# GNU Multiple Precision Arithmetic Library

**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 (operand dimension limit is 2^{32}-1 bits on 32-bit machines and 2^{37} bits on 64-bit machines).[4][5] 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, .NET, OCaml, Perl, PHP, Python, R, Ruby and the Wolfram Language.

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

Initial release | 1991[1] |

Stable release | 6.1.2 (16 December 2016[2]) [±] |

Repository | gmplib |

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

Type | Mathematical software |

License | Dual LGPLv3 and GPLv2[3] |

Website | gmplib |

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.[6]

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 | LGPL |

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 |

Parallel GMP Wrapper for BMDFM | BMDFM LISP / C | Public Domain |

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

luajit-gmp | LuaJIT | MIT |

gmp-wrapper-for-delphi | Delphi | MIT |

Zarith | OCaml | LGPL |

Math.Gmp.Native Library | .NET | MIT |

nim-gmp | Nim | MIT |

## See also

## References

- "GNU MP archive". Retrieved 2018-12-03.
- V6.1.2 - "The GNU MP Bignum Library". Retrieved 2017-01-22.
- "What is GMP?". Retrieved 2014-04-07.
- Granlund, Torbjorn (2009-07-06). "Problems with mpz_set_str and huge strings". Retrieved 2013-03-17.
- "GMP 6.0 News". Retrieved 2019-10-04.
- "GNU MP Bignum Library". Retrieved 2018-12-03.
- "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 GNU 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.