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authorFrancisco Jerez <[email protected]>2017-01-21 13:41:08 -0800
committerFrancisco Jerez <[email protected]>2017-01-31 10:32:45 -0800
commite9ffd12827ac11a2d2002a42fa8eb1df847153ba (patch)
tree51670ec05f1d7d1f4903dba0524a7c2522998d70 /VERSION
parent69042a5be4664c7928a21bd23e4f6795bfb19f60 (diff)
glsl: Rewrite atan2 implementation to fix accuracy and handling of zero/infinity.
This addresses several issues of the current atan2 implementation: - Negative zero (and negative denorms which end up getting flushed to zero) isn't handled correctly by the current implementation. The reason is that it does 'y >= 0' and 'x < 0' comparisons to decide on which side of the branch cut the argument is, which causes us to return incorrect results (off by up to 2π) for very small negative values. - There is a serious precision problem for x values of large enough magnitude introduced by the floating point division operation being implemented as a mul+rcp sequence. This can lead to the quotient getting flushed to zero in some cases introducing an error of over 8e6 ULP in the result -- Or in the most catastrophic case will cause us to return NaN instead of the correct value ±π/2 for y=±∞ and x very large. We can fix this easily by scaling down both arguments when the absolute value of the denominator goes above certain threshold. The error of this atan2 implementation remains below 25 ULP in most of its domain except for a neighborhood of y=0 where it reaches a maximum error of about 180 ULP. - It emits a bunch of instructions including no less than three if-else branches per scalar component that don't seem to get optimized out later on. This implementation uses about 13% less instructions on Intel SKL hardware and doesn't emit any control flow instructions. v2: Fix up argument scaling to take into account the range and precision of exotic FP24 hardware. Flip coordinate system for arguments along the vertical line as if they were on the left half-plane in order to avoid division by zero which may give unspecified results on non-GLSL 4.1-capable hardware. Sprinkle in some more comments. Reviewed-by: Ian Romanick <[email protected]>
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