Manual Reference Pages - MATH::GMP (3)
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NAME
Math::GMP - High speed arbitrary size integer math
CONTENTS
VERSION
version 2.11
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.
$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.
$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.
$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.
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.
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.
Adds to $x and mutates it in-place. $n must be a regular non-GMP, positive,
integer.
($quotient, CW$remainder) = CW$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 $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 $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.
Returns a copy of $x that can be modified without affecting the original.
my CW$verdict = CW$x->gmp_tstbit($bit_index);
Returns whether or not bit No. $bit_index is 1 in $x.
my CW$remainder = CW$dividend->mmod_gmp($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 $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 $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 $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.
Returns the size of $x in base $plain_int_base .
my CW$int = CW$x->intify();
Returns the value of the object as an unblessed (and limited-in-precision)
integer.
gcd()
An alias to bgcd() .
lcm()
An alias to blcm() .
For internal use. <B>Do not use directlyB>.
destroy
For internal use. <B>Do not use directlyB>.
new_from_scalar
For internal use. <B>Do not use directlyB>.
new_from_scalar_with_base
For internal use. <B>Do not use directlyB>.
op_add
For internal use. <B>Do not use directlyB>.
op_div
For internal use. <B>Do not use directlyB>.
op_eq
For internal use. <B>Do not use directlyB>.
op_mod
For internal use. <B>Do not use directlyB>.
op_mul
For internal use. <B>Do not use directlyB>.
op_pow
For internal use. <B>Do not use directlyB>.
op_spaceship
For internal use. <B>Do not use directlyB>.
op_sub
For internal use. <B>Do not use directlyB>.
stringify
For internal use. <B>Do not use directlyB>.
uintify
For internal use. <B>Do not use directlyB>.
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.
AUTHOR
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>.
AUTHOR
Shlomi Fish <shlomif@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-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.
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.
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/perl-Math-GMP>
git clone https://github.com/turnstep/perl-Math-GMP.git
perl v5.20.3 | MATH::GMP (3) | 2015-08-16 |
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