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Computing elementary functions using multi-prime argument reduction
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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 Sch{\"o}nhage, 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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Cited by 1 Pith paper
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Fast Ramanujan-type Series for Logarithms. Part I
The paper introduces new, mostly proven hypergeometric series for log 2, log 3, and log 5 with lower binary splitting costs than Machin-type formulas, plus a variable-p family.
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