On 09/26/2011 04:19 PM, Paul Berry wrote:
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 the formula to:
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-*.
Acked-by: Kenneth Graunke <kenn...@whitecape.org>
I just looked up the formula and implemented that, back in the
day...this whole numerical instability thing is foreign to me. Thanks
for improving this.
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