gcd48

gcd48 is a lightweight open-source software library that provides highly optimized implementations of the greatest common divisor (GCD) for 48-bit integer arithmetic. It is designed for embedded and performance-sensitive environments where division is expensive or unavailable. The library offers support for 8-, 16-, 32-, and 48-bit operands and is intended to be easily integrated into C and C++ projects.

The core of gcd48 centers on the binary GCD algorithm (Stein) with platform-specific optimizations. The implementation minimizes division by using bit operations, shifts, and conditional subtraction. For larger operands, it applies Lehmer's trick to reduce the number of expensive operations, improving throughput on typical hardware. The code is designed to be portable across compilers and architectures and emphasizes deterministic performance.

The library exposes a small set of functions, including gcd48 for 48-bit inputs, along with helper variants such as gcd8 and gcd16 or gcd32 for smaller widths. The primary function returns the greatest common divisor of two non-negative integers, returning a value that fits in 48 bits. It includes input checks and well-defined behavior for zero inputs.

gcd48 originated from a community effort to optimize GCD for constrained systems. It is released under an open-source license and hosted on a public repository with documented usage and benchmarks. The project welcomes contributions and issue reports, and maintains compatibility with common toolchains.

See also: greatest common divisor, binary GCD algorithm, Stein's algorithm.