glsl 1.30: Fix numerical instabilities in asinh
The formula we were previously using for asinh:
asinh x = ln(x + sqrt(x * x + 1))
is numerically unstable: when x is a large negative value, the quantity
x + sqrt(x * x + 1)
is a small positive value (on the order of 1/(2|x|)). Since the
logarithm function is very sensitive in this range, any error in the
computation of the square root manifests as a large error in the
result.
This patch changes to the equivalent formula:
asinh x = sign(x) * ln(abs(x) + sqrt(x * x + 1))
which is only slightly more expensive to compute, and is numerically
stable for all x.
Fixes piglit tests
spec/glsl-1.30/execution/built-in-functions/[fv]s-asinh-*.
Reviewed-by: Chad Versace <chad@chad-versace.us>
Acked-by: Kenneth Graunke <kenneth@whitecape.org>
Reviewed-by: Eric Anholt <eric@anholt.net>
1 file changed