Arbitrary-precision integer

An arbitrary-precision integer stores an integer using a variable number of machine words. Unlike a fixed-width integer, it grows when more binary digits are needed. The sign and a finite sequence of base-$2^w$ digits represent its exact value.

For example, the integer $10^{100}+7$ requires hundreds of bits but no rounding. Arbitrary-precision integer arithmetic operates on these representations; it is distinct from approximate floating-point arithmetic. Memory and computation still impose practical bounds, so arbitrary precision does not mean infinite available storage.