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Shlomi Fish


Math::GMP - High speed arbitrary size integer math


version 2.09


  use Math::GMP;
  my $n = Math::GMP->new('2');

  $n = $n ** (256*1024);
  $n = $n - 1;
  print "n is now $n\n";


Math::GMP was designed to be a drop-in replacement both for Math::BigInt and for regular integer arithmetic. Unlike BigInt, though, Math::GMP uses the GNU gmp library for all of its calculations, as opposed to straight Perl functions. This can result in speed improvements.

The downside is that this module requires a C compiler to install -- a small tradeoff in most cases. Also, this module is not 100% compatible with Math::BigInt.

A Math::GMP object can be used just as a normal numeric scalar would be -- the module overloads most of the normal arithmetic operators to provide as seamless an interface as possible. However, if you need a perfect interface, you can do the following:

  use Math::GMP qw(:constant);

  $n = 2 ** (256 * 1024);
  print "n is $n\n";

This would fail without the ':constant' since Perl would use normal doubles to compute the 250,000 bit number, and thereby overflow it into meaninglessness (smaller exponents yield less accurate data due to floating point rounding).


Although the non-overload interface is not complete, the following functions do exist:


  $x = Math::GMP->new(123);

Creates a new Math::GMP object from the passed string or scalar.

  $x = Math::GMP->new('abcd', 36);

Creates a new Math::GMP object from the first parameter which should be represented in the base specified by the second parameter.


  $x = Math::GMP->new(5);
  my $val = $x->bfac();      # 1*2*3*4*5 = 120
  print $val;

Calculates the factorial of $x and returns the result.


  $x = Math::GMP->new(6);
  $x->band(3);      # 0b110 & 0b11 = 1

Calculates the bit-wise AND of its two arguments and modifies the first argument.


  $x = Math::GMP->new(6);
  $x->bxor(3);      # 0b110 & 0b11 = 0b101

Calculates the bit-wise XOR of its two arguments and modifies the first argument.


  $x = Math::GMP->new(6);
  $x->bior(3);      # 0b110 & 0b11 = 0b111

Calculates the bit-wise OR of its two arguments and modifies the first argument.


  $x = Math::GMP->new(0b11);
  my $result = $x->blshift(4, 0);
  # $result = 0b11 << 4 = 0b110000

Calculates the bit-wise left-shift of its two arguments and returns the result. Second argument is swap.


  $x = Math::GMP->new(0b11001);
  my $result = $x->brshift(3, 0);
  # $result = 0b11001 << 3 = 0b11

Calculates the bit-wise right-shift of its two arguments and returns the result. Second argument is swap.


  $x = Math::GMP->new(6);
  $x->bgcd(4);      # 6 / 2 = 2, 4 / 2 = 2 => 2

Returns the Greatest Common Divisor of the two arguments.


  $x = Math::GMP->new(6);
  $x->blcm(4);      # 6 * 2 = 12, 4 * 3 = 12 => 12

Returns the Least Common Multiple of the two arguments.


  $x = Math::GMP->new(5);
  $x->bmodinv(7);   # 5 * 3 == 1 (mod 7) => 3

Returns the modular inverse of $x (mod $y), if defined. This currently returns 0 if there is no inverse (but that may change in the future). Behaviour is undefined when $y is 0.


  $x = Math::GMP->new(6);
  $x->bsqrt();      # int(sqrt(6)) => 2

Returns the integer square root of its argument.


  $x = Math::GMP->new(6);

Returns the value of the Legendre symbol ($x/$y). The value is defined only when $y is an odd prime; when the value is not defined, this currently returns 0 (but that may change in the future).


  $x = Math::GMP->new(6);

Returns the value of the Jacobi symbol ($x/$y). The value is defined only when $y is odd; when the value is not defined, this currently returns 0 (but that may change in the future).


  $x = Math::GMP::fibonacci(16);

Calculates the n'th number in the Fibonacci sequence.


  $x = Math::GMP->new(7);

Probabilistically determines if the number is a prime. Argument is the number of checks to perform. Returns 0 if the number is definitely not a prime, 1 if it may be, and 2 if it definitely is a prime.


As of version 1.0, Math::GMP is mostly compatible with the old Math::BigInt version. It is not a full replacement for the rewritten Math::BigInt versions, though. See the SEE ALSO section on how to achieve to use Math::GMP and retain full compatibility to Math::BigInt.

There are some slight incompatibilities, such as output of positive numbers not being prefixed by a '+' sign. This is intentional.

There are also some things missing, and not everything might work as expected.


The version control repository of this module is a git repository hosted on GitHub at: https://github.com/turnstep/Math-GMP. Pull requests are welcome.


Math::BigInt has a new interface to use a different library than the default pure Perl implementation. You can use, for instance, Math::GMP with it:

  use Math::BigInt lib => 'GMP';

If Math::GMP is not installed, it will fall back to its own Perl implementation.

See Math::BigInt and Math::BigInt::GMP or Math::BigInt::Pari or Math::BigInt::BitVect.


Chip Turner <chip@redhat.com>, based on the old Math::BigInt by Mark Biggar and Ilya Zakharevich. Further extensive work provided by Tels <tels@bloodgate.com>.


Shlomi Fish <shlomif@cpan.org>


This software is Copyright (c) 2000 by James H. Turner.

This is free software, licensed under:

  The GNU Lesser General Public License, Version 2.1, February 1999


Please report any bugs or feature requests on the bugtracker website https://rt.cpan.org/Public/Dist/Display.html?Name=Math-GMP or by email to bug-math-fft@rt.cpan.org.

When submitting a bug or request, please include a test-file or a patch to an existing test-file that illustrates the bug or desired feature.



You can find documentation for this module with the perldoc command.

  perldoc Math::GMP


The following websites have more information about this module, and may be of help to you. As always, in addition to those websites please use your favorite search engine to discover more resources.

Bugs / Feature Requests

Please report any bugs or feature requests by email to bug-math-gmp at rt.cpan.org, or through the web interface at https://rt.cpan.org/Public/Bug/Report.html?Queue=Math-GMP. You will be automatically notified of any progress on the request by the system.

Source Code

The code is open to the world, and available for you to hack on. Please feel free to browse it and play with it, or whatever. If you want to contribute patches, please send me a diff or prod me to pull from your repository :)


  git clone https://github.com/turnstep/perl-Math-GMP.git