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(-)
diff --git a/src/glsl/builtins/ir/asinh b/src/glsl/builtins/ir/asinh
index 93f73cc..d2dc710 100644
--- a/src/glsl/builtins/ir/asinh
+++ b/src/glsl/builtins/ir/asinh
@@ -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))))))))))
))
--
1.7.6.2
_______________________________________________
mesa-dev mailing list
mesa-dev@lists.freedesktop.org
http://lists.freedesktop.org/mailman/listinfo/mesa-dev
