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Computing elementary functions using multi-prime argument reduction
hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
dc.contributor.author | JOHANSSON, Fredrik | |
dc.date.accessioned | 2024-04-04T02:41:01Z | |
dc.date.available | 2024-04-04T02:41:01Z | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191113 | |
dc.description.abstractEn | 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. | |
dc.description.sponsorship | Sûreté numérique pour les preuves assistées par ordinateur - ANR-20-CE48-0014 | |
dc.language.iso | en | |
dc.title.en | Computing elementary functions using multi-prime argument reduction | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Informatique [cs]/Analyse numérique [cs.NA] | |
dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
dc.identifier.arxiv | 2207.02501 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
hal.identifier | hal-03714660 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-03714660v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=JOHANSSON,%20Fredrik&rft.genre=preprint |
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