Blame CHANGES

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2017-03-15 v1.999811 pjacklam
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 * Fix an old in the Math::BigFloat methods as_hex(), as_oct(), and as_bin()
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   methods resulting in loss of accuracy. This bug was introduced in bug in
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   Math-BigInt-1.76. Due to a naive copy and paste by me, and lack of tests,
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   this bug was also present in the newer to_hex(), to_oct(), and to_bin()
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   methods. This shows the bug, as it did not print "0xffff...":
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       print Math::BigFloat -> from_hex("f" x 30) -> as_hex();
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 * Fix incorrect formatting in the output from the Math::BigFloat methods
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   to_hex(), to_oct(), and to_bin() when the output was zero. A prefix was
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   added when it shouldn't have been.
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 * Add tests to bigintpm.inc and bigfltpm.inc for better testing of as_hex(),
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   as_oct(), and as_bin() as well as to_hex(), to_oct(), and to_bin().
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 * "Synchronize" tests and code formatting in bigintpm.inc and bigfltpm.inc.
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2017-03-01 v1.999810 pjacklam
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 * CPAN RT #120240 revealed that the problems with undefined values is still
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   present. After a close examination, I believe the only way to get this
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   really working is to to make blog() call objectify() differently depending
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   on whether the base for the logarithm is undefined or not. That way we can
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   avoid objectify() converting the undefined value to a zero. Ideally, we
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   should warn about undefined values when used in any other context, but we'll
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   handle that in a later release. See also the related changelog entry for
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   v1.999801.
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 * Fix the way the argument count is computed in objectify(). When an argument
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   count of 0 is given, it means that we should objectify all input arguments.
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   However, it turned out that the actual argument count was computed
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   incorrectly.
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 * Fix CPAN RT #120242 rearding c3 method resolution.
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2017-02-10 v1.999809 pjacklam
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 * When a new method is added to Math::BigInt or Math::BigFloat, and this new
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   method requires a new backend library method, die with a suitable error
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   message if the installed backend library does not support this new method.
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   The error message says that the method requires a newer version of the
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   backend library.
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 * Fix typos in Math::BigFloat and Math::BigInt.
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 * Add bfib() and blucas() to Math::BigInt. They return Fibonacci and Lucas
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   numbers, respectively. The actual computation of the numbers is done by the
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   backend library. Documented both methods in POD. Add test files bfib-mbi.t
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   and blucas-mbi.t.
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 * Add _fib() and _lucas() to Math::BigInt::Lib. They return Fibonacci and
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   Lucas numbers, respectively. Document both methods in POD. Add test files
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   author-lib-arithmetic-unary-_fib.t and author-lib-arithmetic-unary-_lucas.t.
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2017-01-11 v1.999808 pjacklam
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 * In Math::BigInt and Math::BigFloat, add methods bdfac() for double
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   factorial. Add tests for this method.
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 * In Math::BigInt and Math::BigFloat, add methods to_hex(), to_oct(), and
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   to_bin() for hexadecimal, octal, and binary string output without prefix.
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   Even for Math::BigFloat there is still only support for integer output. Add
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   tests for these methods.
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 * Add test for as_oct() corresponding to the old tests for as_hex() and
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   as_bin().
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 * In Math::BigInt::Lib, add method _dfac() for double factorial. Add
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   corresponding tests.
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 * In Math::BigInt::Lib, fix bug in overloaded "int".
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 * In Math::BigInt::Lib, implement much faster versions of _from_hex(),
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   _from_oct(), and _from_bin().
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 * In Makefile.PL, improve the wording in the message displayed if some of
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   the installed backend libraries are not a subclass of Math::BigInt::Lib (and
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   hence will not provide
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 * Fix minor bugs in some of the author library test files (t/author-lib*.t).
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 * Allow leading and trailing whitespace in the input to from_hex(),
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   from_oct(), and from_bin().  Add tests to verify. This is a regressions
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   (CPAN RT #119805).
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2016-12-23 v1.999807 pjacklam
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 * Add a message to Makefile.PL recommending upgrade if old libraries are
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   installed. This message is more or less equivalent to the one appearing in
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   Math-BigInt up until v1.997.
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 * Improve the documentation (POD) in Math::BigInt::Lib.
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 * Speed up _sqrt() and _root() in Math::BigInt::Lib.
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 * Remove checking for exception cases (cases that would return +Inf, -Inf, or
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   NaN) in Math::BigInt::Lib. It has been documented for a long time that such
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   checking should be done by the caller.
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 * Add library methods _to_bin(), _to_oct(), _to_hex(), which are equivalent to
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   the _as_bin(), _as_oct(), and _as_hex() methods respectively, except that
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   the _to_*() methods don't use a prefix in the output. This removes the need
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   for the frequent removal of the various prefixes. Now each _as_*() method
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   calls the equivalent _to_*() method, adds a prefix, and returns the output.
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   The _to_*() methods are faster than the equivalent _as_*() methods were.
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 * Add author test files for the methods _to_bin(), _to_oct(), and _to_hex().
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 * Add library method _to_bytes(). The method _as_bytes() would have been
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   called _to_bytes() if I had thought of it earlier. The method _as_bytes() is
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   now just an alias to _to_bytes(). The _to_bytes() method also fixes a bug
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   that was present in the _as_bytes() method. (CPAN RT #119346).
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 * Add author test files for the method _to_bytes().
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 * Add more tests for library methods _inc() and _dec(). When trying to bring
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   the Math::BigInt::BitVect library back to life I realized that the test
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   suite didn't catch certain errors in _inc() and _dec().
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 * Die if trying to use as_bytes() or from_bytes() with a backend library that
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   doesn't support the corresponding library methods.
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 * Correct minor errors in the output messages in the test files.
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 * Improve/correct various comments in the source code.
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 * More diagnostic output is displayed by the author test files if the
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   AUTHOR_DEBUGGING environment variable is set.
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2016-12-13 v1.999806 pjacklam
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 * Add more logic to Makefile.PL regarding INSTALLDIRS (CPAN RT #119199
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   and #119225).
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 * In the TODO file, remove stuff that has been implemented.
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2016-12-11 v1.999805 pjacklam
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 * Fix Makefile.PL so that this module installs over the core version.
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 * Add more tests for _nok() (binomial coefficient "n over k"). These new tests
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   revealed some problems with some of the backend libraries when _nok() was
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   given very large arguments.
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 * Remove t/Math/BigFloat/#Subclass.pm#, which is an Emacs temporary file
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   included by accident.
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2016-12-07 v1.999804 pjacklam
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 * Implement as_bytes(), as requested (CPAN RT 119096). Also implement the
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   inverse conversion from_bytes(). This applies to Math::BigInt only. (Alas,
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   these methods will be inherited from Math::BigInt into Math::BigFloat,
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   Math::BigRat etc. where the methods won't work. Fixing this class
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   relationship is an issue of its own.)
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 * Implement _as_bytes() and _from_bytes() in Math::BigInt::Lib. Preferably,
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   the various backend libraries will implement faster versions of their
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   own. Add author test files for testing these methods thorougly.
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 * Fix from_hex(), from_oct(), and from_bin().
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   - When called as instance methods, the new value should be assigned to the
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     invocand unless the invocand is read-only (a constant).
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   - When called as instance methods, the assigned value was incorrect, if the
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     invocand was inf or NaN.
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   - Add tests to t/from_hex-mbf.t, t/from_oct-mbf.t, and t/from_bin-mbf.t
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     to confirm the fix.
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   - Add new test files t/from_hex-mbi.t, t/from_oct-mbi.t, and
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     t/from_bin-mbi.t for better testing of these methods with Math::BigInt.
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 * Correct typo in Math/BigInt/Lib.pm (otherise -> otherwise) (CPAN RT 118829).
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 * Add POD coverage testing of Math::BigInt::Lib to t/03podcov.t.
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2016-12-03 v1.999803 pjacklam
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 * Remove BENCHMARK file. The information was obsolete.
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 * Use ExtUtils::MakeMaker rather than Module::Install in Makefile.PL
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 * Reorder CHANGES file (this file) so the newest entries appear at the top.
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 * Fix error in test information text in various author test files.
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 * Remove author information in LICENSE file.
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 * Inform that the TODO file is not up to date.
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2016-11-28 v1.999802 pjacklam
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 * When bzero(), bone(), binf(), and bnan() are used as constructors, don't
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   check whether the class allows the object to be modified. A constructor
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   isn't modifying any existing object. This applies to both Math::BigInt and
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   Math::BigFloat.
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 * Improve bgcd() and blcm(). This applies to both Math::BigInt and
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   Math::BigFloat.
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2016-11-23 v1.999801 pjacklam
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 * Fix, hopefully once and for all, the longstanding problem of handling undef
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   as an operand to mathematical methods. The only method that accepts undef as
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   an operand is blog(), where the second operand might be undef, as in
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   $x->blog() or $x->blog($b), where $b is undef. The undef signifies that
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   Euler's number should be used as the base. With this fix, we should be able
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   to get Math::BigInt::Lite working again.
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 * Add least common multiple method _lcm() to Math::BigInt::Lib, and add
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   corresponding test file t/author-lib-arithmetic-binary-_lcm.t and test data
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   file t/author-lib-arithmetic-binary-_lcm.dat.
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 * Remove internal function __lcm() which has become redundant now that _lcm()
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   is in the library.
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 * Make it possible to use bgcd() and blcm() as class methods, since other
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   methods can be used as class methods. This applies to both Math::BigInt and
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   Math::BigFloat.
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 * Fix blcm() with negative input. The LCM should always be non-negative. This
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   applies to both Math::BigInt and Math::BigFloat.
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 * Add tests for bgcd() and blcm() in t/bigintpm.t and t/bigfltpm.t.
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 * Fix tests for blcm() assuming that LCM(0,0) should be a NaN. LCM(0,0) is 0
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   by convention.
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 * Prefer Class->config('option') over Class->config()->{option}. However, this
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   does not seem to be working for all options. It seems that this won't work
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   properly until we move the global variables into the OO interface.
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 * Explicitly specify the library in all test files that are shared between
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   Math-BigInt and the library distributions (FaatCalc, GMP, Pari, ...) with,
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   e.g., "use Math::BigInt only => 'Calc';". This way, it will fail immediately
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   if the specified library can't be loaded rather than using the fallback
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   library.
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2016-11-15 v1.999800 pjacklam
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 * Upgrade bundled Module::Install from version 1.16 to version 1.17.
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 * Add Math::BigInt::Lib (lib/Math/BigInt/Lib.pm), a parent class for
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   Math::BigInt backend libraries.
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 * Use objects in Math::BigInt::Calc, not just array refs. Also use OO-style,
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   i.e., use $class->_add($x, $y) rather than _add($class, $x, $y).
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 * Not all library methods modify the invocand, so call library methods as,
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   e.g, $x = $LIB->method($x, $y) rather than just $LIB->method($x, $y).
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 * Math::BigInt::Calc is now a subclass of Math::BigInt::Lib.
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 * Add Math::BigInt::Lib::Minimal (t/Math/BigInt/Lib/Minimal.pm) for testing
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   inheritance from Math::BigInt::Lib.
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 * Minor simplification in Math::BigInt::Calc->_str().
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 * Speed up Math::BigInt::Calc->_root().
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 * Remove test files that were included in the previous release by accident.
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 * Add more tests and use more verbose output in some tests.
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 * Fix typo in lib/Math/BigFloat.pm
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 * Fix documentation error in lib/Math/Calc.pm
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 * Use Config::Tiny and an .ini file to handle the library specific
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   configuration for the author-lib*.t test files.
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2016-11-04 v1.999727 pjacklam
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 * Skip test exceeding the range of VAX floating point number in t/bigintpm.inc
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   (CPAN RT 118468).
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 * Fix typo in lib/Math/BigInt.pm (CPAN RT 118550).
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2016-07-15 v1.999726 pjacklam
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 * Re-insert Math::BigFloat->DESTROY, which was accidentally removed in
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   v1.999725.
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2016-07-13 v1.999725 pjacklam
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Changes:
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 * Add method is_finite().
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 * In Math::BigInt and Math::BigFloat, remove warnings about deprecated usage,
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   at least until we have removed this usage from the "bignum" distribution.
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   These warnings were too annoying for some people.
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Improvements:
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 * Faster bnok() when the library (backend) does not support it.
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 * In the Math::BigFloat method bpi(), use a precomputed list of digits when
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   the accuracy is <= 1000. This speeds up the trigonometric functions
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   considerably, when I will introduce range reduction in a later release. This
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   makes the _atan_inv() method redundant, so remove it. Also, the _alen()
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   library method is now only used in _log_int(), which is good, because it
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   isn't clear from the docs and tests what it was supposed to do.
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Fixes:
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 * Fix bug in the Math::BigInt::Calc library method _digit(). It would
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   sometimes return undef or an empty string when it should have returned zero.
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 * Fix bug in the Math::BigInt::Calc library method _rsft(). It would sometimes
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   return two output arguments.
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 * Fix bug in the Math::BigInt::Calc library method _lsft(). When the number
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   zero was shifted N places in base 10, the result was not zero, but an
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   invalid object.
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 * Fix bug in the Math::BigInt::Calc library methods _and(), _or(), and _xor().
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   They always assigned zero to the first input argument (the invocand).
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 * Improve the Math::BigInt::Calc library method _log_int() for the cases when
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   the output is zero or one. Also simplify the code.
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 * Simplify the code for the Math::BigInt::Calc library method _zeros().
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 * Reformat Math::BigInt::Calc so it is easier to read, for me anyway.
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 * Add file t/author-bnok-mbi.t
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 * Add one test file for every method in the libraries, including
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   t/Math/BigInt/Lib/TestUtil.pm with test utilities.
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 * Clean up whitespace in all files in the distribution.
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 * Better testing in t/author-bpi-mbf.t
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 * The Math::BigInt::Calc library now always uses integers inside the objects,
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   so there is no longer any need for all the "0 + ..." to convert strings to
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   numbers, and the "int()" inside "length(int(...))" to determine the length
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   of an array element. The only case that needs "0 + ..." now is the
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   constructor _new(), whose input is a string.
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   Note, however, that the Math::BigInt::FastCalc library method _new() still
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   creates objects with leading zeros, so until that is fixed, we can't remove
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   all the "0 + ..." etc. until Math::BigInt::FastCalc has been modified.
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2016-06-19 v1.999724 pjacklam
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 * In Math/BigInt.pm and Math/BigFloat.pm, correct and improve to the
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   documentation, e.g., reorder the methods so that methods that belogin
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   together are grouped together.
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 * In Math/BigInt.pm and Math/BigFloat.pm, refactor the code so that methods
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   that belong together are grouped together. Also use consistent code
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   formatting.
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 * In Math/BigInt/Calc.pm, reformat the code.
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2016-06-09 v1.999723 pjacklam
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 * Add Math::BigInt and Math::BigFloat methods bnstr(), bestr(), and bdstr(),
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   as well as corresponding methods nparts(), eparts(), and dparts(). Also add
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   test files bdstr-mbf.t, bdstr-mbi.t, bestr-mbf.t, bestr-mbi.t, bnstr-mbf.t,
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   bnstr-mbi.t, bsstr-mbf.t, bsstr-mbi.t, dparts-mbf.t, dparts-mbi.t,
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   eparts-mbf.t, eparts-mbi.t, nparts-mbf.t, nparts-mbi.t, sparts-mbf.t, and
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   sparts-mbi.t.
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 * Fix documentation errors.
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2016-04-26 v1.999722 pjacklam
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 * Fix bug in bone() and binf() when used as a function. The error caused
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   warnings about using an unitialized variable. This fix applies to both
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   Math::BigInt and Math::BigFloat.
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2016-04-26 v1.999721 pjacklam
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 * Prevent Math::BigFloat methods band(), bior(), bxor(), and bnot() from
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   modifying unmodifiable objects.
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2016-04-26 v1.999720 pjacklam
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 * Overloaded 'int' should not modify it's argument.
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 * Better documentation of blsft() and brsft().
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2016-04-25 v1.999719 pjacklam
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 * Revert the change to Math::BigFloat's blsft() and brsft() methods, which
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   truncated the input (and output) to integers. However, now convert the base
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   to an object only when the base isn't an object already. Also return NaN if
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   any of the three operands is a NaN.
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 * Change t/bigfltpm.inc to reflect the changes to blsft() and brsft(). Also,
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   when a method should be tested, actually test that method, not the
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   overloaded operator, which doesn't necessarily behave in the exact same
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   manner as the method. This applies to the methods binc(), bdec(), bpow(),
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   badd(), bsub(), bmul(), bdiv() in scalar context, brsft(), blsft(), and
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   bmod().
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 * The first output argument from objectify() is the class name, so use the
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   variable name $class, not $self.
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2016-04-22 v1.999718 pjacklam
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 * Improve documentation on large, unquoted input values to Math::BigInt.
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 * Remove stuff from bitfltpm.inc that was placed into author-numify-mbf.t, but
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   accidentally still present in bitfltpm.inc. Adjusted test counts as needed.
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 * Fix file headers in author-bmod-bdiv-mbi.t and author-btmod-btdiv-mbi.t.
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 * Add bnan(), binf(), and bsub() methods to Math::BigFloat. This is a step
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   along the way to having Math::BigFloat no longer being a subclass of
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   Math::BigInt.
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 * Using bnan, binf(), bzero() and bone() as functions is deprecated. This is a
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   step along the way to a pure object oriented design.
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 * When bnan() and binf() are used as instance methods, they no longer delete
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   the accuracy and precision instance variables.
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 * Add test files from_bin-mbf.t, from_oct-mbf.t, and new-mbf.t.
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 * Remove some code for Perl prior to 5.6. Such old versions are no longer
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   support anyway.
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 * Fix buggy handling of NaN in bcmp().
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 * Add methods beq(), bne(), blt(), ble(), bgt(), and bge() to Math::BigInt and
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   Math::BigFloat. These methods are called for the overloaded operators.
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 * Add overloading of '==', '!=', '<', '<=', '>', to to Math::BigInt and
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   Math::BigFloat and fix the broken overloading of '>='. These overloaded
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   operators now behave like the equivalent core Perl operators.
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 * Add test file author-relop-mbi-mbf.t for testing bcmp(), beq(), bne(),
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   blt(), ble(), bgt(), and bge(), as well as the overloaded operators '==',
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   '!=', '<', '<=', '>', and '>='.
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 * 'int' now truncates a Math::BigFloat object to an integer without converting
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   it to a Math::BigInt. When an object becomes a Math::BigInt, further
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   computations with that object as invocand causes the arguments to be
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   converted to Math::BigInt objects too, leading to unexpected results. This
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   is confusing people. Unless downgrading is in effect, no Math::BigFloat
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   object should become a Math::BigInt unless a Math::BigInt is explicitly
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   requested.
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 * For Math::BigFloat, modify bitwise operations brsft() and brsft(), and add
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   band(), bior(), bxor(), and bnot(). These now handle floating point numbers
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   the same way as core Perl does, i.e., truncate non-integers to integers
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   before applying the bitwise operator. This change will also make Perl's
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   behaviour more consistent whether 'use bignum' is in effect or not.
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 * Add overloading of '~' (bitwise not). It just calls bnot(), which has been
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   implemented for ages.
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 * Fix error in POD for bone().
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 * Take parts of the code in t/calling.t and move it into the new files
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   t/calling-class-methods.t and t/calling-instance-methods.t.
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 * Improve test descriptions in t/mbimbf.inc.
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2016-04-16 v1.999717 pjacklam
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 * Using new() with an undefined argument no longer gives a warning. Explicit
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   use of this is discouraged, but it is sometimes used by the modules
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   themselves issuing warnings that is confusing to the end user. Just
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   uncomment the code, since we plan to reintroduce this warning later.
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 * Avoid using L<> around e-mail addressess in POD.
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2016-04-03 v1.999716 pjacklam
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 * $x->new(...) can no longer be used to assign a value to $x. This was a
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   mistake introduced in v1.999712. As the name "new" implies, it should always
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   return a new object.
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 * Using new() with no argument no longer gives a warning. This use has been
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   discouraged, in favour of bzero(), for many years, but people are still
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   using it, so I am reintroducing the support for this.
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 * Added btdiv() and btmod() for truncated division (T-division) and ditto
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   remainder. Add tests.
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 * Add test files author-bmod-bdiv-mbi.t author-btmod-btdiv-mbi.t with more
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   thorough testing of bdiv(), bmod(), btdiv(), and btmod().
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 * When new() is used as an instance method, the new object is initialized as a
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   copy of the invocand.
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 * Move test for numfiy() of +Inf, -Inf, NaN, and big integers from
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   bigfltpm.inc and bigintpm.inc into author-numify-mbi.t and
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   author-numify-mbf.t.
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 * Improved wording and fixed typos in earlier changelog entries.
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2016-01-05 v1.999715 pjacklam
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 * Fix Math::BigFloat->bexp() based on patch by DANAJ (Dana Jacobsen).
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 * Add Math::BigFloat->bexp() tests to "t/biglog.t" and new file
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   "t/author-bexp-mbf.t".
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 * Fix flawed test in test_bpow. It used ok($x, $y) rather than is($x, $y).
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 * Add better descriptions (test names) to a few tests.
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 * Wrap long line in the CHANGES file.
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2016-01-03 v1.999714 pjacklam
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 * Add code to speed up Math::BigFloat->batan(). Thanks to DANAJ (Dana
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   Jacobsen) for the patch.
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 * Re-write Math::BigFloat->batan2() completely, except for the parts related
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   to the rounding. The old version was sometimes correct, sometimes off by pi,
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   and sometimes very inaccurate. Also add more tests.
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 * Make it clearer in Math::BigFloat->bpi() when it is called as a method vs.
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   as a function.
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 * The Math::BigFloat->bpi() method can now be used as an instance method to
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   assign pi to $x, as in $x->bpi().
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 * Add tests for as_oct().
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 * Minor simplifications in Math::BigInt->as_oct() and
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   Math::BigInt::Calc::_as_oct().
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2015-12-31 v1.999713 pjacklam
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 * Fix Math::BigInt->new(), which had a faulty handling in the shortcut for
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   non-zero scalar integers with no non-zero exponent, like "12", "12.000",
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   "12e3", and "12.000e4". Added tests for this in t/bigintpm.inc.
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2015-12-29 v1.999712 pjacklam
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 * Fix bug in internal function _e_add() and _e_sub() which causes it to return
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   "-0" in some cases.
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 * Let new() be used for assignment. Now $x->new(3) assigns 3 to $x.
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 * Improve code in new() for non-zero scalar integers with no exponent.
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 * Allow both "inf" and "infinity". Allow a leading sign, and ignore letter
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   case. This is to be consistent with core Perl.
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 * Be more consistent about allowed whitespace in input. E.g., "23 " gave 23,
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   but "inf " gave a NaN.
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 * Core Perl allows both "0x" and "0X" as hexadecimal prefix, and both "0b" and
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   "0B" as binary prefix, so we do too. Previously, only 0x and 0b were
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   allowed.
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 * Math::BigFloat now has its own from_bin() method which supports binary
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   floating point numbers, e.g., "0b1.1001p-4". This complements from_hex().
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 * Math::BigFloat now has its own from_oct() method which supports octal
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   floating point numbers, e.g., "1.3267p-4". This complements from_hex().
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 * The Math::BigInt and Math::BigFloat methods from_hex(), from_oct(), and
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   from_bin() can now be used as instance methods to assign values to the
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   invocand, e.g, $x->from_oct("10") assigns 8 to $x.
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 * Update documentation. Perl now uses "Inf", not "inf" to represent infinity.
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 * When the new() method is called with an undefined argument, the round
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   parameters are now passed on to bzero(). This applies to both Math::BigInt
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   and Math::BigFloat.
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 * Replace "UNIVERSAL::isa($this, $that)" with "$this->isa($that)", and ditto
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   for "can()", where possible. Not every instance of "UNIVERSAL::Isa()" has
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   been replaced, though, since the change causes some tests to fail. This must
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   be looked into.
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 * Simplify the copy() methods. Always copy accuracy and precision parameters,
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   even when they are undefined.
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 * Reformat more of the code in accordancw with the "perlstyle" manual page.
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   This makes the code a lot easier to read -- for me, anyway.
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 * Use a more generic regex in t/calling.t, since the exact wording of the
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   error message depends not on the Perl version, but on the module that does
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   the version checking.
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 * Avoid infinite loop in the Math::BigFloat->batan() method. Thanks to DANAJ
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   (Dana Jacobsen) for the patch. This was not intended to be added before the
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   next release, but was included in this release by accident.
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2015-11-12 v1.999710 pjacklam
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 * New method Math::BigFloat -> from_hex() which supports hexadecimal floating
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   point numbers, e.g., "0x1.999ap-4".
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 * New test file t/from_hex-mbf.t for testing Math::BigFloat -> from_hex().
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 * Add 'from_hex' and 'from_bin' to list of methods in the Math::BigInt POD.
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2015-11-06 v1.999709 pjacklam
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 * Represent and return zero as 0E0, not 0E1. The old POD said "A zero is
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   represented and returned as 0E1, not 0E0 (after Knuth)." I find no
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   references to Knuth ever having said this. The closest reference I can find
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   is that Knuth says 0**0 should be defined to be 1, not 0, but that is
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   something else than 0e0, which is 0*10**0. I have yet to see any other
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   mathematical software that represents and returns zero as 0e1 rather than
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   0e0.
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 * Required version of Test::More is 0.9301.
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2015-11-03 v1.999708 pjacklam
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 * Use bxxx() method names consistently, rather than mixing bxxx() and fxxx()
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   in code and test files. The fxxx() methods for Math::BigFloat objects are
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   still available through autoloading. However, we leave the fround() method
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   in Math::BigInt, as it seems to provide some kind of compatibility with
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   Math::BigFloat.
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 * Correct author information in the README file.
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 * Remove INSTALL file, which by accident wasn't removed in v1.999707.
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 * Use present tense, not past tense, in CHANGES file.
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 * Add '#!perl' to Makefile.PL for correct syntax highlighting in editors
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   supporting this.
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 * Use Math::Complex::Inf() in testfiles also (for generating Perl scalar
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   infinity) since it is more portable.
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2015-10-29 v1.999707 pjacklam
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 * Add dependency on Math::Complex 1.39 for Math::Complex::Inf(), which is
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   used for numifying infinity.
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 * Update author information.
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 * Update information in the file README.
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 * Remove the files INSTALL and LICENSE as this information is already covered
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   in the file README.
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 * Enable 'use warnings' in all modules. We require a Perl newer than 5.6.0
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   anyway.
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 * Replace 'use vars ...' with 'our ...'. We require a Perl newer than 5.6.0
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   anyway.
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 * Avoid indirect object syntax in documentation.
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 * Moved 'Test::More' from 'build_requires' to 'test_requires' in Makefile.PL.
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2015-10-28 v1.999706 pjacklam
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 * Correct release date of v1.999705 in CHANGES.
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 * Add code and tests for numify() on non-finite objects.
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2015-10-26 v1.999705 pjacklam
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 * Avoid using "my" in a false conditional. See "Deprecated use of my() in
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   false conditional" in perldiag(1).
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 * Faster algorithm for bpi() when accuracy is >= 1000.
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2015-09-25 v1.999704 pjacklam
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 * objectify() in lib/Math/BigInt.pm now uses 'isa' not 'eq' to check object
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   relationship. This is necessary for correct handling of subclasses.
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 * objectify() in lib/Math/BigInt.pm no longer expects as_int(), as_number()
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   and as_float() to return objects, but allows them to return numbers
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   formatted as strings. This is used by some other modules on CPAN.
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 * Better documentation of as_int() and as_number() in lib/Math/BigInt.pm.
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 * Add documentation for as_float() in lib/Math/BigFloat.pm
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 * Add test files t/objectify_mbf.t and t/objectify_mbi.t.
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2015-09-21 v1.999703 pjacklam
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 * Fix blog() in Math::BigInt and Math::BigFloat to work correctly regardless
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   of the base.
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 * Correct existing tests in bigintpm.inc and bigfltpm.inc.
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 * Update test plans (number of tests) in t/bare_mbi.t, t/bigintpm.t, and
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   t/sub_mbi.t.
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 * Add test files t/blog-mbf.t and t/blog-mbi.t for better testing of the
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   blog() methods.
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2015-09-17 v1.999702 pjacklam
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 * The overloaded log() is a unary operator, so don't pass additional
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   arguments.
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 * Fix blog() so the cases $x->blog() and $x->blog(undef) work correctly. An
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   undefined base means that blog() should use base e (Euler's number).
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 * Both CORE::log() and other mathematical software returns inf for log(inf),
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   so we do the same.
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 * Add tests for log() as well as templates for future tests of the other
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   overloadable functions.
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 * Improve descriptions of a few tests.
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2015-09-11 v1.999701 pjacklam
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 * The POD documentation, as well as the comments in the code, said that
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   $x->bdiv($y) in list context should return quotient $q and remainder $r so
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   that $x = $q * $y + $r, and that the remainder (modulo) $r should correspond
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   to Perl's % operator as well as the bmod() method. This has not been the
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   actual behaviour. This is now fixed. In scalar context, only the quotient is
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   returned.
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 * Clearer POD documentation for the bdiv() and bmod() methods.
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 * All non-integer input values to Math::BigInt gave a NaN, except non-zero
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   numbers in the range (-1,1) that were written without an exponent, e.g.,
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   "-0.75" and "0.5". Now also these return a NaN.
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 * Input values with a large (absolute value) negative exponent, e.g.,
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   1e-9999999, now return NaN. The former behaviour was to die with the message
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   "Quantifier in {,} bigger than 32766 in regex; marked by ..."
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 * Intermediate computations in blog() increased the number of digits
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   significantly in some cases. Now reduce the number of digits by rounding.
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   However, keep some extra digits for remaining intermediate computations
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   before the final rounding.
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 * When $x is a Math::BigFloat, $x -> bceil() and $x -> bint() for -1 < $x < 0
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   returned -0. Negative zero is never used by Math::Big(Int|Float), and care
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   has been taken to avoid it, so this bug is surely an oversight.
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 * Explicitly specify the backend (lib => 'Calc') in t/mbimbf.t for easier
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   release management of the backend distributions.
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 * Add "use warnings" to test scripts, since Perl 5.6.2 is required anyway, and
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   "use warnings" was introduced in Perl 5.6.1.
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 * Modified test scripts so the difference between the test files in the
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   Math-BigInt distribution and the backend distributions are as few and as
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   small as possible. This makes for easier release management.
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2015-08-12 v1.9997 pjacklam
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 CHANGES
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  * Add recent changes.
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 t/bigintpm.inc
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  * Correct spelling errors.
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 t/upgrade.inc
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  * Correct spelling errors.
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2015-08-12 v1.9996 pjacklam
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 CHANGES
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  * Add recent changes.
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  * Use present tense in change descriptions.
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 lib/Math/BigInt.pm
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  * Change incorrect use of ok() to is() in example.
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2015-08-11 v1.9995 pjacklam
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 CHANGES
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  * Move changes that were incorrectly reported as being for the release 1.9994
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    when they were in fact for release 1.9993.
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  * Add changes both for release 1.9994 and 1.9995.
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 lib/Math/BigInt.pm
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  * Break lines to avoid lines with more than 80 characters.
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  * Improve objectify() for better handling of subclasses.
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2015-08-10 v1.9994 pjacklam
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 CHANGES
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  * Add recent changes.
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 lib/Math/BigFloat.pm
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  * Fix blog() which sometimes returns incorrect result.
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  * bdiv() in list context now returns the integer quotient and the remainder.
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 t/bigfltpm.inc
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  * Modify tests for blog() in list context.
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 t/biglog.t
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  * Change incorrect use of ok() to is().
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 t/upgrade.inc
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  * Modify tests for blog() in list context.
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 inc/Module/Install*
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  * Upgrade bundled Module::Install from version 1.08 to version 1.16.
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2014-04-03 v1.9993 pjacklam
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 BUGS
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  * Add reference to CPAN RT for the Math-BigInt distro.
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 CHANGES
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  * Add recent changes.
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 examples/hailstone.pl
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  * Remove this file as it doesn't seem to be working.
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 lib/Math/BigFloat.pm
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  * Correct spelling errors.
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  * Reformat code to avoid long lines.
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  * Improve POD formatting.
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  * Add meta-documentation (CPAN ratings, CPAN testers matrix, etc.)
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  * Add the bint() method.
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 lib/Math/BigInt.pm
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  * Correct spelling errors.
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  * Reformat code to avoid long lines.
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  * Improve POD formatting.
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  * Add meta-documentation (CPAN ratings, CPAN testers matrix, etc.)
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  * Add the bint() method.
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  * Remove references to the obsolete Math::Big
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 lib/Math/BigInt/Calc.pm
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  * Correct spelling errors.
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  * Added meta-documentation (CPAN ratings, CPAN testers matrix, etc.)
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 lib/Math/BigInt/CalcEmu.pm
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  * Correct spelling errors.
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  * Improve POD formatting.
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  * Add meta-documentation (CPAN ratings, CPAN testers matrix, etc.)
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  * Remove references to Math::BigInt::BitVect, which is no longer on CPAN.
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 Makefile.PL
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  * Remove code that checks for compatible versions of distributions that
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    depend on Math-BigInt. Such checking should be done in the distributions
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    that depend on Math-BigInt, not in Math-BigInt itself.
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 NEW
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  * This file now only refers to the change log.
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 t/bigfltpm.inc
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  * Add tests for fint().
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 t/bigintpm.inc
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  * Add tests for int().
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 t/upgrade.inc
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  * Add tests for int().
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 t/*.t
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  * Increment test counts as needed for the new tests in the t/*.inc files.
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 inc/Module/Install*
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  * Upgrade bundled Module::Install from version 1.01 to version 1.08.
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2012-12-10 v1.9997_11 pjacklam
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This release introduces no changes in the library code, i.e., the .pm files in
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the 'lib' directory, but there are a lot of changes in the test files. Since
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there are so many changes, I let this be a development release.
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 * Add 'use strict;' and 'use warnings;' to all test files.
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 * Reformat code in the test files according to the "perlstyle" manual page.
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   This makes the code a lot easier to read -- for me, anyway.
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 * Decrement required version of Perl from v5.6.2 to v5.6.1. All tests pass
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   when running the test suite with Perl 5.6.1 on Cygwin.
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 * Replace "use vars ..." with "our ..." in test files.
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 * Replace "BEGIN { unshift @INC, 't'; }" with "use lib 't';" in test files.
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 * Use "our $x; $x = ...;" rather than "our $x = ...;" since the latter causes
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   Perl 5.6.1 to complain about variables only used once.
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 * Add comment to all tests. Now the tests no longer says just "ok 123", but
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   rather "ok 123 - $x->blog(2)" etc. This makes it easier to identify failed
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   tests, especially in the smoke testing reports.
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 * Fix various flawed tests, e.g., ok($x, 2) was used testing whether $x was 2.
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 * Use the skip() feature of Test::More for skipping tests.
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 * Use more descriptive variable names in test files.
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 * Remove unused variables in test files.
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 * Move variable declarations to limit their scope in test files.
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 * Remove trailing whitespace in test files.
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 * Wrap (most) lines to fit 80 columns in test files.
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2011-09-04 v1.997 pjacklam
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 * Document actual behaviour of from_xxx() methods. [perl #85334] (Peter John
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   Acklam)
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 * Make bmuladd() able to handle third arg properly. [perl #85482] (Peter John
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   Acklam)
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 * Add sign function bsgn() as a complement to babs(). (Peter John Acklam)
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 * Fix objectify()'s handling of "foreign objects". (RT #16221 and #52124)
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   (Peter John Acklam)
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 * Rewrap some verbatim pod in Math::BigInt. (Father Chrysostomos)
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 * Correct links to sections. (Alexandr Ciornii)
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 * Remove incorrect formatting inside verbatim paragraphs. (Alexandr Ciornii)
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 * Upgrade bundled modules in "inc" to latest version. (Peter John Acklam)
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 * Include "^MYMETA\.(yml|json)\z" in MANIFEST.SKIP. Whereas META.* are
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   generated by the distribution author at packaging time, MYMETA.* are
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   generated by the end user at configure time after any dynamic dependencies
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   are known. (Peter John Acklam)
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2011-02-26 v1.993 pjacklam
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 * Change default backend library from Math::BigInt::FastCalc to
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   Math::BigInt::Calc, which is included in the Math-BigInt distro. This
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   avoids recursive distribution dependency (RT #65976) (Peter John Acklam).
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2011-02-18 v1.992 pjacklam
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 * Math::BigInt::Calc->_nok(): Use symmetry property nok(n,k) = nok(n,n-k) to
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   speed up execution when k is large. Also general code cleanup. (Peter John
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   Acklam).
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 * Math::BigInt::Calc->_gcd(): Speed up by reducing amount of data copying
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   (Peter John Acklam).
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 * Add '01load.t' for basic module loading and diagnostics useful for
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   debugging. Rename '00-signature.t' to '00sig.t', 'pod.t' to '02pod.t', and
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   'pod_cov.t' to '03podcov.t' (Peter John Acklam).
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 * Math::BigInt:: Make from_hex(), from_oct(), and behave more like hex() and
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   oct() in the Perl core, and make from_bin() consistent with from_hex() and
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   from_oct() (this is related to RT #58954) (Peter John Acklam).
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 * Math::BigInt::Calc->_rem(): Modify first input arg always, not just
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   sometimes (Peter John Acklam).
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 * Math::BigInt::Calc->_modinv(): be more consistent with the _modinv() method
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   in other libraries (Math::BigInt::GMP, etc.) (Peter John Acklam)
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 * Math::BigInt::Calc->_nok(): use symmetry property nok(n,k) = nok(n,n-k).
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   This cuts computation time tremendously when n and k are large (Peter John
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   Acklam).
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 * Math::BigInt::Calc->_gcd(): quickly handle zero cases, avoid code
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   duplication, and always modify the first input argument in-place (Peter John
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   Acklam).
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 * Clean up code and add more code comments (Peter John Acklam).
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 * Fix typos (Peter John Acklam).
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2011-02-05 v1.991 pjacklam
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 * Add workaround for library inconsistencies (Math::BigInt::Calc vs.
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   Math::BigInt::GMP). This makes older versions of Math::BigInt::GMP
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   work with latest version of Math::BigInt (Peter John Acklam).
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 * Correct and extend API documentation (Peter John Acklam).
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2011-01-29 v1.99_05 pjacklam
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 * Fix typos (reminder -> remainder etc.) (Peter John Acklam)
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 * Fix Math::BigInt::Calc::_num returning NaN, not Inf, when it overflowed
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   (Peter John Acklam) (Closes: RT #25274).
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 * Fix Math::BigFloat->bcmp() so it can handle arbitrarily large exponents
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   (Peter John Acklam) (Closes: RT #62764).
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 * Fix bmodpow() in Math::BigInt 1.99 mis-calculating powers of one
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   (Peter John Acklam) (Closes: RT #63237).
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 * Fix bmodpow() and bmodinv() in Math::BigInt to handle negative input
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   (Peter John Acklam) (Closes: RT #61543)
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 * Clean up whitespace (Nicholas Clark).
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 * Added file t/00-signature.t for testing SIGNATURE (Peter John Acklam).
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Complete version history of the rewrite project
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===============================================
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If you just want to see which things are new and different from the original
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Math::* in the Perl core, see HISTORY.
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##############################################################################
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Math::BigInt::Calc:
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2007-09-16 v0.52 Tels
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 * fix 64bit ints on Perl v5.8.0 (thanx zefram)
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2007-05-30 v0.51 Tels
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 * use CORE::hex() instead of hex() to help bigint/bignum/bigrat
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 * use 9 digit parts on 64bit integer or long double systems
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2007-05-05 v0.50 Tels
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 * speed up _mul() by "use integer;"
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 * we do not need to remove zeros after mul()
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 * implement an alternative algorithm for _fac()
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2007-04-16 v0.49 Tels
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 * API version 2.0 support: add _1ex(), _alen()
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 * make _fac() about twice as fast
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2007-01-27 v0.48 Tels
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 * support for octal numbers
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2005-05-17 v0.47 Tels
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 * remove shortcut in div(), it wasn't working properly
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2005-03-29 v0.46 Tels
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 * avoid crash in FastCalc by making $BASE and $BASE_LEN use vars qw//;
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2005-03-20 v0.45 Tels
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 * fix the div() shortcut for short numbers to actually work
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2005-01-01 v0.44 Tels
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 * small cleanups
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 * shortcut for numbers of same length in _div, where X > Y
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2004-10-10 v0.42 Tels
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 * fix critical bug in _from_hex() with parts that were to big for one part
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   (introduced in v1.72, thanx Mark Lakata for finding it!)
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2004-07-30 v0.41 Tels
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 * from_hex() convert 28 bits (vs 16) at a time, faster (helps from_bin(), too)
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 * potential bug in padding with '0' in _digit()
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 * fixed undef warnings in fceil(0.222222222222...) (thanx kenny!)
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2004-04-05 v0.41a Tels (not released)
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 * removed the unused integer-detection code and combined the two BEGIN blocks
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2004-03-12 v0.40 Tels
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 * added: api_version(), _ten(), _two(), _is_ten(), _is_two(), _gcd()
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 * streamlined: is_foo() methods
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 * _new() takes scalar, not scalar ref
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 * _str() returns scalar, not scalar ref
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 * _and(): bugfix for [perl #26559]: negative arguments that are shorter
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    than the positive one caused an error due to cutting instead padding
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 * _ior(): forgot to calculate the proper sing of result, making, for
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    instance, 30 | -4 go wrong
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2004-01-25 v0.39 Tels (not released)
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 * _zeros(0) is 0, not 1
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2003-12-30 v0.38 Tels
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 * guess _log_int() result based on $base if $base < $BASE
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 * _pow() handle cases 0 ** Y, 1 ** Y, X ** 0 and X ** 1
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 * _new(): shortcut for short numbers, makes MBI->new() about 20% faster
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 * _root() was wrong for numbers like 9 (0b1001) because they start with
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   the pattern /^0b1(0+)/ (missing '$' in regexp) and after fixing this
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   it was dead slow for large numbers.
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2003-12-11 v0.37 Tels
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 * implemented _log_int() with a simple and fast "iterative" method
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 * fixed bug in _root(): int() rounds sometimes wrong, so use sprintf()
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 * _as_bin() and _as_hex() are faster (for small values) due to inlining
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   is_zero()
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 * _acmp() is about 26% faster for very small numbers or numbers that
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   differ in length, and slightly faster for bigger numbers. This helps
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   both bacmp() and bcmp()
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 * _fac() did:
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   + not modify $x in place for small arguments
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   + something strange for large arguments
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   + not handle 0..2 optimal (code now simplified)
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 * _as_bin() used %b, which was not known to v5.5.3 - workaround that
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 * implemented _log_int(), which is simple and very fast
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 * implemented the missing pieces for _root() (which is quite fast)
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2003-08-31 v0.36 Tels
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 * fixed a bug in div_use_div() that computed remainder wrong if X == X and
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   X was very large
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 * fixed a off-by-one error discovered with mbi_rand.t in _div_use_XXX()
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   (one internal in $x overflowed, thus the wrong computation)
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2003-07-06 v0.35 Tels
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 * fixed a bug in _floor() which caused ffloor(0.1234567) to fail.
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   (Thanx to cpan@ali.as for finding it and sending a fix/testcases)
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 * make _as_hex() and _as_bin() handle 0, and make them faster for very
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   short numbers (less than BASE_LEN digits)
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2002-09-27 v0.34 Tels
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 * fixed bug in mul_use_div() shortcut that used * $RBASE instead of / $MBASE
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 * $caught & 1 != 0 vs ($caught & 1) != 0 (changed to $caught != 2)
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 * $i %= $MBASE does not work on ARM (v5.003), so make it $i -= $car * $MBASE
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 * removed unused LEN_CONVERT code (smaller memory footprint)
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2002-09-09 v0.33 Tels
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 * _fac() keep $n as scalar if possible
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 * test for when to USE_MUL or not was inverted
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 * _mul() is about 6 times faster if $y is small and $x is big
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2002-08-21 v0.32 Tels
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 * fixed bug in _rsft() that did not set result to 0 in some cases
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 * _modinv() now works, thanx to the all-positive algorithm
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 * much more tests in bigintc.t (taken over from FastCalc)
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2002-08-13 v0.31 Tels
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 * _acmp() no longer calls _len() => tad faster
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 * some cleanup of old code, added some more comments
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2002-06-10 v0.30 Tels
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 * undef mul/div in case Calc.pm get's loaded twice
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 * fix in _as_hex() and _as_bin() for older Perls
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 * speedups in _pow() and _modpow()
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2002-06-09 v0.29 Tels
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 * filled in _modpow()
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2002-05-30 v0.28 Tels
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 * added _modinv(), _modpow() (not yet implemented)
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2002-03-17 v0.26 Tels
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 * a fix in _rsft() that left empty array instead of (0)
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 * a fix in _sub(): early out made -1 + 100000000001 == 0 (if length($y) > 8)
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2002-03-03 v0.25 Tels
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 * started _square() (not done yet)
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2002-02-27 v0.24 Tels
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 * streamlined _mod() shortcuts
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 * _div() has shortcut if $y is very small
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2002-02-24 v0.23 Tels
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 * from_bin() repack input and use from_hex(): twice as fast
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2002-02-10 v0.22 Tels
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 * _sqrt1() => _sqrt() (oups)
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 * much better guess for _sqrt() resulting in faster sqrt
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 * added _fac()
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2002-01-07 v0.20 Tels
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 * better detection of higher-int-only base (but disabled due to failures)
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 * streamlined converting
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 * turned dual-basis off by default (now 7-7 on 32 bit and 9-9 on most 64 it)
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 * _str() uses int() on first part to avoid '0000' instead of '0'
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2001-12-23 v0.19 Tels
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 * first working version of using two different bases: one for mul/div, the
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   other for all other ops, including converting via _to_large()/_to_small()
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2001-12-20 v0.18 Tels
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 * added _as_hex() and _as_bin() with 16 bit chunks
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 * from_bin() now uses oct() and 16 bits per iteration
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 * removed needless return statements
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2001-12-06 v0.17 Tels
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 * added _sqrt() for more speed
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 * _sqrt() shortcut for small (< $BASE) numbers for better performance
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 * shortcut in _mul for small numbers (< $BASE_LEN2)
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 * added _and, _or, and _xor and let them use more than 16 bits
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 * find out how many bits _and, _or and _xor can safely use (cap at 23)
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 * div() might leave empty array, so __strip_zeros fixes these
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 * streamlined _acmp()
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 * cap of 5 for BASE for UTS and UNICOS/Cray
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 * better test to find out what BASE should be (use +0.0 to force floats)
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2001-11-19 v0.16 Tels
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 * fixed comments a bit
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 * finished _mod() when $y < $BASE and $BASE % $y != 0 and $BASE % $y != 1
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 * streamlined _mod() loops a bit
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 * added _pow() for faster bpow()
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 * small fix to make 5.005_03 happy ($x = shift @prod vs $x = shift @prod || 0)
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2001-11-11 v0.15 Tels
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 * added _dec() and _inc() for much faster $x++ and $x--
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2001-11-04 v0.14 Tels
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 * added _mod() for faster $x % $y
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2001-10-23 v0.13 Tels
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 * better detection of BASELEN by matching against expected pattern
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2001-10-03 v0.12 Tels
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 * _div: 99999 => $BASE-1 ($MAX_VAL), that made some div's fail if $BASE != 5
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2001-09-07 v0.11 Tels
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 * automatically USE_MUL or USE_DIV
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2001-08-24 v0.10 Tels
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 * no longer export anything, ignore import calls
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2001-07-20 v0.09 Tels
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 * don't use warnings for older Perls
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2001-07-15 v0.08 Tels
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 * fixed bug in mul() shortcut
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2001-07-15 v0.07 Tels
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 * applied Philip Newtons spelling and doc patch(s)
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 * accidentally had the old, slow mul() code in. Oups.
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 * fixed also a bug in that new code
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 * also the speedup in mul() occurs with $x having lots of zeros, not $y.
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 * first argument is always classname, so removed checks and shift
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 * shift in base ten by _lsft() and _rsft()
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2001-07-09 v0.06 Tels
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 * first release
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##############################################################################
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Math::BigInt::CalcEmu:
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2004-03-12 v0.04 Tels
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 * removed unnec. emulation routines (all except _signed_foo)
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2004-01-13 v0.03 Tels
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 * $VERSION was overriding the $VERSION from MBI (Thanx Gisle Aas!)
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2003-12-30 v0.02 Tels
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 * the code in Calc::_root() uses now sprintf(), but the one in Emu was not
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2003-12-26 v0.01 Tels
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 * first version, taken over all the code from BigInt
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##############################################################################
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Math::BigInt::Scalar:
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2002-01-07 v0.11 Tels
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 * fixed version
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 * added DESCRIPTION section to stop pod2man complaining
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 * added _dec, _inc
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2001-08-24 v0.10 Tels
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 * no longer export anything, ignore import calls
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2001-07-20 v0.06 Tels
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 * don't use warnings for older Perls
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2001-07-15 v0.05 Tels
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 * first argument is always classname, so removed checks and shift
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2001-07-09 v0.04 Tels
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 * first release
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##############################################################################
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Math::BigFloat:
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2008-04-20 v1.60 Tels
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 * fix #34459: bsqrt() breaks on floats with enough digits (Thanx Niko Tyni!)
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 * fix #35238: batan2() handles inf/+inf wrong
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 * fix #35162: MBI segfault (as_number(Math::BigRat()) was wrong)
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2007-06-30 v1.58 Tels
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 * remove Exporer from @ISA
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 * support config('lib') as shortcut for config()->{lib}
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 * add bpi(), bcos(), bsin(), batan(), batan2() methods
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 * add bmuladd()
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 * streamline the is_xxx() and copy() methods
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2007-05-05 v1.57 Tels
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 * add bnok() method (n over k)
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 * add all the missing modify() hooks
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2007-04-16 v1.55 Tels
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 * make bexp() much faster (esp. under GMP) by caching the first coefficients
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   and rewriting the inner loop
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 * support "try" and "only" in import()
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2007-04-09 v1.54 Tels
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 * fix bug #21747: Re: weirdity in bignum... (powers and high precision):
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   infinite loops for blog() (and consequently bpow()) if you requested
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   an accuracy greater than 67 digits (uses _log() now, and not blog())
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   Thanx to darconc!
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 * cache the result of _log(2) and _log(10) so that subsequent calculations
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   can re-use the already done work
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 * instead of computing _log(10), compute _log(1.25) and _log(2) and then do:
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    _log(1.25 * 2 * 2 * 2) = _log(1.25) + _log(2) + _log(2) + _log(2)
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   This makes computing _log(10) much faster, so that computing blog(N) is
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   about a factor of 5 faster when N >= 10 or N <= 0.1
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 * add bexp()
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2007-03-04 v1.53 Tels
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 * fix #25144: [PATCH] Math::BigFloat->new considers any reference a BigInt
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   (Thanx mschwern!)
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 * fix bug #13866: NaN (in bignum queue)
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 * fix bug #21586: Incorrect result when comparing with NaN
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 * fix bug #15896: "==" overloading is broken for "NaN"
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2007-01-27 v1.52 Tels
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 * fix brsft() and bpow() in list context only return on number (bug #21413)
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 * make as_int() return a BigInt, too (not just as_number()) (bug #21412)
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 * add as_oct()
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 * bpow(): handle negative X and negative Y (instead of returning NaN)
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2005-04-10 v1.51 Tels
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 * fix new() to work with Math::BigInt::Pari
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2005-03-29 v1.50 Tels
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 * fix rounding doc, add notes about prevision vs. accuracy
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 * set FastCalc as default (we still use whatever MBI uses)
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2005-03-20 v1.49 Tels
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 * remove dependecy on Scalar::Util in bdiv()
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 * bdiv() cache result of "!$y->is_one()" for wantarray case to make
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   ($res,$rem) = $x->bdiv($y); about 10% faster
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2005-01-01 v1.48 Tels
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 * use new interface to _scale_a() and _scale_p() in BigInt
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 * add bneg() and inline is_zero() in it, making it 1.6 times faster
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 * replace ref($_[0]) w/ undef when it isn't actually needed. This
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   makes some ops (bsstr(), bneg etc) about 2% faster for small numbers
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 * use MBI::_register_callback() to get notified of lib changes
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 * bgcd()/blcm() never worked, so fix them for integers and add tests
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2004-10-10 v1.47 Tels
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 * inf/NaN fixes for bpow()
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 * eliminate the need for _zeros() in new() (speed-up for GMP et. al.)
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 * eliminate _is_zero() in new() (small speed up)
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 * added shortcut for simple numbers in new() (speed up)
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2004-08-13 v1.46 Tels
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 * blog(10,10) ($x == $y) returned '1.0000...' instead of '1'
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2004-07-30 v1.45 Tels
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 * simple inherit bsub() from BigInt, also fixes bsub() failing under
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   $x -= $x - Thanx Peter J. Acklam!
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 * bdiv() failed when passed a variable twice (thanx Peter J. Acklam!)
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 * bfround() and bround() are about 10% faster when going via Math::BigInt's
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   bround() due to constructing a fake BigInt instead of going via ->new()
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 * fixed undef warnings in bpow(0,$y) ($y non-integer) (thanx kenny!)
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2004-03-12 v1.44 Tels
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 * bpow() computed -X ** Y wrong for Y that are odd
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 * use $HALF instead of 0.5 to speed up broot()
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 * use Calc instead of BigInt for parts, that makes it roughly 2x faster
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   it also saves memory (419 vs. 767 bytes per (small number) object)
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 * bmod() did needlessly test for NaN arguments twice
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2004-01-13 v1.43 Tels
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 * small fixes in AUTOLOAD
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 * delete $x->{_a} vs. $x->{_a} = undef to save memory
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2003-12-30 v1.42 Tels
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 * ffac(inf) is inf, not NaN
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 * flog() calculate integer result first, and if it fits, return it
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   this makes it much faster in case the result is a perfect integer
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 * require (instead of use) Exporter
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 * froot() calculates an integer result first, and it if fits, returns it
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2003-12-11 v1.41 Tels
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 * flog(): 0.5, 0.25, 0.125, 2, 4 and 8 were not scaled properly back to
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   1, instead they remained 0.5 and 2, respectively. This was a '<' vs.
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   '>=' respective '<' vs. '<=' issue. No other values are affected
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   (neither getting slower nor faster), but the ones in question (incl.
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   their multiples like 20, 80, 0.0125 etc) are now tremendously faster -
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   about a factor of 30 to 60! :-)
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 * removed some crufty logic from _log_10() and made the special cases of
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   2, 10 and 0.1 slightly faster. This also helps log($x,2) and log($x,10).
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 * bfac() slightly faster for small arguments
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 * downgrading to bigint failed for .2e2 (produced 200 vs. 20)
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2003-09-23 v1.40 Tels
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 * bstr(): removed unnec. BigInt math and inlined is_zero() => great speedup
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   (10% to factor 6.5 depending on input)
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 * replace $self->_one() by $self->bone()
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2003-07-06 v1.39 Tels
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 * $x->blog($base) can handle a $base which is a Math::Bigint
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 * replace die() with Carp::croak
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2002-11-03 v1.39 Tels
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 * $x->bpow($y,0), $x->blog($base,0) and $x->bdiv($y,0) were still not doing
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    the right thing and no tests caught it *sigh*
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 * blog():
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   + MUCH faster when $x > 10 or $x < 0.1 (constant time vs.
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     time * 10 when doubling/halving $x)
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   + also much faster if $x has many digits (like 1/3 or 123**123)
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   + for $x < 1 and $x > 0 did not work at all (bacmp vs bcmp)
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   + returns now NaN if $base <= 0 or $base == 1
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   + does handle other bases than "undef" (aka e) properly now
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 * require Math::BigFloat did not work (opposed to BigInt, where it does)
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 * _pow() suffered the same bug of bacmp vs bcmp (so 0.2 ** 0.2 failed)
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 * removed unused _pow2() routine
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 * _find_round_parameters() returns ($x,$a,$p,$r) and not ($a,$p,$r), so
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   use it correctly, and also test for $x = NaN afterwards
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  (happens when $a and $p were set and thus $x became NaN)
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 * bsqrt() failed since v1.63 for values like 0.2, 0.002, 0.00134 etc
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 * added broot() method (albeit slow for now)
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 * $x->is_one('-') was broken (never returned true for $x == -1)
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 * config() can take arguments and set them, croak on wrong ones
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 * config(trap_nan => 1) to manipulate former $NaNOK variable
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 * config(trap_inf => 1), too
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 * trap_nan/trap_inf really croak on any attempt to create an NaN/inf
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 * spellings of Bigint => BigInt
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 * simplify config() by using SUPER::config()
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2002-09-08 v1.38 Tels
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 * fix that bsqrt() would hang for certain inputs. Instead of using Newton's,
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   we now rely on the fact that sqrt(x*y) = sqrt(x) * sqrt(y) by setting y to
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   100. This removes the while loop entirely and makes it much faster while
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   fixing the bug at the same time.
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 * $x->bsqrt(0) did needless warn about undef values, and round to 4 digits
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   instead of beeing equivalent to $x->bsqrt(undef)
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 * ditto for $x->bpow($y,0), $x->blog($base,0) and $x->bdiv($y,0)
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 * use File::Spec was needless, since it was required later on again
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2002-08-20 v1.37 Tels
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 * bcmp()/bacmp() upgrade now if requested
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2002-08-13 v1.36 Tels
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 * as_hex() and as_bin() work now at least for inf, NaN and integers
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 * fixed bsstr() (and thus also numify()) for negative numbers - Ouch!
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 * $x->new("0.02"); $x->accuracy($a); $x->bdiv($y,$d) failed to round
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   when $d > $a
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 * numify() returned '+inf' instead of 'inf'
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 * (more) tests for bsstr(), numify(), as_hex(), as_bin
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2002-07-07 v1.35 Tels
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 * bfround() used accidentally BigInt math; is now about 5.6 times faster for
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   small numbers
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 * bdiv()/badd() etc skip objectify() if possible and are thus faster
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 * doc for accuracy()/precision()
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 * $x->bmod() was not modifying $x in place when returning NaN/inf/-inf
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 * avoid unec. calls to objectify() for binary op's
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2002-06-10 v1.34 Tels
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 * upgrade used badd() instead of bmul() inside bmul() (again! arg!)
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2002-06-09 v1.33 Tels
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 * import() fixed for older Perls
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2002-05-19 v1.32 Tels
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 * upgrade used badd() instead of bmul() inside bmul()
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 * bpow() now uses slower, but more correct way for fractions (this needs work)
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2002-03-03 v1.31 Tels
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 * bpow() can handle second arguments beeing non-integer (f.i. 2 ** 0.2)
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 * $x->bpow(0.5) optimized to $x->bsqrt();
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2002-02-25 v1.30 Tels
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 * bug in bsub() with not rounding when $x->bsub(0) was also in MBF
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 * bcmp() and bacmp() 5 times faster due to numify() (might have now impose a
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   limit on exponent - but I couldn't find a test that breaks it)
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 * streamlined ffloor() and fceil()
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 * fixed bug in $x->bsub(0) and $x->badd(0) (both forgot to round result)
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 * new() downgrade integers if $downgrade is in effect
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 * optimized fpow() (one is_zero() less)
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 * optimized as_number (nearly twice as fast)
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 * $x->badd(0) forgot to round $x
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 * downgrade and upgrade are valid methods for inheritance
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2002-02-24 v1.29 Tels
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 * overload for 'log' now inherited by BigInt
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 * _binf(), _bnan(), _bone() and _bzero() instead of longer bone() etc
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 * inf/NaN fixes from v1.51 were missing for BigFloat
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 * bdiv() upgrades if applicable
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2002-02-16 v1.28 Tels
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 * fixed use Math::BigFloat ':constant';
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 * fixed flog() function to calc right result, honour rounding-globals
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2002-02-10 v1.27 Tels (forgot to increase version)
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 * ffac()
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 * various: disable Math::BigInt::upgrade to avoid deep recursion
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2002-01-06 v1.27 Tels
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 * overload for log() and flog()/blog()
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 * bzero()/bone() handling of A & P was broken
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 * bround()/bfround() handling of zeros forgot to set A & P
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 * fdiv: fixed a bug in round to A with given round_mode (always used global)
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 * fsqrt(): would hang/fail if either $x's or global A or P were set
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 * fsqrt() didn't modify $x sometimes, but returned a new reference
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 * fsqrt(): calc 4 more digits for rounding, not 1 (endless looping otherwise)
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 * fmod() now actually works
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2001-12-06 v1.26 Tels
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 * fneg() failed (now hand up to MBI)
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 * frsft() and flsft() were no aliases to brsft() and blsft()
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 * fone() was no alias for bone()
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 * blsft() and brsft() were missing altogether
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 * streamlined: fpow() and fmul()
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 * removed the EXPORT_OK
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 * fqsrt() uses now BigInt::bsqrt() as guess: greatly improved performance
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 * make fsqrt() subclass proof by using $self instead of Math::BigFloat
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 * bzero(), bone(): take additional A and P and store 'em
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 * bnan(), binf(): clear A and P
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2001-11-18 v1.25 Tels
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 * streamlining fixes in new() were missing
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 * further streamlining in new() for 12345e1234 cases (fraction part empty)
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 * added $rnd_mode support for compatibility
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 * replaced the 'laber schwad blah blah' pod section by a pointer to MBI
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2001-11-11 v1.24 Tels
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 * bacmp() fix for +-inf
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 * streamlined new()
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 * faster finc()/fdec()
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2001-10-05 v1.23 Tels
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 * fixed facmp() (was broken the same way as fcmp())
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 * more rounding fixes from John P.
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2001-10-03 v1.22 Tels
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 * Quite a lot of rounding fixes
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 * $x->bnorm() is 4 times faster if $x == 0
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 * $x->bround($n) is 43 times faster if $n > $x->{_a} (no-op)
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 * added as_number()
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2001-09-03 v1.21 Tels
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 * serious bug in bcmp() caused 1.5 to be greater than 2. Yikes!
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 * bcmp() did not only return -1,0,1 and undef but other values, too
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 * new('inf') produced NaN (was expecting '+inf')
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 * exponent(), mantissa() & parts() failed or returned scalars for inf,-inf,NaN
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 * include finf in AUTOLOAD list
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2001-08-03 v1.20 Tels
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 * streamlined bcmp
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 * drop leading '+' for inf
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2001-08-02 v1.19 Tels
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 * 123/+-inf => 0, test for that and -1,0 / NaN => NaN
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 * +123 / 0 => +inf, -123 / 0 => -inf (was missing in MBF)
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 * fixed +-inf handling in bacmp/bcmp/bsub/badd/bdiv and tests for that
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 * padd bstr() output of numbers with set A or P
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 * remove bfloat() (Math::BigInt->bfloat() did not work, anyway, see bint())
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2001-07-15 v1.17 Tels
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 * applied Philip Newtons spelling and doc patch(s)
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 * added bone()
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 * tests for bnan() and bone()
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2001-07-09 v1.16 Tels
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 * is_positive(), is_negative()
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 * various pod fixes (overlong =item, spelling erorrs etc)
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 * removed internal _set() and the tests for it
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 * infinity support for fcmp(), fpow()
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 * nailed the bug in fdiv() that caused fsqrt() to fail. fsqr() works now, too.
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 * more tests
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2001-06-15 v1.15 Tels
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 * added bfloor(), bceil()
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2001-06-13 1.14 Tels:
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 * accuracy/precision rounding after fdiv() was missing
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 * binary integer input (0b01110 etc)
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 * A/P rounding after fdiv() was missing
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 * '-0x0' would wrongly leave '-0'
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 * as_number() was wrong for negative numbers and had no tests
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 * added is_even(), is_odd(), _set(), the inherited ones were broken
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 * fixed is_zero() for NaN
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 * $x->bpow($y) for negative $y was unfinished
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 * added is_inf(), binf() and some support for +-inf in new(), bsstr() etc
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 * added tests for is_odd(), is_even(), _set() and is_zero(), is_inf(), bsstr()
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2001-06-09 1.13 Tels:
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 * adjusted fdiv() so that it now works proper with old testcases
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 * (except a few nits, see testsuite and ACCURACY)
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 * fdiv() in listmode (uses non-working fmod())
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 * fixed/test A/P after each op
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 * $x->accuracy(), $x->precision() actually round $x to the value A/P
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 * fixed fpow(), added tests for it
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 * hexadecimal integer input (0xdeadbeef)
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 * is_one() for -1 was wrongly true, tests for is_one()
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2001-05-11 1.12 Tels
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 * taken over testsuite from John P.
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 * added tests for compare with fraction
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 * fixed fcmp/fround/ffround
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 * added accuracy/precision/fallback/round_mode
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 * bsstr('NaN') returned 'NaNeNaN'
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2001-05-09 1.11: bug bcmp() (1e-08 was < 0, aka fractions were broken)
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2001-05-07 1.10: Tom's round fixes (minus one nit)
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                 new: .xxx, -.xxx, +.xxx etc are valid inputs, while
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                 '.', 'x x x' and 'Exxx' are now invalid
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                 finally got rid of C&P of overload section and clone()
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2001-04-23 1.09: length() in list context return length of mantissa & exponent
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                 bug in bstr() for '0.x' style strings
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                 added bsqrt()
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                 workaround for Perl v5.6.0 overload-bool bug (via MBI)
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                 fixed rounding
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2001-04-18 1.08: exponent(), mantissa() and parts() now return BigInt's
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                 bnorm: 0Ey => 0E1 (was wrongly 0E0)
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                 fixed is_zero()
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                 added bround() and bfround() (only truncate mode)
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                 fixed bug in bstr() for 1.203E-2 style numbers (Thanx Tom!)
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2001-04-07 1.07: bug in bstr() for 0.xxx style numbers, as well as for "-xxx"
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                 babs(), bneg(), bint() work now
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                 empty stubs for bsqrt(), bround() and bmod()
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                 exponent(), mantissa(), parts() work now as expected
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2001-04-05 1.06: bstr() returns NaN for NaN's
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                 renamed _norm to bnorm, added it to AUTOLOAD for compatibility
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                 fixed bug Math::BigFloat->new(Math::BigInt->new(3));
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                 bug mul/div when second arg was BigInt
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                 bdiv() works now with precision
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                 precision()
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                 doc about mixing different objects in overloaded math
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2001-03-31 1.05: fixed bstr() and bsstr()
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                 added AUTOLOAD for fxxx() to work as well as bxxx()
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                 enhanced and fixed testsuite for mul/cmp/add/new
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2001-03-27 1.04: bmul/bdiv/cmp work now, better _norm()
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2001-03-06 1.03: layed more foundations (mul() etc)
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2001-02-24 1.02: add()/sub() should work now
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2001-02-22 1.01: new() and bstr() work now (sort of)
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2001-02-18 1.00: started work
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##############################################################################
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Math::BigInt:
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2010-11-15 v1.99 rafl
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 * Stop as_int/as_number from losing precision (Peter John Acklam)
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   (Closes: RT#43694)
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 * Fix Math::BigInt::Calc::_modpow for (0 ** $x) % $y, with $x > 0
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   (Peter John Acklam) (Closes: RT#62918).
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 * Stop $x -> bmodpow(1, 1) from failing when $x is large (Peter John Acklam)
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   (Closes: RT#62949).
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2010-11-08 v1.98 rafl
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 * Fix from_bin() documentation error (Peter John Acklam) (Closes: RT#61845).
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 * Make as_int($inf) return inf, not NaN (Peter John Acklam) (Closes RT#62101).
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 * Fix various typos in documentation and tests (Peter John Acklam)
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   (Closes RT#62643).
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 * Make digit($n) return 0 for "out of range"-digits (Peter John Acklam)
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   (Closes RT#61812).
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2010-11-07 v1.97 rafl
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 * Reorder the list return of Math::BigInt::Calc::_base_len() (Nicholas Clark)
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   This change requires an update of Math::BigInt::FastCalc to version 0.24.
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 * Fix segfault when upgrading irrational numbers (Father Chrysostomos)
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2010-09-28 v1.96 rafl
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 * Various documentation fixes provided by gregor herrmann
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2010-09-14 v1.95 rafl
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 * Re-upload v1.94 as a stable release
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2010-09-13 v1.94 rafl DEVELOPMENT RELEASE
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 * Attempt to fix Math::BigInt::Lite failures
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2010-09-13 v1.93 rafl
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 * Depend on perl >= 5.6.2
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 * Remove obsolete core test directory boilerplate
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 * Convert from Test to Test::More
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2010-09-10 v1.92 rafl
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 * re-upload v1.91 with a fixed SIGNATURE
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2010-09-10 v1.91 rafl
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 * fix various documentation bugs
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2010-09-03 v1.90 rafl
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 * fix bnok() for k==0 and k==n-1
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2008-04-20 v1.89 Tels
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 * fix #35238: batan2() handles inf/+inf wrong
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2007-09-22 v1.88 Tels
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 * fix wide ints on Perl v5.8.0 (Thanx zefram!)
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 * minimum required is Perl v5.6 (tested by zefram)
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 * _find_round_parameters(), _scale_a() and _scale_p(): trunc A/P to integers
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 * fix from_oct(), from_bin() and from_hex()
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2007-06-30 v1.87 Tels
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 * fix undef base in blog()
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 * support config('lib') as shortcut for config()->{lib}
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 * _find_round_parameters(): convert $a & $p to normal scalars, or bad
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   things will happen during rounding of BigFloats
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 * add bpi(), bcos(), bsin(), batan(), batan2() methods
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 * add bmuladd()
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 * streamline the is_xxx() and copy() methods
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2007-05-05 v1.86 Tels
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 * bump version
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2007-05-05 v1.85 Tels
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 * bump version
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2007-05-04 v1.84 Tels
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 * add bnok() method (n over k)
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2007-04-16 v1.83 Tels
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 * bump version
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2007-04-09 v1.82 Tels
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 * use $CALC->_zeros() directly (instead _trailing_zeros()) to speed up
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   exponent() and mantissa()
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 * fix documentation that blsft() and brsft() default to base 2 (not 10)
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 * add bexp() and fix overloading for exp()
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2007-03-16 v1.81 Tels
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 * no code change, just a package update
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2007-03-04 v1.80 Tels
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 * require Perl v5.6.2 as minimum
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 * fix bug #24969 (Can't use an undefined value as an ARRAY reference)
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 * fix bug #12857: Subclasses and overload
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 * fix bug #13866: NaN (in bignum queue)
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 * fix bug #21586: Incorrect result when comparing with NaN
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 * fix bug #15896: "==" overloading is broken for "NaN"
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2007-02-02 v1.79 Tels
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 * fix typos
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2007-01-27 v1.78 Tels
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 * implement "try" and "only" as replacements for "lib"
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 * make 'use Math::BigInt lib => "foo"' warn if foo cannot be loaded and a
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   fallback occurs
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 * fix bug #21446 - Docs/code inconsistency for bnorm() method
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 * fix bug #21964 - A patch to include a rounding mode of 'common'
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 * fix bug #21445 - Documentation error for exponent() method
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 * fix bug perl #41050 - NaN returned when raising integer value to negative
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   power
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 * add from_hex(), from_oct(), and from_bin()
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 * add as_oct()
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2005-05-17 v1.77 Tels
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 * bump version
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2005-04-10 v1.76 Tels
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 * fix rounding doc, add notes about prevision vs. accuracy
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 * trap inf and -inf in new()
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 * load FastCalc as default
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2005-03-20 v1.75 Tels
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 * use a trick to remove the dependency on Scalar::Util in bsub()
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 * fix atan2(), it did not preserve the order of arguments
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   (Thanx to Ambros & Zaxo for report and patch!)
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2005-01-01 v1.74 Tels
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 * streamline _scale_a() and _scale_p() for more speed in rounding
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 * remove the now unnec. support for MB_NEVER_ROUND and {_f}, this
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   makes all ops that call round() a tad faster (one exists is
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   removed) and shrinks the codesize a bit
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 * streamline bneg(), inline is_zero(): makes it 1.6 times faster
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 * replace ref($_[0]) w/ undef when it isn't actually needed. This
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   makes some ops (bsstr(), bneg etc) about 2% faster for small numbers
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 * restrict low-level math library names to sane chars to avoid
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   exploitation of eval()
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 * fill_can_cache() accidentally did checks for 'or' & 'xor'
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 * inline _fill_can_cache
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 * add _register_callback() to notify subclasses of lower math lib changes
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 * bgcd() is now about 10% faster
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 * is_positive(0) == 0, since 0 is neither positive nor negative
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 * streamline bmod() a bit
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 * fix blog() constructing arguments (broke Math::BigInt::Constant)
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2004-10-10 v1.73 Tels
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 * overloading of <<= and >>= makes these ops about 10% faster and fixes the
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   problem that "$a <<= 2" would create a different object for $a to point to
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 * quite a lot of fixes for NaN/inf handling in bpow() (bmul already did it
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   right) - bug report by jeff at thekidders com and Hugo - Thank you!
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2004-07-13 v1.72 Tels
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 * no changes
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2004-07-08 v1.71 Tels
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 * fixed bsub() failing under $x -= $x; Thanx Peter J. Acklam!
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 * _scan_for_nonzero() reuses length/stringform of $x and is thus faster, this
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   helps rounding if the number after the roundposition is '5'
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2004-03-12 v1.70 Tels
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 * bpow() computed -X ** Y wrong for Y that are odd
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 * 0 ** -Y => +inf (was NaN) due to 0 ** -Y => 1/0**Y => 1/0 => +inf
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 * fixed bug in perl -Mbignum -le 'print 2 ** 46 * 3' under Bigint::Lite
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   leading to "Can't use an undefined value as an ARRAY reference at
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   /usr/local/lib/perl5/5.8.2/Math/BigInt/Calc.pm line 462."
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 * fixed upgrading of blog() with base = undef (means: base e)
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 * make the synopsis actually runnable (Thanx Paul McCarthy)
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 * blcm(): handle a list of strings (instead one obj and some strings), too
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2004-01-13 v1.69 Tels
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 * bacmp(+-$x,-inf) was wrong (Thanx William T. Morgan!)
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 * digit($x,$y) segfaulted under 5.6.1 if $y was a BigInt
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 * blog() was missing the modify() check (breaking MBI::Constant)
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 * delete $x->{_a} vs. $x->{_a} = undef to save memory
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2003-12-26 v1.68 Tels
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 * bfac(inf) is inf, not NaN
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 * added alias names: as_int() (as_number()), is_pos(), is_neg() and doc
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 * factored out all the emulation code and moved it to Math::BigInt::CalcEmu
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 * binary/hexadecimal input was twice as slow as v1.66 due to a typo in v1.67
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 * streamlined overload for boolean context (20% faster "... if $x;")
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 * round() was missing a croak() in path testing for wrong roundmode
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 * badd(): optimize away setting of sign if it is already right
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 * bdec() is about 10% faster for negative numbers
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 * bpow(): removed some now needless tests for 0 and 1: about 30% faster
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   for small numbers
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 * streamlined exponent() (parts() benefits from this, too)
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2003-12-02 v1.67 Tels
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 * overload for cos/sin/exp/atan2 to make cos(Math::BigInt->new(...)) work
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 * implemented blog() with a simple and fast "iterative" method
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 * use _log_int() in $CALC if possible
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 * cache $CALC->can(...) calls in global %CAN hash for speed
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 * reorder is_zero() check for band(), bior() and bxor() to speed up the
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   case for when the underlying lib has _and(), _ior() and _xor()
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 * implement a new way of emulating AND, OR and XOR, this tremendously
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    helps if band() et. al. are called with negative arguments
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 * try to call _signed_or(), _signed_and() and _signed_xor() in lib
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 * is_foobar() methods are slightly faster
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 * bnot() is about 12% faster
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 * bsqrt(): moved is_zero() || is_one() test out of the way => 28% faster
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   for "small" values (Calc and GMP)
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 * small change for overload::constant
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 * bfac(): do 0 or 1 check only if CALC cannot do _fac() (thus faster)
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 * removed a needless _copy in bmod() with negative arguments (slightly faster)
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2003-09-01 v1.66 Tels
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 * document accepted inputs better
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 * fix wrong upgrade and undef-parameter handling in broot()
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 * implement broot() if lib doesn't have a _root() routine for $y that are
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   powers of two and for small $x
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 * warn if broot() cannot yet compute proper result
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 * remove needless _one(): 3% speedup for binc()
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 * remove needless _swap(): 1% (Calc) - 6% (GMP) speedup for overloaded math
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2003-07-13 v1.65 Tels
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 * document that config() can set certain values
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 * replace die() with Carp::croak()
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 * remove needless is_zero() check in as_bin() and as_hex(), making them
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   faster, especially when under a different lib like GMP.
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 * Fixed the infinite recursion in bignum. See http://xrl.us/k6y
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 * fix handling of 0e999, 0e-999 etc
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2002-11-03 v1.64 Tels
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 * removed needless "my $c = ...;" statements in binf() and bnan()
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 * forgot () around "$x->{_f} & MB_NEVER_ROUND"
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 * bsqrt(inf) == inf, not NaN
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 * $x->bdiv($x) did not round the resulting 1 properly
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 * removed the shortcut testcode in bdiv() (Calc handles this now)
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 * added (non-working for now) broot() method
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 * changed length() to CORE::length() in two places (thanx Liz!)
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 * config() can take arguments and set them, croak on wrong ones
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 * config(trap_nan => 1) to manipulate former $NaNOK variable
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 * config(trap_inf => 1), too
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 * trap_nan/trap_inf really croak on any attempt to create an NaN/inf
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 * spellings of Bigint => BigInt
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 * _find_rounding_parameters(): set $a to undef if it is 0
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2002-09-08 v1.63 Tels
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 * bsqrt() did not modify $x but returned new object when lib does not have
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   a _sqrt() routine (BareCalc, BitVect and Pari are affected, Calc, FastCalc
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   and GMP were not)
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2002-08-21 v1.62 Tels
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 * bcmp()/bacmp() upgrade now if requested
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 * bmodinv() uses an all-positive algorithm, speeding it up by about 5-8%
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   and allowing to implement the same algorithm in Calc for factor 4 speedup
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2002-08-13 v1.61 Tels
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 * tests for bsstr()/numify() with negative/special inputs
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 * bround() keeps $scale as scalar for speed and less problems
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 * fix for trailing newlines in input
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 * some doc fixes (especially return values of is_foo() methods)
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 * make testsuite so that it will pass under FastCalc easily
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2002-07-07 v1.60 Tels
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 * shortcuts to avoid calls to objectify for add/sub/mul/div/mod/pow/bcmp etc
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 * fix overloaded bcmp() so that the objectify()-avoidance kicks in
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 * avoid calling round() when BigFloat requested 'no rounding please'
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 * bcmp()'s shortcut for comparing x <=> 0, 0 <=> 0, 0 <=> $y was making things
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   slower than just handing the compare to Calc. Even more so for Pari et al.
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 * $x->accuracy() and $x->precision() returned undef, instead of 0 if
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   A/P of $x was 0 and global A/P was undef.
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 * $x->bmod() did not modify $x in place when returning NaN/inf/-inf
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 * some binary ops (band/bxor/bior/bpow) were not properly rounding the result
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   to the requested A/P/R; the same ops also forgot to take $y into account
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 * doc for accuracy()/precision()
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2002-06-10 v1.59 Tels
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 * pod fixes for bmodpow()/bmodinv()
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 * fix in as_hex() and as_bin() for older Perls
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 * speedups in bpow(), bmodin() and bmodpow()
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2002-06-09 v1.58 Tels
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 * invalid inputs with two dot's (1.2.3 or 1..2 etc) are now really invalid
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2002-05-30 v1.57 Tels
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 * fixed objectify() to make "perl -Mbigrat -le 'print 1+2/3'" work
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 * added bmodpow() and bmodinv() as (not-working yet) stubs
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2002-03-17 v1.56 Tels
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 * documented config()
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 * simplified import() logic a bit
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 * changed some isa->($upgrade) => !$isa->($self);
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2002-03-17 v1.55 Tels
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 * :constant picks up binary/hexadecimal constants
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 * Math::BigInt->digit(123) works now
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2002-03-03 v1.54 Tels
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 * really fixed overlong pod =item
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 * downgrade() and upgrade() with undef as argument didn't clear the variable
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 * bmul() upgrades if second argument is non-integer
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 * bdiv() upgrades if $x > $y
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 * bpow() upgrades if second argument is non-integer
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 * objectify disable downgrade (for MBF)
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 * new() twice as fast due to shortcut simple numbers, save _split() & _round()
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2002-02-27 v1.53 Tels
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 * precisision typo
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 * fixed overlong pod =item
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 * added downgrade()
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2002-02-24 v1.52 Tels
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 * hooks for _bin(), _bnan(), _bone() and _bzero()
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 * =head2 section for accuracy
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2002-02-16 v1.51 Tels
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 * fixed bfround(-x) (f.i. 0.004->bfround(-2) resulted in 0.01, not 0.00)
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 * bfround(x) rounded at wrong place (off by one)
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 * calling bfround(x) rounded further and further instead of keeping result
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 * blog() upgrades if requested
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 * added doc stub for every public function
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2002-02-10 v1.50 Tels
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 * bfac() and hook for _fac() in libs
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 * documented sub-classing and auto-upgrade
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 * < 4 test in bsqrt() after the CALC call for more performance
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 * added overload for sqrt()
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 * added possibility to upgrade via use Math::BigInt upgrade => 'Foo::Bar'
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 * Math::Big(Int|Float)->accuracy() clears precision, and vice versa
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 * small optimization in bdiv() regarding abs($x) < abs($y)
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 * brsft() for negative numbers in base 2 was completely wrong
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2002-01-07 v1.49 Tels
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 * as_hex() and as_bin() use 16 instead of 8 bits per iteration
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 * overload for log() and blog()
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 * tricks to make 'require Math::BigInt' and 'use Math::BigInt();' work again
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 * use $CALC instead of require for newer Perls (test for $] > 5.006 vs 5.6)
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 * bzero()/bone() handling of A & P was broken
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 * bround()/bfround() forgot to set A or P for zeros
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 * embedded _find_round_parameters into round(), streamlined both versions
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 * round() now uses string-add to make it almost twice as fast
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 * bnot() did round twice
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2001-12-06 v1.48 Tels
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 * fixed pod in many places
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 * bmod: use round(), not bround()
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 * bsqrt: use _sqrt() from lib, if possible
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 * bsqrt: would hang for certain (most?) inputs
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 * bdiv: slow check for 1 || -1 replaced by much faster version
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 * bdiv: call _div() only when nec. in list context, otherwise scalar
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 * streamlined copy(), _find_round_parameters()
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 * removed the EXPORT_OK except for objectify, _swap and bgcd/blcm
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 * bzero(), bone(): take additional A and P and store 'em
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 * bnan(), binf(): clear A and P
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2001-11-18 v1.47 Tels
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 * added $rnd_mode support for compatibility
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 * two 'my $t = ... if ..;' cases to 'my $t; $t = ... if ...;'
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 * added overload for %=, |=, &= and ^= for more speed
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 * _split(): check for 1e2e3 and reject it
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2001-11-11 v1.46 Tels
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 * binc(),bdec() use lib (via _inc(),_dec()) => faster (see BENCHMARK)
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 * avoid the unnec. rounding bsub()/binc()/bdec() (badd() already took care)
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 * made bsub() faster by removing the bneg() overhead from it
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2001-11-04 v1.45 Tels
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 * tests run now in subclass, too
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 * bmod() can use _mod in lib
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 * lots of tests fixed (assumed wrong base etc) and added
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 * bpow() about 10-15% faster for small numbers (like 2 ** 150, 3 * 200 etc)
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2001-10-05 v1.43 Tels
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 * $x->bround($n) is 43 times faster if $n > $x->{_a} (no-op)
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 * Heaploads of rounding fixes (and tests)
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 * Test for 99999-bug in Calc
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2001-09-03 v1.42 Tels
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 * bug in overload section causing performance losses in subclasses
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 * call $CALC->import() with list of libs
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 * odd numbers never have trailing zeros, so don't convert them to DEC to look
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 * as_hex() and as_bin()
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 * $x->bmod() did not modify $x, only returned result. Oups.
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 * new('inf') produced NaN (was expecting '+inf')
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 * exponent(), mantissa() & parts() failed or returned scalars for inf,-inf,NaN
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2001-08-08 v1.41 Tels
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 * fixed inf test (coredumps)
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2001-08-03 v1.40 Tels
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 * bxor(-$x,-$y) was broken (and not tested *sigh*)
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 * streamlined bcmp
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 * drop leading '+' for inf
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 * bxor(), band(), bior() with negative arguments don't get passed to lib
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   (makes it work with BitVect, Pari, GMP etc)
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2001-08-02 v1.39 Tels
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 * fixed history (duh!)
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 * assign return values from $CALC back to $x->{value}
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 * fixed +-inf handling in a lot of places and tests for that
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 * band(), bxor() and bior() now work with negative inputs
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 * remove bint() (Math::BigFloat->bint() just DNDWIM and no sense, either)
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2001-07-15 v1.38 Tels
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 * test for mul() shortcut
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2001-07-15 v1.37 Tels
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 * applied Philip Newtons spelling and doc patch(s)
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 * Benjamin Trott: _split() is faster for numbers that need no splitting
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 * Benjamin Trott: don't take shortcut in badd(), or Pari won't work
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 * allow use Math::BigInt lib => 'Pari,BitVect,Foo,Bar';
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 * delegate shifting to CALC if possible, otherwise fallback
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 * test for self-pow, to see if lib's fail (since BitVect failed for self-pow)
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 * _one() => bone()
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 * +x / 0 => +inf, -x / 0 => -inf, while 0/0 and +-x % 0 are still NaN
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 * tests for bnan() and bone()
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 * Math::BigInt::Calc now determines biggest $BASE to use. Default should now
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   be 1e7 on most systems, giving 20% to 40% speedups.
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2001-07-04 v1.36 Tels
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 * is_positive(), is_negative()
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 * various pod fixes (overlong =item, spelling erorrs etc)
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 * torn out the bones from under the flesh and moved them to Math::BigInt::Calc
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 * added Math::BigInt::Calc, Math::BigInt::Small (and Math::BigInt::BitVect)
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 * fixed tests for bacmp() (could never fail)
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 * removed internal _set() and tests for it
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 * +-inf handling in bcmp(), bpow()
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2001-06-15 v1.35 Tels
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 * added bfloor(), bceil()
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 * fixed bior(), bxor(), band() for $x->bxxx(NaN,0), added modify() to them
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2001-06-13 v1.34 Tels
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 * binary integer input (0b01110 etc)
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 * fixed: '-0x0' left '-0'
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 * added is_inf(), binf() and some support for +-inf in new(), bsstr() etc
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 * added tests for is_odd(), is_even(), _set() and is_zero(), is_inf(), bsstr()
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2001-06-09 v1.33 Tels
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 * bround() no longer uses 10 ** $pad and is thus much faster when rounding up
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 * fixed and added rounding benchmark (did time bmul instead bround)
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 * blsft(),brsft(): can work in different bases, check against invalid
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   inputs, more tests, speedup when in base 10
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 * _trailing_zeros is 50% faster
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 * A/P after each op, tests for it in accuracy.t
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 * round() instead of bnorm()
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 * $x->accuracy(), $x->precision() actually round $x to the set value
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 * tests for is_one()
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 * hexadecimal integer input (0xcafebabe etc)
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2001-05-11 v1.32 Tels
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 * added accuracy/precision/fallback/round_mode
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2001-05-08 v1.31 Tels
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 * _ between digits now accepted, ' ' no longer valid inside (but at front/end)
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 * Exxx is NaN, and no longer produces warning
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 * .xxx style numbers are valid input
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 * tests for 1E1, 123E-2, 1E2 etc style input to Bigint.pm
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 * fixed overload (w/ _swap/copy), subclasses can inherit it easily
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 * removed clone()
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 * added bsstr()
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2001-04-23 v1.3 Tels
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 * added (compatible to MBF) mantissa(), exponent() & parts() as well as tests
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 * _trailing_zeros()
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 * fixed as_number() to return copy of BigInt
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 * added bround(), bfround() and support for round_mode() as well as $rnd_mode
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 * fixed bug in bdiv() wich left reminder "-0", causing further op's to die()
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 * added is_valid to testsuite to see whether invalid objects are created
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 * added bsqrt()
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 * workaround coredump bug in bool() for v5.6.1
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2001-04-07 v1.23 Tels
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 * spelling errors in pod
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2001-04-05 v1.22 Tels
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 * documented Peters OS/390 patch/changes (fix was in for quite some time)
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 * fixed bug Math::BigInt->new(Math::BigFloat->new(3));
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 * objectify() with other objects than BigInt as further args, copy() etc
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 * $x->digit($n) to query fast value of Nth digit
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 * as_number()
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2001-03-30 v1.21 Tels
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 * bool() works now under 5_005
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 * bug in bsub where numbers with at least 6 trailing digits after any op failed
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2001-03-24 v1.20 Tels
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 * added: is_nan()
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 * bug in bmod/bdiv, I forgot some cases with negatives. Thanx to Bruce Fields!
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 * documented ':constant' and eval() crash on Perl 5.00x
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 * documented BigInts behaviour of bmod/bdiv and use integer
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2001-03-09 v1.16 Tels
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 * Math::BigInt::badd(4,5) and Math::SomeChildOfBI->badd(4,5) work now
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 * '$x = scalar (**|%|+|-|*|\) $object;' failed (was not tested, either)
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 * 'if ($x)' is now O(1) instead of O(N) and at least twice as fast
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 * fixed nasty bug in _digits that caused <=> after add/sub/mul etc to fail
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   if result was between 100001 and 109999, added test for this
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 * added test cases for op's that should preserve args (+,+=,abs(), neg() etc)
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 * added tests for overloaded 'bool'
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 * added test.pl and some examples (prime.pl, bigprimes.pl)
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 * tests after "use Math::BigInt :constant" were screwed due to not using eval
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 * $x->numify() (for $array[$x] = 0; etc) is much faster now
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 * added caveat documentation for $x = -$x; and $x *= string1 operator string2;
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2001-02-24 v1.15 Tels
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 * $x / $x is now a lot faster (more O(1) than O(N))
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 * 10 ** $x is now a lot faster (more O(N/5) instead of O(N))
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 * overload of **= makes $x **= $y faster
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 * 0 ** 0 was NaN, not 1
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 * -a % b = +c (was -c) to be compatible with perl
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 * added $x->length() and test for it; fixed _digits() (was off by 1)
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 * objectify() was not exported, added tests for objectify()
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2001-02-21 v1.14 Tels
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 * overload +=, -=, *= and /= for about 20-30% more speed if both args have
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   roughly same length
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 * shortcut in add() makes $x += $y; $x -= $y; for large $x and small $y
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   an O(1) case instead of O(N)
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 * fixed (non-critical) bug that caused objectify in numify/bool/stringify to
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   create scratch objects from undef params.
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2001-02-18 v1.13 Tels
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 * got rid of duplicated copy() code in new()
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2001-02-16 v1.12 Tels
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 * accidentally dropped self-multiply test in bigintpm.t
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 * fixed bug in overloading cmp
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 * after correcting the overload for 'cmp', I got a lot of test failings and
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   finally discovered that the bstr()'s return of '[+-][0-9]+' instead of
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   Perls ways of '[-]?[0-9]+' breaks string comparisons with numbers :(
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   F.i. ok() from Test.pm uses 'eq' and you can not do ok($a,3*3) where $a
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   is a BigInt. IMNSHO clearly wrong. And only changing the way cmp is
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   overloaded would lead to the curios situation that the following:
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   'print "$a eq $b" if $a eq $b;' would print "+3 eq 3", which looks wrong.
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   Mark B. said go ahead and change bstr(), so I changed it ;) to drop
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   the '+', adapted all the tests, changed the doc, etc.
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   BigInts behave now transparently like build-in scalars in integer/string
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   context ;o)
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2001-02-14 v1.11 Tels (first release)
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 * fixed bug in band(), bxor(), etc that used badd($x, fixed_number_here);
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 * since subclasses might not be happy with fixed numbers, make sure we pass
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   BigInts all the time if using something like $someclass->badd();
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 * fixed bug in band/bxor/bior which destroyed second argument
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 * bxor/band/bior work now correctly for subclasses
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 * ++ and -- are now a tad (ca 5%) faster
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2000-11-24 v1.10 Tels
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 * finally made it Math::BigInt (w/o trailing 's')
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2000-11-23 v1.09 Tels
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 * fixed bug in bmul (and thus bpow) (self multiply works now)
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2000-11-22 v1.08 Tels
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 * fixed all but one test (band bior bxor etc)
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2000-11-20 v1.07 Tels
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 * objectify fixed to not make copies and work with subclasses
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2000-11-19 v1.06 Tels
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 * 7 tests remain
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 * bgcd accepts lists, added blcm
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2000-11-16 v1.05 Tels
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 * 8 tests remain
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 * new copies _all_ fields, not only Math::Bigint ones
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2000-11-15 v1.04 Tels
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 * fixed bigintpm to test '++' and '--' properly
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 * done div, fixed mul/bpow (13 tests remain)
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2000-11-14 v1.03 Tels
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 * x**0 => 1 (instead of x)
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 * fixed bigintpm to include bpow, binc, bdec, new() test
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2000-11-13 v1.02 Tels
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 * fixed sub and mul (sort of)
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 * found out that "$wanted = shift || return bzero()" causes a call to numify,
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 * testing for undefined fixes this problem (but might waste more time for
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 * a new(0), will save time on average.