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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>
This commit is contained in:
Paul Berry 2011-09-26 15:51:39 -07:00
parent b79782cbed
commit 9c75527299
1 changed files with 36 additions and 4 deletions
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40
src/glsl/builtins/ir/asinh
View File

@ -2,20 +2,52 @@
(signature float
(parameters
(declare (in) float x))
((return (expression float log (expression float + (var_ref x) (expression float sqrt (expression float + (expression float * (var_ref x) (var_ref x)) (constant float (1)))))))))
((return (expression float *
(expression float sign (var_ref x))
(expression float log
(expression float +
(expression float abs (var_ref x))
(expression float sqrt
(expression float +
(expression float * (var_ref x) (var_ref x))
(constant float (1))))))))))
(signature vec2
(parameters
(declare (in) vec2 x))
((return (expression vec2 log (expression vec2 + (var_ref x) (expression vec2 sqrt (expression vec2 + (expression vec2 * (var_ref x) (var_ref x)) (constant float (1)))))))))
((return (expression vec2 *
(expression vec2 sign (var_ref x))
(expression vec2 log
(expression vec2 +
(expression vec2 abs (var_ref x))
(expression vec2 sqrt
(expression vec2 +
(expression vec2 * (var_ref x) (var_ref x))
(constant float (1))))))))))
(signature vec3
(parameters
(declare (in) vec3 x))
((return (expression vec3 log (expression vec3 + (var_ref x) (expression vec3 sqrt (expression vec3 + (expression vec3 * (var_ref x) (var_ref x)) (constant float (1)))))))))
((return (expression vec3 *
(expression vec3 sign (var_ref x))
(expression vec3 log
(expression vec3 +
(expression vec3 abs (var_ref x))
(expression vec3 sqrt
(expression vec3 +
(expression vec3 * (var_ref x) (var_ref x))
(constant float (1))))))))))
(signature vec4
(parameters
(declare (in) vec4 x))
((return (expression vec4 log (expression vec4 + (var_ref x) (expression vec4 sqrt (expression vec4 + (expression vec4 * (var_ref x) (var_ref x)) (constant float (1)))))))))
((return (expression vec4 *
(expression vec4 sign (var_ref x))
(expression vec4 log
(expression vec4 +
(expression vec4 abs (var_ref x))
(expression vec4 sqrt
(expression vec4 +
(expression vec4 * (var_ref x) (var_ref x))
(constant float (1))))))))))
))