Module: Mesa
Branch: master
Commit: d4c80f5f85c749df3fc091ff07b60ef4989fa6d9
URL:
http://cgit.freedesktop.org/mesa/mesa/commit/?id=d4c80f5f85c749df3fc091ff07b60ef4989fa6d9
Author: Paul Berry <stereotype...@gmail.com>
Date: Wed Jul 27 14:34:12 2011 -0700
glsl: improve the accuracy of the asin() builtin function.
The previous formula for asin(x) was algebraically equivalent to:
sign(x)*(pi/2 - sqrt(1-|x|)*(A + B|x| + C|x|^2))
where A, B, and C were arbitrary constants determined by a curve fit.
This formula had a worst case absolute error of 0.00448, an unbounded
worst case relative error, and a discontinuity near x=0.
Changed the formula to:
sign(x)*(pi/2 - sqrt(1-|x|)*(pi/2 + (pi/4-1)|x| + A|x|^2 + B|x|^3))
where A and B are arbitrary constants determined by a curve fit. This
has a worst case absolute error of 0.00039, a worst case relative
error of 0.000405, and no discontinuities.
I don't expect a significant performance degradation, since the extra
multiply-accumulate should be fast compared to the sqrt() computation.
Fixes piglit tests {vs,fs}-asin-float and {vs,fs}-atan-*
---
src/glsl/builtins/ir/asin | 68 ++++++++++++++++++++++++++------------------
1 files changed, 40 insertions(+), 28 deletions(-)
diff --git a/src/glsl/builtins/ir/asin b/src/glsl/builtins/ir/asin
index e230ad6..45d9e67 100644
--- a/src/glsl/builtins/ir/asin
+++ b/src/glsl/builtins/ir/asin
@@ -5,23 +5,26 @@
((return (expression float *
(expression float sign (var_ref x))
(expression float -
- (expression float *
- (constant float (3.1415926))
- (constant float (0.5)))
+ (constant float (1.5707964))
(expression float *
(expression float sqrt
(expression float -
(constant float (1.0))
(expression float abs (var_ref x))))
(expression float +
- (constant float (1.5707288))
+ (constant float (1.5707964))
(expression float *
(expression float abs (var_ref x))
(expression float +
- (constant float (-0.2121144))
+ (constant float (-0.21460183))
(expression float *
- (constant float (0.0742610))
- (expression float abs (var_ref x))))))))))))
+ (expression float abs (var_ref x))
+ (expression float +
+ (constant float (0.086566724))
+ (expression float *
+ (expression float abs (var_ref x))
+ (constant float (-0.03102955))
+ ))))))))))))
(signature vec2
(parameters
@@ -29,23 +32,26 @@
((return (expression vec2 *
(expression vec2 sign (var_ref x))
(expression vec2 -
- (expression float *
- (constant float (3.1415926))
- (constant float (0.5)))
+ (constant float (1.5707964))
(expression vec2 *
(expression vec2 sqrt
(expression vec2 -
(constant float (1.0))
(expression vec2 abs (var_ref x))))
(expression vec2 +
- (constant float (1.5707288))
+ (constant float (1.5707964))
(expression vec2 *
(expression vec2 abs (var_ref x))
(expression vec2 +
- (constant float (-0.2121144))
+ (constant float (-0.21460183))
(expression vec2 *
- (constant float (0.0742610))
- (expression vec2 abs (var_ref x))))))))))))
+ (expression vec2 abs (var_ref x))
+ (expression vec2 +
+ (constant float (0.086566724))
+ (expression vec2 *
+ (expression vec2 abs (var_ref x))
+ (constant float (-0.03102955))
+ ))))))))))))
(signature vec3
(parameters
@@ -53,23 +59,26 @@
((return (expression vec3 *
(expression vec3 sign (var_ref x))
(expression vec3 -
- (expression float *
- (constant float (3.1415926))
- (constant float (0.5)))
+ (constant float (1.5707964))
(expression vec3 *
(expression vec3 sqrt
(expression vec3 -
(constant float (1.0))
(expression vec3 abs (var_ref x))))
(expression vec3 +
- (constant float (1.5707288))
+ (constant float (1.5707964))
(expression vec3 *
(expression vec3 abs (var_ref x))
(expression vec3 +
- (constant float (-0.2121144))
+ (constant float (-0.21460183))
(expression vec3 *
- (constant float (0.0742610))
- (expression vec3 abs (var_ref x))))))))))))
+ (expression vec3 abs (var_ref x))
+ (expression vec3 +
+ (constant float (0.086566724))
+ (expression vec3 *
+ (expression vec3 abs (var_ref x))
+ (constant float (-0.03102955))
+ ))))))))))))
(signature vec4
(parameters
@@ -77,21 +86,24 @@
((return (expression vec4 *
(expression vec4 sign (var_ref x))
(expression vec4 -
- (expression float *
- (constant float (3.1415926))
- (constant float (0.5)))
+ (constant float (1.5707964))
(expression vec4 *
(expression vec4 sqrt
(expression vec4 -
(constant float (1.0))
(expression vec4 abs (var_ref x))))
(expression vec4 +
- (constant float (1.5707288))
+ (constant float (1.5707964))
(expression vec4 *
(expression vec4 abs (var_ref x))
(expression vec4 +
- (constant float (-0.2121144))
+ (constant float (-0.21460183))
(expression vec4 *
- (constant float (0.0742610))
- (expression vec4 abs (var_ref x))))))))))))
+ (expression vec4 abs (var_ref x))
+ (expression vec4 +
+ (constant float (0.086566724))
+ (expression vec4 *
+ (expression vec4 abs (var_ref x))
+ (constant float (-0.03102955))
+ ))))))))))))
))
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