Editing Arbitrary-precision arithmetic (section)

{{Short description|Calculations where numbers' precision is only limited by computer memory}}
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In [[computer science]], '''arbitrary-precision arithmetic''', also called '''bignum arithmetic''', '''multiple-precision arithmetic''', or sometimes '''infinite-precision arithmetic''', indicates that [[calculation]]s are performed on numbers whose [[numerical digit|digits]] of [[precision (arithmetic)|precision]] are potentially limited only by the available [[memory (computers)|memory]] of the host system.  This contrasts with the faster [[fixed-precision arithmetic]] found in most [[arithmetic logic unit]] (ALU) hardware, which typically offers between 8 and 64 [[bit]]s of precision.

Several modern [[programming language]]s have built-in support for bignums,<ref>{{Cite web|last=dotnet-bot|title=BigInteger Struct (System.Numerics)|url=https://docs.microsoft.com/en-us/dotnet/api/system.numerics.biginteger|access-date=2022-02-22|website=docs.microsoft.com|language=en-us}}</ref><ref>{{Cite web|title=PEP 237 -- Unifying Long Integers and Integers|url=https://peps.python.org/pep-0237/|access-date=2022-05-23|website=Python.org|language=en}}</ref><ref>{{Cite web|title=BigInteger (Java Platform SE 7 )|url=https://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html|access-date=2022-02-22|website=docs.oracle.com}}</ref><ref>{{Cite web|title=BigInt - JavaScript {{!}} MDN|url=https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt|access-date=2022-02-22|website=developer.mozilla.org|language=en-US}}</ref> and others have libraries available for arbitrary-precision [[Integer_(computer_science)|integer]] and [[floating-point]] math. Rather than storing values as a fixed number of bits related to the size of the [[processor register]], these implementations typically use variable-length [[array data structure|arrays]] of digits.

Arbitrary precision is used in applications where the speed of [[arithmetic]] is not a limiting factor, or where [[Floating point error mitigation|precise results]] with very large numbers are required.  It should not be confused with the [[symbolic computation]] provided by many [[computer algebra system]]s, which represent numbers by expressions such as {{math|''π''·sin(2)}}, and can thus ''represent'' any [[computable number]] with infinite precision.