Editing Arbitrary-precision arithmetic (section)

==Software libraries==
{{See also|List of arbitrary-precision arithmetic software}}

Arbitrary-precision arithmetic in most computer software is implemented by calling an external [[library (computer science)|library]] that provides [[data type]]s and [[subroutine]]s to store numbers with the requested precision and to perform computations.

Different libraries have different ways of representing arbitrary-precision numbers, some libraries work only with integer numbers, others store [[floating point]] numbers in a variety of bases (decimal or binary powers). Rather than representing a number as single value, some store numbers as a numerator/denominator pair ([[rational number|rationals]]) and some can fully represent [[computable number]]s, though only up to some storage limit. Fundamentally, [[Turing machine]]s cannot represent all [[real number]]s, as the [[cardinality]] of <math>\mathbb{R}</math> exceeds the cardinality of <math>\mathbb{Z}</math>.