GNU Multiple Precision Arithmetic Library (GMP) is a

free Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procur ...

library for

arbitrary-precision arithmetic In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are l ...

, operating on signed

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

rational numbers In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all r ...

, and

floating-point numbers In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be r ...

. There are no practical limits to the precision except the ones implied by the available

memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered ...

(operands may be of up to 2³²−1 bits on 32-bit machines and 2³⁷ bits on 64-bit machines). 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 Julia is usually a feminine given name. It is a Latinate feminine form of the name Julio and Julius. (For further details on etymology, see the Wiktionary entry "Julius".) The given name ''Julia'' had been in use throughout Late Antiquity (e ...

, .NET,

OCaml OCaml ( , formerly Objective Caml) is a general-purpose, multi-paradigm programming language which extends the Caml dialect of ML with object-oriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, D ...

Perl Perl is a family of two High-level programming language, high-level, General-purpose programming language, general-purpose, Interpreter (computing), interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it ...

PHP PHP is a General-purpose programming language, general-purpose scripting language geared toward web development. It was originally created by Danish-Canadian programmer Rasmus Lerdorf in 1993 and released in 1995. The PHP reference implementati ...

, Python, R,

Ruby A ruby is a pinkish red to blood-red colored gemstone, a variety of the mineral corundum (aluminium oxide). Ruby is one of the most popular traditional jewelry gems and is very durable. Other varieties of gem-quality corundum are called sapp ...

, and

Rust Rust is an iron oxide, a usually reddish-brown oxide formed by the reaction of iron and oxygen in the catalytic presence of water or air moisture. Rust consists of hydrous iron(III) oxides (Fe2O3·nH2O) and iron(III) oxide-hydroxide (FeO(OH), ...

. Prior to 2008, Kaffe, a

Java virtual machine A Java virtual machine (JVM) is a virtual machine that enables a computer to run Java programs as well as programs written in other languages that are also compiled to Java bytecode. The JVM is detailed by a specification that formally describ ...

, used GMP to support Java built-in arbitrary precision arithmetic. Shortly after, GMP support was added to GNU Classpath. The main target applications of GMP are

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adve ...

applications and research, Internet security applications, and

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The ...

s. GMP aims to be faster than any other

bignum In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are l ...

library for all operand sizes. Some important factors in doing this are: * Using full

words A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no conse ...

as the basic arithmetic type. * Using different

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s for different

operand In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above exa ...

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 loop Inner loop may refer to: * Inner loop in computer programs * Inner Loop (Phoenix), a section of Interstate 10 in downtown Phoenix, Arizona, United States * Inner Loop (Rochester), an expressway around downtown Rochester, New York, United States *In ...

s, specialized for different processors. The first GMP release was made in 1991. It is constantly developed and maintained. GMP is part of the

GNU GNU () is an extensive collection of free software Free software or libre software is computer software distributed under terms that allow users to run the software for any purpose as well as to study, change, and distribute it and any ...

project (although its website being off gnu.org may cause confusion), and is distributed under the

GNU Lesser General Public License The GNU Lesser General Public License (LGPL) is a free-software license published by the Free Software Foundation (FSF). The license allows developers and companies to use and integrate a software component released under the LGPL into their own ...

(LGPL). GMP is used for integer arithmetic in many

s such as

Mathematica Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimi ...

and

Maple ''Acer'' () is a genus of trees and shrubs commonly known as maples. The genus is placed in the family Sapindaceae.Stevens, P. F. (2001 onwards). Angiosperm Phylogeny Website. Version 9, June 2008 nd more or less continuously updated since ht ...

. It is also used in the

Computational Geometry Algorithms Library The Computational Geometry Algorithms Library (CGAL) is an open source software library of computational geometry algorithms. While primarily written in C++, Scilab bindings and bindings generated with SWIG (supporting Python and Java for now ...

(CGAL). GMP is needed to build the

GNU Compiler Collection The GNU Compiler Collection (GCC) is an optimizing compiler produced by the GNU Project supporting various programming languages, hardware architectures and operating systems. The Free Software Foundation (FSF) distributes GCC as free sof ...

(GCC).GCC uses the GNU MPFR library, which in turn relies on GMP.

Examples

Here is an example of C code showing the use of the GMP library to multiply and print large numbers: #include #include int main(void) 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 #include int main()

Language bindings

References

External links

* {{DEFAULTSORT:Gnu Multi-Precision Library Assembly language software C (programming language) libraries Computer arithmetic Free software programmed in C Multiple Precision Arithmetic Library Numerical libraries Software using the LGPL license

Examples

Language bindings

See also

References

External links