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Johansson, Fredrik (2015)
Publisher: HAL CCSD
Languages: English
Types: Conference object
Subjects: Computer Science - Numerical Analysis, Computer Science - Mathematical Software, [INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA], [INFO.INFO-MS] Computer Science [cs]/Mathematical Software [cs.MS], [INFO.INFO-AO] Computer Science [cs]/Computer Arithmetic

Classified by OpenAIRE into

arxiv: Computer Science::Mathematical Software
International audience; 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.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

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