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author | Paul Berry <[email protected]> | 2011-07-27 14:34:12 -0700 |
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committer | Paul Berry <[email protected]> | 2011-08-01 14:37:38 -0700 |
commit | d4c80f5f85c749df3fc091ff07b60ef4989fa6d9 (patch) | |
tree | ab95a4da310d6f2cb68c493115e139c2203969a3 /src/gallium/auxiliary | |
parent | 5541920e0ac4ea8383c7f896daba24a304aafec6 (diff) |
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-*
Diffstat (limited to 'src/gallium/auxiliary')
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