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authorPaul Berry <[email protected]>2011-07-27 14:34:12 -0700
committerPaul Berry <[email protected]>2011-08-01 14:37:38 -0700
commitd4c80f5f85c749df3fc091ff07b60ef4989fa6d9 (patch)
treeab95a4da310d6f2cb68c493115e139c2203969a3 /src/glsl/builtins/ir/atan
parent5541920e0ac4ea8383c7f896daba24a304aafec6 (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-*
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