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-*. --- src/glsl/builtins/ir/asinh | 40 ++++++++++++++++++++++++++++++++++++---- 1 files changed, 36 insertions(+), 4 deletions(-)
I would mention in the commit message that the new formula is equivalent to the old. This isn't evident at first glance, and I first thought that the new was perhaps just a good, stable approximation of the old. Reviewed-by: Chad Versace <c...@chad-versace.us> -- Chad Versace c...@chad-versace.us _______________________________________________ mesa-dev mailing list mesa-dev@lists.freedesktop.org http://lists.freedesktop.org/mailman/listinfo/mesa-dev
