biginteger

A big integer, or bignum, is an integer with arbitrary precision, limited only by available memory. It represents numbers larger than those supported by fixed-size machine integers such as 32- or 64-bit types. Typical implementations store a sign and a sequence of digits in a chosen base, such as 2^32 or 10^9, enabling arithmetic on numbers of any size.

A big integer supports standard arithmetic operations: addition, subtraction, multiplication, division, modulo, and comparison, along with conversion to and from strings. Many implementations are immutable, meaning operations return new values rather than modifying the original one. Performance grows with the number of digits, and memory usage is proportional to the number of stored limbs.

Under the hood, big integers use multi-precision algorithms. Multiplication ranges from schoolbook to Karatsuba, Toom-Cook, or FFT-based methods for very large numbers. Division uses generalized long division. Primality testing, greatest common divisor, and modular arithmetic are supported for cryptographic and mathematical computations.

Uses include cryptography (RSA, elliptic-curve schemes), exact mathematical computations, and financial calculations requiring precise whole-number results. Language ecosystems provide multiple options: Python’s int, Java’s BigInteger, JavaScript’s BigInt, C#’s BigInteger, Go’s math/big, Ruby’s Integer, and GMP-based libraries for C and C++. Some environments offer arbitrary-precision decimals in addition to integers.

See also: arbitrary-precision arithmetic, big-number library, modular arithmetic.