RLIBM-32: High Performance Correctly Rounded Math Libraries for 32-bit Floating Point Representations

TL;DR

This paper introduces techniques for creating high-performance, correctly rounded math libraries for 32-bit floating point and posit types, improving accuracy and efficiency over existing libraries.

Contribution

It extends the RLibm approach to 32-bit types, proposing new algorithms for polynomial generation, domain splitting, and range reduction to ensure correct rounding.

Findings

Faster than state-of-the-art 32-bit float math libraries

Provides correctly rounded elementary functions for 32-bit posits

Uses counterexample guided polynomial generation and bit-pattern domain splitting

Abstract

This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLibm approach that frames the problem of generating correctly rounded libraries as a linear programming problem in the context of 16-bit types to scale to 32-bit types. Specifically, this paper proposes new algorithms to (1) generate polynomials that produce correctly rounded outputs for all inputs using counterexample guided polynomial generation, (2) generate efficient piecewise polynomials with bit-pattern based domain splitting, and (3) deduce the amount of freedom available to produce correct results when range reduction involves multiple elementary functions. The resultant math library for the 32-bit float type is faster than state-of-the-art math libraries while producing the correct output for all inputs. We have also developed a set of correctly rounded elementary functions for 32-bit posits.