mesa/src/glsl/builtins
Paul Berry d4c80f5f85 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-*
2011-08-01 14:37:38 -07:00
..
ir glsl: improve the accuracy of the asin() builtin function. 2011-08-01 14:37:38 -07:00
profiles glsl: Add compiler support for ARB_shader_texture_lod. 2011-05-09 11:23:54 -07:00
tools glsl/generate_builtins.py: Remove regexp to kill pointer addresses. 2011-06-14 18:29:48 -07:00