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glsl: improve the accuracy of the asin() builtin function.

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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-*
This commit is contained in:
Paul Berry 2011-07-27 14:34:12 -07:00
parent 5541920e0a
commit d4c80f5f85
1 changed files with 40 additions and 28 deletions
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68
src/glsl/builtins/ir/asin
View file

@ -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))
))))))))))))
))