Range Reduction Based on Pythagorean Triples for Trigonometric Function Evaluation

Hugues de Lassus Saint-Geniès 1 David Defour 1 Guillaume Revy 1
1 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : Software evaluation of elementary functions usually requires three steps: a range reduction, a polynomial evaluation, and a reconstruction step. These evaluation schemes are designed to give the best performance for a given accuracy, which requires a fine control of errors. One of the main issues is to minimize the number of sources of error and / or their influence on the final result. The work presented in this article addresses this problem as it removes one source of error for the evaluation of trigonometric functions. We propose a method that eliminates rounding errors from tabulated values used in the second range reduction for the sine and cosine evaluation. When targeting correct rounding, we show that such tables are smaller, and make the reconstruction step cheaper than existing method. This approach relies on Pythagorean triples generators. Finally, we show how to generate tables indexed by up to 10 bits in a reasonable time and with little memory consumption.
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Hugues de Lassus Saint-Geniès, David Defour, Guillaume Revy. Range Reduction Based on Pythagorean Triples for Trigonometric Function Evaluation. 26th IEEE International Conference Application-specific Systems, Architectures and Processors (ASAP 2015), Jul 2015, Toronto, Canada. pp.74-81, ⟨10.1109/ASAP.2015.7245712⟩. ⟨hal-01134232v2⟩

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