrt();|; } elsif ($f eq "bfac") { $try .= qq| $setup; \$x->bfac();|; } elsif ($f eq "bdfac") { $try .= qq| $setup; \$x->bdfac();|; } elsif ($f eq "blog") { if (defined $args[1] && $args[1] ne '') { $try .= qq| \$y = $CLASS->new($args[1]);|; $try .= qq| $setup; \$x->blog(\$y);|; } else { $try .= qq| $setup; \$x->blog();|; } } else { # binary operators $try .= qq| \$y = $CLASS->new("$args[1]");|; if ($f eq "bgcd") { if (defined $args[2]) { $try .= qq| \$z = $CLASS->new("$args[2]");|; } $try .= qq| $CLASS\::bgcd(\$x, \$y|; $try .= qq|, \$z| if defined $args[2]; $try .= qq|);|; } elsif ($f eq "blcm") { if (defined $args[2]) { $try .= qq| \$z = $CLASS->new("$args[2]");|; } $try .= qq| $CLASS\::blcm(\$x, \$y|; $try .= qq|, \$z| if defined $args[2]; $try .= qq|);|; } elsif ($f eq "bcmp") { $try .= ' $x->bcmp($y);'; } elsif ($f eq "bacmp") { $try .= ' $x->bacmp($y);'; } elsif ($f eq "bpow") { $try .= ' $x->bpow($y);'; } elsif ($f eq "bnok") { $try .= ' $x->bnok($y);'; } elsif ($f eq "bcos") { $try .= ' $x->bcos($y);'; } elsif ($f eq "bsin") { $try .= ' $x->bsin($y);'; } elsif ($f eq "batan") { $try .= ' $x->batan($y);'; } elsif ($f eq "broot") { $try .= qq| $setup; \$x->broot(\$y);|; } elsif ($f eq "badd") { $try .= ' $x->badd($y);'; } elsif ($f eq "bsub") { $try .= ' $x->bsub($y);'; } elsif ($f eq "bmul") { $try .= ' $x->bmul($y);'; } elsif ($f eq "bdiv") { $try .= qq| $setup; scalar \$x->bdiv(\$y);|; } elsif ($f eq "bdiv-list") { $try .= qq| $setup; join(",", \$x->bdiv(\$y));|; } elsif ($f eq "brsft") { $try .= ' $x->brsft($y);'; } elsif ($f eq "blsft") { $try .= ' $x->blsft($y);'; } elsif ($f eq "bmod") { $try .= ' $x->bmod($y);'; } else { # Functions with three arguments $try .= qq| \$z = $CLASS->new("$args[2]");|; if ($f eq "bmodpow") { $try .= ' $x->bmodpow($y, $z);'; } elsif ($f eq "bmuladd") { $try .= ' $x->bmuladd($y, $z);'; } elsif ($f eq "batan2") { $try .= ' $x->batan2($y, $z);'; } else { warn qq|Unknown op "$f"|; } } } $got = eval $try; print "# Error: $@\n" if $@; if ($want =~ m|^/(.*)$|) { my $pat = $1; like($got, qr/$pat/, $try); } else { if ($want eq "") { is($got, undef, $try); } else { is($got, $want, $try); if (ref($got) eq $CLASS) { # float numbers are normalized (for now), so mantissa shouldn't # have trailing zeros print $got->_trailing_zeros(), "\n"; is($CALC->_zeros($got->{_m}), 0, $try); } } } # end pattern or string } # end while # check whether $CLASS->new(Math::BigInt->new()) destroys it # ($y == 12 in this case) $x = Math::BigInt->new(1200); $y = $CLASS->new($x); is($y, 1200, q|$x = Math::BigInt->new(1200); $y = $CLASS->new($x); # check $y|); is($x, 1200, q|$x = Math::BigInt->new(1200); $y = $CLASS->new($x); # check $x|); ############################################################################### # Really huge, big, ultra-mega-biggy-monster exponents. Technically, the # exponents should not be limited (they are Math::BigInt objects), but # practically there are a few places were they are limited to a Perl scalar. # This is sometimes for speed, sometimes because otherwise the number wouldn't # fit into your memory (just think of 1e123456789012345678901234567890 + 1!) # anyway. We don't test everything here, but let's make sure it just basically # works. my $monster = '1e1234567890123456789012345678901234567890'; # new and exponent is($CLASS->new($monster)->bsstr(), '1e+1234567890123456789012345678901234567890', qq|$CLASS->new("$monster")->bsstr()|); is($CLASS->new($monster)->exponent(), '1234567890123456789012345678901234567890', qq|$CLASS->new("$monster")->exponent()|); # cmp is($CLASS->new($monster) > 0, 1, qq|$CLASS->new("$monster") > 0|); # sub/mul is($CLASS->new($monster)->bsub($monster), 0, qq|$CLASS->new("$monster")->bsub("$monster")|); is($CLASS->new($monster)->bmul(2)->bsstr(), '2e+1234567890123456789012345678901234567890', qq|$CLASS->new("$monster")->bmul(2)->bsstr()|); # mantissa $monster = '1234567890123456789012345678901234567890e2'; is($CLASS->new($monster)->mantissa(), '123456789012345678901234567890123456789', qq|$CLASS->new("$monster")->mantissa()|); ############################################################################### # zero, inf, one, nan $x = $CLASS->new(2); $x->bzero(); is($x->{_a}, undef, qq|\$x = $CLASS->new(2); \$x->bzero(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $CLASS->new(2); \$x->bzero(); \$x->{_p}|); $x = $CLASS->new(2); $x->binf(); is($x->{_a}, undef, qq|\$x = $CLASS->new(2); \$x->binf(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $CLASS->new(2); \$x->binf(); \$x->{_p}|); $x = $CLASS->new(2); $x->bone(); is($x->{_a}, undef, qq|\$x = $CLASS->new(2); \$x->bone(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $CLASS->new(2); \$x->bone(); \$x->{_p}|); $x = $CLASS->new(2); $x->bnan(); is($x->{_a}, undef, qq|\$x = $CLASS->new(2); \$x->bnan(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $CLASS->new(2); \$x->bnan(); \$x->{_p}|); ############################################################################### # bone/binf etc as plain calls (Lite failed them) is($CLASS->bzero(), 0, qq|$CLASS->bzero()|); is($CLASS->bone(), 1, qq|$CLASS->bone()|); is($CLASS->bone("+"), 1, qq|$CLASS->bone("+")|); is($CLASS->bone("-"), -1, qq|$CLASS->bone("-")|); is($CLASS->bnan(), "NaN", qq|$CLASS->bnan()|); is($CLASS->binf(), "inf", qq|$CLASS->binf()|); is($CLASS->binf("+"), "inf", qq|$CLASS->binf("+")|); is($CLASS->binf("-"), "-inf", qq|$CLASS->binf("-")|); is($CLASS->binf("-inf"), "-inf", qq|$CLASS->binf("-inf")|); $CLASS->accuracy(undef); # reset $CLASS->precision(undef); # reset ############################################################################### # bsqrt() with set global A/P or A/P enabled on $x, also a test whether bsqrt() # correctly modifies $x $x = $CLASS->new(12); $CLASS->precision(-2); $x->bsqrt(); is($x, '3.46', qq|\$x = $CLASS->new(12); $CLASS->precision(-2); \$x->bsqrt();|); $CLASS->precision(undef); $x = $CLASS->new(12); $CLASS->precision(0); $x->bsqrt(); is($x, '3', qq|$CLASS->precision(undef); \$x = $CLASS->new(12);| . qq| $CLASS->precision(0); \$x->bsqrt();|); $CLASS->precision(-3); $x = $CLASS->new(12); $x->bsqrt(); is($x, '3.464', qq|$CLASS->precision(-3); \$x = $CLASS->new(12); \$x->bsqrt();|); { no strict 'refs'; # A and P set => NaN ${${CLASS}.'::accuracy'} = 4; $x = $CLASS->new(12); $x->bsqrt(3); is($x, 'NaN', "A and P set => NaN"); # supplied arg overrides set global $CLASS->precision(undef); $x = $CLASS->new(12); $x->bsqrt(3); is($x, '3.46', "supplied arg overrides set global"); # reset for further tests $CLASS->accuracy(undef); $CLASS->precision(undef); } ############################################################################# # can we call objectify (broken until v1.52) { no strict; $try = '@args' . " = $CLASS" . "::objectify(2, $CLASS, 4, 5);" . ' join(" ", @args);'; $want = eval $try; is($want, "$CLASS 4 5", $try); } ############################################################################# # is_one('-') (broken until v1.64) is($CLASS->new(-1)->is_one(), 0, qq|$CLASS->new(-1)->is_one()|); is($CLASS->new(-1)->is_one("-"), 1, qq|$CLASS->new(-1)->is_one("-")|); ############################################################################# # bug 1/0.5 leaving 2e-0 instead of 2e0 is($CLASS->new(1)->bdiv("0.5")->bsstr(), "2e+0", qq|$CLASS->new(1)->bdiv("0.5")->bsstr()|); ############################################################################### # [perl #30609] bug with $x -= $x not being 0, but 2*$x $x = $CLASS->new(3); $x -= $x; is($x, 0, qq|\$x = $CLASS->new(3); \$x -= \$x;|); $x = $CLASS->new(-3); $x -= $x; is($x, 0, qq|\$x = $CLASS->new(-3); \$x -= \$x;|); $x = $CLASS->new(3); $x += $x; is($x, 6, qq|\$x = $CLASS->new(3); \$x += \$x;|); $x = $CLASS->new(-3); $x += $x; is($x, -6, qq|\$x = $CLASS->new(-3); \$x += \$x;|); $x = $CLASS->new("NaN"); $x -= $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("NaN"); \$x -= \$x;|); $x = $CLASS->new("inf"); $x -= $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("inf"); \$x -= \$x;|); $x = $CLASS->new("-inf"); $x -= $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("-inf"); \$x -= \$x;|); $x = $CLASS->new("NaN"); $x += $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("NaN"); \$x += \$x;|); $x = $CLASS->new("inf"); $x += $x; is($x->is_inf(), 1, qq|\$x = $CLASS->new("inf"); \$x += \$x;|); $x = $CLASS->new("-inf"); $x += $x; is($x->is_inf("-"), 1, qq|\$x = $CLASS->new("-inf"); \$x += \$x;|); $x = $CLASS->new("3.14"); $x -= $x; is($x, 0, qq|\$x = $CLASS->new("3.14"); \$x -= \$x;|); $x = $CLASS->new("-3.14"); $x -= $x; is($x, 0, qq|\$x = $CLASS->new("-3.14"); \$x -= \$x;|); $x = $CLASS->new("3.14"); $x += $x; is($x, "6.28", qq|$x = $CLASS->new("3.14"); $x += $x;|); $x = $CLASS->new("-3.14"); $x += $x; is($x, "-6.28", qq|$x = $CLASS->new("-3.14"); $x += $x;|); $x = $CLASS->new("3.14"); $x *= $x; is($x, "9.8596", qq|$x = $CLASS->new("3.14"); $x *= $x;|); $x = $CLASS->new("-3.14"); $x *= $x; is($x, "9.8596", qq|$x = $CLASS->new("-3.14"); $x *= $x;|); $x = $CLASS->new("3.14"); $x /= $x; is($x, "1", qq|$x = $CLASS->new("3.14"); $x /= $x;|); $x = $CLASS->new("-3.14"); $x /= $x; is($x, "1", qq|$x = $CLASS->new("-3.14"); $x /= $x;|); $x = $CLASS->new("3.14"); $x %= $x; is($x, "0", qq|$x = $CLASS->new("3.14"); $x %= $x;|); $x = $CLASS->new("-3.14"); $x %= $x; is($x, "0", qq|$x = $CLASS->new("-3.14"); $x %= $x;|); ############################################################################### # the following two were reported by "kenny" via hotmail.com: #perl -MMath::BigFloat -wle 'print Math::BigFloat->new(0)->bpow(".1")' #Use of uninitialized value in numeric le (<=) at BigFloat.pm line 1851. $x = $CLASS->new(0); $y = $CLASS->new("0.1"); is($x ** $y, 0, qq|\$x = $CLASS->new(0); \$y = $CLASS->new("0.1"); \$x ** \$y|); #perl -MMath::BigFloat -lwe 'print Math::BigFloat->new(".222222222222222222222222222222222222222222")->bceil()' #Use of uninitialized value in numeric le (<=) at BigFloat.pm line 1851. $x = $CLASS->new(".222222222222222222222222222222222222222222"); is($x->bceil(), 1, qq|$x = $CLASS->new(".222222222222222222222222222222222222222222");| . qq| $x->bceil();|); ############################################################################### # test **=, <<=, >>= # ((2**148)+1)/17 $x = $CLASS->new(2); $x **= 148; $x++; $x->bdiv(17, 60)->bfloor(); $x->accuracy(undef); is($x, "20988936657440586486151264256610222593863921", "value of ((2**148)+1)/17"); is($x->length(), length("20988936657440586486151264256610222593863921"), "number of digits in ((2**148)+1)/17"); $x = $CLASS->new("2"); $y = $CLASS->new("18"); is($x <<= $y, 2 << 18, qq|\$x = $CLASS->new("2"); \$y = $CLASS->new("18");| . q| $x <<= $y|); is($x, 2 << 18, qq|\$x = $CLASS->new("2"); \$y = $CLASS->new("18");| . q| $x <<= $y; $x|); is($x >>= $y, 2, qq|\$x = $CLASS->new("2"); \$y = $CLASS->new("18");| . q| $x <<= $y; $x >>= $y|); is($x, 2, qq|\$x = $CLASS->new("2"); \$y = $CLASS->new("18");| . q| $x <<= $y; $x >>= $y; $x|); $x = $CLASS->new("2"); $y = $CLASS->new("18.2"); # 2 * (2 ** int(18.2)); $x <<= $y; is($x->copy()->bfround(-9), "602248.763144685", qq|\$x = $CLASS->new("2"); \$y = $CLASS->new("18.2");| . q| $x <<= $y; $x->copy()->bfround(-9);|); # 2 * (2 ** 18.2) / (2 ** 18.2) => 2 is($x >>= $y, 2, qq|\$x = $CLASS->new("2"); \$y = $CLASS->new("18.2");| . q| $x <<= $y; $x->copy()->bfround(-9); $x >>= $y|); is($x, 2, qq|\$x = $CLASS->new("2"); \$y = $CLASS->new("18.2");| . q| $x <<= $y; $x->copy()->bfround(-9); $x >>= $y; $x|); __DATA__ &bgcd inf:12:NaN -inf:12:NaN 12:inf:NaN 12:-inf:NaN inf:inf:NaN inf:-inf:NaN -inf:-inf:NaN abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:0 +0:+1:1 +1:+0:1 +1:+1:1 +2:+3:1 +3:+2:1 -3:+2:1 -3:-2:1 -144:-60:12 144:-60:12 144:60:12 100:625:25 4096:81:1 1034:804:2 27:90:56:1 27:90:54:9 &blcm abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:NaN +1:+0:0 +0:+1:0 +27:+90:270 +1034:+804:415668 $div_scale = 40 &bcos 1.2:10:0.3623577545 2.4:12:-0.737393715541 0:10:1 0:20:1 1:10:0.5403023059 1:12:0.540302305868 &bsin 1:10:0.8414709848 0:10:0 0:20:0 2.1:12:0.863209366649 1.2:13:0.9320390859672 0.2:13:0.1986693307951 3.2:12:-0.0583741434276 &batan NaN:10:NaN inf:14:1.5707963267949 -inf:14:-1.5707963267949 0:14:0 0:10:0 0.1:14:0.099668652491162 0.2:13:0.1973955598499 0.2:14:0.19739555984988 0.5:14:0.46364760900081 1:14:0.78539816339744 -1:14:-0.78539816339744 1.5:14:0.98279372324732 2.0:14:1.1071487177941 2.5:14:1.1902899496825 3.0:14:1.2490457723982 6.0:14:1.4056476493803 12:14:1.4876550949064 24:14:1.5291537476963 48:14:1.5499660067587 &batan2 NaN:1:10:NaN NaN:NaN:10:NaN 1:NaN:10:NaN -inf:-inf:14:-2.3561944901923 -inf:-1:14:-1.5707963267949 -inf:0:14:-1.5707963267949 -inf:+1:14:-1.5707963267949 -inf:+inf:14:-0.78539816339745 -1:-inf:14:-3.1415926535898 -1:-1:14:-2.3561944901923 -1:0:14:-1.5707963267949 -1:+1:14:-0.78539816339745 -1:+inf:14:0 0:-inf:14:3.1415926535898 0:-1:14:3.1415926535898 0:0:14:0 0:+1:14:0 0:+inf:14:0 +1:-inf:14:3.1415926535898 +1:-1:14:2.3561944901923 +1:0:14:1.5707963267949 +1:+1:14:0.78539816339745 +1:+inf:14:0 +inf:-inf:14:2.3561944901923 +inf:-1:14:1.5707963267949 +inf:0:14:1.5707963267949 +inf:+1:14:1.5707963267949 +inf:+inf:14:0.78539816339745 1:5:13:0.1973955598499 1:5:14:0.19739555984988 0:2:14:0 5:0:14:1.5707963267949 -1:0:11:-1.5707963268 -2:0:77:-1.5707963267948966192313216916397514420985846996875529104874722961539082031431 2:0:77:1.5707963267948966192313216916397514420985846996875529104874722961539082031431 -1:5:14:-0.19739555984988 1:5:14:0.19739555984988 -1:8:14:-0.12435499454676 1:8:14:0.12435499454676 # test an argument X > 1 and one X < 1 1:2:24:0.463647609000806116214256 2:1:14:1.1071487177941 -2:1:14:-1.1071487177941 &bpi 150:3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940813 77:3.1415926535897932384626433832795028841971693993751058209749445923078164062862 +0:3.141592653589793238462643383279502884197 11:3.1415926536 &bnok +inf:10:inf NaN:NaN:NaN NaN:1:NaN 1:NaN:NaN 1:1:1 # k > n 1:2:0 2:3:0 # k < 0 1:-2:0 # 7 over 3 = 35 7:3:35 7:6:7 100:90:17310309456440 100:95:75287520 2:0:1 7:0:1 2:1:2 &blog 0::-inf -1::NaN -2::NaN # base > 0, base != 1 2:-1:NaN 2:0:0 2:1:NaN # log(1) 1::0 1:1:NaN 1:2:0 2::0.6931471805599453094172321214581765680755 2.718281828::0.9999999998311266953289851340574956564911 $div_scale = 20 2.718281828::0.99999999983112669533 $div_scale = 15 123::4.81218435537242 10::2.30258509299405 1000::6.90775527898214 100::4.60517018598809 2::0.693147180559945 3.1415::1.14470039286086 12345::9.42100640177928 0.001::-6.90775527898214 # bug until v1.71: 10:10:1 100:100:1 # reset for further tests $div_scale = 40 1::0 &brsft NaNbrsft:2:NaN 0:2:0 1:1:0.5 2:1:1 4:1:2 123:1:61.5 32:3:4 &blsft NaNblsft:0:NaN 2:1:4 4:3:32 5:3:40 1:2:4 0:5:0 &bnorm 1:1 -0:0 bnormNaN:NaN +inf:inf -inf:-inf 123:123 -123.4567:-123.4567 # invalid inputs 1__2:NaN 1E1__2:NaN 11__2E2:NaN .2E-3.:NaN 1e3e4:NaN # strange, but valid .2E2:20 1.E3:1000 # some inputs that result in zero 0e0:0 +0e0:0 +0e+0:0 -0e+0:0 0e-0:0 -0e-0:0 +0e-0:0 000:0 00e2:0 00e02:0 000e002:0 000e1230:0 00e-3:0 00e+3:0 00e-03:0 00e+03:0 -000:0 -00e2:0 -00e02:0 -000e002:0 -000e1230:0 -00e-3:0 -00e+3:0 -00e-03:0 -00e+03:0 &as_number 0:0 1:1 1.2:1 2.345:2 -2:-2 -123.456:-123 -200:-200 -inf:-inf inf:inf NaN:NaN 71243225429896467497217836789578596379:71243225429896467497217836789578596379 # test for bug in brsft() not handling cases that return 0 0.000641:0 0.0006412:0 0.00064123:0 0.000641234:0 0.0006412345:0 0.00064123456:0 0.000641234567:0 0.0006412345678:0 0.00064123456789:0 0.1:0 0.01:0 0.001:0 0.0001:0 0.00001:0 0.000001:0 0.0000001:0 0.00000001:0 0.000000001:0 0.0000000001:0 0.00000000001:0 0.12345:0 0.123456:0 0.1234567:0 0.12345678:0 0.123456789:0 &binf 1:+:inf 2:-:-inf 3:abc:inf &as_hex +inf:inf -inf:-inf hexNaN:NaN 0:0x0 5:0x5 -5:-0x5 &as_bin +inf:inf -inf:-inf hexNaN:NaN 0:0b0 5:0b101 -5:-0b101 &numify # uses bsstr() so 5 => 5e+0 to be compatible w/ Perls output 0:0 +1:1 1234:1234 -5:-5 100:100 -100:-100 &bnan abc:NaN 2:NaN -2:NaN 0:NaN &bone 2:+:1 -2:-:-1 -2:+:1 2:-:-1 0::1 -2::1 abc::1 2:abc:1 &bsstr +inf:inf -inf:-inf abcfsstr:NaN -abcfsstr:NaN 1234.567:1234567e-3 123:123e+0 -5:-5e+0 -100:-1e+2 &bstr +inf:::inf -inf:::-inf abcfstr:::NaN 1234.567:9::1234.56700 1234.567::-6:1234.567000 12345:5::12345 0.001234:6::0.00123400 0.001234::-8:0.00123400 0:4::0 0::-4:0.0000 &bnorm inf:inf +inf:inf -inf:-inf +infinity:inf +-inf:NaN abc:NaN 1 a:NaN 1bcd2:NaN 11111b:NaN +1z:NaN -1z:NaN 0e999:0 0e-999:0 -0e999:0 -0e-999:0 0:0 +0:0 +00:0 +0_0_0:0 000000_0000000_00000:0 -0:0 -0000:0 +1:1 +01:1 +001:1 +00000100000:100000 123456789:123456789 -1:-1 -01:-1 -001:-1 -123456789:-123456789 -00000100000:-100000 123.456a:NaN 123.456:123.456 0.01:0.01 .002:0.002 +.2:0.2 -0.0003:-0.0003 -.0000000004:-0.0000000004 123456E2:12345600 123456E-2:1234.56 -123456E2:-12345600 -123456E-2:-1234.56 1e1:10 2e-11:0.00000000002 # exercise _split .02e-1:0.002 000001:1 -00001:-1 -1:-1 000.01:0.01 -000.0023:-0.0023 1.1e1:11 -3e111:-3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 -4e-1111:-0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004 &bpow NaN:1:NaN 1:NaN:NaN NaN:-1:NaN -1:NaN:NaN NaN:-21:NaN -21:NaN:NaN NaN:21:NaN 21:NaN:NaN 0:0:1 0:1:0 0:9:0 0:-2:inf 2:2:4 1:2:1 1:3:1 -1:2:1 -1:3:-1 123.456:2:15241.383936 2:-2:0.25 2:-3:0.125 128:-2:0.00006103515625 abc:123.456:NaN 123.456:abc:NaN +inf:123.45:inf -inf:123.45:-inf +inf:-123.45:inf -inf:-123.45:-inf -2:2:4 -2:3:-8 -2:4:16 -2:5:-32 -3:2:9 -3:3:-27 -3:4:81 -3:5:-243 # 2 ** 0.5 == sqrt(2) # 1.41..7 and not 1.4170 since fallback (bsqrt(9) is '3', not 3.0...0) 2:0.5:1.41421356237309504880168872420969807857 #2:0.2:1.148698354997035006798626946777927589444 #6:1.5:14.6969384566990685891837044482353483518 $div_scale = 20 #62.5:12.5:26447206647554886213592.3959144 $div_scale = 40 &bneg bnegNaN:NaN +inf:-inf -inf:inf +0:0 +1:-1 -1:1 +123456789:-123456789 -123456789:123456789 +123.456789:-123.456789 -123456.789:123456.789 &babs babsNaN:NaN +inf:inf -inf:inf +0:0 +1:1 -1:1 +123456789:123456789 -123456789:123456789 +123.456789:123.456789 -123456.789:123456.789 &bround $round_mode = "trunc" +inf:5:inf -inf:5:-inf 0:5:0 NaNfround:5:NaN +10123456789:5:10123000000 -10123456789:5:-10123000000 +10123456789.123:5:10123000000 -10123456789.123:5:-10123000000 +10123456789:9:10123456700 -10123456789:9:-10123456700 +101234500:6:101234000 -101234500:6:-101234000 $round_mode = "zero" +20123456789:5:20123000000 -20123456789:5:-20123000000 +20123456789.123:5:20123000000 -20123456789.123:5:-20123000000 +20123456789:9:20123456800 -20123456789:9:-20123456800 +201234500:6:201234000 -201234500:6:-201234000 $round_mode = "+inf" +30123456789:5:30123000000 -30123456789:5:-30123000000 +30123456789.123:5:30123000000 -30123456789.123:5:-30123000000 +30123456789:9:30123456800 -30123456789:9:-30123456800 +301234500:6:301235000 -301234500:6:-301234000 $round_mode = "-inf" +40123456789:5:40123000000 -40123456789:5:-40123000000 +40123456789.123:5:40123000000 -40123456789.123:5:-40123000000 +40123456789:9:40123456800 -40123456789:9:-40123456800 +401234500:6:401234000 -401234500:6:-401235000 $round_mode = "odd" +50123456789:5:50123000000 -50123456789:5:-50123000000 +50123456789.123:5:50123000000 -50123456789.123:5:-50123000000 +50123456789:9:50123456800 -50123456789:9:-50123456800 +501234500:6:501235000 -501234500:6:-501235000 $round_mode = "even" +60123456789:5:60123000000 -60123456789:5:-60123000000 +60123456789:9:60123456800 -60123456789:9:-60123456800 +601234500:6:601234000 -601234500:6:-601234000 +60123456789.0123:5:60123000000 -60123456789.0123:5:-60123000000 $round_mode = "common" +60123456789:5:60123000000 -60123456789:5:-60123000000 +60123456789:6:60123500000 -60123456789:6:-60123500000 +60123456789:9:60123456800 -60123456789:9:-60123456800 +601234500:6:601235000 -601234500:6:-601235000 +601234400:6:601234000 -601234400:6:-601234000 +601234600:6:601235000 -601234600:6:-601235000 +601234300:6:601234000 +60123456789.0123:5:60123000000 -60123456789.0123:5:-60123000000 &bfround $round_mode = "trunc" +inf:5:inf -inf:5:-inf 0:5:0 NaNffround:5:NaN +1.23:-1:1.2 +1.234:-1:1.2 +1.2345:-1:1.2 +1.23:-2:1.23 +1.234:-2:1.23 +1.2345:-2:1.23 +1.23:-3:1.230 +1.234:-3:1.234 +1.2345:-3:1.234 -1.23:-1:-1.2 +1.27:-1:1.2 -1.27:-1:-1.2 +1.25:-1:1.2 -1.25:-1:-1.2 +1.35:-1:1.3 -1.35:-1:-1.3 -0.0061234567890:-1:0.0 -0.0061:-1:0.0 -0.00612:-1:0.0 -0.00612:-2:0.00 -0.006:-1:0.0 -0.006:-2:0.00 -0.0006:-2:0.00 -0.0006:-3:0.000 -0.0065:-3:/-0\.006|-6e-03 -0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 -0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 0.05:0:0 0.5:0:0 0.51:0:0 0.41:0:0 $round_mode = "zero" +2.23:-1:/2.2(?:0{5}\d+)? -2.23:-1:/-2.2(?:0{5}\d+)? +2.27:-1:/2.(?:3|29{5}\d+) -2.27:-1:/-2.(?:3|29{5}\d+) +2.25:-1:/2.2(?:0{5}\d+)? -2.25:-1:/-2.2(?:0{5}\d+)? +2.35:-1:/2.(?:3|29{5}\d+) -2.35:-1:/-2.(?:3|29{5}\d+) -0.0065:-1:0.0 -0.0065:-2:/-0\.01|-1e-02 -0.0065:-3:/-0\.006|-6e-03 -0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 -0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 0.05:0:0 0.5:0:0 0.51:0:1 0.41:0:0 $round_mode = "+inf" +3.23:-1:/3.2(?:0{5}\d+)? -3.23:-1:/-3.2(?:0{5}\d+)? +3.27:-1:/3.(?:3|29{5}\d+) -3.27:-1:/-3.(?:3|29{5}\d+) +3.25:-1:/3.(?:3|29{5}\d+) -3.25:-1:/-3.2(?:0{5}\d+)? +3.35:-1:/3.(?:4|39{5}\d+) -3.35:-1:/-3.(?:3|29{5}\d+) -0.0065:-1:0.0 -0.0065:-2:/-0\.01|-1e-02 -0.0065:-3:/-0\.006|-6e-03 -0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 -0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 0.05:0:0 0.5:0:1 0.51:0:1 0.41:0:0 $round_mode = "-inf" +4.23:-1:/4.2(?:0{5}\d+)? -4.23:-1:/-4.2(?:0{5}\d+)? +4.27:-1:/4.(?:3|29{5}\d+) -4.27:-1:/-4.(?:3|29{5}\d+) +4.25:-1:/4.2(?:0{5}\d+)? -4.25:-1:/-4.(?:3|29{5}\d+) +4.35:-1:/4.(?:3|29{5}\d+) -4.35:-1:/-4.(?:4|39{5}\d+) -0.0065:-1:0.0 -0.0065:-2:/-0\.01|-1e-02 -0.0065:-3:/-0\.007|-7e-03 -0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 -0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 0.05:0:0 0.5:0:0 0.51:0:1 0.41:0:0 $round_mode = "odd" +5.23:-1:/5.2(?:0{5}\d+)? -5.23:-1:/-5.2(?:0{5}\d+)? +5.27:-1:/5.(?:3|29{5}\d+) -5.27:-1:/-5.(?:3|29{5}\d+) +5.25:-1:/5.(?:3|29{5}\d+) -5.25:-1:/-5.(?:3|29{5}\d+) +5.35:-1:/5.(?:3|29{5}\d+) -5.35:-1:/-5.(?:3|29{5}\d+) -0.0065:-1:0.0 -0.0065:-2:/-0\.01|-1e-02 -0.0065:-3:/-0\.007|-7e-03 -0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 -0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 0.05:0:0 0.5:0:1 0.51:0:1 0.41:0:0 $round_mode = "even" +6.23:-1:/6.2(?:0{5}\d+)? -6.23:-1:/-6.2(?:0{5}\d+)? +6.27:-1:/6.(?:3|29{5}\d+) -6.27:-1:/-6.(?:3|29{5}\d+) +6.25:-1:/6.(?:2(?:0{5}\d+)?|29{5}\d+) -6.25:-1:/-6.(?:2(?:0{5}\d+)?|29{5}\d+) +6.35:-1:/6.(?:4|39{5}\d+|29{8}\d+) -6.35:-1:/-6.(?:4|39{5}\d+|29{8}\d+) -0.0065:-1:0.0 -0.0065:-2:/-0\.01|-1e-02 -0.0065:-3:/-0\.006|-7e-03 -0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 -0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03 0.05:0:0 0.5:0:0 0.51:0:1 0.41:0:0 0.01234567:-3:0.012 0.01234567:-4:0.0123 0.01234567:-5:0.01235 0.01234567:-6:0.012346 0.01234567:-7:0.0123457 0.01234567:-8:0.01234567 0.01234567:-9:0.012345670 0.01234567:-12:0.012345670000 &bcmp bcmpNaN:bcmpNaN: bcmpNaN:+0: +0:bcmpNaN: +0:+0:0 -1:+0:-1 +0:-1:1 +1:+0:1 +0:+1:-1 -1:+1:-1 +1:-1:1 -1:-1:0 +1:+1:0 -1.1:0:-1 +0:-1.1:1 +1.1:+0:1 +0:+1.1:-1 +123:+123:0 +123:+12:1 +12:+123:-1 -123:-123:0 -123:-12:-1 -12:-123:1 +123:+124:-1 +124:+123:1 -123:-124:1 -124:-123:-1 0:0.01:-1 0:0.0001:-1 0:-0.0001:1 0:-0.1:1 0.1:0:1 0.00001:0:1 -0.0001:0:-1 -0.1:0:-1 0:0.0001234:-1 0:-0.0001234:1 0.0001234:0:1 -0.0001234:0:-1 0.0001:0.0005:-1 0.0005:0.0001:1 0.005:0.0001:1 0.001:0.0005:1 0.000001:0.0005:-1 0.00000123:0.0005:-1 0.00512:0.0001:1 0.005:0.000112:1 0.00123:0.0005:1 1.5:2:-1 2:1.5:1 1.54321:234:-1 234:1.54321:1 1e1234567890987654321:1e1234567890987654320:1 1e-1234567890987654321:1e-1234567890987654320:-1 # infinity -inf:5432112345:-1 +inf:5432112345:1 -inf:-5432112345:-1 +inf:-5432112345:1 -inf:54321.12345:-1 +inf:54321.12345:1 -inf:-54321.12345:-1 +inf:-54321.12345:1 +inf:+inf:0 -inf:-inf:0 +inf:-inf:1 -inf:+inf:-1 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &bacmp bcmpNaN:bcmpNaN: bcmpNaN:+0: +0:bcmpNaN: +0:+0:0 -1:+0:1 +0:-1:-1 +1:+0:1 +0:+1:-1 -1:+1:0 +1:-1:0 -1:-1:0 +1:+1:0 -1.1:0:1 +0:-1.1:-1 +1.1:+0:1 +0:+1.1:-1 +123:+123:0 +123:+12:1 +12:+123:-1 -123:-123:0 -123:-12:1 -12:-123:-1 +123:+124:-1 +124:+123:1 -123:-124:-1 -124:-123:1 0:0.01:-1 0:0.0001:-1 0:-0.0001:-1 0:-0.1:-1 0.1:0:1 0.00001:0:1 -0.0001:0:1 -0.1:0:1 0:0.0001234:-1 0:-0.0001234:-1 0.0001234:0:1 -0.0001234:0:1 0.0001:0.0005:-1 0.0005:0.0001:1 0.005:0.0001:1 0.001:0.0005:1 0.000001:0.0005:-1 0.00000123:0.0005:-1 0.00512:0.0001:1 0.005:0.000112:1 0.00123:0.0005:1 1.5:2:-1 2:1.5:1 1.54321:234:-1 234:1.54321:1 # infinity -inf:5432112345:1 +inf:5432112345:1 -inf:-5432112345:1 +inf:-5432112345:1 -inf:54321.12345:1 +inf:54321.12345:1 -inf:-54321.12345:1 +inf:-54321.12345:1 +inf:+inf:0 -inf:-inf:0 +inf:-inf:0 -inf:+inf:0 5:inf:-1 -1:inf:-1 5:-inf:-1 -1:-inf:-1 # return undef +inf:bacmpNaN: bacmpNaN:inf: -inf:bacmpNaN: bacmpNaN:-inf: &bdec bdecNaN:NaN +inf:inf -inf:-inf +0:-1 +1:0 -1:-2 1.23:0.23 -1.23:-2.23 100:99 101:100 -100:-101 -99:-100 -98:-99 99:98 &binc bincNaN:NaN +inf:inf -inf:-inf +0:1 +1:2 -1:0 1.23:2.23 -1.23:-0.23 100:101 -100:-99 -99:-98 -101:-100 99:100 &badd abc:abc:NaN abc:+0:NaN +0:abc:NaN +inf:-inf:NaN -inf:+inf:NaN +inf:+inf:inf -inf:-inf:-inf baddNaN:+inf:NaN baddNaN:+inf:NaN +inf:baddNaN:NaN -inf:baddNaN:NaN +0:+0:0 +1:+0:1 +0:+1:1 +1:+1:2 -1:+0:-1 +0:-1:-1 -1:-1:-2 -1:+1:0 +1:-1:0 +9:+1:10 +99:+1:100 +999:+1:1000 +9999:+1:10000 +99999:+1:100000 +999999:+1:1000000 +9999999:+1:10000000 +99999999:+1:100000000 +999999999:+1:1000000000 +9999999999:+1:10000000000 +99999999999:+1:100000000000 +10:-1:9 +100:-1:99 +1000:-1:999 +10000:-1:9999 +100000:-1:99999 +1000000:-1:999999 +10000000:-1:9999999 +100000000:-1:99999999 +1000000000:-1:999999999 +10000000000:-1:9999999999 +123456789:+987654321:1111111110 -123456789:+987654321:864197532 -123456789:-987654321:-1111111110 +123456789:-987654321:-864197532 0.001234:0.0001234:0.0013574 &bsub abc:abc:NaN abc:+0:NaN +0:abc:NaN +inf:-inf:inf -inf:+inf:-inf +inf:+inf:NaN -inf:-inf:NaN baddNaN:+inf:NaN baddNaN:+inf:NaN +inf:baddNaN:NaN -inf:baddNaN:NaN +0:+0:0 +1:+0:1 +0:+1:-1 +1:+1:0 -1:+0:-1 +0:-1:1 -1:-1:0 -1:+1:-2 +1:-1:2 +9:+1:8 +99:+1:98 +999:+1:998 +9999:+1:9998 +99999:+1:99998 +999999:+1:999998 +9999999:+1:9999998 +99999999:+1:99999998 +999999999:+1:999999998 +9999999999:+1:9999999998 +99999999999:+1:99999999998 +10:-1:11 +100:-1:101 +1000:-1:1001 +10000:-1:10001 +100000:-1:100001 +1000000:-1:1000001 +10000000:-1:10000001 +100000000:-1:100000001 +1000000000:-1:1000000001 +10000000000:-1:10000000001 +123456789:+987654321:-864197532 -123456789:+987654321:-1111111110 -123456789:-987654321:864197532 +123456789:-987654321:1111111110 &bmuladd abc:abc:0:NaN abc:+0:0:NaN +0:abc:0:NaN +0:0:abc:NaN NaNmul:+inf:0:NaN NaNmul:-inf:0:NaN -inf:NaNmul:0:NaN +inf:NaNmul:0:NaN +inf:+inf:0:inf +inf:-inf:0:-inf -inf:+inf:0:-inf -inf:-inf:0:inf +0:+0:0:0 +0:+1:0:0 +1:+0:0:0 +0:-1:0:0 -1:+0:0:0 123456789123456789:0:0:0 0:123456789123456789:0:0 -1:-1:0:1 -1:-1:0:1 -1:+1:0:-1 +1:-1:0:-1 +1:+1:0:1 +2:+3:0:6 -2:+3:0:-6 +2:-3:0:-6 -2:-3:0:6 111:111:0:12321 10101:10101:0:102030201 1001001:1001001:0:1002003002001 100010001:100010001:0:10002000300020001 10000100001:10000100001:0:100002000030000200001 11111111111:9:0:99999999999 22222222222:9:0:199999999998 33333333333:9:0:299999999997 44444444444:9:0:399999999996 55555555555:9:0:499999999995 66666666666:9:0:599999999994 77777777777:9:0:699999999993 88888888888:9:0:799999999992 99999999999:9:0:899999999991 11111111111:9:1:100000000000 22222222222:9:1:199999999999 33333333333:9:1:299999999998 44444444444:9:1:399999999997 55555555555:9:1:499999999996 66666666666:9:1:599999999995 77777777777:9:1:699999999994 88888888888:9:1:799999999993 99999999999:9:1:899999999992 -3:-4:-5:7 3:-4:-5:-17 -3:4:-5:-17 3:4:-5:7 -3:4:5:-7 3:-4:5:-7 9999999999999999999:10000000000000000000:1234567890:99999999999999999990000000001234567890 3.2:5.7:8.9:27.14 -3.2:5.197:6.05:-10.5804 &bmodpow 3:4:8:1 3:4:7:4 3:4:7:4 77777:777:123456789:99995084 3.2:6.2:5.2:2.970579856718063040273642739529400818 &bmul abc:abc:NaN abc:+0:NaN +0:abc:NaN +inf:NaNmul:NaN +inf:NaNmul:NaN NaNmul:+inf:NaN NaNmul:-inf:NaN +inf:+inf:inf +inf:-inf:-inf +inf:-inf:-inf +inf:+inf:inf +inf:123.34:inf +inf:-123.34:-inf -inf:123.34:-inf -inf:-123.34:inf 123.34:+inf:inf -123.34:+inf:-inf 123.34:-inf:-inf -123.34:-inf:inf +0:+0:0 +0:+1:0 +1:+0:0 +0:-1:0 -1:+0:0 +123456789123456789:+0:0 +0:+123456789123456789:0 -1:-1:1 -1:+1:-1 +1:-1:-1 +1:+1:1 +2:+3:6 -2:+3:-6 +2:-3:-6 -2:-3:6 +111:+111:12321 +10101:+10101:102030201 +1001001:+1001001:1002003002001 +100010001:+100010001:10002000300020001 +10000100001:+10000100001:100002000030000200001 +11111111111:+9:99999999999 +22222222222:+9:199999999998 +33333333333:+9:299999999997 +44444444444:+9:399999999996 +55555555555:+9:499999999995 +66666666666:+9:599999999994 +77777777777:+9:699999999993 +88888888888:+9:799999999992 +99999999999:+9:899999999991 6:120:720 10:10000:100000 &bdiv-list 0:0:NaN,0 0:1:0,0 9:4:2,1 9:5:1,4 # bug in v1.74 with bdiv in list context, when $y is 1 or -1 2.1:-1:-2.1,0 2.1:1:2.1,0 -2.1:-1:2.1,0 -2.1:1:-2.1,0 &bdiv $div_scale = 40; $round_mode = "even" abc:abc:NaN abc:+1:abc:NaN +1:abc:NaN -1:abc:NaN 0:abc:NaN +0:+0:NaN +0:+1:0 +1:+0:inf +3214:+0:inf +0:-1:0 -1:+0:-inf -3214:+0:-inf +1:+1:1 -1:-1:1 +1:-1:-1 -1:+1:-1 +1:+2:0.5 +2:+1:2 123:+inf:0 123:-inf:0 +10:+5:2 +100:+4:25 +1000:+8:125 +10000:+16:625 +10000:-16:-625 +999999999999:+9:111111111111 +999999999999:+99:10101010101 +999999999999:+999:1001001001 +999999999999:+9999:100010001 +999999999999999:+99999:10000100001 +1000000000:+9:111111111.1111111111111111111111111111111 +2000000000:+9:222222222.2222222222222222222222222222222 +3000000000:+9:333333333.3333333333333333333333333333333 +4000000000:+9:444444444.4444444444444444444444444444444 +5000000000:+9:555555555.5555555555555555555555555555556 +6000000000:+9:666666666.6666666666666666666666666666667 +7000000000:+9:777777777.7777777777777777777777777777778 +8000000000:+9:888888888.8888888888888888888888888888889 +9000000000:+9:1000000000 +35500000:+113:314159.2920353982300884955752212389380531 +71000000:+226:314159.2920353982300884955752212389380531 +106500000:+339:314159.2920353982300884955752212389380531 +1000000000:+3:333333333.3333333333333333333333333333333 2:25.024996000799840031993601279744051189762:0.07992009269196593320152084692285869265447 123456:1:123456 $div_scale = 20 +1000000000:+9:111111111.11111111111 +2000000000:+9:222222222.22222222222 +3000000000:+9:333333333.33333333333 +4000000000:+9:444444444.44444444444 +5000000000:+9:555555555.55555555556 +6000000000:+9:666666666.66666666667 +7000000000:+9:777777777.77777777778 +8000000000:+9:888888888.88888888889 +9000000000:+9:1000000000 1:10:0.1 1:100:0.01 1:1000:0.001 1:10000:0.0001 1:504:0.001984126984126984127 2:1.987654321:1.0062111801179738436 123456789.123456789123456789123456789:1:123456789.12345678912 # the next two cases are the "old" behaviour, but are now (>v0.01) different #+35500000:+113:314159.292035398230088 #+71000000:+226:314159.292035398230088 +35500000:+113:314159.29203539823009 +71000000:+226:314159.29203539823009 +106500000:+339:314159.29203539823009 +1000000000:+3:333333333.33333333333 $div_scale = 1 # round to accuracy 1 after bdiv +124:+3:40 123456789.1234:1:100000000 # reset scale for further tests $div_scale = 40 &bmod +9:4:1 +9:5:4 +9000:56:40 +56:9000:56 # inf handling, see table in doc 0:inf:0 0:-inf:0 5:inf:5 5:-inf:-inf -5:inf:inf -5:-inf:-5 inf:5:NaN -inf:5:NaN inf:-5:NaN -inf:-5:NaN 5:5:0 -5:-5:0 inf:inf:NaN -inf:-inf:NaN -inf:inf:NaN inf:-inf:NaN 8:0:8 inf:0:inf -inf:0:-inf -8:0:-8 0:0:0 abc:abc:NaN abc:1:abc:NaN 1:abc:NaN 0:1:0 1:0:1 0:-1:0 -1:0:-1 1:1:0 -1:-1:0 1:-1:0 -1:1:0 1:2:1 2:1:0 1000000000:9:1 2000000000:9:2 3000000000:9:3 4000000000:9:4 5000000000:9:5 6000000000:9:6 7000000000:9:7 8000000000:9:8 9000000000:9:0 35500000:113:33 71000000:226:66 106500000:339:99 1000000000:3:1 10:5:0 100:4:0 1000:8:0 10000:16:0 999999999999:9:0 999999999999:99:0 999999999999:999:0 999999999999:9999:0 999999999999999:99999:0 -9:+5:1 +9:-5:-1 -9:-5:-4 -5:3:1 -2:3:1 4:3:1 1:3:1 -5:-3:-2 -2:-3:-2 4:-3:-2 1:-3:-2 4095:4095:0 100041000510123:3:0 152403346:12345:4321 87654321:87654321:0 # now some floating point tests 123:2.5:0.5 1230:2.5:0 123.4:2.5:0.9 123e1:25:5 -2.1:1:0.9 2.1:1:0.1 -2.1:-1:-0.1 2.1:-1:-0.9 -3:1:0 3:1:0 -3:-1:0 3:-1:0 &bfac Nanfac:NaN -1:NaN +inf:inf -inf:NaN 0:1 1:1 2:2 3:6 4:24 5:120 6:720 10:3628800 11:39916800 12:479001600 &bdfac NaN:NaN -1:NaN +inf:inf -inf:NaN 0:1 1:1 2:2 3:3 4:8 5:15 6:48 7:105 8:384 9:945 10:3840 11:10395 12:46080 &broot # sqrt() +0:2:0 +1:2:1 -1:2:NaN # -$x ** (1/2) => -$y, but not in broot() -123.456:2:NaN +inf:2:inf -inf:2:NaN 2:2:1.41421356237309504880168872420969807857 -2:2:NaN 4:2:2 9:2:3 16:2:4 100:2:10 123.456:2:11.11107555549866648462149404118219234119 15241.38393:2:123.4559999756998444766131352122991626468 1.44:2:1.2 12:2:3.464101615137754587054892683011744733886 0.49:2:0.7 0.0049:2:0.07 # invalid ones 1:NaN:NaN -1:NaN:NaN 0:NaN:NaN -inf:NaN:NaN +inf:NaN:NaN NaN:0:NaN NaN:2:NaN NaN:inf:NaN NaN:inf:NaN 12:-inf:NaN 12:inf:NaN +0:0:NaN +1:0:NaN -1:0:NaN -2:0:NaN -123.45:0:NaN +inf:0:NaN 12:1:12 -12:1:NaN 8:-1:NaN -8:-1:NaN # cubic root 8:3:2 -8:3:NaN # fourths root 16:4:2 81:4:3 # see t/bigroot() for more tests &bsqrt +0:0 -1:NaN -2:NaN -16:NaN -123.45:NaN nanbsqrt:NaN +inf:inf -inf:NaN 1:1 2:1.41421356237309504880168872420969807857 4:2 9:3 16:4 100:10 123.456:11.11107555549866648462149404118219234119 15241.38393:123.4559999756998444766131352122991626468 1.44:1.2 # sqrt(1.44) = 1.2, sqrt(e10) = e5 => 12e4 1.44E10:120000 2e10:141421.356237309504880168872420969807857 144e20:120000000000 # proved to be an endless loop under 7-9 12:3.464101615137754587054892683011744733886 0.49:0.7 0.0049:0.07 &is_nan 123:0 abc:1 NaN:1 -123:0 &is_inf +inf::1 -inf::1 abc::0 1::0 NaN::0 -1::0 +inf:-:0 +inf:+:1 -inf:-:1 -inf:+:0 -inf:-inf:1 -inf:+inf:0 +inf:-inf:0 +inf:+inf:1 +iNfInItY::1 -InFiNiTy::1 &is_odd abc:0 0:0 -1:1 -3:1 1:1 3:1 1000001:1 1000002:0 +inf:0 -inf:0 123.45:0 -123.45:0 2:0 &is_int NaNis_int:0 0:1 1:1 2:1 -2:1 -1:1 -inf:0 +inf:0 123.4567:0 -0.1:0 -0.002:0 &is_even abc:0 0:1 -1:0 -3:0 1:0 3:0 1000001:0 1000002:1 2:1 +inf:0 -inf:0 123.456:0 -123.456:0 0.01:0 -0.01:0 120:1 1200:1 -1200:1 &is_positive 0:0 1:1 -1:0 -123:0 NaN:0 -inf:0 +inf:1 &is_negative 0:0 1:0 -1:1 -123:1 NaN:0 -inf:1 +inf:0 &parts 0:0 0 1:1 0 123:123 0 -123:-123 0 -1200:-12 2 NaNparts:NaN NaN +inf:inf inf -inf:-inf inf &exponent 0:0 1:0 123:0 -123:0 -1200:2 +inf:inf -inf:inf NaNexponent:NaN &mantissa 0:0 1:1 123:123 -123:-123 -1200:-12 +inf:inf -inf:-inf NaNmantissa:NaN &length 123:3 -123:3 0:1 1:1 12345678901234567890:20 &is_zero NaNzero:0 +inf:0 -inf:0 0:1 -1:0 1:0 &is_one NaNone:0 +inf:0 -inf:0 0:0 2:0 1:1 -1:0 -2:0 &bfloor 0:0 abc:NaN +inf:inf -inf:-inf 1:1 -51:-51 -51.2:-52 12.2:12 0.12345:0 0.123456:0 0.1234567:0 0.12345678:0 0.123456789:0 &bceil 0:0 abc:NaN +inf:inf -inf:-inf 1:1 -51:-51 -51.2:-51 12.2:13 -0.4:0 &bint 0:0 NaN:NaN +inf:inf -inf:-inf 1:1 -51:-51 -51.2:-51 12.2:12 -0.4:0 # overloaded functions &log -1:NaN 0:-inf 1:0 2:0.6931471805599453094172321214581765680755 3:1.098612288668109691395245236922525704647 123456789:18.63140176616801803319393334796320420971 1234567890987654321:41.657252696908474880343847955484513481 -inf:inf inf:inf NaN:NaN &exp &sin &cos &atan2 &int &neg &abs &sqrt Math-BigInt-1.999808/t/bigfltpm.t0000644403072340010010000000470413031667210016576 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 2436 # tests in require'd file + 19; # tests in this file use Math::BigInt only => 'Calc'; use Math::BigFloat; our ($CLASS, $CALC); $CLASS = "Math::BigFloat"; $CALC = Math::BigInt -> config('lib'); # backend library is($CLASS->config()->{class}, $CLASS, "$CLASS->config()->{class}"); is($CLASS->config()->{with}, $CALC, "$CLASS->config()->{with}"); # bug #17447: Can't call method Math::BigFloat->bsub, not a valid method my $c = Math::BigFloat->new('123.3'); is($c->bsub(123), '0.3', qq|\$c = Math::BigFloat -> new("123.3"); \$y = \$c -> bsub("123")|); # Bug until Math::BigInt v1.86, the scale wasn't treated as a scalar: $c = Math::BigFloat->new('0.008'); my $d = Math::BigFloat->new(3); my $e = $c->bdiv(Math::BigFloat->new(3), $d); is($e, '0.00267', '0.008 / 3 = 0.0027'); my $x; ############################################################################# # bgcd() as function, class method and instance method. my $gcd0 = Math::BigFloat::bgcd(-12, 18, 27); isa_ok($gcd0, "Math::BigFloat", "bgcd() as function"); is($gcd0, 3, "bgcd() as function"); my $gcd1 = Math::BigFloat->bgcd(-12, 18, 27); isa_ok($gcd1, "Math::BigFloat", "bgcd() as class method"); is($gcd1, 3, "bgcd() as class method"); $x = Math::BigFloat -> new(-12); my $gcd2 = $x -> bgcd(18, 27); isa_ok($gcd2, "Math::BigFloat", "bgcd() as instance method"); is($gcd2, 3, "bgcd() as instance method"); is($x, -12, "bgcd() does not modify invocand"); ############################################################################# # blcm() as function, class method and instance method. my $lcm0 = Math::BigFloat::blcm(-12, 18, 27); isa_ok($lcm0, "Math::BigFloat", "blcm() as function"); is($lcm0, 108, "blcm() as function"); my $lcm1 = Math::BigFloat->blcm(-12, 18, 27); isa_ok($lcm1, "Math::BigFloat", "blcm() as class method"); is($lcm1, 108, "blcm() as class method"); $x = Math::BigFloat -> new(-12); my $lcm2 = $x -> blcm(18, 27); isa_ok($lcm2, "Math::BigFloat", "blcm() as instance method"); is($lcm2, 108, "blcm() as instance method"); is($x, -12, "blcm() does not modify invocand"); ############################################################################# SKIP: { skip("skipping test which is not for this backend", 1) unless $CALC eq 'Math::BigInt::Calc'; is(ref($e->{_e}->[0]), '', '$e->{_e}->[0] is a scalar'); } require 't/bigfltpm.inc'; # all tests here for sharing Math-BigInt-1.999808/t/bigintc.t0000644403072340010010000006152012741473540016420 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 379; use Math::BigInt::Calc; my ($BASE_LEN, undef, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN_SMALL, $MAX_VAL) = Math::BigInt::Calc->_base_len(); print "# BASE_LEN = $BASE_LEN\n"; print "# MAX_VAL = $MAX_VAL\n"; print "# AND_BITS = $AND_BITS\n"; print "# XOR_BITS = $XOR_BITS\n"; print "# IOR_BITS = $OR_BITS\n"; # testing of Math::BigInt::Calc my $CALC = 'Math::BigInt::Calc'; # pass classname to sub's # _new and _str my $x = $CALC->_new("123"); my $y = $CALC->_new("321"); is(ref($x), "Math::BigInt::Calc", q|ref($x) is an Math::BigInt::Calc|); is($CALC->_str($x), 123, qq|$CALC->_str(\$x) = 123|); is($CALC->_str($y), 321, qq|$CALC->_str(\$y) = 321|); ############################################################################### # _add, _sub, _mul, _div is($CALC->_str($CALC->_add($x, $y)), 444, qq|$CALC->_str($CALC->_add(\$x, \$y)) = 444|); is($CALC->_str($CALC->_sub($x, $y)), 123, qq|$CALC->_str($CALC->_sub(\$x, \$y)) = 123|); is($CALC->_str($CALC->_mul($x, $y)), 39483, qq|$CALC->_str($CALC->_mul(\$x, \$y)) = 39483|); is($CALC->_str($CALC->_div($x, $y)), 123, qq|$CALC->_str($CALC->_div(\$x, \$y)) = 123|); ############################################################################### # check that mul/div doesn't change $y # and returns the same reference, not something new is($CALC->_str($CALC->_mul($x, $y)), 39483, qq|$CALC->_str($CALC->_mul(\$x, \$y)) = 39483|); is($CALC->_str($x), 39483, qq|$CALC->_str(\$x) = 39483|); is($CALC->_str($y), 321, qq|$CALC->_str(\$y) = 321|); is($CALC->_str($CALC->_div($x, $y)), 123, qq|$CALC->_str($CALC->_div(\$x, \$y)) = 123|); is($CALC->_str($x), 123, qq|$CALC->_str(\$x) = 123|); is($CALC->_str($y), 321, qq|$CALC->_str(\$y) = 321|); $x = $CALC->_new("39483"); my ($x1, $r1) = $CALC->_div($x, $y); is("$x1", "$x", q|"$x1" = "$x"|); $CALC->_inc($x1); is("$x1", "$x", q|"$x1" = "$x"|); is($CALC->_str($r1), "0", qq|$CALC->_str(\$r1) = "0"|); $x = $CALC->_new("39483"); # reset ############################################################################### my $z = $CALC->_new("2"); is($CALC->_str($CALC->_add($x, $z)), 39485, qq|$CALC->_str($CALC->_add(\$x, \$z)) = 39485|); my ($re, $rr) = $CALC->_div($x, $y); is($CALC->_str($re), 123, qq|$CALC->_str(\$re) = 123|); is($CALC->_str($rr), 2, qq|$CALC->_str(\$rr) = 2|); # is_zero, _is_one, _one, _zero is($CALC->_is_zero($x) || 0, 0, qq/$CALC->_is_zero(\$x) || 0 = 0/); is($CALC->_is_one($x) || 0, 0, qq/$CALC->_is_one(\$x) || 0 = 0/); is($CALC->_str($CALC->_zero()), "0", qq|$CALC->_str($CALC->_zero()) = "0"|); is($CALC->_str($CALC->_one()), "1", qq|$CALC->_str($CALC->_one()) = "1"|); # _two() and _ten() is($CALC->_str($CALC->_two()), "2", qq|$CALC->_str($CALC->_two()) = "2"|); is($CALC->_str($CALC->_ten()), "10", qq|$CALC->_str($CALC->_ten()) = "10"|); is($CALC->_is_ten($CALC->_two()), 0, qq|$CALC->_is_ten($CALC->_two()) = 0|); is($CALC->_is_two($CALC->_two()), 1, qq|$CALC->_is_two($CALC->_two()) = 1|); is($CALC->_is_ten($CALC->_ten()), 1, qq|$CALC->_is_ten($CALC->_ten()) = 1|); is($CALC->_is_two($CALC->_ten()), 0, qq|$CALC->_is_two($CALC->_ten()) = 0|); is($CALC->_is_one($CALC->_one()), 1, qq|$CALC->_is_one($CALC->_one()) = 1|); is($CALC->_is_one($CALC->_two()), 0, qq|$CALC->_is_one($CALC->_two()) = 0|); is($CALC->_is_one($CALC->_ten()), 0, qq|$CALC->_is_one($CALC->_ten()) = 0|); is($CALC->_is_one($CALC->_zero()) || 0, 0, qq/$CALC->_is_one($CALC->_zero()) || 0 = 0/); is($CALC->_is_zero($CALC->_zero()), 1, qq|$CALC->_is_zero($CALC->_zero()) = 1|); is($CALC->_is_zero($CALC->_one()) || 0, 0, qq/$CALC->_is_zero($CALC->_one()) || 0 = 0/); # is_odd, is_even is($CALC->_is_odd($CALC->_one()), 1, qq/$CALC->_is_odd($CALC->_one()) = 1/); is($CALC->_is_odd($CALC->_zero()) || 0, 0, qq/$CALC->_is_odd($CALC->_zero()) || 0 = 0/); is($CALC->_is_even($CALC->_one()) || 0, 0, qq/$CALC->_is_even($CALC->_one()) || 0 = 0/); is($CALC->_is_even($CALC->_zero()), 1, qq/$CALC->_is_even($CALC->_zero()) = 1/); # _len for my $method (qw/_alen _len/) { $x = $CALC->_new("1"); is($CALC->$method($x), 1, qq|$CALC->$method(\$x) = 1|); $x = $CALC->_new("12"); is($CALC->$method($x), 2, qq|$CALC->$method(\$x) = 2|); $x = $CALC->_new("123"); is($CALC->$method($x), 3, qq|$CALC->$method(\$x) = 3|); $x = $CALC->_new("1234"); is($CALC->$method($x), 4, qq|$CALC->$method(\$x) = 4|); $x = $CALC->_new("12345"); is($CALC->$method($x), 5, qq|$CALC->$method(\$x) = 5|); $x = $CALC->_new("123456"); is($CALC->$method($x), 6, qq|$CALC->$method(\$x) = 6|); $x = $CALC->_new("1234567"); is($CALC->$method($x), 7, qq|$CALC->$method(\$x) = 7|); $x = $CALC->_new("12345678"); is($CALC->$method($x), 8, qq|$CALC->$method(\$x) = 8|); $x = $CALC->_new("123456789"); is($CALC->$method($x), 9, qq|$CALC->$method(\$x) = 9|); $x = $CALC->_new("8"); is($CALC->$method($x), 1, qq|$CALC->$method(\$x) = 1|); $x = $CALC->_new("21"); is($CALC->$method($x), 2, qq|$CALC->$method(\$x) = 2|); $x = $CALC->_new("321"); is($CALC->$method($x), 3, qq|$CALC->$method(\$x) = 3|); $x = $CALC->_new("4321"); is($CALC->$method($x), 4, qq|$CALC->$method(\$x) = 4|); $x = $CALC->_new("54321"); is($CALC->$method($x), 5, qq|$CALC->$method(\$x) = 5|); $x = $CALC->_new("654321"); is($CALC->$method($x), 6, qq|$CALC->$method(\$x) = 6|); $x = $CALC->_new("7654321"); is($CALC->$method($x), 7, qq|$CALC->$method(\$x) = 7|); $x = $CALC->_new("87654321"); is($CALC->$method($x), 8, qq|$CALC->$method(\$x) = 8|); $x = $CALC->_new("987654321"); is($CALC->$method($x), 9, qq|$CALC->$method(\$x) = 9|); $x = $CALC->_new("0"); is($CALC->$method($x), 1, qq|$CALC->$method(\$x) = 1|); $x = $CALC->_new("20"); is($CALC->$method($x), 2, qq|$CALC->$method(\$x) = 2|); $x = $CALC->_new("320"); is($CALC->$method($x), 3, qq|$CALC->$method(\$x) = 3|); $x = $CALC->_new("4320"); is($CALC->$method($x), 4, qq|$CALC->$method(\$x) = 4|); $x = $CALC->_new("54320"); is($CALC->$method($x), 5, qq|$CALC->$method(\$x) = 5|); $x = $CALC->_new("654320"); is($CALC->$method($x), 6, qq|$CALC->$method(\$x) = 6|); $x = $CALC->_new("7654320"); is($CALC->$method($x), 7, qq|$CALC->$method(\$x) = 7|); $x = $CALC->_new("87654320"); is($CALC->$method($x), 8, qq|$CALC->$method(\$x) = 8|); $x = $CALC->_new("987654320"); is($CALC->$method($x), 9, qq|$CALC->$method(\$x) = 9|); for (my $i = 1; $i < 9; $i++) { my $a = "$i" . '0' x ($i - 1); $x = $CALC->_new($a); is($CALC->_len($x), $i, qq|$CALC->_len(\$x) = $i|); } } # _digit $x = $CALC->_new("123456789"); is($CALC->_digit($x, 0), 9, qq|$CALC->_digit(\$x, 0) = 9|); is($CALC->_digit($x, 1), 8, qq|$CALC->_digit(\$x, 1) = 8|); is($CALC->_digit($x, 2), 7, qq|$CALC->_digit(\$x, 2) = 7|); is($CALC->_digit($x, 8), 1, qq|$CALC->_digit(\$x, 8) = 1|); is($CALC->_digit($x, 9), 0, qq|$CALC->_digit(\$x, 9) = 0|); is($CALC->_digit($x, -1), 1, qq|$CALC->_digit(\$x, -1) = 1|); is($CALC->_digit($x, -2), 2, qq|$CALC->_digit(\$x, -2) = 2|); is($CALC->_digit($x, -3), 3, qq|$CALC->_digit(\$x, -3) = 3|); is($CALC->_digit($x, -9), 9, qq|$CALC->_digit(\$x, -9) = 9|); is($CALC->_digit($x, -10), 0, qq|$CALC->_digit(\$x, -10) = 0|); # _copy foreach (qw/ 1 12 123 1234 12345 123456 1234567 12345678 123456789/) { $x = $CALC->_new("$_"); is($CALC->_str($CALC->_copy($x)), "$_", qq|$CALC->_str($CALC->_copy(\$x)) = "$_"|); is($CALC->_str($x), "$_", # did _copy destroy original x? qq|$CALC->_str(\$x) = "$_"|); } # _zeros $x = $CALC->_new("1256000000"); is($CALC->_zeros($x), 6, qq|$CALC->_zeros(\$x) = 6|); $x = $CALC->_new("152"); is($CALC->_zeros($x), 0, qq|$CALC->_zeros(\$x) = 0|); $x = $CALC->_new("123000"); is($CALC->_zeros($x), 3, qq|$CALC->_zeros(\$x) = 3|); $x = $CALC->_new("0"); is($CALC->_zeros($x), 0, qq|$CALC->_zeros(\$x) = 0|); # _lsft, _rsft $x = $CALC->_new("10"); $y = $CALC->_new("3"); is($CALC->_str($CALC->_lsft($x, $y, 10)), 10000, qq|$CALC->_str($CALC->_lsft(\$x, \$y, 10)) = 10000|); $x = $CALC->_new("20"); $y = $CALC->_new("3"); is($CALC->_str($CALC->_lsft($x, $y, 10)), 20000, qq|$CALC->_str($CALC->_lsft(\$x, \$y, 10)) = 20000|); $x = $CALC->_new("128"); $y = $CALC->_new("4"); is($CALC->_str($CALC->_lsft($x, $y, 2)), 128 << 4, qq|$CALC->_str($CALC->_lsft(\$x, \$y, 2)) = 128 << 4|); $x = $CALC->_new("1000"); $y = $CALC->_new("3"); is($CALC->_str($CALC->_rsft($x, $y, 10)), 1, qq|$CALC->_str($CALC->_rsft(\$x, \$y, 10)) = 1|); $x = $CALC->_new("20000"); $y = $CALC->_new("3"); is($CALC->_str($CALC->_rsft($x, $y, 10)), 20, qq|$CALC->_str($CALC->_rsft(\$x, \$y, 10)) = 20|); $x = $CALC->_new("256"); $y = $CALC->_new("4"); is($CALC->_str($CALC->_rsft($x, $y, 2)), 256 >> 4, qq|$CALC->_str($CALC->_rsft(\$x, \$y, 2)) = 256 >> 4|); $x = $CALC->_new("6411906467305339182857313397200584952398"); $y = $CALC->_new("45"); is($CALC->_str($CALC->_rsft($x, $y, 10)), 0, qq|$CALC->_str($CALC->_rsft(\$x, \$y, 10)) = 0|); # _acmp $x = $CALC->_new("123456789"); $y = $CALC->_new("987654321"); is($CALC->_acmp($x, $y), -1, qq|$CALC->_acmp(\$x, \$y) = -1|); is($CALC->_acmp($y, $x), 1, qq|$CALC->_acmp(\$y, \$x) = 1|); is($CALC->_acmp($x, $x), 0, qq|$CALC->_acmp(\$x, \$x) = 0|); is($CALC->_acmp($y, $y), 0, qq|$CALC->_acmp(\$y, \$y) = 0|); $x = $CALC->_new("12"); $y = $CALC->_new("12"); is($CALC->_acmp($x, $y), 0, qq|$CALC->_acmp(\$x, \$y) = 0|); $x = $CALC->_new("21"); is($CALC->_acmp($x, $y), 1, qq|$CALC->_acmp(\$x, \$y) = 1|); is($CALC->_acmp($y, $x), -1, qq|$CALC->_acmp(\$y, \$x) = -1|); $x = $CALC->_new("123456789"); $y = $CALC->_new("1987654321"); is($CALC->_acmp($x, $y), -1, qq|$CALC->_acmp(\$x, \$y) = -1|); is($CALC->_acmp($y, $x), +1, qq|$CALC->_acmp(\$y, \$x) = +1|); $x = $CALC->_new("1234567890123456789"); $y = $CALC->_new("987654321012345678"); is($CALC->_acmp($x, $y), 1, qq|$CALC->_acmp(\$x, \$y) = 1|); is($CALC->_acmp($y, $x), -1, qq|$CALC->_acmp(\$y, \$x) = -1|); is($CALC->_acmp($x, $x), 0, qq|$CALC->_acmp(\$x, \$x) = 0|); is($CALC->_acmp($y, $y), 0, qq|$CALC->_acmp(\$y, \$y) = 0|); $x = $CALC->_new("1234"); $y = $CALC->_new("987654321012345678"); is($CALC->_acmp($x, $y), -1, qq|$CALC->_acmp(\$x, \$y) = -1|); is($CALC->_acmp($y, $x), 1, qq|$CALC->_acmp(\$y, \$x) = 1|); is($CALC->_acmp($x, $x), 0, qq|$CALC->_acmp(\$x, \$x) = 0|); is($CALC->_acmp($y, $y), 0, qq|$CALC->_acmp(\$y, \$y) = 0|); # _modinv $x = $CALC->_new("8"); $y = $CALC->_new("5033"); my ($xmod, $sign) = $CALC->_modinv($x, $y); is($CALC->_str($xmod), "629", # -629 % 5033 == 4404 qq|$CALC->_str(\$xmod) = "629"|); is($sign, "-", q|$sign = "-"|); # _div $x = $CALC->_new("3333"); $y = $CALC->_new("1111"); is($CALC->_str(scalar($CALC->_div($x, $y))), 3, qq|$CALC->_str(scalar($CALC->_div(\$x, \$y))) = 3|); $x = $CALC->_new("33333"); $y = $CALC->_new("1111"); ($x, $y) = $CALC->_div($x, $y); is($CALC->_str($x), 30, qq|$CALC->_str(\$x) = 30|); is($CALC->_str($y), 3, qq|$CALC->_str(\$y) = 3|); $x = $CALC->_new("123"); $y = $CALC->_new("1111"); ($x, $y) = $CALC->_div($x, $y); is($CALC->_str($x), 0, qq|$CALC->_str(\$x) = 0|); is($CALC->_str($y), 123, qq|$CALC->_str(\$y) = 123|); # _num foreach (qw/1 12 123 1234 12345 1234567 12345678 123456789 1234567890/) { $x = $CALC->_new("$_"); is(ref($x), "Math::BigInt::Calc", q|ref($x) = "Math::BigInt::Calc"|); is($CALC->_str($x), "$_", qq|$CALC->_str(\$x) = "$_"|); $x = $CALC->_num($x); is(ref($x), "", q|ref($x) = ""|); is($x, $_, qq|\$x = $_|); } # _sqrt $x = $CALC->_new("144"); is($CALC->_str($CALC->_sqrt($x)), "12", qq|$CALC->_str($CALC->_sqrt(\$x)) = "12"|); $x = $CALC->_new("144000000000000"); is($CALC->_str($CALC->_sqrt($x)), "12000000", qq|$CALC->_str($CALC->_sqrt(\$x)) = "12000000"|); # _root $x = $CALC->_new("81"); my $n = $CALC->_new("3"); # 4*4*4 = 64, 5*5*5 = 125 is($CALC->_str($CALC->_root($x, $n)), "4", qq|$CALC->_str($CALC->_root(\$x, \$n)) = "4"|); # 4.xx => 4.0 $x = $CALC->_new("81"); $n = $CALC->_new("4"); # 3*3*3*3 == 81 is($CALC->_str($CALC->_root($x, $n)), "3", qq|$CALC->_str($CALC->_root(\$x, \$n)) = "3"|); # _pow (and _root) $x = $CALC->_new("0"); $n = $CALC->_new("3"); # 0 ** y => 0 is($CALC->_str($CALC->_pow($x, $n)), 0, qq|$CALC->_str($CALC->_pow(\$x, \$n)) = 0|); $x = $CALC->_new("3"); $n = $CALC->_new("0"); # x ** 0 => 1 is($CALC->_str($CALC->_pow($x, $n)), 1, qq|$CALC->_str($CALC->_pow(\$x, \$n)) = 1|); $x = $CALC->_new("1"); $n = $CALC->_new("3"); # 1 ** y => 1 is($CALC->_str($CALC->_pow($x, $n)), 1, qq|$CALC->_str($CALC->_pow(\$x, \$n)) = 1|); $x = $CALC->_new("5"); $n = $CALC->_new("1"); # x ** 1 => x is($CALC->_str($CALC->_pow($x, $n)), 5, qq|$CALC->_str($CALC->_pow(\$x, \$n)) = 5|); $x = $CALC->_new("81"); $n = $CALC->_new("3"); # 81 ** 3 == 531441 is($CALC->_str($CALC->_pow($x, $n)), 81 ** 3, qq|$CALC->_str($CALC->_pow(\$x, \$n)) = 81 ** 3|); is($CALC->_str($CALC->_root($x, $n)), 81, qq|$CALC->_str($CALC->_root(\$x, \$n)) = 81|); $x = $CALC->_new("81"); is($CALC->_str($CALC->_pow($x, $n)), 81 ** 3, qq|$CALC->_str($CALC->_pow(\$x, \$n)) = 81 ** 3|); is($CALC->_str($CALC->_pow($x, $n)), "150094635296999121", # 531441 ** 3 qq|$CALC->_str($CALC->_pow(\$x, \$n)) = "150094635296999121"|); is($CALC->_str($CALC->_root($x, $n)), "531441", qq|$CALC->_str($CALC->_root(\$x, \$n)) = "531441"|); is($CALC->_str($CALC->_root($x, $n)), "81", qq|$CALC->_str($CALC->_root(\$x, \$n)) = "81"|); $x = $CALC->_new("81"); $n = $CALC->_new("14"); is($CALC->_str($CALC->_pow($x, $n)), "523347633027360537213511521", qq|$CALC->_str($CALC->_pow(\$x, \$n)) = "523347633027360537213511521"|); is($CALC->_str($CALC->_root($x, $n)), "81", qq|$CALC->_str($CALC->_root(\$x, \$n)) = "81"|); $x = $CALC->_new("523347633027360537213511520"); is($CALC->_str($CALC->_root($x, $n)), "80", qq|$CALC->_str($CALC->_root(\$x, \$n)) = "80"|); $x = $CALC->_new("523347633027360537213511522"); is($CALC->_str($CALC->_root($x, $n)), "81", qq|$CALC->_str($CALC->_root(\$x, \$n)) = "81"|); my $res = [ qw/9 31 99 316 999 3162 9999 31622 99999/ ]; # 99 ** 2 = 9801, 999 ** 2 = 998001 etc for my $i (2 .. 9) { $x = '9' x $i; $x = $CALC->_new($x); $n = $CALC->_new("2"); my $rc = '9' x ($i-1). '8' . '0' x ($i - 1) . '1'; print "# _pow( ", '9' x $i, ", 2) \n" unless is($CALC->_str($CALC->_pow($x, $n)), $rc, qq|$CALC->_str($CALC->_pow(\$x, \$n)) = $rc|); SKIP: { # If $i > $BASE_LEN, the test takes a really long time. skip "$i > $BASE_LEN", 2 unless $i <= $BASE_LEN; $x = '9' x $i; $x = $CALC->_new($x); $n = '9' x $i; $n = $CALC->_new($n); print "# _root( ", '9' x $i, ", ", 9 x $i, ") \n"; print "# _root( ", '9' x $i, ", ", 9 x $i, ") \n" unless is($CALC->_str($CALC->_root($x, $n)), '1', qq|$CALC->_str($CALC->_root(\$x, \$n)) = '1'|); $x = '9' x $i; $x = $CALC->_new($x); $n = $CALC->_new("2"); print "# BASE_LEN $BASE_LEN _root( ", '9' x $i, ", ", 9 x $i, ") \n" unless is($CALC->_str($CALC->_root($x, $n)), $res->[$i-2], qq|$CALC->_str($CALC->_root(\$x, \$n)) = $res->[$i-2]|); } } ############################################################################## # _fac $x = $CALC->_new("0"); is($CALC->_str($CALC->_fac($x)), "1", qq|$CALC->_str($CALC->_fac(\$x)) = "1"|); $x = $CALC->_new("1"); is($CALC->_str($CALC->_fac($x)), "1", qq|$CALC->_str($CALC->_fac(\$x)) = "1"|); $x = $CALC->_new("2"); is($CALC->_str($CALC->_fac($x)), "2", qq|$CALC->_str($CALC->_fac(\$x)) = "2"|); $x = $CALC->_new("3"); is($CALC->_str($CALC->_fac($x)), "6", qq|$CALC->_str($CALC->_fac(\$x)) = "6"|); $x = $CALC->_new("4"); is($CALC->_str($CALC->_fac($x)), "24", qq|$CALC->_str($CALC->_fac(\$x)) = "24"|); $x = $CALC->_new("5"); is($CALC->_str($CALC->_fac($x)), "120", qq|$CALC->_str($CALC->_fac(\$x)) = "120"|); $x = $CALC->_new("10"); is($CALC->_str($CALC->_fac($x)), "3628800", qq|$CALC->_str($CALC->_fac(\$x)) = "3628800"|); $x = $CALC->_new("11"); is($CALC->_str($CALC->_fac($x)), "39916800", qq|$CALC->_str($CALC->_fac(\$x)) = "39916800"|); $x = $CALC->_new("12"); is($CALC->_str($CALC->_fac($x)), "479001600", qq|$CALC->_str($CALC->_fac(\$x)) = "479001600"|); $x = $CALC->_new("13"); is($CALC->_str($CALC->_fac($x)), "6227020800", qq|$CALC->_str($CALC->_fac(\$x)) = "6227020800"|); # test that _fac modifies $x in place for small arguments $x = $CALC->_new("3"); $CALC->_fac($x); is($CALC->_str($x), "6", qq|$CALC->_str(\$x) = "6"|); $x = $CALC->_new("13"); $CALC->_fac($x); is($CALC->_str($x), "6227020800", qq|$CALC->_str(\$x) = "6227020800"|); ############################################################################## # _inc and _dec for (qw/1 11 121 1231 12341 1234561 12345671 123456781 1234567891/) { $x = $CALC->_new("$_"); $CALC->_inc($x); my $expected = substr($_, 0, length($_) - 1) . '2'; is($CALC->_str($x), $expected, qq|$CALC->_str(\$x) = $expected|); $CALC->_dec($x); is($CALC->_str($x), $_, qq|$CALC->_str(\$x) = $_|); } for (qw/19 119 1219 12319 1234519 12345619 123456719 1234567819/) { $x = $CALC->_new("$_"); $CALC->_inc($x); my $expected = substr($_, 0, length($_)-2) . '20'; is($CALC->_str($x), $expected, qq|$CALC->_str(\$x) = $expected|); $CALC->_dec($x); is($CALC->_str($x), $_, qq|$CALC->_str(\$x) = $_|); } for (qw/999 9999 99999 9999999 99999999 999999999 9999999999 99999999999/) { $x = $CALC->_new("$_"); $CALC->_inc($x); my $expected = '1' . '0' x (length($_)); is($CALC->_str($x), $expected, qq|$CALC->_str(\$x) = $expected|); $CALC->_dec($x); is($CALC->_str($x), $_, qq|$CALC->_str(\$x) = $_|); } $x = $CALC->_new("1000"); $CALC->_inc($x); is($CALC->_str($x), "1001", qq|$CALC->_str(\$x) = "1001"|); $CALC->_dec($x); is($CALC->_str($x), "1000", qq|$CALC->_str(\$x) = "1000"|); my $BL; { no strict 'refs'; $BL = &{"$CALC"."::_base_len"}(); } $x = '1' . '0' x $BL; $z = '1' . '0' x ($BL - 1); $z .= '1'; $x = $CALC->_new($x); $CALC->_inc($x); is($CALC->_str($x), $z, qq|$CALC->_str(\$x) = $z|); $x = '1' . '0' x $BL; $z = '9' x $BL; $x = $CALC->_new($x); $CALC->_dec($x); is($CALC->_str($x), $z, qq|$CALC->_str(\$x) = $z|); # should not happen: # $x = $CALC->_new("-2"); # $y = $CALC->_new("4"); # is($CALC->_acmp($x, $y), -1, qq|$CALC->_acmp($x, $y) = -1|); ############################################################################### # _mod $x = $CALC->_new("1000"); $y = $CALC->_new("3"); is($CALC->_str(scalar($CALC->_mod($x, $y))), 1, qq|$CALC->_str(scalar($CALC->_mod(\$x, \$y))) = 1|); $x = $CALC->_new("1000"); $y = $CALC->_new("2"); is($CALC->_str(scalar($CALC->_mod($x, $y))), 0, qq|$CALC->_str(scalar($CALC->_mod(\$x, \$y))) = 0|); # _and, _or, _xor $x = $CALC->_new("5"); $y = $CALC->_new("2"); is($CALC->_str(scalar($CALC->_xor($x, $y))), 7, qq|$CALC->_str(scalar($CALC->_xor(\$x, \$y))) = 7|); $x = $CALC->_new("5"); $y = $CALC->_new("2"); is($CALC->_str(scalar($CALC->_or($x, $y))), 7, qq|$CALC->_str(scalar($CALC->_or(\$x, \$y))) = 7|); $x = $CALC->_new("5"); $y = $CALC->_new("3"); is($CALC->_str(scalar($CALC->_and($x, $y))), 1, qq|$CALC->_str(scalar($CALC->_and(\$x, \$y))) = 1|); # _from_hex, _from_bin, _from_oct is($CALC->_str($CALC->_from_hex("0xFf")), 255, qq|$CALC->_str($CALC->_from_hex("0xFf")) = 255|); is($CALC->_str($CALC->_from_bin("0b10101011")), 160+11, qq|$CALC->_str($CALC->_from_bin("0b10101011")) = 160+11|); is($CALC->_str($CALC->_from_oct("0100")), 8*8, qq|$CALC->_str($CALC->_from_oct("0100")) = 8*8|); is($CALC->_str($CALC->_from_oct("01000")), 8*8*8, qq|$CALC->_str($CALC->_from_oct("01000")) = 8*8*8|); is($CALC->_str($CALC->_from_oct("010001")), 8*8*8*8+1, qq|$CALC->_str($CALC->_from_oct("010001")) = 8*8*8*8+1|); is($CALC->_str($CALC->_from_oct("010007")), 8*8*8*8+7, qq|$CALC->_str($CALC->_from_oct("010007")) = 8*8*8*8+7|); # _as_hex, _as_bin, as_oct is($CALC->_str($CALC->_from_hex($CALC->_as_hex($CALC->_new("128")))), 128, qq|$CALC->_str($CALC->_from_hex($CALC->_as_hex(| . qq|$CALC->_new("128")))) = 128|); is($CALC->_str($CALC->_from_bin($CALC->_as_bin($CALC->_new("128")))), 128, qq|$CALC->_str($CALC->_from_bin($CALC->_as_bin(| . qq|$CALC->_new("128")))) = 128|); is($CALC->_str($CALC->_from_oct($CALC->_as_oct($CALC->_new("128")))), 128, qq|$CALC->_str($CALC->_from_oct($CALC->_as_oct(| . qq|$CALC->_new("128")))) = 128|); is($CALC->_str($CALC->_from_oct($CALC->_as_oct($CALC->_new("123456")))), 123456, qq|$CALC->_str($CALC->_from_oct($CALC->_as_oct| . qq|($CALC->_new("123456")))) = 123456|); is($CALC->_str($CALC->_from_oct($CALC->_as_oct($CALC->_new("123456789")))), "123456789", qq|$CALC->_str($CALC->_from_oct($CALC->_as_oct(| . qq|$CALC->_new("123456789")))) = "123456789"|); is($CALC->_str($CALC->_from_oct($CALC->_as_oct($CALC->_new("1234567890123")))), "1234567890123", qq|$CALC->_str($CALC->_from_oct($CALC->_as_oct(| . qq|$CALC->_new("1234567890123")))) = "1234567890123"|); my $long = "123456789012345678901234567890"; is($CALC->_str($CALC->_from_hex($CALC->_as_hex($CALC->_new($long)))), $long, qq|$CALC->_str($CALC->_from_hex($CALC->_as_hex(| . qq|$CALC->_new("$long")))) = "$long"|); is($CALC->_str($CALC->_from_bin($CALC->_as_bin($CALC->_new($long)))), $long, qq|$CALC->_str($CALC->_from_bin($CALC->_as_bin(| . qq|$CALC->_new("$long")))) = "$long"|); is($CALC->_str($CALC->_from_oct($CALC->_as_oct($CALC->_new($long)))), $long, qq|$CALC->_str($CALC->_from_oct($CALC->_as_oct(| . qq|$CALC->_new("$long")))) = "$long"|); is($CALC->_str($CALC->_from_hex($CALC->_as_hex($CALC->_new("0")))), 0, qq|$CALC->_str($CALC->_from_hex($CALC->_as_hex(| . qq|$CALC->_new("0")))) = 0|); is($CALC->_str($CALC->_from_bin($CALC->_as_bin($CALC->_new("0")))), 0, qq|$CALC->_str($CALC->_from_bin($CALC->_as_bin(| . qq|$CALC->_new("0")))) = 0|); is($CALC->_str($CALC->_from_oct($CALC->_as_oct($CALC->_new("0")))), 0, qq|$CALC->_str($CALC->_from_oct($CALC->_as_oct(| . qq|$CALC->_new("0")))) = 0|); is($CALC->_as_hex($CALC->_new("0")), "0x0", qq|$CALC->_as_hex($CALC->_new("0")) = "0x0"|); is($CALC->_as_bin($CALC->_new("0")), "0b0", qq|$CALC->_as_bin($CALC->_new("0")) = "0b0"|); is($CALC->_as_oct($CALC->_new("0")), "00", qq|$CALC->_as_oct($CALC->_new("0")) = "00"|); is($CALC->_as_hex($CALC->_new("12")), "0xc", qq|$CALC->_as_hex($CALC->_new("12")) = "0xc"|); is($CALC->_as_bin($CALC->_new("12")), "0b1100", qq|$CALC->_as_bin($CALC->_new("12")) = "0b1100"|); is($CALC->_as_oct($CALC->_new("64")), "0100", qq|$CALC->_as_oct($CALC->_new("64")) = "0100"|); # _1ex is($CALC->_str($CALC->_1ex(0)), "1", qq|$CALC->_str($CALC->_1ex(0)) = "1"|); is($CALC->_str($CALC->_1ex(1)), "10", qq|$CALC->_str($CALC->_1ex(1)) = "10"|); is($CALC->_str($CALC->_1ex(2)), "100", qq|$CALC->_str($CALC->_1ex(2)) = "100"|); is($CALC->_str($CALC->_1ex(12)), "1000000000000", qq|$CALC->_str($CALC->_1ex(12)) = "1000000000000"|); is($CALC->_str($CALC->_1ex(16)), "10000000000000000", qq|$CALC->_str($CALC->_1ex(16)) = "10000000000000000"|); # _check $x = $CALC->_new("123456789"); is($CALC->_check($x), 0, qq|$CALC->_check(\$x) = 0|); is($CALC->_check(123), "123 is not a reference", qq|$CALC->_check(123) = "123 is not a reference"|); ############################################################################### # __strip_zeros { no strict 'refs'; # correct empty arrays $x = &{$CALC."::__strip_zeros"}([]); is(@$x, 1, q|@$x = 1|); is($x->[0], 0, q|$x->[0] = 0|); # don't strip single elements $x = &{$CALC."::__strip_zeros"}([0]); is(@$x, 1, q|@$x = 1|); is($x->[0], 0, q|$x->[0] = 0|); $x = &{$CALC."::__strip_zeros"}([1]); is(@$x, 1, q|@$x = 1|); is($x->[0], 1, q|$x->[0] = 1|); # don't strip non-zero elements $x = &{$CALC."::__strip_zeros"}([0, 1]); is(@$x, 2, q|@$x = 2|); is($x->[0], 0, q|$x->[0] = 0|); is($x->[1], 1, q|$x->[1] = 1|); $x = &{$CALC."::__strip_zeros"}([0, 1, 2]); is(@$x, 3, q|@$x = 3|); is($x->[0], 0, q|$x->[0] = 0|); is($x->[1], 1, q|$x->[1] = 1|); is($x->[2], 2, q|$x->[2] = 2|); # but strip leading zeros $x = &{$CALC."::__strip_zeros"}([0, 1, 2, 0]); is(@$x, 3, q|@$x = 3|); is($x->[0], 0, q|$x->[0] = 0|); is($x->[1], 1, q|$x->[1] = 1|); is($x->[2], 2, q|$x->[2] = 2|); $x = &{$CALC."::__strip_zeros"}([0, 1, 2, 0, 0]); is(@$x, 3, q|@$x = 3|); is($x->[0], 0, q|$x->[0] = 0|); is($x->[1], 1, q|$x->[1] = 1|); is($x->[2], 2, q|$x->[2] = 2|); $x = &{$CALC."::__strip_zeros"}([0, 1, 2, 0, 0, 0]); is(@$x, 3, q|@$x = 3|); is($x->[0], 0, q|$x->[0] = 0|); is($x->[1], 1, q|$x->[1] = 1|); is($x->[2], 2, q|$x->[2] = 2|); # collapse multiple zeros $x = &{$CALC."::__strip_zeros"}([0, 0, 0, 0]); is(@$x, 1, q|@$x = 1|); is($x->[0], 0, q|$x->[0] = 0|); } # done 1; Math-BigInt-1.999808/t/bigintpm.inc0000644403072340010010000020571013031672326017115 0ustar ospjadomain users#include this file into another for subclass testing use strict; use warnings; our ($CLASS, $CALC); ############################################################################## # for testing inheritance of _swap package Math::Foo; use Math::BigInt lib => $main::CALC; our @ISA = qw/Math::BigInt/; use overload # customized overload for sub, since original does not use swap there '-' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bsub($a[1]); }; sub _swap { # a fake _swap, which reverses the params my $self = shift; # for override in subclass if ($_[2]) { my $c = ref($_[0]) || 'Math::Foo'; return( $_[0]->copy(), $_[1] ); } else { return( Math::Foo->new($_[1]), $_[0] ); } } ############################################################################## package main; is($CLASS->config('lib'), $CALC, "$CLASS->config('lib')"); my ($x, $y, $z, @args, $try, $got, $want); my ($f, $round_mode, $expected_class); while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($m, $e); if (s/^&//) { $f = $_; next; } if (/^\$/) { $round_mode = $_; $round_mode =~ s/^\$/$CLASS\->/; next; } @args = split(/:/, $_, 99); $want = pop(@args); $expected_class = $CLASS; if ($want =~ /(.*?)=(.*)/) { $expected_class = $2; $want = $1; } $try = qq|\$x = $CLASS->new("$args[0]");|; if ($f eq "bnorm") { $try = qq|\$x = $CLASS->bnorm("$args[0]");|; } elsif ($f =~ /^is_(zero|one|odd|even|negative|positive|nan|int)$/) { $try .= " \$x->$f() || 0;"; } elsif ($f eq "is_inf") { $try .= qq| \$x->is_inf("$args[1]");|; } elsif ($f eq "binf") { $try .= qq| \$x->binf("$args[1]");|; } elsif ($f eq "bone") { $try .= qq| \$x->bone("$args[1]");|; # some unary ops } elsif ($f =~ /^b(nan|floor|ceil|int|sstr|neg|abs|sgn|inc|dec|not|sqrt|fac)$/) { $try .= " \$x->$f();"; # overloaded functions } elsif ($f =~ /^(log|exp|sin|cos|atan2|int|neg|abs|sqrt)$/) { $try .= " \$x = $f(\$x);"; } elsif ($f =~ /^(numify|length|stringify)$/) { $try .= " \$x->$f();"; } elsif ($f =~ /^(to|as)_(hex|oct|bin)$/) { $try .= " \$x->$f();"; } elsif ($f eq "exponent") { # ->bstr() to see if an object is returned $try .= ' $x = $x->exponent()->bstr();'; } elsif ($f eq "mantissa") { # ->bstr() to see if an object is returned $try .= ' $x = $x->mantissa()->bstr();'; } elsif ($f eq "parts") { $try .= ' ($m, $e) = $x->parts();'; # ->bstr() to see if an object is returned $try .= ' $m = $m->bstr(); $m = "NaN" if !defined $m;'; $try .= ' $e = $e->bstr(); $e = "NaN" if !defined $e;'; $try .= ' "$m,$e";'; } elsif ($f eq "bexp") { $try .= " \$x->bexp();"; } elsif ($f eq "bpi") { $try .= " $CLASS\->bpi(\$x);"; } else { # binary operators $try .= qq| \$y = $CLASS->new("$args[1]");|; if ($f eq "bcmp") { $try .= ' $x->bcmp($y);'; } elsif ($f eq "bround") { $try .= " $round_mode; \$x->bround(\$y);"; } elsif ($f eq "bacmp") { $try .= ' $x->bacmp($y);'; } elsif ($f eq "badd") { $try .= ' $x->badd($y);'; } elsif ($f eq "bsub") { $try .= ' $x->bsub($y);'; } elsif ($f eq "bmul") { $try .= ' $x->bmul($y);'; } elsif ($f eq "bdiv") { $try .= ' $x->bdiv($y);'; } elsif ($f eq "bdiv-list") { $try .= ' join(",", $x->bdiv($y));'; } elsif ($f eq "btdiv") { $try .= ' $x->btdiv($y);'; } elsif ($f eq "btdiv-list") { $try .= ' join (",", $x->btdiv($y));'; # overload via x= } elsif ($f =~ /^.=$/) { $try .= " \$x $f \$y;"; # overload via x } elsif ($f =~ /^.$/) { $try .= " \$x $f \$y;"; } elsif ($f eq "bmod") { $try .= ' $x % $y;'; } elsif ($f eq "bgcd") { if (defined $args[2]) { $try .= qq| \$z = $CLASS->new("$args[2]");|; } $try .= " $CLASS\::bgcd(\$x, \$y"; $try .= ", \$z" if defined $args[2]; $try .= ");"; } elsif ($f eq "blcm") { if (defined $args[2]) { $try .= qq| \$z = $CLASS->new("$args[2]");|; } $try .= " $CLASS\::blcm(\$x, \$y"; $try .= ", \$z" if defined $args[2]; $try .= ");"; } elsif ($f eq "blsft") { if (defined $args[2]) { $try .= " \$x->blsft(\$y, $args[2]);"; } else { $try .= " \$x << \$y;"; } } elsif ($f eq "brsft") { if (defined $args[2]) { $try .= " \$x->brsft(\$y, $args[2]);"; } else { $try .= " \$x >> \$y;"; } } elsif ($f eq "bnok") { $try .= " \$x->bnok(\$y);"; } elsif ($f eq "broot") { $try .= " \$x->broot(\$y);"; } elsif ($f eq "blog") { $try .= " \$x->blog(\$y);"; } elsif ($f eq "band") { $try .= " \$x & \$y;"; } elsif ($f eq "bior") { $try .= " \$x | \$y;"; } elsif ($f eq "bxor") { $try .= " \$x ^ \$y;"; } elsif ($f eq "bpow") { $try .= " \$x ** \$y;"; } elsif ( $f eq "bmodinv") { $try .= " \$x->bmodinv(\$y);"; } elsif ($f eq "digit") { $try .= " \$x->digit(\$y);"; } elsif ($f eq "batan2") { $try .= " \$x->batan2(\$y);"; } else { # Functions with three arguments $try .= qq| \$z = $CLASS->new("$args[2]");|; if ( $f eq "bmodpow") { $try .= " \$x->bmodpow(\$y, \$z);"; } elsif ($f eq "bmuladd") { $try .= " \$x->bmuladd(\$y, \$z);"; } else { warn "Unknown op '$f'"; } } } # end else all other ops $got = eval $try; print "# Error: $@\n" if $@; # convert hex/binary targets to decimal if ($want =~ /^(0x0x|0b0b)/) { $want =~ s/^0[xb]//; $want = Math::BigInt->new($want)->bstr(); } if ($want eq "") { is($got, undef, $try); } else { # print "try: $try ans: $got $want\n"; is($got, $want, $try); is(ref($got), $expected_class, qq|output is a "$expected_class" object|) if $expected_class ne $CLASS; } # check internal state of number objects is_valid($got, $f) if ref $got; } # end while data tests close DATA; # test whether self-multiplication works correctly (result is 2**64) $try = qq|\$x = $CLASS->new("4294967296");|; $try .= ' $a = $x->bmul($x);'; $got = eval $try; is($got, $CLASS->new(2) ** 64, $try); # test self-pow $try = qq|\$x = $CLASS->new(10);|; $try .= ' $a = $x->bpow($x);'; $got = eval $try; is($got, $CLASS->new(10) ** 10, $try); ############################################################################### # test whether op destroys args or not (should better not) $x = $CLASS->new(3); $y = $CLASS->new(4); $z = $x & $y; is($x, 3, '$z = $x & $y; $x'); is($y, 4, '$z = $x & $y; $y'); is($z, 0, '$z = $x & $y; $z'); $z = $x | $y; is($x, 3, '$z = $x | $y; $x'); is($y, 4, '$z = $x | $y; $y'); is($z, 7, '$z = $x | $y; $z'); $x = $CLASS->new(1); $y = $CLASS->new(2); $z = $x | $y; is($x, 1, '$z = $x | $y; $x'); is($y, 2, '$z = $x | $y; $y'); is($z, 3, '$z = $x | $y; $z'); $x = $CLASS->new(5); $y = $CLASS->new(4); $z = $x ^ $y; is($x, 5, '$z = $x ^ $y; $x'); is($y, 4, '$z = $x ^ $y; $y'); is($z, 1, '$z = $x ^ $y; $z'); $x = $CLASS->new(-5); $y = -$x; is($x, -5, '$y = -$x; $x'); $x = $CLASS->new(-5); $y = abs($x); is($x, -5, '$y = abs($x); $x'); $x = $CLASS->new(8); $y = $CLASS->new(-1); $z = $CLASS->new(5033); my $u = $x->copy()->bmodpow($y, $z); is($u, 4404, '$x->copy()->bmodpow($y, $z); $u'); is($y, -1, '$x->copy()->bmodpow($y, $z); $y'); is($z, 5033, '$x->copy()->bmodpow($y, $z); $z'); $x = $CLASS->new(-5); $y = -$x; is($x, -5, '$y = -$x; $x'); is($y, 5, '$y = -$x; $y'); $x = $CLASS->new(-5); $y = $x->copy()->bneg(); is($x, -5, '$y = $x->copy()->bneg(); $x'); is($y, 5, '$y = $x->copy()->bneg(); $y'); $x = $CLASS->new(-5); $y = $CLASS->new(3); $x->bmul($y); is($x, -15, '$x->bmul($y); $x'); is($y, 3, '$x->bmul($y); $y'); $x = $CLASS->new(-5); $y = $CLASS->new(3); $x->badd($y); is($x, -2, '$x->badd($y); $x'); is($y, 3, '$x->badd($y); $y'); $x = $CLASS->new(-5); $y = $CLASS->new(3); $x->bsub($y); is($x, -8, '$x->bsub($y); $x'); is($y, 3, '$x->bsub($y); $y'); $x = $CLASS->new(-15); $y = $CLASS->new(3); $x->bdiv($y); is($x, -5, '$x->bdiv($y); $x'); is($y, 3, '$x->bdiv($y); $y'); $x = $CLASS->new(-5); $y = $CLASS->new(3); $x->bmod($y); is($x, 1, '$x->bmod($y); $x'); is($y, 3, '$x->bmod($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(3); $x->bmul($y); is($x, 15, '$x->bmul($y); $x'); is($y, 3, '$x->bmul($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(3); $x->badd($y); is($x, 8, '$x->badd($y); $x'); is($y, 3, '$x->badd($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(3); $x->bsub($y); is($x, 2, '$x->bsub($y); $x'); is($y, 3, '$x->bsub($y); $y'); $x = $CLASS->new(15); $y = $CLASS->new(3); $x->bdiv($y); is($x, 5, '$x->bdiv($y); $x'); is($y, 3, '$x->bdiv($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(3); $x->bmod($y); is($x, 2, '$x->bmod($y); $x'); is($y, 3, '$x->bmod($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(-3); $x->bmul($y); is($x, -15, '$x->bmul($y); $x'); is($y, -3, '$x->bmul($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(-3); $x->badd($y); is($x, 2, '$x->badd($y); $x'); is($y, -3, '$x->badd($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(-3); $x->bsub($y); is($x, 8, '$x->bsub($y); $x'); is($y, -3, '$x->bsub($y); $y'); $x = $CLASS->new(15); $y = $CLASS->new(-3); $x->bdiv($y); is($x, -5, '$x->bdiv($y); $x'); is($y, -3, '$x->bdiv($y); $y'); $x = $CLASS->new(5); $y = $CLASS->new(-3); $x->bmod($y); is($x, -1, '$x->bmod($y); $x'); is($y, -3, '$x->bmod($y); $y'); ############################################################################### # check whether overloading cmp works $try = '$x = $CLASS->new(0);'; $try .= ' $y = 10;'; $try .= ' $x ne $y;'; $want = eval $try; ok($want, "overloading cmp works"); # We can't test for working cmpt with other objects here, we would need a dummy # object with stringify overload for this. See Math::String tests as example. ############################################################################### # check reversed order of arguments $try = "\$x = $CLASS->new(10); \$x = 2 ** \$x; \$x == 1024;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS->new(10); \$x = 2 * \$x; \$x == 20;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS->new(10); \$x = 2 + \$x; \$x == 12;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS\->new(10); \$x = 2 - \$x; \$x == -8;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS\->new(10); \$x = 20 / \$x; \$x == 2;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS\->new(3); \$x = 20 % \$x; \$x == 2;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS\->new(7); \$x = 20 & \$x; \$x == 4;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS\->new(7); \$x = 0x20 | \$x; \$x == 0x27;"; $want = eval $try; ok($want, $try); $try = "\$x = $CLASS\->new(7); \$x = 0x20 ^ \$x; \$x == 0x27;"; $want = eval $try; ok($want, $try); ############################################################################### # check badd(4, 5) form $try = "\$x = $CLASS\->badd(4, 5); \$x == 9;"; $want = eval $try; ok($want, $try); ############################################################################### # check undefs: NOT DONE YET ############################################################################### # bool $x = $CLASS->new(1); if ($x) { pass("\$x = $CLASS->new(1); \$x is true"); } else { fail("\$x = $CLASS->new(1); \$x is true"); } $x = $CLASS->new(0); if (!$x) { pass("\$x = $CLASS->new(0); !\$x is false"); } else { fail("\$x = $CLASS->new(0); !\$x is false"); } ############################################################################### # objectify() @args = Math::BigInt::objectify(2, 4, 5); is(scalar(@args), 3, "objectify(2, 4, 5) gives $CLASS, 4, 5"); like($args[0], qr/^Math::BigInt/, "first arg matches /^Math::BigInt/"); is($args[1], 4, "second arg is 4"); is($args[2], 5, "third arg is 5"); @args = Math::BigInt::objectify(0, 4, 5); is(scalar(@args), 3, "objectify(0, 4, 5) gives $CLASS, 4, 5"); like($args[0], qr/^Math::BigInt/, "first arg matches /^Math::BigInt/"); is($args[1], 4, "second arg is 4"); is($args[2], 5, "third arg is 5"); @args = Math::BigInt::objectify(2, 4, 5); is(scalar(@args), 3, "objectify(2, 4, 5) gives $CLASS, 4, 5"); like($args[0], qr/^Math::BigInt/, "first arg matches /^Math::BigInt/"); is($args[1], 4, "second arg is 4"); is($args[2], 5, "third arg is 5"); @args = Math::BigInt::objectify(2, 4, 5, 6, 7); is(scalar(@args), 5, "objectify(2, 4, 5, 6, 7) gives $CLASS, 4, 5, 6, 7"); like($args[0], qr/^Math::BigInt/, "first arg matches /^Math::BigInt/"); is($args[1], 4, "second arg is 4"); is(ref($args[1]), $args[0], "second arg is a $args[0] object"); is($args[2], 5, "third arg is 5"); is(ref($args[2]), $args[0], "third arg is a $args[0] object"); is($args[3], 6, "fourth arg is 6"); is(ref($args[3]), '', "fourth arg is a scalar"); is($args[4], 7, "fifth arg is 7"); is(ref($args[4]), '', "fifth arg is a scalar"); @args = Math::BigInt::objectify(2, $CLASS, 4, 5, 6, 7); is(scalar(@args), 5, "objectify(2, $CLASS, 4, 5, 6, 7) gives $CLASS, 4, 5, 6, 7"); is($args[0], $CLASS, "first arg is $CLASS"); is($args[1], 4, "second arg is 4"); is(ref($args[1]), $args[0], "second arg is a $args[0] object"); is($args[2], 5, "third arg is 5"); is(ref($args[2]), $args[0], "third arg is a $args[0] object"); is($args[3], 6, "fourth arg is 6"); is(ref($args[3]), '', "fourth arg is a scalar"); is($args[4], 7, "fifth arg is 7"); is(ref($args[4]), '', "fifth arg is a scalar"); ############################################################################### # test whether an opp calls objectify properly or not (or at least does what # it should do given non-objects, w/ or w/o objectify()) is($CLASS->new(123)->badd(123), 246, qq|$CLASS->new(123)->badd(123) = 246|);; is($CLASS->badd(123, 321), 444, qq|$CLASS->badd(123, 321) = 444|);; is($CLASS->badd(123, $CLASS->new(321)), 444, qq|$CLASS->badd(123, $CLASS->new(321)) = 444|);; is($CLASS->new(123)->bsub(122), 1, qq|$CLASS->new(123)->bsub(122) = 1|);; is($CLASS->bsub(321, 123), 198, qq|$CLASS->bsub(321, 123) = 198|);; is($CLASS->bsub(321, $CLASS->new(123)), 198, qq|$CLASS->bsub(321, $CLASS->new(123)) = 198|);; is($CLASS->new(123)->bmul(123), 15129, qq|$CLASS->new(123)->bmul(123) = 15129|);; is($CLASS->bmul(123, 123), 15129, qq|$CLASS->bmul(123, 123) = 15129|);; is($CLASS->bmul(123, $CLASS->new(123)), 15129, qq|$CLASS->bmul(123, $CLASS->new(123)) = 15129|);; is($CLASS->new(15129)->bdiv(123), 123, qq|$CLASS->new(15129)->bdiv(123) = 123|);; is($CLASS->bdiv(15129, 123), 123, qq|$CLASS->bdiv(15129, 123) = 123|);; is($CLASS->bdiv(15129, $CLASS->new(123)), 123, qq|$CLASS->bdiv(15129, $CLASS->new(123)) = 123|);; is($CLASS->new(15131)->bmod(123), 2, qq|$CLASS->new(15131)->bmod(123) = 2|);; is($CLASS->bmod(15131, 123), 2, qq|$CLASS->bmod(15131, 123) = 2|);; is($CLASS->bmod(15131, $CLASS->new(123)), 2, qq|$CLASS->bmod(15131, $CLASS->new(123)) = 2|);; is($CLASS->new(2)->bpow(16), 65536, qq|$CLASS->new(2)->bpow(16) = 65536|);; is($CLASS->bpow(2, 16), 65536, qq|$CLASS->bpow(2, 16) = 65536|);; is($CLASS->bpow(2, $CLASS->new(16)), 65536, qq|$CLASS->bpow(2, $CLASS->new(16)) = 65536|);; is($CLASS->new(2**15)->brsft(1), 2**14, qq|$CLASS->new(2**15)->brsft(1) = 2**14|);; is($CLASS->brsft(2**15, 1), 2**14, qq|$CLASS->brsft(2**15, 1) = 2**14|);; is($CLASS->brsft(2**15, $CLASS->new(1)), 2**14, qq|$CLASS->brsft(2**15, $CLASS->new(1)) = 2**14|);; is($CLASS->new(2**13)->blsft(1), 2**14, qq|$CLASS->new(2**13)->blsft(1) = 2**14|);; is($CLASS->blsft(2**13, 1), 2**14, qq|$CLASS->blsft(2**13, 1) = 2**14|);; is($CLASS->blsft(2**13, $CLASS->new(1)), 2**14, qq|$CLASS->blsft(2**13, $CLASS->new(1)) = 2**14|);; ############################################################################### # test for floating-point input (other tests in bnorm() below) $z = 1050000000000000; # may be int on systems with 64bit? $x = $CLASS->new($z); is($x->bsstr(), '105e+13', # not 1.05e+15 qq|\$x = $CLASS->new($z); \$x->bsstr() = "105e+13"|); $z = 1e+129; # definitely a float (may fail on UTS) # don't compare to $z, since some Perl versions stringify $z into something # like '1.e+129' or something equally ugly SKIP:{ my $vax_float = (pack("d", 1) =~ /^[\x80\x10]\x40/); skip("vax float range smaller", 1) if $vax_float; $x = $CLASS->new($z); is($x -> bsstr(), '1e+129', qq|\$x = $CLASS->new($z); \$x->bsstr() = "1e+129"|); } ############################################################################### # test for whitespace including newlines to be handled correctly # is($Math::BigInt::strict, 1); # the default foreach my $c (qw/1 12 123 1234 12345 123456 1234567 12345678 123456789 1234567890/) { my $m = $CLASS->new($c); is($CLASS->new("$c"), $m, qq|$CLASS->new("$c") = $m|); is($CLASS->new(" $c"), $m, qq|$CLASS->new(" $c") = $m|); is($CLASS->new("$c "), $m, qq|$CLASS->new("$c ") = $m|); is($CLASS->new(" $c "), $m, qq|$CLASS->new(" $c ") = $m|); is($CLASS->new("\n$c"), $m, qq|$CLASS->new("\\n$c") = $m|); is($CLASS->new("$c\n"), $m, qq|$CLASS->new("$c\\n") = $m|); is($CLASS->new("\n$c\n"), $m, qq|$CLASS->new("\\n$c\\n") = $m|); is($CLASS->new(" \n$c\n"), $m, qq|$CLASS->new(" \\n$c\\n") = $m|); is($CLASS->new(" \n$c \n"), $m, qq|$CLASS->new(" \\n$c \\n") = $m|); is($CLASS->new(" \n$c\n "), $m, qq|$CLASS->new(" \\n$c\\n ") = $m|); is($CLASS->new(" \n$c\n1"), 'NaN', qq|$CLASS->new(" \\n$c\\n1") = 'NaN'|); is($CLASS->new("1 \n$c\n1"), 'NaN', qq|$CLASS->new("1 \\n$c\\n1") = 'NaN'|); } ############################################################################### # prime number tests, also test for **= and length() # found on: http://www.utm.edu/research/primes/notes/by_year.html # ((2^148)+1)/17 $x = $CLASS->new(2); $x **= 148; $x++; $x = $x / 17; is($x, "20988936657440586486151264256610222593863921", "value of ((2^148)+1)/17"); is($x->length(), length("20988936657440586486151264256610222593863921"), "number of digits in ((2^148)+1)/17"); # MM7 = 2^127-1 $x = $CLASS->new(2); $x **= 127; $x--; is($x, "170141183460469231731687303715884105727", "value of 2^127-1"); $x = $CLASS->new('215960156869840440586892398248'); ($x, $y) = $x->length(); is($x, 30, "number of digits in 2^127-1"); is($y, 0, "number of digits in fraction part of 2^127-1"); $x = $CLASS->new('1_000_000_000_000'); ($x, $y) = $x->length(); is($x, 13, "number of digits in 1_000_000_000_000"); is($y, 0, "number of digits in fraction part of 1_000_000_000_000"); # test <<=, >>= $x = $CLASS->new('2'); $y = $CLASS->new('18'); is($x <<= $y, 2 << 18, "2 <<= 18 with $CLASS objects"); is($x, 2 << 18, "2 <<= 18 with $CLASS objects"); is($x >>= $y, 2, "2 >>= 18 with $CLASS objects"); is($x, 2, "2 >>= 18 with $CLASS objects"); # I am afraid the following is not yet possible due to slowness # Also, testing for 2 meg output is a bit hard ;) #$x = $CLASS->new(2); #$x **= 6972593; #$x--; # 593573509*2^332162+1 has exactly 1,000,000 digits # takes about 24 mins on 300 Mhz, so cannot be done yet ;) #$x = $CLASS->new(2); #$x **= 332162; #$x *= "593573509"; #$x++; #is($x->length(), 1_000_000); ############################################################################### # inheritance and overriding of _swap $x = Math::Foo->new(5); $x = $x - 8; # 8 - 5 instead of 5-8 is($x, 3, '$x = Math::Foo->new(5); $x = $x - 8; $x = 3'); is(ref($x), 'Math::Foo', '$x is an object of class "Math::Foo"'); $x = Math::Foo->new(5); $x = 8 - $x; # 5 - 8 instead of 8 - 5 is($x, -3, '$x = Math::Foo->new(5); $x = 8 - $x; $x = -3'); is(ref($x), 'Math::Foo', '$x is an object of class "Math::Foo"'); ############################################################################### # Test whether +inf eq inf # # This tried to test whether Math::BigInt inf equals Perl inf. Unfortunately, # Perl hasn't (before 5.7.3 at least) a consistent way to say inf, and some # things like 1e100000 crash on some platforms. So simple test for the string # 'inf'. $x = $CLASS->new('+inf'); is($x, 'inf', qq|$CLASS->new("+inf") = "inf"|); ############################################################################### # numify() and 64 bit integer support require Config; SKIP: { skip("no 64 bit integer support", 4) if ! $Config::Config{use64bitint} || ! $Config::Config{use64bitall} || $] <= 5.006002; # The following should not give "1.84467440737096e+19". $x = $CLASS -> new(2) -> bpow(64) -> bdec(); is($x -> bstr(), "18446744073709551615", "bigint 2**64-1 as string"); is($x -> numify(), "18446744073709551615", "bigint 2**64-1 as number"); # The following should not give "-9.22337203685478e+18". $x = $CLASS -> new(2) -> bpow(63) -> bneg(); is($x -> bstr(), "-9223372036854775808", "bigint -2**63 as string"); is($x -> numify(), "-9223372036854775808", "bigint -2**63 as number"); }; ############################################################################### ############################################################################### # the following tests only make sense with Math::BigInt::Calc or BareCalc or # FastCalc SKIP: { # skip GMP, Pari et al. skip("skipping tests not intended for the backend $CALC", 50) unless $CALC =~ /^Math::BigInt::(Bare|Fast)?Calc$/; ########################################################################### # check proper length of internal arrays my $bl = $CALC->_base_len(); my $BASE = '9' x $bl; my $MAX = $BASE; $BASE++; # f.i. 9999 $x = $CLASS->new($MAX); is_valid($x); # 10000 $x += 1; is($x, $BASE, "\$x == $BASE"); is_valid($x); # 9999 again $x -= 1; is($x, $MAX, "\$x == $MAX"); is_valid($x); ########################################################################### # check numify $x = $CLASS->new($BASE-1); is($x->numify(), $BASE-1, q|$x->numify() = $BASE-1|); $x = $CLASS->new(-($BASE-1)); is($x->numify(), -($BASE-1), q|$x->numify() = -($BASE-1)|); # +0 is to protect from 1e15 vs 100000000 (stupid to_string aaarglburbll...) $x = $CLASS->new($BASE); is($x->numify()+0, $BASE+0, q|$x->numify()+0 = $BASE+0|); $x = $CLASS->new(-$BASE); is($x->numify(), -$BASE, q|$x->numify() = -$BASE|); $x = $CLASS->new(-($BASE*$BASE*1+$BASE*1+1)); is($x->numify(), -($BASE*$BASE*1+$BASE*1+1), q|$x->numify() = -($BASE*$BASE*1+$BASE*1+1))|); ########################################################################### # test bug in _digits with length($c[-1]) where $c[-1] was "00001" instead # of 1 $x = $CLASS->new($BASE - 2); $x++; $x++; $x++; $x++; ok($x > $BASE, '$x > $BASE'); $x = $CLASS->new($BASE + 3); $x++; ok($x > $BASE, '$x > $BASE'); # test for +0 instead of int(): $x = $CLASS->new($MAX); is($x->length(), length($MAX), q|$x->length() = length($MAX)|); ########################################################################### # test bug that $CLASS->digit($string) did not work is($CLASS->digit(123, 2), 1, qq|$CLASS->digit(123, 2) = 1|); ########################################################################### # bug in sub where number with at least 6 trailing zeros after any op failed $x = $CLASS->new(123456); $z = $CLASS->new(10000); $z *= 10; $x -= $z; is($z, 100000, "testing bug in sub"); is($x, 23456, "testing bug in sub"); ########################################################################### # bug in shortcut in mul() # construct a number with a zero-hole of BASE_LEN_SMALL { my @bl = $CALC->_base_len(); my $bl = $bl[5]; $x = '1' x $bl . '0' x $bl . '1' x $bl . '0' x $bl; $y = '1' x (2 * $bl); $x = $CLASS->new($x)->bmul($y); # result is 123..$bl . $bl x (3*bl-1) . $bl...321 . '0' x $bl $y = ''; my $d = ''; for (my $i = 1; $i <= $bl; $i++) { $y .= $i; $d = $i . $d; } $y .= $bl x (3 * $bl - 1) . $d . '0' x $bl; is($x, $y, "testing number with a zero-hole of BASE_LEN_SMALL"); ######################################################################### # see if mul shortcut for small numbers works $x = '9' x $bl; $x = $CLASS->new($x); # 999 * 999 => 998 . 001, 9999*9999 => 9998 . 0001 is($x * $x, '9' x ($bl - 1) . '8' . '0' x ($bl - 1) . '1', "see if mul shortcut for small numbers works"); } ########################################################################### # bug with rest "-0" in div, causing further div()s to fail $x = $CLASS->new('-322056000'); ($x, $y) = $x->bdiv('-12882240'); is($y, '0', '-322056000 / -12882240 has remainder 0'); is_valid($y); # $y not '-0' ########################################################################### # bug in $x->bmod($y) # if $x < 0 and $y > 0 $x = $CLASS->new('-629'); is($x->bmod(5033), 4404, q|$x->bmod(5033) = 4404|); ########################################################################### # bone/binf etc as plain calls (Lite failed them) is($CLASS->bzero(), 0, qq|$CLASS->bzero() = 0|); is($CLASS->bone(), 1, qq|$CLASS->bone() = 1|); is($CLASS->bone("+"), 1, qq|$CLASS->bone("+") = 1|); is($CLASS->bone("-"), -1, qq|$CLASS->bone("-") = -1|); is($CLASS->bnan(), "NaN", qq|$CLASS->bnan() = "NaN"|); is($CLASS->binf(), "inf", qq|$CLASS->binf() = "inf"|); is($CLASS->binf("+"), "inf", qq|$CLASS->binf("+") = "inf"|); is($CLASS->binf("-"), "-inf", qq|$CLASS->binf("-") = "-inf"|); is($CLASS->binf("-inf"), "-inf", qq|$CLASS->binf("-inf") = "-inf"|); ########################################################################### # is_one("-") is($CLASS->new(1)->is_one("-"), 0, qq|$CLASS->new(1)->is_one("-") = 0|); is($CLASS->new(-1)->is_one("-"), 1, qq|$CLASS->new(-1)->is_one("-") = 1|); is($CLASS->new(1)->is_one(), 1, qq|$CLASS->new(1)->is_one() = 1|); is($CLASS->new(-1)->is_one(), 0, qq|$CLASS->new(-1)->is_one() = 0|); ########################################################################### # [perl #30609] bug with $x -= $x not being 0, but 2*$x $x = $CLASS->new(3); $x -= $x; is($x, 0, qq|\$x = $CLASS->new(3); \$x -= \$x; = 0|); $x = $CLASS->new(-3); $x -= $x; is($x, 0, qq|\$x = $CLASS->new(-3); \$x -= \$x; = 0|); $x = $CLASS->new("NaN"); $x -= $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("NaN"); \$x -= \$x; \$x->is_nan() = 1|); $x = $CLASS->new("inf"); $x -= $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("inf"); \$x -= \$x; \$x->is_nan() = 1|); $x = $CLASS->new("-inf"); $x -= $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("-inf"); \$x -= \$x; \$x->is_nan() = 1|); $x = $CLASS->new("NaN"); $x += $x; is($x->is_nan(), 1, qq|\$x = $CLASS->new("NaN"); \$x += \$x; \$x->is_nan() = 1|); $x = $CLASS->new("inf"); $x += $x; is($x->is_inf(), 1, qq|\$x = $CLASS->new("inf"); \$x += \$x; \$x->is_inf() = 1|); $x = $CLASS->new("-inf"); $x += $x; is($x->is_inf("-"), 1, qq|\$x = $CLASS->new("-inf"); \$x += \$x; \$x->is_inf("-") = 1|); $x = $CLASS->new(3); $x += $x; is($x, 6, qq|\$x = $CLASS->new(3); \$x += \$x; \$x = 6|); $x = $CLASS->new(-3); $x += $x; is($x, -6, qq|\$x = $CLASS->new(-3); \$x += \$x; \$x = -6|); $x = $CLASS->new(3); $x *= $x; is($x, 9, qq|\$x = $CLASS->new(3); \$x *= \$x; \$x = 9|); $x = $CLASS->new(-3); $x *= $x; is($x, 9, qq|\$x = $CLASS->new(-3); \$x *= \$x; \$x = 9|); $x = $CLASS->new(3); $x /= $x; is($x, 1, qq|\$x = $CLASS->new(3); \$x /= \$x; \$x = 1|); $x = $CLASS->new(-3); $x /= $x; is($x, 1, qq|\$x = $CLASS->new(-3); \$x /= \$x; \$x = 1|); $x = $CLASS->new(3); $x %= $x; is($x, 0, qq|\$x = $CLASS->new(3); \$x %= \$x; \$x = 0|); $x = $CLASS->new(-3); $x %= $x; is($x, 0, qq|\$x = $CLASS->new(-3); \$x %= \$x; \$x = 0|); } ############################################################################### # all tests done 1; ############################################################################### # sub to check validity of a Math::BigInt internally, to ensure that no op # leaves a number object in an invalid state (f.i. "-0") sub is_valid { my ($x, $f) = @_; my $e = 0; # error? # allow the check to pass for all Lite, and all MBI and subclasses # ok as reference? $e = 'Not a reference to Math::BigInt' if ref($x) !~ /^Math::BigInt/; if (ref($x) ne 'Math::BigInt::Lite') { # has ok sign? $e = qq|Illegal sign $x->{sign}| . qq| (expected: "+", "-", "-inf", "+inf" or "NaN"| if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/; $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0; $e = $CALC->_check($x->{value}) if $e eq '0'; } # test done, see if error did crop up if ($e eq '0') { pass('is a valid object'); return; } fail($e . " after op '$f'"); } __DATA__ &.= 1234:-345:1234-345 &+= 1:2:3 -1:-2:-3 &-= 1:2:-1 -1:-2:1 &*= 2:3:6 -1:5:-5 &%= 100:3:1 8:9:8 -629:5033:4404 &/= 100:3:33 -8:2:-4 &|= 2:1:3 &&= 5:7:5 &^= 5:7:2 &blog # NaNlog:2:NaN 122:NaNlog:NaN NaNlog1:NaNlog:NaN # 122:inf:0 inf:122:inf 122:-inf:0 -inf:122:inf -inf:-inf:NaN 0:4:-inf -21:4:NaN 21:-21:NaN # 0:-inf:NaN 0:-1:NaN 0:0:NaN 0:1:NaN 0:inf:NaN # 1:-inf:0 1:-1:0 1:0:0 1:1:NaN 1:4:0 1:inf:0 # inf:-inf:NaN inf:-1:NaN inf:0:NaN inf:1:NaN inf:4:inf inf:inf:NaN # # normal results 1024:2:10 81:3:4 # 3.01.. truncate 82:3:4 # 3.9... truncate 80:3:3 4096:2:12 15625:5:6 15626:5:6 15624:5:5 1000:10:3 10000:10:4 100000:10:5 1000000:10:6 10000000:10:7 100000000:10:8 8916100448256:12:12 8916100448257:12:12 8916100448255:12:11 2251799813685248:8:17 72057594037927936:2:56 144115188075855872:2:57 288230376151711744:2:58 576460752303423488:2:59 1329227995784915872903807060280344576:2:120 # $x == $base => result 1 3:3:1 # $x < $base => result 0 ($base ** 0 <= $x) 3:4:0 # $x == 1 => result 0 1:5:0 &is_negative 0:0 -1:1 1:0 +inf:0 -inf:1 NaNneg:0 &is_positive 0:0 -1:0 1:1 +inf:1 -inf:0 NaNneg:0 &is_int -inf:0 +inf:0 NaNis_int:0 1:1 0:1 123e12:1 &is_odd abc:0 0:0 1:1 3:1 -1:1 -3:1 10000001:1 10000002:0 2:0 120:0 121:1 &is_even abc:0 0:1 1:0 3:0 -1:0 -3:0 10000001:0 10000002:1 2:1 120:1 121:0 &bacmp +0:-0:0 +0:+1:-1 -1:+1:0 +1:-1:0 -1:+2:-1 +2:-1:1 -123456789:+987654321:-1 +123456789:-987654321:-1 +987654321:+123456789:1 -987654321:+123456789:1 -123:+4567889:-1 # NaNs acmpNaN:123: 123:acmpNaN: acmpNaN:acmpNaN: # infinity +inf:+inf:0 -inf:-inf:0 +inf:-inf:0 -inf:+inf:0 +inf:123:1 -inf:123:1 +inf:-123:1 -inf:-123:1 123:-inf:-1 -123:inf:-1 -123:-inf:-1 123:inf:-1 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &bnorm 0e999:0 0e-999:0 -0e999:0 -0e-999:0 123:123 123.000:123 123e0:123 123e+0:123 123e-0:123 123.000e0:123 123.000e+0:123 123.000e-0:123 # binary input 0babc:NaN 0b123:NaN 0b0:0 -0b0:0 -0b1:-1 0b0001:1 0b001:1 0b011:3 0b101:5 0b1001:9 0b10001:17 0b100001:33 0b1000001:65 0b10000001:129 0b100000001:257 0b1000000001:513 0b10000000001:1025 0b100000000001:2049 0b1000000000001:4097 0b10000000000001:8193 0b100000000000001:16385 0b1000000000000001:32769 0b10000000000000001:65537 0b100000000000000001:131073 0b1000000000000000001:262145 0b10000000000000000001:524289 0b100000000000000000001:1048577 0b1000000000000000000001:2097153 0b10000000000000000000001:4194305 0b100000000000000000000001:8388609 0b1000000000000000000000001:16777217 0b10000000000000000000000001:33554433 0b100000000000000000000000001:67108865 0b1000000000000000000000000001:134217729 0b10000000000000000000000000001:268435457 0b100000000000000000000000000001:536870913 0b1000000000000000000000000000001:1073741825 0b10000000000000000000000000000001:2147483649 0b100000000000000000000000000000001:4294967297 0b1000000000000000000000000000000001:8589934593 0b10000000000000000000000000000000001:17179869185 0b__101:NaN 0b1_0_1:5 0b0_0_0_1:1 # hex input -0x0:0 0xabcdefgh:NaN 0x1234:4660 0xabcdef:11259375 -0xABCDEF:-11259375 -0x1234:-4660 0x12345678:305419896 0x1_2_3_4_56_78:305419896 0xa_b_c_d_e_f:11259375 0x__123:NaN 0x9:9 0x11:17 0x21:33 0x41:65 0x81:129 0x101:257 0x201:513 0x401:1025 0x801:2049 0x1001:4097 0x2001:8193 0x4001:16385 0x8001:32769 0x10001:65537 0x20001:131073 0x40001:262145 0x80001:524289 0x100001:1048577 0x200001:2097153 0x400001:4194305 0x800001:8388609 0x1000001:16777217 0x2000001:33554433 0x4000001:67108865 0x8000001:134217729 0x10000001:268435457 0x20000001:536870913 0x40000001:1073741825 0x80000001:2147483649 0x100000001:4294967297 0x200000001:8589934593 0x400000001:17179869185 0x800000001:34359738369 # bug found by Mark Lakata in Calc.pm creating too big one-element numbers # in _from_hex() 0x2dd59e18a125dbed30a6ab1d93e9c855569f44f75806f0645dc9a2e98b808c3:1295719234436071846486578237372801883390756472611551858964079371952886122691 # inf input inf:inf +inf:inf -inf:-inf 0inf:NaN # abnormal input :NaN abc:NaN 1 a:NaN 1bcd2:NaN 11111b:NaN +1z:NaN -1z:NaN # only one underscore between two digits _123:NaN _123_:NaN 123_:NaN 1__23:NaN 1E1__2:NaN 1_E12:NaN 1E_12:NaN 1_E_12:NaN +_1E12:NaN +0_1E2:100 +0_0_1E2:100 -0_0_1E2:-100 -0_0_1E+0_0_2:-100 E1:NaN E23:NaN 1.23E1:NaN 1.23E-1:NaN # bug with two E's in number being valid 1e2e3:NaN 1e2r:NaN 1e2.0:NaN # bug with two '.' in number being valid 1.2.2:NaN 1.2.3e1:NaN -1.2.3:NaN -1.2.3e-4:NaN 1.2e3.4:NaN 1.2e-3.4:NaN 1.2.3.4:NaN 1.2.t:NaN 1..2:NaN 1..2e1:NaN 1..2e1..1:NaN 12e1..1:NaN ..2:NaN .-2:NaN # leading zeros 012:12 0123:123 01234:1234 012345:12345 0123456:123456 01234567:1234567 012345678:12345678 0123456789:123456789 01234567891:1234567891 012345678912:12345678912 0123456789123:123456789123 01234567891234:1234567891234 # some inputs that result in zero 0e0:0 +0e0:0 +0e+0:0 -0e+0:0 0e-0:0 -0e-0:0 +0e-0:0 000:0 00e2:0 00e02:0 000e002:0 000e1230:0 00e-3:0 00e+3:0 00e-03:0 00e+03:0 -000:0 -00e2:0 -00e02:0 -000e002:0 -000e1230:0 -00e-3:0 -00e+3:0 -00e-03:0 -00e+03:0 # normal input 0:0 +0:0 +00:0 +000:0 000000000000000000:0 -0:0 -0000:0 +1:1 +01:1 +001:1 +00000100000:100000 123456789:123456789 -1:-1 -01:-1 -001:-1 -123456789:-123456789 -00000100000:-100000 1_2_3:123 10000000000E-1_0:1 1E2:100 1E1:10 1E0:1 1.23E2:123 100E-1:10 # floating point input # .2e2:20 1.E3:1000 1.01E2:101 1010E-1:101 -1010E0:-1010 -1010E1:-10100 1234.00:1234 # non-integer numbers -1010E-2:NaN -1.01E+1:NaN -1.01E-1:NaN 1E-999999:NaN 0.5:NaN &bnan 1:NaN 2:NaN abc:NaN &bone 2:+:1 2:-:-1 boneNaN:-:-1 boneNaN:+:1 2:abc:1 3::1 &binf 1:+:inf 2:-:-inf 3:abc:inf &is_nan 123:0 abc:1 NaN:1 -123:0 &is_inf +inf::1 -inf::1 abc::0 1::0 NaN::0 -1::0 +inf:-:0 +inf:+:1 -inf:-:1 -inf:+:0 -inf:-inf:1 -inf:+inf:0 +inf:-inf:0 +inf:+inf:1 +iNfInItY::1 -InFiNiTy::1 &blsft abc:abc:NaN +2:+2:8 +1:+32:4294967296 +1:+48:281474976710656 +8:-2:NaN # exercise base 10 +12345:4:10:123450000 -1234:0:10:-1234 +1234:0:10:1234 +2:2:10:200 +12:2:10:1200 +1234:-3:10:NaN 1234567890123:12:10:1234567890123000000000000 -3:1:2:-6 -5:1:2:-10 -2:1:2:-4 -102533203:1:2:-205066406 &brsft abc:abc:NaN +8:+2:2 +4294967296:+32:1 +281474976710656:+48:1 +2:-2:NaN # exercise base 10 -1234:0:10:-1234 +1234:0:10:1234 +200:2:10:2 +1234:3:10:1 +1234:2:10:12 +1234:-3:10:NaN 310000:4:10:31 12300000:5:10:123 1230000000000:10:10:123 09876123456789067890:12:10:9876123 1234561234567890123:13:10:123456 820265627:1:2:410132813 # test shifting negative numbers in base 2 -15:1:2:-8 -14:1:2:-7 -13:1:2:-7 -12:1:2:-6 -11:1:2:-6 -10:1:2:-5 -9:1:2:-5 -8:1:2:-4 -7:1:2:-4 -6:1:2:-3 -5:1:2:-3 -4:1:2:-2 -3:1:2:-2 -2:1:2:-1 -1:1:2:-1 -1640531254:2:2:-410132814 -1640531254:1:2:-820265627 -820265627:1:2:-410132814 -205066405:1:2:-102533203 &bsstr +inf:inf -inf:-inf 1e+34:1e+34 123.456E3:123456e+0 100:1e+2 bsstrabc:NaN -5:-5e+0 -100:-1e+2 &numify 5:5 -5:-5 100:100 -100:-100 &bneg bnegNaN:NaN +inf:-inf -inf:inf abd:NaN 0:0 1:-1 -1:1 +123456789:-123456789 -123456789:123456789 &babs babsNaN:NaN +inf:inf -inf:inf 0:0 1:1 -1:1 +123456789:123456789 -123456789:123456789 &bsgn NaN:NaN +inf:1 -inf:-1 0:0 +123456789:1 -123456789:-1 &bcmp bcmpNaN:bcmpNaN: bcmpNaN:0: 0:bcmpNaN: 0:0:0 -1:0:-1 0:-1:1 1:0:1 0:1:-1 -1:1:-1 1:-1:1 -1:-1:0 1:1:0 123:123:0 123:12:1 12:123:-1 -123:-123:0 -123:-12:-1 -12:-123:1 123:124:-1 124:123:1 -123:-124:1 -124:-123:-1 100:5:1 -123456789:987654321:-1 +123456789:-987654321:1 -987654321:123456789:-1 -inf:5432112345:-1 +inf:5432112345:1 -inf:-5432112345:-1 +inf:-5432112345:1 +inf:+inf:0 -inf:-inf:0 +inf:-inf:1 -inf:+inf:-1 5:inf:-1 5:inf:-1 -5:-inf:1 -5:-inf:1 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &binc abc:NaN +inf:inf -inf:-inf +0:1 +1:2 -1:0 &bdec abc:NaN +inf:inf -inf:-inf +0:-1 +1:0 -1:-2 &badd abc:abc:NaN abc:0:NaN +0:abc:NaN +inf:-inf:NaN -inf:+inf:NaN +inf:+inf:inf -inf:-inf:-inf baddNaN:+inf:NaN baddNaN:+inf:NaN +inf:baddNaN:NaN -inf:baddNaN:NaN 0:0:0 1:0:1 0:1:1 1:1:2 -1:0:-1 0:-1:-1 -1:-1:-2 -1:+1:0 +1:-1:0 +9:+1:10 +99:+1:100 +999:+1:1000 +9999:+1:10000 +99999:+1:100000 +999999:+1:1000000 +9999999:+1:10000000 +99999999:+1:100000000 +999999999:+1:1000000000 +9999999999:+1:10000000000 +99999999999:+1:100000000000 +10:-1:9 +100:-1:99 +1000:-1:999 +10000:-1:9999 +100000:-1:99999 +1000000:-1:999999 +10000000:-1:9999999 +100000000:-1:99999999 +1000000000:-1:999999999 +10000000000:-1:9999999999 +123456789:987654321:1111111110 -123456789:987654321:864197532 -123456789:-987654321:-1111111110 +123456789:-987654321:-864197532 -1:10001:10000 -1:100001:100000 -1:1000001:1000000 -1:10000001:10000000 -1:100000001:100000000 -1:1000000001:1000000000 -1:10000000001:10000000000 -1:100000000001:100000000000 -1:1000000000001:1000000000000 -1:10000000000001:10000000000000 -1:-10001:-10002 -1:-100001:-100002 -1:-1000001:-1000002 -1:-10000001:-10000002 -1:-100000001:-100000002 -1:-1000000001:-1000000002 -1:-10000000001:-10000000002 -1:-100000000001:-100000000002 -1:-1000000000001:-1000000000002 -1:-10000000000001:-10000000000002 &bsub abc:abc:NaN abc:+0:NaN +0:abc:NaN +inf:-inf:inf -inf:+inf:-inf +inf:+inf:NaN -inf:-inf:NaN +0:+0:0 +1:+0:1 +0:+1:-1 +1:+1:0 -1:+0:-1 +0:-1:1 -1:-1:0 -1:+1:-2 +1:-1:2 +9:+1:8 +99:+1:98 +999:+1:998 +9999:+1:9998 +99999:+1:99998 +999999:+1:999998 +9999999:+1:9999998 +99999999:+1:99999998 +999999999:+1:999999998 +9999999999:+1:9999999998 +99999999999:+1:99999999998 +10:-1:11 +100:-1:101 +1000:-1:1001 +10000:-1:10001 +100000:-1:100001 +1000000:-1:1000001 +10000000:-1:10000001 +100000000:-1:100000001 +1000000000:-1:1000000001 +10000000000:-1:10000000001 +123456789:+987654321:-864197532 -123456789:+987654321:-1111111110 -123456789:-987654321:864197532 +123456789:-987654321:1111111110 10001:1:10000 100001:1:100000 1000001:1:1000000 10000001:1:10000000 100000001:1:100000000 1000000001:1:1000000000 10000000001:1:10000000000 100000000001:1:100000000000 1000000000001:1:1000000000000 10000000000001:1:10000000000000 10001:-1:10002 100001:-1:100002 1000001:-1:1000002 10000001:-1:10000002 100000001:-1:100000002 1000000001:-1:1000000002 10000000001:-1:10000000002 100000000001:-1:100000000002 1000000000001:-1:1000000000002 10000000000001:-1:10000000000002 &bmuladd abc:abc:0:NaN abc:+0:0:NaN +0:abc:0:NaN +0:0:abc:NaN NaNmul:+inf:0:NaN NaNmul:-inf:0:NaN -inf:NaNmul:0:NaN +inf:NaNmul:0:NaN +inf:+inf:0:inf +inf:-inf:0:-inf -inf:+inf:0:-inf -inf:-inf:0:inf +0:+0:0:0 +0:+1:0:0 +1:+0:0:0 +0:-1:0:0 -1:+0:0:0 123456789123456789:0:0:0 0:123456789123456789:0:0 -1:-1:0:1 -1:-1:0:1 -1:+1:0:-1 +1:-1:0:-1 +1:+1:0:1 +2:+3:0:6 -2:+3:0:-6 +2:-3:0:-6 -2:-3:0:6 111:111:0:12321 10101:10101:0:102030201 1001001:1001001:0:1002003002001 100010001:100010001:0:10002000300020001 10000100001:10000100001:0:100002000030000200001 11111111111:9:0:99999999999 22222222222:9:0:199999999998 33333333333:9:0:299999999997 44444444444:9:0:399999999996 55555555555:9:0:499999999995 66666666666:9:0:599999999994 77777777777:9:0:699999999993 88888888888:9:0:799999999992 99999999999:9:0:899999999991 11111111111:9:1:100000000000 22222222222:9:1:199999999999 33333333333:9:1:299999999998 44444444444:9:1:399999999997 55555555555:9:1:499999999996 66666666666:9:1:599999999995 77777777777:9:1:699999999994 88888888888:9:1:799999999993 99999999999:9:1:899999999992 -3:-4:-5:7 3:-4:-5:-17 -3:4:-5:-17 3:4:-5:7 -3:4:5:-7 3:-4:5:-7 9999999999999999999:10000000000000000000:1234567890:99999999999999999990000000001234567890 2:3:12345678901234567890:12345678901234567896 &bmul abc:abc:NaN abc:+0:NaN +0:abc:NaN NaNmul:+inf:NaN NaNmul:-inf:NaN -inf:NaNmul:NaN +inf:NaNmul:NaN +inf:+inf:inf +inf:-inf:-inf -inf:+inf:-inf -inf:-inf:inf +0:+0:0 +0:+1:0 +1:+0:0 +0:-1:0 -1:+0:0 123456789123456789:0:0 0:123456789123456789:0 -1:-1:1 -1:+1:-1 +1:-1:-1 +1:+1:1 +2:+3:6 -2:+3:-6 +2:-3:-6 -2:-3:6 111:111:12321 10101:10101:102030201 1001001:1001001:1002003002001 100010001:100010001:10002000300020001 10000100001:10000100001:100002000030000200001 11111111111:9:99999999999 22222222222:9:199999999998 33333333333:9:299999999997 44444444444:9:399999999996 55555555555:9:499999999995 66666666666:9:599999999994 77777777777:9:699999999993 88888888888:9:799999999992 99999999999:9:899999999991 +25:+25:625 +12345:+12345:152399025 +99999:+11111:1111088889 9999:10000:99990000 99999:100000:9999900000 999999:1000000:999999000000 9999999:10000000:99999990000000 99999999:100000000:9999999900000000 999999999:1000000000:999999999000000000 9999999999:10000000000:99999999990000000000 99999999999:100000000000:9999999999900000000000 999999999999:1000000000000:999999999999000000000000 9999999999999:10000000000000:99999999999990000000000000 99999999999999:100000000000000:9999999999999900000000000000 999999999999999:1000000000000000:999999999999999000000000000000 9999999999999999:10000000000000000:99999999999999990000000000000000 99999999999999999:100000000000000000:9999999999999999900000000000000000 999999999999999999:1000000000000000000:999999999999999999000000000000000000 9999999999999999999:10000000000000000000:99999999999999999990000000000000000000 &bdiv-list # Divide by zero and modulo zero. inf:0:inf,inf 5:0:inf,5 0:0:NaN,0 -5:0:-inf,-5 -inf:0:-inf,-inf # Numerator (dividend) is +/-inf, and denominator is finite and non-zero. inf:-inf:NaN,NaN inf:-5:-inf,NaN inf:5:inf,NaN inf:inf:NaN,NaN -inf:-inf:NaN,NaN -inf:-5:inf,NaN -inf:5:-inf,NaN -inf:inf:NaN,NaN # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf # are covered above. -5:inf:-1,inf 0:inf:0,0 5:inf:0,5 -5:-inf:0,-5 0:-inf:0,0 5:-inf:-1,-inf # Numerator is finite, and denominator is finite and non-zero. -5:-5:1,0 -5:-2:2,-1 -5:-1:5,0 -5:1:-5,0 -5:2:-3,1 -5:5:-1,0 -2:-5:0,-2 -2:-2:1,0 -2:-1:2,0 -2:1:-2,0 -2:2:-1,0 -2:5:-1,3 -1:-5:0,-1 -1:-2:0,-1 -1:-1:1,0 -1:1:-1,0 -1:2:-1,1 -1:5:-1,4 0:-5:0,0 0:-2:0,0 0:-1:0,0 0:1:0,0 0:2:0,0 0:5:0,0 1:-5:-1,-4 1:-2:-1,-1 1:-1:-1,0 1:1:1,0 1:2:0,1 1:5:0,1 2:-5:-1,-3 2:-2:-1,0 2:-1:-2,0 2:1:2,0 2:2:1,0 2:5:0,2 5:-5:-1,0 5:-2:-3,-1 5:-1:-5,0 5:1:5,0 5:2:2,1 5:5:1,0 # test the shortcut in Calc if @$x == @$yorg 1234567812345678:123456712345678:10,688888898 12345671234567:1234561234567:10,58888897 123456123456:12345123456:10,4888896 1234512345:123412345:10,388895 1234567890999999999:1234567890:1000000000,999999999 1234567890000000000:1234567890:1000000000,0 1234567890999999999:9876543210:124999998,9503086419 1234567890000000000:9876543210:124999998,8503086420 96969696969696969696969696969678787878626262626262626262626262:484848484848484848484848486666666666666689898989898989898989:199,484848484848484848484848123012121211954972727272727272727451 # bug in v1.76 1267650600228229401496703205375:1267650600228229401496703205376:0,1267650600228229401496703205375 # exercise shortcut for numbers of the same length in div 999999999999999999999999999999999:999999999999999999999999999999999:1,0 999999999999999999999999999999999:888888888888888888888888888888888:1,111111111111111111111111111111111 999999999999999999999999999999999:777777777777777777777777777777777:1,222222222222222222222222222222222 999999999999999999999999999999999:666666666666666666666666666666666:1,333333333333333333333333333333333 999999999999999999999999999999999:555555555555555555555555555555555:1,444444444444444444444444444444444 999999999999999999999999999999999:444444444444444444444444444444444:2,111111111111111111111111111111111 999999999999999999999999999999999:333333333333333333333333333333333:3,0 999999999999999999999999999999999:222222222222222222222222222222222:4,111111111111111111111111111111111 999999999999999999999999999999999:111111111111111111111111111111111:9,0 9999999_9999999_9999999_9999999:3333333_3333333_3333333_3333333:3,0 9999999_9999999_9999999_9999999:3333333_0000000_0000000_0000000:3,999999999999999999999 9999999_9999999_9999999_9999999:3000000_0000000_0000000_0000000:3,999999999999999999999999999 9999999_9999999_9999999_9999999:2000000_0000000_0000000_0000000:4,1999999999999999999999999999 9999999_9999999_9999999_9999999:1000000_0000000_0000000_0000000:9,999999999999999999999999999 9999999_9999999_9999999_9999999:100000_0000000_0000000_0000000:99,99999999999999999999999999 9999999_9999999_9999999_9999999:10000_0000000_0000000_0000000:999,9999999999999999999999999 9999999_9999999_9999999_9999999:1000_0000000_0000000_0000000:9999,999999999999999999999999 9999999_9999999_9999999_9999999:100_0000000_0000000_0000000:99999,99999999999999999999999 9999999_9999999_9999999_9999999:10_0000000_0000000_0000000:999999,9999999999999999999999 9999999_9999999_9999999_9999999:1_0000000_0000000_0000000:9999999,999999999999999999999 &bdiv # Divide by zero and modulo zero. inf:0:inf 5:0:inf 0:0:NaN -5:0:-inf -inf:0:-inf # Numerator (dividend) is +/-inf, and denominator is finite and non-zero. inf:-inf:NaN inf:-5:-inf inf:5:inf inf:inf:NaN -inf:-inf:NaN -inf:-5:inf -inf:5:-inf -inf:inf:NaN # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf # are covered above. -5:inf:-1 0:inf:0 5:inf:0 -5:-inf:0 0:-inf:0 5:-inf:-1 # Numerator is finite, and denominator is finite and non-zero. 5:5:1 -5:-5:1 11:2:5 -11:-2:5 -11:2:-6 11:-2:-6 0:1:0 0:-1:0 1:1:1 -1:-1:1 1:-1:-1 -1:1:-1 1:2:0 2:1:2 1:26:0 1000000000:9:111111111 2000000000:9:222222222 3000000000:9:333333333 4000000000:9:444444444 5000000000:9:555555555 6000000000:9:666666666 7000000000:9:777777777 8000000000:9:888888888 9000000000:9:1000000000 35500000:113:314159 71000000:226:314159 106500000:339:314159 1000000000:3:333333333 +10:+5:2 +100:+4:25 +1000:+8:125 +10000:+16:625 999999999999:9:111111111111 999999999999:99:10101010101 999999999999:999:1001001001 999999999999:9999:100010001 999999999999999:99999:10000100001 +1111088889:99999:11111 -5:-3:1 -5:3:-2 4:3:1 4:-3:-2 1:3:0 1:-3:-1 -2:-3:0 -2:3:-1 8:3:2 -8:3:-3 14:-3:-5 -14:3:-5 -14:-3:4 14:3:4 # bug in Calc with '99999' vs $BASE-1 10000000000000000000000000000000000000000000000000000000000000000000000000000000000:10000000375084540248994272022843165711074:999999962491547381984643365663244474111576 # test the shortcut in Calc if @$x == @$yorg 1234567812345678:123456712345678:10 12345671234567:1234561234567:10 123456123456:12345123456:10 1234512345:123412345:10 1234567890999999999:1234567890:1000000000 1234567890000000000:1234567890:1000000000 1234567890999999999:9876543210:124999998 1234567890000000000:9876543210:124999998 96969696969696969696969696969678787878626262626262626262626262:484848484848484848484848486666666666666689898989898989898989:199 # bug up to v0.35 in Calc (--$q one too many) 84696969696969696956565656566184292929292929292847474747436308080808080808086765396464646464646465:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999999 84696969696969696943434343434871161616161616161452525252486813131313131313143230042929292929292930:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999998 84696969696969696969696969697497424242424242424242424242385803030303030303030300750000000000000000:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6450000000000000000 84696969696969696930303030303558030303030303030057575757537318181818181818199694689393939393939395:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999997 # exercise shortcut for numbers of the same length in div 999999999999999999999999999999999:999999999999999999999999999999999:1 999999999999999999999999999999999:888888888888888888888888888888888:1 999999999999999999999999999999999:777777777777777777777777777777777:1 999999999999999999999999999999999:666666666666666666666666666666666:1 999999999999999999999999999999999:555555555555555555555555555555555:1 999999999999999999999999999999999:444444444444444444444444444444444:2 999999999999999999999999999999999:333333333333333333333333333333333:3 999999999999999999999999999999999:222222222222222222222222222222222:4 999999999999999999999999999999999:111111111111111111111111111111111:9 9999999_9999999_9999999_9999999:3333333_3333333_3333333_3333333:3 9999999_9999999_9999999_9999999:3333333_0000000_0000000_0000000:3 9999999_9999999_9999999_9999999:3000000_0000000_0000000_0000000:3 9999999_9999999_9999999_9999999:2000000_0000000_0000000_0000000:4 9999999_9999999_9999999_9999999:1000000_0000000_0000000_0000000:9 9999999_9999999_9999999_9999999:100000_0000000_0000000_0000000:99 9999999_9999999_9999999_9999999:10000_0000000_0000000_0000000:999 9999999_9999999_9999999_9999999:1000_0000000_0000000_0000000:9999 9999999_9999999_9999999_9999999:100_0000000_0000000_0000000:99999 9999999_9999999_9999999_9999999:10_0000000_0000000_0000000:999999 9999999_9999999_9999999_9999999:1_0000000_0000000_0000000:9999999 # bug with shortcut in Calc 0.44 949418181818187070707070707070707070:181818181853535353535353535353535353:5 &btdiv-list # Divide by zero and modulo zero. inf:0:inf,inf 5:0:inf,5 0:0:NaN,0 -5:0:-inf,-5 -inf:0:-inf,-inf # Numerator (dividend) is +/-inf, and denominator is finite and non-zero. inf:-inf:NaN,NaN inf:-5:-inf,NaN inf:5:inf,NaN inf:inf:NaN,NaN -inf:-inf:NaN,NaN -inf:-5:inf,NaN -inf:5:-inf,NaN -inf:inf:NaN,NaN # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf # are covered above. -5:inf:0,-5 0:inf:0,0 5:inf:0,5 -5:-inf:0,-5 0:-inf:0,0 5:-inf:0,5 # Numerator is finite, and denominator is finite and non-zero. -5:-5:1,0 -5:-2:2,-1 -5:-1:5,0 -5:1:-5,0 -5:2:-2,-1 -5:5:-1,0 -2:-5:0,-2 -2:-2:1,0 -2:-1:2,0 -2:1:-2,0 -2:2:-1,0 -2:5:0,-2 -1:-5:0,-1 -1:-2:0,-1 -1:-1:1,0 -1:1:-1,0 -1:2:0,-1 -1:5:0,-1 0:-5:0,0 0:-2:0,0 0:-1:0,0 0:1:0,0 0:2:0,0 0:5:0,0 1:-5:0,1 1:-2:0,1 1:-1:-1,0 1:1:1,0 1:2:0,1 1:5:0,1 2:-5:0,2 2:-2:-1,0 2:-1:-2,0 2:1:2,0 2:2:1,0 2:5:0,2 5:-5:-1,0 5:-2:-2,1 5:-1:-5,0 5:1:5,0 5:2:2,1 5:5:1,0 &btdiv # Divide by zero and modulo zero. inf:0:inf 5:0:inf 0:0:NaN -5:0:-inf -inf:0:-inf # Numerator (dividend) is +/-inf, and denominator is finite and non-zero. inf:-inf:NaN inf:-5:-inf inf:5:inf inf:inf:NaN -inf:-inf:NaN -inf:-5:inf -inf:5:-inf -inf:inf:NaN # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf # are covered above. -5:inf:0 0:inf:0 5:inf:0 -5:-inf:0 0:-inf:0 5:-inf:0 # Numerator is finite, and denominator is finite and non-zero. -5:-5:1 -5:-2:2 -5:-1:5 -5:1:-5 -5:2:-2 -5:5:-1 -2:-5:0 -2:-2:1 -2:-1:2 -2:1:-2 -2:2:-1 -2:5:0 -1:-5:0 -1:-2:0 -1:-1:1 -1:1:-1 -1:2:0 -1:5:0 0:-5:0 0:-2:0 0:-1:0 0:1:0 0:2:0 0:5:0 1:-5:0 1:-2:0 1:-1:-1 1:1:1 1:2:0 1:5:0 2:-5:0 2:-2:-1 2:-1:-2 2:1:2 2:2:1 2:5:0 5:-5:-1 5:-2:-2 5:-1:-5 5:1:5 5:2:2 5:5:1 ############################################################################### &bmodinv # format: number:modulus:result # bmodinv Data errors abc:abc:NaN abc:5:NaN 5:abc:NaN # bmodinv Expected Results from normal use 1:5:1 3:5:2 3:-5:-3 -2:5:2 8:5033:4404 1234567891:13:6 -1234567891:13:7 324958749843759385732954874325984357439658735983745:2348249874968739:1741662881064902 -2:1:0 -1:1:0 0:1:0 1:1:0 2:1:0 3:1:0 4:1:0 -2:3:1 -1:3:2 0:3:NaN 1:3:1 2:3:2 3:3:NaN 4:3:1 -2:4:NaN -1:4:3 0:4:NaN 1:4:1 2:4:NaN 3:4:3 4:4:NaN ## bmodinv Error cases / useless use of function inf:5:NaN 5:inf:NaN -inf:5:NaN 5:-inf:NaN &bmodpow # format: number:exponent:modulus:result # bmodpow Data errors abc:abc:abc:NaN 5:abc:abc:NaN abc:5:abc:NaN abc:abc:5:NaN 5:5:abc:NaN 5:abc:5:NaN abc:5:5:NaN 3:5:0:3 # bmodpow Expected results 0:0:2:1 1:0:2:1 0:3:5:0 -2:-2:1:0 -1:-2:1:0 0:-2:1:0 1:-2:1:0 2:-2:1:0 3:-2:1:0 4:-2:1:0 -2:-1:1:0 -1:-1:1:0 0:-1:1:0 1:-1:1:0 2:-1:1:0 3:-1:1:0 4:-1:1:0 -2:0:1:0 -1:0:1:0 0:0:1:0 1:0:1:0 2:0:1:0 3:0:1:0 4:0:1:0 -2:1:1:0 -1:1:1:0 0:1:1:0 1:1:1:0 2:1:1:0 3:1:1:0 4:1:1:0 -2:2:1:0 -1:2:1:0 0:2:1:0 1:2:1:0 2:2:1:0 3:2:1:0 4:2:1:0 -2:3:1:0 -1:3:1:0 0:3:1:0 1:3:1:0 2:3:1:0 3:3:1:0 4:3:1:0 -2:4:1:0 -1:4:1:0 0:4:1:0 1:4:1:0 2:4:1:0 3:4:1:0 4:4:1:0 -2:-2:3:1 -1:-2:3:1 0:-2:3:NaN 1:-2:3:1 2:-2:3:1 3:-2:3:NaN 4:-2:3:1 -2:-1:3:1 -1:-1:3:2 0:-1:3:NaN 1:-1:3:1 2:-1:3:2 3:-1:3:NaN 4:-1:3:1 -2:0:3:1 -1:0:3:1 0:0:3:1 1:0:3:1 2:0:3:1 3:0:3:1 4:0:3:1 -2:1:3:1 -1:1:3:2 0:1:3:0 1:1:3:1 2:1:3:2 3:1:3:0 4:1:3:1 -2:2:3:1 -1:2:3:1 0:2:3:0 1:2:3:1 2:2:3:1 3:2:3:0 4:2:3:1 -2:3:3:1 -1:3:3:2 0:3:3:0 1:3:3:1 2:3:3:2 3:3:3:0 4:3:3:1 -2:4:3:1 -1:4:3:1 0:4:3:0 1:4:3:1 2:4:3:1 3:4:3:0 4:4:3:1 -2:-2:4:NaN -1:-2:4:1 0:-2:4:NaN 1:-2:4:1 2:-2:4:NaN 3:-2:4:1 4:-2:4:NaN -2:-1:4:NaN -1:-1:4:3 0:-1:4:NaN 1:-1:4:1 2:-1:4:NaN 3:-1:4:3 4:-1:4:NaN -2:0:4:1 -1:0:4:1 0:0:4:1 1:0:4:1 2:0:4:1 3:0:4:1 4:0:4:1 -2:1:4:2 -1:1:4:3 0:1:4:0 1:1:4:1 2:1:4:2 3:1:4:3 4:1:4:0 -2:2:4:0 -1:2:4:1 0:2:4:0 1:2:4:1 2:2:4:0 3:2:4:1 4:2:4:0 -2:3:4:0 -1:3:4:3 0:3:4:0 1:3:4:1 2:3:4:0 3:3:4:3 4:3:4:0 -2:4:4:0 -1:4:4:1 0:4:4:0 1:4:4:1 2:4:4:0 3:4:4:1 4:4:4:0 8:-1:16:NaN 8:-1:5033:4404 8:7:5032:3840 8:8:-5:-4 1e50:1:1:0 98436739867439843769485798542749827593285729587325:43698764986460981048259837659386739857456983759328457:6943857329857295827698367:3104744730915914415259518 # bmodpow Error cases inf:5:13:NaN 5:inf:13:NaN &bmod # Divide by zero and modulo zero. inf:0:inf 5:0:5 0:0:0 -5:0:-5 -inf:0:-inf # Numerator (dividend) is +/-inf, and denominator is finite and non-zero. inf:-inf:NaN inf:-5:NaN inf:5:NaN inf:inf:NaN -inf:-inf:NaN -inf:-5:NaN -inf:5:NaN -inf:inf:NaN # Denominator (divisor) is +/-inf. The cases when the numerator is +/-inf # are covered above. -5:inf:inf 0:inf:0 5:inf:5 -5:-inf:-5 0:-inf:0 5:-inf:-inf # Numerator is finite, and denominator is finite and non-zero. 5:5:0 -5:-5:0 0:1:0 0:-1:0 1:1:0 -1:-1:0 1:-1:0 -1:1:0 1:2:1 2:1:0 1000000000:9:1 2000000000:9:2 3000000000:9:3 4000000000:9:4 5000000000:9:5 6000000000:9:6 7000000000:9:7 8000000000:9:8 9000000000:9:0 35500000:113:33 71000000:226:66 106500000:339:99 1000000000:3:1 10:5:0 100:4:0 1000:8:0 10000:16:0 999999999999:9:0 999999999999:99:0 999999999999:999:0 999999999999:9999:0 999999999999999:99999:0 -9:+5:1 +9:-5:-1 -9:-5:-4 -5:3:1 -2:3:1 4:3:1 1:3:1 -5:-3:-2 -2:-3:-2 4:-3:-2 1:-3:-2 4095:4095:0 100041000510123:3:0 152403346:12345:4321 9:5:4 # test shortcuts in Calc # 1ex % 9 is always == 1, 1ex % 113 is != 1 for x = (4..9), 1ex % 10 = 0 1234:9:1 123456:9:3 12345678:9:0 1234567891:9:1 123456789123:9:6 12345678912345:9:6 1234567891234567:9:1 123456789123456789:9:0 1234:10:4 123456:10:6 12345678:10:8 1234567891:10:1 123456789123:10:3 12345678912345:10:5 1234567891234567:10:7 123456789123456789:10:9 1234:113:104 123456:113:60 12345678:113:89 1234567891:113:64 123456789123:113:95 12345678912345:113:53 1234567891234567:113:56 123456789123456789:113:39 # bug in bmod() not modifying the variable in place -629:5033:4404 # bug in bmod() in Calc in the _div_use_div() shortcut code path, # when X == X and X was big 111111111111111111111111111111:111111111111111111111111111111:0 12345678901234567890:12345678901234567890:0 &bgcd inf:12:NaN -inf:12:NaN 12:inf:NaN 12:-inf:NaN inf:inf:NaN inf:-inf:NaN -inf:-inf:NaN abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:0 +0:+1:1 +1:+0:1 +1:+1:1 +2:+3:1 +3:+2:1 -3:+2:1 -3:-2:1 -144:-60:12 144:-60:12 144:60:12 100:625:25 4096:81:1 1034:804:2 27:90:56:1 27:90:54:9 &blcm abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:0 +1:+0:0 +0:+1:0 +27:+90:270 +1034:+804:415668 &band abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:0 3:2:2 +8:+2:0 +281474976710656:0:0 +281474976710656:1:0 +281474976710656:+281474976710656:281474976710656 281474976710656:-1:281474976710656 -2:-3:-4 -1:-1:-1 -6:-6:-6 -7:-4:-8 -7:4:0 -4:7:4 # negative argument is bitwise shorter than positive [perl #26559] 30:-3:28 123:-1:123 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0x0xFFFF 0xFFFFFF:0xFFFFFF:0x0xFFFFFF 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0x0xF0F0 0x0F0F:0x0F0F:0x0x0F0F 0xF0F0F0:0xF0F0F0:0x0xF0F0F0 0x0F0F0F:0x0F0F0F:0x0x0F0F0F 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F 0x1F0F0F0F0F0F:0x3F0F0F0F0F0F:0x0x1F0F0F0F0F0F &bior abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:3 +8:+2:10 +281474976710656:0:281474976710656 +281474976710656:1:281474976710657 +281474976710656:281474976710656:281474976710656 -2:-3:-1 -1:-1:-1 -6:-6:-6 -7:4:-3 -4:7:-1 +281474976710656:-1:-1 30:-3:-1 30:-4:-2 300:-76:-68 -76:300:-68 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0x0xFFFF 0xFFFFFF:0xFFFFFF:0x0xFFFFFF 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0:0xFFFF:0x0xFFFF 0:0xFFFFFF:0x0xFFFFFF 0:0xFFFFFFFF:0x0xFFFFFFFF 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xFFFF:0:0x0xFFFF 0xFFFFFF:0:0x0xFFFFFF 0xFFFFFFFF:0:0x0xFFFFFFFF 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0x0xF0F0 0x0F0F:0x0F0F:0x0x0F0F 0xF0F0:0x0F0F:0x0xFFFF 0xF0F0F0:0xF0F0F0:0x0xF0F0F0 0x0F0F0F:0x0F0F0F:0x0x0F0F0F 0x0F0F0F:0xF0F0F0:0x0xFFFFFF 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF 0x1F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF &bxor abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:3 +8:+2:10 +281474976710656:0:281474976710656 +281474976710656:1:281474976710657 +281474976710656:281474976710656:0 -2:-3:3 -1:-1:0 -6:-6:0 -7:4:-3 -4:7:-5 4:-7:-3 -4:-7:5 30:-3:-29 30:-4:-30 300:-76:-360 -76:300:-360 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0 0xFFFFFF:0xFFFFFF:0 0xFFFFFFFF:0xFFFFFFFF:0 0xFFFFFFFFFF:0xFFFFFFFFFF:0 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0 0:0xFFFF:0x0xFFFF 0:0xFFFFFF:0x0xFFFFFF 0:0xFFFFFFFF:0x0xFFFFFFFF 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xFFFF:0:0x0xFFFF 0xFFFFFF:0:0x0xFFFFFF 0xFFFFFFFF:0:0x0xFFFFFFFF 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0 0x0F0F:0x0F0F:0 0xF0F0:0x0F0F:0x0xFFFF 0xF0F0F0:0xF0F0F0:0 0x0F0F0F:0x0F0F0F:0 0x0F0F0F:0xF0F0F0:0x0xFFFFFF 0xF0F0F0F0:0xF0F0F0F0:0 0x0F0F0F0F:0x0F0F0F0F:0 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF 0xF0F0F0F0F0:0xF0F0F0F0F0:0 0x0F0F0F0F0F:0x0F0F0F0F0F:0 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF &bnot abc:NaN +0:-1 +8:-9 +281474976710656:-281474976710657 -1:0 -2:1 -12:11 &digit 0:0:0 12:0:2 12:1:1 123:0:3 123:1:2 123:2:1 123:-1:1 123:-2:2 123:-3:3 123456:0:6 123456:1:5 123456:2:4 123456:3:3 123456:4:2 123456:5:1 123456:-1:1 123456:-2:2 123456:-3:3 100000:-3:0 100000:0:0 100000:1:0 &mantissa abc:NaN 1e4:1 2e0:2 123:123 -1:-1 -2:-2 +inf:inf -inf:-inf &exponent abc:NaN 1e4:4 2e0:0 123:0 -1:0 -2:0 0:0 +inf:inf -inf:inf &parts abc:NaN,NaN 1e4:1,4 2e0:2,0 123:123,0 -1:-1,0 -2:-2,0 0:0,0 +inf:inf,inf -inf:-inf,inf &bfac -1:NaN NaNfac:NaN +inf:inf -inf:NaN 0:1 1:1 2:2 3:6 4:24 5:120 6:720 7:5040 8:40320 9:362880 10:3628800 11:39916800 12:479001600 20:2432902008176640000 22:1124000727777607680000 69:171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000 &bpow abc:12:NaN 12:abc:NaN 0:0:1 0:1:0 0:2:0 0:-1:inf 0:-2:inf 1:0:1 1:1:1 1:2:1 1:3:1 1:-1:1 1:-2:1 1:-3:1 2:0:1 2:1:2 2:2:4 2:3:8 3:3:27 -2:2:4 -2:3:-8 -2:4:16 -2:5:-32 2:-1:NaN -2:-1:NaN 2:-2:NaN -2:-2:NaN # inf tests +inf:1234500012:inf -inf:1234500012:inf -inf:1234500013:-inf +inf:-12345000123:inf -inf:-12345000123:-inf # -inf * -inf = inf -inf:2:inf -inf:0:NaN -inf:-1:0 -inf:inf:NaN 2:inf:inf 2:-inf:0 0:inf:0 0:-inf:inf -1:-inf:NaN -1:inf:NaN -2:inf:NaN -2:-inf:0 NaN:inf:NaN NaN:-inf:NaN -inf:NaN:NaN inf:NaN:NaN inf:-inf:NaN 1:inf:1 1:-inf:1 # 1 ** -x => 1 / (1 ** x) -1:0:1 -2:0:1 -1:1:-1 -1:2:1 -1:3:-1 -1:4:1 -1:5:-1 -1:-1:-1 -1:-2:1 -1:-3:-1 -1:-4:1 10:2:100 10:3:1000 10:4:10000 10:5:100000 10:6:1000000 10:7:10000000 10:8:100000000 10:9:1000000000 10:20:100000000000000000000 123456:2:15241383936 -2:2:4 -2:3:-8 -2:4:16 -2:5:-32 -3:2:9 -3:3:-27 -3:4:81 -3:5:-243 &length 100:3 10:2 1:1 0:1 12345:5 10000000000000000:17 -123:3 215960156869840440586892398248:30 &broot # sqrt() +0:2:0 +1:2:1 -1:2:NaN # -$x ** (1/2) => -$y, but not in broot() -123:2:NaN +inf:2:inf -inf:2:NaN 2:2:1 -2:2:NaN 4:2:2 9:2:3 16:2:4 100:2:10 123:2:11 15241:2:123 144:2:12 12:2:3 # invalid ones 1:NaN:NaN -1:NaN:NaN 0:NaN:NaN -inf:NaN:NaN +inf:NaN:NaN NaN:0:NaN NaN:2:NaN NaN:inf:NaN NaN:inf:NaN 12:-inf:NaN 12:inf:NaN +0:0:NaN +1:0:NaN -1:0:NaN -2:0:NaN -123.45:0:NaN +inf:0:NaN 12:1:12 -12:1:NaN 8:-1:NaN -8:-1:NaN # cubic root 8:3:2 -8:3:NaN # fourths root 16:4:2 81:4:3 # 2 ** 64 18446744073709551616:4:65536 18446744073709551616:8:256 18446744073709551616:16:16 18446744073709551616:32:4 18446744073709551616:64:2 18446744073709551616:128:1 # 213 ** 15 84274086103068221283760416414557757:15:213 # see t/bigroot.t for more tests &bsqrt 145:12 144:12 143:11 16:4 170:13 169:13 168:12 4:2 3:1 2:1 9:3 12:3 256:16 100000000:10000 4000000000000:2000000 152399026:12345 152399025:12345 152399024:12344 # 2 ** 64 => 2 ** 32 18446744073709551616:4294967296 84274086103068221283760416414557757:290299993288095377 1:1 0:0 -2:NaN -123:NaN Nan:NaN +inf:inf -inf:NaN # see t/biglog.t for more tests &bexp NaN:NaN inf:inf 1:2 2:7 &batan2 NaN:1:10:NaN NaN:NaN:10:NaN 1:NaN:10:NaN inf:1:14:1 -inf:1:14:-1 0:-inf:14:3 -1:-inf:14:-3 1:-inf:14:3 0:inf:14:0 inf:-inf:14:2 -inf:-inf:14:-2 # +- 0.78.... inf:+inf:14:0 -inf:+inf:14:0 1:5:13:0 1:5:14:0 0:0:10:0 0:1:14:0 0:2:14:0 1:0:14:1 5:0:14:1 -1:0:11:-1 -2:0:77:-1 2:0:77:1 -1:5:14:0 1:5:14:0 -1:8:14:0 1:8:14:0 -1:1:14:0 &bpi 77:3 +0:3 11:3 # see t/bignok.t for more tests &bnok +inf:10:inf NaN:NaN:NaN NaN:1:NaN 1:NaN:NaN 1:1:1 # k > n 1:2:0 2:3:0 # k < 0 1:-2:0 # 7 over 3 = 35 7:3:35 7:6:7 100:90:17310309456440 100:95:75287520 2:0:1 7:0:1 2:1:2 &bround $round_mode("trunc") 0:12:0 NaNbround:12:NaN +inf:12:inf -inf:12:-inf 1234:0:1234 1234:2:1200 123456:4:123400 123456:5:123450 123456:6:123456 +10123456789:5:10123000000 -10123456789:5:-10123000000 +10123456789:9:10123456700 -10123456789:9:-10123456700 +101234500:6:101234000 -101234500:6:-101234000 #+101234500:-4:101234000 #-101234500:-4:-101234000 $round_mode("zero") +20123456789:5:20123000000 -20123456789:5:-20123000000 +20123456789:9:20123456800 -20123456789:9:-20123456800 +201234500:6:201234000 -201234500:6:-201234000 #+201234500:-4:201234000 #-201234500:-4:-201234000 +12345000:4:12340000 -12345000:4:-12340000 $round_mode("+inf") +30123456789:5:30123000000 -30123456789:5:-30123000000 +30123456789:9:30123456800 -30123456789:9:-30123456800 +301234500:6:301235000 -301234500:6:-301234000 #+301234500:-4:301235000 #-301234500:-4:-301234000 +12345000:4:12350000 -12345000:4:-12340000 $round_mode("-inf") +40123456789:5:40123000000 -40123456789:5:-40123000000 +40123456789:9:40123456800 -40123456789:9:-40123456800 +401234500:6:401234000 +401234500:6:401234000 #-401234500:-4:-401235000 #-401234500:-4:-401235000 +12345000:4:12340000 -12345000:4:-12350000 $round_mode("odd") +50123456789:5:50123000000 -50123456789:5:-50123000000 +50123456789:9:50123456800 -50123456789:9:-50123456800 +501234500:6:501235000 -501234500:6:-501235000 #+501234500:-4:501235000 #-501234500:-4:-501235000 +12345000:4:12350000 -12345000:4:-12350000 $round_mode("even") +60123456789:5:60123000000 -60123456789:5:-60123000000 +60123456789:9:60123456800 -60123456789:9:-60123456800 +601234500:6:601234000 -601234500:6:-601234000 #+601234500:-4:601234000 #-601234500:-4:-601234000 #-601234500:-9:0 #-501234500:-9:0 #-601234500:-8:0 #-501234500:-8:0 +1234567:7:1234567 +1234567:6:1234570 +12345000:4:12340000 -12345000:4:-12340000 $round_mode("common") +60123456789:5:60123000000 +60123199999:5:60123000000 +60123299999:5:60123000000 +60123399999:5:60123000000 +60123499999:5:60123000000 +60123500000:5:60124000000 +60123600000:5:60124000000 +60123700000:5:60124000000 +60123800000:5:60124000000 +60123900000:5:60124000000 -60123456789:5:-60123000000 -60123199999:5:-60123000000 -60123299999:5:-60123000000 -60123399999:5:-60123000000 -60123499999:5:-60123000000 -60123500000:5:-60124000000 -60123600000:5:-60124000000 -60123700000:5:-60124000000 -60123800000:5:-60124000000 -60123900000:5:-60124000000 &is_zero 0:1 NaNzero:0 +inf:0 -inf:0 123:0 -1:0 1:0 &is_one 0:0 NaNone:0 +inf:0 -inf:0 1:1 2:0 -1:0 -2:0 # floor, ceil, and int are pretty pointless in integer space, but play safe &bfloor 0:0 NaNfloor:NaN +inf:inf -inf:-inf -1:-1 -2:-2 2:2 3:3 abc:NaN &bceil NaNceil:NaN +inf:inf -inf:-inf 0:0 -1:-1 -2:-2 2:2 3:3 abc:NaN &bint NaN:NaN +inf:inf -inf:-inf 0:0 -1:-1 -2:-2 2:2 3:3 &as_hex 128:0x80 -128:-0x80 0:0x0 -0:0x0 1:0x1 0x123456789123456789:0x123456789123456789 +inf:inf -inf:-inf NaNas_hex:NaN &as_bin 128:0b10000000 -128:-0b10000000 0:0b0 -0:0b0 1:0b1 0b1010111101010101010110110110110110101:0b1010111101010101010110110110110110101 0x123456789123456789:0b100100011010001010110011110001001000100100011010001010110011110001001 +inf:inf -inf:-inf NaNas_bin:NaN &as_oct 128:0200 -128:-0200 0:00 -0:00 1:01 0b1010111101010101010110110110110110101:01275252666665 0x123456789123456789:044321263611044321263611 +inf:inf -inf:-inf NaNas_oct:NaN # overloaded functions &log -1:NaN 0:-inf 1:0 2:0 3:1 123456789:18 1234567890987654321:41 -inf:inf inf:inf NaN:NaN &exp &sin &cos &atan2 &int &neg &abs &sqrt Math-BigInt-1.999808/t/bigintpm.t0000644403072340010010000000504313035444636016611 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 3913 # tests in require'd file + 20; # tests in this file use Math::BigInt only => 'Calc'; our ($CLASS, $CALC); $CLASS = "Math::BigInt"; $CALC = Math::BigInt -> config('lib'); # backend library my $x; ############################################################################# # bgcd() as function, class method and instance method. my $gcd0 = Math::BigInt::bgcd(-12, 18, 27); isa_ok($gcd0, "Math::BigInt", "bgcd() as function"); is($gcd0, 3, "bgcd() as function"); my $gcd1 = Math::BigInt->bgcd(-12, 18, 27); isa_ok($gcd1, "Math::BigInt", "bgcd() as class method"); is($gcd1, 3, "bgcd() as class method"); $x = Math::BigInt -> new(-12); my $gcd2 = $x -> bgcd(18, 27); isa_ok($gcd2, "Math::BigInt", "bgcd() as instance method"); is($gcd2, 3, "bgcd() as instance method"); is($x, -12, "bgcd() does not modify invocand"); ############################################################################# # blcm() as function, class method and instance method. my $lcm0 = Math::BigInt::blcm(-12, 18, 27); isa_ok($lcm0, "Math::BigInt", "blcm() as function"); is($lcm0, 108, "blcm() as function"); my $lcm1 = Math::BigInt->blcm(-12, 18, 27); isa_ok($lcm1, "Math::BigInt", "blcm() as class method"); is($lcm1, 108, "blcm() as class method"); $x = Math::BigInt -> new(-12); my $lcm2 = $x -> blcm(18, 27); isa_ok($lcm2, "Math::BigInt", "blcm() as instance method"); is($lcm2, 108, "blcm() as instance method"); is($x, -12, "blcm() does not modify invocand"); ############################################################################# # from_hex(), from_bin() and from_oct() tests $x = Math::BigInt->from_hex('0xcafe'); is($x, "51966", qq|Math::BigInt->from_hex("0xcafe")|); $x = Math::BigInt->from_hex('0xcafebabedead'); is($x, "223195403574957", qq|Math::BigInt->from_hex("0xcafebabedead")|); $x = Math::BigInt->from_bin('0b1001'); is($x, "9", qq|Math::BigInt->from_bin("0b1001")|); $x = Math::BigInt->from_bin('0b1001100110011001100110011001'); is($x, "161061273", qq|Math::BigInt->from_bin("0b1001100110011001100110011001");|); $x = Math::BigInt->from_oct('0775'); is($x, "509", qq|Math::BigInt->from_oct("0775");|); $x = Math::BigInt->from_oct('07777777777777711111111222222222'); is($x, "9903520314281112085086151826", qq|Math::BigInt->from_oct("07777777777777711111111222222222");|); ############################################################################# # all the other tests require 't/bigintpm.inc'; # all tests here for sharing Math-BigInt-1.999808/t/bigints.t0000644403072340010010000001103212740677024016433 0ustar ospjadomain users#!perl use strict; use warnings; use lib 't'; use Test::More tests => 50; # testing of Math::BigInt:Scalar (used by the testsuite), # primarily for interface/api and not for the math functionality use Math::BigInt::Scalar; my $class = 'Math::BigInt::Scalar'; # pass classname to sub's # _new and _str my $x = $class->_new("123"); my $y = $class->_new("321"); is(ref($x), 'SCALAR', 'ref($x)'); is($class->_str($x), 123, "$class->_str(\$x)"); is($class->_str($y), 321, "$class->_str(\$y)"); # _add, _sub, _mul, _div is($class->_str($class->_add($x, $y)), 444, "$class->_str($class->_add(\$x, \$y)"); is($class->_str($class->_sub($x, $y)), 123, "$class->_str($class->_sub(\$x, \$y)"); is($class->_str($class->_mul($x, $y)), 39483, "$class->_str($class->_mul(\$x, \$y))"); is($class->_str($class->_div($x, $y)), 123, "$class->_str($class->_div(\$x, \$y)"); $class->_mul($x, $y); is($class->_str($x), 39483, "$class->_str(\$x)"); is($class->_str($y), 321, "$class->_str(\$y)"); my $z = $class->_new("2"); is($class->_str($class->_add($x, $z)), 39485, "$class->_str($class->_add(\$x, \$z)"); my ($re, $rr) = $class->_div($x, $y); is($class->_str($re), 123, "$class->_str(\$re)"); is($class->_str($rr), 2, "$class->_str(\$rr)"); # is_zero, _is_one, _one, _zero is($class->_is_zero($x), 0, "$class->_is_zero($x)"); is($class->_is_one($x), 0, "$class->_is_one($x)"); is($class->_is_one($class->_one()), 1, "$class->_is_one($class->_one())"); is($class->_is_one($class->_zero()), 0, "$class->_is_one($class->_zero())"); is($class->_is_zero($class->_zero()), 1, "$class->_is_zero($class->_zero())"); is($class->_is_zero($class->_one()), 0, "$class->_is_zero($class->_one())"); # is_odd, is_even is($class->_is_odd($class->_one()), 1, "$class->_is_odd($class->_one())"); is($class->_is_odd($class->_zero()), 0, "$class->_is_odd($class->_zero())"); is($class->_is_even($class->_one()), 0, "$class->_is_even($class->_one())"); is($class->_is_even($class->_zero()), 1, "$class->_is_even($class->_zero())"); # _digit $x = $class->_new("123456789"); is($class->_digit($x, 0), 9, "$class->_digit(\$x, 0)"); is($class->_digit($x, 1), 8, "$class->_digit(\$x, 1)"); is($class->_digit($x, 2), 7, "$class->_digit(\$x, 2)"); is($class->_digit($x, -1), 1, "$class->_digit(\$x, -1)"); is($class->_digit($x, -2), 2, "$class->_digit(\$x, -2)"); is($class->_digit($x, -3), 3, "$class->_digit(\$x, -3)"); # _copy $x = $class->_new("12356"); is($class->_str($class->_copy($x)), 12356, "$class->_str($class->_copy(\$x))"); # _acmp $x = $class->_new("123456789"); $y = $class->_new("987654321"); is($class->_acmp($x, $y), -1, "$class->_acmp(\$x, \$y)"); is($class->_acmp($y, $x), 1, "$class->_acmp(\$y, \$x)"); is($class->_acmp($x, $x), 0, "$class->_acmp(\$x, \$x)"); is($class->_acmp($y, $y), 0, "$class->_acmp(\$y, \$y)"); # _div $x = $class->_new("3333"); $y = $class->_new("1111"); is($class->_str(scalar $class->_div($x, $y)), 3, "$class->_str(scalar $class->_div(\$x, \$y))"); $x = $class->_new("33333"); $y = $class->_new("1111"); ($x, $y) = $class->_div($x, $y); is($class->_str($x), 30, "$class->_str(\$x)"); is($class->_str($y), 3, "$class->_str(\$y)"); $x = $class->_new("123"); $y = $class->_new("1111"); ($x, $y) = $class->_div($x, $y); is($class->_str($x), 0, "$class->_str(\$x)"); is($class->_str($y), 123, "$class->_str(\$y)"); # _num $x = $class->_new("12345"); $x = $class->_num($x); is(ref($x) || '', '', 'ref($x) || ""'); is($x, 12345, '$x'); # _len $x = $class->_new("12345"); $x = $class->_len($x); is(ref($x) || '', '', 'ref($x) || ""'); is($x, 5, '$x'); # _and, _or, _xor $x = $class->_new("3"); $y = $class->_new("4"); is($class->_str($class->_or($x, $y)), 7, "$class->_str($class->_or($x, $y))"); $x = $class->_new("1"); $y = $class->_new("4"); is($class->_str($class->_xor($x, $y)), 5, "$class->_str($class->_xor($x, $y))"); $x = $class->_new("7"); $y = $class->_new("3"); is($class->_str($class->_and($x, $y)), 3, "$class->_str($class->_and($x, $y))"); # _pow $x = $class->_new("2"); $y = $class->_new("4"); is($class->_str($class->_pow($x, $y)), 16, "$class->_str($class->_pow($x, $y))"); $x = $class->_new("2"); $y = $class->_new("5"); is($class->_str($class->_pow($x, $y)), 32, "$class->_str($class->_pow($x, $y))"); $x = $class->_new("3"); $y = $class->_new("3"); is($class->_str($class->_pow($x, $y)), 27, "$class->_str($class->_pow($x, $y))"); # _check $x = $class->_new("123456789"); is($class->_check($x), 0, "$class->_check(\$x)"); is($class->_check(123), '123 is not a reference', "$class->_check(123)"); Math-BigInt-1.999808/t/biglog.t0000644403072340010010000002206313015321462016231 0ustar ospjadomain users#!perl # Test blog function (and bpow, since it uses blog), as well as bexp(). # It is too slow to be simple included in bigfltpm.inc, where it would get # executed 3 times. One time would be under Math::BigInt::BareCalc, which # shouldn't make any difference since there is no CALC->_log() function, and # one time under a subclass, which *should* work. # But it is better to test the numerical functionality, instead of not testing # it at all (which did lead to wrong answers for 0 < $x < 1 in blog() in # versions up to v1.63, and for bsqrt($x) when $x << 1 for instance). use strict; use warnings; use Test::More tests => 73; use Math::BigFloat only => 'Calc'; use Math::BigInt; my $class = "Math::BigInt"; ############################################################################### # test $n->blog() in Math::BigInt (broken until 1.80) is($class->new(2)->blog(), '0', "$class->new(2)->blog()"); is($class->new(288)->blog(), '5', "$class->new(288)->blog()"); is($class->new(2000)->blog(), '7', "$class->new(2000)->blog()"); ############################################################################### # test $n->bexp() in Math::BigInt is($class->new(1)->bexp(), '2', "$class->new(1)->bexp()"); is($class->new(2)->bexp(), '7', "$class->new(2)->bexp()"); is($class->new(3)->bexp(), '20', "$class->new(3)->bexp()"); ############################################################################### ############################################################################### # Math::BigFloat tests ############################################################################### # test $n->blog(undef, N) where N > 67 (broken until 1.82) $class = "Math::BigFloat"; # These tests can take quite a while, but are necessary. Maybe protect them # with some alarm()? # this triggers the calculation and caching of ln(2): is($class->new(5)->blog(undef, 71), '1.6094379124341003746007593332261876395256013542685177219126478914741790', "$class->new(5)->blog(undef, 71)"); # if the cache was correct, we should get this result, fast: is($class->new(2)->blog(undef, 71), '0.69314718055994530941723212145817656807550013436025525412068000949339362', "$class->new(2)->blog(undef, 71)"); is($class->new(11)->blog(undef, 71), '2.3978952727983705440619435779651292998217068539374171752185677091305736', "$class->new(11)->blog(undef, 71)"); is($class->new(21)->blog(undef, 71), '3.0445224377234229965005979803657054342845752874046106401940844835750742', "$class->new(21)->blog(undef, 71)"); ############################################################################### # These tests are now really fast, since they collapse to blog(10), basically # Don't attempt to run them with older versions. You are warned. # $x < 0 => NaN is($class->new(-2)->blog(), 'NaN', "$class->new(-2)->blog()"); is($class->new(-1)->blog(), 'NaN', "$class->new(-1)->blog()"); is($class->new(-10)->blog(), 'NaN', "$class->new(-10)->blog()"); is($class->new(-2, 2)->blog(), 'NaN', "$class->new(-2, 2)->blog()"); my $ten = $class->new(10)->blog(); # 10 is cached (up to 75 digits) is($class->new(10)->blog(), '2.302585092994045684017991454684364207601', qq|$class->new(10)->blog()|); # 0.1 is using the cached value for log(10), too is($class->new("0.1")->blog(), -$ten, qq|$class->new("0.1")->blog()|); is($class->new("0.01")->blog(), -$ten * 2, qq|$class->new("0.01")->blog()|); is($class->new("0.001")->blog(), -$ten * 3, qq|$class->new("0.001")->blog()|); is($class->new("0.0001")->blog(), -$ten * 4, qq|$class->new("0.0001")->blog()|); # also cached is($class->new(2)->blog(), '0.6931471805599453094172321214581765680755', qq|$class->new(2)->blog()|); is($class->new(4)->blog(), $class->new(2)->blog * 2, qq|$class->new(4)->blog()|); # These are still slow, so do them only to 10 digits is($class->new("0.2")->blog(undef, 10), "-1.609437912", qq|$class->new("0.2")->blog(undef, 10)|); is($class->new("0.3")->blog(undef, 10), "-1.203972804", qq|$class->new("0.3")->blog(undef, 10)|); is($class->new("0.4")->blog(undef, 10), "-0.9162907319", qq|$class->new("0.4")->blog(undef, 10)|); is($class->new("0.5")->blog(undef, 10), "-0.6931471806", qq|$class->new("0.5")->blog(undef, 10)|); is($class->new("0.6")->blog(undef, 10), "-0.5108256238", qq|$class->new("0.6")->blog(undef, 10)|); is($class->new("0.7")->blog(undef, 10), "-0.3566749439", qq|$class->new("0.7")->blog(undef, 10)|); is($class->new("0.8")->blog(undef, 10), "-0.2231435513", qq|$class->new("0.8")->blog(undef, 10)|); is($class->new("0.9")->blog(undef, 10), "-0.1053605157", qq|$class->new("0.9")->blog(undef, 10)|); is($class->new("9")->blog(undef, 10), "2.197224577", qq|$class->new("9")->blog(undef, 10)|); is($class->new("10")->blog(10, 10), "1.000000000", qq|$class->new("10")->blog(10, 10)|); is($class->new("20")->blog(20, 10), "1.000000000", qq|$class->new("20")->blog(20, 10)|); is($class->new("100")->blog(100, 10), "1.000000000", qq|$class->new("100")->blog(100, 10)|); is($class->new("100")->blog(10, 10), "2.000000000", # 10 ** 2 == 100 qq|$class->new("100")->blog(10, 10)|); is($class->new("400")->blog(20, 10), "2.000000000", # 20 ** 2 == 400 qq|$class->new("400")->blog(20, 10)|); is($class->new("4")->blog(2, 10), "2.000000000", # 2 ** 2 == 4 qq|$class->new("4")->blog(2, 10)|); is($class->new("16")->blog(2, 10), "4.000000000", # 2 ** 4 == 16 qq|$class->new("16")->blog(2, 10)|); is($class->new("1.2")->bpow("0.3", 10), "1.056219968", qq|$class->new("1.2")->bpow("0.3", 10)|); is($class->new("10")->bpow("0.6", 10), "3.981071706", qq|$class->new("10")->bpow("0.6", 10)|); # blog should handle bigint input is(Math::BigFloat::blog(Math::BigInt->new(100), 10), 2, "blog(100)"); ############################################################################### # some integer results is($class->new(2)->bpow(32)->blog(2), "32", "2 ** 32"); is($class->new(3)->bpow(32)->blog(3), "32", "3 ** 32"); is($class->new(2)->bpow(65)->blog(2), "65", "2 ** 65"); my $x = Math::BigInt->new('777') ** 256; my $base = Math::BigInt->new('12345678901234'); is($x->copy()->blog($base), 56, 'blog(777**256, 12345678901234)'); $x = Math::BigInt->new('777') ** 777; $base = Math::BigInt->new('777'); is($x->copy()->blog($base), 777, 'blog(777**777, 777)'); ############################################################################### # test for bug in bsqrt() not taking negative _e into account test_bpow('200', '0.5', 10, '14.14213562'); test_bpow('20', '0.5', 10, '4.472135955'); test_bpow('2', '0.5', 10, '1.414213562'); test_bpow('0.2', '0.5', 10, '0.4472135955'); test_bpow('0.02', '0.5', 10, '0.1414213562'); test_bpow('0.49', '0.5', undef, '0.7'); test_bpow('0.49', '0.5', 10, '0.7000000000'); test_bpow('0.002', '0.5', 10, '0.04472135955'); test_bpow('0.0002', '0.5', 10, '0.01414213562'); test_bpow('0.0049', '0.5', undef, '0.07'); test_bpow('0.0049', '0.5', 10, '0.07000000000'); test_bpow('0.000002', '0.5', 10, '0.001414213562'); test_bpow('0.021', '0.5', 10, '0.1449137675'); test_bpow('1.2', '0.5', 10, '1.095445115'); test_bpow('1.23', '0.5', 10, '1.109053651'); test_bpow('12.3', '0.5', 10, '3.507135583'); test_bpow('9.9', '0.5', 10, '3.146426545'); test_bpow('9.86902225', '0.5', 10, '3.141500000'); test_bpow('9.86902225', '0.5', undef, '3.1415'); ############################################################################### # other tests for bpow() test_bpow('0.2', '0.41', 10, '0.5169187652'); is($class->new("0.01")->bpow("28.4", 40)->bsstr(), '1584893192461113485202101373391507013269e-96', qq|$class->new("0.01")->bpow("28.4", 40)->bsstr()|); # The following test takes too long. #is($class->new("2")->bpow("-1034.5", 40)->bsstr(), # '3841222690408590466868250378242558090957e-351', # qq|$class->new("2")->bpow("-1034.5", 40)|); ############################################################################### # test bexp() with cached results is($class->new(1)->bexp(), '2.718281828459045235360287471352662497757', 'bexp(1)'); is($class->new(2)->bexp(40), $class->new(1)->bexp(45)->bpow(2, 40), 'bexp(2)'); is($class->new("12.5")->bexp(61), $class->new(1)->bexp(65)->bpow(12.5, 61), 'bexp(12.5)'); ############################################################################### # test bexp() with big values (non-cached) is($class->new(1)->bexp(100), '2.7182818284590452353602874713526624977572470936999' . '59574966967627724076630353547594571382178525166427', qq|$class->new(1)->bexp(100)|); is($class->new("12.5")->bexp(91), $class->new(1)->bexp(95)->bpow(12.5, 91), qq|$class->new("12.5")->bexp(91)|); is($class->new("-118.5")->bexp(20)->bsstr(), '34364014567198602057e-71', qq|$class->new("-118.5")->bexp(20)->bsstr()|); is($class->new("-394.84010945715266885")->bexp(20)->bsstr(), '33351796227864913873e-191', qq|$class->new("-118.5")->bexp(20)->bsstr()|); # all done 1; ############################################################################### sub test_bpow { my ($x, $y, $scale, $result) = @_; is($class->new($x)->bpow($y, $scale), $result, qq|$class->new($x)->bpow($y, | . (defined($scale) ? $scale : 'undef') . qq|)|); } Math-BigInt-1.999808/t/bigroot.t0000644403072340010010000000323313015321401016422 0ustar ospjadomain users#!perl # Test broot function (and bsqrt() function, since it is used by broot()). # It is too slow to be simple included in bigfltpm.inc, where it would get # executed 3 times. # But it is better to test the numerical functionality, instead of not testing # it at all. use strict; # restrict unsafe constructs use warnings; # enable optional warnings use Test::More tests => 4 * 2; use Math::BigFloat only => 'Calc'; use Math::BigInt; my $mbf = "Math::BigFloat"; my $mbi = "Math::BigInt"; # 2 ** 240 = # 1766847064778384329583297500742918515827483896875618958121606201292619776 # takes way too long #test_broot('2', '240', 8, undef, # '1073741824'); #test_broot('2', '240', 9, undef, # '106528681.3099908308759836475139583940127'); #test_broot('2', '120', 9, undef, # '10321.27324073880096577298929482324664787'); #test_broot('2', '120', 17, undef, # '133.3268493632747279600707813049418888729'); test_broot('2', '120', 8, undef, '32768'); test_broot('2', '60', 8, undef, '181.0193359837561662466161566988413540569'); test_broot('2', '60', 9, undef, '101.5936673259647663841091609134277286651'); test_broot('2', '60', 17, undef, '11.54672461623965153271017217302844672562'); sub test_broot { my ($x, $n, $y, $scale, $expected) = @_; my $s = $scale || 'undef'; is($mbf->new($x)->bpow($n)->broot($y, $scale), $expected, "Try: $mbf->new($x)->bpow($n)->broot($y, $s) == $expected"); $expected =~ s/\..*//; is($mbi->new($x)->bpow($n)->broot($y, $scale), $expected, "Try: $mbi->new($x)->bpow($n)->broot($y, $s) == $expected"); } Math-BigInt-1.999808/t/big_pi_e.t0000644403072340010010000000134012741400260016515 0ustar ospjadomain users#!perl # Test bpi() and bexp() use strict; use warnings; use Test::More tests => 8; use Math::BigFloat; ############################################################################# my $pi = Math::BigFloat::bpi(); is($pi->{_a}, undef, 'A is not defined'); is($pi->{_p}, undef, 'P is not defined'); $pi = Math::BigFloat->bpi(); is($pi->{_a}, undef, 'A is not defined'); is($pi->{_p}, undef, 'P is not defined'); $pi = Math::BigFloat->bpi(10); is($pi->{_a}, 10, 'A is defined'); is($pi->{_p}, undef, 'P is not defined'); ############################################################################# my $e = Math::BigFloat->new(1)->bexp(); is($e->{_a}, undef, 'A is not defined'); is($e->{_p}, undef, 'P is not defined'); Math-BigInt-1.999808/t/bnstr-mbf.t0000644403072340010010000001151612740677024016675 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 460; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); { my $test = qq|\$x = Math::BigFloat -> new("$x_str");| . qq| \$str = \$x -> bnstr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0e+0 # positive numbers 0.000000000001:1e-12 0.00000000001:1e-11 0.0000000001:1e-10 0.000000001:1e-9 0.00000001:1e-8 0.0000001:1e-7 0.000001:1e-6 0.00001:1e-5 0.0001:1e-4 0.001:1e-3 0.01:1e-2 0.1:1e-1 1:1e+0 10:1e+1 100:1e+2 1000:1e+3 10000:1e+4 100000:1e+5 1000000:1e+6 10000000:1e+7 100000000:1e+8 1000000000:1e+9 10000000000:1e+10 100000000000:1e+11 1000000000000:1e+12 0.0000000000012:1.2e-12 0.000000000012:1.2e-11 0.00000000012:1.2e-10 0.0000000012:1.2e-9 0.000000012:1.2e-8 0.00000012:1.2e-7 0.0000012:1.2e-6 0.000012:1.2e-5 0.00012:1.2e-4 0.0012:1.2e-3 0.012:1.2e-2 0.12:1.2e-1 1.2:1.2e+0 12:1.2e+1 120:1.2e+2 1200:1.2e+3 12000:1.2e+4 120000:1.2e+5 1200000:1.2e+6 12000000:1.2e+7 120000000:1.2e+8 1200000000:1.2e+9 12000000000:1.2e+10 120000000000:1.2e+11 1200000000000:1.2e+12 0.00000000000123:1.23e-12 0.0000000000123:1.23e-11 0.000000000123:1.23e-10 0.00000000123:1.23e-9 0.0000000123:1.23e-8 0.000000123:1.23e-7 0.00000123:1.23e-6 0.0000123:1.23e-5 0.000123:1.23e-4 0.00123:1.23e-3 0.0123:1.23e-2 0.123:1.23e-1 1.23:1.23e+0 12.3:1.23e+1 123:1.23e+2 1230:1.23e+3 12300:1.23e+4 123000:1.23e+5 1230000:1.23e+6 12300000:1.23e+7 123000000:1.23e+8 1230000000:1.23e+9 12300000000:1.23e+10 123000000000:1.23e+11 1230000000000:1.23e+12 0.000000000001234:1.234e-12 0.00000000001234:1.234e-11 0.0000000001234:1.234e-10 0.000000001234:1.234e-9 0.00000001234:1.234e-8 0.0000001234:1.234e-7 0.000001234:1.234e-6 0.00001234:1.234e-5 0.0001234:1.234e-4 0.001234:1.234e-3 0.01234:1.234e-2 0.1234:1.234e-1 1.234:1.234e+0 12.34:1.234e+1 123.4:1.234e+2 1234:1.234e+3 12340:1.234e+4 123400:1.234e+5 1234000:1.234e+6 12340000:1.234e+7 123400000:1.234e+8 1234000000:1.234e+9 12340000000:1.234e+10 123400000000:1.234e+11 1234000000000:1.234e+12 0.000003141592:3.141592e-6 0.00003141592:3.141592e-5 0.0003141592:3.141592e-4 0.003141592:3.141592e-3 0.03141592:3.141592e-2 0.3141592:3.141592e-1 3.141592:3.141592e+0 31.41592:3.141592e+1 314.1592:3.141592e+2 3141.592:3.141592e+3 31415.92:3.141592e+4 314159.2:3.141592e+5 3141592:3.141592e+6 # negative numbers -0.000000000001:-1e-12 -0.00000000001:-1e-11 -0.0000000001:-1e-10 -0.000000001:-1e-9 -0.00000001:-1e-8 -0.0000001:-1e-7 -0.000001:-1e-6 -0.00001:-1e-5 -0.0001:-1e-4 -0.001:-1e-3 -0.01:-1e-2 -0.1:-1e-1 -1:-1e+0 -10:-1e+1 -100:-1e+2 -1000:-1e+3 -10000:-1e+4 -100000:-1e+5 -1000000:-1e+6 -10000000:-1e+7 -100000000:-1e+8 -1000000000:-1e+9 -10000000000:-1e+10 -100000000000:-1e+11 -1000000000000:-1e+12 -0.0000000000012:-1.2e-12 -0.000000000012:-1.2e-11 -0.00000000012:-1.2e-10 -0.0000000012:-1.2e-9 -0.000000012:-1.2e-8 -0.00000012:-1.2e-7 -0.0000012:-1.2e-6 -0.000012:-1.2e-5 -0.00012:-1.2e-4 -0.0012:-1.2e-3 -0.012:-1.2e-2 -0.12:-1.2e-1 -1.2:-1.2e+0 -12:-1.2e+1 -120:-1.2e+2 -1200:-1.2e+3 -12000:-1.2e+4 -120000:-1.2e+5 -1200000:-1.2e+6 -12000000:-1.2e+7 -120000000:-1.2e+8 -1200000000:-1.2e+9 -12000000000:-1.2e+10 -120000000000:-1.2e+11 -1200000000000:-1.2e+12 -0.00000000000123:-1.23e-12 -0.0000000000123:-1.23e-11 -0.000000000123:-1.23e-10 -0.00000000123:-1.23e-9 -0.0000000123:-1.23e-8 -0.000000123:-1.23e-7 -0.00000123:-1.23e-6 -0.0000123:-1.23e-5 -0.000123:-1.23e-4 -0.00123:-1.23e-3 -0.0123:-1.23e-2 -0.123:-1.23e-1 -1.23:-1.23e+0 -12.3:-1.23e+1 -123:-1.23e+2 -1230:-1.23e+3 -12300:-1.23e+4 -123000:-1.23e+5 -1230000:-1.23e+6 -12300000:-1.23e+7 -123000000:-1.23e+8 -1230000000:-1.23e+9 -12300000000:-1.23e+10 -123000000000:-1.23e+11 -1230000000000:-1.23e+12 -0.000000000001234:-1.234e-12 -0.00000000001234:-1.234e-11 -0.0000000001234:-1.234e-10 -0.000000001234:-1.234e-9 -0.00000001234:-1.234e-8 -0.0000001234:-1.234e-7 -0.000001234:-1.234e-6 -0.00001234:-1.234e-5 -0.0001234:-1.234e-4 -0.001234:-1.234e-3 -0.01234:-1.234e-2 -0.1234:-1.234e-1 -1.234:-1.234e+0 -12.34:-1.234e+1 -123.4:-1.234e+2 -1234:-1.234e+3 -12340:-1.234e+4 -123400:-1.234e+5 -1234000:-1.234e+6 -12340000:-1.234e+7 -123400000:-1.234e+8 -1234000000:-1.234e+9 -12340000000:-1.234e+10 -123400000000:-1.234e+11 -1234000000000:-1.234e+12 -0.000003141592:-3.141592e-6 -0.00003141592:-3.141592e-5 -0.0003141592:-3.141592e-4 -0.003141592:-3.141592e-3 -0.03141592:-3.141592e-2 -0.3141592:-3.141592e-1 -3.141592:-3.141592e+0 -31.41592:-3.141592e+1 -314.1592:-3.141592e+2 -3141.592:-3.141592e+3 -31415.92:-3.141592e+4 -314159.2:-3.141592e+5 -3141592:-3.141592e+6 Math-BigInt-1.999808/t/bnstr-mbi.t0000644403072340010010000000466612740677024016710 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 220; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); { my $test = qq|\$x = Math::BigInt -> new("$x_str");| . qq| \$str = \$x -> bnstr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0e+0 # positive numbers 1:1e+0 10:1e+1 100:1e+2 1000:1e+3 10000:1e+4 100000:1e+5 1000000:1e+6 10000000:1e+7 100000000:1e+8 1000000000:1e+9 10000000000:1e+10 100000000000:1e+11 1000000000000:1e+12 12:1.2e+1 120:1.2e+2 1200:1.2e+3 12000:1.2e+4 120000:1.2e+5 1200000:1.2e+6 12000000:1.2e+7 120000000:1.2e+8 1200000000:1.2e+9 12000000000:1.2e+10 120000000000:1.2e+11 1200000000000:1.2e+12 123:1.23e+2 1230:1.23e+3 12300:1.23e+4 123000:1.23e+5 1230000:1.23e+6 12300000:1.23e+7 123000000:1.23e+8 1230000000:1.23e+9 12300000000:1.23e+10 123000000000:1.23e+11 1230000000000:1.23e+12 1234:1.234e+3 12340:1.234e+4 123400:1.234e+5 1234000:1.234e+6 12340000:1.234e+7 123400000:1.234e+8 1234000000:1.234e+9 12340000000:1.234e+10 123400000000:1.234e+11 1234000000000:1.234e+12 3:3e+0 31:3.1e+1 314:3.14e+2 3141:3.141e+3 31415:3.1415e+4 314159:3.14159e+5 3141592:3.141592e+6 # negative numbers -1:-1e+0 -10:-1e+1 -100:-1e+2 -1000:-1e+3 -10000:-1e+4 -100000:-1e+5 -1000000:-1e+6 -10000000:-1e+7 -100000000:-1e+8 -1000000000:-1e+9 -10000000000:-1e+10 -100000000000:-1e+11 -1000000000000:-1e+12 -12:-1.2e+1 -120:-1.2e+2 -1200:-1.2e+3 -12000:-1.2e+4 -120000:-1.2e+5 -1200000:-1.2e+6 -12000000:-1.2e+7 -120000000:-1.2e+8 -1200000000:-1.2e+9 -12000000000:-1.2e+10 -120000000000:-1.2e+11 -1200000000000:-1.2e+12 -123:-1.23e+2 -1230:-1.23e+3 -12300:-1.23e+4 -123000:-1.23e+5 -1230000:-1.23e+6 -12300000:-1.23e+7 -123000000:-1.23e+8 -1230000000:-1.23e+9 -12300000000:-1.23e+10 -123000000000:-1.23e+11 -1230000000000:-1.23e+12 -1234:-1.234e+3 -12340:-1.234e+4 -123400:-1.234e+5 -1234000:-1.234e+6 -12340000:-1.234e+7 -123400000:-1.234e+8 -1234000000:-1.234e+9 -12340000000:-1.234e+10 -123400000000:-1.234e+11 -1234000000000:-1.234e+12 -3:-3e+0 -31:-3.1e+1 -314:-3.14e+2 -3141:-3.141e+3 -31415:-3.1415e+4 -314159:-3.14159e+5 -3141592:-3.141592e+6 Math-BigInt-1.999808/t/bsstr-mbf.t0000644403072340010010000001122712740677024016701 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 460; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); my $test = qq|\$x = Math::BigFloat -> new("$x_str");| . qq| \$str = \$x -> bsstr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0e+0 # positive numbers 0.000000000001:1e-12 0.00000000001:1e-11 0.0000000001:1e-10 0.000000001:1e-9 0.00000001:1e-8 0.0000001:1e-7 0.000001:1e-6 0.00001:1e-5 0.0001:1e-4 0.001:1e-3 0.01:1e-2 0.1:1e-1 1:1e+0 10:1e+1 100:1e+2 1000:1e+3 10000:1e+4 100000:1e+5 1000000:1e+6 10000000:1e+7 100000000:1e+8 1000000000:1e+9 10000000000:1e+10 100000000000:1e+11 1000000000000:1e+12 0.0000000000012:12e-13 0.000000000012:12e-12 0.00000000012:12e-11 0.0000000012:12e-10 0.000000012:12e-9 0.00000012:12e-8 0.0000012:12e-7 0.000012:12e-6 0.00012:12e-5 0.0012:12e-4 0.012:12e-3 0.12:12e-2 1.2:12e-1 12:12e+0 120:12e+1 1200:12e+2 12000:12e+3 120000:12e+4 1200000:12e+5 12000000:12e+6 120000000:12e+7 1200000000:12e+8 12000000000:12e+9 120000000000:12e+10 1200000000000:12e+11 0.00000000000123:123e-14 0.0000000000123:123e-13 0.000000000123:123e-12 0.00000000123:123e-11 0.0000000123:123e-10 0.000000123:123e-9 0.00000123:123e-8 0.0000123:123e-7 0.000123:123e-6 0.00123:123e-5 0.0123:123e-4 0.123:123e-3 1.23:123e-2 12.3:123e-1 123:123e+0 1230:123e+1 12300:123e+2 123000:123e+3 1230000:123e+4 12300000:123e+5 123000000:123e+6 1230000000:123e+7 12300000000:123e+8 123000000000:123e+9 1230000000000:123e+10 0.000000000001234:1234e-15 0.00000000001234:1234e-14 0.0000000001234:1234e-13 0.000000001234:1234e-12 0.00000001234:1234e-11 0.0000001234:1234e-10 0.000001234:1234e-9 0.00001234:1234e-8 0.0001234:1234e-7 0.001234:1234e-6 0.01234:1234e-5 0.1234:1234e-4 1.234:1234e-3 12.34:1234e-2 123.4:1234e-1 1234:1234e+0 12340:1234e+1 123400:1234e+2 1234000:1234e+3 12340000:1234e+4 123400000:1234e+5 1234000000:1234e+6 12340000000:1234e+7 123400000000:1234e+8 1234000000000:1234e+9 0.000003141592:3141592e-12 0.00003141592:3141592e-11 0.0003141592:3141592e-10 0.003141592:3141592e-9 0.03141592:3141592e-8 0.3141592:3141592e-7 3.141592:3141592e-6 31.41592:3141592e-5 314.1592:3141592e-4 3141.592:3141592e-3 31415.92:3141592e-2 314159.2:3141592e-1 3141592:3141592e+0 # negative numbers -0.000000000001:-1e-12 -0.00000000001:-1e-11 -0.0000000001:-1e-10 -0.000000001:-1e-9 -0.00000001:-1e-8 -0.0000001:-1e-7 -0.000001:-1e-6 -0.00001:-1e-5 -0.0001:-1e-4 -0.001:-1e-3 -0.01:-1e-2 -0.1:-1e-1 -1:-1e+0 -10:-1e+1 -100:-1e+2 -1000:-1e+3 -10000:-1e+4 -100000:-1e+5 -1000000:-1e+6 -10000000:-1e+7 -100000000:-1e+8 -1000000000:-1e+9 -10000000000:-1e+10 -100000000000:-1e+11 -1000000000000:-1e+12 -0.0000000000012:-12e-13 -0.000000000012:-12e-12 -0.00000000012:-12e-11 -0.0000000012:-12e-10 -0.000000012:-12e-9 -0.00000012:-12e-8 -0.0000012:-12e-7 -0.000012:-12e-6 -0.00012:-12e-5 -0.0012:-12e-4 -0.012:-12e-3 -0.12:-12e-2 -1.2:-12e-1 -12:-12e+0 -120:-12e+1 -1200:-12e+2 -12000:-12e+3 -120000:-12e+4 -1200000:-12e+5 -12000000:-12e+6 -120000000:-12e+7 -1200000000:-12e+8 -12000000000:-12e+9 -120000000000:-12e+10 -1200000000000:-12e+11 -0.00000000000123:-123e-14 -0.0000000000123:-123e-13 -0.000000000123:-123e-12 -0.00000000123:-123e-11 -0.0000000123:-123e-10 -0.000000123:-123e-9 -0.00000123:-123e-8 -0.0000123:-123e-7 -0.000123:-123e-6 -0.00123:-123e-5 -0.0123:-123e-4 -0.123:-123e-3 -1.23:-123e-2 -12.3:-123e-1 -123:-123e+0 -1230:-123e+1 -12300:-123e+2 -123000:-123e+3 -1230000:-123e+4 -12300000:-123e+5 -123000000:-123e+6 -1230000000:-123e+7 -12300000000:-123e+8 -123000000000:-123e+9 -1230000000000:-123e+10 -0.000000000001234:-1234e-15 -0.00000000001234:-1234e-14 -0.0000000001234:-1234e-13 -0.000000001234:-1234e-12 -0.00000001234:-1234e-11 -0.0000001234:-1234e-10 -0.000001234:-1234e-9 -0.00001234:-1234e-8 -0.0001234:-1234e-7 -0.001234:-1234e-6 -0.01234:-1234e-5 -0.1234:-1234e-4 -1.234:-1234e-3 -12.34:-1234e-2 -123.4:-1234e-1 -1234:-1234e+0 -12340:-1234e+1 -123400:-1234e+2 -1234000:-1234e+3 -12340000:-1234e+4 -123400000:-1234e+5 -1234000000:-1234e+6 -12340000000:-1234e+7 -123400000000:-1234e+8 -1234000000000:-1234e+9 -0.000003141592:-3141592e-12 -0.00003141592:-3141592e-11 -0.0003141592:-3141592e-10 -0.003141592:-3141592e-9 -0.03141592:-3141592e-8 -0.3141592:-3141592e-7 -3.141592:-3141592e-6 -31.41592:-3141592e-5 -314.1592:-3141592e-4 -3141.592:-3141592e-3 -31415.92:-3141592e-2 -314159.2:-3141592e-1 -3141592:-3141592e+0 Math-BigInt-1.999808/t/bsstr-mbi.t0000644403072340010010000000453412740677024016707 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 220; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $expected) = split /:/; my ($x, $str); { my $test = qq|\$x = Math::BigInt -> new("$x_str");| . qq| \$str = \$x -> bsstr();|; note "\n$test\n\n"; eval $test; is($str, $expected, qq|input value is "$x_str"|); is($x, $x_str, "input object is unmodified"); } } __DATA__ NaN:NaN inf:inf -inf:-inf 0:0e+0 # positive numbers 1:1e+0 10:1e+1 100:1e+2 1000:1e+3 10000:1e+4 100000:1e+5 1000000:1e+6 10000000:1e+7 100000000:1e+8 1000000000:1e+9 10000000000:1e+10 100000000000:1e+11 1000000000000:1e+12 12:12e+0 120:12e+1 1200:12e+2 12000:12e+3 120000:12e+4 1200000:12e+5 12000000:12e+6 120000000:12e+7 1200000000:12e+8 12000000000:12e+9 120000000000:12e+10 1200000000000:12e+11 123:123e+0 1230:123e+1 12300:123e+2 123000:123e+3 1230000:123e+4 12300000:123e+5 123000000:123e+6 1230000000:123e+7 12300000000:123e+8 123000000000:123e+9 1230000000000:123e+10 1234:1234e+0 12340:1234e+1 123400:1234e+2 1234000:1234e+3 12340000:1234e+4 123400000:1234e+5 1234000000:1234e+6 12340000000:1234e+7 123400000000:1234e+8 1234000000000:1234e+9 3:3e+0 31:31e+0 314:314e+0 3141:3141e+0 31415:31415e+0 314159:314159e+0 3141592:3141592e+0 # negative numbers -1:-1e+0 -10:-1e+1 -100:-1e+2 -1000:-1e+3 -10000:-1e+4 -100000:-1e+5 -1000000:-1e+6 -10000000:-1e+7 -100000000:-1e+8 -1000000000:-1e+9 -10000000000:-1e+10 -100000000000:-1e+11 -1000000000000:-1e+12 -12:-12e+0 -120:-12e+1 -1200:-12e+2 -12000:-12e+3 -120000:-12e+4 -1200000:-12e+5 -12000000:-12e+6 -120000000:-12e+7 -1200000000:-12e+8 -12000000000:-12e+9 -120000000000:-12e+10 -1200000000000:-12e+11 -123:-123e+0 -1230:-123e+1 -12300:-123e+2 -123000:-123e+3 -1230000:-123e+4 -12300000:-123e+5 -123000000:-123e+6 -1230000000:-123e+7 -12300000000:-123e+8 -123000000000:-123e+9 -1230000000000:-123e+10 -1234:-1234e+0 -12340:-1234e+1 -123400:-1234e+2 -1234000:-1234e+3 -12340000:-1234e+4 -123400000:-1234e+5 -1234000000:-1234e+6 -12340000000:-1234e+7 -123400000000:-1234e+8 -1234000000000:-1234e+9 -3:-3e+0 -31:-31e+0 -314:-314e+0 -3141:-3141e+0 -31415:-31415e+0 -314159:-314159e+0 -3141592:-3141592e+0 Math-BigInt-1.999808/t/calling-class-methods.t0000644403072340010010000000402012740677024021150 0ustar ospjadomain users#!perl # test calling conventions, and :constant overloading use strict; use warnings; use Test::More tests => 148; ############################################################################## package Math::BigInt::Test; use Math::BigInt; our @ISA = qw/Math::BigInt/; # subclass of MBI use overload; ############################################################################## package Math::BigFloat::Test; use Math::BigFloat; our @ISA = qw/Math::BigFloat/; # subclass of MBI use overload; ############################################################################## package main; use Math::BigInt try => 'Calc'; use Math::BigFloat; my ($x, $y, $z, $u); ############################################################################### # check whether op's accept normal strings, even when inherited by subclasses # do one positive and one negative test to avoid false positives by "accident" my ($method, $expected); while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines if (s/^&//) { $method = $_; next; } my @args = split /:/, $_, 99; $expected = pop @args; foreach my $class (qw/ Math::BigInt Math::BigFloat Math::BigInt::Test Math::BigFloat::Test /) { my $arg = $args[0] =~ /"/ || $args[0] eq "" ? $args[0] : qq|"$args[0]"|; my $try = "$class -> $method($arg);"; my $got = eval $try; is($got, $expected, $try); } } __END__ &is_zero 1:0 0:1 &is_one 1:1 0:0 &is_positive 1:1 -1:0 &is_negative 1:0 -1:1 &is_nan abc:1 1:0 &is_inf inf:1 0:0 &bstr 5:5 10:10 -10:-10 abc:NaN "+inf":inf "-inf":-inf &bsstr 1:1e+0 0:0e+0 2:2e+0 200:2e+2 -5:-5e+0 -100:-1e+2 abc:NaN "+inf":inf &babs -1:1 1:1 #&bnot #-2:1 #1:-2 &bzero :0 &bnan :NaN abc:NaN &bone :1 "+":1 "-":-1 &binf :inf "+":inf "-":-inf Math-BigInt-1.999808/t/calling-instance-methods.t0000644403072340010010000000403212740677024021652 0ustar ospjadomain users#!perl # test calling conventions, and :constant overloading use strict; use warnings; use Test::More tests => 140; ############################################################################## package Math::BigInt::Test; use Math::BigInt; our @ISA = qw/Math::BigInt/; # subclass of MBI use overload; ############################################################################## package Math::BigFloat::Test; use Math::BigFloat; our @ISA = qw/Math::BigFloat/; # subclass of MBI use overload; ############################################################################## package main; use Math::BigInt try => 'Calc'; use Math::BigFloat; my ($x, $y, $z, $u); ############################################################################### # check whether op's accept normal strings, even when inherited by subclasses # do one positive and one negative test to avoid false positives by "accident" my ($method, $expected); while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines if (s/^&//) { $method = $_; next; } my @args = split /:/, $_, 99; $expected = pop @args; foreach my $class (qw/ Math::BigInt Math::BigFloat Math::BigInt::Test Math::BigFloat::Test /) { my $arg = $args[0] =~ /"/ || $args[0] eq "" ? $args[0] : qq|"$args[0]"|; my $try = "$class -> new($arg) -> $method();"; my $got = eval $try; is($got, $expected, $try); } } __END__ &is_zero 1:0 0:1 &is_one 1:1 0:0 &is_positive 1:1 -1:0 &is_negative 1:0 -1:1 &is_nan abc:1 1:0 &is_inf inf:1 0:0 &bstr 5:5 10:10 -10:-10 abc:NaN "+inf":inf "-inf":-inf &bsstr 1:1e+0 0:0e+0 2:2e+0 200:2e+2 -5:-5e+0 -100:-1e+2 abc:NaN "+inf":inf &babs -1:1 1:1 &bnot -2:1 1:-2 &bzero :0 &bnan :NaN abc:NaN &bone :1 #"+":1 #"-":-1 &binf :inf #"+":inf #"-":-inf Math-BigInt-1.999808/t/calling.t0000644403072340010010000000367413033512264016410 0ustar ospjadomain users#!perl # test calling conventions, and :constant overloading use strict; use warnings; use lib 't'; my $VERSION = '1.999808'; # adjust manually to match latest release use Test::More tests => 5; ############################################################################## package Math::BigInt::Test; use Math::BigInt; our @ISA = qw/Math::BigInt/; # subclass of MBI use overload; ############################################################################## package Math::BigFloat::Test; use Math::BigFloat; our @ISA = qw/Math::BigFloat/; # subclass of MBF use overload; ############################################################################## package main; use Math::BigInt try => 'Calc'; use Math::BigFloat; my ($x, $expected, $try); my $class = 'Math::BigInt'; # test whether use Math::BigInt qw/VERSION/ works $try = "use $class (" . ($VERSION . '1') .");"; $try .= ' $x = $class->new(123); $x = "$x";'; eval $try; like($@, qr/ ^ Math::BigInt \s+ ( version \s+ )? \S+ \s+ required--this \s+ is \s+ only \s+ version \s+ \S+ /x, $try); # test whether fallback to calc works $try = qq|use $class ($VERSION, "try", "foo, bar, ");| . qq| $class\->config('lib');|; $expected = eval $try; like($expected, qr/^Math::BigInt::(Fast)?Calc\z/, $try); # test whether constant works or not, also test for qw($VERSION) # bgcd() is present in subclass, too $try = qq|use $class ($VERSION, "bgcd", ":constant");| . q| $x = 2**150; bgcd($x); $x = "$x";|; $expected = eval $try; is($expected, "1427247692705959881058285969449495136382746624", $try); # test whether Math::BigInt::Scalar via use works (w/ dff. spellings of calc) $try = qq|use $class ($VERSION, "lib", "Scalar");| . q| $x = 2**10; $x = "$x";|; $expected = eval $try; is($expected, "1024", $try); $try = qq|use $class ($VERSION, "lib", "$class\::Scalar");| . q| $x = 2**10; $x = "$x";|; $expected = eval $try; is($expected, "1024", $try); Math-BigInt-1.999808/t/config.t0000644403072340010010000000736313015012520016231 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 55; # test whether Math::BigInt->config() and Math::BigFloat->config() works use Math::BigInt lib => 'Calc'; use Math::BigFloat; my $mbi = 'Math::BigInt'; my $mbf = 'Math::BigFloat'; ############################################################################## # Math::BigInt { can_ok($mbi, 'config'); my $cfg = $mbi->config(); is(ref($cfg), 'HASH', 'ref() of output from $mbi->config()'); is($cfg->{lib}, 'Math::BigInt::Calc', 'lib'); is($cfg->{lib_version}, $Math::BigInt::Calc::VERSION, 'lib_version'); is($cfg->{class}, $mbi, 'class'); is($cfg->{upgrade} || '', '', 'upgrade'); is($cfg->{div_scale}, 40, 'div_Scale'); is($cfg->{precision} || 0, 0, 'precision'); # should test for undef is($cfg->{accuracy} || 0, 0, 'accuracy'); is($cfg->{round_mode}, 'even', 'round_mode'); is($cfg->{trap_nan}, 0, 'trap_nan'); is($cfg->{trap_inf}, 0, 'trap_inf'); is($mbi->config('lib'), 'Math::BigInt::Calc', 'config("lib")'); # can set via hash ref? $cfg = $mbi->config({ trap_nan => 1 }); is($cfg->{trap_nan}, 1, 'can set "trap_nan" via hash ref'); # reset for later $mbi->config(trap_nan => 0); } ############################################################################## # Math::BigFloat { can_ok($mbf, 'config'); my $cfg = $mbf->config(); is(ref($cfg), 'HASH', 'ref() of output from $mbf->config()'); is($cfg->{lib}, 'Math::BigInt::Calc', 'lib'); is($cfg->{with}, 'Math::BigInt::Calc', 'with'); is($cfg->{lib_version}, $Math::BigInt::Calc::VERSION, 'lib_version'); is($cfg->{class}, $mbf, 'class'); is($cfg->{upgrade} || '', '', 'upgrade'); is($cfg->{div_scale}, 40, 'div_Scale'); is($cfg->{precision} || 0, 0, 'precision'); # should test for undef is($cfg->{accuracy} || 0, 0, 'accuracy'); is($cfg->{round_mode}, 'even', 'round_mode'); is($cfg->{trap_nan}, 0, 'trap_nan'); is($cfg->{trap_inf}, 0, 'trap_inf'); is($mbf->config('lib'), 'Math::BigInt::Calc', 'config("lib")'); # can set via hash ref? $cfg = $mbf->config({ trap_nan => 1 }); is($cfg->{trap_nan}, 1, 'can set "trap_nan" via hash ref'); # reset for later $mbf->config(trap_nan => 0); } ############################################################################## # test setting values my $test = { trap_nan => 1, trap_inf => 1, accuracy => 2, precision => 3, round_mode => 'zero', div_scale => '100', upgrade => 'Math::BigInt::SomeClass', downgrade => 'Math::BigInt::SomeClass', }; my $c; foreach my $key (keys %$test) { # see if setting in MBI works eval { $mbi->config($key => $test->{$key}); }; $c = $mbi->config(); is("$key = $c->{$key}", "$key = $test->{$key}", "$key = $test->{$key}"); $c = $mbf->config(); # see if setting it in MBI leaves MBF alone ok(($c->{$key} || 0) ne $test->{$key}, "$key ne \$c->{$key}"); # see if setting in MBF works eval { $mbf->config($key => $test->{$key}); }; $c = $mbf->config(); is("$key = $c->{$key}", "$key = $test->{$key}", "$key = $test->{$key}"); } ############################################################################## # test setting illegal keys (should croak) eval { $mbi->config('some_garbage' => 1); }; like($@, qr/ ^ Illegal \s+ key\(s\) \s+ 'some_garbage' \s+ passed \s+ to \s+ Math::BigInt->config\(\) \s+ at /x, 'Passing invalid key to Math::BigInt->config() causes an error.'); eval { $mbf->config('some_garbage' => 1); }; like($@, qr/ ^ Illegal \s+ key\(s\) \s+ 'some_garbage' \s+ passed \s+ to \s+ Math::BigFloat->config\(\) \s+ at /x, 'Passing invalid key to Math::BigFloat->config() causes an error.'); Math-BigInt-1.999808/t/constant.t0000644403072340010010000000251712740677025016636 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 7; use Math::BigInt ':constant'; is(2 ** 255, '578960446186580977117854925043439539266' . '34992332820282019728792003956564819968', '2 ** 255'); { no warnings 'portable'; # protect against "non-portable" warnings # hexadecimal constants is(0x123456789012345678901234567890, Math::BigInt->new('0x123456789012345678901234567890'), 'hexadecimal constant 0x123456789012345678901234567890'); # binary constants is(0b01010100011001010110110001110011010010010110000101101101, Math::BigInt->new('0b0101010001100101011011000111' . '0011010010010110000101101101'), 'binary constant 0b0101010001100101011011000111' . '0011010010010110000101101101'); } use Math::BigFloat ':constant'; is(1.0 / 3.0, '0.3333333333333333333333333333333333333333', '1.0 / 3.0 = 0.3333333333333333333333333333333333333333'); # stress-test Math::BigFloat->import() Math::BigFloat->import(qw/:constant/); pass('Math::BigFloat->import(qw/:constant/);'); Math::BigFloat->import(qw/:constant upgrade Math::BigRat/); pass('Math::BigFloat->import(qw/:constant upgrade Math::BigRat/);'); Math::BigFloat->import(qw/upgrade Math::BigRat :constant/); pass('Math::BigFloat->import(qw/upgrade Math::BigRat :constant/);'); # all tests done Math-BigInt-1.999808/t/const_mbf.t0000644403072340010010000000062312740677025016753 0ustar ospjadomain users#!perl # test Math::BigFloat constants alone (w/o Math::BigInt loading) use strict; use warnings; use Test::More tests => 2; use Math::BigFloat ':constant'; is(1.0 / 3.0, '0.3333333333333333333333333333333333333333', "1.0 / 3.0 = 0.3333333333333333333333333333333333333333"); # Math::BigInt was not loaded with ':constant', so only floats are handled is(ref(2 ** 2), '', "2 ** 2 is a scalar"); Math-BigInt-1.999808/t/downgrade.t0000644403072340010010000000407112740677025016754 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 15; use Math::BigInt upgrade => 'Math::BigFloat'; use Math::BigFloat downgrade => 'Math::BigInt', upgrade => 'Math::BigInt'; our ($CLASS, $EXPECTED_CLASS, $CALC); $CLASS = "Math::BigInt"; $EXPECTED_CLASS = "Math::BigFloat"; $CALC = "Math::BigInt::Calc"; # backend # simplistic test for now is(Math::BigFloat->downgrade(), 'Math::BigInt', 'Math::BigFloat->downgrade()'); is(Math::BigFloat->upgrade(), 'Math::BigInt', 'Math::BigFloat->upgrade()'); # these downgrade is(ref(Math::BigFloat->new("inf")), "Math::BigInt", qq|ref(Math::BigFloat->new("inf"))|); is(ref(Math::BigFloat->new("-inf")), "Math::BigInt", qq|ref(Math::BigFloat->new("-inf"))|); is(ref(Math::BigFloat->new("NaN")), "Math::BigInt", qq|ref(Math::BigFloat->new("NaN"))|); is(ref(Math::BigFloat->new("0")), "Math::BigInt", qq|ref(Math::BigFloat->new("0"))|); is(ref(Math::BigFloat->new("1")), "Math::BigInt", qq|ref(Math::BigFloat->new("1"))|); is(ref(Math::BigFloat->new("10")), "Math::BigInt", qq|ref(Math::BigFloat->new("10"))|); is(ref(Math::BigFloat->new("-10")), "Math::BigInt", qq|ref(Math::BigFloat->new("-10"))|); is(ref(Math::BigFloat->new("-10.0E1")), "Math::BigInt", qq|ref(Math::BigFloat->new("-10.0E1"))|); # bug until v1.67: is(Math::BigFloat->new("0.2E0"), "0.2", qq|Math::BigFloat->new("0.2E0")|); is(Math::BigFloat->new("0.2E1"), "2", qq|Math::BigFloat->new("0.2E1")|); # until v1.67 resulted in 200: is(Math::BigFloat->new("0.2E2"), "20", qq|Math::BigFloat->new("0.2E2")|); # disable, otherwise it screws calculations Math::BigFloat->upgrade(undef); is(Math::BigFloat->upgrade() || "", "", qq/Math::BigFloat->upgrade() || ""/); Math::BigFloat->div_scale(20); # make it a bit faster my $x = Math::BigFloat->new(2); # downgrades # the following test upgrade for bsqrt() and also makes new() NOT downgrade # for the bpow() side is(Math::BigFloat->bpow("2", "0.5"), $x->bsqrt(), qq|Math::BigFloat->bpow("2", "0.5")|); #require 'upgrade.inc'; # all tests here for sharing Math-BigInt-1.999808/t/dparts-mbf.t0000644403072340010010000001427112740677025017044 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 1840; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $int_str, $frc_str) = split /:/; note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| (\$i, \$f) = \$x -> dparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my ($int_got, $frc_got) = $x -> dparts(); isa_ok($int_got, "Math::BigFloat"); isa_ok($frc_got, "Math::BigFloat"); is($int_got, $int_str, "value of integer part"); is($frc_got, $frc_str, "value of fraction part"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| \$i = \$x -> dparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my $int_got = $x -> dparts(); isa_ok($int_got, "Math::BigFloat"); is($int_got, $int_str, "value of integer part"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:0 inf:inf:0 -inf:-inf:0 0:0:0 # positive numbers 0.000000000001:0:0.000000000001 0.00000000001:0:0.00000000001 0.0000000001:0:0.0000000001 0.000000001:0:0.000000001 0.00000001:0:0.00000001 0.0000001:0:0.0000001 0.000001:0:0.000001 0.00001:0:0.00001 0.0001:0:0.0001 0.001:0:0.001 0.01:0:0.01 0.1:0:0.1 1:1:0 10:10:0 100:100:0 1000:1000:0 10000:10000:0 100000:100000:0 1000000:1000000:0 10000000:10000000:0 100000000:100000000:0 1000000000:1000000000:0 10000000000:10000000000:0 100000000000:100000000000:0 1000000000000:1000000000000:0 0.0000000000012:0:0.0000000000012 0.000000000012:0:0.000000000012 0.00000000012:0:0.00000000012 0.0000000012:0:0.0000000012 0.000000012:0:0.000000012 0.00000012:0:0.00000012 0.0000012:0:0.0000012 0.000012:0:0.000012 0.00012:0:0.00012 0.0012:0:0.0012 0.012:0:0.012 0.12:0:0.12 1.2:1:0.2 12:12:0 120:120:0 1200:1200:0 12000:12000:0 120000:120000:0 1200000:1200000:0 12000000:12000000:0 120000000:120000000:0 1200000000:1200000000:0 12000000000:12000000000:0 120000000000:120000000000:0 1200000000000:1200000000000:0 0.00000000000123:0:0.00000000000123 0.0000000000123:0:0.0000000000123 0.000000000123:0:0.000000000123 0.00000000123:0:0.00000000123 0.0000000123:0:0.0000000123 0.000000123:0:0.000000123 0.00000123:0:0.00000123 0.0000123:0:0.0000123 0.000123:0:0.000123 0.00123:0:0.00123 0.0123:0:0.0123 0.123:0:0.123 1.23:1:0.23 12.3:12:0.3 123:123:0 1230:1230:0 12300:12300:0 123000:123000:0 1230000:1230000:0 12300000:12300000:0 123000000:123000000:0 1230000000:1230000000:0 12300000000:12300000000:0 123000000000:123000000000:0 1230000000000:1230000000000:0 0.000000000001234:0:0.000000000001234 0.00000000001234:0:0.00000000001234 0.0000000001234:0:0.0000000001234 0.000000001234:0:0.000000001234 0.00000001234:0:0.00000001234 0.0000001234:0:0.0000001234 0.000001234:0:0.000001234 0.00001234:0:0.00001234 0.0001234:0:0.0001234 0.001234:0:0.001234 0.01234:0:0.01234 0.1234:0:0.1234 1.234:1:0.234 12.34:12:0.34 123.4:123:0.4 1234:1234:0 12340:12340:0 123400:123400:0 1234000:1234000:0 12340000:12340000:0 123400000:123400000:0 1234000000:1234000000:0 12340000000:12340000000:0 123400000000:123400000000:0 1234000000000:1234000000000:0 0.000003141592:0:0.000003141592 0.00003141592:0:0.00003141592 0.0003141592:0:0.0003141592 0.003141592:0:0.003141592 0.03141592:0:0.03141592 0.3141592:0:0.3141592 3.141592:3:0.141592 31.41592:31:0.41592 314.1592:314:0.1592 3141.592:3141:0.592 31415.92:31415:0.92 314159.2:314159:0.2 3141592:3141592:0 # negative numbers -0.000000000001:0:-0.000000000001 -0.00000000001:0:-0.00000000001 -0.0000000001:0:-0.0000000001 -0.000000001:0:-0.000000001 -0.00000001:0:-0.00000001 -0.0000001:0:-0.0000001 -0.000001:0:-0.000001 -0.00001:0:-0.00001 -0.0001:0:-0.0001 -0.001:0:-0.001 -0.01:0:-0.01 -0.1:0:-0.1 -1:-1:0 -10:-10:0 -100:-100:0 -1000:-1000:0 -10000:-10000:0 -100000:-100000:0 -1000000:-1000000:0 -10000000:-10000000:0 -100000000:-100000000:0 -1000000000:-1000000000:0 -10000000000:-10000000000:0 -100000000000:-100000000000:0 -1000000000000:-1000000000000:0 -0.0000000000012:0:-0.0000000000012 -0.000000000012:0:-0.000000000012 -0.00000000012:0:-0.00000000012 -0.0000000012:0:-0.0000000012 -0.000000012:0:-0.000000012 -0.00000012:0:-0.00000012 -0.0000012:0:-0.0000012 -0.000012:0:-0.000012 -0.00012:0:-0.00012 -0.0012:0:-0.0012 -0.012:0:-0.012 -0.12:0:-0.12 -1.2:-1:-0.2 -12:-12:0 -120:-120:0 -1200:-1200:0 -12000:-12000:0 -120000:-120000:0 -1200000:-1200000:0 -12000000:-12000000:0 -120000000:-120000000:0 -1200000000:-1200000000:0 -12000000000:-12000000000:0 -120000000000:-120000000000:0 -1200000000000:-1200000000000:0 -0.00000000000123:0:-0.00000000000123 -0.0000000000123:0:-0.0000000000123 -0.000000000123:0:-0.000000000123 -0.00000000123:0:-0.00000000123 -0.0000000123:0:-0.0000000123 -0.000000123:0:-0.000000123 -0.00000123:0:-0.00000123 -0.0000123:0:-0.0000123 -0.000123:0:-0.000123 -0.00123:0:-0.00123 -0.0123:0:-0.0123 -0.123:0:-0.123 -1.23:-1:-0.23 -12.3:-12:-0.3 -123:-123:0 -1230:-1230:0 -12300:-12300:0 -123000:-123000:0 -1230000:-1230000:0 -12300000:-12300000:0 -123000000:-123000000:0 -1230000000:-1230000000:0 -12300000000:-12300000000:0 -123000000000:-123000000000:0 -1230000000000:-1230000000000:0 -0.000000000001234:0:-0.000000000001234 -0.00000000001234:0:-0.00000000001234 -0.0000000001234:0:-0.0000000001234 -0.000000001234:0:-0.000000001234 -0.00000001234:0:-0.00000001234 -0.0000001234:0:-0.0000001234 -0.000001234:0:-0.000001234 -0.00001234:0:-0.00001234 -0.0001234:0:-0.0001234 -0.001234:0:-0.001234 -0.01234:0:-0.01234 -0.1234:0:-0.1234 -1.234:-1:-0.234 -12.34:-12:-0.34 -123.4:-123:-0.4 -1234:-1234:0 -12340:-12340:0 -123400:-123400:0 -1234000:-1234000:0 -12340000:-12340000:0 -123400000:-123400000:0 -1234000000:-1234000000:0 -12340000000:-12340000000:0 -123400000000:-123400000000:0 -1234000000000:-1234000000000:0 -0.000003141592:0:-0.000003141592 -0.00003141592:0:-0.00003141592 -0.0003141592:0:-0.0003141592 -0.003141592:0:-0.003141592 -0.03141592:0:-0.03141592 -0.3141592:0:-0.3141592 -3.141592:-3:-0.141592 -31.41592:-31:-0.41592 -314.1592:-314:-0.1592 -3141.592:-3141:-0.592 -31415.92:-31415:-0.92 -314159.2:-314159:-0.2 -3141592:-3141592:0 Math-BigInt-1.999808/t/dparts-mbi.t0000644403072340010010000000611412740677025017044 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 784; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $int_str, $frc_str) = split /:/; note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| (\$i, \$f) = \$x -> dparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my ($int_got, $frc_got) = $x -> dparts(); isa_ok($int_got, "Math::BigInt"); isa_ok($frc_got, "Math::BigInt"); is($int_got, $int_str, "value of integer part"); is($frc_got, $frc_str, "value of fraction part"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| \$i = \$x -> dparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my $int_got = $x -> dparts(); isa_ok($int_got, "Math::BigInt"); is($int_got, $int_str, "value of integer part"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:0 inf:inf:0 -inf:-inf:0 0:0:0 # positive numbers 1:1:0 10:10:0 100:100:0 1000:1000:0 10000:10000:0 100000:100000:0 1000000:1000000:0 10000000:10000000:0 100000000:100000000:0 1000000000:1000000000:0 10000000000:10000000000:0 100000000000:100000000000:0 1000000000000:1000000000000:0 12:12:0 120:120:0 1200:1200:0 12000:12000:0 120000:120000:0 1200000:1200000:0 12000000:12000000:0 120000000:120000000:0 1200000000:1200000000:0 12000000000:12000000000:0 120000000000:120000000000:0 1200000000000:1200000000000:0 123:123:0 1230:1230:0 12300:12300:0 123000:123000:0 1230000:1230000:0 12300000:12300000:0 123000000:123000000:0 1230000000:1230000000:0 12300000000:12300000000:0 123000000000:123000000000:0 1230000000000:1230000000000:0 1234:1234:0 12340:12340:0 123400:123400:0 1234000:1234000:0 12340000:12340000:0 123400000:123400000:0 1234000000:1234000000:0 12340000000:12340000000:0 123400000000:123400000000:0 1234000000000:1234000000000:0 3141592:3141592:0 # negative numbers -1:-1:0 -10:-10:0 -100:-100:0 -1000:-1000:0 -10000:-10000:0 -100000:-100000:0 -1000000:-1000000:0 -10000000:-10000000:0 -100000000:-100000000:0 -1000000000:-1000000000:0 -10000000000:-10000000000:0 -100000000000:-100000000000:0 -1000000000000:-1000000000000:0 -12:-12:0 -120:-120:0 -1200:-1200:0 -12000:-12000:0 -120000:-120000:0 -1200000:-1200000:0 -12000000:-12000000:0 -120000000:-120000000:0 -1200000000:-1200000000:0 -12000000000:-12000000000:0 -120000000000:-120000000000:0 -1200000000000:-1200000000000:0 -123:-123:0 -1230:-1230:0 -12300:-12300:0 -123000:-123000:0 -1230000:-1230000:0 -12300000:-12300000:0 -123000000:-123000000:0 -1230000000:-1230000000:0 -12300000000:-12300000000:0 -123000000000:-123000000000:0 -1230000000000:-1230000000000:0 -1234:-1234:0 -12340:-12340:0 -123400:-123400:0 -1234000:-1234000:0 -12340000:-12340000:0 -123400000:-123400000:0 -1234000000:-1234000000:0 -12340000000:-12340000000:0 -123400000000:-123400000000:0 -1234000000000:-1234000000000:0 -3141592:-3141592:0 Math-BigInt-1.999808/t/eparts-mbf.t0000644403072340010010000001237612740677025017051 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 1840; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $mant_str, $expo_str) = split /:/; note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| (\$m, \$e) = \$x -> eparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my ($mant_got, $expo_got) = $x -> eparts(); isa_ok($mant_got, "Math::BigFloat"); isa_ok($expo_got, "Math::BigFloat"); is($mant_got, $mant_str, "value of mantissa"); is($expo_got, $expo_str, "value of exponent"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| \$m = \$x -> eparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my $mant_got = $x -> eparts(); isa_ok($mant_got, "Math::BigFloat"); is($mant_got, $mant_str, "value of mantissa"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:NaN inf:inf:inf -inf:-inf:inf 0:0:0 # positive numbers 0.000000000001:1:-12 0.00000000001:10:-12 0.0000000001:100:-12 0.000000001:1:-9 0.00000001:10:-9 0.0000001:100:-9 0.000001:1:-6 0.00001:10:-6 0.0001:100:-6 0.001:1:-3 0.01:10:-3 0.1:100:-3 1:1:0 10:10:0 100:100:0 1000:1:3 10000:10:3 100000:100:3 1000000:1:6 10000000:10:6 100000000:100:6 1000000000:1:9 10000000000:10:9 100000000000:100:9 1000000000000:1:12 0.0000000000012:1.2:-12 0.000000000012:12:-12 0.00000000012:120:-12 0.0000000012:1.2:-9 0.000000012:12:-9 0.00000012:120:-9 0.0000012:1.2:-6 0.000012:12:-6 0.00012:120:-6 0.0012:1.2:-3 0.012:12:-3 0.12:120:-3 1.2:1.2:0 12:12:0 120:120:0 1200:1.2:3 12000:12:3 120000:120:3 1200000:1.2:6 12000000:12:6 120000000:120:6 1200000000:1.2:9 12000000000:12:9 120000000000:120:9 1200000000000:1.2:12 0.00000000000123:1.23:-12 0.0000000000123:12.3:-12 0.000000000123:123:-12 0.00000000123:1.23:-9 0.0000000123:12.3:-9 0.000000123:123:-9 0.00000123:1.23:-6 0.0000123:12.3:-6 0.000123:123:-6 0.00123:1.23:-3 0.0123:12.3:-3 0.123:123:-3 1.23:1.23:0 12.3:12.3:0 123:123:0 1230:1.23:3 12300:12.3:3 123000:123:3 1230000:1.23:6 12300000:12.3:6 123000000:123:6 1230000000:1.23:9 12300000000:12.3:9 123000000000:123:9 1230000000000:1.23:12 0.000000000001234:1.234:-12 0.00000000001234:12.34:-12 0.0000000001234:123.4:-12 0.000000001234:1.234:-9 0.00000001234:12.34:-9 0.0000001234:123.4:-9 0.000001234:1.234:-6 0.00001234:12.34:-6 0.0001234:123.4:-6 0.001234:1.234:-3 0.01234:12.34:-3 0.1234:123.4:-3 1.234:1.234:0 12.34:12.34:0 123.4:123.4:0 1234:1.234:3 12340:12.34:3 123400:123.4:3 1234000:1.234:6 12340000:12.34:6 123400000:123.4:6 1234000000:1.234:9 12340000000:12.34:9 123400000000:123.4:9 1234000000000:1.234:12 0.000003141592:3.141592:-6 0.00003141592:31.41592:-6 0.0003141592:314.1592:-6 0.003141592:3.141592:-3 0.03141592:31.41592:-3 0.3141592:314.1592:-3 3.141592:3.141592:0 31.41592:31.41592:0 314.1592:314.1592:0 3141.592:3.141592:3 31415.92:31.41592:3 314159.2:314.1592:3 3141592:3.141592:6 # negativ: numbers -0.000000000001:-1:-12 -0.00000000001:-10:-12 -0.0000000001:-100:-12 -0.000000001:-1:-9 -0.00000001:-10:-9 -0.0000001:-100:-9 -0.000001:-1:-6 -0.00001:-10:-6 -0.0001:-100:-6 -0.001:-1:-3 -0.01:-10:-3 -0.1:-100:-3 -1:-1:0 -10:-10:0 -100:-100:0 -1000:-1:3 -10000:-10:3 -100000:-100:3 -1000000:-1:6 -10000000:-10:6 -100000000:-100:6 -1000000000:-1:9 -10000000000:-10:9 -100000000000:-100:9 -1000000000000:-1:12 -0.0000000000012:-1.2:-12 -0.000000000012:-12:-12 -0.00000000012:-120:-12 -0.0000000012:-1.2:-9 -0.000000012:-12:-9 -0.00000012:-120:-9 -0.0000012:-1.2:-6 -0.000012:-12:-6 -0.00012:-120:-6 -0.0012:-1.2:-3 -0.012:-12:-3 -0.12:-120:-3 -1.2:-1.2:0 -12:-12:0 -120:-120:0 -1200:-1.2:3 -12000:-12:3 -120000:-120:3 -1200000:-1.2:6 -12000000:-12:6 -120000000:-120:6 -1200000000:-1.2:9 -12000000000:-12:9 -120000000000:-120:9 -1200000000000:-1.2:12 -0.00000000000123:-1.23:-12 -0.0000000000123:-12.3:-12 -0.000000000123:-123:-12 -0.00000000123:-1.23:-9 -0.0000000123:-12.3:-9 -0.000000123:-123:-9 -0.00000123:-1.23:-6 -0.0000123:-12.3:-6 -0.000123:-123:-6 -0.00123:-1.23:-3 -0.0123:-12.3:-3 -0.123:-123:-3 -1.23:-1.23:0 -12.3:-12.3:0 -123:-123:0 -1230:-1.23:3 -12300:-12.3:3 -123000:-123:3 -1230000:-1.23:6 -12300000:-12.3:6 -123000000:-123:6 -1230000000:-1.23:9 -12300000000:-12.3:9 -123000000000:-123:9 -1230000000000:-1.23:12 -0.000000000001234:-1.234:-12 -0.00000000001234:-12.34:-12 -0.0000000001234:-123.4:-12 -0.000000001234:-1.234:-9 -0.00000001234:-12.34:-9 -0.0000001234:-123.4:-9 -0.000001234:-1.234:-6 -0.00001234:-12.34:-6 -0.0001234:-123.4:-6 -0.001234:-1.234:-3 -0.01234:-12.34:-3 -0.1234:-123.4:-3 -1.234:-1.234:0 -12.34:-12.34:0 -123.4:-123.4:0 -1234:-1.234:3 -12340:-12.34:3 -123400:-123.4:3 -1234000:-1.234:6 -12340000:-12.34:6 -123400000:-123.4:6 -1234000000:-1.234:9 -12340000000:-12.34:9 -123400000000:-123.4:9 -1234000000000:-1.234:12 -0.000003141592:-3.141592:-6 -0.00003141592:-31.41592:-6 -0.0003141592:-314.1592:-6 -0.003141592:-3.141592:-3 -0.03141592:-31.41592:-3 -0.3141592:-314.1592:-3 -3.141592:-3.141592:0 -31.41592:-31.41592:0 -314.1592:-314.1592:0 -3141.592:-3.141592:3 -31415.92:-31.41592:3 -314159.2:-314.1592:3 -3141592:-3.141592:6 Math-BigInt-1.999808/t/eparts-mbi.t0000644403072340010010000000515512740677025017051 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 784; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $mant_str, $expo_str) = split /:/; note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| (\$m, \$e) = \$x -> eparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my ($mant_got, $expo_got) = $x -> eparts(); isa_ok($mant_got, "Math::BigInt"); isa_ok($expo_got, "Math::BigInt"); is($mant_got, $mant_str, "value of mantissa"); is($expo_got, $expo_str, "value of exponent"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| \$m = \$x -> eparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my $mant_got = $x -> eparts(); isa_ok($mant_got, "Math::BigInt"); is($mant_got, $mant_str, "value of mantissa"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:NaN inf:inf:inf -inf:-inf:inf 0:0:0 # positive numbers 1:1:0 10:10:0 100:100:0 1000:1:3 10000:10:3 100000:100:3 1000000:1:6 10000000:10:6 100000000:100:6 1000000000:1:9 10000000000:10:9 100000000000:100:9 1000000000000:1:12 12:12:0 120:120:0 1200:NaN:3 12000:12:3 120000:120:3 1200000:NaN:6 12000000:12:6 120000000:120:6 1200000000:NaN:9 12000000000:12:9 120000000000:120:9 1200000000000:NaN:12 123:123:0 1230:NaN:3 12300:NaN:3 123000:123:3 1230000:NaN:6 12300000:NaN:6 123000000:123:6 1230000000:NaN:9 12300000000:NaN:9 123000000000:123:9 1230000000000:NaN:12 1234:NaN:3 12340:NaN:3 123400:NaN:3 1234000:NaN:6 12340000:NaN:6 123400000:NaN:6 1234000000:NaN:9 12340000000:NaN:9 123400000000:NaN:9 1234000000000:NaN:12 3141592:NaN:6 # negativ: numbers -1:-1:0 -10:-10:0 -100:-100:0 -1000:-1:3 -10000:-10:3 -100000:-100:3 -1000000:-1:6 -10000000:-10:6 -100000000:-100:6 -1000000000:-1:9 -10000000000:-10:9 -100000000000:-100:9 -1000000000000:-1:12 -12:-12:0 -120:-120:0 -1200:NaN:3 -12000:-12:3 -120000:-120:3 -1200000:NaN:6 -12000000:-12:6 -120000000:-120:6 -1200000000:NaN:9 -12000000000:-12:9 -120000000000:-120:9 -1200000000000:NaN:12 -123:-123:0 -1230:NaN:3 -12300:NaN:3 -123000:-123:3 -1230000:NaN:6 -12300000:NaN:6 -123000000:-123:6 -1230000000:NaN:9 -12300000000:NaN:9 -123000000000:-123:9 -1230000000000:NaN:12 -1234:NaN:3 -12340:NaN:3 -123400:NaN:3 -1234000:NaN:6 -12340000:NaN:6 -123400000:NaN:6 -1234000000:NaN:9 -12340000000:NaN:9 -123400000000:NaN:9 -1234000000000:NaN:12 -3141592:NaN:6 Math-BigInt-1.999808/t/from_bin-mbf.t0000644403072340010010000000365713035445273017344 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 729; my $class; BEGIN { $class = 'Math::BigFloat'; } BEGIN { use_ok($class, '1.999710'); } my @data; my $space = "\t\r\n "; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($in0, $out0) = split /:/; push @data, [ $in0, $out0 ], [ $in0 . $space, $out0 ], [ $space . $in0, $out0 ], [ $space . $in0 . $space, $out0 ]; } for my $entry (@data) { my ($in0, $out0) = @$entry; # As class method. { my $x; my $test = qq|\$x = $class -> from_bin("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } # As instance method. { for my $str ("-1", "0", "1", "-inf", "+inf", "NaN") { my $x; my $test = qq|\$x = $class -> new("$str");| . qq| \$x -> from_bin("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } } } __END__ 0b1p+0:1 0b.1p+1:1 0b.01p+2:1 0b.001p+3:1 0b.0001p+4:1 0b10p-1:1 0b100p-2:1 0b1000p-3:1 -0b1p+0:-1 0b0p+0:0 0b0p+7:0 0b0p-7:0 0b0.p+0:0 0b.0p+0:0 0b0.0p+0:0 0b1100101011111110:51966 b1100101011111110:51966 1100101011111110:51966 0b1.1001p+3:12.5 0b10010.001101p-1:9.1015625 -0b.11110001001101010111100110111101111p+31:-2023406814.9375 0b10.0100011010001010110011110001001101p+34:39093746765 NaN:NaN +inf:NaN -inf:NaN 0b.p+0:NaN Math-BigInt-1.999808/t/from_bin-mbi.t0000644403072340010010000000571313035445141017334 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 1373; my $class; BEGIN { $class = 'Math::BigInt'; } BEGIN { use_ok($class); } my @data; my $space = "\t\r\n "; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($in0, $out0) = split /:/; push @data, [ $in0, $out0 ], [ $in0 . $space, $out0 ], [ $space . $in0, $out0 ], [ $space . $in0 . $space, $out0 ]; } for my $entry (@data) { my ($in0, $out0) = @$entry; # As class method. { my $x; my $test = qq|\$x = $class -> from_bin("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } # As instance method. { for my $str ("-1", "0", "1", "-inf", "+inf", "NaN") { my $x; my $test = qq|\$x = $class -> new("$str");| . qq| \$x -> from_bin("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } } } __END__ 0b0:0 0b1:1 0b10:2 0b11:3 0b100:4 0b101:5 0b110:6 0b111:7 0b1000:8 0b1001:9 0b1010:10 0b1011:11 0b1100:12 0b1101:13 0b1110:14 0b1111:15 0b10000:16 0b10001:17 0b11111110:254 0b11111111:255 0b100000000:256 0b100000001:257 0b1111111111111110:65534 0b1111111111111111:65535 0b10000000000000000:65536 0b10000000000000001:65537 0b111111111111111111111110:16777214 0b111111111111111111111111:16777215 0b1000000000000000000000000:16777216 0b1000000000000000000000001:16777217 0b11111111111111111111111111111110:4294967294 0b11111111111111111111111111111111:4294967295 0b100000000000000000000000000000000:4294967296 0b100000000000000000000000000000001:4294967297 0b1111111111111111111111111111111111111110:1099511627774 0b1111111111111111111111111111111111111111:1099511627775 0b10000000000000000000000000000000000000000:1099511627776 0b10000000000000000000000000000000000000001:1099511627777 0b111111111111111111111111111111111111111111111110:281474976710654 0b111111111111111111111111111111111111111111111111:281474976710655 0b1000000000000000000000000000000000000000000000000:281474976710656 0b1000000000000000000000000000000000000000000000001:281474976710657 0b11111111111111111111111111111111111111111111111111111110:72057594037927934 0b11111111111111111111111111111111111111111111111111111111:72057594037927935 0b100000000000000000000000000000000000000000000000000000000:72057594037927936 0b100000000000000000000000000000000000000000000000000000001:72057594037927937 NaN:NaN +inf:NaN -inf:NaN Math-BigInt-1.999808/t/from_hex-mbf.t0000644403072340010010000000350113035445304017337 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 729; my $class; BEGIN { $class = 'Math::BigFloat'; } BEGIN { use_ok($class, '1.999710'); } my @data; my $space = "\t\r\n "; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($in0, $out0) = split /:/; push @data, [ $in0, $out0 ], [ $in0 . $space, $out0 ], [ $space . $in0, $out0 ], [ $space . $in0 . $space, $out0 ]; } for my $entry (@data) { my ($in0, $out0) = @$entry; # As class method. { my $x; my $test = qq|\$x = $class -> from_hex("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } # As instance method. { for my $str ("-1", "0", "1", "-inf", "+inf", "NaN") { my $x; my $test = qq|\$x = $class -> new("$str");| . qq| \$x -> from_hex("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } } } __END__ 0x1p+0:1 0x.8p+1:1 0x.4p+2:1 0x.2p+3:1 0x.1p+4:1 0x2p-1:1 0x4p-2:1 0x8p-3:1 -0x1p+0:-1 0x0p+0:0 0x0p+7:0 0x0p-7:0 0x0.p+0:0 0x.0p+0:0 0x0.0p+0:0 0xcafe:51966 xcafe:51966 cafe:51966 0x1.9p+3:12.5 0x12.34p-1:9.1015625 -0x.789abcdefp+32:-2023406814.9375 0x12.3456789ap+31:39093746765 NaN:NaN +inf:NaN -inf:NaN 0x.p+0:NaN Math-BigInt-1.999808/t/from_hex-mbi.t0000644403072340010010000000440313035445410017342 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 1373; my $class; BEGIN { $class = 'Math::BigInt'; } BEGIN { use_ok($class); } my @data; my $space = "\t\r\n "; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($in0, $out0) = split /:/; push @data, [ $in0, $out0 ], [ $in0 . $space, $out0 ], [ $space . $in0, $out0 ], [ $space . $in0 . $space, $out0 ]; } for my $entry (@data) { my ($in0, $out0) = @$entry; # As class method. { my $x; my $test = qq|\$x = $class -> from_hex("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } # As instance method. { for my $str ("-1", "0", "1", "-inf", "+inf", "NaN") { my $x; my $test = qq|\$x = $class -> new("$str");| . qq| \$x -> from_hex("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } } } __END__ 0x0:0 0x1:1 0x2:2 0x3:3 0x4:4 0x5:5 0x6:6 0x7:7 0x8:8 0x9:9 0xa:10 0xb:11 0xc:12 0xd:13 0xe:14 0xf:15 0x10:16 0x11:17 0xfe:254 0xff:255 0x100:256 0x101:257 0xfffe:65534 0xffff:65535 0x10000:65536 0x10001:65537 0xfffffe:16777214 0xffffff:16777215 0x1000000:16777216 0x1000001:16777217 0xfffffffe:4294967294 0xffffffff:4294967295 0x100000000:4294967296 0x100000001:4294967297 0xfffffffffe:1099511627774 0xffffffffff:1099511627775 0x10000000000:1099511627776 0x10000000001:1099511627777 0xfffffffffffe:281474976710654 0xffffffffffff:281474976710655 0x1000000000000:281474976710656 0x1000000000001:281474976710657 0xfffffffffffffe:72057594037927934 0xffffffffffffff:72057594037927935 0x100000000000000:72057594037927936 0x100000000000001:72057594037927937 NaN:NaN +inf:NaN -inf:NaN Math-BigInt-1.999808/t/from_oct-mbf.t0000644403072340010010000000345713035445322017352 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 729; my $class; BEGIN { $class = 'Math::BigFloat'; } BEGIN { use_ok($class, '1.999710'); } my @data; my $space = "\t\r\n "; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($in0, $out0) = split /:/; push @data, [ $in0, $out0 ], [ $in0 . $space, $out0 ], [ $space . $in0, $out0 ], [ $space . $in0 . $space, $out0 ]; } for my $entry (@data) { my ($in0, $out0) = @$entry; # As class method. { my $x; my $test = qq|\$x = $class -> from_oct("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } # As instance method. { for my $str ("-1", "0", "1", "-inf", "+inf", "NaN") { my $x; my $test = qq|\$x = $class -> new("$str");| . qq| \$x -> from_oct("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } } } __END__ 01p+0:1 0.4p+1:1 0.2p+2:1 0.1p+3:1 0.04p+4:1 02p-1:1 04p-2:1 010p-3:1 -1p+0:-1 0p+0:0 0p+7:0 0p-7:0 0.p+0:0 .0p+0:0 0.0p+0:0 145376:51966 0145376:51966 00145376:51966 3.1p+2:12.5 22.15p-1:9.1015625 -0.361152746757p+32:-2023406814.9375 44.3212636115p+30:39093746765 NaN:NaN +inf:NaN -inf:NaN .p+0:NaN Math-BigInt-1.999808/t/from_oct-mbi.t0000644403072340010010000000437113035445336017356 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 1373; my $class; BEGIN { $class = 'Math::BigInt'; } BEGIN { use_ok($class); } my @data; my $space = "\t\r\n "; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($in0, $out0) = split /:/; push @data, [ $in0, $out0 ], [ $in0 . $space, $out0 ], [ $space . $in0, $out0 ], [ $space . $in0 . $space, $out0 ]; } for my $entry (@data) { my ($in0, $out0) = @$entry; # As class method. { my $x; my $test = qq|\$x = $class -> from_oct("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } # As instance method. { for my $str ("-1", "0", "1", "-inf", "+inf", "NaN") { my $x; my $test = qq|\$x = $class -> new("$str");| . qq| \$x -> from_oct("$in0");|; eval $test; die $@ if $@; # this should never happen subtest $test, sub { plan tests => 2, is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } } } __END__ 0:0 1:1 2:2 3:3 4:4 5:5 6:6 7:7 10:8 11:9 12:10 13:11 14:12 15:13 16:14 17:15 20:16 21:17 376:254 377:255 400:256 401:257 177776:65534 177777:65535 200000:65536 200001:65537 77777776:16777214 77777777:16777215 100000000:16777216 100000001:16777217 37777777776:4294967294 37777777777:4294967295 40000000000:4294967296 40000000001:4294967297 17777777777776:1099511627774 17777777777777:1099511627775 20000000000000:1099511627776 20000000000001:1099511627777 7777777777777776:281474976710654 7777777777777777:281474976710655 10000000000000000:281474976710656 10000000000000001:281474976710657 3777777777777777776:72057594037927934 3777777777777777777:72057594037927935 4000000000000000000:72057594037927936 4000000000000000001:72057594037927937 NaN:NaN +inf:NaN -inf:NaN Math-BigInt-1.999808/t/inf_nan.t0000644403072340010010000001554212740677025016417 0ustar ospjadomain users#!perl # test inf/NaN handling all in one place # Thanx to Jarkko for the excellent explanations and the tables use strict; use warnings; use lib 't'; use Test::More tests => 2052; use Math::BigInt; use Math::BigFloat; use Math::BigInt::Subclass; use Math::BigFloat::Subclass; my @biclasses = qw/ Math::BigInt Math::BigInt::Subclass /; my @bfclasses = qw/ Math::BigFloat Math::BigFloat::Subclass /; my (@args, $x, $y, $z); # + foreach (qw/ -inf:-inf:-inf -1:-inf:-inf -0:-inf:-inf 0:-inf:-inf 1:-inf:-inf inf:-inf:NaN NaN:-inf:NaN -inf:-1:-inf -1:-1:-2 -0:-1:-1 0:-1:-1 1:-1:0 inf:-1:inf NaN:-1:NaN -inf:0:-inf -1:0:-1 -0:0:0 0:0:0 1:0:1 inf:0:inf NaN:0:NaN -inf:1:-inf -1:1:0 -0:1:1 0:1:1 1:1:2 inf:1:inf NaN:1:NaN -inf:inf:NaN -1:inf:inf -0:inf:inf 0:inf:inf 1:inf:inf inf:inf:inf NaN:inf:NaN -inf:NaN:NaN -1:NaN:NaN -0:NaN:NaN 0:NaN:NaN 1:NaN:NaN inf:NaN:NaN NaN:NaN:NaN /) { @args = split /:/, $_; for my $class (@biclasses, @bfclasses) { $x = $class->new($args[0]); $y = $class->new($args[1]); $args[2] = '0' if $args[2] eq '-0'; # Math::Big(Int|Float) has no -0 my $r = $x->badd($y); is($x->bstr(), $args[2], "x $class $args[0] + $args[1]"); is($x->bstr(), $args[2], "r $class $args[0] + $args[1]"); } } # - foreach (qw/ -inf:-inf:NaN -1:-inf:inf -0:-inf:inf 0:-inf:inf 1:-inf:inf inf:-inf:inf NaN:-inf:NaN -inf:-1:-inf -1:-1:0 -0:-1:1 0:-1:1 1:-1:2 inf:-1:inf NaN:-1:NaN -inf:0:-inf -1:0:-1 -0:0:-0 0:0:0 1:0:1 inf:0:inf NaN:0:NaN -inf:1:-inf -1:1:-2 -0:1:-1 0:1:-1 1:1:0 inf:1:inf NaN:1:NaN -inf:inf:-inf -1:inf:-inf -0:inf:-inf 0:inf:-inf 1:inf:-inf inf:inf:NaN NaN:inf:NaN -inf:NaN:NaN -1:NaN:NaN -0:NaN:NaN 0:NaN:NaN 1:NaN:NaN inf:NaN:NaN NaN:NaN:NaN /) { @args = split /:/, $_; for my $class (@biclasses, @bfclasses) { $x = $class->new($args[0]); $y = $class->new($args[1]); $args[2] = '0' if $args[2] eq '-0'; # Math::Big(Int|Float) has no -0 my $r = $x->bsub($y); is($x->bstr(), $args[2], "x $class $args[0] - $args[1]"); is($r->bstr(), $args[2], "r $class $args[0] - $args[1]"); } } # * foreach (qw/ -inf:-inf:inf -1:-inf:inf -0:-inf:NaN 0:-inf:NaN 1:-inf:-inf inf:-inf:-inf NaN:-inf:NaN -inf:-1:inf -1:-1:1 -0:-1:0 0:-1:-0 1:-1:-1 inf:-1:-inf NaN:-1:NaN -inf:0:NaN -1:0:-0 -0:0:-0 0:0:0 1:0:0 inf:0:NaN NaN:0:NaN -inf:1:-inf -1:1:-1 -0:1:-0 0:1:0 1:1:1 inf:1:inf NaN:1:NaN -inf:inf:-inf -1:inf:-inf -0:inf:NaN 0:inf:NaN 1:inf:inf inf:inf:inf NaN:inf:NaN -inf:NaN:NaN -1:NaN:NaN -0:NaN:NaN 0:NaN:NaN 1:NaN:NaN inf:NaN:NaN NaN:NaN:NaN /) { @args = split /:/, $_; for my $class (@biclasses, @bfclasses) { $x = $class->new($args[0]); $y = $class->new($args[1]); $args[2] = '0' if $args[2] eq '-0'; # Math::Big(Int|Float) has no -0 my $r = $x->bmul($y); is($x->bstr(), $args[2], "x $class $args[0] * $args[1]"); is($r->bstr(), $args[2], "r $class $args[0] * $args[1]"); } } # / foreach (qw/ -inf:-inf:NaN -1:-inf:0 -0:-inf:0 0:-inf:-0 1:-inf:-1 inf:-inf:NaN NaN:-inf:NaN -inf:-1:inf -1:-1:1 -0:-1:0 0:-1:-0 1:-1:-1 inf:-1:-inf NaN:-1:NaN -inf:0:-inf -1:0:-inf -0:0:NaN 0:0:NaN 1:0:inf inf:0:inf NaN:0:NaN -inf:1:-inf -1:1:-1 -0:1:-0 0:1:0 1:1:1 inf:1:inf NaN:1:NaN -inf:inf:NaN -1:inf:-1 -0:inf:-0 0:inf:0 1:inf:0 inf:inf:NaN NaN:inf:NaN -inf:NaN:NaN -1:NaN:NaN -0:NaN:NaN 0:NaN:NaN 1:NaN:NaN inf:NaN:NaN NaN:NaN:NaN /) { @args = split /:/, $_; for my $class (@biclasses, @bfclasses) { $x = $class->new($args[0]); $y = $class->new($args[1]); $args[2] = '0' if $args[2] eq '-0'; # Math::Big(Int|Float) has no -0 my $t = $x->copy(); my $tmod = $t->copy(); # bdiv in scalar context unless ($class =~ /^Math::BigFloat/) { my $r = $x->bdiv($y); is($x->bstr(), $args[2], "x $class $args[0] / $args[1]"); is($r->bstr(), $args[2], "r $class $args[0] / $args[1]"); } # bmod and bdiv in list context my ($d, $rem) = $t->bdiv($y); # bdiv in list context is($t->bstr(), $args[2], "t $class $args[0] / $args[1]"); is($d->bstr(), $args[2], "d $class $args[0] / $args[1]"); # bmod my $m = $tmod->bmod($y); # bmod() agrees with bdiv? is($m->bstr(), $rem->bstr(), "m $class $args[0] % $args[1]"); # bmod() return agrees with set value? is($tmod->bstr(), $m->bstr(), "o $class $args[0] % $args[1]"); } } # / foreach (qw/ -inf:-inf:NaN -1:-inf:0 -0:-inf:0 0:-inf:-0 1:-inf:-0 inf:-inf:NaN NaN:-inf:NaN -inf:-1:inf -1:-1:1 -0:-1:0 0:-1:-0 1:-1:-1 inf:-1:-inf NaN:-1:NaN -inf:0:-inf -1:0:-inf -0:0:NaN 0:0:NaN 1:0:inf inf:0:inf NaN:0:NaN -inf:1:-inf -1:1:-1 -0:1:-0 0:1:0 1:1:1 inf:1:inf NaN:1:NaN -inf:inf:NaN -1:inf:-0 -0:inf:-0 0:inf:0 1:inf:0 inf:inf:NaN NaN:inf:NaN -inf:NaN:NaN -1:NaN:NaN -0:NaN:NaN 0:NaN:NaN 1:NaN:NaN inf:NaN:NaN NaN:NaN:NaN /) { @args = split /:/, $_; for my $class (@bfclasses) { $x = $class->new($args[0]); $y = $class->new($args[1]); $args[2] = '0' if $args[2] eq '-0'; # Math::Big(Int|Float) has no -0 my $t = $x->copy(); my $tmod = $t->copy(); # bdiv in scalar context my $r = $x->bdiv($y); is($x->bstr(), $args[2], "x $class $args[0] / $args[1]"); is($r->bstr(), $args[2], "r $class $args[0] / $args[1]"); } } ############################################################################# # overloaded comparisons foreach my $c (@biclasses, @bfclasses) { my $x = $c->bnan(); my $y = $c->bnan(); # test with two different objects, too my $z = $c->bzero(); is($x == $y, '', 'NaN == NaN: ""'); is($x != $y, 1, 'NaN != NaN: 1'); is($x == $x, '', 'NaN == NaN: ""'); is($x != $x, 1, 'NaN != NaN: 1'); is($z != $x, 1, '0 != NaN: 1'); is($z == $x, '', '0 == NaN: ""'); is($z < $x, '', '0 < NaN: ""'); is($z <= $x, '', '0 <= NaN: ""'); is($z >= $x, '', '0 >= NaN: ""'); #is($z > $x, '', '0 > NaN: ""'); # Bug! Todo: fix it! } # All done. Math-BigInt-1.999808/t/isa.t0000644403072340010010000000241412740677025015555 0ustar ospjadomain users#!perl use strict; use warnings; use lib 't'; use Test::More tests => 11; use Math::BigInt::Subclass; use Math::BigFloat::Subclass; use Math::BigInt; use Math::BigFloat; my $class = "Math::BigInt::Subclass"; my $CALC = "Math::BigInt::Calc"; # Check that a subclass is still considered a Math::BigInt isa_ok($class->new(123), 'Math::BigInt'); # ditto for plain Math::BigInt isa_ok(Math::BigInt->new(123), 'Math::BigInt'); # But Math::BigFloats aren't ok(!Math::BigFloat->new(123)->isa('Math::BigInt'), "A Math::BigFloat isn't a Math::BigInt"); { # see what happens if we feed a Math::BigFloat into new() my $x = Math::BigInt->new(Math::BigFloat->new(123)); is(ref($x), 'Math::BigInt', 'ref($x) = "Math::BigInt"'); isa_ok($x, 'Math::BigInt'); } { # ditto for subclass my $x = Math::BigInt->new(Math::BigFloat::Subclass->new(123)); is(ref($x), 'Math::BigInt', 'ref($x) = "Math::BigInt"'); isa_ok($x, 'Math::BigInt'); } { my $x = Math::BigFloat->new(Math::BigInt->new(123)); is(ref($x), 'Math::BigFloat', 'ref($x) = "Math::BigFloat"'); isa_ok($x, 'Math::BigFloat'); } { my $x = Math::BigFloat->new(Math::BigInt::Subclass->new(123)); is(ref($x), 'Math::BigFloat', 'ref($x) = "Math::BigFloat"'); isa_ok($x, 'Math::BigFloat'); } Math-BigInt-1.999808/t/lib_load.t0000644403072340010010000000167713015011251016533 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 4; use lib 't'; # first load Math::BigInt with Math::BigInt::Calc use Math::BigInt lib => 'Calc'; # Math::BigFloat will remember that we loaded Math::BigInt::Calc require Math::BigFloat; is(Math::BigFloat::config()->{lib}, 'Math::BigInt::Calc', 'Math::BigFloat got Math::BigInt::Calc'); # now load Math::BigInt again with a different lib Math::BigInt->import(lib => 'BareCalc'); # and finally test that Math::BigFloat knows about Math::BigInt::BareCalc is(Math::BigFloat::config()->{lib}, 'Math::BigInt::BareCalc', 'Math::BigFloat was notified'); # See that Math::BigFloat supports "only" eval "Math::BigFloat->import('only' => 'Calc')"; is(Math::BigFloat::config()->{lib}, 'Math::BigInt::Calc', '"only" worked'); # See that Math::BigFloat supports "try" eval "Math::BigFloat->import('try' => 'BareCalc')"; is(Math::BigFloat::config()->{lib}, 'Math::BigInt::BareCalc', '"try" worked'); Math-BigInt-1.999808/t/Math/0000705403072340010010000000000013035475727015502 5ustar ospjadomain usersMath-BigInt-1.999808/t/Math/BigFloat/0000705403072340010010000000000013035475727017171 5ustar ospjadomain usersMath-BigInt-1.999808/t/Math/BigFloat/Subclass.pm0000644403072340010010000000202412740677025021306 0ustar ospjadomain users#!perl # for testing subclassing Math::BigFloat package Math::BigFloat::Subclass; require 5.006; use strict; use warnings; use Exporter; use Math::BigFloat 1.38; our ($accuracy, $precision, $round_mode, $div_scale); our @ISA = qw(Exporter Math::BigFloat); our $VERSION = "0.06"; use overload; # inherit overload from BigInt # Globals $accuracy = $precision = undef; $round_mode = 'even'; $div_scale = 40; sub new { my $proto = shift; my $class = ref($proto) || $proto; my $value = shift; my $a = $accuracy; $a = $_[0] if defined $_[0]; my $p = $precision; $p = $_[1] if defined $_[1]; # Store the floating point value my $self = Math::BigFloat->new($value, $a, $p, $round_mode); bless $self, $class; $self->{'_custom'} = 1; # make sure this never goes away return $self; } BEGIN { *objectify = \&Math::BigInt::objectify; # to allow Math::BigFloat::Subclass::bgcd( ... ) style calls *bgcd = \&Math::BigFloat::bgcd; *blcm = \&Math::BigFloat::blcm; } 1; Math-BigInt-1.999808/t/Math/BigInt/0000705403072340010010000000000013035475727016656 5ustar ospjadomain usersMath-BigInt-1.999808/t/Math/BigInt/BareCalc.pm0000644403072340010010000000044113020747751020645 0ustar ospjadomain users#!perl package Math::BigInt::BareCalc; use strict; use warnings; our $VERSION = '1.999803'; # Package to to test Bigint's simulation of Calc use Math::BigInt::Calc '1.9998'; our @ISA = qw(Math::BigInt::Calc); print "# BareCalc using Calc v", Math::BigInt::Calc -> VERSION, "\n"; 1; Math-BigInt-1.999808/t/Math/BigInt/Lib/0000705403072340010010000000000013035475727017364 5ustar ospjadomain usersMath-BigInt-1.999808/t/Math/BigInt/Lib/Minimal.pm0000644403072340010010000006555113005656461021322 0ustar ospjadomain users# This is a rather minimalistic library, whose purpose is to test inheritance # from its parent class. package Math::BigInt::Lib::Minimal; use 5.006001; use strict; use warnings; use Carp; use Math::BigInt::Lib; our @ISA = ('Math::BigInt::Lib'); #my $BASE_LEN = 4; my $BASE_LEN = 9; my $BASE = 0 + ("1" . ("0" x $BASE_LEN)); my $MAX_VAL = $BASE - 1; # Do we need api_version() at all, now that we have a virtual parent class that # will provide any missing methods? Fixme! sub api_version () { 2; } sub _new { my ($class, $str) = @_; croak "Invalid input string '$str'" unless $str =~ /^([1-9]\d*|0)\z/; my $n = length $str; my $p = int($n / $BASE_LEN); my $q = $n % $BASE_LEN; my $format = $] < 5.9008 ? "a$BASE_LEN" x $p : "(a$BASE_LEN)*"; $format = "a$q" . $format if $q > 0; my $self = [ reverse(map { 0 + $_ } unpack($format, $str)) ]; return bless $self, $class; } ############################################################################## # convert back to string and number sub _str { my ($class, $x) = @_; my $idx = $#$x; # index of last element # Handle first one differently, since it should not have any leading zeros. my $str = int($x->[$idx]); if ($idx > 0) { my $z = '0' x ($BASE_LEN - 1); while (--$idx >= 0) { $str .= substr($z . $x->[$idx], -$BASE_LEN); } } $str; } ############################################################################## # actual math code sub _add { # (ref to int_num_array, ref to int_num_array) # # Routine to add two base 1eX numbers stolen from Knuth Vol 2 Algorithm A # pg 231. There are separate routines to add and sub as per Knuth pg 233. # This routine modifies array x, but not y. my ($c, $x, $y) = @_; # $x + 0 => $x return $x if @$y == 1 && $y->[0] == 0; # 0 + $y => $y->copy if (@$x == 1 && $x->[0] == 0) { @$x = @$y; return $x; } # For each in Y, add Y to X and carry. If after that, something is left in # X, foreach in X add carry to X and then return X, carry. Trades one # "$j++" for having to shift arrays. my $i; my $car = 0; my $j = 0; for $i (@$y) { $x->[$j] -= $BASE if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0; $j++; } while ($car != 0) { $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++; } $x; } sub _sub { # (ref to int_num_array, ref to int_num_array, swap) # # Subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y # subtract Y from X by modifying x in place my ($c, $sx, $sy, $s) = @_; my $car = 0; my $i; my $j = 0; if (!$s) { for $i (@$sx) { last unless defined $sy->[$j] || $car; $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++; } # might leave leading zeros, so fix that return __strip_zeros($sx); } for $i (@$sx) { # We can't do an early out if $x < $y, since we need to copy the high # chunks from $y. Found by Bob Mathews. #last unless defined $sy->[$j] || $car; $sy->[$j] += $BASE if $car = ($sy->[$j] = $i - ($sy->[$j] || 0) - $car) < 0; $j++; } # might leave leading zeros, so fix that __strip_zeros($sy); } # The following _mul function is an exact copy of _mul_use_div_64 in # Math::BigInt::Calc. sub _mul { # (ref to int_num_array, ref to int_num_array) # multiply two numbers in internal representation # modifies first arg, second need not be different from first # works for 64 bit integer with "use integer" my ($c, $xv, $yv) = @_; use integer; if (@$yv == 1) { # shortcut for two small numbers, also handles $x == 0 if (@$xv == 1) { # shortcut for two very short numbers (improved by Nathan Zook) # works also if xv and yv are the same reference, and handles also $x == 0 if (($xv->[0] *= $yv->[0]) >= $BASE) { $xv->[0] = $xv->[0] - ($xv->[1] = $xv->[0] / $BASE) * $BASE; } return $xv; } # $x * 0 => 0 if ($yv->[0] == 0) { @$xv = (0); return $xv; } # multiply a large number a by a single element one, so speed up my $y = $yv->[0]; my $car = 0; foreach my $i (@$xv) { #$i = $i * $y + $car; $car = $i / $BASE; $i -= $car * $BASE; $i = $i * $y + $car; $i -= ($car = $i / $BASE) * $BASE; } push @$xv, $car if $car != 0; return $xv; } # shortcut for result $x == 0 => result = 0 return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) ); # since multiplying $x with $x fails, make copy in this case $yv = $c->_copy($xv) if $xv == $yv; # same references? my @prod = (); my ($prod, $car, $cty, $xi, $yi); for $xi (@$xv) { $car = 0; $cty = 0; # looping through this if $xi == 0 is silly - so optimize it away! $xi = (shift @prod || 0), next if $xi == 0; for $yi (@$yv) { $prod = $xi * $yi + ($prod[$cty] || 0) + $car; $prod[$cty++] = $prod - ($car = $prod / $BASE) * $BASE; } $prod[$cty] += $car if $car; # need really to check for 0? $xi = shift @prod || 0; # || 0 makes v5.005_3 happy } push @$xv, @prod; $xv; } # The following _div function is an exact copy of _div_use_div_64 in # Math::BigInt::Calc. sub _div { # ref to array, ref to array, modify first array and return remainder if # in list context # This version works on 64 bit integers my ($c, $x, $yorg) = @_; use integer; # the general div algorithm here is about O(N*N) and thus quite slow, so # we first check for some special cases and use shortcuts to handle them. # This works, because we store the numbers in a chunked format where each # element contains 5..7 digits (depending on system). # if both numbers have only one element: if (@$x == 1 && @$yorg == 1) { # shortcut, $yorg and $x are two small numbers if (wantarray) { my $rem = [ $x->[0] % $yorg->[0] ]; bless $rem, $c; $x->[0] = int($x->[0] / $yorg->[0]); return ($x, $rem); } else { $x->[0] = int($x->[0] / $yorg->[0]); return $x; } } # if x has more than one, but y has only one element: if (@$yorg == 1) { my $rem; $rem = $c->_mod($c->_copy($x), $yorg) if wantarray; # shortcut, $y is < $BASE my $j = @$x; my $r = 0; my $y = $yorg->[0]; my $b; while ($j-- > 0) { $b = $r * $BASE + $x->[$j]; $x->[$j] = int($b/$y); $r = $b % $y; } pop @$x if @$x > 1 && $x->[-1] == 0; # splice up a leading zero return ($x, $rem) if wantarray; return $x; } # now x and y have more than one element # check whether y has more elements than x, if yet, the result will be 0 if (@$yorg > @$x) { my $rem; $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; # only x, which is [0] now } # check whether the numbers have the same number of elements, in that case # the result will fit into one element and can be computed efficiently if (@$yorg == @$x) { my $rem; # if $yorg has more digits than $x (it's leading element is longer than # the one from $x), the result will also be 0: if (length(int($yorg->[-1])) > length(int($x->[-1]))) { $rem = $c->_copy($x) if wantarray; # make copy @$x = 0; # set to 0 return ($x, $rem) if wantarray; # including remainder? return $x; } # now calculate $x / $yorg if (length(int($yorg->[-1])) == length(int($x->[-1]))) { # same length, so make full compare my $a = 0; my $j = @$x - 1; # manual way (abort if unequal, good for early ne) while ($j >= 0) { last if ($a = $x->[$j] - $yorg->[$j]); $j--; } # $a contains the result of the compare between X and Y # a < 0: x < y, a == 0: x == y, a > 0: x > y if ($a <= 0) { $rem = $c->_zero(); # a = 0 => x == y => rem 0 $rem = $c->_copy($x) if $a != 0; # a < 0 => x < y => rem = x @$x = 0; # if $a < 0 $x->[0] = 1 if $a == 0; # $x == $y return ($x, $rem) if wantarray; # including remainder? return $x; } # $x >= $y, so proceed normally } } # all other cases: my $y = $c->_copy($yorg); # always make copy to preserve my ($car, $bar, $prd, $dd, $xi, $yi, @q, $v2, $v1, @d, $tmp, $q, $u2, $u1, $u0); $car = $bar = $prd = 0; if (($dd = int($BASE / ($y->[-1] + 1))) != 1) { for $xi (@$x) { $xi = $xi * $dd + $car; $xi -= ($car = int($xi / $BASE)) * $BASE; } push(@$x, $car); $car = 0; for $yi (@$y) { $yi = $yi * $dd + $car; $yi -= ($car = int($yi / $BASE)) * $BASE; } } else { push(@$x, 0); } # @q will accumulate the final result, $q contains the current computed # part of the final result @q = (); ($v2, $v1) = @$y[-2, -1]; $v2 = 0 unless $v2; while ($#$x > $#$y) { ($u2, $u1, $u0) = @$x[-3..-1]; $u2 = 0 unless $u2; #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n" # if $v1 == 0; $q = (($u0 == $v1) ? $MAX_VAL : int(($u0 * $BASE + $u1) / $v1)); --$q while ($v2 * $q > ($u0 * $BASE +$ u1- $q*$v1) * $BASE + $u2); if ($q) { ($car, $bar) = (0, 0); for ($yi = 0, $xi = $#$x - $#$y - 1; $yi <= $#$y; ++$yi, ++$xi) { $prd = $q * $y->[$yi] + $car; $prd -= ($car = int($prd / $BASE)) * $BASE; $x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0)); } if ($x->[-1] < $car + $bar) { $car = 0; --$q; for ($yi = 0, $xi = $#$x - $#$y - 1; $yi <= $#$y; ++$yi, ++$xi) { $x->[$xi] -= $BASE if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE)); } } } pop(@$x); unshift(@q, $q); } if (wantarray) { my $d = bless [], $c; if ($dd != 1) { $car = 0; for $xi (reverse @$x) { $prd = $car * $BASE + $xi; $car = $prd - ($tmp = int($prd / $dd)) * $dd; unshift(@$d, $tmp); } } else { @$d = @$x; } @$x = @q; __strip_zeros($x); __strip_zeros($d); return ($x, $d); } @$x = @q; __strip_zeros($x); $x; } # The following _mod function is an exact copy of _mod in Math::BigInt::Calc. sub _mod { # if possible, use mod shortcut my ($c, $x, $yo) = @_; # slow way since $y too big if (@$yo > 1) { my ($xo, $rem) = $c->_div($x, $yo); @$x = @$rem; return $x; } my $y = $yo->[0]; # if both are single element arrays if (@$x == 1) { $x->[0] %= $y; return $x; } # if @$x has more than one element, but @$y is a single element my $b = $BASE % $y; if ($b == 0) { # when BASE % Y == 0 then (B * BASE) % Y == 0 # (B * BASE) % $y + A % Y => A % Y # so need to consider only last element: O(1) $x->[0] %= $y; } elsif ($b == 1) { # else need to go through all elements in @$x: O(N), but loop is a bit # simplified my $r = 0; foreach (@$x) { $r = ($r + $_) % $y; # not much faster, but heh... #$r += $_ % $y; $r %= $y; } $r = 0 if $r == $y; $x->[0] = $r; } else { # else need to go through all elements in @$x: O(N) my $r = 0; my $bm = 1; foreach (@$x) { $r = ($_ * $bm + $r) % $y; $bm = ($bm * $b) % $y; #$r += ($_ % $y) * $bm; #$bm *= $b; #$bm %= $y; #$r %= $y; } $r = 0 if $r == $y; $x->[0] = $r; } @$x = $x->[0]; # keep one element of @$x return $x; } sub __strip_zeros { # Internal normalization function that strips leading zeros from the array. # Args: ref to array my $x = shift; push @$x, 0 if @$x == 0; # div might return empty results, so fix it return $x if @$x == 1; # early out #print "strip: cnt $cnt i $i\n"; # '0', '3', '4', '0', '0', # 0 1 2 3 4 # cnt = 5, i = 4 # i = 4 # i = 3 # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos) # >= 1: skip first part (this can be zero) my $i = $#$x; while ($i > 0) { last if $x->[$i] != 0; $i--; } $i++; splice(@$x, $i) if $i < @$x; $x; } ############################################################################### # check routine to test internal state for corruptions sub _check { # used by the test suite my ($class, $x) = @_; return "Undefined" unless defined $x; return "$x is not a reference" unless ref($x); return "Not an '$class'" unless ref($x) eq $class; for (my $i = 0 ; $i <= $#$x ; ++ $i) { my $e = $x -> [$i]; return "Element at index $i is undefined" unless defined $e; return "Element at index $i is a '" . ref($e) . "', which is not a scalar" unless ref($e) eq ""; return "Element at index $i is '$e', which does not look like an" . " normal integer" #unless $e =~ /^([1-9]\d*|0)\z/; unless $e =~ /^\d+\z/; return "Element at index $i is '$e', which is negative" if $e < 0; return "Element at index $i is '$e', which is not smaller than" . " the base '$BASE'" if $e >= $BASE; return "Element at index $i (last element) is zero" if $#$x > 0 && $i == $#$x && $e == 0; } return 0; } ############################################################################## ############################################################################## 1; __END__ =pod =head1 NAME Math::BigInt::Calc - Pure Perl module to support Math::BigInt =head1 SYNOPSIS This library provides support for big integer calculations. It is not intended to be used by other modules. Other modules which support the same API (see below) can also be used to support Math::BigInt, like Math::BigInt::GMP and Math::BigInt::Pari. =head1 DESCRIPTION In this library, the numbers are represented in base B = 10**N, where N is the largest possible value that does not cause overflow in the intermediate computations. The base B elements are stored in an array, with the least significant element stored in array element zero. There are no leading zero elements, except a single zero element when the number is zero. For instance, if B = 10000, the number 1234567890 is represented internally as [3456, 7890, 12]. =head1 THE Math::BigInt API In order to allow for multiple big integer libraries, Math::BigInt was rewritten to use a plug-in library for core math routines. Any module which conforms to the API can be used by Math::BigInt by using this in your program: use Math::BigInt lib => 'libname'; 'libname' is either the long name, like 'Math::BigInt::Pari', or only the short version, like 'Pari'. =head2 General Notes A library only needs to deal with unsigned big integers. Testing of input parameter validity is done by the caller, so there is no need to worry about underflow (e.g., in C<_sub()> and C<_dec()>) nor about division by zero (e.g., in C<_div()>) or similar cases. For some methods, the first parameter can be modified. That includes the possibility that you return a reference to a completely different object instead. Although keeping the reference and just changing its contents is preferred over creating and returning a different reference. Return values are always objects, strings, Perl scalars, or true/false for comparison routines. =head2 API version 1 The following methods must be defined in order to support the use by Math::BigInt v1.70 or later. =head3 API version =over 4 =item I Return API version as a Perl scalar, 1 for Math::BigInt v1.70, 2 for Math::BigInt v1.83. =back =head3 Constructors =over 4 =item I<_new(STR)> Convert a string representing an unsigned decimal number to an object representing the same number. The input is normalize, i.e., it matches C<^(0|[1-9]\d*)$>. =item I<_zero()> Return an object representing the number zero. =item I<_one()> Return an object representing the number one. =item I<_two()> Return an object representing the number two. =item I<_ten()> Return an object representing the number ten. =item I<_from_bin(STR)> Return an object given a string representing a binary number. The input has a '0b' prefix and matches the regular expression C<^0[bB](0|1[01]*)$>. =item I<_from_oct(STR)> Return an object given a string representing an octal number. The input has a '0' prefix and matches the regular expression C<^0[1-7]*$>. =item I<_from_hex(STR)> Return an object given a string representing a hexadecimal number. The input has a '0x' prefix and matches the regular expression C<^0x(0|[1-9a-fA-F][\da-fA-F]*)$>. =back =head3 Mathematical functions Each of these methods may modify the first input argument, except I<_bgcd()>, which shall not modify any input argument, and I<_sub()> which may modify the second input argument. =over 4 =item I<_add(OBJ1, OBJ2)> Returns the result of adding OBJ2 to OBJ1. =item I<_mul(OBJ1, OBJ2)> Returns the result of multiplying OBJ2 and OBJ1. =item I<_div(OBJ1, OBJ2)> Returns the result of dividing OBJ1 by OBJ2 and truncating the result to an integer. =item I<_sub(OBJ1, OBJ2, FLAG)> =item I<_sub(OBJ1, OBJ2)> Returns the result of subtracting OBJ2 by OBJ1. If C is false or omitted, OBJ1 might be modified. If C is true, OBJ2 might be modified. =item I<_dec(OBJ)> Decrement OBJ by one. =item I<_inc(OBJ)> Increment OBJ by one. =item I<_mod(OBJ1, OBJ2)> Return OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1 by OBJ2. =item I<_sqrt(OBJ)> Return the square root of the object, truncated to integer. =item I<_root(OBJ, N)> Return Nth root of the object, truncated to int. N is E= 3. =item I<_fac(OBJ)> Return factorial of object (1*2*3*4*...). =item I<_pow(OBJ1, OBJ2)> Return OBJ1 to the power of OBJ2. By convention, 0**0 = 1. =item I<_modinv(OBJ1, OBJ2)> Return modular multiplicative inverse, i.e., return OBJ3 so that (OBJ3 * OBJ1) % OBJ2 = 1 % OBJ2 The result is returned as two arguments. If the modular multiplicative inverse does not exist, both arguments are undefined. Otherwise, the arguments are a number (object) and its sign ("+" or "-"). The output value, with its sign, must either be a positive value in the range 1,2,...,OBJ2-1 or the same value subtracted OBJ2. For instance, if the input arguments are objects representing the numbers 7 and 5, the method must either return an object representing the number 3 and a "+" sign, since (3*7) % 5 = 1 % 5, or an object representing the number 2 and "-" sign, since (-2*7) % 5 = 1 % 5. =item I<_modpow(OBJ1, OBJ2, OBJ3)> Return modular exponentiation, (OBJ1 ** OBJ2) % OBJ3. =item I<_rsft(OBJ, N, B)> Shift object N digits right in base B and return the resulting object. This is equivalent to performing integer division by B**N and discarding the remainder, except that it might be much faster, depending on how the number is represented internally. For instance, if the object $obj represents the hexadecimal number 0xabcde, then C<$obj->_rsft(2, 16)> returns an object representing the number 0xabc. The "remainer", 0xde, is discarded and not returned. =item I<_lsft(OBJ, N, B)> Shift the object N digits left in base B. This is equivalent to multiplying by B**N, except that it might be much faster, depending on how the number is represented internally. =item I<_log_int(OBJ, B)> Return integer log of OBJ to base BASE. This method has two output arguments, the OBJECT and a STATUS. The STATUS is Perl scalar; it is 1 if OBJ is the exact result, 0 if the result was truncted to give OBJ, and undef if it is unknown whether OBJ is the exact result. =item I<_gcd(OBJ1, OBJ2)> Return the greatest common divisor of OBJ1 and OBJ2. =back =head3 Bitwise operators Each of these methods may modify the first input argument. =over 4 =item I<_and(OBJ1, OBJ2)> Return bitwise and. If necessary, the smallest number is padded with leading zeros. =item I<_or(OBJ1, OBJ2)> Return bitwise or. If necessary, the smallest number is padded with leading zeros. =item I<_xor(OBJ1, OBJ2)> Return bitwise exclusive or. If necessary, the smallest number is padded with leading zeros. =back =head3 Boolean operators =over 4 =item I<_is_zero(OBJ)> Returns a true value if OBJ is zero, and false value otherwise. =item I<_is_one(OBJ)> Returns a true value if OBJ is one, and false value otherwise. =item I<_is_two(OBJ)> Returns a true value if OBJ is two, and false value otherwise. =item I<_is_ten(OBJ)> Returns a true value if OBJ is ten, and false value otherwise. =item I<_is_even(OBJ)> Return a true value if OBJ is an even integer, and a false value otherwise. =item I<_is_odd(OBJ)> Return a true value if OBJ is an even integer, and a false value otherwise. =item I<_acmp(OBJ1, OBJ2)> Compare OBJ1 and OBJ2 and return -1, 0, or 1, if OBJ1 is less than, equal to, or larger than OBJ2, respectively. =back =head3 String conversion =over 4 =item I<_str(OBJ)> Return a string representing the object. The returned string should have no leading zeros, i.e., it should match C<^(0|[1-9]\d*)$>. =item I<_as_bin(OBJ)> Return the binary string representation of the number. The string must have a '0b' prefix. =item I<_as_oct(OBJ)> Return the octal string representation of the number. The string must have a '0x' prefix. Note: This method was required from Math::BigInt version 1.78, but the required API version number was not incremented, so there are older libraries that support API version 1, but do not support C<_as_oct()>. =item I<_as_hex(OBJ)> Return the hexadecimal string representation of the number. The string must have a '0x' prefix. =back =head3 Numeric conversion =over 4 =item I<_num(OBJ)> Given an object, return a Perl scalar number (int/float) representing this number. =back =head3 Miscellaneous =over 4 =item I<_copy(OBJ)> Return a true copy of the object. =item I<_len(OBJ)> Returns the number of the decimal digits in the number. The output is a Perl scalar. =item I<_zeros(OBJ)> Return the number of trailing decimal zeros. The output is a Perl scalar. =item I<_digit(OBJ, N)> Return the Nth digit as a Perl scalar. N is a Perl scalar, where zero refers to the rightmost (least significant) digit, and negative values count from the left (most significant digit). If $obj represents the number 123, then I<$obj->_digit(0)> is 3 and I<_digit(123, -1)> is 1. =item I<_check(OBJ)> Return a true value if the object is OK, and a false value otherwise. This is a check routine to test the internal state of the object for corruption. =back =head2 API version 2 The following methods are required for an API version of 2 or greater. =head3 Constructors =over 4 =item I<_1ex(N)> Return an object representing the number 10**N where N E= 0 is a Perl scalar. =back =head3 Mathematical functions =over 4 =item I<_nok(OBJ1, OBJ2)> Return the binomial coefficient OBJ1 over OBJ1. =back =head3 Miscellaneous =over 4 =item I<_alen(OBJ)> Return the approximate number of decimal digits of the object. The output is one Perl scalar. =back =head2 API optional methods The following methods are optional, and can be defined if the underlying lib has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence slow) fallback routines to emulate these: =head3 Signed bitwise operators. Each of these methods may modify the first input argument. =over 4 =item I<_signed_or(OBJ1, OBJ2, SIGN1, SIGN2)> Return the signed bitwise or. =item I<_signed_and(OBJ1, OBJ2, SIGN1, SIGN2)> Return the signed bitwise and. =item I<_signed_xor(OBJ1, OBJ2, SIGN1, SIGN2)> Return the signed bitwise exclusive or. =back =head1 WRAP YOUR OWN If you want to port your own favourite c-lib for big numbers to the Math::BigInt interface, you can take any of the already existing modules as a rough guideline. You should really wrap up the latest Math::BigInt and Math::BigFloat testsuites with your module, and replace in them any of the following: use Math::BigInt; by this: use Math::BigInt lib => 'yourlib'; This way you ensure that your library really works 100% within Math::BigInt. =head1 BUGS Please report any bugs or feature requests to C, or through the web interface at L (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes. =head1 SUPPORT You can find documentation for this module with the perldoc command. perldoc Math::BigInt::Calc You can also look for information at: =over 4 =item * RT: CPAN's request tracker L =item * AnnoCPAN: Annotated CPAN documentation L =item * CPAN Ratings L =item * Search CPAN L =item * CPAN Testers Matrix L =item * The Bignum mailing list =over 4 =item * Post to mailing list C =item * View mailing list L =item * Subscribe/Unsubscribe L =back =back =head1 LICENSE This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. =head1 AUTHORS =over 4 =item * Original math code by Mark Biggar, rewritten by Tels L in late 2000. =item * Separated from BigInt and shaped API with the help of John Peacock. =item * Fixed, speed-up, streamlined and enhanced by Tels 2001 - 2007. =item * API documentation corrected and extended by Peter John Acklam, Epjacklam@online.noE =back =head1 SEE ALSO L, L, L, L and L. =cut Math-BigInt-1.999808/t/Math/BigInt/Lib/TestUtil.pm0000644403072340010010000000133413012312745021466 0ustar ospjadomain users#!perl package Math::BigInt::Lib::TestUtil; use strict; use warnings; use Exporter; our @ISA = qw< Exporter >; our @EXPORT_OK = qw< randstr >; # randstr NUM, BASE # # Generate a string representing a NUM digit number in base BASE. sub randstr { die "randstr: wrong number of input arguments\n" unless @_ == 2; my $n = shift; my $b = shift; die "randstr: first input argument must be >= 0" unless $n >= 0; die "randstr: second input argument must be in the range 2 .. 36\n" unless 2 <= $b && $b <= 36; return '' if $n == 0; my @dig = (0 .. 9, 'a' .. 'z'); my $str = $dig[ 1 + int rand ($b - 1) ]; $str .= $dig[ int rand $b ] for 2 .. $n; return $str; } 1; Math-BigInt-1.999808/t/Math/BigInt/Scalar.pm0000644403072340010010000001145212740677025020426 0ustar ospjadomain users############################################################################### # core math lib for BigInt, representing big numbers by normal int/float's # for testing only, will fail any bignum test if range is exceeded package Math::BigInt::Scalar; use 5.006; use strict; use warnings; require Exporter; our @ISA = qw(Exporter); our $VERSION = '0.13'; sub api_version() { 1; } ############################################################################## # global constants, flags and accessory # constants for easier life my $nan = 'NaN'; ############################################################################## # create objects from various representations sub _new { # create scalar ref from string my $d = $_[1]; my $x = $d; # make copy \$x; } sub _from_hex { # not used } sub _from_oct { # not used } sub _from_bin { # not used } sub _zero { my $x = 0; \$x; } sub _one { my $x = 1; \$x; } sub _two { my $x = 2; \$x; } sub _ten { my $x = 10; \$x; } sub _copy { my $x = $_[1]; my $z = $$x; \$z; } # catch and throw away sub import { } ############################################################################## # convert back to string and number sub _str { # make string "${$_[1]}"; } sub _num { # make a number 0+${$_[1]}; } sub _zeros { my $x = $_[1]; $x =~ /\d(0*)$/; length($1 || ''); } sub _rsft { # not used } sub _lsft { # not used } sub _mod { # not used } sub _gcd { # not used } sub _sqrt { # not used } sub _root { # not used } sub _fac { # not used } sub _modinv { # not used } sub _modpow { # not used } sub _log_int { # not used } sub _as_hex { sprintf("0x%x", ${$_[1]}); } sub _as_bin { sprintf("0b%b", ${$_[1]}); } sub _as_oct { sprintf("0%o", ${$_[1]}); } ############################################################################## # actual math code sub _add { my ($c, $x, $y) = @_; $$x += $$y; return $x; } sub _sub { my ($c, $x, $y) = @_; $$x -= $$y; return $x; } sub _mul { my ($c, $x, $y) = @_; $$x *= $$y; return $x; } sub _div { my ($c, $x, $y) = @_; my $u = int($$x / $$y); my $r = $$x % $$y; $$x = $u; return ($x, \$r) if wantarray; return $x; } sub _pow { my ($c, $x, $y) = @_; my $u = $$x ** $$y; $$x = $u; return $x; } sub _and { my ($c, $x, $y) = @_; my $u = int($$x) & int($$y); $$x = $u; return $x; } sub _xor { my ($c, $x, $y) = @_; my $u = int($$x) ^ int($$y); $$x = $u; return $x; } sub _or { my ($c, $x, $y) = @_; my $u = int($$x) | int($$y); $$x = $u; return $x; } sub _inc { my ($c, $x) = @_; my $u = int($$x)+1; $$x = $u; return $x; } sub _dec { my ($c, $x) = @_; my $u = int($$x)-1; $$x = $u; return $x; } ############################################################################## # testing sub _acmp { my ($c, $x, $y) = @_; return ($$x <=> $$y); } sub _len { return length("${$_[1]}"); } sub _digit { # return the nth digit, negative values count backward # 0 is the rightmost digit my ($c, $x, $n) = @_; $n ++; # 0 => 1, 1 => 2 return substr($$x, -$n, 1); # 1 => -1, -2 => 2 etc } ############################################################################## # _is_* routines sub _is_zero { # return true if arg is zero my ($c, $x) = @_; ($$x == 0) <=> 0; } sub _is_even { # return true if arg is even my ($c, $x) = @_; (!($$x & 1)) <=> 0; } sub _is_odd { # return true if arg is odd my ($c, $x) = @_; ($$x & 1) <=> 0; } sub _is_one { # return true if arg is one my ($c, $x) = @_; ($$x == 1) <=> 0; } sub _is_two { # return true if arg is one my ($c, $x) = @_; ($$x == 2) <=> 0; } sub _is_ten { # return true if arg is one my ($c, $x) = @_; ($$x == 10) <=> 0; } ############################################################################### # check routine to test internal state of corruptions sub _check { # no checks yet, pull it out from the test suite my ($c, $x) = @_; return "$x is not a reference" if !ref($x); return 0; } 1; __END__ =head1 NAME Math::BigInt::Scalar - Pure Perl module to test Math::BigInt with scalars =head1 SYNOPSIS Provides support for big integer calculations via means of 'small' int/floats. Only for testing purposes, since it will fail at large values. But it is simple enough not to introduce bugs on it's own and to serve as a testbed. =head1 DESCRIPTION Please see Math::BigInt::Calc. =head1 LICENSE This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. =head1 AUTHOR Tels http://bloodgate.com in 2001 - 2007. =head1 SEE ALSO L, L. =cut Math-BigInt-1.999808/t/Math/BigInt/Subclass.pm0000644403072340010010000000343112740677025020776 0ustar ospjadomain users#!perl package Math::BigInt::Subclass; require 5.005_02; use strict; use warnings; use Exporter; use Math::BigInt 1.64; # $lib is for the "lib => " test our $lib; our ($accuracy, $precision, $round_mode, $div_scale); our @ISA = qw(Exporter Math::BigInt); our @EXPORT_OK = qw(bgcd objectify); our $VERSION = "0.05"; use overload; # inherit overload from BigInt # Globals $accuracy = $precision = undef; $round_mode = 'even'; $div_scale = 40; $lib = ''; sub new { my $proto = shift; my $class = ref($proto) || $proto; my $value = shift; my $a = $accuracy; $a = $_[0] if defined $_[0]; my $p = $precision; $p = $_[1] if defined $_[1]; my $self = Math::BigInt->new($value, $a, $p, $round_mode); bless $self, $class; $self->{'_custom'} = 1; # make sure this never goes away return $self; } sub bgcd { Math::BigInt::bgcd(@_); } sub blcm { Math::BigInt::blcm(@_); } sub as_int { Math::BigInt->new($_[0]); } BEGIN { *objectify = \&Math::BigInt::objectify; # these are called by AUTOLOAD from BigFloat, so we need at least these. # We cheat, of course.. *bneg = \&Math::BigInt::bneg; *babs = \&Math::BigInt::babs; *bnan = \&Math::BigInt::bnan; *binf = \&Math::BigInt::binf; *bzero = \&Math::BigInt::bzero; *bone = \&Math::BigInt::bone; } sub import { my $self = shift; my @a; my $t = 0; foreach (@_) { # remove the "lib => foo" parameters and store it if ($t == 1) { $lib = $_; $t = 0; next; } if ($_ eq 'lib') { $t = 1; next; } push @a, $_; } $self->SUPER::import(@a); # need it for subclasses $self->export_to_level(1, $self, @a); # need this ? } 1; Math-BigInt-1.999808/t/mbf_ali.t0000644403072340010010000000027112740677025016371 0ustar ospjadomain users#!perl # test that the new alias names work use strict; use warnings; use Test::More tests => 6; use Math::BigFloat; our $CLASS; $CLASS = 'Math::BigFloat'; require 't/alias.inc'; Math-BigInt-1.999808/t/mbimbf.inc0000644403072340010010000013015313014574717016544 0ustar ospjadomain users# test rounding, accuracy, precision and fallback, round_mode and mixing # of classes # Make sure you always quote any bare floating-point values, lest 123.46 will # be stringified to 123.4599999999 due to limited float prevision. use strict; use warnings; my ($x, $y, $z, $u, $rc); our ($mbi, $mbf); ############################################################################### # test defaults and set/get { no strict 'refs'; is(${"$mbi\::accuracy"}, undef, qq|\${"$mbi\::accuracy"}|); is(${"$mbi\::precision"}, undef, qq|\${"$mbi\::precision"}|); is($mbi->accuracy(), undef, qq|$mbi->accuracy()|); is($mbi->precision(), undef, qq|$mbi->precision()|); is(${"$mbi\::div_scale"}, 40, qq|\${"$mbi\::div_scale"}|); is(${"$mbi\::round_mode"}, 'even', qq|\${"$mbi\::round_mode"}|); is($mbi->round_mode(), 'even', qq|$mbi->round_mode()|); is(${"$mbf\::accuracy"}, undef, qq|\${"$mbf\::accuracy"}|); is(${"$mbf\::precision"}, undef, qq|\${"$mbf\::precision"}|); is($mbf->precision(), undef, qq|$mbf->precision()|); is($mbf->precision(), undef, qq|$mbf->precision()|); is(${"$mbf\::div_scale"}, 40, qq|\${"$mbf\::div_scale"}|); is(${"$mbf\::round_mode"}, 'even', qq|\${"$mbf\::round_mode"}|); is($mbf->round_mode(), 'even', qq|$mbf->round_mode()|); } # accessors foreach my $class ($mbi, $mbf) { is($class->accuracy(), undef, qq|$class->accuracy()|); is($class->precision(), undef, qq|$class->precision()|); is($class->round_mode(), "even", qq|$class->round_mode()|); is($class->div_scale(), 40, qq|$class->div_scale()|); is($class->div_scale(20), 20, qq|$class->div_scale(20)|); $class->div_scale(40); is($class->div_scale(), 40, qq|$class->div_scale()|); is($class->round_mode("odd"), "odd", qq|$class->round_mode("odd")|); $class->round_mode("even"); is($class->round_mode(), "even", qq|$class->round_mode()|); is($class->accuracy(2), 2, qq|$class->accuracy(2)|); $class->accuracy(3); is($class->accuracy(), 3, qq|$class->accuracy()|); is($class->accuracy(undef), undef, qq|$class->accuracy(undef)|); is($class->precision(2), 2, qq|$class->precision(2)|); is($class->precision(-2), -2, qq|$class->precision(-2)|); $class->precision(3); is($class->precision(), 3, qq|$class->precision()|); is($class->precision(undef), undef, qq|$class->precision(undef)|); } { no strict 'refs'; # accuracy foreach (qw/5 42 -1 0/) { is(${"$mbf\::accuracy"} = $_, $_, qq|\${"$mbf\::accuracy"} = $_|); is(${"$mbi\::accuracy"} = $_, $_, qq|\${"$mbi\::accuracy"} = $_|); } is(${"$mbf\::accuracy"} = undef, undef, qq|\${"$mbf\::accuracy"} = undef|); is(${"$mbi\::accuracy"} = undef, undef, qq|\${"$mbi\::accuracy"} = undef|); # precision foreach (qw/5 42 -1 0/) { is(${"$mbf\::precision"} = $_, $_, qq|\${"$mbf\::precision"} = $_|); is(${"$mbi\::precision"} = $_, $_, qq|\${"$mbi\::precision"} = $_|); } is(${"$mbf\::precision"} = undef, undef, qq|\${"$mbf\::precision"} = undef|); is(${"$mbi\::precision"} = undef, undef, qq|\${"$mbi\::precision"} = undef|); # fallback foreach (qw/5 42 1/) { is(${"$mbf\::div_scale"} = $_, $_, qq|\${"$mbf\::div_scale"} = $_|); is(${"$mbi\::div_scale"} = $_, $_, qq|\${"$mbi\::div_scale"} = $_|); } # illegal values are possible for fallback due to no accessor # round_mode foreach (qw/odd even zero trunc +inf -inf/) { is(${"$mbf\::round_mode"} = $_, $_, qq|\${"$mbf\::round_mode"} = "$_"|); is(${"$mbi\::round_mode"} = $_, $_, qq|\${"$mbi\::round_mode"} = "$_"|); } ${"$mbf\::round_mode"} = 'zero'; is(${"$mbf\::round_mode"}, 'zero', qq|\${"$mbf\::round_mode"}|); is(${"$mbi\::round_mode"}, '-inf', qq|\${"$mbi\::round_mode"}|); # reset for further tests ${"$mbi\::accuracy"} = undef; ${"$mbi\::precision"} = undef; ${"$mbf\::div_scale"} = 40; } # local copies $x = $mbf->new('123.456'); is($x->accuracy(), undef, q|$x->accuracy()|); is($x->accuracy(5), 5, q|$x->accuracy(5)|); is($x->accuracy(undef), undef, q|$x->accuracy(undef)|); is($x->precision(), undef, q|$x->precision()|); is($x->precision(5), 5, q|$x->precision(5)|); is($x->precision(undef), undef, q|$x->precision(undef)|); { no strict 'refs'; # see if MBF changes MBIs values is(${"$mbi\::accuracy"} = 42, 42, qq|\${"$mbi\::accuracy"} = 42|); is(${"$mbf\::accuracy"} = 64, 64, qq|\${"$mbf\::accuracy"} = 64|); is(${"$mbi\::accuracy"}, 42, qq|\${"$mbi\::accuracy"} = 42|); is(${"$mbf\::accuracy"}, 64, qq|\${"$mbf\::accuracy"} = 64|); } ############################################################################### # see if creating a number under set A or P will round it { no strict 'refs'; ${"$mbi\::accuracy"} = 4; ${"$mbi\::precision"} = undef; is($mbi->new(123456), 123500, qq|$mbi->new(123456) = 123500|); # with A ${"$mbi\::accuracy"} = undef; ${"$mbi\::precision"} = 3; is($mbi->new(123456), 123000, qq|$mbi->new(123456) = 123000|); # with P ${"$mbf\::accuracy"} = 4; ${"$mbf\::precision"} = undef; ${"$mbi\::precision"} = undef; is($mbf->new("123.456"), "123.5", qq|$mbf->new("123.456") = 123.5|); ${"$mbf\::accuracy"} = undef; ${"$mbf\::precision"} = -1; is($mbf->new("123.456"), "123.5", qq|$mbf->new("123.456") = 123.5|); ${"$mbf\::precision"} = undef; # reset } ############################################################################### # see if MBI leaves MBF's private parts alone { no strict 'refs'; ${"$mbi\::precision"} = undef; ${"$mbf\::precision"} = undef; ${"$mbi\::accuracy"} = 4; ${"$mbf\::accuracy"} = undef; is($mbf->new("123.456"), "123.456", qq|$mbf->new("123.456") = 123.456|); ${"$mbi\::accuracy"} = undef; # reset } ############################################################################### # see if setting accuracy/precision actually rounds the number $x = $mbf->new("123.456"); $x->accuracy(4); is($x, "123.5", qq|\$x = $mbf->new("123.456"); \$x->accuracy(4)|); $x = $mbf->new("123.456"); $x->precision(-2); is($x, "123.46", qq|\$x = $mbf->new("123.456"); \$x->precision(-2)|); $x = $mbi->new(123456); $x->accuracy(4); is($x, 123500, qq|\$x = $mbi->new(123456); \$x->accuracy(4)|); $x = $mbi->new(123456); $x->precision(2); is($x, 123500, qq|\$x = $mbi->new(123456); \$x->precision(2)|); ############################################################################### # test actual rounding via round() $x = $mbf->new("123.456"); is($x->copy()->round(5), "123.46", qq|\$x = $mbf->new("123.456"); \$x->copy()->round(5)|); is($x->copy()->round(4), "123.5", qq|\$x = $mbf->new("123.456"); \$x->copy()->round(4)|); is($x->copy()->round(5, 2), "NaN", qq|\$x = $mbf->new("123.456"); \$x->copy()->round(5, 2)|); is($x->copy()->round(undef, -2), "123.46", qq|\$x = $mbf->new("123.456"); \$x->copy()->round(undef, -2)|); is($x->copy()->round(undef, 2), 120, qq|\$x = $mbf->new("123.456"); \$x->copy()->round(undef, 2)|); $x = $mbi->new("123"); is($x->round(5, 2), "NaN", qq|\$x = $mbi->new("123"); \$x->round(5, 2)|); $x = $mbf->new("123.45000"); is($x->copy()->round(undef, -1, "odd"), "123.5", qq|\$x = $mbf->new("123.45000"); \$x->copy()->round(undef, -1, "odd")|); # see if rounding is 'sticky' $x = $mbf->new("123.4567"); $y = $x->copy()->bround(); # no-op since nowhere A or P defined is($y, 123.4567, qq|\$x = $mbf->new("123.4567"); \$y = \$x->copy()->bround()|); $y = $x->copy()->round(5); is($y->accuracy(), 5, q|$y = $x->copy()->round(5); $y->accuracy()|); is($y->precision(), undef, # A has precedence, so P still unset q|$y = $x->copy()->round(5); $y->precision()|); $y = $x->copy()->round(undef, 2); is($y->precision(), 2, q|$y = $x->copy()->round(undef, 2); $y->precision()|); is($y->accuracy(), undef, # P has precedence, so A still unset q|$y = $x->copy()->round(undef, 2); $y->accuracy()|); # see if setting A clears P and vice versa $x = $mbf->new("123.4567"); is($x, "123.4567", q|$x = $mbf->new("123.4567")|); is($x->accuracy(4), 4, q|$x->accuracy(4)|); is($x->precision(-2), -2, q|$x->precision(-2)|); # clear A is($x->accuracy(), undef, q|$x->accuracy()|); $x = $mbf->new("123.4567"); is($x, "123.4567", q|$x = $mbf->new("123.4567")|); is($x->precision(-2), -2, q|$x->precision(-2)|); is($x->accuracy(4), 4, q|$x->accuracy(4)|); # clear P is($x->precision(), undef, q|$x->precision()|); # does copy work? $x = $mbf->new(123.456); $x->accuracy(4); $x->precision(2); $z = $x->copy(); is($z->accuracy(), undef, q|$z = $x->copy(); $z->accuracy()|); is($z->precision(), 2, q|$z = $x->copy(); $z->precision()|); # does $x->bdiv($y, d) work when $d > div_scale? $x = $mbf->new("0.008"); $x->accuracy(8); for my $e (4, 8, 16, 32) { is(scalar $x->copy()->bdiv(3, $e), "0.002" . ("6" x ($e - 2)) . "7", qq|\$x->copy()->bdiv(3, $e)|); } # does accuracy()/precision work on zeros? foreach my $class ($mbi, $mbf) { $x = $class->bzero(); $x->accuracy(5); is($x->{_a}, 5, qq|\$x = $class->bzero(); \$x->accuracy(5); \$x->{_a}|); $x = $class->bzero(); $x->precision(5); is($x->{_p}, 5, qq|\$x = $class->bzero(); \$x->precision(5); \$x->{_p}|); $x = $class->new(0); $x->accuracy(5); is($x->{_a}, 5, qq|\$x = $class->new(0); \$x->accuracy(5); \$x->{_a}|); $x = $class->new(0); $x->precision(5); is($x->{_p}, 5, qq|\$x = $class->new(0); \$x->precision(5); \$x->{_p}|); $x = $class->bzero(); $x->round(5); is($x->{_a}, 5, qq|\$x = $class->bzero(); \$x->round(5); \$x->{_a}|); $x = $class->bzero(); $x->round(undef, 5); is($x->{_p}, 5, qq|\$x = $class->bzero(); \$x->round(undef, 5); \$x->{_p}|); $x = $class->new(0); $x->round(5); is($x->{_a}, 5, qq|\$x = $class->new(0); \$x->round(5); \$x->{_a}|); $x = $class->new(0); $x->round(undef, 5); is($x->{_p}, 5, qq|\$x = $class->new(0); \$x->round(undef, 5); \$x->{_p}|); # see if trying to increasing A in bzero() doesn't do something $x = $class->bzero(); $x->{_a} = 3; $x->round(5); is($x->{_a}, 3, qq|\$x = $class->bzero(); \$x->{_a} = 3; \$x->round(5); \$x->{_a}|); } ############################################################################### # test whether an opp calls objectify properly or not (or at least does what # it should do given non-objects, w/ or w/o objectify()) foreach my $class ($mbi, $mbf) { # ${"$class\::precision"} = undef; # reset # ${"$class\::accuracy"} = undef; # reset is($class->new(123)->badd(123), 246, qq|$class->new(123)->badd(123)|); is($class->badd(123, 321), 444, qq|$class->badd(123, 321)|); is($class->badd(123, $class->new(321)), 444, qq|$class->badd(123, $class->new(321))|); is($class->new(123)->bsub(122), 1, qq|$class->new(123)->bsub(122)|); is($class->bsub(321, 123), 198, qq|$class->bsub(321, 123)|); is($class->bsub(321, $class->new(123)), 198, qq|$class->bsub(321, $class->new(123))|); is($class->new(123)->bmul(123), 15129, qq|$class->new(123)->bmul(123)|); is($class->bmul(123, 123), 15129, qq|$class->bmul(123, 123)|); is($class->bmul(123, $class->new(123)), 15129, qq|$class->bmul(123, $class->new(123))|); # is($class->new(15129)->bdiv(123), 123, qq|$class->new(15129)->bdiv(123)|); # is($class->bdiv(15129, 123), 123, qq|$class->bdiv(15129, 123)|); # is($class->bdiv(15129, $class->new(123)), 123, # qq|$class->bdiv(15129, $class->new(123))|); is($class->new(15131)->bmod(123), 2, qq|$class->new(15131)->bmod(123)|); is($class->bmod(15131, 123), 2, qq|$class->bmod(15131, 123)|); is($class->bmod(15131, $class->new(123)), 2, qq|$class->bmod(15131, $class->new(123))|); is($class->new(2)->bpow(16), 65536, qq|$class->new(2)->bpow(16)|); is($class->bpow(2, 16), 65536, qq|$class->bpow(2, 16)|); is($class->bpow(2, $class->new(16)), 65536, qq|$class->bpow(2, $class->new(16))|); is($class->new(2**15)->brsft(1), 2**14, qq|$class->new(2**15)->brsft(1)|); is($class->brsft(2**15, 1), 2**14, qq|$class->brsft(2**15, 1)|); is($class->brsft(2**15, $class->new(1)), 2**14, qq|$class->brsft(2**15, $class->new(1))|); is($class->new(2**13)->blsft(1), 2**14, qq|$class->new(2**13)->blsft(1)|); is($class->blsft(2**13, 1), 2**14, qq|$class->blsft(2**13, 1)|); is($class->blsft(2**13, $class->new(1)), 2**14, qq|$class->blsft(2**13, $class->new(1))|); } ############################################################################### # Test whether operations round properly afterwards. # These tests are not complete, since they do not exercise every "return" # statement in the op's. But heh, it's better than nothing... $x = $mbf->new("123.456"); $y = $mbf->new("654.321"); $x->{_a} = 5; # $x->accuracy(5) would round $x straight away $y->{_a} = 4; # $y->accuracy(4) would round $x straight away $z = $x + $y; is($z, "777.8", q|$z = $x + $y|); $z = $y - $x; is($z, "530.9", q|$z = $y - $x|); $z = $y * $x; is($z, "80780", q|$z = $y * $x|); $z = $x ** 2; is($z, "15241", q|$z = $x ** 2|); $z = $x * $x; is($z, "15241", q|$z = $x * $x|); # not: #$z = -$x; #is($z, '-123.46'); #is($x, '123.456'); $z = $x->copy(); $z->{_a} = 2; $z = $z / 2; is($z, 62, q|$z = $z / 2|); $x = $mbf->new(123456); $x->{_a} = 4; $z = $x->copy; $z++; is($z, 123500, q|$z++|); $x = $mbi->new(123456); $y = $mbi->new(654321); $x->{_a} = 5; # $x->accuracy(5) would round $x straight away $y->{_a} = 4; # $y->accuracy(4) would round $x straight away $z = $x + $y; is($z, 777800, q|$z = $x + $y|); $z = $y - $x; is($z, 530900, q|$z = $y - $x|); $z = $y * $x; is($z, 80780000000, q|$z = $y * $x|); $z = $x ** 2; is($z, 15241000000, q|$z = $x ** 2|); # not yet: $z = -$x; # is($z, -123460, qq|$z|); # is($x, 123456, qq|$x|); $z = $x->copy; $z++; is($z, 123460, q|$z++|); $z = $x->copy(); $z->{_a} = 2; $z = $z / 2; is($z, 62000, q|$z = $z / 2|); $x = $mbi->new(123400); $x->{_a} = 4; is($x->bnot(), -123400, q|$x->bnot()|); # not -1234001 # both babs() and bneg() don't need to round, since the input will already # be rounded (either as $x or via new($string)), and they don't change the # value. The two tests below peek at this by using _a (illegally) directly $x = $mbi->new(-123401); $x->{_a} = 4; is($x->babs(), 123401, q|$x->babs()|); $x = $mbi->new(-123401); $x->{_a} = 4; is($x->bneg(), 123401, q|$x->bneg()|); # test bdiv rounding to A and R (bug in v1.48 and maybe earlier versions) $mbf->round_mode('even'); $x = $mbf->new('740.7')->bdiv('6', 4, undef, 'zero'); is($x, '123.4', q|$x|); $x = $mbi->new('123456'); $y = $mbi->new('123456'); $y->{_a} = 6; is($x->bdiv($y), 1, q|$x->bdiv($y)|); is($x->{_a}, 6, q|$x->{_a}|); # carried over $x = $mbi->new('123456'); $y = $mbi->new('123456'); $x->{_a} = 6; is($x->bdiv($y), 1, q|$x->bdiv($y)|); is($x->{_a}, 6, q|$x->{_a}|); # carried over $x = $mbi->new('123456'); $y = $mbi->new('223456'); $y->{_a} = 6; is($x->bdiv($y), 0, q|$x->bdiv($y)|); is($x->{_a}, 6, q|$x->{_a}|); # carried over $x = $mbi->new('123456'); $y = $mbi->new('223456'); $x->{_a} = 6; is($x->bdiv($y), 0, q|$x->bdiv($y)|); is($x->{_a}, 6, q|$x->{_a}|); # carried over ############################################################################### # test that bop(0) does the same than bop(undef) $x = $mbf->new('1234567890'); is($x->copy()->bsqrt(0), $x->copy()->bsqrt(undef), q|$x->copy()->bsqrt(...)|); is($x->copy->bsqrt(0), '35136.41828644462161665823116758077037159', q|$x->copy->bsqrt(...)|); is($x->{_a}, undef, q|$x->{_a}|); # test that bsqrt() modifies $x and does not just return something else # (especially under Math::BigInt::BareCalc) $z = $x->bsqrt(); is($z, $x, q|$z = $x->bsqrt(); $z|); is($x, '35136.41828644462161665823116758077037159', q|$z = $x->bsqrt(); $x|); $x = $mbf->new('1.234567890123456789'); is($x->copy()->bpow('0.5', 0), $x->copy()->bpow('0.5', undef), q|$x->copy()->bpow(...)|); is($x->copy()->bpow('0.5', 0), $x->copy()->bsqrt(undef), q|$x->copy()->bpow(...) vs. $x->copy()->bsqrt(...)|); is($x->copy()->bpow('2', 0), '1.524157875323883675019051998750190521', q|$x->copy()->bpow('2', 0)|); ############################################################################### # test (also under Bare) that bfac() rounds at last step is($mbi->new(12)->bfac(), '479001600', q|$mbi->new(12)->bfac()|); is($mbi->new(12)->bfac(2), '480000000', q|$mbi->new(12)->bfac(2)|); $x = $mbi->new(12); $x->accuracy(2); is($x->bfac(), '480000000', qq|\$x = $mbi->new(12); \$x->accuracy(2); \$x->bfac()|); $x = $mbi->new(13); $x->accuracy(2); is($x->bfac(), '6200000000', qq|\$x = $mbi->new(13); \$x->accuracy(2); \$x->bfac()|); $x = $mbi->new(13); $x->accuracy(3); is($x->bfac(), '6230000000', qq|\$x = $mbi->new(13); \$x->accuracy(3); \$x->bfac()|); $x = $mbi->new(13); $x->accuracy(4); is($x->bfac(), '6227000000', qq|\$x = $mbi->new(13); \$x->accuracy(4); \$x->bfac()|); # this does 1, 2, 3...9, 10, 11, 12...20 $x = $mbi->new(20); $x->accuracy(1); is($x->bfac(), '2000000000000000000', qq|\$x = $mbi->new(20); \$x->accuracy(1); \$x->bfac()|); ############################################################################### # test bsqrt) rounding to given A/P/R (bug prior to v1.60) $x = $mbi->new('123456')->bsqrt(2, undef); is($x, '350', qq|\$x = $mbi->new("123456")->bsqrt(2, undef)|); # not 351 $x = $mbi->new('3')->bsqrt(2, undef); is($x->accuracy(), 2, q|$x->accuracy()|); $mbi->round_mode('even'); $x = $mbi->new('126025')->bsqrt(2, undef, '+inf'); is($x, '360', q|$x = 360|); # not 355 nor 350 $x = $mbi->new('126025')->bsqrt(undef, 2); is($x, '400', q|$x = 400|); # not 355 ############################################################################### # test mixed arguments $x = $mbf->new(10); $u = $mbf->new(2.5); $y = $mbi->new(2); $z = $x + $y; is($z, 12, q|$z = $x + $y;|); is(ref($z), $mbf, qq|\$z is a "$mbf" object|); $z = $x / $y; is($z, 5, q|$z = $x / $y;|); is(ref($z), $mbf, qq|\$z is a "$mbf" object|); $z = $u * $y; is($z, 5, q|$z = $u * $y;|); is(ref($z), $mbf, qq|\$z is a "$mbf" object|); $y = $mbi->new(12345); $z = $u->copy()->bmul($y, 2, undef, 'odd'); is($z, 31000, q|$z = 31000|); $z = $u->copy()->bmul($y, 3, undef, 'odd'); is($z, 30900, q|$z = 30900|); $z = $u->copy()->bmul($y, undef, 0, 'odd'); is($z, 30863, q|$z = 30863|); $z = $u->copy()->bmul($y, undef, 1, 'odd'); is($z, 30863, q|$z = 30863|); $z = $u->copy()->bmul($y, undef, 2, 'odd'); is($z, 30860, q|$z = 30860|); $z = $u->copy()->bmul($y, undef, 3, 'odd'); is($z, 30900, q|$z = 30900|); $z = $u->copy()->bmul($y, undef, -1, 'odd'); is($z, 30862.5, q|$z = 30862.5|); my $warn = ''; $SIG{__WARN__} = sub { $warn = shift; }; # These should no longer warn, even though '3.17' is a NaN in Math::BigInt # (>= returns now false, bug until v1.80). $warn = ''; eval '$z = 3.17 <= $y'; is($z, '', q|$z = ""|); unlike($warn, qr/^Use of uninitialized value (\$y )?(in numeric le \(<=\) |)at/, q|"$z = $y >= 3.17" gives warning as expected|); $warn = ''; eval '$z = $y >= 3.17'; is($z, '', q|$z = ""|); unlike($warn, qr/^Use of uninitialized value (\$y )?(in numeric ge \(>=\) |)at/, q|"$z = $y >= 3.17" gives warning as expected|); # XXX TODO breakage: # # $z = $y->copy()->bmul($u, 2, 0, 'odd'); # is($z, 31000); # # $z = $y * $u; # is($z, 5); # is(ref($z), $mbi, q|\$z is a $mbi object|); # # $z = $y + $x; # is($z, 12); # is(ref($z), $mbi, q|\$z is a $mbi object|); # # $z = $y / $x; # is($z, 0); # is(ref($z), $mbi, q|\$z is a $mbi object|); ############################################################################### # rounding in bdiv with fallback and already set A or P { no strict 'refs'; ${"$mbf\::accuracy"} = undef; ${"$mbf\::precision"} = undef; ${"$mbf\::div_scale"} = 40; } $x = $mbf->new(10); $x->{_a} = 4; is($x->bdiv(3), '3.333', q|$x->bdiv(3)|); is($x->{_a}, 4, q|$x->{_a}|); # set's it since no fallback $x = $mbf->new(10); $x->{_a} = 4; $y = $mbf->new(3); is($x->bdiv($y), '3.333', q|$x->bdiv($y)|); is($x->{_a}, 4, q|$x->{_a}|); # set's it since no fallback # rounding to P of x $x = $mbf->new(10); $x->{_p} = -2; is($x->bdiv(3), '3.33', q|$x->bdiv(3)|); # round in div with requested P $x = $mbf->new(10); is($x->bdiv(3, undef, -2), '3.33', q|$x->bdiv(3, undef, -2)|); # round in div with requested P greater than fallback { no strict 'refs'; ${"$mbf\::div_scale"} = 5; $x = $mbf->new(10); is($x->bdiv(3, undef, -8), "3.33333333", q|$x->bdiv(3, undef, -8) = "3.33333333"|); ${"$mbf\::div_scale"} = 40; } $x = $mbf->new(10); $y = $mbf->new(3); $y->{_a} = 4; is($x->bdiv($y), '3.333', q|$x->bdiv($y) = '3.333'|); is($x->{_a}, 4, q|$x->{_a} = 4|); is($y->{_a}, 4, q|$y->{_a} = 4|); # set's it since no fallback is($x->{_p}, undef, q|$x->{_p} = undef|); is($y->{_p}, undef, q|$y->{_p} = undef|); # rounding to P of y $x = $mbf->new(10); $y = $mbf->new(3); $y->{_p} = -2; is($x->bdiv($y), '3.33', q|$x->bdiv($y) = '3.33'|); is($x->{_p}, -2, q|$x->{_p} = -2|); is($y->{_p}, -2, q|$y->{_p} = -2|); is($x->{_a}, undef, q|$x->{_a} = undef|); is($y->{_a}, undef, q|$y->{_a} = undef|); ############################################################################### # test whether bround(-n) fails in MBF (undocumented in MBI) eval { $x = $mbf->new(1); $x->bround(-2); }; like($@, qr/^bround\(\) needs positive accuracy/, qq|"\$x->bround(-2)" gives warning as expected|); # test whether rounding to higher accuracy is no-op $x = $mbf->new(1); $x->{_a} = 4; is($x, "1.000", q|$x = "1.000"|); $x->bround(6); # must be no-op is($x->{_a}, 4, q|$x->{_a} = 4|); is($x, "1.000", q|$x = "1.000"|); $x = $mbi->new(1230); $x->{_a} = 3; is($x, "1230", q|$x = "1230"|); $x->bround(6); # must be no-op is($x->{_a}, 3, q|$x->{_a} = 3|); is($x, "1230", q|$x = "1230"|); # bround(n) should set _a $x->bround(2); # smaller works is($x, "1200", q|$x = "1200"|); is($x->{_a}, 2, q|$x->{_a} = 2|); # bround(-n) is undocumented and only used by MBF # bround(-n) should set _a $x = $mbi->new(12345); $x->bround(-1); is($x, "12300", q|$x = "12300"|); is($x->{_a}, 4, q|$x->{_a} = 4|); # bround(-n) should set _a $x = $mbi->new(12345); $x->bround(-2); is($x, "12000", q|$x = "12000"|); is($x->{_a}, 3, q|$x->{_a} = 3|); # bround(-n) should set _a $x = $mbi->new(12345); $x->{_a} = 5; $x->bround(-3); is($x, "10000", q|$x = "10000"|); is($x->{_a}, 2, q|$x->{_a} = 2|); # bround(-n) should set _a $x = $mbi->new(12345); $x->{_a} = 5; $x->bround(-4); is($x, "0", q|$x = "0"|); is($x->{_a}, 1, q|$x->{_a} = 1|); # bround(-n) should be no-op if n too big $x = $mbi->new(12345); $x->bround(-5); is($x, "0", q|$x = "0"|); # scale to "big" => 0 is($x->{_a}, 0, q|$x->{_a} = 0|); # bround(-n) should be no-op if n too big $x = $mbi->new(54321); $x->bround(-5); is($x, "100000", q|$x = "100000"|); # used by MBF to round 0.0054321 at 0.0_6_00000 is($x->{_a}, 0, q|$x->{_a} = 0|); # bround(-n) should be no-op if n too big $x = $mbi->new(54321); $x->{_a} = 5; $x->bround(-6); is($x, "100000", q|$x = "100000"|); # no-op is($x->{_a}, 0, q|$x->{_a} = 0|); # bround(n) should set _a $x = $mbi->new(12345); $x->{_a} = 5; $x->bround(5); # must be no-op is($x, "12345", q|$x = "12345"|); is($x->{_a}, 5, q|$x->{_a} = 5|); # bround(n) should set _a $x = $mbi->new(12345); $x->{_a} = 5; $x->bround(6); # must be no-op is($x, "12345", q|$x = "12345"|); $x = $mbf->new("0.0061"); $x->bfround(-2); is($x, "0.01", q|$x = "0.01"|); $x = $mbf->new("0.004"); $x->bfround(-2); is($x, "0.00", q|$x = "0.00"|); $x = $mbf->new("0.005"); $x->bfround(-2); is($x, "0.00", q|$x = "0.00"|); $x = $mbf->new("12345"); $x->bfround(2); is($x, "12340", q|$x = "12340"|); $x = $mbf->new("12340"); $x->bfround(2); is($x, "12340", q|$x = "12340"|); # MBI::bfround should clear A for negative P $x = $mbi->new("1234"); $x->accuracy(3); $x->bfround(-2); is($x->{_a}, undef, q|$x->{_a} = undef|); # test that bfround() and bround() work with large numbers $x = $mbf->new(1)->bdiv(5678, undef, -63); is($x, "0.000176118351532229658330398027474462839027826699542092286016203", q|$x = "0.000176118351532229658330398027474462839027826699542092286016203"|); $x = $mbf->new(1)->bdiv(5678, undef, -90); is($x, "0.00017611835153222965833039802747446283902782" . "6699542092286016202888340965128566396618527651", q|$x = "0.00017611835153222965833039802747446283902782| . q|6699542092286016202888340965128566396618527651"|); $x = $mbf->new(1)->bdiv(5678, 80); is($x, "0.00017611835153222965833039802747446283902782" . "669954209228601620288834096512856639662", q|$x = "0.00017611835153222965833039802747446283902782| . q|669954209228601620288834096512856639662"|); ############################################################################### # rounding with already set precision/accuracy $x = $mbf->new(1); $x->{_p} = -5; is($x, "1.00000", q|$x = "1.00000"|); # further rounding donw is($x->bfround(-2), "1.00", q|$x->bfround(-2) = "1.00"|); is($x->{_p}, -2, q|$x->{_p} = -2|); $x = $mbf->new(12345); $x->{_a} = 5; is($x->bround(2), "12000", q|$x->bround(2) = "12000"|); is($x->{_a}, 2, q|$x->{_a} = 2|); $x = $mbf->new("1.2345"); $x->{_a} = 5; is($x->bround(2), "1.2", q|$x->bround(2) = "1.2"|); is($x->{_a}, 2, q|$x->{_a} = 2|); # mantissa/exponent format and A/P $x = $mbf->new("12345.678"); $x->accuracy(4); is($x, "12350", q|$x = "12350"|); is($x->{_a}, 4, q|$x->{_a} = 4|); is($x->{_p}, undef, q|$x->{_p} = undef|); #is($x->{_m}->{_a}, undef, q|$x->{_m}->{_a} = undef|); #is($x->{_e}->{_a}, undef, q|$x->{_e}->{_a} = undef|); #is($x->{_m}->{_p}, undef, q|$x->{_m}->{_p} = undef|); #is($x->{_e}->{_p}, undef, q|$x->{_e}->{_p} = undef|); # check for no A/P in case of fallback # result $x = $mbf->new(100) / 3; is($x->{_a}, undef, q|$x->{_a} = undef|); is($x->{_p}, undef, q|$x->{_p} = undef|); # result & remainder $x = $mbf->new(100) / 3; ($x, $y) = $x->bdiv(3); is($x->{_a}, undef, q|$x->{_a} = undef|); is($x->{_p}, undef, q|$x->{_p} = undef|); is($y->{_a}, undef, q|$y->{_a} = undef|); is($y->{_p}, undef, q|$y->{_p} = undef|); ############################################################################### # math with two numbers with different A and P $x = $mbf->new(12345); $x->accuracy(4); # "12340" $y = $mbf->new(12345); $y->accuracy(2); # "12000" is($x+$y, 24000, q|$x+$y = 24000|); # 12340+12000=> 24340 => 24000 $x = $mbf->new(54321); $x->accuracy(4); # "12340" $y = $mbf->new(12345); $y->accuracy(3); # "12000" is($x-$y, 42000, q|$x-$y = 42000|); # 54320+12300=> 42020 => 42000 $x = $mbf->new("1.2345"); $x->precision(-2); # "1.23" $y = $mbf->new("1.2345"); $y->precision(-4); # "1.2345" is($x+$y, "2.46", q|$x+$y = "2.46"|); # 1.2345+1.2300=> 2.4645 => 2.46 ############################################################################### # round should find and use proper class #$x = Foo->new(); #is($x->round($Foo::accuracy), "a" x $Foo::accuracy); #is($x->round(undef, $Foo::precision), "p" x $Foo::precision); #is($x->bfround($Foo::precision), "p" x $Foo::precision); #is($x->bround($Foo::accuracy), "a" x $Foo::accuracy); ############################################################################### # find out whether _find_round_parameters is doing what's it's supposed to do { no strict 'refs'; ${"$mbi\::accuracy"} = undef; ${"$mbi\::precision"} = undef; ${"$mbi\::div_scale"} = 40; ${"$mbi\::round_mode"} = 'odd'; } $x = $mbi->new(123); my @params = $x->_find_round_parameters(); is(scalar(@params), 1, q|scalar(@params) = 1|); # nothing to round @params = $x->_find_round_parameters(1); is(scalar(@params), 4, q|scalar(@params) = 4|); # a=1 is($params[0], $x, q|$params[0] = $x|); # self is($params[1], 1, q|$params[1] = 1|); # a is($params[2], undef, q|$params[2] = undef|); # p is($params[3], "odd", q|$params[3] = "odd"|); # round_mode @params = $x->_find_round_parameters(undef, 2); is(scalar(@params), 4, q|scalar(@params) = 4|); # p=2 is($params[0], $x, q|$params[0] = $x|); # self is($params[1], undef, q|$params[1] = undef|); # a is($params[2], 2, q|$params[2] = 2|); # p is($params[3], "odd", q|$params[3] = "odd"|); # round_mode eval { @params = $x->_find_round_parameters(undef, 2, "foo"); }; like($@, qr/^Unknown round mode 'foo'/, q|round mode "foo" gives a warning as expected|); @params = $x->_find_round_parameters(undef, 2, "+inf"); is(scalar(@params), 4, q|scalar(@params) = 4|); # p=2 is($params[0], $x, q|$params[0] = $x|); # self is($params[1], undef, q|$params[1] = undef|); # a is($params[2], 2, q|$params[2] = 2|); # p is($params[3], "+inf", q|$params[3] = "+inf"|); # round_mode @params = $x->_find_round_parameters(2, -2, "+inf"); is(scalar(@params), 1, q|scalar(@params) = 1|); # error, A and P defined is($params[0], $x, q|$params[0] = $x|); # self { no strict 'refs'; ${"$mbi\::accuracy"} = 1; @params = $x->_find_round_parameters(undef, -2); is(scalar(@params), 1, q|scalar(@params) = 1|); # error, A and P defined is($params[0], $x, q|$params[0] = $x|); # self is($x->is_nan(), 1, q|$x->is_nan() = 1|); # and must be NaN ${"$mbi\::accuracy"} = undef; ${"$mbi\::precision"} = 1; @params = $x->_find_round_parameters(1, undef); is(scalar(@params), 1, q|scalar(@params) = 1|); # error, A and P defined is($params[0], $x, q|$params[0] = $x|); # self is($x->is_nan(), 1, q|$x->is_nan() = 1|); # and must be NaN ${"$mbi\::precision"} = undef; # reset } ############################################################################### # test whether bone/bzero take additional A & P, or reset it etc foreach my $class ($mbi, $mbf) { $x = $class->new(2)->bzero(); is($x->{_a}, undef, qq|\$x = $class->new(2)->bzero(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2)->bzero(); \$x->{_p}|); $x = $class->new(2)->bone(); is($x->{_a}, undef, qq|\$x = $class->new(2)->bone(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2)->bone(); \$x->{_p}|); $x = $class->new(2)->binf(); is($x->{_a}, undef, qq|\$x = $class->new(2)->binf(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2)->binf(); \$x->{_p}|); $x = $class->new(2)->bnan(); is($x->{_a}, undef, qq|\$x = $class->new(2)->bnan(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2)->bnan(); \$x->{_p}|); note "Verify that bnan() does not delete/undefine accuracy and precision."; $x = $class->new(2); $x->{_a} = 1; $x->bnan(); is($x->{_a}, 1, qq|\$x = $class->new(2); \$x->{_a} = 1; \$x->bnan(); \$x->{_a}|); $x = $class->new(2); $x->{_p} = 1; $x->bnan(); is($x->{_p}, 1, qq|\$x = $class->new(2); \$x->{_p} = 1; \$x->bnan(); \$x->{_p}|); note "Verify that binf() does not delete/undefine accuracy and precision."; $x = $class->new(2); $x->{_a} = 1; $x->binf(); is($x->{_a}, 1, qq|\$x = $class->new(2); \$x->{_a} = 1; \$x->binf(); \$x->{_a}|); $x = $class->new(2); $x->{_p} = 1; $x->binf(); is($x->{_p}, 1, qq|\$x = $class->new(2); \$x->{_p} = 1; \$x->binf(); \$x->{_p}|); note "Verify that accuracy can be set as argument to new()."; $x = $class->new(2, 1); is($x->{_a}, 1, qq|\$x = $class->new(2, 1); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2, 1); \$x->{_p}|); note "Verify that precision can be set as argument to new()."; $x = $class->new(2, undef, 1); is($x->{_a}, undef, qq|\$x = $class->new(2, undef, 1); \$x->{_a}|); is($x->{_p}, 1, qq|\$x = $class->new(2, undef, 1); \$x->{_p}|); note "Verify that accuracy set with new() is preserved after calling bzero()."; $x = $class->new(2, 1)->bzero(); is($x->{_a}, 1, qq|\$x = $class->new(2, 1)->bzero(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2, 1)->bzero(); \$x->{_p}|); note "Verify that precision set with new() is preserved after calling bzero()."; $x = $class->new(2, undef, 1)->bzero(); is($x->{_a}, undef, qq|\$x = $class->new(2, undef, 1)->bzero(); \$x->{_a}|); is($x->{_p}, 1, qq|\$x = $class->new(2, undef, 1)->bzero(); \$x->{_p}|); note "Verify that accuracy set with new() is preserved after calling bone()."; $x = $class->new(2, 1)->bone(); is($x->{_a}, 1, qq|\$x = $class->new(2, 1)->bone(); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2, 1)->bone(); \$x->{_p}|); note "Verify that precision set with new() is preserved after calling bone()."; $x = $class->new(2, undef, 1)->bone(); is($x->{_a}, undef, qq|\$x = $class->new(2, undef, 1)->bone(); \$x->{_a}|); is($x->{_p}, 1, qq|\$x = $class->new(2, undef, 1)->bone(); \$x->{_p}|); note "Verify that accuracy can be set with instance method bone('+')."; $x = $class->new(2); $x->bone('+', 2, undef); is($x->{_a}, 2, qq|\$x = $class->new(2); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2); \$x->{_p}|); note "Verify that precision can be set with instance method bone('+')."; $x = $class->new(2); $x->bone('+', undef, 2); is($x->{_a}, undef, qq|\$x = $class->new(2); \$x->bone('+', undef, 2); \$x->{_a}|); is($x->{_p}, 2, qq|\$x = $class->new(2); \$x->bone('+', undef, 2); \$x->{_p}|); note "Verify that accuracy can be set with instance method bone('-')."; $x = $class->new(2); $x->bone('-', 2, undef); is($x->{_a}, 2, qq|\$x = $class->new(2); \$x->bone('-', 2, undef); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2); \$x->bone('-', 2, undef); \$x->{_p}|); note "Verify that precision can be set with instance method bone('-')."; $x = $class->new(2); $x->bone('-', undef, 2); is($x->{_a}, undef, qq|\$x = $class->new(2); \$x->bone('-', undef, 2); \$x->{_a}|); is($x->{_p}, 2, qq|\$x = $class->new(2); \$x->bone('-', undef, 2); \$x->{_p}|); note "Verify that accuracy can be set with instance method bzero()."; $x = $class->new(2); $x->bzero(2, undef); is($x->{_a}, 2, qq|\$x = $class->new(2);\$x->bzero(2, undef); \$x->{_a}|); is($x->{_p}, undef, qq|\$x = $class->new(2);\$x->bzero(2, undef); \$x->{_p}|); note "Verify that precision can be set with instance method bzero()."; $x = $class->new(2); $x->bzero(undef, 2); is($x->{_a}, undef, qq|\$x = $class->new(2); \$x->bzero(undef, 2); \$x->{_a}|); is($x->{_p}, 2, qq|\$x = $class->new(2); \$x->bzero(undef, 2); \$x->{_p}|); } ############################################################################### # test whether bone/bzero honour class variables for my $class ($mbi, $mbf) { note "Verify that class accuracy is copied into new objects."; $class->accuracy(3); # set $x = $class->bzero(); is($x->accuracy(), 3, qq|$class->accuracy(3); \$x = $class->bzero(); \$x->accuracy()|); $x = $class->bone(); is($x->accuracy(), 3, qq|$class->accuracy(3); \$x = $class->bone(); \$x->accuracy()|); $x = $class->new(2); is($x->accuracy(), 3, qq|$class->accuracy(3); \$x = $class->new(2); \$x->accuracy()|); $class->accuracy(undef); # reset note "Verify that class precision is copied into new objects."; $class->precision(-4); # set $x = $class->bzero(); is($x->precision(), -4, qq|$class->precision(-4); \$x = $class->bzero(); \$x->precision()|); $x = $class->bone(); is($x->precision(), -4, qq|$class->precision(-4); \$x = $class->bone(); \$x->precision()|); $x = $class->new(2); is($x->precision(), -4, qq|$class->precision(-4); \$x = $class->new(2); \$x->precision()|); $class->precision(undef); # reset note "Verify that setting accuracy as method argument overrides class variable"; $class->accuracy(2); # set $x = $class->bzero(5); is($x->accuracy(), 5, qq|$class->accuracy(2); \$x = $class->bzero(5); \$x->accuracy()|); SKIP: { skip 1, "this won't work until we have a better OO implementation"; $x = $class->bzero(undef); is($x->accuracy(), undef, qq|$class->accuracy(2); \$x = $class->bzero(undef); \$x->accuracy()|); } $x = $class->bone("+", 5); is($x->accuracy(), 5, qq|$class->accuracy(2); \$x = $class->bone("+", 5); \$x->accuracy()|); SKIP: { skip 1, "this won't work until we have a better OO implementation"; $x = $class->bone("+", undef); is($x->accuracy(), undef, qq|$class->accuracy(2); \$x = $class->bone("+", undef); \$x->accuracy()|); } $x = $class->new(2, 5); is($x->accuracy(), 5, qq|$class->accuracy(2); \$x = $class->new(2, 5); \$x->accuracy()|); SKIP: { skip 1, "this won't work until we have a better OO implementation"; $x = $class->new(2, undef); is($x->accuracy(), undef, qq|$class->accuracy(2); \$x = $class->new(2, undef); \$x->accuracy()|); } $class->accuracy(undef); # reset note "Verify that setting precision as method argument overrides class variable"; $class->precision(-2); # set $x = $class->bzero(undef, -6); is($x->precision(), -6, qq|$class->precision(-2); \$x = $class->bzero(undef, -6); \$x->precision()|); SKIP: { skip 1, "this won't work until we have a better OO implementation"; $x = $class->bzero(undef, undef); is($x->precision(), undef, qq|$class->precision(-2); \$x = $class->bzero(undef, undef); \$x->precision()|); } $x = $class->bone("+", undef, -6); is($x->precision(), -6, qq|$class->precision(-2); \$x = $class->bone("+", undef, -6); \$x->precision()|); SKIP: { skip 1, "this won't work until we have a better OO implementation"; $x = $class->bone("+", undef, undef); is($x->precision(), undef, qq|$class->precision(-2); \$x = $class->bone("+", undef, undef); \$x->precision()|); } $x = $class->new(2, undef, -6); is($x->precision(), -6, qq|$class->precision(-2); \$x = $class->new(2, undef, -6); \$x->precision()|); SKIP: { skip 1, "this won't work until we have a better OO implementation"; $x = $class->new(2, undef, undef); is($x->precision(), undef, qq|$class->precision(-2); \$x = $class->new(2, undef, undef); \$x->precision()|); } $class->precision(undef); # reset } ############################################################################### # check whether mixing A and P creates a NaN # new with set accuracy/precision and with parameters { no strict 'refs'; foreach my $class ($mbi, $mbf) { is($class->new(123, 4, -3), 'NaN', # with parameters "mixing A and P creates a NaN"); ${"$class\::accuracy"} = 42; ${"$class\::precision"} = 2; is($class->new(123), "NaN", # with globals q|$class->new(123) = "NaN"|); ${"$class\::accuracy"} = undef; ${"$class\::precision"} = undef; } } # binary ops foreach my $class ($mbi, $mbf) { #foreach (qw/add sub mul div pow mod/) { foreach my $method (qw/add sub mul pow mod/) { my $try = "my \$x = $class->new(1234); \$x->accuracy(5);"; $try .= " my \$y = $class->new(12); \$y->precision(-3);"; $try .= " \$x->b$method(\$y);"; $rc = eval $try; is($rc, "NaN", $try); } } # unary ops foreach my $method (qw/new bsqrt/) { my $try = "my \$x = $mbi->$method(1234, 5, -3);"; $rc = eval $try; is($rc, "NaN", $try); } # see if $x->bsub(0) and $x->badd(0) really round foreach my $class ($mbi, $mbf) { $x = $class->new(123); $class->accuracy(2); $x->bsub(0); is($x, 120, q|$x = 120|); $class->accuracy(undef); # reset $x = $class->new(123); $class->accuracy(2); $x->badd(0); is($x, 120, q|$x = 120|); $class->accuracy(undef); # reset } ############################################################################### # test whether shortcuts returning zero/one preserve A and P my ($got, $f, $a, $p, $xp, $yp, $xa, $ya, $try, $want, @args); my $CALC = Math::BigInt->config('lib'); while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines if (s/^&//) { $f = $_; # function next; } @args = split(/:/, $_); my $want = pop(@args); ($x, $xa, $xp) = split (/,/, $args[0]); $xa = $xa || ''; $xp = $xp || ''; $try = qq|\$x = $mbi->new("$x");|; $try .= qq| \$x->accuracy($xa);| if $xa ne ''; $try .= qq| \$x->precision($xp);| if $xp ne ''; ($y, $ya, $yp) = split (/,/, $args[1]); $ya = $ya || ''; $yp = $yp || ''; $try .= qq| \$y = $mbi->new("$y");|; $try .= qq| \$y->accuracy($ya);| if $ya ne ''; $try .= qq| \$y->precision($yp);| if $yp ne ''; $try .= ' $x->$f($y);'; # print "trying $try\n"; $rc = eval $try; print "# Error: $@\n" if $@; # convert hex/binary targets to decimal if ($want =~ /^(0x0x|0b0b)/) { $want =~ s/^0[xb]//; $want = $mbi->new($want)->bstr(); } is($rc, $want, $try); # check internal state of number objects is_valid($rc, $f) if ref $rc; # now check whether A and P are set correctly # only one of $a or $p will be set (no crossing here) $a = $xa || $ya; $p = $xp || $yp; # print "Check a=$a p=$p\n"; # print "# Tried: '$try'\n"; if ($a ne '') { unless (is($x->{_a}, $a, qq|\$x->{_a} == $a|) && is($x->{_p}, undef, qq|\$x->{_p} is undef|)) { print "# Check: A = $a and P = undef\n"; print "# Tried: $try\n"; } } if ($p ne '') { unless (is($x->{_p}, $p, qq|\$x->{_p} == $p|) && is($x->{_a}, undef, qq|\$x->{_a} is undef|)) { print "# Check: A = undef and P = $p\n"; print "# Tried: $try\n"; } } } # all done 1; ############################################################################### # sub to check validity of a Math::BigInt object internally, to ensure that no # op leaves a number object in an invalid state (f.i. "-0") sub is_valid { my ($x, $f) = @_; my $e = 0; # error? # ok as reference? $e = 'Not a reference' if !ref($x); # has ok sign? $e = qq|Illegal sign $x->{sign}| . q| (expected: "+", "-", "-inf", "+inf" or "NaN")| if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/; $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0; $e = $CALC->_check($x->{value}) if $e eq '0'; # test done, see if error did crop up if ($e eq '0') { pass('is a valid object'); return; } fail($e . qq| after op "$f"|); } # format is: # x,A,P:x,A,P:result # 123,,3 means 123 with precision 3 (A is undef) # the A or P of the result is calculated automatically __DATA__ &badd 123,,:123,,:246 123,3,:0,,:123 123,,-3:0,,:123 123,,:0,3,:123 123,,:0,,-3:123 &bmul 123,,:1,,:123 123,3,:0,,:0 123,,-3:0,,:0 123,,:0,3,:0 123,,:0,,-3:0 123,3,:1,,:123 123,,-3:1,,:123 123,,:1,3,:123 123,,:1,,-3:123 1,3,:123,,:123 1,,-3:123,,:123 1,,:123,3,:123 1,,:123,,-3:123 &bdiv 123,,:1,,:123 123,4,:1,,:123 123,,:1,4,:123 123,,:1,,-4:123 123,,-4:1,,:123 1,4,:123,,:0 1,,:123,4,:0 1,,:123,,-4:0 1,,-4:123,,:0 &band 1,,:3,,:1 1234,1,:0,,:0 1234,,:0,1,:0 1234,,-1:0,,:0 1234,,:0,,-1:0 0xFF,,:0x10,,:0x0x10 0xFF,2,:0xFF,,:250 0xFF,,:0xFF,2,:250 0xFF,,1:0xFF,,:250 0xFF,,:0xFF,,1:250 &bxor 1,,:3,,:2 1234,1,:0,,:1000 1234,,:0,1,:1000 1234,,3:0,,:1000 1234,,:0,,3:1000 0xFF,,:0x10,,:239 # 250 ^ 255 => 5 0xFF,2,:0xFF,,:5 0xFF,,:0xFF,2,:5 0xFF,,1:0xFF,,:5 0xFF,,:0xFF,,1:5 # 250 ^ 4095 = 3845 => 3800 0xFF,2,:0xFFF,,:3800 # 255 ^ 4100 = 4347 => 4300 0xFF,,:0xFFF,2,:4300 0xFF,,2:0xFFF,,:3800 # 255 ^ 4100 = 10fb => 4347 => 4300 0xFF,,:0xFFF,,2:4300 &bior 1,,:3,,:3 1234,1,:0,,:1000 1234,,:0,1,:1000 1234,,3:0,,:1000 1234,,:0,,3:1000 0xFF,,:0x10,,:0x0xFF # FF | FA = FF => 250 250,2,:0xFF,,:250 0xFF,,:250,2,:250 0xFF,,1:0xFF,,:250 0xFF,,:0xFF,,1:250 &bpow 2,,:3,,:8 2,,:0,,:1 2,2,:0,,:1 2,,:0,2,:1 Math-BigInt-1.999808/t/mbimbf.t0000644403072340010010000000546013014563052016226 0ustar ospjadomain users#!/usr/bin/perl # test rounding, accuracy, precision and fallback, round_mode and mixing # of classes use strict; use warnings; use Test::More tests => 712 # tests in require'd file + 26; # tests in this file use Math::BigInt only => 'Calc'; use Math::BigFloat; our $mbi = 'Math::BigInt'; our $mbf = 'Math::BigFloat'; require 't/mbimbf.inc'; # some tests that won't work with subclasses, since the things are only # guaranteed in the Math::Big(Int|Float) (unless subclass chooses to support # this) Math::BigInt->round_mode("even"); # reset for tests Math::BigFloat->round_mode("even"); # reset for tests is($Math::BigInt::rnd_mode, "even", '$Math::BigInt::rnd_mode = "even"'); is($Math::BigFloat::rnd_mode, "even", '$Math::BigFloat::rnd_mode = "even"'); my $x = eval '$mbi->round_mode("huhmbi");'; like($@, qr/^Unknown round mode 'huhmbi' at/, '$mbi->round_mode("huhmbi")'); $x = eval '$mbf->round_mode("huhmbf");'; like($@, qr/^Unknown round mode 'huhmbf' at/, '$mbf->round_mode("huhmbf")'); # old way (now with test for validity) $x = eval '$Math::BigInt::rnd_mode = "huhmbi";'; like($@, qr/^Unknown round mode 'huhmbi' at/, '$Math::BigInt::rnd_mode = "huhmbi"'); $x = eval '$Math::BigFloat::rnd_mode = "huhmbf";'; like($@, qr/^Unknown round mode 'huhmbf' at/, '$Math::BigFloat::rnd_mode = "huhmbf"'); # see if accessor also changes old variable $mbi->round_mode('odd'); is($Math::BigInt::rnd_mode, 'odd', '$Math::BigInt::rnd_mode = "odd"'); $mbf->round_mode('odd'); is($Math::BigInt::rnd_mode, 'odd', '$Math::BigInt::rnd_mode = "odd"'); foreach my $class (qw/Math::BigInt Math::BigFloat/) { is($class->accuracy(5), 5, "set A ..."); is($class->precision(), undef, "... and now P must be cleared"); is($class->precision(5), 5, "set P ..."); is($class->accuracy(), undef, "... and now A must be cleared"); } foreach my $class (qw/Math::BigInt Math::BigFloat/) { $class->accuracy(42); # $x gets A of 42, too! my $x = $class->new(123); # really? is($x->accuracy(), 42, '$x has A of 42'); # $x has no A, but the global is still in effect for $x so the return value # of that operation should be 42, not undef is($x->accuracy(undef), 42, '$x has A from global'); # so $x should still have A = 42 is($x->accuracy(), 42, '$x has still A of 42'); # reset for further tests $class->accuracy(undef); $class->precision(undef); } # bug with blog(Math::BigFloat, Math::BigInt) $x = Math::BigFloat->new(100); $x = $x->blog(Math::BigInt->new(10)); is($x, 2, 'bug with blog(Math::BigFloat, Math::BigInt)'); # bug until v1.88 for sqrt() with enough digits for my $i (80, 88, 100) { $x = Math::BigFloat->new("1." . ("0" x $i) . "1"); $x = $x->bsqrt; is($x, 1, '$x->bsqrt() with many digits'); } Math-BigInt-1.999808/t/mbi_ali.t0000644403072340010010000000026512740677026016400 0ustar ospjadomain users#!perl # test that the new alias names work use strict; use warnings; use Test::More tests => 6; use Math::BigInt; our $CLASS; $CLASS = 'Math::BigInt'; require 't/alias.inc'; Math-BigInt-1.999808/t/mbi_rand.t0000644403072340010010000000562413014574665016563 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More; my $count = 128; plan(($^O eq 'os390') ? (skip_all => 'takes too long on os390') : (tests => $count*4)); use Math::BigInt only => 'Calc'; my $length = 128; # If you get a failure here, please re-run the test with the printed seed # value as input "perl t/mbi_rand.t seed" and send me the output my $seed = @ARGV == 1 ? $ARGV[0] : int(rand(1165537)); #diag(" seed: $seed\n"); srand($seed); my $_base_len; my @_base_len; #diag(" lib: ", Math::BigInt->config('lib')); if (Math::BigInt->config('lib') =~ /::Calc/) { $_base_len = Math::BigInt::Calc->_base_len(); @_base_len = Math::BigInt::Calc->_base_len(); #diag("base len: $_base_len (scalar context)"); #diag("base len: @_base_len (list contex)"); } my ($A, $B, $A_str, $B_str, $AdivB, $AmodB, $A_len, $B_len); my $two = Math::BigInt->new(2); for (my $i = 0; $i < $count; $i++) { #diag(""); # length of A and B $A_len = int(rand($length) + 1); $B_len = int(rand($length) + 1); $A_str = ''; $B_str = ''; # We create the numbers from "patterns", e.g. get a random number and a # random count and string them together. This means things like # "100000999999999999911122222222" are much more likely. If we just strung # together digits, we would end up with "1272398823211223" etc. It also # means that we get more frequently equal numbers or other special cases. while (length($A_str) < $A_len) { $A_str .= int(rand(100)) x int(rand(16)); } while (length($B_str) < $B_len) { $B_str .= int(rand(100)) x int(rand(16)); } $A_str =~ s/^0+(?=\d)//; $B_str =~ s/^0+(?=\d)//; #diag(" As: $A_str"); #diag(" Bs: $B_str"); $A = Math::BigInt->new($A_str); $B = Math::BigInt->new($B_str); #diag(" A: $A"); #diag(" B: $B"); SKIP: { skip '$A and/or $B are zero.', 4 if $A->is_zero() || $B->is_zero(); # check that int(A / B) * B + A % B == A holds for all inputs # $X = ($A / $B) * $B + 2 * ($A % $B) - ($A % $B); ($AdivB, $AmodB) = $A->copy()->bdiv($B); #diag(" A / B: $AdivB"); #diag(" A % B: $AmodB"); is($AdivB * $B + $two * $AmodB - $AmodB, $A_str, "AdivB * B + 2 * AmodB - AmodB == A"); if (is($AdivB * $B / $B, $AdivB, "AdivB * B / B == AdivB")) { if (Math::BigInt->config('lib') =~ /::Calc/) { #diag("AdivB->[-1]: ", $AdivB->{value}->[-1]); #diag(" B->[-1]: ", $B->{value}->[-1]); } } # swap 'em and try this, too # $X = ($B/$A)*$A + $B % $A; ($AdivB, $AmodB) = $B->copy()->bdiv($A); # print "check: $AdivB $AmodB"; is($AdivB * $A + $two * $AmodB - $AmodB, $B_str, "AdivB * A + 2 * AmodB - AmodB == B"); is($AdivB * $A / $A, $AdivB, "AdivB * A / A == AdivB"); } } Math-BigInt-1.999808/t/nan_cmp.t0000644403072340010010000000213612740677026016416 0ustar ospjadomain users#!perl # test that overloaded compare works when NaN are involved use strict; use warnings; use Test::More tests => 26; use Math::BigInt; use Math::BigFloat; compare('Math::BigInt'); compare('Math::BigFloat'); sub compare { my $class = shift; my $nan = $class->bnan(); my $one = $class->bone(); is($one, $one, "$class->bone() == $class->bone()"); is($one != $nan, 1, "$class->bone() != $class->bnan()"); is($nan != $one, 1, "$class->bnan() != $class->bone()"); is($nan != $nan, 1, "$class->bnan() != $class->bnan()"); is($nan == $one, '', "$class->bnan() == $class->bone()"); is($one == $nan, '', "$class->bone() == $class->bnan()"); is($nan == $nan, '', "$class->bnan() == $class->bnan()"); is($nan <= $one, '', "$class->bnan() <= $class->bone()"); is($one <= $nan, '', "$class->bone() <= $class->bnan()"); is($nan <= $nan, '', "$class->bnan() <= $class->bnan()"); is($nan >= $one, '', "$class->bnan() >= $class->bone()"); is($one >= $nan, '', "$class->bone() >= $class->bnan()"); is($nan >= $nan, '', "$class->bnan() >= $class->bnan()"); } Math-BigInt-1.999808/t/new-mbf.t0000644403072340010010000000374213013420215016316 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 50; my $class; BEGIN { $class = 'Math::BigFloat'; } BEGIN { use_ok($class, '1.999710'); } while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($in0, $out0) = split /:/; my $x; my $test = qq|\$x = $class -> new("$in0");|; my $desc = $test; eval $test; die $@ if $@; # this should never happen subtest $desc, sub { plan tests => 2, # Check output. is(ref($x), $class, "output arg is a $class"); is($x, $out0, 'output arg has the right value'); }; } __END__ NaN:NaN inf:inf infinity:inf +inf:inf +infinity:inf -inf:-inf -infinity:-inf # This is the same data as in from_hex-mbf.t, except that some of them are # commented out, since new() only treats input as hexadecimal if it has a "0x" # or "0X" prefix, possibly with a leading "+" or "-" sign. 0x1p+0:1 0x.8p+1:1 0x.4p+2:1 0x.2p+3:1 0x.1p+4:1 0x2p-1:1 0x4p-2:1 0x8p-3:1 -0x1p+0:-1 0x0p+0:0 0x0p+7:0 0x0p-7:0 0x0.p+0:0 0x.0p+0:0 0x0.0p+0:0 0xcafe:51966 #xcafe:51966 #cafe:51966 0x1.9p+3:12.5 0x12.34p-1:9.1015625 -0x.789abcdefp+32:-2023406814.9375 0x12.3456789ap+31:39093746765 #NaN:NaN #+inf:NaN #-inf:NaN 0x.p+0:NaN # This is the same data as in from_bin-mbf.t, except that some of them are # commented out, since new() only treats input as binary if it has a "0b" or # "0B" prefix, possibly with a leading "+" or "-" sign. Duplicates from above # are also commented out. 0b1p+0:1 0b.1p+1:1 0b.01p+2:1 0b.001p+3:1 0b.0001p+4:1 0b10p-1:1 0b100p-2:1 0b1000p-3:1 -0b1p+0:-1 0b0p+0:0 0b0p+7:0 0b0p-7:0 0b0.p+0:0 0b.0p+0:0 0b0.0p+0:0 0b1100101011111110:51966 #b1100101011111110:51966 #1100101011111110:51966 0b1.1001p+3:12.5 0b10010.001101p-1:9.1015625 -0b.11110001001101010111100110111101111p+31:-2023406814.9375 0b10.0100011010001010110011110001001101p+34:39093746765 #NaN:NaN #+inf:NaN #-inf:NaN 0b.p+0:NaN Math-BigInt-1.999808/t/new_overloaded.t0000644403072340010010000000163212740677026020000 0ustar ospjadomain users#!perl # Math::BigFloat->new had a bug where it would assume any object is a # Math::BigInt which broke overloaded non-Math::BigInt objects. use strict; use warnings; use Test::More tests => 4; ############################################################################## package Overloaded::Num; use overload '0+' => sub { ${$_[0]} }, fallback => 1; sub new { my ($class, $num) = @_; return bless \$num, $class; } package main; use Math::BigFloat; my $overloaded_num = Overloaded::Num->new(2.23); is($overloaded_num, 2.23, 'Overloaded::Num->new(2.23)'); my $bigfloat = Math::BigFloat->new($overloaded_num); is($bigfloat, 2.23, 'Math::BigFloat->new() accepts overloaded numbers'); my $bigint = Math::BigInt->new(Overloaded::Num->new(3)); is($bigint, 3, 'Math::BigInt->new() accepts overloaded numbers'); is(Math::BigFloat->new($bigint), 3, 'Math::BigFloat->new() accepts a Math::BigInt'); Math-BigInt-1.999808/t/nparts-mbf.t0000644403072340010010000001237612740677026017063 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 1840; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $mant_str, $expo_str) = split /:/; note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| (\$m, \$e) = \$x -> nparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my ($mant_got, $expo_got) = $x -> nparts(); isa_ok($mant_got, "Math::BigFloat"); isa_ok($expo_got, "Math::BigFloat"); is($mant_got, $mant_str, "value of mantissa"); is($expo_got, $expo_str, "value of exponent"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| \$m = \$x -> nparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my $mant_got = $x -> nparts(); isa_ok($mant_got, "Math::BigFloat"); is($mant_got, $mant_str, "value of mantissa"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:NaN inf:inf:inf -inf:-inf:inf 0:0:0 # positive numbers 0.000000000001:1:-12 0.00000000001:1:-11 0.0000000001:1:-10 0.000000001:1:-9 0.00000001:1:-8 0.0000001:1:-7 0.000001:1:-6 0.00001:1:-5 0.0001:1:-4 0.001:1:-3 0.01:1:-2 0.1:1:-1 1:1:0 10:1:1 100:1:2 1000:1:3 10000:1:4 100000:1:5 1000000:1:6 10000000:1:7 100000000:1:8 1000000000:1:9 10000000000:1:10 100000000000:1:11 1000000000000:1:12 0.0000000000012:1.2:-12 0.000000000012:1.2:-11 0.00000000012:1.2:-10 0.0000000012:1.2:-9 0.000000012:1.2:-8 0.00000012:1.2:-7 0.0000012:1.2:-6 0.000012:1.2:-5 0.00012:1.2:-4 0.0012:1.2:-3 0.012:1.2:-2 0.12:1.2:-1 1.2:1.2:0 12:1.2:1 120:1.2:2 1200:1.2:3 12000:1.2:4 120000:1.2:5 1200000:1.2:6 12000000:1.2:7 120000000:1.2:8 1200000000:1.2:9 12000000000:1.2:10 120000000000:1.2:11 1200000000000:1.2:12 0.00000000000123:1.23:-12 0.0000000000123:1.23:-11 0.000000000123:1.23:-10 0.00000000123:1.23:-9 0.0000000123:1.23:-8 0.000000123:1.23:-7 0.00000123:1.23:-6 0.0000123:1.23:-5 0.000123:1.23:-4 0.00123:1.23:-3 0.0123:1.23:-2 0.123:1.23:-1 1.23:1.23:0 12.3:1.23:1 123:1.23:2 1230:1.23:3 12300:1.23:4 123000:1.23:5 1230000:1.23:6 12300000:1.23:7 123000000:1.23:8 1230000000:1.23:9 12300000000:1.23:10 123000000000:1.23:11 1230000000000:1.23:12 0.000000000001234:1.234:-12 0.00000000001234:1.234:-11 0.0000000001234:1.234:-10 0.000000001234:1.234:-9 0.00000001234:1.234:-8 0.0000001234:1.234:-7 0.000001234:1.234:-6 0.00001234:1.234:-5 0.0001234:1.234:-4 0.001234:1.234:-3 0.01234:1.234:-2 0.1234:1.234:-1 1.234:1.234:0 12.34:1.234:1 123.4:1.234:2 1234:1.234:3 12340:1.234:4 123400:1.234:5 1234000:1.234:6 12340000:1.234:7 123400000:1.234:8 1234000000:1.234:9 12340000000:1.234:10 123400000000:1.234:11 1234000000000:1.234:12 0.000003141592:3.141592:-6 0.00003141592:3.141592:-5 0.0003141592:3.141592:-4 0.003141592:3.141592:-3 0.03141592:3.141592:-2 0.3141592:3.141592:-1 3.141592:3.141592:0 31.41592:3.141592:1 314.1592:3.141592:2 3141.592:3.141592:3 31415.92:3.141592:4 314159.2:3.141592:5 3141592:3.141592:6 # negativ: numbers -0.000000000001:-1:-12 -0.00000000001:-1:-11 -0.0000000001:-1:-10 -0.000000001:-1:-9 -0.00000001:-1:-8 -0.0000001:-1:-7 -0.000001:-1:-6 -0.00001:-1:-5 -0.0001:-1:-4 -0.001:-1:-3 -0.01:-1:-2 -0.1:-1:-1 -1:-1:0 -10:-1:1 -100:-1:2 -1000:-1:3 -10000:-1:4 -100000:-1:5 -1000000:-1:6 -10000000:-1:7 -100000000:-1:8 -1000000000:-1:9 -10000000000:-1:10 -100000000000:-1:11 -1000000000000:-1:12 -0.0000000000012:-1.2:-12 -0.000000000012:-1.2:-11 -0.00000000012:-1.2:-10 -0.0000000012:-1.2:-9 -0.000000012:-1.2:-8 -0.00000012:-1.2:-7 -0.0000012:-1.2:-6 -0.000012:-1.2:-5 -0.00012:-1.2:-4 -0.0012:-1.2:-3 -0.012:-1.2:-2 -0.12:-1.2:-1 -1.2:-1.2:0 -12:-1.2:1 -120:-1.2:2 -1200:-1.2:3 -12000:-1.2:4 -120000:-1.2:5 -1200000:-1.2:6 -12000000:-1.2:7 -120000000:-1.2:8 -1200000000:-1.2:9 -12000000000:-1.2:10 -120000000000:-1.2:11 -1200000000000:-1.2:12 -0.00000000000123:-1.23:-12 -0.0000000000123:-1.23:-11 -0.000000000123:-1.23:-10 -0.00000000123:-1.23:-9 -0.0000000123:-1.23:-8 -0.000000123:-1.23:-7 -0.00000123:-1.23:-6 -0.0000123:-1.23:-5 -0.000123:-1.23:-4 -0.00123:-1.23:-3 -0.0123:-1.23:-2 -0.123:-1.23:-1 -1.23:-1.23:0 -12.3:-1.23:1 -123:-1.23:2 -1230:-1.23:3 -12300:-1.23:4 -123000:-1.23:5 -1230000:-1.23:6 -12300000:-1.23:7 -123000000:-1.23:8 -1230000000:-1.23:9 -12300000000:-1.23:10 -123000000000:-1.23:11 -1230000000000:-1.23:12 -0.000000000001234:-1.234:-12 -0.00000000001234:-1.234:-11 -0.0000000001234:-1.234:-10 -0.000000001234:-1.234:-9 -0.00000001234:-1.234:-8 -0.0000001234:-1.234:-7 -0.000001234:-1.234:-6 -0.00001234:-1.234:-5 -0.0001234:-1.234:-4 -0.001234:-1.234:-3 -0.01234:-1.234:-2 -0.1234:-1.234:-1 -1.234:-1.234:0 -12.34:-1.234:1 -123.4:-1.234:2 -1234:-1.234:3 -12340:-1.234:4 -123400:-1.234:5 -1234000:-1.234:6 -12340000:-1.234:7 -123400000:-1.234:8 -1234000000:-1.234:9 -12340000000:-1.234:10 -123400000000:-1.234:11 -1234000000000:-1.234:12 -0.000003141592:-3.141592:-6 -0.00003141592:-3.141592:-5 -0.0003141592:-3.141592:-4 -0.003141592:-3.141592:-3 -0.03141592:-3.141592:-2 -0.3141592:-3.141592:-1 -3.141592:-3.141592:0 -31.41592:-3.141592:1 -314.1592:-3.141592:2 -3141.592:-3.141592:3 -31415.92:-3.141592:4 -314159.2:-3.141592:5 -3141592:-3.141592:6 Math-BigInt-1.999808/t/nparts-mbi.t0000644403072340010010000000514112740677026017056 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 784; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $mant_str, $expo_str) = split /:/; note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| (\$m, \$e) = \$x -> nparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my ($mant_got, $expo_got) = $x -> nparts(); isa_ok($mant_got, "Math::BigInt"); isa_ok($expo_got, "Math::BigInt"); is($mant_got, $mant_str, "value of mantissa"); is($expo_got, $expo_str, "value of exponent"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| \$m = \$x -> nparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my $mant_got = $x -> nparts(); isa_ok($mant_got, "Math::BigInt"); is($mant_got, $mant_str, "value of mantissa"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:NaN inf:inf:inf -inf:-inf:inf 0:0:0 # positive numbers 1:1:0 10:1:1 100:1:2 1000:1:3 10000:1:4 100000:1:5 1000000:1:6 10000000:1:7 100000000:1:8 1000000000:1:9 10000000000:1:10 100000000000:1:11 1000000000000:1:12 12:NaN:1 120:NaN:2 1200:NaN:3 12000:NaN:4 120000:NaN:5 1200000:NaN:6 12000000:NaN:7 120000000:NaN:8 1200000000:NaN:9 12000000000:NaN:10 120000000000:NaN:11 1200000000000:NaN:12 123:NaN:2 1230:NaN:3 12300:NaN:4 123000:NaN:5 1230000:NaN:6 12300000:NaN:7 123000000:NaN:8 1230000000:NaN:9 12300000000:NaN:10 123000000000:NaN:11 1230000000000:NaN:12 1234:NaN:3 12340:NaN:4 123400:NaN:5 1234000:NaN:6 12340000:NaN:7 123400000:NaN:8 1234000000:NaN:9 12340000000:NaN:10 123400000000:NaN:11 1234000000000:NaN:12 3141592:NaN:6 # negativ: numbers -1:-1:0 -10:-1:1 -100:-1:2 -1000:-1:3 -10000:-1:4 -100000:-1:5 -1000000:-1:6 -10000000:-1:7 -100000000:-1:8 -1000000000:-1:9 -10000000000:-1:10 -100000000000:-1:11 -1000000000000:-1:12 -12:NaN:1 -120:NaN:2 -1200:NaN:3 -12000:NaN:4 -120000:NaN:5 -1200000:NaN:6 -12000000:NaN:7 -120000000:NaN:8 -1200000000:NaN:9 -12000000000:NaN:10 -120000000000:NaN:11 -1200000000000:NaN:12 -123:NaN:2 -1230:NaN:3 -12300:NaN:4 -123000:NaN:5 -1230000:NaN:6 -12300000:NaN:7 -123000000:NaN:8 -1230000000:NaN:9 -12300000000:NaN:10 -123000000000:NaN:11 -1230000000000:NaN:12 -1234:NaN:3 -12340:NaN:4 -123400:NaN:5 -1234000:NaN:6 -12340000:NaN:7 -123400000:NaN:8 -1234000000:NaN:9 -12340000000:NaN:10 -123400000000:NaN:11 -1234000000000:NaN:12 -3141592:NaN:6 Math-BigInt-1.999808/t/objectify_mbf.t0000644403072340010010000000464512740677026017614 0ustar ospjadomain users#!perl # # Verify that objectify() is able to convert a "foreign" object into what we # want, when what we want is Math::BigFloat or subclass thereof. use strict; use warnings; package main; use Test::More tests => 6; use Math::BigFloat; ############################################################################### for my $class ('Math::BigFloat', 'Math::BigFloat::Subclass') { # This object defines what we want. my $float = $class -> new(10); # Create various objects that should work with the object above after # objectify() has done its thing. my $float_percent1 = My::Percent::Float1 -> new(100); is($float * $float_percent1, 10, qq|\$float = $class -> new(10);| . q| $float_percent1 = My::Percent::Float1 -> new(100);| . q| $float * $float_percent1;|); my $float_percent2 = My::Percent::Float2 -> new(100); is($float * $float_percent2, 10, qq|\$float = $class -> new(10);| . q| $float_percent2 = My::Percent::Float2 -> new(100);| . q| $float * $float_percent2;|); my $float_percent3 = My::Percent::Float3 -> new(100); is($float * $float_percent3, 10, qq|\$float = $class -> new(10);| . q| $float_percent3 = My::Percent::Float3 -> new(100);| . q| $float * $float_percent3;|); } ############################################################################### # Class supports as_float(), which returns a Math::BigFloat. package My::Percent::Float1; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_float { my $self = shift; return Math::BigFloat -> new($$self / 100); } ############################################################################### # Class supports as_float(), which returns a scalar. package My::Percent::Float2; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_float { my $self = shift; return $$self / 100; } ############################################################################### # Class does not support as_float(). package My::Percent::Float3; use overload '""' => sub { $_[0] -> as_string(); }; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_string { my $self = shift; return $$self / 100; } ############################################################################### package Math::BigFloat::Subclass; use base 'Math::BigFloat'; Math-BigInt-1.999808/t/objectify_mbi.t0000644403072340010010000000671712740677026017621 0ustar ospjadomain users#!perl # # Verify that objectify() is able to convert a "foreign" object into what we # want, when what we want is Math::BigInt or subclass thereof. use strict; use warnings; package main; use Test::More tests => 10; use Math::BigInt; ############################################################################### for my $class ('Math::BigInt', 'Math::BigInt::Subclass') { # This object defines what we want. my $int = $class -> new(10); # Create various objects that should work with the object above after # objectify() has done its thing. my $int_percent1 = My::Percent::Int1 -> new(100); is($int * $int_percent1, 10, qq|\$class -> new(10);| . q| $int_percent1 = My::Percent::Int1 -> new(100);| . q| $int * $int_percent1|); my $int_percent2 = My::Percent::Int2 -> new(100); is($int * $int_percent2, 10, qq|\$class -> new(10);| . q| $int_percent2 = My::Percent::Int2 -> new(100);| . q| $int * $int_percent2|); my $int_percent3 = My::Percent::Int3 -> new(100); is($int * $int_percent3, 10, qq|\$class -> new(10);| . q| $int_percent3 = My::Percent::Int3 -> new(100);| . q| $int * $int_percent3|); my $int_percent4 = My::Percent::Int4 -> new(100); is($int * $int_percent4, 10, qq|\$class -> new(10);| . q| $int_percent4 = My::Percent::Int4 -> new(100);| . q| $int * $int_percent4|); my $int_percent5 = My::Percent::Int5 -> new(100); is($int * $int_percent5, 10, qq|\$class -> new(10);| . q| $int_percent5 = My::Percent::Int5 -> new(100);| . q| $int * $int_percent5|); } ############################################################################### # Class supports as_int(), which returns a Math::BigInt. package My::Percent::Int1; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_int { my $self = shift; return Math::BigInt -> new($$self / 100); } ############################################################################### # Class supports as_int(), which returns a scalar. package My::Percent::Int2; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_int { my $self = shift; return $$self / 100; } ############################################################################### # Class does not support as_int(), but supports as_number(), which returns a # Math::BigInt. package My::Percent::Int3; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_number { my $self = shift; return Math::BigInt -> new($$self / 100); } ############################################################################### # Class does not support as_int(), but supports as_number(), which returns a # scalar. package My::Percent::Int4; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_number { my $self = shift; return $$self / 100; } ############################################################################### # Class supports neither as_int() or as_number(). package My::Percent::Int5; use overload '""' => sub { $_[0] -> as_string(); }; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_string { my $self = shift; return $$self / 100; } ############################################################################### package Math::BigInt::Subclass; use base 'Math::BigInt'; Math-BigInt-1.999808/t/require.t0000644403072340010010000000033612740677026016457 0ustar ospjadomain users#!/usr/bin/perl # check that simple requiring Math::BigInt works use strict; use warnings; use Test::More tests => 1; require Math::BigInt; my $x = Math::BigInt->new(1); ++$x; is($x, 2, '$x is 2'); # all tests done Math-BigInt-1.999808/t/req_mbf0.t0000644403072340010010000000035412740677026016476 0ustar ospjadomain users#!perl # check that simple requiring Math::BigFloat and then bzero() works use strict; use warnings; use Test::More tests => 1; require Math::BigFloat; my $x = Math::BigFloat->bzero(); $x++; is($x, 1, '$x is 1'); # all tests done Math-BigInt-1.999808/t/req_mbf1.t0000644403072340010010000000034412740677026016476 0ustar ospjadomain users#!perl # check that simple requiring Math::BigFloat and then bone() works use strict; use warnings; use Test::More tests => 1; require Math::BigFloat; my $x = Math::BigFloat->bone(); is($x, 1, '$x is 1'); # all tests done Math-BigInt-1.999808/t/req_mbfa.t0000644403072340010010000000035312740677026016556 0ustar ospjadomain users#!perl # check that simple requiring Math::BigFloat and then bnan() works use strict; use warnings; use Test::More tests => 1; require Math::BigFloat; my $x = Math::BigFloat->bnan(1); is($x, 'NaN', '$x is NaN'); # all tests done Math-BigInt-1.999808/t/req_mbfi.t0000644403072340010010000000036312740677026016567 0ustar ospjadomain users#!/usr/bin/perl # check that simple requiring Math::BigFloat and then binf() works use strict; use warnings; use Test::More tests => 1; require Math::BigFloat; my $x = Math::BigFloat->binf(); is($x, 'inf', '$x is inf'); # all tests done Math-BigInt-1.999808/t/req_mbfn.t0000644403072340010010000000036212740677026016573 0ustar ospjadomain users#!/usr/bin/perl # check that simple requiring Math::BigFloat and then new() works use strict; use warnings; use Test::More tests => 1; require Math::BigFloat; my $x = Math::BigFloat->new(1); ++$x; is($x, 2, '$x is 2'); # all tests done Math-BigInt-1.999808/t/req_mbfw.t0000644403072340010010000000120213015016216016556 0ustar ospjadomain users#!/usr/bin/perl # check that requiring Math::BigFloat and then calling import() works use strict; use warnings; use Test::More tests => 3; use lib 't'; # normal require that calls import automatically (we thus have MBI afterwards) require Math::BigFloat; my $x = Math::BigFloat->new(1); ++$x; is($x, 2, '$x is 2'); like(Math::BigFloat->config()->{with}, qr/^Math::BigInt::(Fast)?Calc\z/, '"with" ignored'); # now override Math::BigFloat->import(with => 'Math::BigInt::Subclass'); # the "with" argument is ignored like(Math::BigFloat->config()->{with}, qr/^Math::BigInt::(Fast)?Calc\z/, '"with" ignored'); # all tests done Math-BigInt-1.999808/t/round.t0000644403072340010010000000546612740677026016143 0ustar ospjadomain users#!/usr/bin/perl # test rounding with non-integer A and P parameters use strict; use warnings; use Test::More tests => 95; use Math::BigFloat; my $mbf = 'Math::BigFloat'; #my $mbi = 'Math::BigInt'; my $x = $mbf->new('123456.123456'); # unary ops with A _do_a($x, 'round', 3, '123000'); _do_a($x, 'bfround', 3, '123500'); _do_a($x, 'bfround', 2, '123460'); _do_a($x, 'bfround', -2, '123456.12'); _do_a($x, 'bfround', -3, '123456.123'); _do_a($x, 'bround', 4, '123500'); _do_a($x, 'bround', 3, '123000'); _do_a($x, 'bround', 2, '120000'); _do_a($x, 'bsqrt', 4, '351.4'); _do_a($x, 'bsqrt', 3, '351'); _do_a($x, 'bsqrt', 2, '350'); # setting P _do_p($x, 'bsqrt', 2, '350'); _do_p($x, 'bsqrt', -2, '351.36'); # binary ops _do_2_a($x, 'bdiv', 2, 6, '61728.1'); _do_2_a($x, 'bdiv', 2, 4, '61730'); _do_2_a($x, 'bdiv', 2, 3, '61700'); _do_2_p($x, 'bdiv', 2, -6, '61728.061728'); _do_2_p($x, 'bdiv', 2, -4, '61728.0617'); _do_2_p($x, 'bdiv', 2, -3, '61728.062'); # all tests done ############################################################################# sub _do_a { my ($x, $method, $A, $result) = @_; is($x->copy->$method($A), $result, "$method($A)"); is($x->copy->$method($A.'.1'), $result, "$method(${A}.1)"); is($x->copy->$method($A.'.5'), $result, "$method(${A}.5)"); is($x->copy->$method($A.'.6'), $result, "$method(${A}.6)"); is($x->copy->$method($A.'.9'), $result, "$method(${A}.9)"); } sub _do_p { my ($x, $method, $P, $result) = @_; is($x->copy->$method(undef, $P), $result, "$method(undef, $P)"); is($x->copy->$method(undef, $P.'.1'), $result, "$method(undef, ${P}.1)"); is($x->copy->$method(undef, $P.'.5'), $result, "$method(undef.${P}.5)"); is($x->copy->$method(undef, $P.'.6'), $result, "$method(undef, ${P}.6)"); is($x->copy->$method(undef, $P.'.9'), $result, "$method(undef, ${P}.9)"); } sub _do_2_a { my ($x, $method, $y, $A, $result) = @_; my $cy = $mbf->new($y); is($x->copy->$method($cy, $A), $result, "$method($cy, $A)"); is($x->copy->$method($cy, $A.'.1'), $result, "$method($cy, ${A}.1)"); is($x->copy->$method($cy, $A.'.5'), $result, "$method($cy, ${A}.5)"); is($x->copy->$method($cy, $A.'.6'), $result, "$method($cy, ${A}.6)"); is($x->copy->$method($cy, $A.'.9'), $result, "$method($cy, ${A}.9)"); } sub _do_2_p { my ($x, $method, $y, $P, $result) = @_; my $cy = $mbf->new($y); is($x->copy->$method($cy, undef, $P), $result, "$method(undef, $P)"); is($x->copy->$method($cy, undef, $P.'.1'), $result, "$method($cy, undef, ${P}.1)"); is($x->copy->$method($cy, undef, $P.'.5'), $result, "$method($cy, undef, ${P}.5)"); is($x->copy->$method($cy, undef, $P.'.6'), $result, "$method($cy, undef, ${P}.6)"); is($x->copy->$method($cy, undef, $P.'.9'), $result, "$method($cy, undef, ${P}.9)"); } Math-BigInt-1.999808/t/rt-16221.t0000644403072340010010000000312012740677026016073 0ustar ospjadomain users#!/usr/bin/perl # # Verify that # - Math::BigInt::objectify() calls as_int() (or as_number(), as a fallback) # if the target object class is Math::BigInt. # - Math::BigInt::objectify() calls as_float() if the target object class is # Math::BigFloat. # # See RT #16221 and RT #52124. use strict; use warnings; package main; use Test::More tests => 2; use Math::BigInt; use Math::BigFloat; ############################################################################ my $int = Math::BigInt->new(10); my $int_percent = My::Percent::Float->new(100); is($int * $int_percent, 10, '$int * $int_percent = 10'); ############################################################################ my $float = Math::BigFloat->new(10); my $float_percent = My::Percent::Float->new(100); is($float * $float_percent, 10, '$float * $float_percent = 10'); ############################################################################ package My::Percent::Int; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_number { my $self = shift; return Math::BigInt->new($$self / 100); } sub as_string { my $self = shift; return $$self; } ############################################################################ package My::Percent::Float; sub new { my $class = shift; my $num = shift; return bless \$num, $class; } sub as_int { my $self = shift; return Math::BigInt->new($$self / 100); } sub as_float { my $self = shift; return Math::BigFloat->new($$self / 100); } sub as_string { my $self = shift; return $$self; } Math-BigInt-1.999808/t/sparts-mbf.t0000644403072340010010000001215412740677027017063 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 1840; use Math::BigFloat; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $mant_str, $expo_str) = split /:/; note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| (\$m, \$e) = \$x -> sparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my ($mant_got, $expo_got) = $x -> sparts(); isa_ok($mant_got, "Math::BigFloat"); isa_ok($expo_got, "Math::BigFloat"); is($mant_got, $mant_str, "value of mantissa"); is($expo_got, $expo_str, "value of exponent"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigFloat -> new("$x_str");|, qq| \$m = \$x -> sparts();\n\n|); { my $x = Math::BigFloat -> new($x_str); my $mant_got = $x -> sparts(); isa_ok($mant_got, "Math::BigFloat"); is($mant_got, $mant_str, "value of mantissa"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:NaN inf:inf:inf -inf:-inf:inf 0:0:0 # positive numbers 0.000000000001:1:-12 0.00000000001:1:-11 0.0000000001:1:-10 0.000000001:1:-9 0.00000001:1:-8 0.0000001:1:-7 0.000001:1:-6 0.00001:1:-5 0.0001:1:-4 0.001:1:-3 0.01:1:-2 0.1:1:-1 1:1:0 10:1:1 100:1:2 1000:1:3 10000:1:4 100000:1:5 1000000:1:6 10000000:1:7 100000000:1:8 1000000000:1:9 10000000000:1:10 100000000000:1:11 1000000000000:1:12 0.0000000000012:12:-13 0.000000000012:12:-12 0.00000000012:12:-11 0.0000000012:12:-10 0.000000012:12:-9 0.00000012:12:-8 0.0000012:12:-7 0.000012:12:-6 0.00012:12:-5 0.0012:12:-4 0.012:12:-3 0.12:12:-2 1.2:12:-1 12:12:0 120:12:1 1200:12:2 12000:12:3 120000:12:4 1200000:12:5 12000000:12:6 120000000:12:7 1200000000:12:8 12000000000:12:9 120000000000:12:10 1200000000000:12:11 0.00000000000123:123:-14 0.0000000000123:123:-13 0.000000000123:123:-12 0.00000000123:123:-11 0.0000000123:123:-10 0.000000123:123:-9 0.00000123:123:-8 0.0000123:123:-7 0.000123:123:-6 0.00123:123:-5 0.0123:123:-4 0.123:123:-3 1.23:123:-2 12.3:123:-1 123:123:0 1230:123:1 12300:123:2 123000:123:3 1230000:123:4 12300000:123:5 123000000:123:6 1230000000:123:7 12300000000:123:8 123000000000:123:9 1230000000000:123:10 0.000000000001234:1234:-15 0.00000000001234:1234:-14 0.0000000001234:1234:-13 0.000000001234:1234:-12 0.00000001234:1234:-11 0.0000001234:1234:-10 0.000001234:1234:-9 0.00001234:1234:-8 0.0001234:1234:-7 0.001234:1234:-6 0.01234:1234:-5 0.1234:1234:-4 1.234:1234:-3 12.34:1234:-2 123.4:1234:-1 1234:1234:0 12340:1234:1 123400:1234:2 1234000:1234:3 12340000:1234:4 123400000:1234:5 1234000000:1234:6 12340000000:1234:7 123400000000:1234:8 1234000000000:1234:9 0.000003141592:3141592:-12 0.00003141592:3141592:-11 0.0003141592:3141592:-10 0.003141592:3141592:-9 0.03141592:3141592:-8 0.3141592:3141592:-7 3.141592:3141592:-6 31.41592:3141592:-5 314.1592:3141592:-4 3141.592:3141592:-3 31415.92:3141592:-2 314159.2:3141592:-1 3141592:3141592:0 # negativ: numbers -0.000000000001:-1:-12 -0.00000000001:-1:-11 -0.0000000001:-1:-10 -0.000000001:-1:-9 -0.00000001:-1:-8 -0.0000001:-1:-7 -0.000001:-1:-6 -0.00001:-1:-5 -0.0001:-1:-4 -0.001:-1:-3 -0.01:-1:-2 -0.1:-1:-1 -1:-1:0 -10:-1:1 -100:-1:2 -1000:-1:3 -10000:-1:4 -100000:-1:5 -1000000:-1:6 -10000000:-1:7 -100000000:-1:8 -1000000000:-1:9 -10000000000:-1:10 -100000000000:-1:11 -1000000000000:-1:12 -0.0000000000012:-12:-13 -0.000000000012:-12:-12 -0.00000000012:-12:-11 -0.0000000012:-12:-10 -0.000000012:-12:-9 -0.00000012:-12:-8 -0.0000012:-12:-7 -0.000012:-12:-6 -0.00012:-12:-5 -0.0012:-12:-4 -0.012:-12:-3 -0.12:-12:-2 -1.2:-12:-1 -12:-12:0 -120:-12:1 -1200:-12:2 -12000:-12:3 -120000:-12:4 -1200000:-12:5 -12000000:-12:6 -120000000:-12:7 -1200000000:-12:8 -12000000000:-12:9 -120000000000:-12:10 -1200000000000:-12:11 -0.00000000000123:-123:-14 -0.0000000000123:-123:-13 -0.000000000123:-123:-12 -0.00000000123:-123:-11 -0.0000000123:-123:-10 -0.000000123:-123:-9 -0.00000123:-123:-8 -0.0000123:-123:-7 -0.000123:-123:-6 -0.00123:-123:-5 -0.0123:-123:-4 -0.123:-123:-3 -1.23:-123:-2 -12.3:-123:-1 -123:-123:0 -1230:-123:1 -12300:-123:2 -123000:-123:3 -1230000:-123:4 -12300000:-123:5 -123000000:-123:6 -1230000000:-123:7 -12300000000:-123:8 -123000000000:-123:9 -1230000000000:-123:10 -0.000000000001234:-1234:-15 -0.00000000001234:-1234:-14 -0.0000000001234:-1234:-13 -0.000000001234:-1234:-12 -0.00000001234:-1234:-11 -0.0000001234:-1234:-10 -0.000001234:-1234:-9 -0.00001234:-1234:-8 -0.0001234:-1234:-7 -0.001234:-1234:-6 -0.01234:-1234:-5 -0.1234:-1234:-4 -1.234:-1234:-3 -12.34:-1234:-2 -123.4:-1234:-1 -1234:-1234:0 -12340:-1234:1 -123400:-1234:2 -1234000:-1234:3 -12340000:-1234:4 -123400000:-1234:5 -1234000000:-1234:6 -12340000000:-1234:7 -123400000000:-1234:8 -1234000000000:-1234:9 -0.000003141592:-3141592:-12 -0.00003141592:-3141592:-11 -0.0003141592:-3141592:-10 -0.003141592:-3141592:-9 -0.03141592:-3141592:-8 -0.3141592:-3141592:-7 -3.141592:-3141592:-6 -31.41592:-3141592:-5 -314.1592:-3141592:-4 -3141.592:-3141592:-3 -31415.92:-3141592:-2 -314159.2:-3141592:-1 -3141592:-3141592:0 Math-BigInt-1.999808/t/sparts-mbi.t0000644403072340010010000000517312740677027017071 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 784; use Math::BigInt; while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines my ($x_str, $mant_str, $expo_str) = split /:/; note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| (\$m, \$e) = \$x -> sparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my ($mant_got, $expo_got) = $x -> sparts(); isa_ok($mant_got, "Math::BigInt"); isa_ok($expo_got, "Math::BigInt"); is($mant_got, $mant_str, "value of mantissa"); is($expo_got, $expo_str, "value of exponent"); is($x, $x_str, "input is unmodified"); } note(qq|\n\$x = Math::BigInt -> new("$x_str");|, qq| \$m = \$x -> sparts();\n\n|); { my $x = Math::BigInt -> new($x_str); my $mant_got = $x -> sparts(); isa_ok($mant_got, "Math::BigInt"); is($mant_got, $mant_str, "value of mantissa"); is($x, $x_str, "input is unmodified"); } } __DATA__ NaN:NaN:NaN inf:inf:inf -inf:-inf:inf 0:0:0 # positive numbers 1:1:0 10:1:1 100:1:2 1000:1:3 10000:1:4 100000:1:5 1000000:1:6 10000000:1:7 100000000:1:8 1000000000:1:9 10000000000:1:10 100000000000:1:11 1000000000000:1:12 12:12:0 120:12:1 1200:12:2 12000:12:3 120000:12:4 1200000:12:5 12000000:12:6 120000000:12:7 1200000000:12:8 12000000000:12:9 120000000000:12:10 1200000000000:12:11 123:123:0 1230:123:1 12300:123:2 123000:123:3 1230000:123:4 12300000:123:5 123000000:123:6 1230000000:123:7 12300000000:123:8 123000000000:123:9 1230000000000:123:10 1234:1234:0 12340:1234:1 123400:1234:2 1234000:1234:3 12340000:1234:4 123400000:1234:5 1234000000:1234:6 12340000000:1234:7 123400000000:1234:8 1234000000000:1234:9 3141592:3141592:0 # negativ: numbers -1:-1:0 -10:-1:1 -100:-1:2 -1000:-1:3 -10000:-1:4 -100000:-1:5 -1000000:-1:6 -10000000:-1:7 -100000000:-1:8 -1000000000:-1:9 -10000000000:-1:10 -100000000000:-1:11 -1000000000000:-1:12 -12:-12:0 -120:-12:1 -1200:-12:2 -12000:-12:3 -120000:-12:4 -1200000:-12:5 -12000000:-12:6 -120000000:-12:7 -1200000000:-12:8 -12000000000:-12:9 -120000000000:-12:10 -1200000000000:-12:11 -123:-123:0 -1230:-123:1 -12300:-123:2 -123000:-123:3 -1230000:-123:4 -12300000:-123:5 -123000000:-123:6 -1230000000:-123:7 -12300000000:-123:8 -123000000000:-123:9 -1230000000000:-123:10 -1234:-1234:0 -12340:-1234:1 -123400:-1234:2 -1234000:-1234:3 -12340000:-1234:4 -123400000:-1234:5 -1234000000:-1234:6 -12340000000:-1234:7 -123400000000:-1234:8 -1234000000000:-1234:9 -3141592:-3141592:0 Math-BigInt-1.999808/t/sub_ali.t0000644403072340010010000000034012740677027016415 0ustar ospjadomain users#!/usr/bin/perl # test that the new alias names work use strict; use warnings; use Test::More tests => 6; use lib 't'; use Math::BigInt::Subclass; our $CLASS; $CLASS = 'Math::BigInt::Subclass'; require 't/alias.inc'; Math-BigInt-1.999808/t/sub_mbf.t0000644403072340010010000000203013031671433016377 0ustar ospjadomain users#!perl use strict; use warnings; use Test::More tests => 2436 # tests in require'd file + 6; # tests in this file use lib 't'; use Math::BigFloat::Subclass; our ($CLASS, $CALC); $CLASS = "Math::BigFloat::Subclass"; $CALC = Math::BigFloat->config('lib'); # backend library require 't/bigfltpm.inc'; # perform same tests as bigfltpm ############################################################################### # Now do custom tests for Subclass itself my $ms = $CLASS->new(23); is($ms->{_custom}, 1, '$ms has custom attribute \$ms->{_custom}'); # Check that subclass is a Math::BigFloat, but not a Math::Bigint isa_ok($ms, 'Math::BigFloat'); ok(!$ms->isa('Math::BigInt'), "An object of class '" . ref($ms) . "' isn't a 'Math::BigFloat'"); use Math::BigFloat; my $bf = Math::BigFloat->new(23); # same as other $ms += $bf; is($ms, 46, '$ms is 46'); is($ms->{_custom}, 1, '$ms has custom attribute $ms->{_custom}'); is(ref($ms), $CLASS, "\$ms is not an object of class '$CLASS'"); Math-BigInt-1.999808/t/sub_mbi.t0000644403072340010010000000164512740677027016430 0ustar ospjadomain users#!/usr/bin/perl use strict; use warnings; use Test::More tests => 3913 # tests in require'd file + 5; # tests in this file use lib 't'; use Math::BigInt::Subclass; our ($CLASS, $CALC); $CLASS = "Math::BigInt::Subclass"; $CALC = "Math::BigInt::Calc"; # backend require 't/bigintpm.inc'; # perform same tests as bigintpm ############################################################################### # Now do custom tests for Subclass itself my $ms = $CLASS->new(23); is($ms->{_custom}, 1, '$ms has custom attribute \$ms->{_custom}'); # Check that a subclass is still considered a Math::BigInt isa_ok($ms, 'Math::BigInt'); use Math::BigInt; my $bi = Math::BigInt->new(23); # same as other $ms += $bi; is($ms, 46, '$ms is 46'); is($ms->{_custom}, 1, '$ms has custom attribute $ms->{_custom}'); is(ref($ms), $CLASS, "\$ms is not an object of class '$CLASS'"); Math-BigInt-1.999808/t/sub_mif.t0000644403072340010010000000053112740677027016425 0ustar ospjadomain users#!/usr/bin/perl # test rounding, accuracy, precision and fallback, round_mode and mixing # of classes use strict; use warnings; use Test::More tests => 712; use lib 't'; use Math::BigInt::Subclass; use Math::BigFloat::Subclass; our ($mbi, $mbf); $mbi = 'Math::BigInt::Subclass'; $mbf = 'Math::BigFloat::Subclass'; require 't/mbimbf.inc'; Math-BigInt-1.999808/t/trap.t0000644403072340010010000000471413015012524015733 0ustar ospjadomain users#!/usr/bin/perl # test that config ( trap_nan => 1, trap_inf => 1) really works/dies use strict; use warnings; use Test::More tests => 43; use Math::BigInt; use Math::BigFloat; my $mbi = 'Math::BigInt'; my $mbf = 'Math::BigFloat'; my ($cfg, $x); foreach my $class ($mbi, $mbf) { # can do and defaults are okay? ok($class->can('config'), 'can config()'); is($class->config()->{trap_nan}, 0, 'trap_nan defaults to 0'); is($class->config()->{trap_inf}, 0, 'trap_inf defaults to 0'); # can set? $cfg = $class->config( trap_nan => 1 ); is($cfg->{trap_nan}, 1, 'trap_nan now true'); # also test that new() still works normally eval ("\$x = \$class->new('42'); \$x->bnan();"); like($@, qr/^Tried to create/, 'died'); is($x, 42, '$x after new() never modified'); # can reset? $cfg = $class->config( trap_nan => 0 ); is($cfg->{trap_nan}, 0, 'trap_nan disabled'); # can set? $cfg = $class->config( trap_inf => 1 ); is($cfg->{trap_inf}, 1, 'trap_inf enabled'); eval ("\$x = \$class->new('4711'); \$x->binf();"); like($@, qr/^Tried to create/, 'died'); is($x, 4711, '$x after new() never modified'); eval ("\$x = \$class->new('inf');"); like($@, qr/^Tried to create/, 'died'); is($x, 4711, '$x after new() never modified'); eval ("\$x = \$class->new('-inf');"); like($@, qr/^Tried to create/, 'died'); is($x, 4711, '$x after new() never modified'); # +$x/0 => +inf eval ("\$x = \$class->new('4711'); \$x->bdiv(0);"); like($@, qr/^Tried to create/, 'died'); is($x, 4711, '$x after new() never modified'); # -$x/0 => -inf eval ("\$x = \$class->new('-0815'); \$x->bdiv(0);"); like($@, qr/^Tried to create/, 'died'); is($x, '-815', '$x after new not modified'); $cfg = $class->config( trap_nan => 1 ); # 0/0 => NaN eval ("\$x = \$class->new('0'); \$x->bdiv(0);"); like($@, qr/^Tried to create/, 'died'); is($x, '0', '$x after new not modified'); } ############################################################################## # Math::BigInt $x = Math::BigInt->new(2); eval ("\$x = \$mbi->new('0.1');"); is($x, 2, 'never modified since it dies'); eval ("\$x = \$mbi->new('0a.1');"); is($x, 2, 'never modified since it dies'); ############################################################################## # Math::BigFloat $x = Math::BigFloat->new(2); eval ("\$x = \$mbf->new('0.1a');"); is($x, 2, 'never modified since it dies'); # all tests done Math-BigInt-1.999808/t/upgrade.inc0000644403072340010010000007054513031743645016744 0ustar ospjadomain users# include this file into another for subclass testing # This file is nearly identical to bigintpm.t, except that certain results are # _requird_ to be different due to "upgrading" or "promoting" to # Math::BigFloat. The reverse is not true. Any unmarked results can be either # Math::BigInt or Math::BigFloat, depending on how good the internal # optimization is (e.g., it is usually desirable to have 2 ** 2 return a # Math::BigInt, not a Math::BigFloat). # Results that are required to be Math::BigFloat are marked with C<^> at the # end. # Please note that the testcount goes up by two for each extra result marked # with ^, since then we test whether it has the proper class and that it left # the upgrade variable alone. use strict; use warnings; our ($CLASS, $CALC, $EXPECTED_CLASS); ############################################################################## # for testing inheritance of _swap package Math::Foo; use Math::BigInt lib => $main::CALC; our @ISA = (qw/Math::BigInt/); use overload # customized overload for sub, since original does not use swap there '-' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bsub($a[1]); }; sub _swap { # a fake _swap, which reverses the params my $self = shift; # for override in subclass if ($_[2]) { my $c = ref ($_[0] ) || 'Math::Foo'; return ( $_[0]->copy(), $_[1] ); } else { return ( Math::Foo->new($_[1]), $_[0] ); } } ############################################################################## package main; is($CLASS->config('lib'), $CALC, "$CLASS->config('lib')"); my ($x, $y, $z, @args, $a, $m, $e, $try, $got, $want, $exp); my ($f, $round_mode, $expected_class); while () { s/#.*$//; # remove comments s/\s+$//; # remove trailing whitespace next unless length; # skip empty lines if (s/^&//) { $f = $_; next; } if (/^\$/) { $round_mode = $_; $round_mode =~ s/^\$/$CLASS\->/; next; } @args = split(/:/, $_, 99); $want = pop(@args); $expected_class = $CLASS; if ($want =~ /\^$/) { $expected_class = $EXPECTED_CLASS; $want =~ s/\^$//; } $try = qq|\$x = $CLASS->new("$args[0]");|; if ($f eq "bnorm") { $try = qq|\$x = $CLASS->bnorm("$args[0]");|; } elsif ($f =~ /^is_(zero|one|odd|even|negative|positive|nan|int)$/) { $try .= " \$x->$f();"; } elsif ($f =~ /^(to|as)_(hex|oct|bin)$/) { $try .= " \$x->$f();"; } elsif ($f eq "is_inf") { $try .= " \$x->is_inf('$args[1]');"; } elsif ($f eq "binf") { $try .= " \$x->binf('$args[1]');"; } elsif ($f eq "bone") { $try .= " \$x->bone('$args[1]');"; # some unary ops } elsif ($f =~ /^b(nan|floor|ceil|int|sstr|neg|abs|inc|dec|not|sqrt|d?fac)$/) { $try .= " \$x->$f();"; } elsif ($f eq "length") { $try .= ' $x->length();'; } elsif ($f eq "exponent") { # ->bstr() to see if an object is returned $try .= ' $x = $x->exponent()->bstr();'; } elsif ($f eq "mantissa") { # ->bstr() to see if an object is returned $try .= ' $x = $x->mantissa()->bstr();'; } elsif ($f eq "parts") { $try .= ' ($m, $e) = $x->parts();'; # ->bstr() to see if an object is returned $try .= ' $m = $m->bstr(); $m = "NaN" if !defined $m;'; $try .= ' $e = $e->bstr(); $e = "NaN" if !defined $e;'; $try .= ' "$m,$e";'; } else { if ($args[1] !~ /\./) { $try .= qq| \$y = $CLASS->new("$args[1]");|; } else { $try .= qq| \$y = $EXPECTED_CLASS->new("$args[1]");|; } if ($f eq "bcmp") { $try .= ' $x->bcmp($y);'; } elsif ($f eq "bacmp") { $try .= ' $x->bacmp($y);'; } elsif ($f eq "bround") { $try .= " $round_mode; \$x->bround(\$y);"; } elsif ($f eq "broot") { $try .= " \$x->broot(\$y);"; } elsif ($f eq "badd") { $try .= ' $x + $y;'; } elsif ($f eq "bsub") { $try .= ' $x - $y;'; } elsif ($f eq "bmul") { $try .= ' $x * $y;'; } elsif ($f eq "bdiv") { $try .= ' $x / $y;'; } elsif ($f eq "bdiv-list") { $try .= ' join(",", $x->bdiv($y));'; # overload via x= } elsif ($f =~ /^.=$/) { $try .= " \$x $f \$y;"; # overload via x } elsif ($f =~ /^.$/) { $try .= " \$x $f \$y;"; } elsif ($f eq "bmod") { $try .= ' $x % $y;'; } elsif ($f eq "bgcd") { if (defined $args[2]) { $try .= qq| \$z = $CLASS->new("$args[2]");|; } $try .= " $CLASS\::bgcd(\$x, \$y"; $try .= ", \$z" if defined $args[2]; $try .= ");"; } elsif ($f eq "blcm") { if (defined $args[2]) { $try .= qq| \$z = $CLASS->new("$args[2]");|; } $try .= " $CLASS\::blcm(\$x, \$y"; $try .= ", \$z" if defined $args[2]; $try .= ");"; } elsif ($f eq "blsft") { if (defined $args[2]) { $try .= " \$x->blsft(\$y, $args[2]);"; } else { $try .= " \$x << \$y;"; } } elsif ($f eq "brsft") { if (defined $args[2]) { $try .= " \$x->brsft(\$y, $args[2]);"; } else { $try .= " \$x >> \$y;"; } } elsif ($f eq "band") { $try .= " \$x & \$y;"; } elsif ($f eq "bior") { $try .= " \$x | \$y;"; } elsif ($f eq "bxor") { $try .= " \$x ^ \$y;"; } elsif ($f eq "bpow") { $try .= " \$x ** \$y;"; } elsif ($f eq "digit") { $try = qq|\$x = $CLASS->new("$args[0]"); \$x->digit($args[1]);|; } else { warn "Unknown op '$f'"; } } # end else all other ops $got = eval $try; print "# Error: $@\n" if $@; # convert hex/binary targets to decimal if ($want =~ /^(0x0x|0b0b)/) { $want =~ s/^0[xb]//; $want = Math::BigInt->new($want)->bstr(); } if ($want eq "") { is($got, undef, $try); } else { # print "try: $try ans: $got $want\n"; is($got, $want, $try); if ($expected_class ne $CLASS) { is(ref($got), $expected_class, 'ref($got)'); is($Math::BigInt::upgrade, 'Math::BigFloat', '$Math::BigInt::upgrade'); } } # check internal state of number objects is_valid($got, $f) if ref $got; } # endwhile data tests close DATA; my $warn = ''; $SIG{__WARN__} = sub { $warn = shift; }; # these should not warn $warn = ''; eval '$z = 3.17 <= $y'; is($z, 1, '$z = 3.17 <= $y'); is($warn, '', 'the code "$z = 3.17 <= $y" issued no warning'); $warn = ''; eval '$z = $y >= 3.17'; is($z, 1, '$z = $y >= 3.17'); is($warn, '', 'the code "$z = $y >= 3.17" issued no warning'); # all tests done 1; ############################################################################### # sub to check validity of a Math::BigInt internally, to ensure that no op # leaves a number object in an invalid state (f.i. "-0") sub is_valid { my ($x, $f, $c) = @_; # The checks here are loosened a bit to allow Math::BigInt or # Math::BigFloats to pass my $e = 0; # error? # ok as reference? # $e = "Not a reference to $c" if (ref($x) || '') ne $c; # has ok sign? $e = "Illegal sign $x->{sign} (expected: '+', '-', '-inf', '+inf' or 'NaN'" if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/; $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0; #$e = $CALC->_check($x->{value}) if $e eq '0'; # test done, see if error did crop up if ($e eq '0') { pass('is a valid object'); return; } fail($e . " after op '$f'"); } __DATA__ &.= 1234:-345:1234-345 &+= 1:2:3 -1:-2:-3 &-= 1:2:-1 -1:-2:1 &*= 2:3:6 -1:5:-5 &%= 100:3:1 8:9:8 &/= 100:3:33.33333333333333333333333333333333333333 -8:2:-4 &|= 2:1:3 &&= 5:7:5 &^= 5:7:2 &is_negative 0:0 -1:1 1:0 +inf:0 -inf:1 NaNneg:0 &is_positive 0:0 -1:0 1:1 +inf:1 -inf:0 NaNneg:0 &is_odd abc:0 0:0 1:1 3:1 -1:1 -3:1 10000001:1 10000002:0 2:0 120:0 121:1 &is_int NaN:0 inf:0 -inf:0 1:1 12:1 123e12:1 &is_even abc:0 0:1 1:0 3:0 -1:0 -3:0 10000001:0 10000002:1 2:1 120:1 121:0 &bacmp +0:-0:0 +0:+1:-1 -1:+1:0 +1:-1:0 -1:+2:-1 +2:-1:1 -123456789:+987654321:-1 +123456789:-987654321:-1 +987654321:+123456789:1 -987654321:+123456789:1 -123:+4567889:-1 # NaNs acmpNaN:123: 123:acmpNaN: acmpNaN:acmpNaN: # infinity +inf:+inf:0 -inf:-inf:0 +inf:-inf:0 -inf:+inf:0 +inf:123:1 -inf:123:1 +inf:-123:1 -inf:-123:1 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &bnorm 123:123 12.3:12.3^ # binary input 0babc:NaN 0b123:NaN 0b0:0 -0b0:0 -0b1:-1 0b0001:1 0b001:1 0b011:3 0b101:5 0b1001:9 0b10001:17 0b100001:33 0b1000001:65 0b10000001:129 0b100000001:257 0b1000000001:513 0b10000000001:1025 0b100000000001:2049 0b1000000000001:4097 0b10000000000001:8193 0b100000000000001:16385 0b1000000000000001:32769 0b10000000000000001:65537 0b100000000000000001:131073 0b1000000000000000001:262145 0b10000000000000000001:524289 0b100000000000000000001:1048577 0b1000000000000000000001:2097153 0b10000000000000000000001:4194305 0b100000000000000000000001:8388609 0b1000000000000000000000001:16777217 0b10000000000000000000000001:33554433 0b100000000000000000000000001:67108865 0b1000000000000000000000000001:134217729 0b10000000000000000000000000001:268435457 0b100000000000000000000000000001:536870913 0b1000000000000000000000000000001:1073741825 0b10000000000000000000000000000001:2147483649 0b100000000000000000000000000000001:4294967297 0b1000000000000000000000000000000001:8589934593 0b10000000000000000000000000000000001:17179869185 0b__101:NaN 0b1_0_1:5 0b0_0_0_1:1 # hex input -0x0:0 0xabcdefgh:NaN 0x1234:4660 0xabcdef:11259375 -0xABCDEF:-11259375 -0x1234:-4660 0x12345678:305419896 0x1_2_3_4_56_78:305419896 0xa_b_c_d_e_f:11259375 0x__123:NaN 0x9:9 0x11:17 0x21:33 0x41:65 0x81:129 0x101:257 0x201:513 0x401:1025 0x801:2049 0x1001:4097 0x2001:8193 0x4001:16385 0x8001:32769 0x10001:65537 0x20001:131073 0x40001:262145 0x80001:524289 0x100001:1048577 0x200001:2097153 0x400001:4194305 0x800001:8388609 0x1000001:16777217 0x2000001:33554433 0x4000001:67108865 0x8000001:134217729 0x10000001:268435457 0x20000001:536870913 0x40000001:1073741825 0x80000001:2147483649 0x100000001:4294967297 0x200000001:8589934593 0x400000001:17179869185 0x800000001:34359738369 # inf input inf:inf +inf:inf -inf:-inf 0inf:NaN # abnormal input :NaN abc:NaN 1 a:NaN 1bcd2:NaN 11111b:NaN +1z:NaN -1z:NaN # only one underscore between two digits _123:NaN _123_:NaN 123_:NaN 1__23:NaN 1E1__2:NaN 1_E12:NaN 1E_12:NaN 1_E_12:NaN +_1E12:NaN +0_1E2:100 +0_0_1E2:100 -0_0_1E2:-100 -0_0_1E+0_0_2:-100 E1:NaN E23:NaN 1.23E1:12.3^ 1.23E-1:0.123^ # bug with two E's in number being valid 1e2e3:NaN 1e2r:NaN 1e2.0:NaN # leading zeros 012:12 0123:123 01234:1234 012345:12345 0123456:123456 01234567:1234567 012345678:12345678 0123456789:123456789 01234567891:1234567891 012345678912:12345678912 0123456789123:123456789123 01234567891234:1234567891234 # normal input 0:0 +0:0 +00:0 +000:0 000000000000000000:0 -0:0 -0000:0 +1:1 +01:1 +001:1 +00000100000:100000 123456789:123456789 -1:-1 -01:-1 -001:-1 -123456789:-123456789 -00000100000:-100000 1_2_3:123 10000000000E-1_0:1 1E2:100 1E1:10 1E0:1 1.23E2:123 100E-1:10 # floating point input # .2e2:20 1.E3:1000 1.01E2:101 1010E-1:101 -1010E0:-1010 -1010E1:-10100 1234.00:1234 # non-integer numbers -1010E-2:-10.1^ -1.01E+1:-10.1^ -1.01E-1:-0.101^ &bnan 1:NaN 2:NaN abc:NaN &bone 2:+:1 2:-:-1 boneNaN:-:-1 boneNaN:+:1 2:abc:1 3::1 &binf 1:+:inf 2:-:-inf 3:abc:inf &is_nan 123:0 abc:1 NaN:1 -123:0 &is_inf +inf::1 -inf::1 abc::0 1::0 NaN::0 -1::0 +inf:-:0 +inf:+:1 -inf:-:1 -inf:+:0 +iNfInItY::1 -InFiNiTy::1 &blsft abc:abc:NaN +2:+2:8 +1:+32:4294967296 +1:+48:281474976710656 +8:-2:NaN # exercise base 10 +12345:4:10:123450000 -1234:0:10:-1234 +1234:0:10:1234 +2:2:10:200 +12:2:10:1200 +1234:-3:10:NaN 1234567890123:12:10:1234567890123000000000000 &brsft abc:abc:NaN +8:+2:2 +4294967296:+32:1 +281474976710656:+48:1 +2:-2:NaN # exercise base 10 -1234:0:10:-1234 +1234:0:10:1234 +200:2:10:2 +1234:3:10:1 +1234:2:10:12 +1234:-3:10:NaN 310000:4:10:31 12300000:5:10:123 1230000000000:10:10:123 09876123456789067890:12:10:9876123 1234561234567890123:13:10:123456 &bsstr 1e+34:1e+34 123.456E3:123456e+0 100:1e+2 abc:NaN &bneg bnegNaN:NaN +inf:-inf -inf:inf abd:NaN 0:0 1:-1 -1:1 +123456789:-123456789 -123456789:123456789 &babs babsNaN:NaN +inf:inf -inf:inf 0:0 1:1 -1:1 +123456789:123456789 -123456789:123456789 &bcmp bcmpNaN:bcmpNaN: bcmpNaN:0: 0:bcmpNaN: 0:0:0 -1:0:-1 0:-1:1 1:0:1 0:1:-1 -1:1:-1 1:-1:1 -1:-1:0 1:1:0 123:123:0 123:12:1 12:123:-1 -123:-123:0 -123:-12:-1 -12:-123:1 123:124:-1 124:123:1 -123:-124:1 -124:-123:-1 100:5:1 -123456789:987654321:-1 +123456789:-987654321:1 -987654321:123456789:-1 -inf:5432112345:-1 +inf:5432112345:1 -inf:-5432112345:-1 +inf:-5432112345:1 +inf:+inf:0 -inf:-inf:0 +inf:-inf:1 -inf:+inf:-1 5:inf:-1 5:inf:-1 -5:-inf:1 -5:-inf:1 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &binc abc:NaN +inf:inf -inf:-inf +0:1 +1:2 -1:0 &bdec abc:NaN +inf:inf -inf:-inf +0:-1 +1:0 -1:-2 &badd abc:abc:NaN abc:0:NaN +0:abc:NaN +inf:-inf:NaN -inf:+inf:NaN +inf:+inf:inf -inf:-inf:-inf baddNaN:+inf:NaN baddNaN:+inf:NaN +inf:baddNaN:NaN -inf:baddNaN:NaN 0:0:0 1:0:1 0:1:1 1:1:2 -1:0:-1 0:-1:-1 -1:-1:-2 -1:+1:0 +1:-1:0 +9:+1:10 +99:+1:100 +999:+1:1000 +9999:+1:10000 +99999:+1:100000 +999999:+1:1000000 +9999999:+1:10000000 +99999999:+1:100000000 +999999999:+1:1000000000 +9999999999:+1:10000000000 +99999999999:+1:100000000000 +10:-1:9 +100:-1:99 +1000:-1:999 +10000:-1:9999 +100000:-1:99999 +1000000:-1:999999 +10000000:-1:9999999 +100000000:-1:99999999 +1000000000:-1:999999999 +10000000000:-1:9999999999 +123456789:987654321:1111111110 -123456789:987654321:864197532 -123456789:-987654321:-1111111110 +123456789:-987654321:-864197532 2:2.5:4.5^ -123:-1.5:-124.5^ -1.2:1:-0.2^ &bsub abc:abc:NaN abc:+0:NaN +0:abc:NaN +inf:-inf:inf -inf:+inf:-inf +inf:+inf:NaN -inf:-inf:NaN +0:+0:0 +1:+0:1 +0:+1:-1 +1:+1:0 -1:+0:-1 +0:-1:1 -1:-1:0 -1:+1:-2 +1:-1:2 +9:+1:8 +99:+1:98 +999:+1:998 +9999:+1:9998 +99999:+1:99998 +999999:+1:999998 +9999999:+1:9999998 +99999999:+1:99999998 +999999999:+1:999999998 +9999999999:+1:9999999998 +99999999999:+1:99999999998 +10:-1:11 +100:-1:101 +1000:-1:1001 +10000:-1:10001 +100000:-1:100001 +1000000:-1:1000001 +10000000:-1:10000001 +100000000:-1:100000001 +1000000000:-1:1000000001 +10000000000:-1:10000000001 +123456789:+987654321:-864197532 -123456789:+987654321:-1111111110 -123456789:-987654321:864197532 +123456789:-987654321:1111111110 &bmul abc:abc:NaN abc:+0:NaN +0:abc:NaN NaNmul:+inf:NaN NaNmul:-inf:NaN -inf:NaNmul:NaN +inf:NaNmul:NaN +inf:+inf:inf +inf:-inf:-inf -inf:+inf:-inf -inf:-inf:inf +0:+0:0 +0:+1:0 +1:+0:0 +0:-1:0 -1:+0:0 123456789123456789:0:0 0:123456789123456789:0 -1:-1:1 -1:+1:-1 +1:-1:-1 +1:+1:1 +2:+3:6 -2:+3:-6 +2:-3:-6 -2:-3:6 111:111:12321 10101:10101:102030201 1001001:1001001:1002003002001 100010001:100010001:10002000300020001 10000100001:10000100001:100002000030000200001 11111111111:9:99999999999 22222222222:9:199999999998 33333333333:9:299999999997 44444444444:9:399999999996 55555555555:9:499999999995 66666666666:9:599999999994 77777777777:9:699999999993 88888888888:9:799999999992 99999999999:9:899999999991 +25:+25:625 +12345:+12345:152399025 +99999:+11111:1111088889 9999:10000:99990000 99999:100000:9999900000 999999:1000000:999999000000 9999999:10000000:99999990000000 99999999:100000000:9999999900000000 999999999:1000000000:999999999000000000 9999999999:10000000000:99999999990000000000 99999999999:100000000000:9999999999900000000000 999999999999:1000000000000:999999999999000000000000 9999999999999:10000000000000:99999999999990000000000000 99999999999999:100000000000000:9999999999999900000000000000 999999999999999:1000000000000000:999999999999999000000000000000 9999999999999999:10000000000000000:99999999999999990000000000000000 99999999999999999:100000000000000000:9999999999999999900000000000000000 999999999999999999:1000000000000000000:999999999999999999000000000000000000 9999999999999999999:10000000000000000000:99999999999999999990000000000000000000 3:3.5:10.5^ 3.5:3:10.5^ &bdiv-list 100:20:5,0 4095:4095:1,0 -4095:-4095:1,0 4095:-4095:-1,0 -4095:4095:-1,0 123:2:61,1 9:5:1,4 9:4:2,1 # inf handling and general remainder 5:8:0,5 0:8:0,0 11:2:5,1 11:-2:-6,-1 -11:2:-6,1 # see table in documentation in MBI 0:inf:0,0 0:-inf:0,0 5:inf:0,5 5:-inf:-1,-inf -5:inf:-1,inf -5:-inf:0,-5 inf:5:inf,NaN -inf:5:-inf,NaN inf:-5:-inf,NaN -inf:-5:inf,NaN 5:5:1,0 -5:-5:1,0 inf:inf:NaN,NaN -inf:-inf:NaN,NaN -inf:inf:NaN,NaN inf:-inf:NaN,NaN 8:0:inf,8 inf:0:inf,inf # exceptions to remainder rule -8:0:-inf,-8 -inf:0:-inf,-inf 0:0:NaN,0 &bdiv abc:abc:NaN abc:1:NaN 1:abc:NaN 0:0:NaN # inf handling (see table in doc) 0:inf:0 0:-inf:0 5:inf:0 5:-inf:-1 -5:inf:-1 -5:-inf:0 inf:5:inf -inf:5:-inf inf:-5:-inf -inf:-5:inf 5:5:1 -5:-5:1 inf:inf:NaN -inf:-inf:NaN -inf:inf:NaN inf:-inf:NaN 8:0:inf inf:0:inf -8:0:-inf -inf:0:-inf 11:2:5.5^ -11:-2:5.5^ -11:2:-5.5^ 11:-2:-5.5^ 0:1:0 0:-1:0 1:1:1 -1:-1:1 1:-1:-1 -1:1:-1 1:2:0.5^ 2:1:2 1000000000:9:111111111.1111111111111111111111111111111^ 2000000000:9:222222222.2222222222222222222222222222222^ 3000000000:9:333333333.3333333333333333333333333333333^ 4000000000:9:444444444.4444444444444444444444444444444^ 5000000000:9:555555555.5555555555555555555555555555556^ 6000000000:9:666666666.6666666666666666666666666666667^ 7000000000:9:777777777.7777777777777777777777777777778^ 8000000000:9:888888888.8888888888888888888888888888889^ 9000000000:9:1000000000 35500000:113:314159.2920353982300884955752212389380531^ 71000000:226:314159.2920353982300884955752212389380531^ 106500000:339:314159.2920353982300884955752212389380531^ 1000000000:3:333333333.3333333333333333333333333333333^ +10:+5:2 +100:+4:25 +1000:+8:125 +10000:+16:625 999999999999:9:111111111111 999999999999:99:10101010101 999999999999:999:1001001001 999999999999:9999:100010001 999999999999999:99999:10000100001 +1111088889:99999:11111 -5:-3:1.666666666666666666666666666666666666667^ -5:3:-1.666666666666666666666666666666666666667^ 4:3:1.333333333333333333333333333333333333333^ 4:-3:-1.333333333333333333333333333333333333333^ 1:3:0.3333333333333333333333333333333333333333^ 1:-3:-0.3333333333333333333333333333333333333333^ -2:-3:0.6666666666666666666666666666666666666667^ -2:3:-0.6666666666666666666666666666666666666667^ 8:5:1.6^ -8:5:-1.6^ 14:-3:-4.666666666666666666666666666666666666667^ -14:3:-4.666666666666666666666666666666666666667^ -14:-3:4.666666666666666666666666666666666666667^ 14:3:4.666666666666666666666666666666666666667^ # bug in Calc with '99999' vs $BASE-1 #10000000000000000000000000000000000000000000000000000000000000000000000000000000000:10000000375084540248994272022843165711074:999999962491547381984643365663244474111576 12:24:0.5^ &bmod # inf handling, see table in doc 0:inf:0 0:-inf:0 5:inf:5 5:-inf:-inf -5:inf:inf -5:-inf:-5 inf:5:NaN -inf:5:NaN inf:-5:NaN -inf:-5:NaN 5:5:0 -5:-5:0 inf:inf:NaN -inf:-inf:NaN -inf:inf:NaN inf:-inf:NaN 8:0:8 inf:0:inf -inf:0:-inf -8:0:-8 0:0:0 abc:abc:NaN abc:1:abc:NaN 1:abc:NaN 0:1:0 1:0:1 0:-1:0 -1:0:-1 1:1:0 -1:-1:0 1:-1:0 -1:1:0 1:2:1 2:1:0 1000000000:9:1 2000000000:9:2 3000000000:9:3 4000000000:9:4 5000000000:9:5 6000000000:9:6 7000000000:9:7 8000000000:9:8 9000000000:9:0 35500000:113:33 71000000:226:66 106500000:339:99 1000000000:3:1 10:5:0 100:4:0 1000:8:0 10000:16:0 999999999999:9:0 999999999999:99:0 999999999999:999:0 999999999999:9999:0 999999999999999:99999:0 -9:+5:1 +9:-5:-1 -9:-5:-4 -5:3:1 -2:3:1 4:3:1 1:3:1 -5:-3:-2 -2:-3:-2 4:-3:-2 1:-3:-2 4095:4095:0 100041000510123:3:0 152403346:12345:4321 9:5:4 &bgcd abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:0 +0:+1:1 +1:+0:1 +1:+1:1 +2:+3:1 +3:+2:1 -3:+2:1 100:625:25 4096:81:1 1034:804:2 27:90:56:1 27:90:54:9 &blcm abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:0 +1:+0:0 +0:+1:0 +27:+90:270 +1034:+804:415668 &band abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:0 3:2:2 +8:+2:0 +281474976710656:0:0 +281474976710656:1:0 +281474976710656:+281474976710656:281474976710656 -2:-3:-4 -1:-1:-1 -6:-6:-6 -7:-4:-8 -7:4:0 -4:7:4 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0x0xFFFF 0xFFFFFF:0xFFFFFF:0x0xFFFFFF 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0x0xF0F0 0x0F0F:0x0F0F:0x0x0F0F 0xF0F0F0:0xF0F0F0:0x0xF0F0F0 0x0F0F0F:0x0F0F0F:0x0x0F0F0F 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F 0x1F0F0F0F0F0F:0x3F0F0F0F0F0F:0x0x1F0F0F0F0F0F &bior abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:3 +8:+2:10 +281474976710656:0:281474976710656 +281474976710656:1:281474976710657 +281474976710656:281474976710656:281474976710656 -2:-3:-1 -1:-1:-1 -6:-6:-6 -7:4:-3 -4:7:-1 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0x0xFFFF 0xFFFFFF:0xFFFFFF:0x0xFFFFFF 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0:0xFFFF:0x0xFFFF 0:0xFFFFFF:0x0xFFFFFF 0:0xFFFFFFFF:0x0xFFFFFFFF 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xFFFF:0:0x0xFFFF 0xFFFFFF:0:0x0xFFFFFF 0xFFFFFFFF:0:0x0xFFFFFFFF 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0x0xF0F0 0x0F0F:0x0F0F:0x0x0F0F 0xF0F0:0x0F0F:0x0xFFFF 0xF0F0F0:0xF0F0F0:0x0xF0F0F0 0x0F0F0F:0x0F0F0F:0x0x0F0F0F 0x0F0F0F:0xF0F0F0:0x0xFFFFFF 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF 0x1F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF &bxor abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:3 +8:+2:10 +281474976710656:0:281474976710656 +281474976710656:1:281474976710657 +281474976710656:281474976710656:0 -2:-3:3 -1:-1:0 -6:-6:0 -7:4:-3 -4:7:-5 4:-7:-3 -4:-7:5 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0 0xFFFFFF:0xFFFFFF:0 0xFFFFFFFF:0xFFFFFFFF:0 0xFFFFFFFFFF:0xFFFFFFFFFF:0 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0 0:0xFFFF:0x0xFFFF 0:0xFFFFFF:0x0xFFFFFF 0:0xFFFFFFFF:0x0xFFFFFFFF 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xFFFF:0:0x0xFFFF 0xFFFFFF:0:0x0xFFFFFF 0xFFFFFFFF:0:0x0xFFFFFFFF 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0 0x0F0F:0x0F0F:0 0xF0F0:0x0F0F:0x0xFFFF 0xF0F0F0:0xF0F0F0:0 0x0F0F0F:0x0F0F0F:0 0x0F0F0F:0xF0F0F0:0x0xFFFFFF 0xF0F0F0F0:0xF0F0F0F0:0 0x0F0F0F0F:0x0F0F0F0F:0 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF 0xF0F0F0F0F0:0xF0F0F0F0F0:0 0x0F0F0F0F0F:0x0F0F0F0F0F:0 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF &bnot abc:NaN +0:-1 +8:-9 +281474976710656:-281474976710657 -1:0 -2:1 -12:11 &digit 0:0:0 12:0:2 12:1:1 123:0:3 123:1:2 123:2:1 123:-1:1 123:-2:2 123:-3:3 123456:0:6 123456:1:5 123456:2:4 123456:3:3 123456:4:2 123456:5:1 123456:-1:1 123456:-2:2 123456:-3:3 100000:-3:0 100000:0:0 100000:1:0 &mantissa abc:NaN 1e4:1 2e0:2 123:123 -1:-1 -2:-2 +inf:inf -inf:-inf &exponent abc:NaN 1e4:4 2e0:0 123:0 -1:0 -2:0 0:0 +inf:inf -inf:inf &parts abc:NaN,NaN 1e4:1,4 2e0:2,0 123:123,0 -1:-1,0 -2:-2,0 0:0,0 +inf:inf,inf -inf:-inf,inf &bfac -1:NaN NaNfac:NaN +inf:inf -inf:NaN 0:1 1:1 2:2 3:6 4:24 5:120 6:720 10:3628800 11:39916800 12:479001600 &bdfac NaN:NaN -1:NaN +inf:inf -inf:NaN 0:1 1:1 2:2 3:3 4:8 5:15 6:48 7:105 8:384 9:945 10:3840 11:10395 12:46080 &bpow abc:12:NaN 12:abc:NaN 0:0:1 0:1:0 0:2:0 0:-1:inf 0:-2:inf 1:0:1 1:1:1 1:2:1 1:3:1 1:-1:1 1:-2:1 1:-3:1 2:0:1 2:1:2 2:2:4 2:3:8 3:3:27 2:-1:0.5^ -2:-1:-0.5^ 2:-2:0.25^ # Y is even => result positive -2:-2:0.25^ # Y is odd => result negative -2:-3:-0.125^ +inf:1234500012:inf -inf:1234500012:inf -inf:1234500013:-inf +inf:-12345000123:inf -inf:-12345000123:-inf # 1 ** -x => 1 / (1 ** x) -1:0:1 -2:0:1 -1:1:-1 -1:2:1 -1:3:-1 -1:4:1 -1:5:-1 -1:-1:-1 -1:-2:1 -1:-3:-1 -1:-4:1 -2:2:4 -2:3:-8 -2:4:16 -2:5:-32 -3:2:9 -3:3:-27 -3:4:81 -3:5:-243 10:2:100 10:3:1000 10:4:10000 10:5:100000 10:6:1000000 10:7:10000000 10:8:100000000 10:9:1000000000 10:20:100000000000000000000 123456:2:15241383936 #2:0.5:1.41^ &length 100:3 10:2 1:1 0:1 12345:5 10000000000000000:17 -123:3 215960156869840440586892398248:30 # broot always upgrades &broot 144:2:12^ 123:2:11.09053650640941716205160010260993291846^ # bsqrt always upgrades &bsqrt 145:12.04159457879229548012824103037860805243^ 144:12^ 143:11.95826074310139802112984075619561661399^ 16:4 170:13.03840481040529742916594311485836883306^ 169:13 168:12.96148139681572046193193487217599331541^ 4:2 3:1.732050807568877293527446341505872366943^ 2:1.41421356237309504880168872420969807857^ 9:3 12:3.464101615137754587054892683011744733886^ 256:16 100000000:10000 4000000000000:2000000 152399026:12345.00004050222755607815159966235881398^ 152399025:12345 152399024:12344.99995949777231103967404745303741942^ 1:1 0:0 -2:NaN -123:NaN Nan:NaN +inf:inf -inf:NaN &bround $round_mode('trunc') 0:12:0 NaNbround:12:NaN +inf:12:inf -inf:12:-inf 1234:0:1234 1234:2:1200 123456:4:123400 123456:5:123450 123456:6:123456 +10123456789:5:10123000000 -10123456789:5:-10123000000 +10123456789:9:10123456700 -10123456789:9:-10123456700 +101234500:6:101234000 -101234500:6:-101234000 #+101234500:-4:101234000 #-101234500:-4:-101234000 $round_mode('zero') +20123456789:5:20123000000 -20123456789:5:-20123000000 +20123456789:9:20123456800 -20123456789:9:-20123456800 +201234500:6:201234000 -201234500:6:-201234000 #+201234500:-4:201234000 #-201234500:-4:-201234000 +12345000:4:12340000 -12345000:4:-12340000 $round_mode('+inf') +30123456789:5:30123000000 -30123456789:5:-30123000000 +30123456789:9:30123456800 -30123456789:9:-30123456800 +301234500:6:301235000 -301234500:6:-301234000 #+301234500:-4:301235000 #-301234500:-4:-301234000 +12345000:4:12350000 -12345000:4:-12340000 $round_mode('-inf') +40123456789:5:40123000000 -40123456789:5:-40123000000 +40123456789:9:40123456800 -40123456789:9:-40123456800 +401234500:6:401234000 +401234500:6:401234000 #-401234500:-4:-401235000 #-401234500:-4:-401235000 +12345000:4:12340000 -12345000:4:-12350000 $round_mode('odd') +50123456789:5:50123000000 -50123456789:5:-50123000000 +50123456789:9:50123456800 -50123456789:9:-50123456800 +501234500:6:501235000 -501234500:6:-501235000 #+501234500:-4:501235000 #-501234500:-4:-501235000 +12345000:4:12350000 -12345000:4:-12350000 $round_mode('even') +60123456789:5:60123000000 -60123456789:5:-60123000000 +60123456789:9:60123456800 -60123456789:9:-60123456800 +601234500:6:601234000 -601234500:6:-601234000 #+601234500:-4:601234000 #-601234500:-4:-601234000 #-601234500:-9:0 #-501234500:-9:0 #-601234500:-8:0 #-501234500:-8:0 +1234567:7:1234567 +1234567:6:1234570 +12345000:4:12340000 -12345000:4:-12340000 &is_zero 0:1 NaNzero:0 +inf:0 -inf:0 123:0 -1:0 1:0 &is_one 0:0 NaNone:0 +inf:0 -inf:0 1:1 2:0 -1:0 -2:0 # floor and ceil are pretty pointless in integer space, but play safe &bfloor 0:0 NaNfloor:NaN +inf:inf -inf:-inf -1:-1 -2:-2 2:2 3:3 abc:NaN &bceil NaNceil:NaN +inf:inf -inf:-inf 0:0 -1:-1 -2:-2 2:2 3:3 abc:NaN &bint NaN:NaN +inf:inf -inf:-inf 0:0 -1:-1 -2:-2 2:2 3:3 &to_hex 128:80 -128:-80 0:0 -0:0 1:1 0x123456789123456789:123456789123456789 +inf:inf -inf:-inf NaNto_hex:NaN &to_oct 128:200 -128:-200 0:0 -0:0 1:1 0b1010111101010101010110110110110110101:1275252666665 0x123456789123456789:44321263611044321263611 +inf:inf -inf:-inf NaNto_oct:NaN &to_bin 128:10000000 -128:-10000000 0:0 -0:0 1:1 0b1010111101010101010110110110110110101:1010111101010101010110110110110110101 +inf:inf -inf:-inf NaNto_bin:NaN &as_hex 128:0x80 -128:-0x80 0:0x0 -0:0x0 1:0x1 0x123456789123456789:0x123456789123456789 +inf:inf -inf:-inf NaNas_hex:NaN &as_bin 128:0b10000000 -128:-0b10000000 0:0b0 -0:0b0 1:0b1 0b1010111101010101010110110110110110101:0b1010111101010101010110110110110110101 +inf:inf -inf:-inf NaNas_bin:NaN &as_oct 128:0200 -128:-0200 0:00 -0:00 1:01 0b1010111101010101010110110110110110101:01275252666665 0x123456789123456789:044321263611044321263611 +inf:inf -inf:-inf NaNas_oct:NaN Math-BigInt-1.999808/t/upgrade.t0000644403072340010010000000115513031743706016423 0ustar ospjadomain users#!/usr/bin/perl use strict; use warnings; use Test::More tests => 2196 # tests in require'd file + 2; # tests in this file use Math::BigInt upgrade => 'Math::BigFloat'; use Math::BigFloat; our ($CLASS, $EXPECTED_CLASS, $CALC); $CLASS = "Math::BigInt"; $EXPECTED_CLASS = "Math::BigFloat"; $CALC = "Math::BigInt::Calc"; # backend is(Math::BigInt->upgrade(), "Math::BigFloat", qq/Math::BigInt->upgrade()/); is(Math::BigInt->downgrade() || "", "", qq/Math::BigInt->downgrade() || ""/); require 't/upgrade.inc'; # all tests here for sharing Math-BigInt-1.999808/t/upgrade2.t0000644403072340010010000000061412740677027016514 0ustar ospjadomain users#!/usr/bin/perl use strict; use warnings; # Test 2 levels of upgrade classes. This used to cause a segv. use Test::More tests => 1; use Math::BigInt upgrade => 'Math::BigFloat'; use Math::BigFloat upgrade => 'Math::BigMouse'; no warnings 'once'; @Math::BigMouse::ISA = 'Math::BigFloat'; () = sqrt Math::BigInt->new(2); pass('sqrt on a big int does not segv if there are 2 upgrade levels'); Math-BigInt-1.999808/t/upgradef.t0000644403072340010010000000336212740677027016603 0ustar ospjadomain users#!/usr/bin/perl use strict; use warnings; use Test::More tests => 6; ############################################################################### package Math::BigFloat::Test; use Math::BigFloat; require Exporter; our @ISA = qw/Exporter Math::BigFloat/; use overload; sub isa { my ($self, $class) = @_; return if $class =~ /^Math::Big(Int|Float)/; # we aren't one of these UNIVERSAL::isa($self, $class); } sub bmul { return __PACKAGE__->new(123); } sub badd { return __PACKAGE__->new(321); } ############################################################################### package main; # use Math::BigInt upgrade => 'Math::BigFloat'; use Math::BigFloat upgrade => 'Math::BigFloat::Test'; my ($x, $y, $z); our ($CLASS, $EXPECTED_CLASS, $CALC); $CLASS = "Math::BigFloat"; $EXPECTED_CLASS = "Math::BigFloat::Test"; $CALC = "Math::BigInt::Calc"; # backend is(Math::BigFloat->upgrade(), $EXPECTED_CLASS, qq|Math::BigFloat->upgrade()|); is(Math::BigFloat->downgrade() || '', '', qq/Math::BigFloat->downgrade() || ''/); $x = $CLASS->new(123); $y = $EXPECTED_CLASS->new(123); $z = $x->bmul($y); is(ref($z), $EXPECTED_CLASS, qq|\$x = $CLASS->new(123); \$y = $EXPECTED_CLASS->new(123);| . q| $z = $x->bmul($y); ref($z)|); is($z, 123, qq|\$x = $CLASS->new(123); \$y = $EXPECTED_CLASS->new(123);| . q| $z = $x->bmul($y); $z|); $x = $CLASS->new(123); $y = $EXPECTED_CLASS->new(123); $z = $x->badd($y); is(ref($z), $EXPECTED_CLASS, qq|$x = $CLASS->new(123); $y = $EXPECTED_CLASS->new(123);| . q| $z = $x->badd($y); ref($z)|); is($z, 321, qq|$x = $CLASS->new(123); $y = $EXPECTED_CLASS->new(123);| . q| $z = $x->badd($y); $z|); # not yet: #require 't/upgrade.inc'; # all tests here for sharing Math-BigInt-1.999808/t/use.t0000644403072340010010000000064512740677027015603 0ustar ospjadomain users#!/usr/bin/perl # use Module(); doesn't call import() - thanx for cpan testers David. M. Town # and Andreas Marcel Riechert for spotting it. It is fixed by the same code # that fixes require Math::BigInt, but we make a test to be sure it really # works. use strict; use warnings; use Test::More tests => 1; my $x; use Math::BigInt (); $x = Math::BigInt->new(1); ++$x; is($x, 2, '$x = Math::BigInt->new(1); ++$x;'); Math-BigInt-1.999808/t/use_lib1.t0000644403072340010010000000064013014573331016471 0ustar ospjadomain users#!/usr/bin/perl # see if using Math::BigInt and Math::BigFloat works together nicely. # all use_lib*.t should be equivalent use strict; use warnings; use Test::More tests => 2; use lib 't'; use Math::BigFloat lib => 'BareCalc'; is(Math::BigInt->config('lib'), 'Math::BigInt::BareCalc', "Math::BigInt->config('lib')"); is(Math::BigFloat->new(123)->badd(123), 246, 'Math::BigFloat->new(123)->badd(123)'); Math-BigInt-1.999808/t/use_lib2.t0000644403072340010010000000066213014573354016503 0ustar ospjadomain users#!/usr/bin/perl # see if using Math::BigInt and Math::BigFloat works together nicely. # all use_lib*.t should be equivalent use strict; use warnings; use Test::More tests => 2; use lib 't'; use Math::BigInt; use Math::BigFloat lib => 'BareCalc'; is(Math::BigInt->config('lib'), 'Math::BigInt::BareCalc', "Math::BigInt->config('lib')"); is(Math::BigFloat->new(123)->badd(123), 246, 'Math::BigFloat->new(123)->badd(123)'); Math-BigInt-1.999808/t/use_lib3.t0000644403072340010010000000066213014573371016503 0ustar ospjadomain users#!/usr/bin/perl # see if using Math::BigInt and Math::BigFloat works together nicely. # all use_lib*.t should be equivalent use strict; use warnings; use Test::More tests => 2; use lib 't'; use Math::BigInt lib => 'BareCalc'; use Math::BigFloat; is(Math::BigInt->config('lib'), 'Math::BigInt::BareCalc', "Math::BigInt->config('lib')"); is(Math::BigFloat->new(123)->badd(123), 246, 'Math::BigFloat->new(123)->badd(123)'); Math-BigInt-1.999808/t/use_lib4.t0000644403072340010010000000077613014573404016507 0ustar ospjadomain users#!/usr/bin/perl # see if using Math::BigInt and Math::BigFloat works together nicely. # all use_lib*.t should be equivalent, except this, since the later overrides # the former lib statement use strict; use warnings; use lib 't'; use Test::More tests => 2; use Math::BigInt lib => 'BareCalc'; use Math::BigFloat lib => 'Calc'; is(Math::BigInt->config('lib'), 'Math::BigInt::Calc', "Math::BigInt->config('lib')"); is(Math::BigFloat->new(123)->badd(123), 246, 'Math::BigFloat->new(123)->badd(123)'); Math-BigInt-1.999808/t/use_mbfw.t0000644403072340010010000000176513015016252016601 0ustar ospjadomain users#!perl # check that using Math::BigFloat with "with" and "lib" at the same time works # broken in versions up to v1.63 use strict; use warnings; use lib 't'; use Test::More tests => 2; # the replacement lib can handle the lib statement, but it could also ignore it # completely, for instance, when it is a 100% replacement for Math::BigInt, but # doesn't know the concept of alternative libs. But it still needs to cope with # "lib => ". SubClass does record it, so we test here essential if # Math::BigFloat hands the lib properly down, any more is outside out testing # reach. use Math::BigFloat with => 'Math::BigInt::Subclass', lib => 'BareCalc'; is(Math::BigFloat->config()->{with}, 'Math::BigInt::BareCalc', "Math::BigFloat->config()->{with}"); # is($Math::BigInt::Subclass::lib, 'BareCalc'); # it never arrives here, but that is a design decision in SubClass is(Math::BigInt->config()->{lib}, 'Math::BigInt::BareCalc', 'Math::BigInt->config()->{lib}'); # all tests done Math-BigInt-1.999808/t/with_sub.t0000644403072340010010000000114313031667225016616 0ustar ospjadomain users#!perl # Test use Math::BigFloat with => 'Math::BigInt::SomeSubclass'; use strict; use warnings; use Test::More tests => 2436 # tests in require'd file + 1; # tests in this file use Math::BigFloat with => 'Math::BigInt::Subclass', lib => 'Calc'; our ($CLASS, $CALC); $CLASS = "Math::BigFloat"; $CALC = "Math::BigInt::Calc"; # backend # the "with" argument should be ignored is(Math::BigFloat->config()->{with}, 'Math::BigInt::Calc', "Math::BigFloat->config()->{with}"); require 't/bigfltpm.inc'; # all tests here for sharing Math-BigInt-1.999808/t/_e_math.t0000644403072340010010000000571212740677022016376 0ustar ospjadomain users#!perl # test the helper math routines in Math::BigFloat use strict; use warnings; use Test::More tests => 26; use Math::BigFloat lib => 'Calc'; ############################################################################# # add { my $a = Math::BigInt::Calc->_new("123"); my $b = Math::BigInt::Calc->_new("321"); test_add(123, 321, '+', '+'); test_add(123, 321, '+', '-'); test_add(123, 321, '-', '+'); test_add(321, 123, '-', '+'); test_add(321, 123, '+', '-'); test_add(10, 1, '+', '-'); test_add(10, 1, '-', '+'); test_add( 1, 10, '-', '+'); SKIP: { skip q|$x -> _zero() does not (yet?) modify the first argument|, 2; test_add(123, 123, '-', '+'); test_add(123, 123, '+', '-'); } test_add(123, 123, '+', '+'); test_add(123, 123, '-', '-'); test_add(0, 0, '-', '+'); test_add(0, 0, '+', '-'); test_add(0, 0, '+', '+'); test_add(0, 0, '-', '-'); # gives "-0"! TODO: fix this! } ############################################################################# # sub { my $a = Math::BigInt::Calc->_new("123"); my $b = Math::BigInt::Calc->_new("321"); test_sub(123, 321, '+', '-'); test_sub(123, 321, '-', '+'); test_sub(123, 123, '-', '+'); test_sub(123, 123, '+', '-'); SKIP: { skip q|$x -> _zero() does not (yet?) modify the first argument|, 2; test_sub(123, 123, '+', '+'); test_sub(123, 123, '-', '-'); } test_sub(0, 0, '-', '+'); # gives "-0"! TODO: fix this! test_sub(0, 0, '+', '-'); test_sub(0, 0, '+', '+'); test_sub(0, 0, '-', '-'); } ############################################################################### sub test_add { my ($a, $b, $as, $bs) = @_; my $aa = Math::BigInt::Calc -> _new($a); my $bb = Math::BigInt::Calc -> _new($b); my ($x, $xs) = Math::BigFloat::_e_add($aa, $bb, "$as", "$bs"); my $got = $xs . Math::BigInt::Calc->_str($x); my $expected = sprintf("%+d", "$as$a" + "$bs$b"); subtest qq|Math::BigFloat::_e_add($a, $b, "$as", "$bs");| => sub { plan tests => 2; is($got, $expected, 'output has the correct value'); is(Math::BigInt::Calc->_str($x), Math::BigInt::Calc->_str($aa), 'first operand to _e_add() is modified' ); }; } sub test_sub { my ($a, $b, $as, $bs) = @_; my $aa = Math::BigInt::Calc -> _new($a); my $bb = Math::BigInt::Calc -> _new($b); my ($x, $xs) = Math::BigFloat::_e_sub($aa, $bb, "$as", "$bs"); my $got = $xs . Math::BigInt::Calc->_str($x); my $expected = sprintf("%+d", "$as$a" - "$bs$b"); subtest qq|Math::BigFloat::_e_sub($a, $b, "$as", "$bs");| => sub { plan tests => 2; is($got, $expected, 'output has the correct value'); is(Math::BigInt::Calc->_str($x), Math::BigInt::Calc->_str($aa), 'first operand to _e_sub() is modified' ); }; } Math-BigInt-1.999808/TODO0000644403072340010010000000510313024044363015024 0ustar ospjadomain usersThe following list is not up to date: See also various .pm files. General: * Copy on write (helps for $x = -$x; cases etc) (seems to make it slower :/ * run config() and die_on_nan() tests under Subclass.pm Math::BigFloat: * finish upgrading and downgrading * ! bround()/bfround(): some bugs may lurk in there * accuracy() & precision() maybe not finished (bnorm() in every op, testcases) * do not reduce numbers in new(), rather do it in anything that outputs it like bsstr(), bstr(), mantissa(), exponent() and parts(). Reducing the number after each op is slow with a binary core math lib like BitVect. * add bfract() that returns just the fractional part? * tests for frsft() and flsft() with $n != 2 * blog() is still quite slow for non-integer results. See if we can reuse the integer calculation somehow * finish broot() by using different algorithm Math::BigInt: * finish 'upgrade' * remove rounding overhead when no rounding is done, e.g. no $object has A nor P and neither of bround(), bround(), accuracy() or precision() was called * bround() is only used by MBF for -$scale = -$len, anyway. POD is wrong for this, too * overload of cos()/sin()/exp()/atan2() is too DWIM (should return BigInt or BigFloat, not scalar) - also document it * +5 % 0 or -5 % 0 == NaN (should it be something else?) * certain shortcuts returning bzero(), bone() etc may not set the requested rounding parameters, so that $x->foo($y,$a,$p,$r) may return $x without a set $a or $p, thus failing later on: use Test; BEGIN { plan tests => 1; } use Math::BigInt; $x = Math::BigInt->bone(); $x->bsqrt(3,0,'odd'); # $x = 0, but _a is not 3! ok ($x + '12345','12300'); # fails (12346 instead of 12300) The shortcuts in code that return $x->bzero() or similar things need to do $x->bzero($a,$p); and this needs tests. Update: Should now work for most things. Check for completeness. Given the fact that we are be able to plug-in a much faster core-lib, the following are pretty much ultra-low-priority: Math::BigInt::Calc: * look at div() for more speed (I have the hunch that the general _div() routine does way too much work for normal div (e.g. when we don't need the reminder). A simplified version could take care of this. * alternative mul() method using shifts * implement in Calc (and GMP etc) to calculate band(), bior(), bxor() for negative inputs (_signed_or() etc) * _root() doesn't scale too well Please send me test-reports, your experiences with this and your ideas - I love to hear about my work!