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Math::GMP(3pm) User Contributed Perl Documentation Math::GMP(3pm)
NAME
Math::GMP - High speed arbitrary size integer math
VERSION
version 2.24
SYNOPSIS
use Math::GMP;
my $n = Math::GMP->new('2');
$n = $n ** (256*1024);
$n = $n - 1;
print "n is now $n\n";
DESCRIPTION
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).
METHODS
Although the non-overload interface is not complete, the following functions do exist:
new
$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.
bfac
$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.
$n->bnok($k)
$x = Math::GMP->new(5);
my $val = $x->bnok(2); # 1*2*3*4*5/(1*2)/(1*2*3) = 10
print $val;
Calculates the binomial coefficient of $n over $k and returns the result. Equals to
$n!/($k!*($n-$k)!).
( Added in version 2.23 .)
my $val = $x->band($y, $swap)
$x = Math::GMP->new(6);
my $val = $x->band(3, 0); # 0b110 & 0b11 = 1
print $val;
Calculates the bit-wise AND of its two arguments and returns the result. $swap should be
provided but is ignored.
my $ret = $x->bxor($y, $swap);
$x = Math::GMP->new(6);
my $val = $x->bxor(3, 0); # 0b110 ^ 0b11 = 0b101
print $val;
Calculates the bit-wise XOR of its two arguments and returns the result.
my $ret = $x->bior($y, $swap);
$x = Math::GMP->new(6);
my $val = $x->bior(3); # 0b110 | 0b11 = 0b111
print $val;
Calculates the bit-wise OR of its two arguments and returns the result.
blshift
$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.
brshift
$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.
bgcd
my $x = Math::GMP->new(6);
my $gcd = $x->bgcd(4);
# 6 / 2 = 3, 4 / 2 = 2 => 2
print $gcd
Returns the Greatest Common Divisor of the two arguments.
blcm
my $x = Math::GMP->new(6);
my $lcm = $x->blcm(4); # 6 * 2 = 12, 4 * 3 = 12 => 12
print $lcm;
Returns the Least Common Multiple of the two arguments.
bmodinv
my $x = Math::GMP->new(5);
my $modinv = $x->bmodinv(7); # 5 * 3 == 1 (mod 7) => 3
print $modinv;
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.
broot
my $x = Math::GMP->new(100);
my $root = $x->root(3); # int(100 ** (1/3)) => 4
print $root;
Returns the integer n'th root of its argument, given a positive integer n.
brootrem
my $x = Math::GMP->new(100);
my($root, $rem) = $x->rootrem(3); # 4 ** 3 + 36 = 100
print "$x is $rem more than the cube of $root";
Returns the integer n'th root of its argument, and the difference such that " $root ** $n
+ $rem == $x ".
bsqrt
my $x = Math::GMP->new(6);
my $root = $x->bsqrt(); # int(sqrt(6)) => 2
print $root;
Returns the integer square root of its argument.
bsqrtrem
my $x = Math::GMP->new(7);
my($root, $rem) = $x->sqrtrem(); # 2 ** 2 + 3 = 7
print "$x is $rem more than the square of $root";
Returns the integer square root of its argument, and the difference such that " $root ** 2
+ $rem == $x ".
is_perfect_power
my $x = Math::GMP->new(100);
my $is_power = $x->is_perfect_power();
print "$x is " . ($is_power ? "" : "not ") . "a perfect power";
Returns "TRUE" if its argument is a power, ie if there exist integers a and b with b > 1
such that " $x == $a ** $b ".
is_perfect_square
my $x = Math::GMP->new(100);
my $is_square = $x->is_perfect_square();
print "$x is " . ($is_square ? "" : "not ") . "a perfect square";
Returns "TRUE" if its argument is the square of an integer.
legendre
$x = Math::GMP->new(6);
my $ret = $x->legendre(3);
Returns the value of the Legendre symbol ($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).
jacobi
my $x = Math::GMP->new(6);
my $jacobi_verdict = $x->jacobi(3);
Returns the value of the Jacobi symbol ($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).
fibonacci
my $fib = Math::GMP::fibonacci(16);
Calculates the n'th number in the Fibonacci sequence.
probab_prime
my $x = Math::GMP->new(7);
my $is_prime_verdict = $x->probab_prime(10);
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.
$x->add_ui_gmp($n)
Adds to $x and mutates it in-place. $n must be a regular non-GMP, positive, integer.
($quotient, $remainder) = $x->bdiv($y);
my $x = Math::GMP->new(7);
my ($quo, $rem) = $x->bdiv(3);
Returns both the division and the modulo of an integer division operation.
my $ret = $x->div_2exp_gmp($n);
my $x = Math::GMP->new(200);
my $ret = $x->div_2exp_gmp(2);
Returns a right-shift of the Math::GMP object by an unsigned regular integer. Also look
at blshift() .
my $str = $x->get_str_gmp($base)
my $init_n = 3 * 7 + 2 * 7 * 7 + 6 * 7 * 7 * 7;
my $x = Math::GMP->new($init_n);
my $ret = $x->get_str_gmp(7);
print $ret; # Prints "6230".
Returns a string representation of the number in base $base.
my $clone = $x->gmp_copy()
Returns a copy of $x that can be modified without affecting the original.
my $verdict = $x->gmp_tstbit($bit_index);
Returns whether or not bit No. $bit_index is 1 in $x.
my $remainder = $dividend->mmod_gmp($divisor)
my $x = Math::GMP->new(2 . ('0' x 200) . 4);
my $y = Math::GMP->new(5);
my $ret = $x->mmod_gmp($y);
# $ret is now Math::GMP of 4.
From the GMP documentation:
Divide dividend and divisor and put the remainder in remainder. The remainder is always
positive, and its value is less than the value of the divisor.
my $result = $x->mod_2exp_gmp($shift);
my $x = Math::GMP->new(0b10001011);
my $ret = $x->mod_2exp_gmp(4);
# $ret is now Math::GMP of 0b1011
Returns a Math::GMP object containing the lower $shift bits of $x (while not modifying
$x).
my $left_shifted = $x->mul_2exp_gmp($shift);
my $x = Math::GMP->new(0b10001011);
my $ret = $x->mul_2exp_gmp(4);
# $ret is now Math::GMP of 0b1000_1011_0000
Returns a Math::GMP object containing $x shifted by $shift bits (where $shift is a plain
integer).
my $multiplied = $x->bmulf($float)
my $x = Math::GMP->new(3)->bpow(100);
my $ret = $x->bmulf(1.5);
# $ret is now Math::GMP of floor(3^101 / 2)
Returns a Math::GMP object representing $x multiplied by the floating point value $float
(with the result truncated towards zero).
( Added in version 2.23 .)
my $ret = $base->powm_gmp($exp, $mod);
my $base = Math::GMP->new(157);
my $exp = Math::GMP->new(100);
my $mod = Math::GMP->new(5013);
my $ret = $base->powm_gmp($exp, $mod);
# $ret is now (($base ** $exp) % $mod)
Returns $base raised to the power of $exp modulo $mod.
my $plain_int_ret = $x->sizeinbase_gmp($plain_int_base);
Returns the size of $x in base $plain_int_base .
my $int = $x->intify();
Returns the value of the object as an unblessed (and limited-in-precision) integer.
_gmp_build_version()
my $gmp_version = Math::GMP::_gmp_build_version;
if ($gmp_version ge 6.0.0) {
print "Math::GMP was built against libgmp-6.0.0 or later";
}
Class method that returns as a vstring the version of libgmp against which this module was
built.
_gmp_lib_version()
my $gmp_version = Math::GMP::_gmp_lib_version;
if ($gmp_version ge 6.0.0) {
print "Math::GMP is now running with libgmp-6.0.0 or later";
}
Class method that returns as a vstring the version of libgmp it is currently running.
gcd()
An alias to bgcd() .
lcm()
An alias to blcm() .
constant
For internal use. Do not use directly.
destroy
For internal use. Do not use directly.
new_from_scalar
For internal use. Do not use directly.
new_from_scalar_with_base
For internal use. Do not use directly.
op_add
For internal use. Do not use directly.
op_div
For internal use. Do not use directly.
op_eq
For internal use. Do not use directly.
op_mod
For internal use. Do not use directly.
op_mul
For internal use. Do not use directly.
op_pow
For internal use. Do not use directly.
op_spaceship
For internal use. Do not use directly.
op_sub
For internal use. Do not use directly.
stringify
For internal use. Do not use directly.
uintify
For internal use. Do not use directly.
DIVISION BY ZERO
Whereas perl normally catches division by zero to provide a standard perl-level error
message, "libgmp" does not; the result is usually a SIGFPE (floating point exception)
giving a core dump if you ever attempt to divide a "Math::GMP" object by anything that
evaluates to zero. This can make it hard to diagnose where the error has occurred in your
perl code.
As of perl-5.36.0, SIGFPE is delivered in a way that can be caught by a %SIG handler. So
you can get a stack trace with code like:
use Carp; # load it up front
local $SIG{FPE} = sub { confess(@_) };
Before perl-5.36.0 this approach won't work: you'll need to use "sigaction" in POSIX
instead:
use Carp;
use POSIX qw{ sigaction SIGFPE };
sigaction(SIGFPE, POSIX::SigAction->new(sub { confess(@_) }));
In either case, you should not attempt to return from the signal handler, since the signal
will just be thrown again.
BUGS
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.
VERSION CONTROL
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.
SEE ALSO
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.
See Math::GMPz, Math::GMPq, and friends ( <https://metacpan.org/search?q=math%3A%3Agmp> )
for bindings of other parts of GMP / MPFR / etc.
AUTHOR
Chip Turner <chip AT redhat.com>, based on the old Math::BigInt by Mark Biggar and Ilya
Zakharevich. Further extensive work provided by Tels <tels AT bloodgate.com>.
Shlomi Fish ( <https://www.shlomifish.org/> ) has done some maintenance work while putting
his changes under CC0.
AUTHOR
Shlomi Fish <shlomif AT cpan.org>
COPYRIGHT AND LICENSE
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
BUGS
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-gmp AT rt.org <mailto:bug-math-gmp AT rt.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.
SUPPORT
Perldoc
You can find documentation for this module with the perldoc command.
perldoc Math::GMP
Websites
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.
o MetaCPAN
A modern, open-source CPAN search engine, useful to view POD in HTML format.
<https://metacpan.org/release/Math-GMP>
o RT: CPAN's Bug Tracker
The RT ( Request Tracker ) website is the default bug/issue tracking system for CPAN.
<https://rt.cpan.org/Public/Dist/Display.html?Name=Math-GMP>
o CPANTS
The CPANTS is a website that analyzes the Kwalitee ( code metrics ) of a distribution.
<http://cpants.cpanauthors.org/dist/Math-GMP>
o CPAN Testers
The CPAN Testers is a network of smoke testers who run automated tests on uploaded
CPAN distributions.
<http://www.cpantesters.org/distro/M/Math-GMP>
o CPAN Testers Matrix
The CPAN Testers Matrix is a website that provides a visual overview of the test
results for a distribution on various Perls/platforms.
<http://matrix.cpantesters.org/?dist=Math-GMP>
o CPAN Testers Dependencies
The CPAN Testers Dependencies is a website that shows a chart of the test results of
all dependencies for a distribution.
<http://deps.cpantesters.org/?module=Math::GMP>
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 :)
<https://github.com/turnstep/Math-GMP>
git clone https://github.com/turnstep/Math-GMP.git
perl v5.34.0 2022-02-06 Math::GMP(3pm)
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On Apache
Under GNU General Public License
2025-11-18 18:02 @216.73.216.116 CrawledBy Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)