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Preprints, Working Papers, ... Year : 2022

Computing elementary functions using multi-prime argument reduction

Abstract

We describe an algorithm for arbitrary-precision computation of the elementary functions (exp, log, sin, atan, etc.) which, after a cheap precomputation, gives roughly a factor-two speedup over previous state-of-the-art algorithms at precision from a few thousand bits up to millions of bits. Following an idea of Schönhage, we perform argument reduction using Diophantine combinations of logarithms of primes; our contribution is to use a large set of primes instead of a single pair, aided by a fast algorithm to solve the associated integer relation problem. We also list new, optimized Machin-like formulas for the necessary logarithm and arctangent precomputations.
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Dates and versions

hal-03714660 , version 1 (05-07-2022)

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Fredrik Johansson. Computing elementary functions using multi-prime argument reduction. 2022. ⟨hal-03714660⟩
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