Information AboutBignum |
| CATEGORIES ABOUT ARBITRARY-PRECISION ARITHMETIC | |
| computer arithmetic | |
| arbitrary precision algorithms | |
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Perhaps the earliest widespread implementation of arbitrary precision arithmetic was in Maclisp . Later, the VAX / VMS Operating System offered bignum facilities as a collection of String Function s. Today, bignum libraries are available for most modern programming languages (see below). Almost all Computer Algebra System s implement arbitrary precision arithmetic. APPLICATIONS Arbitrary-precision arithmetic is usually much slower than arithmetic using numbers that fit entirely within processor registers, since the latter are usually implemented in Hardware Arithmetic whereas the former must be implemented in software. Consequently, arbitrary precision is only used in a limited range of applications that require extremely precise results or exact integer arithmetic with very large numbers. The most common application is Encryption , whose algorithms commonly employ arithmetic with integers of hundreds or thousands of digits. Arbitrary precision arithmetic is also used to compute fundamental Mathematical Constant s such as Pi to millions or more digits and to analyze their properties. ALGORITHMS Numerous Algorithms have been developed to efficiently perform arithmetic operations on numbers stored with arbitrary precision. In particular, supposing that ''N'' digits are employed, algorithms have been designed to minimize the asymptotic Complexity for large ''N''. The simplest algorithm is for Addition , where one simply adds the digits in sequence, carrying as necessary, which yields an ''O''(''N'') algorithm (see Big O Notation ). For Multiplication , the most straightforward algorithms used for multiplying numbers by hand requires operations, but Multiplication Algorithm s have been devised (and also algorithms with slightly worse complexity but with sometimes superior real-world performance for moderate ''N''). INFINITE PRECISION It is possible to provide infinite precision for real number computations. A typical algorithm involves storing a s. ARBITRARY-PRECISION SOFTWARE Arbitrary-precision arithmetic in most computer software is implemented by calling an external Library that provides Datatype s and Subroutine s to store numbers with the requested precision and to perform computations.
Stand-alone Application Software that supports arbitrary precision computations.
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