Data tables of Pythagorean triples for trigonometric and hyperbolic functions approximations.
This repository contains lookup tables that can be used in approximations of trigonometric and hyperbolic sine and cosine functions, commonly found in mathematical libraries such as the GNU glibc libm. Detailed descriptions of their generation and usage are available in two published papers as well as in the second chapter of my Ph.D. thesis, all three referenced below.
Two modes of addressing are available:
base: the firstpbits of an input define the beginning of its corresponding table entry. The corrective terms are bounded by2^-p.symmetric: an input correctly rounded to the nearestp-bit number define the center of its table entry. The corrective terms are bounded by2^-(p+1).
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H. de Lassus Saint-Geniès, D. Defour and G. Revy, "Exact Lookup Tables for the Evaluation of Trigonometric and Hyperbolic Functions," in IEEE Transactions on Computers, vol. 66, no. 12, pp. 2058-2071, 1 Dec. 2017, doi: 10.1109/TC.2017.2703870, preprint: PDF.
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H. de Lassus Saint-Geniès, D. Defour and G. Revy, "Range reduction based on Pythagorean triples for trigonometric function evaluation," 2015 IEEE 26th International Conference on Application-specific Systems, Architectures and Processors (ASAP), Toronto, ON, 2015, pp. 74-81, doi: 10.1109/ASAP.2015.7245712, preprint: PDF.
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Hugues de Lassus Saint-Geniès. "Elementary functions : towards automatically generated, efficient, and vectorizable implementations", Other [cs.OH]. Université de Perpignan, 2018. English. NNT : 2018PERP0010. tel-01841424.