GNU Multiple Precision Arithmetic Library (GMP) is a free 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 po ...

, operating on signed

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

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

, and

floating-point numbers In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base. Numbers of this form ...

. 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 remembe ...

(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,

.NET The .NET platform (pronounced as "''dot net"'') is a free and open-source, managed code, managed computer software framework for Microsoft Windows, Windows, Linux, and macOS operating systems. The project is mainly developed by Microsoft emplo ...

OCaml OCaml ( , formerly Objective Caml) is a General-purpose programming language, general-purpose, High-level programming language, high-level, Comparison of multi-paradigm programming languages, multi-paradigm programming language which extends the ...

Perl Perl is a high-level, general-purpose, interpreted, dynamic programming language. Though Perl is not officially an acronym, there are various backronyms in use, including "Practical Extraction and Reporting Language". Perl was developed ...

PHP PHP is a general-purpose scripting language geared towards web development. It was originally created by Danish-Canadian programmer Rasmus Lerdorf in 1993 and released in 1995. The PHP reference implementation is now produced by the PHP Group. ...

, Python, R,

Ruby 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 sapph ...

, 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 descr ...

, 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 "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

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 de ...

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 numerical digit, digits of p ...

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

words A word is a basic element of language that carries 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 consensus among linguists on its ...

are the basic type for all arithmetic. * Different

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

s are used 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. Unknown operands in equalities of expressions can be found by equation solving. Example The following arithmetic expres ...

sizes; algorithms which are more efficient with large numbers are not used when dealing with small numbers. *

Assembly language In computing, assembly language (alternatively assembler language or symbolic machine code), often referred to simply as assembly and commonly abbreviated as ASM or asm, is any low-level programming language with a very strong correspondence bet ...

(specialized for different processors) is used in the most common inner loops to optimize them as much as possible. The first GMP release was made in 1991. It is constantly developed and maintained. 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 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 (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ...

and

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

. It is also used in the Computational Geometry Algorithms Library (CGAL). GMP is needed to build the

GNU Compiler Collection The GNU Compiler Collection (GCC) is a collection of compilers from the GNU Project that support various programming languages, Computer architecture, hardware architectures, and operating systems. The Free Software Foundation (FSF) distributes ...

(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 GNU Lesser General Public License

Examples

Language bindings

See also

References

External links