On 27 September 2011 10:12, Chad Versace <<a href="mailto:chad@chad-versace.us">chad@chad-versace.us</a>> wrote: <div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"> <div class="im">On 09/26/2011 04:19 PM, Paul Berry wrote: <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> 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(-) </blockquote> </div> 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. </blockquote><div> Good point. I'll update the commit message. Thanks for the review. </div><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;"> Reviewed-by: Chad Versace <<a href="mailto:chad@chad-versace.us" target="_blank">chad@chad-versace.us</a>> -- Chad Versace <a href="mailto:chad@chad-versace.us" target="_blank">chad@chad-versace.us</a> </blockquote></div>