Editing GNU Multiple Precision Arithmetic Library

{{Short description|Free software}}
{{Infobox software
| name = GNU Multiple Precision Arithmetic Library
| logo = GMPLogo.svg
| screenshot = 
| caption = 
| developer = [[GNU Project]]
| released = {{Start date and age|1991}}<ref>{{cite web
 | url=https://gmplib.org/download/gmp/archive/
 | title=GNU MP archive
 | access-date=2018-12-03}}</ref>
| latest release version = {{wikidata|property|preferred|references|edit|Q1205818|P348|P548=Q2804309}}
| latest release date = {{wikidata|qualifier|preferred|single|Q1205818|P348|P548=Q2804309|P577}}
| latest preview version = {{wikidata|property|preferred|references|edit|Q1205818|P348|P548=Q51930650}}
| latest preview date = {{wikidata|qualifier|preferred|single|Q1205818|P348|P548=Q51930650|P577}}
| programming language = [[C (programming language)|C]], ([[C++]], [[assembly language|assembly]] optionally)
| genre = [[Mathematical software]]
| license = Dual [[GNU Lesser General Public License|LGPLv3]] and [[GNU General Public License|GPLv2]]<ref name=what/>
| website = {{URL|https://gmplib.org}}
| repo = {{URL|https://gmplib.org/repo/}}
}}

'''GNU Multiple Precision Arithmetic Library''' ('''GMP''') is a [[free software|free]] library for [[arbitrary-precision arithmetic]], operating on [[Sign (mathematics)|signed]] [[integer]]s, [[Rational data type|rational numbers]], and [[Floating-point arithmetic|floating-point numbers]].<ref name=what>{{cite web
| url=https://gmplib.org/#WHAT
| title=What is GMP?
| access-date=2014-04-07}}</ref> There are no practical limits to the precision except the ones implied by the available [[virtual memory|memory]] (operands may be of up to 2<sup>32</sup>−1 bits on 32-bit machines and 2<sup>37</sup> bits on 64-bit machines).<ref>{{cite web
| url=https://gmplib.org/list-archives/gmp-bugs/2009-July/001538.html
| title=Problems with mpz_set_str and huge strings
| last=Granlund
| first=Torbjorn
| date=2009-07-06
| access-date=2013-03-17}}</ref><ref>{{cite web
| url=https://gmplib.org/gmp6.0.html
| title=GMP 6.0 News
| access-date=2019-10-04}}</ref> GMP has a rich set of functions, and the functions have a regular interface. The basic interface is for [[C (programming language)|C]], but [[Wrapper function|wrappers]] exist for other languages, including [[Ada (programming language)|Ada]], [[C++]], [[C Sharp (programming language)|C#]], [[Julia (programming language)|Julia]], [[.NET Framework|.NET]], [[OCaml]], [[Perl]], [[PHP]], [[Python (programming language)|Python]], [[R (programming language)|R]], [[Ruby (programming language)|Ruby]], and [[Rust (programming language)|Rust]]. Prior to 2008, [[Kaffe]], a [[Java virtual machine]], used GMP to support Java built-in arbitrary precision arithmetic.<ref>{{cite web
| url=http://www.kaffe.org/pipermail/kaffe/2008-February/191039.html
| title=Removed GMP math?
| last=Hughes
| first=Andrew John
| date=2008-02-28
| access-date=2013-03-17}}</ref> Shortly after, GMP support was added to [[GNU Classpath]].<ref>{{cite web
| url=https://www.gnu.org/software/classpath/announce/20090205.html
| title=GNU Classpath 0.98 "Better Late Than Never"
| date=2009-02-05
| access-date=2013-03-17}}</ref>

The main target applications of GMP are [[cryptography]] applications and research, Internet security applications, and [[computer algebra system]]s.

GMP aims to be faster than any other [[bignum]] library for all operand sizes. Some important factors in doing this are:
* Full [[word (data type)|words]] are the basic type for all arithmetic.
* Different [[algorithm]]s are used for different [[operand]] sizes; algorithms which are more efficient with large numbers are not used when dealing with small numbers.
* [[Assembly language]] (specialized for different [[central processing unit|processors]]) is used in the most common inner loops to [[optimization_(computer_science)|optimize]] them as much as possible.

The first GMP release was made in 1991. It is constantly developed and maintained.<ref name=main>{{cite web
 | url=https://gmplib.org/
 | title=GNU MP Bignum Library
 | access-date=2018-12-03}}</ref>

GMP is part of the [[GNU]] project (although its website being off gnu.org may cause confusion), and is distributed under the [[GNU Lesser General Public License]] (LGPL).

GMP is used for integer arithmetic in many [[computer algebra system]]s such as [[Mathematica]]<ref>{{cite web
| url=https://library.wolfram.com/infocenter/Conferences/7518/Macalester_talk.txt
| title=The Mathematica Kernel: Issues in the Design and Implementation
| date=October 2006
| access-date=2013-03-17}}</ref> and [[Maple (software)|Maple]].<ref>{{cite web
| url=https://www.maplesoft.com/support/help/AddOns/view.aspx?path=GMP
| title= The GNU Multiple Precision (GMP) Library
| publisher=[[Maplesoft]]
| access-date=2013-03-17}}</ref> It is also used in the [[Computational Geometry Algorithms Library]] (CGAL).

GMP is needed to build the [[GNU Compiler Collection]] (GCC).<ref>GCC uses the [[GNU MPFR]] library, which in turn relies on GMP. {{cite web
| url=https://gcc.gnu.org/gcc-4.3/changes.html#mpfropts
| title=GCC 4.3 Release Series: Changes, New Features, and Fixes
| date=2012-11-02
| access-date=2013-03-17}}</ref>

== Examples ==

Here is an example of C code showing the use of the GMP library to multiply and print large numbers:

<syntaxhighlight lang="C">
#include <stdio.h>
#include <gmp.h>

int main(void) {
  mpz_t x, y, result;

  mpz_init_set_str(x, "7612058254738945", 10);
  mpz_init_set_str(y, "9263591128439081", 10);
  mpz_init(result);

  mpz_mul(result, x, y);
  gmp_printf("    %Zd\n"
             "*\n"
             "    %Zd\n"
             "--------------------\n"
             "%Zd\n", x, y, result);

  /* free used memory */
  mpz_clear(x);
  mpz_clear(y);
  mpz_clear(result);

  return 0;
}
</syntaxhighlight>

This code calculates the value of 7612058254738945 × 9263591128439081.

Compiling and running this program gives this result. (The <code>-lgmp</code> flag is used if compiling on Unix-type systems.)

<syntaxhighlight lang="text">
    7612058254738945
*
    9263591128439081
--------------------
70514995317761165008628990709545
</syntaxhighlight>

For comparison, one can write instead the following equivalent C++ program. (The <code>-lgmpxx -lgmp</code> flags are used if compiling on Unix-type systems.)

<syntaxhighlight lang="cpp">
#include <iostream>
#include <gmpxx.h>

int main() {
  mpz_class x("7612058254738945");
  mpz_class y("9263591128439081");

  std::cout << "    " << x << "\n"
            << "*\n"
            << "    " << y << "\n"
            << "--------------------\n"
            << x * y << "\n";

  return 0;
}
</syntaxhighlight>

== Language bindings ==
{| class="wikitable"
|-
! Library name
! Language
! License
|-
| [https://gmplib.org/ GNU Multi-Precision Library]
| [[C (programming language)|C]], [[C++]]
| [[GNU Lesser General Public License|LGPL]]
|-
| [https://metacpan.org/pod/Math::GMP Math::GMP]
| [[Perl]]
| [[GNU Lesser General Public License|LGPL]]
|-
| [https://metacpan.org/pod/Math::GMPz Math::GMPz], [https://metacpan.org/pod/Math::GMPf Math::GMPf] and [https://metacpan.org/pod/Math::GMPq Math::GMPq]
| [[Perl]]
| [[Artistic License]] v1.0 + [[GNU General Public License|GPL]] v1.0-or-later
|-
| [https://github.com/aleaxit/gmpy General Multiprecision Python Project]
| [[Python (programming language)|Python]]
| LGPL
|-
| [https://cran.r-project.org/web/packages/gmp/index.html R package 'gmp']
| [[R (programming language)|R]]
| GPL
|-
| [https://rubygems.org/gems/gmp The RubyGems project]
| [[Ruby (programming language)|Ruby]]
| [[Apache License|Apache 2.0]]
|-
| [https://lib.rs/crates/gmp-mpfr-sys Rust FFI bindings for GMP, MPFR and MPC]
| [[Rust (programming language)|Rust]]
| [[GNU Lesser General Public License|LGPL]]
|-
| [https://www.php.net/gmp GNU Multi-Precision Library for PHP]
| [[PHP]]
| [[PHP License|PHP]]
|-
| [http://www.math.uni.wroc.pl/~hebisch/prog/ GNU Multi-Precision Routines for SBCL]
| [[Common Lisp]]
| [[Public domain software|Public Domain]]
|-
| [http://chgmp.sourceforge.net/ Ch GMP]
| [[Ch (computer programming)|Ch]]
| [[Proprietary software|Proprietary]]
|-
| [http://bmdfm.com/ Parallel GMP Wrapper for BMDFM]
| [[BMDFM | BMDFM LISP / C]]
| [[Public domain software|Public Domain]]
|-
| [[Glasgow Haskell Compiler]]<br /><small>(The implementation of <code>Integer</code><br />is basically a binding to GMP)</small>
| [[Haskell (programming language)|Haskell]]
| [[BSD licenses|BSD]]
|-
| [https://github.com/Playermet/luajit-gmp luajit-gmp]
| [[Lua (programming language)|LuaJIT]]
| [[MIT License|MIT]]
|-
| [https://code.google.com/archive/p/gmp-wrapper-for-delphi gmp-wrapper-for-delphi]
| [[Delphi (programming language)|Delphi]]
| [[MIT License|MIT]]
|-
| [https://github.com/ocaml/Zarith Zarith]
| [[OCaml]]
| LGPL
|-
| [https://github.com/MachineCognitis/Math.Gmp.Native Math.Gmp.Native Library]
| [[.NET Framework|.NET]]
| [[MIT License|MIT]]
|-
| [https://github.com/FedeOmoto/nim-gmp nim-gmp]
| [[Nim (programming language)|Nim]]
| [[MIT License|MIT]]
|-
| [https://github.com/jandom-devel/JGMP JGMP]
| [[Java (programming language)|Java]]
| [[GNU Lesser General Public License|LGPL]]
|}

== See also ==
* [[GNU MPFR]] – a library for arbitrary-precision computations with correct rounding, based on GNU MP
* [[Class Library for Numbers|CLN]] – a class library for arbitrary precision 
* [[MPIR (mathematics software)|MPIR]] – a fork of GMP, not maintained any more

== References ==
{{Reflist}}

== External links ==
* {{Official website}}

{{GNU}}
{{Authority control}}

{{DEFAULTSORT:Gnu Multi-Precision Library}}
[[Category:Assembly language software]]
[[Category:C (programming language) libraries]]
[[Category:Computer arithmetic]]
[[Category:Free software programmed in C]]
[[Category:GNU Project software|Multiple Precision Arithmetic Library]]
[[Category:Numerical libraries]]
[[Category:Software using the GNU Lesser General Public License]]