2007/08/28 by Sylvie Boldo, Boldo, Sylvie, Marc Daumas +4 · 1 citation
Computer Science · #FOS: Computer and information sciences #Formal Methods in Verification #Logic, programming, and type systems #Mathematical Software (cs.MS) #Numerical Methods and Algorithms #Performance (cs.PF) #cs.MS #cs.PF
paper · pdf · doi:10.48550/arxiv.0708.3722
arxiv created 2007/08/28 · openalex publication_date 2007/08/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed with a fused-multiply-add provides a fully accurate result for many possible values of the input with a constant almost accurate to the full working precision. We also present an algorithm for a fully accurate second reduction step to reach double full accuracy (all the significand bits of two numbers are significant) even in the worst cases of argument reduction. Our work recalls the common algorithms and presents proofs of correctness. All the proofs are formally verified using the Coq automatic proof checker.