tree 7bad80af703406ea8917c214f99ff545fddc333d
parent a728b0ba7cf6316e0c2e79f8d725654a40d62081
author Brian Kessler <brian.m.kessler@gmail.com> 1536257205 -0600
committer Robert Griesemer <gri@golang.org> 1544680902 +0000

math: implement trignometric range reduction for huge arguments

This change implements Payne-Hanek range reduction by Pi/4
to properly calculate trigonometric functions of huge arguments.

The implementation is based on:

"ARGUMENT REDUCTION FOR HUGE ARGUMENTS: Good to the Last Bit"
K. C. Ng et al, March 24, 1992

The major difference with the reference is that the simulated
multi-precision calculation of x*B is implemented using 64-bit
integer arithmetic rather than floating point to ease extraction
of the relevant bits of 4/Pi.

The assembly implementations for 386 were removed since the trigonometric
instructions only use a 66-bit representation of Pi internally for
reduction.  It is not possible to use these instructions and maintain
accuracy without a prior accurate reduction in software as recommended
by Intel.

Fixes #6794

Change-Id: I31bf1369e0578891d738c5473447fe9b10560196
Reviewed-on: https://go-review.googlesource.com/c/153059
Reviewed-by: Robert Griesemer <gri@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>