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Bill O'Farrell authored
Note, most math functions are structured to use stubs, so that they can be accelerated with assembly on any platform. Sinh, cosh, and tanh were not structued with stubs, so this CL does that. This set of routines was chosen as likely to produce good speedups with assembly on any platform. Technique used was minimax polynomial approximation using tables of polynomial coefficients, with argument range reduction. A table of scaling factors was also used for cosh and log10. before after speedup BenchmarkCos 22.1 ns/op 6.79 ns/op 3.25x BenchmarkCosh 125 ns/op 11.7 ns/op 10.68x BenchmarkLog10 48.4 ns/op 12.5 ns/op 3.87x BenchmarkSin 22.2 ns/op 6.55 ns/op 3.39x BenchmarkSinh 125 ns/op 14.2 ns/op 8.80x BenchmarkTanh 65.0 ns/op 15.1 ns/op 4.30x Accuracy was tested against a high precision reference function to determine maximum error. Approximately 4,000,000 points were tested for each function, producing the following result. Note: ulperr is error in "units in the last place" max ulperr sin 1.43 (returns NaN beyond +-2^50) cos 1.79 (returns NaN beyond +-2^50) cosh 1.05 sinh 3.02 tanh 3.69 log10 1.75 Also includes a set of tests to test non-vector functions even when SIMD is enabled Change-Id: Icb45f14d00864ee19ed973d209c3af21e4df4edc Reviewed-on: https://go-review.googlesource.com/32352 Run-TryBot: Michael Munday <munday@ca.ibm.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Michael Munday <munday@ca.ibm.com>
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