A bignum package in a computer or program allows internal representation of very large integers, rational numbers, decimal numbers, or floating-point numbers (limitted only by available memory), and provides a set of arithmetic operations on such numbers. Numbers are typically stored as either one or two lists of digits (or higher-ordered values), encoded in binary. Unlike hardware data types, bignums can vary in size, using dynamically allocated memory. A computer is a device or machine for processing information according to a program — a compiled list of instructions. ... The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ... In mathematics, a rational number (or informally fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ... Decimal, or less commonly, denary, usually refers to the base 10 numeral system. ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... The binary numeral system represents numeric values using two symbols, typically 0 and 1. ... On computer science, a datatype (often simply type) is a name or label for a set of values and some operations which can be performed on that set of values. ...

Bignums were first implemented in MacLisp. Later, the VAX/VMS operating system offered bignum facilities as a collection of string functions. Today, bignum libraries are available for most modern programming languages. The GNU Multi-Precision Library is a free C library that offers bignum features. All computer algebra systems implement bignum facilities. MacLisp is a dialect of the Lisp programming language. ... VAX is a 32-bit computing architecture that supports an orthogonal instruction set (machine language) and virtual addressing (i. ... OpenVMS (Open Virtual Memory System or just VMS) is the name of a high-end computer server operating system that runs on the VAX and Alpha family of computers developed by Digital Equipment Corporation of Maynard, Massachusetts (now owned by Hewlett-Packard); it has also recently been ported to servers... In computing, an operating system (OS) is the system software responsible for the direct control and management of hardware and basic system operations. ... In various branches of mathematics and computer science, strings are sequences of various simple objects (symbols, tokens, characters, etc. ... In computer science, a subroutine (function, procedure, or subprogram) is a sequence of code which performs a specific task, as part of a larger program, and is grouped as one, or more, statement blocks; such code is sometimes collected into software libraries. ... The GNU Multiple-Precision Library, also known as GMP, is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. ... Free software, as defined by the Free Software Foundation, can be used, copied, studied, modified and redistributed. ... The C Programming Language, Brian Kernighan and Dennis Ritchie, the original edition that served for many years as an informal specification of the language The C programming language is a standardized imperative computer programming language developed in the early 1970s by Ken Thompson and Dennis Ritchie for use on the... A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. ...

Bignum systems often employ fast multiplication and division algorithms, and many provide number theoretic primitives such as modular exponentiation. A multiplication algorithm is an algorithm (or method) to multiply two numbers. ... The division algorithm is a theorem in mathematics which precisely expresses the outcome of the usual process of division of integers. ... Flowcharts are often used to represent algorithms. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... Modular exponentiation is a type of exponentiation performed over a modulus. ...

See also: large numbers. For information on how large numbers are named in English, see names of large numbers. ...