JOHANSSON, Fredrik

doi:10.1109/ARITH.2015.16

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Licencia de uso del documento

JOHANSSON, Fredrik
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

Idioma

Communication dans un congrès

Este ítem está publicado en

22nd IEEE Symposium on Computer Arithmetic (ARITH22), 2015-06, Lyon.

Resumen en inglés

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.< Leer menos