FloatLib: Verified Floating-Point Arithmetic in Lean (leandojo.org)

FloatLib, a new library developed in Lean, offers verified arbitrary-precision floating-point arithmetic that significantly enhances computational reliability in machine learning and numerical software. Key features include support for various formats such as IEEE binary and decimal, arbitrary-width posits, and customized user-defined formats, allowing developers to specify exponent and fraction widths, bias, and encoding policies. Each backend in FloatLib is rigorously certified to align with its encoded specifications, ensuring precise handling of signed zeros, exceptional values, and correctly rounded arithmetic. The significance of FloatLib lies in its capability to produce verified numerical proofs directly connected to the execution code, including guarantees for correctly rounded results and specified error bounds. Its design accommodates the complexities of modern machine learning tasks while maintaining performance through efficient execution strategies like lookup tables and limb algorithms. Performance benchmarks demonstrate its abilities across an extensive range of bit widths, solidifying FloatLib as a crucial tool for developers seeking accuracy and efficiency in floating-point operations.