[Mesa-dev] [PATCH] glsl 1.30: Fix numerical instabilities in asinh

[Chad Versace]

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 <chad at chad-versace.us>

-- 
Chad Versace
chad at chad-versace.us