Very large numbers often occur in fields such as mathematics, cosmology, cryptography and statistical mechanics. That numbers are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions. The term typically refers to large positive integers, or more generally, large positive real numbers, but it may also be used in other contexts.
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 which digits of precision are limited only by the available 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 bits of precision.
Several modern programming languages have built-in support for large numbers (also known as infinite precision integers or bignums), such as lisp, smalltalk, rexx and haskell. Other languages which do not support this concept as a top-level construct may have libraries available to represent very large numbers using arrays of smaller variables, such as java and c# biginteger class or perl bigint package.
Other languages have libraries available for arbitrary-precision integer and floating-point math. Rather than store values as a fixed number of binary bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.
