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>
Iskander Sharipov
erifan01
Thanabodee Charoenpiriyakij
Bill O'Farrell
Russ Cox