math/cmplx: use signed zero to correct branch cuts

Branch cuts for the elementary complex functions along real or imaginary axes
should be resolved in floating point calculations by one-sided continuity with
signed zero as described in:

"Branch Cuts for Complex Elementary Functions or Much Ado About Nothing's Sign Bit"
W. Kahan

Available at: https://people.freebsd.org/~das/kahan86branch.pdf

And as described in the C99 standard which is claimed as the original cephes source.

Sqrt did not return the correct branch when imag(x) == 0. The branch is now
determined by sign(imag(x)).  This incorrect branch choice was affecting the behavior
of the Trigonometric/Hyperbolic functions that use Sqrt in intermediate calculations.

Asin, Asinh and Atan had spurious domain checks, whereas the functions should be valid
over the whole complex plane with appropriate branch cuts.

Fixes #6888

Change-Id: I9b1278af54f54bfb4208276ae345bbd3ddf3ec83
Reviewed-on: https://go-review.googlesource.com/46492
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Russ Cox <rsc@golang.org>

0 files changed, 0 insertions, 0 deletions