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 li ...

, 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 languag ...

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 rat ...

, 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 ...

. 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 Ada may refer to: Places Africa * Ada Foah, a town in Ghana * Ada (Ghana parliament constituency) * Ada, Osun, a town in Nigeria Asia * Ada, Urmia, a village in West Azerbaijan Province, Iran * Ada, Karaman, a village in Karaman Province, ...

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

, 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.g ...

, .NET,

OCaml OCaml ( , formerly Objective Caml) is a general-purpose programming language, general-purpose, multi-paradigm programming language which extends the Caml dialect of ML (programming language), ML with object-oriented programming, object-oriented ...

Perl Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages. "Perl" refers to Perl 5, but from 2000 to 2019 it also referred to its redesigned "sister language", Perl 6, before the latter's name was offici ...

PHP PHP is a 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 implementation is now produced by The PHP Group. ...

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (pro ...

, 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 sa ...

, 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 Kaffe is a discontinued "clean room design" (reverse engineering) version of a Java Virtual Machine. It comes with a subset of the Java Platform, Standard Edition (Java SE), Java API, and tools needed to provide a Java runtime environment. Like m ...

, 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 describes ...

, used GMP to support Java built-in arbitrary precision arithmetic. Shortly after, GMP support was added to

GNU Classpath GNU Classpath is a free software implementation of the standard class library for the Java programming language. Most classes from J2SE 1.4 and 5.0 are implemented. Classpath can thus be used to run Java-based applications. GNU Classpath is a pa ...

. 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 adver ...

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 digits of precision are li ...

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 consen ...

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 Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

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 examp ...

sizes; algorithms that are faster for very big numbers are usually slower for small numbers. * Highly optimized

assembly language In computer programming, assembly language (or 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 be ...

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 * I ...

s, specialized for different

processors A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, ...

. 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 (383 packages as of January 2022), which can be used as an operating system or can be used in parts with other operating systems. The use of the completed GNU tools led to the family of operat ...

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, optimizat ...

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 http ...

. 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 software ...

(GCC).GCC uses the

GNU MPFR The GNU Multiple Precision Floating-Point Reliable Library (GNU MPFR) is a GNU portable C library for arbitrary-precision binary floating-point computation with correct rounding, based on GNU Multi-Precision Library. Library MPFR's computatio ...

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