BigInts

BigInt refers to an integer data type with arbitrary precision, capable of representing integers of any size limited only by available memory. Unlike fixed-size primitive integers, BigInts grow in length as needed to avoid overflow. Internally they are typically stored as a sign along with a sequence of digits or limbs in a base such as 2^32 or 10^n, enabling arithmetic to be performed on large magnitudes.

Arbitrary-precision integers are essential for exact arithmetic, cryptography, and certain financial calculations where rounding errors are unacceptable. They enable operations on numbers far larger than standard hardware integers, but they incur higher memory consumption and slower arithmetic. Most implementations provide standard operators for addition, subtraction, multiplication, division, and comparison, with special care for negative values and zero.

Many languages provide built-in BigInt support or standard libraries. For example, Python's int uses arbitrarily large precision; JavaScript offers a BigInt type; Java provides BigInteger; C and C++ rely on external libraries such as GMP. Conversions to and from fixed-size types and strings are common features, and interoperability with native integers may require explicit casting or limiting conversion ranges.

Implementation details vary, but common design choices include using a sign bit and an array of limbs, and implementing multiplication and division with algorithms such as schoolbook, Karatsuba, Toom-Cook, or FFT-based methods for large operands. Time complexity is typically superlinear for large numbers, and memory usage grows with the number of limbs. Performance depends on the chosen base, algorithms, and the quality of the library.