# GNU Multiple Precision Arithmetic Library

Developer(s) | GNU Project |
---|---|

Initial release |
1991^{[1]} |

Stable release |
6.1.1 (20 July 2016^{[2]}) [±] |

Repository |
gmplib |

Written in | C, (C++, assembly optionally) |

Operating system | Cross-platform |

Type | Mathematical software |

License |
Dual LGPLv3 and GPLv2^{[3]} |

Website |
gmplib |

The **GNU Multiple Precision Arithmetic Library** (**GMP**) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers.^{[3]} There are no practical limits to the precision except the ones implied by the available memory in the machine GMP runs on (operand dimension limit is 2^{32}-1 bits on 32-bit machines and 2^{37} bits on 64-bit machines).^{[4]} GMP has a rich set of functions, and the functions have a regular interface. The basic interface is for C but wrappers exist for other languages including Ada, C++, C#, Julia, OCaml, Perl, PHP, Python, R, Ruby and the Wolfram Language. In the past, the Kaffe Java virtual machine used GMP to support Java built-in arbitrary precision arithmetic. This feature has been removed from recent releases, causing protests from people who claim that they used Kaffe solely for the speed benefits afforded by GMP.^{[5]} As a result, GMP support has been added to GNU Classpath.^{[6]}

The main target applications of GMP are cryptography applications and research, Internet security applications, and computer algebra systems.

GMP aims to be faster than any other bignum library for all operand sizes. Some important factors in doing this are:

- Using full words as the basic arithmetic type.
- Using different algorithms for different operand sizes; algorithms that are faster for very big numbers are usually slower for small numbers.
- Highly optimized assembly language code for the most important inner loops, specialized for different processors.

The first GMP release was made in 1991. It is constantly developed and maintained.^{[1]}

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 systems such as Mathematica^{[7]} and Maple.^{[8]} It is also used in the Computational Geometry Algorithms Library (CGAL) because geometry algorithms tend to 'explode' when using ordinary floating point CPU math.^{[9]}

GMP is needed to build the GNU Compiler Collection (GCC).^{[10]}

## Examples

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

```
#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;
}
```

This code calculates the value of 7612058254738945 × 9263591128439081.

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

```
7612058254738945
*
9263591128439081
--------------------
70514995317761165008628990709545
```

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

```
#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;
}
```

## Language bindings

Library name | Language | License |
---|---|---|

GNU Multi-Precision Library | C, C++ | LGPL |

Math::GMP | Perl | GPL |

General Multiprecision Python Project | Python | LGPL |

R package 'gmp' | R | GPL |

The RubyGems project | Ruby | Apache 2.0 |

GNU Multi-Precision Library for PHP | PHP | PHP |

GNU Multi-Precision Routines for SBCL | Common Lisp | Public Domain |

Ch GMP | Ch | Proprietary |

Glasgow Haskell Compiler (The implementation of `Integer` is basically a binding to GMP) |
Haskell | BSD |

luajit-gmp | LuaJIT | MIT |

## See also

- MPFR – library for arbitrary-precision computations with correct rounding, based on GNU MP
- CLN – a class library for arbitrary precision
- MPIR – a fork of GMP with mostly compatible interface which aims to provide MSVC-based compilation system for Windows platforms

## References

- 1 2 "The GNU MP Bignum Library". Retrieved 2013-03-17.
- ↑ V6.1.1 - "The GNU MP Bignum Library". Retrieved 2016-08-01.
- 1 2 "What is GMP?". Retrieved 2014-04-07.
- ↑ Granlund, Torbjorn (2009-07-06). "Problems with mpz_set_str and huge strings". Retrieved 2013-03-17.
- ↑ Hughes, Andrew John (2008-02-28). "Removed GMP math?". Retrieved 2013-03-17.
- ↑ "GNU Classpath 0.98 "Better Late Than Never"". 2009-02-05. Retrieved 2013-03-17.
- ↑ "The Mathematica Kernel: Issues in the Design and Implementation". October 2006. Retrieved 2013-03-17.
- ↑ "The GNU Multiple Precision (GMP) Library". Maplesoft. Retrieved 2013-03-17.
- ↑ "CGAL Manuals".
- ↑ GCC uses the MPFR library, which in turn relies on GMP. "GCC 4.3 Release Series: Changes, New Features, and Fixes". 2012-11-02. Retrieved 2013-03-17.