Year: 2025
Type: article
Abstract: This paper describes our experience developing polynomial approximations for trigonometric functions that produce correctly rounded results for multiple representations and rounding modes using the RLIBM approach.A key challenge with trigonometric functions concerns range reduction with π, which reduces a given input in the domain of a 32-bit float to a small domain.Any rounding error in the value of π is amplified during range reduction, which can result in wrong results.We describe our experience implementing fast range reduction techniques that maintain a large number of bits of π both with floating-point and integer computations.The resulting implementations for trigonometric functions are fast and produce correctly rounded results for all inputs for multiple representations up to 32-bits with a single implementation.
DOI: 10.4204/eptcs.432.9
Authors: Sehyeok Park, Santosh Nagarakatte
Institution: Rutgers, The State University of New Jersey
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: SHF: Small: Efficient, Deterministic and Formally Certified Methods for Solving Low-dimensional Linear Programs with Floating-point Precision, SHF:Small:Techniques for Generating Correctly Rounded Math Libraries, SHF: Small: Formalisms, Implementations, and Verification Procedures for Alternatives to Floating Point
OpenAlex ID: W4415169281
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