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Efficient implementation of elementary functions in the medium-precision range

hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJOHANSSON, Fredrik
dc.date.accessioned2024-04-04T03:17:56Z
dc.date.available2024-04-04T03:17:56Z
dc.date.conference2015-06
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194352
dc.description.abstractEnWe describe a new implementation of the elementary transcendental functions exp, sin, cos, log and atan for variable precision up to approximately 4096 bits. Compared to the MPFR library, we achieve a maximum speedup ranging from a factor 3 for cos to 30 for atan. Our implementation uses table-based argument reduction together with rectangular splitting to evaluate Taylor series. We collect denominators to reduce the number of divisions in the Taylor series, and avoid overhead by doing all multiprecision arithmetic using the mpn layer of the GMP library. Our implementation provides rigorous error bounds.
dc.language.isoen
dc.title.enEfficient implementation of elementary functions in the medium-precision range
dc.typeCommunication dans un congrès
dc.identifier.doi10.1109/ARITH.2015.16
dc.subject.halInformatique [cs]/Analyse numérique [cs.NA]
dc.subject.halInformatique [cs]/Arithmétique des ordinateurs
dc.subject.halInformatique [cs]/Logiciel mathématique [cs.MS]
dc.identifier.arxiv1410.7176
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.title22nd IEEE Symposium on Computer Arithmetic (ARITH22)
bordeaux.countryFR
bordeaux.conference.cityLyon
bordeaux.peerReviewedoui
hal.identifierhal-01079834
hal.version1
hal.invitednon
hal.proceedingsoui
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01079834v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=JOHANSSON,%20Fredrik&rft.genre=unknown


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