Efficient implementation of elementary functions in the medium-precision range
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JOHANSSON, Fredrik | |
| dc.date.accessioned | 2024-04-04T03:17:56Z | |
| dc.date.available | 2024-04-04T03:17:56Z | |
| dc.date.conference | 2015-06 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194352 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.title.en | Efficient implementation of elementary functions in the medium-precision range | |
| dc.type | Communication dans un congrès | |
| dc.identifier.doi | 10.1109/ARITH.2015.16 | |
| dc.subject.hal | Informatique [cs]/Analyse numérique [cs.NA] | |
| dc.subject.hal | Informatique [cs]/Arithmétique des ordinateurs | |
| dc.subject.hal | Informatique [cs]/Logiciel mathématique [cs.MS] | |
| dc.identifier.arxiv | 1410.7176 | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | 22nd IEEE Symposium on Computer Arithmetic (ARITH22) | |
| bordeaux.country | FR | |
| bordeaux.conference.city | Lyon | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01079834 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01079834v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=JOHANSSON,%20Fredrik&rft.genre=unknown |
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